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Vanderbilt University, M. Douglas...
Robert Hesketh of Rowan University,...
Introducing the Stochastic Simulation...
Construction and Visualization...
Frontiers of Chemical Engineering:...
How to Survive Engineering School,...
Analysis of Membrane Processes...
A Press RO System: An Interdisciplinary...
Book Review
Letter to the Editor
A Compendium of Open-Ended Membrane...
Stirred Pots
Exploring the Potential of Electrodialysis,...
Tools for Teaching Gas Separation...
Membrane Projects with an Industrial...
A Simple Analysis for Gas Separation...
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Material Information
Chemical engineering education
Alternate Title:
Abbreviated Title:
Chem. eng. educ.
American Society for Engineering Education -- Chemical Engineering Division
Chemical Engineering Division, American Society for Engineering Education
Publication Date:
Annual[ FORMER 1960-1961]
Physical Description:
v. : ill. ; 22-28 cm.
Subjects / Keywords:
Chemical engineering -- Study and teaching -- Periodicals ( lcsh )
Chemical abstracts
Additional Physical Form:
Also issued online.
Dates or Sequential Designation:
1960-June 1964 ; v. 1, no. 1 (Oct. 1965)-
Numbering Peculiarities:
Publication suspended briefly: issue designated v. 1, no. 4 (June 1966) published Nov. 1967.
General Note:
Title from cover.
General Note:
Place of publication varies: Rochester, N.Y., 1965-1967; Gainesville, Fla., 1968-
Record Information
Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
TP165 .C18 ( lcc )
660/.2/071 ( ddc )
UFDC Membership
Chemical Engineering Documents
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Full Text
Chemical Engineering Education
Department of Chemical Engineering
University of Florida Gainesville, FL 32611
PHONE and FAX: 352-392-0861
e-mail: firstname.lastname@example.com
Tim Anderson
Phillip C. Wankat
Carole Yocum
James O. Wilkes, U. 1fi;, /"-,,
William J. Koros, CG. .. -;, Institute of Technology
E. Dendy Sloan, Jr.
Colorado School of Mines
Pablo Debenedetti
Princeton University
Dianne Dorland
Rowan University
Thomas F. Edgar
University of Texas at Austin
Richard M. Felder
North Carolina State University
Bruce A. Finlayson
University of Washington
H. Scott Fogler
University of Michigan
William J. Koros
Georgia Institute of Technology
David F. Ollis
North Carolina State University
Ronald W. Rousseau
Georgia Institute of Technology
Stanley I Sandler
University of Delaware
Richard C. Seagrave
Iowa State University
C. Stewart Slater
Rowan University
James E. Stice
University of Texas at Austin
Donald R. Woods
McMaster University
Chemical Engineering Education
Volume 37 Number 1 Winter 2003
2 Vanderbilt University, M. Douglas LeVan
8 Robert Hesketh of Rowan University, C. Stewart Slater
14 Introducing the Stochastic Simulation of Chemical Reactions: Using
the Gillespie Algorithm and MATLAB,
Joaquin Martinez-Urreaga, Jose Mira, Camino Gonzdlez-Ferndndez
20 Construction and Visualization of VLE Envelopes in Mathcad,
Jasper L. Dickson, John A. Hart, IV Wei-Yin Chen
24 Frontiers of Chemical Engineering: A Chemical Engineering Freshman
Frank M. Bowman, R. Robert Balcarcel, G. Kane Jennings,
Bridget R. Rogers
30 How to Survive Engineering School
Richard M. Felder
> MEMBRANES IN ChE EDUCATION
32 Introduction
33 Analysis of Membrane Processes in the Introduction-to-ChE Course,
Andrew L. Zydney
38 A Press RO System: An Interdisciplinary Reverse Osmosis Project for
First-Year Engineering Students,
S. Scott Moor Edmond P. Saliklis, Scott R. Hummel, Yih-C i ..... Yu
46 A Compendium of Open-Ended Membrane Problems in the Curricu
lum, G. Glenn Lipscomb
52 Exploring the Potential of Electrodialysis,
Stephanie Farrell, Robert P. Hesketh, C. Stewart Slater
60 Tools for Teaching Gas Separation Using Polymers,
David T Coker Rajeev Prabhakar Benny D. Freeman
68 Membrane Projects with an Industrial Focus in the Curriculum,
Stephanie Farrell, Robert P. Hesketh, Mariano J. Savelski,
Kevin D. Dahm, C. Stewart Slater
74 A Simple Analysis for Gas Separation Membrane Experiments,
Richard A. Davis, Orville C. Sandall
44 Book Review
45 Letter to the Editor
51 Stirred Pots
CHEMICAL ENGINEERING EDUCATION (ISSN 0009-2479) is published quarterly by the Chemical Engineering
Division, American Society for Engineering Education, and is edited at the University of Florida. Correspondence
regarding editorial matter, circulation, and changes of address should be sent to CEE, Chemical Engineering Department,
University of Florida, Gainesville, FL 32611-6005. Copyright 2003 by the Chemical Engineering Division, American
Society for Engineering Education. The statements and opinions expressed in this periodical are those of the writers and not
necessarily those of the ChE Division, ASEE, which body assumes no responsibility for them. Defective copies replaced if
notified within 120 days of publication. Write for information on subscription costs andfor back copy costs and availability.
POSTMASTER: Send address changes to Chemical Engineering Education, ChemicalEngineering Department., University
of Florida, Gainesville, FL 32611-6005. Periodicals Postage Paid at Gainesville, Florida and additional post offices.
Winter 2003
]f department
ChE at...
Vanderbilt University Nashville, TN 37235
Like our discipline, the Department of Chemical
Engineering at Vanderbilt University is experi-
encing a significant expansion beyond its tradi-
tional roots toward advanced materials, bioengineering,
and other product and application areas. To respond to
changes in the field and to take a strong leadership role
in research developments in the future, the Department
has concentrated on building expertise through faculty
recruitment, revising both undergraduate and graduate
curricula, and cultivating ambitious interdisciplinary re-
search thrusts. The University's established world-class
research prominence in medicine, biology, and environ-
mental studies augments its advantages in reaching its
future goals.
Established in 1873, Vanderbilt University has a long-
standing tradition for academic excellence. Cornelius
Vanderbilt, "The Commodore," contributed approxi-
mately one million dollars of his personal fortune to build
a university that could help repair the post-Civil-War rifts
among geographical areas of the nation. The University
continues to cultivate a tradition of collegiality, interdis-
ciplinary teamwork, and cohesion.
The University, now a national arboretum, is located
on 330 park-like acres one and one-half miles from down-
town Nashville. It has ten schools, which provide a full
range of undergraduate, graduate, and professional pro-
grams. There are four schools with undergraduate pro-
grams: the School of Engineering, the College of Arts
and Science, Peabody College (education), and the Blair
School of Music. The Graduate School confers MA, MS,
Olin Hall, home of Chemical Engineering at Vanderbilt.
and PhD degrees. The PhD is offered in 39 disciplines. In addition,
there are schools of medicine, nursing, management, law, and di-
vinity. Vanderbilt has about 1,900 full-time faculty members and a
diverse student body with 6,200 undergraduates and 4,300 gradu-
ate and professional students.
Vanderbilt's Chancellor, Gordon Gee, joined the University two
years ago after having been President of West Virginia University,
the University of Colorado, Ohio State University, and Brown Uni-
versity. Changes have been occurring throughout the University. A
residential college system for undergraduates is being strongly con-
sidered, and graduate research is an area of considerable focus.
The Board of Trust, the University's governing body, has con-
tributed significant funds for several new interdisciplinary re-
search initiatives.
Nashville is called the "Athens of the South" and "Music City
Copyright ChE Division of ASEE 2003
Chemical Engineering Education
____ 9-_________a_
Nashville from across the Cumberland River.
USA" and is the capital of Tennessee. The city and surrounding
area support a wide range of activities with performing arts and
museums, professional sports teams, and many outdoor activi-
ties. Nashville is one of the South's major focal points for bank-
ing, healthcare, insurance, publishing, and entertainment. The
Nashville area is home to more than a dozen colleges and uni-
versities. Vanderbilt is a major contributor to the intellectual
life of Nashville.
In 1874, the year following the founding donation by Cornelius
Vanderbilt to the University, engineering was announced as one of
ten schools within the Department of Philosophy, Science, and Lit-
erature. Engineering classes began in 1879 in drafting, surveying,
applied mechanics, structures, water supply, sanitary engineering,
and mechanical power. The first Bachelor of Engineering degree
was awarded in 1880. Engineering was organized as a department
in 1886 and became a school again in 1915, when departments were
renamed schools and schools were renamed departments.
Graduate work in the School of Engineering began with chemi-
cal engineering. An MS program in chemical engineering was ap-
proved in 1943, and the first two MS degrees were awarded in
1946. The first PhD program in engineering to be approved by
the Graduate School was in chemical engineering in 1962. The
first PhD conferred in engineering went to a chemical engi-
neering student in 1964.
Kenneth F. Galloway joined Vanderbilt in Fall 1996 as Dean of
the School of Engineering and Professor of Electrical Engineering.
Dean Galloway restructured the School by consolidating some de-
partmental administrative structures. The School now has five De-
partments: Biomedical Engineering, Chemical Engineering, Civil
... the
Department of
at Vanderbilt
is experiencing
a significant
beyond its
'- p (," -roots
D and other
product and
Professor Bowman
and Environmental Engineering, Electrical Engineering
and Computer Science, and Mechanical Engineering. The
Department of Electrical Engineering and Computer Sci-
ence also offers a degree in Computer Engineering. The
School also offers degrees through programs in Engineer-
ing Science, Management of Tcili 1ih -1, -., and an Interdis-
ciplinary Program in Materials Science.
Dean Galloway encouraged growth of research pro-
grams. Sponsored research activity within the School has
more than doubled since 1996, and research expenditures
currently average $300,000 per faculty member.
The Dean also began a vigorous program of fund rais-
ing to improve facilities within the School. A new center-
piece of the School, Featheringill Hall, was formally dedi-
cated in September 2002. It has a large three-story
atrium and many areas for small-group interactions.
Undergraduates throughout Vanderbilt have voted it the
best building on campus.
Winter 2003
A Vanderbilt's Chemical Engineering Class of 2003.
Professor Balcarcel with PhD candidate Yuansheng Yang. N
A Chemical Engineering Program was first announced at
Vanderbilt in 1903 as a joint program between engineering
and chemistry. A Department of Chemical Engineering was
established in 1938 with the first head appointed in 1939.
The Department has had seven Chairs. The early ones were
Roy S. Hanslick (1939-1941), E. E. Litkenhous (1941-1961),
and W. Dennis Threadgill (1961-1972). E. E. Litkenhous had
influence far outside the field of chemical engineering; in
1930, while still an undergraduate at the University of Louis-
ville, he developed a system for rating athletic teams and pre-
dicting the outcome of a sporting event based on a "points
spread"-this basic system is still in use today.
The School was reorganized in 1972 into a grid system
with John A. Roth as Chairman of the Division of Chemical,
Fluid, and Thermal Sciences, which was comprised of chemi-
cal engineering and mechanical engineering; Thomas M.
Goldbold (1972-1975) was Director of the Chemical Engi-
neering Program. In 1975, the School returned to a normal
departmental structure.
Recent Chairs have been W. Dennis Threadgill (1975-1980),
Karl B. Schnelle, Jr. (1980-1988), Thomas M. Godbold (Act-
ing Chair, 1988-1989), Tomlinson Fort (1989-1996), and M.
Douglas LeVan (1997-present).
The current home of the Department is Olin Hall, a gift of
the Olin Foundation, which opened in 1974. The building is
occupied by the Department of Chemical Engineering, most
of the Department of Mechanical Engineering, and much
of the Interdisciplinary Materials Science Program. The
Department occupies approximately 20,000 square feet,
including space for a high-bay undergraduate unit opera-
tions laboratory.
The Department provides an intimate environment for un-
dergraduate and graduate students. Each faculty member cares
a great deal about education and student welfare. Classes are
small and are all taught by faculty members. Advising is done
face-to-face with faculty members.
We have many distinguished alumni. Our graduates hold
positions of major responsibility in large corporations, in small
entrepreneurial and consulting firms, and in federal and state
government agencies. Some PhDs continue their research in
post-doctoral positions or enter the teaching profession.
M. Douglas LeVan joined the Department as Chair in 1997.
At mid-year, the tenured/tenure-track faculty was all tenured
and consisted of Professors Robert J. Bayuzick, Kenneth A.
Debelak, Tomlinson Fort, M. Douglas LeVan, John A. Roth,
Karl B. Schnelle, Jr., and Robert D. Tanner. Each had well
over 15 years of university teaching experience. We also had
two experienced research faculty, Professors William H.
Hofmeister and Ales Prokop. A clear opportunity existed to
hire new faculty.
Three research thrust areas were identified: materials,
bioengineering, and environmental engineering. All are in-
terdisciplinary and important at Vanderbilt. We sought (and
continue to seek) candidates who can contribute fundamen-
tally and broadly to one or more of these focus areas. We also
sought faculty with indications of excellent teaching abili-
Chemical Engineering Education
ties; at Vanderbilt, teaching performance is a strong consid-
eration in promotion and tenure decisions.
Beginning in January 1998, we added four faculty at the
assistant-professor level: Frank M. Bowman (Ph.D., Califor-
nia Institute of Tcliii-l ,ih* ., 1997) has research interests in
atmospheric chemistry and gas-aerosol transport; G. Kane
Jennings (Ph.D., Massachusetts Institute of Technology, 1998)
works on surface modification and experimental molecular
engineering; Bridget R. Rogers (Ph.D., Arizona State Uni-
versity, 1998) focuses on nucleation and microstructure evo-
lution of thin films and microelectronic materials process-
ing; and R. Robert Balcarcel (Ph.D., Massachusetts Institute
of Tcl 1in1 ih ,. 1999) who studies biological cell life cycles,
metabolism, and apoptosis for recombinant therapeutic pro-
tein production, cancer therapies, and environmental sens-
ing. All of our new faculty have established significant ex-
ternal funding for their research programs. Professors Bow-
man and Rogers have won NSF CAREER awards. Professor
Jennings won the School's teaching award last year.
Our newest faculty member is Peter T. Cummings, who
joined us in August 2002 as the John R. Hall Professor of
Chemical Engineering. This chaired position was endowed
by the Ashland Foundation in honor of John R. Hall, a gradu-
ate of the Department, former Chairman and CEO of Ashland,
Inc., and recent President of the Board of Trust of Vanderbilt
University. Prof. Cummings is acknowledged as an interna-
tional expert in molecular simulation and computational
nanoscience and nanoengineering. He has retained his role at
Oak Ridge National Laboratory as Director of the
Nanomaterials Theory Institute within the Center for
Nanophase Materials Sciences.
Current departmental faculty are listed in Table 1. The spe-
cial team-teaching role of Professor Julie E. Sharp deserves
Current Chemical Engineering Faculty at Vanderbilt University
E R. Robert Balcarcel
Assistant Professor (PhD, Massachusetts Institute of Technology)
Biotechnology and bioengineering; mammalian cell cultures; cell
cycles; pharmaceutical production
[1 Robert J. Bayuzick
Professor (PhD, Vanderbilt University)
Solidification; nucleation; evolution ofmicrostructure; microgravity
science; physical metallurgy; containerless processing; oxide
superconductor processing
[1 Frank M. Bowman
Assistant Professor (PhD, California Institute of Technology)
Air pollution; atmospheric chemistry mechanisms; gas-aerosol
transport; modeling complex chemical reaction systems
[Peter T. Cummings
John R. Hall Professor (PhD, University of Melbourne)
Computational nanoscience and nanoengineering; molecular
modeling offluid and amorphous systems; computational materials
science; parallel computing
[ Kenneth A. Debelak
Associate Professor (PhD, University of Kentucky)
Development of plant-wide control algorithms; intelligent process
control; activity modeling; effect of changing particle structures in
gas-solid reactions; environmentally benign chemical processes;
mixing in bioreactors
[ Tomlinson Fort
Centennial Professor, Emeritus (PhD, University of Tennessee)
Capillarity; insoluble- -- .. ..... I -B films; adsorption; contact
angles and wetting; polymer interfaces; ... on liquid
surfaces; fine particles; flow in porous media
E William H. Hofmeister
Research Associate Professor (PhD, Vanderbilt University)
Materials science and engineering; nucleation and solidification
kinetics; microgravity science; high-speed thermal imaging;
biological applications of materials science
E G. Kane Jennings
Assistant Professor (PhD, Massachusetts Institute of Technology)
Surface modification; experimental molecular engineering;
corrosion inhibition; microelectronics processing
E M. Douglas LeVan
Centennial Professor and Chair (PhD, University of California,
Fixed-bed adsorption; adsorption equilibria; adsorption processes
(pressure-swing adsorption, temperature-swing adsorption,
adsorptive refrigeration); process design
E Ales Prokop
Research Professor (PhD, Czechoslovak Academy of Sciences)
Bioengineering; bioartificial liver and pancreas; cell encapsulation
and immunoisolation devices; ... '. ..'
protein recovery
E Bridget R. Rogers
Assistant Professor (PhD, Arizona State University)
Nucleation and microstructure evolution of thin films; fundamentals
of thin; j', .. for microelectronic applications (mass
transport, kinetics, and effects of substrate topography on CVD,
sputter deposition and etch processes)
E John A. Roth
Professor (PhD, University of Louisville)
Chemical reactor design; industrial wastewater treatment; sorption
processes; chemical oxidation for waste treatment; hazardous waste
management; electrochemistry
E Karl B. Schnelle, Jr.
Professor (PhD, Carnegie Mellon University)
Turbulent transport in the environment; control of toxic emissions
and S02 and NOxfrom coalfired boilers; solution thermodynam-
ics; applications of process simulation to microcomputers;
supercritical extraction applied to soil remediation
E Julie E. Sharp
Associate Professor of the Practice of Technical Communication
(PhD, Vanderbilt University)
Written and oral technical communications; technical reporting;
Kolb learning style theory in engineering education
E Robert D. Tanner
Professor (PhD, Case Western Reserve University)
In situ bubble fractionation of excreted proteins from growing
baker's yeast; selective protein recovery from a semi-solid air
fluidized bed fermentation process; bubble and foam fractionation
Winter 2003
mention. A practice was
started by Professors
Debelak and Roth of devel-
oping written communica-
tion skills in design and
laboratory courses through
the team-teaching efforts of
an expert in technical
communications. Their ef-
forts won an ASEE best pa-
per award in 1983. Dr.
Sharp has been involved
with the Department as the
expert in technical commu-
nications since 1982. Each
semester she co-teaches the Professor Rogers with BS
undergraduate laboratory
courses, where she instructs
students in written and oral communications, and in addition
she teaches two sections of a technical communications course
for the School, for which she serves as coordinator. She is
active within the ASEE and regularly publishes her research
on learning styles. She has been instrumental in the consider-
ation of Kolb learning styles within the School of Engineer-
ing. Her efforts have won praise from alumni and ABET.
In addition to those shown in Table 1, five faculty currently
have secondary appointments in the Department. Professors
Todd D. Giorgio, Thomas R. Harris, K. Arthur Overholser,
and Robert J. Roselli (all former faculty in the Department of
Chemical Fi .iilciiiil- have their primary appointments in
the Department of Biomedical Engineering. Professor David
S. Kosson has his primary appointment in the Department of
Civil and Environmental Engineering.
In addition, the Department is fortunate to have the ser-
vices of staff members Margarita Talavera, Mary M. Gilleran,
Anita K. Patterson, and Mark V. Holmes.
The undergraduate program in chemical engineering was
accredited by the Engineers' Council for Professional Devel-
opment (ECPD) in 1952. Accreditation by the Accreditation
Board for Engineering and Tccliiil ,h:, (ABET) followed
beginning in the 1980s as ECPD was replaced. The most re-
cent accreditation visit occurred in October 2001.
The undergraduate curriculum was revised for the 1998-
1999 academic year and again for the 2002-2003 academic
year. Both of these curricula are on our website. The changes
for 1998-99 were made to present material in a more logical
order, to change computer languages, and to increase effi-
ciency. We retained a 3-hour engineering economy course,
but collapsed two 3-hour senior design courses into a single
4-hour capstone course. Graduation requirements were re-
duced to 128 hours.
/MS student Virginia Wahlig.
programming and numerical
chemical engineering problem
The changes for the cur-
rent academic year in-
volved improving the struc-
ture of our thermodynam-
ics sequence, eliminating
engineering courses (but
not physics courses) in stat-
ics-dynamics and electrical
circuits, and adding flex-
ibility. We are now teach-
ing all of thermodynamics,
not relying on the Depart-
ment of Chemistry. We are
also increasing the expo-
sure of our sophomores to
simulation; instead of
teaching just Aspen, we
now also apply additional
problem-solving methods to
The new open curriculum makes it easy for students to mi-
nor or pursue their own chosen direction. There are six hu-
manities-social science electives spread uniformly through-
out the curriculum. We have moved all technical and open
electives into the junior and senior years, and as a result, stu-
dents have a technical elective each semester of the junior
and senior years plus two open electives in the senior year.
The Department encourages minors in environmental engi-
neering, materials science and engineering, and management
of tcchllin ihi -1 ,. these require 15 hours. Students also minor in
chemistry, mathematics, economics, etc. The Department is
offering a new concentration in biotechnology that requires
13 hours. Additionally, a special, intensive program leads to
a dual degree in chemical and biomedical engineering.
For the last four years, the School of Engineering has of-
fered elective seminar courses to entering freshmen. The
Department has participated heavily, offering several courses.
Our regular offering, however, has been the course "Fron-
tiers in Chemical Engineering," which has been team-taught
every year by our assistant professors based on their research
interests. (This course is the subject of an article published in
this issue of Chemical F,, r.i.. -#i i. Education.)
Our undergraduates have research opportunities also. Each
year many of them work side-by-side with graduate students
in our research laboratories. In the summers, external and
School support has been available to provide research expe-
riences for undergraduates.
We have an active AIChE student chapter with a long his-
tory. A Chemical Engineering Club, formed in 1936, became
the Tau Alpha Tau Society in 1940 and then the Vanderbilt
Chapter of the American Institute of Chemical Engineers in
1947. Students participate in a wide variety of activities, in-
cluding Rube Goldberg competitions. Last year eight under-
Chemical Engineering Education
graduates attended the AIChE Student Conference in Puerto
Rico. For the 2002 Annual AIChE Meeting, the Department
supported a trip for 12 undergraduates to attend.
A majority of our graduate students are PhD students. Most
are supported in their first year as teaching assistants, although
some support for new students as research assistants is usu-
ally available. After the first academic year, almost all stu-
dents are supported as research assistants from research grants
for the duration of their studies. Some multi-year "topping"
awards are also available.
Graduate course requirements were changed for the 1999-
2000 academic year and again for the 2002-2003 academic
year. For 1999-2000, we revised our graduate core course
requirements, moving to a more research-oriented chemical
engineering science core. For 2002-2003, we reduced
coursework requirements for PhD students and made some
modifications to our core course structure. We now offer six
core courses: applied mathematics for chemical engineers,
thermodynamics, transport phenomena, chemical kinetics,
simulation, and separation science and engineering.
An MS student must take 24 hours of coursework, a gradu-
ate school requirement. This includes five core courses. A
thesis is required. (The Master of Engineering, an ad-
vanced professional degree, is offered by the School of
We require a PhD student to take a minimum of 30 hours
of coursework beyond the bachelor's degree. This includes
the six core courses. Many students take more than 30 hours
of coursework, but this load is designed to allow students to
spend the majority of their studies on original research for
the dissertation. PhD students work with their research advi-
sor under the guidance of a PhD committee towards fulfill-
ing all requirements for the degree.
Research laboratories within the Department are equipped
for experimental and computational investigations of mate-
rials, bioengineering, environmental engineering, adsorption
and surface chemistry, chemical reaction engineering, and
process modeling and control. Interdisciplinary research op-
portunities exist with researchers in other departments in the
School of Engineering, the natural sciences, and medicine.
Our faculty participate in the Interdisciplinary Program in
Materials Science and in an NSF-sponsored Engineering
Research Center for Bioengineering Educational Technolo-
gies. We also participate in two new University-supported
interdisciplinary research initiatives-the Vanderbilt Institute
for Nanoscale Science and Engineering (VINSE) and the
Vanderbilt Institute for Integrative Bioengineering Research
and Education (VIIBRE). Activities are currently develop-
ing within the Vanderbilt Institute for Environmental Risk
and Resources Management (VIERRM).
We currently have an annual Tis Lahiri Memorial Seminar,
named after a former graduate student and supported by an
endowment. This seminar has an educational flavor. Recent
speakers include H. Scott Fogler, Richard M. Felder, Phillip
C. Wankat, Ronald W. Rousseau, John M. Prausnitz, Edward
L. Cussler, and Arthur W. Westerberg.
We also have an active Chemical Engineering Graduate
Student Association (ChEGSA) that represents graduate
student interests and sponsors a variety of social events.
They have had great leadership and help the Department
in many ways.
The Chemical Engineering Department has changed con-
siderably in the last six years. Nine of the fourteen full-time
faculty members listed in Table 1 were not in the Department
in late 1996. We have been working toward improved under-
graduate and graduate curricula and expanding our research
activities. The changes will continue.
Our curricula and research programs reflect the broaden-
ing of the chemical engineering profession from its chemical
and petrochemical heritage toward advanced materials,
bioengineering, environmental concerns, and other applica-
tion-based and product areas. Vanderbilt University as a whole
is strong in biological research, with a world-class research
hospital; this creates broad opportunities for collaborative
research on biologically related topics.
We seek advice on our programs in many ways. A princi-
pal avenue is through our Departmental External Advisory
Committee. We also seek advice from alumni and corporate
friends through a newsletter, "The Catalyst," edited by Pro-
fessors Schnelle and Sharp. The Chair has formed an Under-
graduate Student Council, which provides him with advice
on the undergraduate program, and he serves as advisor to
Essentially all Departments want to improve not only their
rankings but also their quality and visibility. We are certainly
no exception. We have been working on improvements from
all angles. We recognize the many opportunities that we have
at Vanderbilt.
Information: More information on the Department is avail-
able at http://www/vuse.vanderbilt.edu/-cheinfo/che.htm.
Questions should be directed to firstname.lastname@example.com.
A .. 1/..1.. I./.. i,i,. Photographs were taken by David
Crenshaw and Darryl Nelson. Kenneth A. Debelak, Vivian F
Cooper-Capps, and Julie E. Sharp provided many helpful
Reference: Jacobs, D., "102 Years: A Story of the First Cen-
tury of Vanderbilt University School of Engineering,"
Vanderbilt University Alumni Association, Nashville, 1975.
Winter 2003
Robert Hesketh
of Rowan University
Rowan University Glassboro, NJ 08028
I first met Robert Hesketh at the 1992 Chemical Engineering Sum-
mer School in Bozeman, Montana. Phil Wankat and I led a work-
shop that he attended, and I immediately noticed his enthusiasm
for engineering education. As a result of that meeting, he and I later co-
authored an article on separations for CEE.m1 Little did I know that I
would eventually have the opportunity to hire him as one of the found-
ing members of the Rowan Chemical Engineering Department!
During Robert's faculty interview at Rowan we were impressed with
his enthusiasm and his ideas for the freshman engineering program.
We knew that his ideas on the use of a coffee machine would work as a
basis for our hands-on approach to engineering education at Rowan.
We felt he was a perfect fit for the new engineering education program
at Rowan, and his dedication to teaching has since been rewarded by
several educational awards from ASEE, including the 2002 Robert G.
Quinn Award, the 1999 Ray W. Fahien Award, the 1998 Dow Out-
standing New Faculty Award, the 2001, 1999, and 1998 Joseph J.
Martin Awards, and four other teaching awards. To date he has
obtained over $2 million in external funding from federal, state
and industrial sources.
As one of the founding faculty members of the College of Engineer-
ing and Chemical Engineering Department at Rowan University, Rob-
ert has spearheaded an effort to develop the industrial component of
the four-year sequence of the multidisciplinary engineering clinic. In
addition, he has created several courses that integrate experiments and
lectures in an inductive framework within chemical engineering. He
has made many major contributions in laboratory methods that dem-
onstrate chemical engineering practice and principles, the most notable
of which uses the coffee maker. He has helped advance the state-of-
the-art in laboratory-based education nationally through his many
publications, presentations, and seminars at ASEE and workshops
supported by NSF.
ROBERT'S EARLY YEARS Hesketh in front of the
What were the major influences in Robert's early years? His mother, distillation column he helped
Joyce, claims it was the time she spent with him in his crucial develop- to design for Rowan University's
mental years. "He was always happy and singing," she says. Robert Chemical Engineering Department.
Copyright ChE Division ofASEE 2003
Chemical Engineering Education
was born into a family with music and engineering skills on
September 28, 1960, near Philadelphia, Pennsylvania. His
mother is an accomplishedmusician with specialties in French
horn, piano, organ and harp. His father, Howard, received
three degrees in chemical engineering from Pennsylvania
State University-State College and is also an accomplished
violinist. After earning his Master's degree, Howard served
in the army and later returned to DuPont, where he be-
came a senior chemical engineer. He returned to col-
lege for his PhD in chemical engineering after work-
ing for Beryllium Corporation and Bell Laboratories
of Western Electric. In 1970 he accepted a faculty po-
sition at Southern Illinois University. During his years
at SIU he wrote 18 books in the areas of air pollution
and hazardous waste management. Based on his indus-
trial experience, Robert's dad always had a special ap-
preciation for the practical side of engineering.
Robert's enthusiastic personality is reflected by the activi-
ties of his early childhood: playing the cello, Boy Scouts,
running, and academics. He started playing cello in fourth
grade and joined the family ensemble, together with brothers
Howard and Ryan and sisters Joy and Melody. There are many
theories on the effect of classical music on improving math
skillsE21 and it appears that Robert benefited, as evidenced by
his receiving the O. K. Bowen Award for Mathematics upon
graduation from Carbondale Community High School. He
believes that playing a musical instrument also develops a
philosophy of practice-makes-perfect. He feels that while it
is often impossible to solve a complex problem right at the
beginning, just as it is impossible to master a new orchestral
piece of music on first reading, through music he learned at
an early age how to break the music or a problem into
smaller, more manageable, pieces to work on. Music was
one of the aspects of Robert's life that gave him confi-
dence in who he is today.
Robert was a nontraditional sports enthusiast. His dad be-
lieved that physical activities are an essential part of life, so
he began running with his father at the SIU playing fields
and eventually set his high school's record in the mile with a
time of 4:29 minutes. He also led his cross-country team for
the last two years in high school. Again, these early experi-
ences helped Robert develop his work ethic. By practicing
(in this case running) every day he was able to drop his half-
mile, mile, and two-mile times a few seconds each race. His
dad also had plenty of work around the house for Robert to
attend to, including installing a swimming pool, building sev-
eral new houses, mowing the multi-acre lawn, etc. Robert
was raised with the philosophy that one needs to work hard
to become excellent.
Robert and his brothers developed a love for the outdoors
in Boy Scouts. His father was the Scout Master and led a
monthly expedition into the forests of Southern Illinois. Many
adventures were had by Robert and his family such as 20-
mile hikes, camping in below freezing weather, and back-
packing on extended weekends. Robert later became an Eagle
Scout, the highest rank obtainable in Scouting. One of his
merit badges was in orienteering, where he was able to com-
bine his passion for running through the woods with his prob-
lem-solving abilities. He tells me that he still enjoys standing
alone in the woods with a map and a compass asking him-
Robert has spearheaded an effort to develop the
industrial component of the four-year sequence
of the multidisciplinary engineering clinic
[and]has created several courses that
integrate experiments and lectures
in an inductive framework...
self, "Where am I now?"! Robert became very successful at
orienteering and traveled around the country on weekends to
compete in national competitions. The highlight of his
orienteering was competing on the U.S. Team at the 1984
University World Championships in Jonkoping, Sweden.
Robert started working on environmental projects as a re-
sult of his father's work in air pollution control. In the 1970s,
Robert's dad started a pilot plant project at the SIU power
plant to show that sulfur dioxide emissions from coal could
be controlled using venturi scrubbers. Robert and his broth-
ers became a team and assisted their dad on stack tests. In
many cases these tests were done either in freezing condi-
tions on the top of a building or in the middle of summer at
elevated rooftop temperatures.
Robert had two requisites in selecting a college: running
and chemical engineering. He was good at math, chemistry,
and physics and was a natural for chemical engineering.
Robert's dad said that he could go to any university in the
country, but agreed only to pay an amount of tuition equal to
SIU's! The result was that Robert went to SIU for two years
and then transferred to the University of Illinois at Champaign-
Urbana. While at SIU, Robert continued working with his
father by conducting developmental work to support a patent
on the catenary grid scrubber. This work resulted in Robert's
first publication as an undergraduate and gave him practical
experience in designing experiments-he learned that duct
tape was excellent for temporary seals on large clear plastic
sections of piping! In addition, Robert's father wrote his first
textbookin 1972 titled, U,.1. i ,i, t i, -: & C. -,ii. -11i,..* AirPol-
lution.E?3 It would eventually be used in over fifty universi-
ties as a text in air-pollution control and would be updated
several times.J41 Robert was extremely fortunate to watch how
his father produced a text, and he worked as an office assistant,
typing portions of the copy that were sent to the publisher.
Winter 2003
A Robert, far
right holding
the dog, at the
start of a 1974
trip (brother
Ryan at
Robert and Fiona Cutting their house
cello wedding cake, 1990. V construction
of parent's
house in
Carbondale, 1978.
A Hiking
and Fiona
in Rocky
S1 Peak in
Robert continued his work on environmental engineering
problems through two summers of employment in Orlando,
Florida, for an environmental engineering consulting firm,
Cross-Tessitore and Associates. During this time Robert ex-
perienced not only the rigors of environmental audits and
assessments, but also the Florida life style of Frank Cross.
He felt fortunate to be able to live with the Cross family, who
introduced him to white-water kayaking!
In 1982 Robert graduated with a BS with Distinction in
Chemical Engineering from the University of Illinois and
started graduate school at the University of Delaware. At the
University of Delaware, Robert had a special opportunity to
work with T. W. Fraser Russellf51 and Arthur W. Etchells, who
is now a DuPont Fellow distinguished by his work in mix-
ing. Working with both Fraser Russell and Art Etchells fur-
thered Robert's appreciation for the practical side of engi-
neering. In this work, Robert developed a correlation for
bubble size in turbulent fluid flow that has been cited in over
25 journal articles and is currently being used in the chemi-
cal industry for the design of multiphase reactors and piping
networks. Both Fraser and Art have helped Robert immensely
throughout his career, from shaping and guiding his research
to giving him advice on career moves. He recalls one inci-
dence when he was struggling with a bubble breakage func-
tion for a population balance model; he had found numerous
complicated models and was trying to figure out which was
the best. Fraser, with the wisdom of experience, looked at
him and asked, "Have you tried a first-order rate?" Fraser's
ability to look for the simple solution to problems remains a
cornerstone in Robert's teaching philosophy.
After completing graduate school, Robert had both a job
offer with a major pharmaceutical company and an offer of
postdoctoral work at Cambridge University in England. Rob-
ert was destined for academics, however, and chose to work
with Professor and Department Head, John F Davidson, at
Cambridge University. There, he added very fast chemical
kinetics to multiphase fluid flow by working on combustion
problems in fluidized beds. This work continued his envi-
ronmental theme of working with coal combustion that results
in lower emissions of pollutants than conventional burners.
Robert enjoyed his stay in England from 1987 to 1990, and
while there he also decided to improve his musical abilities
by taking cello lessons. Attending a concert in 1987, he com-
pared a list of cello teachers with the concert program and
found a match; not only for cello lessons, but for the person
who later became the love of his life-Fiona L. Stafford! Rob-
Chemical Engineering Education
A Running in the
in 1983.
ert became one of Fiona's biggest fans. Their wedding in
1990 was notable in that the cello section of the Cam-
bridge Philharmonic Society played before the wedding
and their cake was in the shape of a cello! As a special
treat for Robert's relatives, he held the wedding rehearsal
dinner at Trinity College, where they got a real taste of
Cambridge University life.
where he worked with Martin Abraham, John Henshaw (ME),
and Keith Wisecarver. In these programs Robert expanded
his coffee-machine experience into a series of young schol-
ars experiments and as an outreach tool for student recruit-
ment. At Tulsa Robert also was influenced by the work of
Ramon Cerro in both his hands-on laboratory experiments as
well as his love of theory.
Robert's passion for engineering education
had its genesis at Cambridge. The English love
tea, which is served twice a day to all the fac-
ulty, staff and students, but Robert wanted real
coffee (not the jars of instant had by all other
postgrads) and formed a coffee club. It was
highly successful until the coffee machine
plugged up. So, Robert and his future best man,
A. B. Pandit, took the coffee machine apart
and cleaned out the tubular heat exchanger.
He learned two things: that Cambridge has
very hard water and that coffee machines are
Robert's next decision was whether to accept
ajob offer from a British university or one from
Tulsa University in Oklahoma. He had intro-
ducedFionato San Francisco at the 1989 AIChE
annual meeting and apparently convinced her
that the rest of the United States was just like
San Francisco, so Tulsa won out.
At Tulsa Robert was profoundly influenced
in engineering education by his colleagues Ri-
He is one of
the founding
professors of
the new and
clinic. His for-
ideas on mea-
surement, de-
sign, and course
content were
incorporated into
the engineering
clinic starting
from the time of
his first inter-
view at Rowan
chard Thompson, Ramon Cerro, and Martin Abraham. As
Department Chair, Rich Thompson introduced Robert to the
American Society of Engineering Education by sending him
to his first Chemical Engineering Summer School in Mon-
tana. The friendships he formed at this first summer school
helped guide him as an engineering educator. Rich Felder
and Rebecca Brent are still major influences on his teaching
style. He has attended at least four effective-teaching work-
shops and has avidly tried new teaching strategies from each
workshop. Based on these workshops, he has employed co-
operative learning and an inductive teaching style in his
classes. He has also gained important aspects of teaching from
educational leaders such as Jim Stice (instructional objec-
tives) and Don Woods (problem-based lc.iiii-ii).
Robert also developed a successful teaching and research
program at Tulsa and ultimately received three teaching
awards, including Professor of the Year in the College of En-
gineering and Applied Sciences. By the end of his tenure in
Tulsa, he had obtained $670,000 in external funding, includ-
ing NSF Research Initiation and DuPont Young Professor
awards. An outlet for Robert's teaching enthusiasm was found
in a series of three NSF Young Scholars Programs at Tulsa,
Robert is a leader in teaching innovations at
Rowan. He is one of the founding professors of
the new and innovative engineering clinic. His
forward-looking ideas on measurement, design,
and course content were incorporated into the
engineering clinic starting from the time of his
first interview at Rowan University. After ob-
serving Robert's excellent leadership skills,
Dean James Tracey chose him to be the Fresh-
man Engineering Clinic Coordinator. The en-
gineering clinic at Rowan is unique to engineer-
ing education in that engineers are actively
engaged in hands-on engineering science and
practice through the interdisciplinary clinic
for eight semesters.
As a founding faculty member of the Col-
lege of Engineering, Robert has taken a lead-
ing role in developing the engineering clinic
program-one of the most innovative vehicles for educating
engineers. Starting from the novel hands-on freshman semes-
ters in measurement and reverse engineering, he has influ-
enced each subsequent engineering clinic. In the sophomore
clinic, he started the detailed planning of the original linkage
between the writing faculty and the engineering projects. This
planning was further developed by Drs. Anthony Marchese
and Jim Newell. The junior and senior clinics have been de-
veloped into industrially related engineering projects. Rob-
ert brought the first industrially funded project and helped
formulate the Clinic Affiliates program where industry is
asked to sponsor engineering clinic projects for the junior
and senior years. The upper-level engineering clinic has been
vertically integrated by having juniors, seniors, and graduate
students work on projects funded by industry and the gov-
ernment. He has also worked on integrating the Rowan hall-
marks into the syllabus of the clinic. None of these achieve-
ments would have been possible without the energetic, inno-
vative, idea-generating faculty of the engineering college.
Robert works with every member of the chemical engi-
neering faculty on industrial and classroom projects. He serves
as a mentor for faculty to bring in these projects and has
Winter 2003
worked with our chemical engineering faculty on almost ev-
ery industrial project. As a result, his industrial involvement
has included relationships with companies such as Johnson
Matthey, Sony Music, Givaudan-Roure, Campbell Soup Co.,
Pepperidge Farm, Value Recovery, General Mills, and
DuPont. Because of this industrial involvement, Robert has
had the opportunity to work in fields such as supercritical
fluid extraction, microfiltration, liquid-liquid extraction, elec-
trochemical separations such as plating and electrodialysis, ad-
sorption, and ion exchange. He says that the clinic experience
is one of the greatest joys of his work at Rowan University.
In the Freshman year of the clinic, Robert uses a common
consumer product, the coffee
machine, as a vehicle for illus-
trating engineering science and
practice. It contains examples
of engineering principles from
many disciplines. For example,
chemical and mechanical engi-
neers are required to design
heaters, condensers, and sys-
tems for multiphase transport of
fluids, and to fabricate plastic
and glass components. The pro- S
cess of leaching the organic
compounds from the coffee
beans uses principles from mass Robert examining
transfer, which is unique to coffee.
chemical engineering. Automa-
tion of processes requires concepts from electrical, mechani-
cal, and chemical engineering. Finally, engineering decisions
are required to select the components of a system and place
them within an affordable, compact unit that can be easily
used by the consumer. This innovative example has been
adopted for use at many other institutions. Robert has contin-
ued his development of the freshman clinic with Dr. Stephanie
Farrell in grants from the National Science Foundation on
reaction engineering and drug delivery.
The first year the coffee machine was used, the students
not only reverse engineered the unit, but also designed a
new system. This is the only project I am aware of where
the students actually used what they were making so that
they could do an "all-nighter" to ready their final presen-
tations in freshman clinic!
Another innovation Robert incorporated into the freshman
clinic is a module on process measurements using the
university's cogeneration facility. He worked with the plant's
director to set up tours for each of the five sections (115 stu-
dents). On the tour, students took readings of pressure, tem-
perature, and flow from gauges, thermometers, and the plant's
data-acquisition system. They used these measurements to
g the
calculate material and energy balances on two heat exchang-
ers. First, the students used their readings as input for a chemi-
cal process simulation, using HYSYS, to determine the heat
duty for each heat exchanger. Then for homework they manu-
ally calculated the heat duty using all of the engineering equa-
tions used by the simulator. This experience was a simula-
tion of the day in the life of a chemical process engineer-
truly a unique experience for freshmen.
Robert uses the technique of cooperative learning in his
courses. He creatively employs cooperative learning in lec-
tures and in homework and semester design projects. In the
classroom, students form small groups and within a short
period of time solve engineering
problems. Robert creatively
works with these groups to help
them focus on the problem dur-
ing this session. Using coopera-
tive learning in the classroom
creates an active learning expe-
rience for students and improves
their retention of the material
over a pure lecture format. In
group homework and design
problems he has employed a va-
riety of assessment tools to make
each person in the group account-
internals of a able for achieving all the objec-
hine. tives. This technique is at the
forefront of engineering educa-
tion methods and Robert's use of it shows that he is at the
leading edge of teaching pc~ a ,.
Robert has been transforming his courses so that both the
content and the lecture format are in an inductive order. With
the inductive order of presentation the professor starts with
an experiment, demonstration, or the results of an experiment
and finishes the lecture with the derivation and solution of
equations describing these results. The second concept is plac-
ing the course content in an inductive order. For example,
heat transfer could be taught starting with heat exchangers
and overall heat transfer coefficients followed by sections on
the factors that contribute to the overall heat transfer coeffi-
cient, such as conduction and convection. Finally this area
of transport could end with coverage of unsteady-state
heat transfer. Each of the lectures presented in this novel
topical order can be done in an inductive manner, starting
from experimental observations and ending with a deri-
vation and solution of the governing equation. Robert has
been working with Stephanie Farrell on converting lec-
tures, courses, and labs to an inductive order for fluid
Chemical Engineering Education
mechanics, heat transfer, and transport.
Robert came full circle with respect to his dad's textbooks.
After helping with the production of an earlier version, he
finally taught a course in air pollution control using his father's
1996 textbook.E61 In addition to this course, Robert is cur-
rently conducting research on methods to reduce the emis-
sions from diesel engines in school buses, with funding from
the New Jersey Department of Transportation. The chief prob-
lem in this area is particulate emissions, and his dad's text,
Fine Particulates in Gaseous Media, E has been very useful.
Robert is currently leading an effort to integrate green en-
gineering into the undergraduate curriculum. Green engineer-
ing is the design, commercialization, and use of processes
and products that are feasible and economical, while mini-
mizing generation of pollution at the source and risk to hu-
man health and the environment. This way of thinking em-
braces the concept that decisions to protect human health and
the environment can have the greatest impact and cost effec-
tiveness when applied early to the design and development
phase of process orproduct. With the help of Kathryn Hollar,
Robertjustreceivedathree-year grant from the EPA to over-
see the development of course-specific modules in green
engineering and is looking for faculty who will help him
with this endeavor.
Using hands-on experiments, Roberthas presentedhis ideas
on education at national meetings and workshops. At the 1997
ASEE Chemical Engineering Summer School for university
faculty, he co-led a one-day workshop on Undergraduate
Laboratories. At this workshop he led participants through
heat transfer, pressure measurement, and coffee strength ex-
periments. He also gave a presentation on innovative teach-
ing techniques in the laboratory. In the summers of 1998 and
1999, Robert and I led a series of workshops based on a grant
we wrote together titled, "A Multidisciplinary Workshop on
Novel Process Science and Engineering Principles for Col-
lege Faculty." For this workshop Robert developed new ex-
periments in batch processing (a breadmaker), reaction engi-
neering (catalytic oxidation of VOCs), and polymers (fluid-
ized bed i i iin.i. and continued to develop experiments us-
ing the coffeemaker. These experiments were conducted by
participating faculty from around the country through sup-
port from the NSF Undergraduate Faculty Enhancement Pro-
gram. At the 1998 AIChE annual meeting Robert helped Phil
Wankat and myself direct a workshop on teaching effective-
ness where he presented a session on active learning tech-
niques in lecture courses and had faculty perform an experi-
ment with the instrumented coffee machine. Most recently
Robert co-led a workshop on Innovative Laboratory Experi-
ments with Stephanie Farrell and myself at the 2002 ASEE
Chemical Engineering Summer School in Boulder, Colorado.
Robert is highly active in both ASEE and AIChE. He has
published and presented his work in ASEE's Chemical Engi-
,.. i., i:. Education, the proceedings of the Annual Confer-
ence, and atASEE zone and regional meetings. He has chaired
sessions in education for both ASEE and AIChE. Most nota-
bly, he organized the first ever Topical Conference on Edu-
cation at an AIChE annual meeting titled, "Chemical Engi-
neering Education in the New Millennium." Currently he is
the chair of Group 4-Education in AIChE and was previ-
ously Vice-Chair of 4 and Chair of 4a-Undergraduate Edu-
cation. In addition to this service work, Robert has helped
formulate the Chem-E-Car competition and has served as the
competition's emcee since the races began.
Robert retains his passion for music and the outdoors. His
family has grown from two cellos to four with the addition of
Alexander (5 years old) and Natasha (9 years old). They also
love to travel as a family to the Rocky Mountain National
Park on hiking expeditions. They have gone to the moun-
tains nearly every summer since getting the "mountain bug"
in 1992 at the Bozeman Chemical Engineering Summer
School. Robert enjoys hikes with his family, and last sum-
mer their longest hike was by Odessa Lake (with an eleva-
tion of 10,020 ft and total distance of 9.5 miles) and the most
thrilling was climbing up a waterfall to Sky Pond (for a total
distance of 9.2 miles).
Robert is destined to climb higher mountains not only in
Colorado, but also in his professional life. Throughout his
life he has uniquely mixed chemical engineering with his love
of music and the outdoors. His educational innovations have
touched the lives of numerous students, not only at Rowan
and Tulsa, but also at many schools throughout the country
that have adopted these methods. He is a trusted friend and a
key member of the Rowan chemical engineering team.
1. Wankat, P. C., R. P. Hesketh, K. H. Schulz, and C. S. Slater, "Separa-
tions What to Teach Undergraduates." Chem. Eng. Educ., 28 (1) 12
2. Shaw, G. L., Keeping Mozart in Mind, Academic Press, September
3. Hesketh, Howard E.,' ** .. ... & ControllingAirPollution, Ann
Arbor Science Publishers, Inc. Ann Arbor MI, (1972 and 1974)
4. Hesketh, Howard E., Air Pollution Control, Ann Arbor Science Pub-
lishers, Inc. Ann Arbor MI, (1979 and 1981)
5. "T. W. Fraser Russell-An Appreciation by his Colleagues," Chem.
Eng. Educ., 31(2) 74 (1997)
6. Hesketh, Howard E., Air Pollution Control: Traditional and Hazard-
ous Pollutants, Technomic Publishing Co., Inc., Lancaster, PA (1991
and 1996)
7. Hesketh, H. E., Fine Particles in Gaseous Media, 2nd Ed., Lewis Pub-
lishers, Chelsea, Michigan (1986) 1
Winter 2003
Using the Gillespie Algorithm and MATLAB
Universidad Politecnica de Madrid Jose Gutierrez Abascal-2 28006 Madrid, Spain
here are two main approaches to numerically model
and simulate the time evolution of chemical reacting
systems. In the deterministic approach, the set of dif-
ferential equations describing the time evolution of the con-
centrations is solved using either analytical or numerical meth-
ods such as Euler or Runge-Kutta. It is assumed that the com-
plete time evolution of the reacting system is contained in
the solution of the set of equations, i.e., given a set of initial
conditions, only one trajectory is possible. In this paper, a
trajectory is a concentration-time curve. It corresponds to a
reacting species in a given experiment and describes the time
evolution of the reacting system in such an experiment.
In the stochastic approach, each individual reaction is con-
sidered a random event that can take place with a certain prob-
ability. Thus the time evolution of the concentrations depends
on a series of consecutive probabilistic events. Given a set of
initial conditions, there are many possible trajectories, each
with its own probability and with the sum of probabilities
adding up to one. These trajectories may be drawn by using
the probabilistic rate law.
The increasing interest of stochastic methods has been
pointed out by Schieber in this journal.11 More recently,
Scappin and CanuE2l have reviewed the use of stochastic mod-
els for simulating the dynamics of complex chemical sys-
tems and have shown that these models allow for easy iden-
tification of the main reaction paths in reacting systems in-
volving hundreds of elementary steps.
In addition, several other authorsP3,41 have pointed out that
deterministic models cannot accurately simulate the dynam-
ics of systems in which the time evolution depends on the
behavior of a very small number of molecules. Interesting
examples of such systems are individual cells in living or-
ganisms. McAdams and ArkinE41 have pointed out that
... Even in clonal cell populations and under the most uniform
experimental conditions, considerable variation is observed in the
rates of development, morphology, and the concentration of each
molecular species in each cell. These fluctuations ... play a
fundamental role in the evolution of the living systems ...
These fluctuations may be predicted and explained by the
stochastic models but not by the deterministic ones.
Traditionally, the deterministic methods are by far the most
commonly used in modeling the time evolution of chemical
Joaquin Martinez Urreaga is Associate Pro-
fessor in the Department of Industrial Chemical
Engineering at the Universidad Polit6cnica de
Madrid, Spain. He received his MSc (1982) and
PhD (1988) from the Universidad de Zaragoza
(Spain). His current fields of interest include
teaching chemistry and research on interfaces
and degradation in materials.
Copyright ChE Division ofASEE 2003
Chemical Engineering Education
Jos6 Mira obtained a Masters Degree in En-
gineering in 1986 and in 1995 a PhD in Ap-
plied Statistics, both from the Universidad
Polit6cnica de Madrid. He is presently an As-
sociate Professor at that University.
Camino Gonzalez-Fernandez obtained her de-
gree in Nuclear Engineering in 1987 and her
PhD in 1993, both from the Universidad
Polit6cnica de Madrid. She is Associate Pro-
fessor in the Department of Statistics at the
Universidad Polit6cnica de Madrid. Her current
fields of interest include teaching and research
on applied statistics.
reacting systems. The above remarks, however, may justify
the usefulness of introducing undergraduate students to the
use of stochastic methods to model chemical reactions.
In order to achieve better understanding of the fundamen-
tals of the stochastic simulation of chemical reactions, it is
interesting that students develop their own software tools to
carry out the simulation. We present here the basics of the
stochastic simulation of a well-known, simple process-the
AB equilibrium process-compared to the deterministic simu-
lation of the same process. In the stochastic simulation, we
follow the numerical method developed by Gillespie.E51
Both simulations are carried out with MATLAB, a nu-
merical computation package of increasing use in chemi-
cal engineering education.
This example may prove useful for studying how the pre-
dictions of the stochastic model relate to the deterministic
predictions (and to real-life experiences). To extend the sto-
chastic simulation to other chemical processes, the students
can either develop the corresponding MATLAB software,
taking as a starting point the MATLAB software supplied in
this paper, or they can use commercial simulation software.
Two of these commercial programs (freely downloadable
from the Internet) are noted in this paper.
We have chosen as our example the process
400 600
Time (seconds)
Figure 1. Deterministic (solid) and stochastic (dash, dot)
trajectories for the AB equilibrium process. The stochastic
trajectories were obtained in two consecutive runs. Initial
conditions were
NA(O)= 175; N,() = 25; k, = 4 e-3 s-; k2 = 1 e-3 s-.
Winter 2003
It describes various real processes, such as the hy-
drolysis of lactone to 7-hydroxybutyric acid in strong
hydrochloric acid.E61
It has been previously treated by different authors.E6'7
It is simple enough to be modeled by the undergradu-
ate students. In order to make the modeling easier, we
will assume an isothermal process at constant volume.
Deterministic Simulation
The differential rate laws can be written as
dNA() k2NB(t)-klNA(t) (1)
dN(t = klNA(t) k2NB(t) (2)
where NA(t) and NB(t) are the numbers of molecules after a
given reaction time t, and k1 and k2 are the direct and reverse
reaction rate constants.
Once the initial values of NA(t) and NB(t), (NA(O) and NB(0))
are specified, it is assumed that the solution of these differen-
tial equations describes the complete time evolution of the
reacting system. Figure 1 shows an example of the time evo-
lution of N(t) and NB(t) predicted by this approach for NA(0)
= 175, NB(0) = 25, k, = 0.004 s-' and k, = 0.001 s-1. These
trajectories were calculated using the MATLAB programs
listed in Appendices 1 and 2. In the deterministic approach,
given a set of initial conditions, all runs will give the same
The equilibrium values of NA and NB (NAeq and NBeq) may
be easily calculated by the students. At equilibrium,
klNA,eq = k2NB,eq (3)
Using the mass balance, we obtain
NA,eq =[NA(0) + NB(0)]/[ + (k / k2)] (4)
In our case, NAeq = 200/5 = 40 and NB.eq = 160.
Stochastic Simulation
As mentioned above, the stochastic simulation of a chemi-
cal reacting system is rather different from the deterministic
one. Each reaction is a random event that can take place with
a given probability, which is a function of the reaction rate
constants and the number of molecules. There are many pos-
sible trajectories, which we can draw by using the probabi-
listic rate law. Thus the development of the stochastic simu-
lation requires a deep foundation of the probability theory. A
complete description of the stochastic treatment of the AB
equilibrium process can be found in a text by Steinfeld, Fran-
cisco, and Hase.E7
In this paper we describe the development of a MATLAB
application for the generation of stochastic trajectories by
using the Gillespie algorithm.E51 Gillespie developed an el-
egant and efficient algorithm that uses Monte Carlo techniques
to carry out the numerical stochastic simulation of any given
chemical reacting system and demonstrated that this simula-
tion gives an accurate description of the time evolution of the
In the Gillespie algorithm, the probability of each reaction
is obtained by multiplying the reaction rate constant by the
number of combinations of molecules that can lead to the
reaction. For the AB process, the numbers of combinations
and =NB
respectively. In order to develop this algorithm, we first must
a time interval so small that either only one reaction or
no reaction at all can occur in the interval (t, t+dt) (i.e.,
dNA(t) = NA(t+dt) NA(t) can only take the values -1, 0,
and 1).
Sk1, k2
k1 is defined so that kldt is the probability that any A
molecule will react to give a B molecule in (t, t+dt) and
similarly for k2.
SWJ[N,(t)], W_[NA(t)
two positive functions such that W+[NA(t)]dt and W
[NA(t)]dt are the probabilities that, given that the num-
ber of molecules of A at time t is NA(t), at time t+dt the
number of molecules NA(t+dt) is equal to NA(t)+l and
NA(t)-1, respectively. W+[NA(t)]dt and W [NA(t)]dt are
conditional probabilities (conditional on the value of
NA(t)) and play an essential role in defining the sto-
chastic model. In our example, taking into account the
above definitions of k1 and k2, these functions are
W+[NA(t)] = k2NB(t) (5)
W_[NA(t)] = kNA(t) (6)
After defining the initial conditions, N(0) and the constant
k, the Gillespie algorithm generates time steps of variable
length, depending on the probabilities of the reactions and on
the random nature of the process (a random number is used
to generate the time steps). Subsequently, a second random
number is generated to determine which of the two possible
reactions occurs, taking into account the reaction probabili-
ties. Next, the N(t) values are updated according to the sto-
ichiometry and the process is repeated.
In order to determine the above reaction probabilities and
time steps, we need to define
> a[NA(t)]
a non-negative function such that a[NA(t)]dt is the
probability that the number of molecules of A, which
takes the value NA(t) at time t, suffers a unitary in-
crement (positive or negative) in the differential in-
terval (t, t+dt). It verifies
a[NA(t)] = W+[NA(t)]+W_[NA(t)] (7)
> w [Nx(t)]
probability that the process, which has suffered an
increment of one on either sense, does it positively
or negatively (+1 for w+ and -1 for w). These are
also conditional probabilities (conditional on the fact
that a reaction has taken place). Evidently
w+[Nx(t)]+ w_[Nx(t)] = 1 (8)
w+[Nx(t)] W+[Nx(t)]
random time step. It is the random variable "time to
the next reaction given that the number of molecules
of A at time t is NA(t)."
> po[NA(t), u]
complementary distribution function for u. Probabil-
ity that the number of molecules of X, which takes
the value NA(t) in time t, does not suffer any changes
in (t, t+u). It can be shown[51 that
p[NA(t), u]= exp{-a[NA(t)u]} (10)
The distribution of u is an exponential with mean l/a[NA(t)].
Using the Monte Carlo method, we can generate a suitable
value of the random number u um\l' 1
u = /a[NA(t)]}log( /r) (11)
where r is a random number of the uniform distribution be-
tween 0 and 1. Note that the random time step decreases in
average as the probability that any chemical change takes
place in the time interval increases.
Thus the algorithm of generation of stochastic trajectories
can be written
1. Initialize t=0. Introduce the initial values NA(0) and
NB(0), k1 and k2. Define the total number of reactions
2. Generate a value of u: first a random number r is
generated from the uniform distribution in (0,1) and
then u = { /a[NA(t)]} log(l/r).
3. Generate a second number r' from the uniform
distribution in (0,1). This random number determines
which reaction will occur, based on conditional
probabilities. If w_[NA(t)] > r', then take v = -1 and if
not, v = 1.
4. Update the process: t = t + u; NA(t+u) = NA(t) + v
5. If the total number of reactions i < Z, go back to step
Chemical Engineering Education
2. If i > Z, then stop.
An example of the MATLAB program (stochasticab.m),
which implements the above algorithm for the simulation of
the AB equilibrium process, is listed in Appendix 3. We em-
phasize the practical importance of using a random number
generator as good as possible to achieve an accurate simula-
tion, including those processes having a wide range of rate
constant magnitudes. In this work we have used the random
number generation algorithm provided by MATLAB, which
is applied extensively in statistical research.
Figure 1 shows the trajectories calculated by the above sto-
chastic algorithm in two consecutive runs, as well as the deter-
0 200 400 600 800 1000
Time (seconds)
Figure 2. Stochastic trajectories (two runs) with NA(O)=
3500 and NB(O) = 500; k, and k, are the same
as in Figure 1.
200 240 280 320
Time (seconds)
Figure 3. Deterministc and stochastic (single and
averages) trajectories [NA(t)] for the AB process. The
initial conditions are the same as in Figure 1.
ministic trajectories, using the same initial values in all
cases. These trajectories can be used to carry out a com-
parative study on the two simulation approaches-stochas-
tic and deterministic.
We can see that there are clear differences. The stochastic
trajectories show important fluctuations. Moreover, two con-
secutive runs predict different trajectories, although the ini-
tial conditions are the same ones, i.e., we cannot assure the
value of NA(t) at each time point. On the other hand, the de-
terministic simulation will always predict the same trajec-
tory, given a set of initial conditions, and it does not present
fluctuations in the time evolution. When these results are
analyzed, some interesting questions arise. For instance,
do these fluctuations (also called stochastic noise) have
some physical meaning? Is it possible that we cannot pre-
dict with certainty the value of Na(t) at each time point in
a real-life experience?
The students should know that the fluctuations are a real
consequence of the probabilistic nature of each chemical re-
action. Some interesting real experiments showing stochas-
tic effects have been presented by de Levie.P3I We can't see
these fluctuations in most real-life experiments, however.
Which are the factors that determine the importance of the
fluctuations? In order to develop an answer, the students can
repeat the simulations and vary the input conditions.
Figure 2 shows two new trajectories obtained through the
stochastic algorithm, but using a much larger number of ini-
tial molecules than in Figure 1, namely NA(0) = 3500 and
NB(0) = 500. It can be seen that the fluctuations are only im-
portant when the process starts with a small number of mol-
ecules. As the initial number of molecules increases, the fluc-
tuations decrease and the stochastic trajectory approaches the
deterministic one. This result was explained by GillespieE51
showing that the relative fluctuations in NA(t) around the mean
value of NA(t) (
, which can be obtained from repeated
runs) are approximately of the order of (
This is an important result, as it explains how the fluctua-
tions are not important in most real-life experiments. When
we work with 1020 molecules, the relative fluctuations (-10-
10), i.e., the uncertainties in the value of NA, are absolutely
negligible. In that case, a deterministic model allows an
adequate representation of most processes (with some ex-
ceptions-see below).
In many microscopic systems, however, the intrinsic fluc-
tuations are important. For instance, some biochemical reac-
tions taking place in individual cells of living organisms
depend on ten or less molecules. In that case, the fluctua-
tions can play a fundamental role in the behavior of the
system. Deterministic models cannot adequately describe
such behavior.
Figure 3 can be used to explain the relationship between
deterministic and stochastic trajectories. It can be seen how
Winter 2003
the average of stochastic trajectories approaches the deter-
ministic trajectory as the number of averaged trajectories
increases (i.e., the deterministic trajectories can be ex-
plained as the average behavior of the whole set of pos-
sible stochastic trajectories).
Finally, students can see that both the stochastic and deter-
ministic approaches predict the same final state for the AB
equilibrium process, but this is not evident in all cases, even
at a macroscopic scale. There are processes with more than
one possible stable final state. These processes will evolve
toward one of the possible final states, each evolution having
a probability that depends on the initial conditions. This is an
infrequent behavior in nature, which can be explained and
predicted using a stochastic approach.51
Once the students understand the fundamentals of the sto-
chastic simulation of chemical reactions, the application to
the simulation of other chemical processes can be carried out
using commercial simulation programs or even by develop-
ing new MATLAB software similar to the programs presented
here. The key point of this development is obtaining the func-
tions W[NA(t)] and W_[NA(t)], which represent the sources
and wells of A molecules in each chemical process.
The commercial programs save user time since he/she only
has to provide a suitable mechanism and the set of initial
data. Moreover, most of these programs include a built-in
collection of developed (and iill i cil ii--) examples. Of the
several commercial packages available, we will focus on
two high-quality programs that can be freely downloaded
from the Internet.
Chemical Kinetics Simulator (CKS 1.01 currently avail-
able in versions for OS 2 2.x and higher, Apple Macintosh
and Power Macintosh, and Microsoft Windows, 3.1/Windows,
95/Windows NT) was developed at IBM's Almaden Research
Center in San Jose, California, and can be downloaded from
its homepage.J81 It is an easy-to-use program (with an excel-
lent tutorial) that allows the accurate stochastic simulation of
chemical reactions, including those in which changes in vol-
ume, pressure, or temperature are expected. For instance, it
may work with explosions. The simulations included in the
package may also be useful as learning tools. Some examples
of these simulations are the copolymerization of two mono-
mers, a catalytic process in a batch reactor, and the simula-
tion of gas phase reactions in a CVD reactor.
StochSim is a stochastic simulator with a marked focus on
biochemical processes. In this case the examples included
simulate, for instance the Michaelis-Menten enzyme kinet-
ics and the Lotka Volterra process. It was written by Carl
Firth at the University of Cambridge. The currently available
version 1.491] consists of a platform-independent core simula-
tion engine encapsulating the stochastic algorithm and a sepa-
rate graphical user interface. The stochastic algorithm used
in this program is rather different from the Gillespie algo-
rithm; here each molecule is represented as a separate soft-
ware object. This is advantageous for simulating processes
in which the physical and chemical properties of the reacting
molecules change in the course of the reaction.101
Stochastic models are playing an increasing role in the simu-
lation of chemical and biochemical processes, as they allow
adequate prediction of the so-called stochastic effects, includ-
ing the intrinsic fluctuations of the system. These fluctua-
tions can play a fundamental role in the evolution of the
living systems and, in general, in the behavior of many
microscopic systems.
In this paper the Gillespie algorithm is proposed as a suit-
able tool for introducing undergraduate students to the basics
of the stochastic simulation of chemical reactions. Applica-
tion of the Gillespie algorithm to a simple and well-known
reaction, the AB equilibrium process, is presented. Using this
algorithm, the students can develop their own MATLAB pro-
grams to carry out the stochastic simulations of the AB
process and then use the results to analyze the main dif-
ferences between the stochastic and the deterministic mod-
eling of a chemical reaction.
Two examples of MATLAB programs are presented. Stu-
dents can also easily adapt these two programs to other reac-
tion schemes. Finally, two commercial simulation programs
(freely downloadable from the Internet) are proposed as ad-
ditional tools for extending the stochastic simulation to other
chemical processes.
The authors are grateful to the referees for their helpful
comments and suggestions.
1. Schieber, J.D., "Applied Stochastic for Engineering," Chem. Eng. Ed.,
27(4), 170 (1993)
2. Scappin, M., and P. Canu, "Analysis of Reaction Mechanisms through
Stochastic Simulation," Chem. Eng. Sci., 56, 5157 (2001)
3. De Levie, R., "Stochastics: The Basis of Chemical Dynamics," J. Chem.
Ed., 77(6), 771 (2000)
4. McAdams, H.H., and A. Arkin, "It's a Noisy Business! Genetic Regu-
lation at the Nanomolar Scale," Trends in Genetics, 15(2), 65 (1999)
5. Gillespie. D., Markov Processes: An Introduction for Physical Scien-
tists, Academic Press, Inc., New York, NY (1984)
6. Fahidy, T.Z., "Solving Chemical Kinetics Problems by the Markov
Chain Approach," Chem. Eng. Ed., 27(1), 42 (1993)
7. Steinfeld, J.I., J.S. Francisco, and W.L. Hase, Chemical Kinetics and
Dynamics, Prentice Hall, Englewood Cliffs, NJ (1989)
8. CKS home page:
Sept. 2002)
9. Download StochSim:
Sept. 2002)
Chemical Engineering Education
10. StochSim homepage:
StochSim.html> (Available Sept. 2002)
Program deterab.m for deterministic simulation
% This program performs the deterministic simulation of the
AB chemical % process
% kl y k2 are the direct and reverse reaction rate constants
% na0 and nb0 are the initial numbers of molecules
% final is the total reaction time
timestep= 1;
matrix=[T Y na0+nb0)-Y];
save figure 1.dat matrix/ascii;%save results
% plot curves
Auxiliary functionfisomer for
deterministic simulation
function F = fisomer(time,Y,flag,na0,nb0,kl,k2)
Program stochasticab.m for
stochastic simulation
% This program performs the stochastic simulation of the
AB process
% kl y k2 are the direct and reverse reaction rate constants
% na0 and nb0 are the initial numbers of molecules
% Z is the total number of reactions
% numtray is the number of trajectories to be generated
% in this example we generate and plot just two trajectories
for m=l:numtray;
for i=2:N;
wplus(i)=l *nb/((h*na)+(l *nb));
u(i)=(1/a)*log(1/unif(m,i, 1));
if wminus(i)>unif(m,i,2)
% close loop for each trajectory
% close loop for number of trajectories
plh ll I Ic l i,,l 1, ,iI IIc 2, i,'i2, i.,l I ,l I, ',b II IllII, [ ,i,\ 2,
% plot two trajectories
save figure2.dat matrix/ascii;
% save results
Winter 2003
University of Mississippi University, MS 38677-1848
ne of the major objectives of a thermodynamics
course is to introduce the modeling of vapor-liquid
equilibrium (VLE). Over the past 25 years, Profes-
sor Kenneth Jolls has developed visual aides to graphically
demonstrate various thermodynamic functions and phase dia-
grams. According to Dr. Jolls, "One of the problems with
thermodynamics is that, to many students, it has no solid be-
ginning. It doesn't start with concrete notions."E'1 The devel-
opment and implementation of three-dimensional graphics
facilitate the cognition of important building blocks of chemi-
cal engineering thermodynamics. Its significance is also re-
flected by the fact that P-xy-T phase diagrams are shown on
the covers of the newest editions of the two popular text-
books on chemical engineering thermodynamics.E2 3
There have been various engines used to generate three-
dimensional graphs. In Dr. Jolls's earliest attempts to display
the steam tables graphically, a simple, locally developed 3-D
graphing program was used to generate the plots.1'4'51 Since
that time, he has used more sophisticated software to pro-
duce more complicated plots. For example, he used the graph-
ing package MOVIE.BYUE" to produce the three-dimensional
surfaces of the Peng-Robinson equation of state (PR EOS).
Using these drawings, the unstable, metastable, and stable zones
can easily be illustrated. He has also developed three-dimen-
sional graphs for the ideal and the van der Waals gases as well
as the Joule-Thomson expansion coefficient.E11
Several commercial software packages have been devel-
oped over the years for various computational applications
in teaching, including the construction of three-dimensional
diagrams. At the University of Mississippi, Mathcad is intro-
duced early in the chemical engineering curriculum and is
used as one of the computational tools for courses at differ-
ent levels; it is also selected as the principal computational
workhorse for courses on thermodynamics.
Using limited P-x and P-xy data of a benzene/cyclopentane
system, this paper demonstrates the construction of three-di-
mensional, P-xy-T, phase envelopes based on two indepen-
dent procedures in Mathcad; both examples have served as
the templates in our pedagogical process. In the first approach,
the phase envelope is constructed based on Barker's algo-
rithm along with the Wilson equations and virial EOS for the
estimations of the activity coefficients and fugacity coeffi-
cients, respectively. In the second approach, the phase dia-
gram is constructed based on the Peng-Robinson equation of
state along with the one- and two-parameter models of the
van der Waals mixing rule. Regression of three sets of P-xy
data at three different temperatures yields the parameters
in these governing equations. Using these parameters, the
P-xy-T envelopes were generated and extended to the
mixture's critical region.
The experimental data used for the VLE modeling was
obtained from Hermsen and Prausnitz.E6' The data included
total pressures and liquid-phase compositions for the ben-
zene/cyclopentane system at three temperatures: 250C,
350C, and 450C. The component properties were obtained
from Reid, et al.E7'
Jasper L. Dickson received his MS and BS in Chemical Engineering from
the University of Mississippi. He is currently pursuing a PhD in Chemical
Engineering at the University of Texas at Austin. His research interests
have been in the area of colloid science.
John A. Hart, IV is a graduate student at the Department of Chemical
Engineering of the University of Mississippi. He has received his BS in
Forensic Chemistry and his BS in Chemical Engineering from the Univer-
sity of Mississippi also. His research interest is environmental remediation.
Wei-Yin Chen is Professor of Chemical Engineering at the University of
Mississippi. His teaching and research interests have been in reaction
engineering, thermodynamics, and mathematical modeling. He received a
PhD in Chemical Engineering from the City University of New York, an MS
in Chemical Engineering from the Polytechnic Institute of New York, an
MS in Applied Mathematics and Statistics from the State University of New
York at Stony Brook, and a BS in Chemical Engineering from Tunghai
Copyright ChE Division ofASEE 2003
Chemical Engineering Education
Model 1
Barker's Algorithm
To construct the phase envelope using Barker's algorithm,[8] the two
perature-dependent parameters in a model for the activity coefficient
recovered through regression, a Mathcad solve block (see Table 1).
"Given-MinErr" solve block in Table 1 consists of a powerful, built-i
gression procedure in Mathcad for recovering parameters. To avoid
sible experimental errors in the vapor-phase compositions, these dat
not used in the estimation of activity coefficient in Barker's algorithm
The term denoted by Psatprime in Table 1 represents the ratio of the fi
ity of the pure liquid of interest to the fugacity coefficient of that co
nent in the vapor mixture under equilibrium, or f / i. This ratio d
mines the partial pressure, yi, through the equation governing the f
0iYiP= yixifi fori=1,2
The fugacity of liquid can be related to its properties at its saturation p
thus, the ratio mentioned above can also be visualized as the product o
saturation pressure, the Poynting factor, and the ratio of the fugacity c
pure component of interest at its saturation pressure to the fugacity c
cient of that component in the vapor mixture. When the second virial c
clients are used in estimation of the non-idealities, or the fugacities, Psat_
can be expressed as18
l v -Bii -Psat-Py 12
psat f Ppsat exp (v B)(P- p)
1 i 1 RT
Given-MinErr Block for Barker's Algorithm
initial guesses: :=[800 ].joule
[A21 LI00 J mole
S[P experunental (xly 1(A 12,A21) .Psatlprime +x2-y2(A12,A21).Psat2_prime )]=0
] 12
:=MinErr (A12,A21)
Figure 1. Model Fits.
where B denotes the second virial coefficient, and
612 = 2B12 Bl1 B22
tem- In this example, the Wilson equation was used
were for the estimation of the activity coefficient, and
The regression yielded the two parameters of Wilson
in re- equations for the activity coefficients, A12 (T) and
pos- A21(T). After the recoveries of these parameters
a are at three temperatures, regression was conducted
m.[38] to recover the parameter associated with the expo-
ugac- nential dependence of temperature.
eter- Once the functions of A12(T) and A21(T) were
phase generated, the total system pressures at various
compositions were determined by summing the
partial pressures. Vapor-phase compositions, y 's,
(1) were estimated after the total pressures were ob-
oint; trained. The vapor-phase compositions, y's are
)f the used only for comparison after total pressures are
)f the obtained because the aforementioned activity co-
oeffi- efficient conforms to the Gibbs-Duhem equation.
oeffi- Since the vapor-phase compositions were not known
rime initially, the vapor-phase compositions, y 's in Eq.
(2), were set equal to zero in Psatprime for the ini-
tial regression for Aii. With a set of coarse estima-
(2) tions of y's in hand, a second round of regression
was performed using the full version of Psat_prime.181
The inclusion of y1's only slightly altered the values
of A12 and A21 in this example. Using these new
values of A12 and A21, the refined total pressure
and vapor phase compositions were calculated.
Figure 1 presents the comparisons of the experi-
mentally measured and predicted P-xy data from
both Barker's algorithm and the EOS model.
Since the number of traces in Mathcad is lim-
ited to sixteen, only two groups of the data at
250C and 450C are shown.
S Figures 2 and 3 (next page) represent the three-
dimensional P-xy-T phase envelopes. The former
illustrates the phase envelope around the experi-
mental conditions, and the latter illustrates the phase
envelope extended to the mixture's critical region
through the temperature dependence of A12 (T) and
A21(T) in the Wilson equation.
For extrapolation, an expression similar to the
one in the "Given-MinErr" solve block in Table 1
was used to calculate the system pressure at vari-
ous temperatures. Once the system pressure was
known, the vapor phase mole fraction was calcu-
lated in the same manner as above. A surface plot
graph was then inserted into the Mathcad
worksheet. Smoother phase envelopes can be con-
structed if more data sets at different temperature
levels are included. Figures 2 and 3 present results
Winter 2003
from only three and four sets of P-xy data, respectively.
Mathcad, unfortunately, does not allow titles to be included
for the axes of the 3-D graphs. Vertical axes in these figures
represent pressure in bar, and the two horizontal axes repre-
sent temperature K and mole fraction.
It is interesting to note that the envelope observed in Fig-
ure 2 becomes much thinner as the temperature is extended
to the critical region. As the temperature approaches the
critical temperature for the mixture, the phase diagram
begins to converge. A three-dimensional figure in Mathcad
can be rotated to illustrate the features of curvatures by
dragging the mouse.
Model 2
Peng-Robinson EOS with
van der Waals Mixing Rules
To demonstrate Mathcad's ability to process more compli-
cated algorithms, the same system was modeled with Peng-
Robinson EOS and the van der Waals mixing rules.[9] Both
the one- and two-parameter models for the van der Waals
mixing rule were included in the computation. When a cubic
EOS is used for estimating the properties of both the vapor and
the liquid, the fugacity coefficient of component i in a liquid
mixture can be defined in the same manner as that for the vapor
phase. Therefore, the equation governing the phase equilibrium
can be expressed as
0yi i=ixi fori=1,2 (3)
where the fugacity coefficients in both phases of the mixture
were estimated by
bi PV 1 nP(V-b) a 2 aji
In,=- ---1 -iIn
1b RT ) RT 2-ibRT a
Mole fractions, y 's, in the above equation were re-
placed by x 's when the fugacity coefficients of com-
ponent i in the liquid were estimated. Moreover, the
parameters of the PR EOS for mixtures a and b were
related to their counterparts for the pure component,
mole fractions in the phase of interest, and the bi-
nary interaction parameters, k When the one-param-
eter van der Waals mixing rule is implemented, k is
the only adjustable parameter in the model. When
the two-parameter mixing rule is used, it is expressed
kij = Kijxi + Kjixj (5:
and Kl and K1 are adjustable parameters in the model.
To find the mole volumes of the mixture in the in-
dividual phases, the PR EOS was expanded in vol-
ume and solved for the three roots by using the built-
in command "polyroots." The maximum and minimum roots
correspond to the vapor and liquid volumes, respectively.
To find the parameters kI or K by regression, a "Given-
MinnErr" block similar to Table 1 was executed. The equa-
tion below the Given command, however, was replaced by
minimizing the sum of the differences between the left-hand
side and right-hand side of Eq. (3). Once the values for k
and K 's were obtained, the system pressure and vapor phase
compositions were determined by a bubble point calculation
(see Table 2.) The two equations shown in Table 2 state
that the sum of the mole fractions must be equal to one.
They also suggest the efficiency of using vector notations
for handling data for multiple points in Mathcad. It should
be mentioned that, since the experimental data concern-
ing the vapor-phase composition are not readily available,
the outputs from Barker's algorithm were used as experi-
mentally measured data for y.
The fit from the two-parameter PR EOS is presented in
Figure 1. Calculations for Barker's algorithm took a shorter
processing time and produced a better fit. The extended
processing time for the PR EOS was primarily due to the
bubble point calculation.
As with Barker's algorithm, it was desirable to use the PR
EOS to predict the system pressure and vapor-phase compo-
sition near the mixture's critical temperature. To accomplish
this extension, the values for k or K 's were assumed to be
temperature independent. Vapor-phase compositions were
estimated using a bubble point calculation. The key to the
extension was the estimation of the vapor- and liquid-mole
volumes. In the development of the P-xy diagram, the ex-
b V+( 1+4)b
b V+ 1- 2)b
Chemical Engineering Education
Bubble-point Calculation
S l(xlexp,2e2e,K 12,K 21,Pcale, V lquidj 2( xlexp,exexpK 12,K21,Pcal, Vliqu d) V
*2 ylcalc ,y2calc ,K 2,K21,Pcal,Vapor
S(1'ylcalc ,y2cal,K 12,K21,Pcalc,Vapor
S1 xlxp exp, x2ep K 1 2, K 21, Pcal, V liquid ) 2 xl ep, 2p,K 2 21,Pcal, VIqid
I1(ylcalc,y2calc,K 12,K 21,Pcalc,Vvapor 2 yl ca,y2calc ,K 2K21Pcalc, Vvapor
ylcalc I =MinErr(Pcalc,ylcalc ,y2calc)
3r 0.2 0'.4 0.6 0.8
Figure 2. Phase envelope developed by
Barker's algorithm.
30 0.2 0.4 06 0.8
Figure 3. Extended phase envelope developed by Barker's
o.e. u ..
,3 0.2 0.4 0.6 0.8
Figure 4. Phase envelope developed by Peng-Robinson equa-
tion of state and two-parameter van der Waals mixing rule.
3Q .2 0.4 0.6 0o.
Figure 5. Extended phase envelope developed by Peng-
Robinson equation of state and two-parameter van der Waals
mixing rule.
Winter 2003
perimentally measured pressure was used to calculate the
vapor and liquid molar volumes. Since the pressure is not
known as the phase envelope is extended, however, this
method could not be used. To solve this problem, the vapor
and liquid volumes were expressed as functions of pressure
in the worksheet. Therefore, every time the pressure was al-
tered in the iterative process, the vapor and liquid volumes
were recalculated. The phase envelopes developed from these
procedures, one for the region where the experimental data
were collected and the other near the critical region, are shown
in Figures 4 and 5, respectively.
The Mathcad worksheets for Barker's algorithm and those
for the PR EOS discussed above have been used in our ther-
modynamics classes. Recoveries of parameters at various
temperatures are split into several files for convenience
and speedy results. They have been posted on the web
under the index "Mathcad Programs for Thermodynam-
ics" at
Vapor-liquid equilibrium data were modeled in Mathcad
using both Barker's algorithm and the Peng-Robinson cubic
equation of state model. Using the experimental data at three
temperatures, Mathcad was capable of calculating the neces-
sary parameters for each of the two models. Once the param-
eters were determined, Mathcad was used to predict the sys-
tem pressure and the vapor- and liquid-phase compositions.
Both models yielded reasonable fits with the experimental
data. The three-dimensional P-xy-T phase diagrams were then
extended to the mixture's critical region. The data reduction
procedures described herein are representative for students
who are learning VLE for the first time; moreover, the three-
dimensional phase envelopes give students concrete notions
concerning the phase behaviors.
1. Jolls, K.R., "Visualization in Classical Thermodynamics," Proc. ABET
Ann. Meet., p. 28 (1996)
2. Sandler, S.I., ( .. ..' .. i ...... Thermodynamics, 3rd ed., Wiley,
New York (1999)
3. Smith, J.M., H.C. van Ness, and M.M. Abbott, Introduction to Chemical
Engineering Thermodynamics, 6th ed. McGraw-Hill, New York (2001)
4. Balbuena, PB., "An Eye for the Abstract," Science, 286, p. 430 (1999)
5. Jolls, K.R., and K.S. Tian, "Fluid-Phase Equilibria from a Chemical Pro-
cess Simulator," Paper presented at the Annual Meeting of the ASEE,
Milwaukee, WI (1997)
6. Hermsen, R.W., and J.M. Prausnitz, "Thermodynamics Properties of the
Benzene and Cyclopentane System," Chem. Eng. Science, 18, p. 485
7. Reid, R.C., J.M. Prausnitz, and B.E. Poling, The Properties of Gases
and Liquids, 4th ed., McGraw-Hill, New York (1987)
8. Prausnitz, J.M., R.N. Lichtenthaler, and E.G. de Azevedo, Molecular
Thermodynamics ofFluid-Phase Equilibria, 3rd ed., Prentice Hall, New
Jersey, p. 236 (1999)
9. Orbey, H., and S.I. Sandler, Modeling Vapor-Liquid Equilibria, Cubic
Equations ofState, and Their Mixing Rules, Cambridge University Press,
New York (1998) 1
A Chemical Engineering Freshman Seminar
Vanderbilt University Nashville, TN 37235-1604
n this paper we will describe a new seminar elective for
freshman engineering students titled "Frontiers of Chemi-
cal Engineering." We have designed the seminar to in-
troduce freshmen to the field and profession of chemical en-
gineering by using examples from cutting-edge research to
illustrate fundamental concepts. Exposing students to chemi-
cal engineering in their first semester provides an earlier
chance for them to catch the excitement of chemical engi-
neering and should help them make better-informed decisions
regarding their educational plans.
Chemical engineering students at many universities receive
little, if any, exposure to chemical engineering as freshmen.
For example, at Vanderbilt University freshman chemical
engineering majors primarily take large lecture courses in
math, physics, chemistry, and general engineering. Their
sophomore year consists of only a single chemical engineer-
ing course each term, along with organic chemistry, math,
and physics. This traditional curriculum leaves students with
few opportunities to interact with professors in their major
until their junior and senior years. Additionally, the large in-
troductory lecture courses of the freshman year, which of-
ten provide little opportunity for student involvement, set
a pattern of expectation, hopefully incorrect, for the learn-
ing and teaching methods to be used throughout the re-
mainder of their program.
Compounding these problems, most freshmen have a poor
understanding of the engineering profession in general and
chemical engineering in particular. Often, students do not
begin to see the big picture of the chemical engineering pro-
fession until the senior capstone design course. Consequently,
they form impressions of chemical engineering, make deci-
sions on which major to pursue, and set expectations for
the college learning environment early in the college ca-
reer-all based almost entirely on non-engineering courses
and professors.
We feel that our chemical engineering profession has an
obligation to educate prospective chemical engineering stu-
dents regarding the broad applicability of chemical engineer-
ing principles, the multitude of available career paths, and
the many other opportunities that our graduates normally re-
ceive. Such information should be made available to students
as early as possible-certainly to new students in the first
semester of their freshman year.
Many engineering programs across the country have modi-
fied their freshman curricula to address these challenges. A
variety of approaches has been used, including general engi-
neering courses, design-based courses,E'-4 orientation
courses,E5-8 and seminars.E1-11 General engineering courses
bring together students from all engineering majors to pro-
vide a consistent grounding in basic engineering principles
and skills, such as engineering problem solving, communi-
cation tools and skills, basic computer literacy, mathematical
Frank Bowman is Assistant Professor of Chemical Engineering at
Vanderbilt University He received his BS from Brigham Young Univer-
sity in 1991 and his PhD from Caltech in 1997, both in chemical engi-
neering. His research interests include atmospheric aerosol modeling
and chemical mechanism analysis.
Robert Balcarcel is Assistant Professor of Chemical Engineering at
Vanderbilt University He received his BS from the University of Califor-
nia, Berkeley, in 1993 and his PhD from MIT in 1999, both in chemical
engineering. His research interests include improvement and metabolic
engineering of mammalian cell cultures for biopharmaceutical produc-
tion and analysis of chemical and biological agents.
Kane Jennings is Assistant Professor of Chemical Engineering at
Vanderbilt University. He received his BS in chemical engineering from
Auburn University in 1993, an MS in chemical engineering practice from
MIT in 1996, and a PhD in chemical engineering from MIT in 1998. His
research is focused on ultrathin organic films.
Bridget Rogers is Assistant Professor of Chemical Engineering at
Vanderbilt University She received her PhD and MS degrees from Ari-
zona State University and her BS degree from the University of Colo-
rado, Boulder, all in chemical engineering. Her research program fo-
cuses on film formation, microstructure evolution, and material proper-
ties of UHV-CVD deposited high permittivity dielectric thin films.
Copyright ChE Division ofASEE 2003
Chemical Engineering Education
modeling, and computer programming. Design-based courses
use real-world, hands-on experiences to introduce the engi-
neering design process, teamwork, and engineering prob-
lem-solving skills. Orientation-type courses help students
make the transition from high school to college and intro-
duce them to the engineering profession, including topics such
as campus policies and resources, time management and study
skills, exposure to various engineering disciplines and job
functions, and professional ethics. Seminar courses foster stu-
dent/engineering faculty interactions using small-group dis-
cussions on a variety of engineering related topics.
The Vanderbilt University School of Engineering has re-
cently introduced a variety of freshman seminar electives for
the purpose of providing students greater access to engineer-
ing faculty, helping them make more informed career choices,
and developing diverse learning and problem-solving skills.E11]
These seminars are one-semester-hour courses, taught entirely
by full-time professors, with a limited student enrollment
(typically 10-15 students). Faculty involvement is voluntary
and professors are free to teach on anything within their area
of expertise. In the academic year 2001-2002, approximately
half of the freshman engineering students participated in a
freshman seminar. Both student and faculty response to the
program has been very favorable. These seminars comple-
ment the existing freshman engineering curriculum. Within
Objectives for Freshman Chemical Engineering Seminar
0 Demonstrate What Chemical Engineering Is
Enable students to
Explain what a chemical engineer does
Identify products that chemical engineers make
Identify companies that employ chemical engineers
0 Touch on Chemical Engineering Principles
Introduce students to the chemical engineering principles of
Material balances
Chemical and phase equilibrium
Mass transfer
Reaction kinetics
0 Introduce the Frontiers of Chemical Engineering
Provide students with an introduction to the nontraditional
chemical engineering topics of
Biopharmaceutical production
Molecular self-assembly
Atmospheric particles
Semiconductor fabrication
0 Get the Freshmen Off to a Good Start
Excite them about engineering and chemical engineering
Provide an opportunity for them to get to know each other
Introduce them to chemical engineering faculty
Prepare and encourage them to participate in under-
graduate research
We have designed the seminar
to introduce freshmen to the field and
profession of chemical engineering
by using examples from cutting-
edge research to illustrate
fundamental concepts.
the School of Engineering, the choice of engineering major
is formally delayed until the beginning of the sophomore year.
All freshman engineering students take a common general
engineering course ("Introduction to Computing in Engineer-
ing"-teamwork skills, engineering method, computer tools)
and a C++- or Matlab-based programming course ("Program-
ming and Problem Solving").
As part of the seminar program, we have developed and
teach a "Frontiers in Chemical Engineering" seminar. Each
professor spends three to four weeks teaching a unit that is
focused on his or her research area. During the past three
years we have used examples from the modern topics of
biopharmaceutical production, semiconductor fabrication,
atmospheric particle formation, and molecular self-assem-
bly to introduce the profession and principles of chemical
engineering to the students.
In designing the course, we have identified the four main
elements listed in Table 1. The first three items are specific
academic objectives that help guide the selection of course
content (what is taught). The last item is more general and
defines the desired learning environment (how the course is
taught). Within the individual research units, each of these
elements is repeated. The goal is for students to see several
different fields within chemical engineering, to see different
applications of the same principles, and to interact with dif-
ferent faculty members.
Real-world applications that are familiar to students are
used to motivate interest in each of the research topics. For
example, biopharmaceutical production is introduced as a way
to treat diseases such as diabetes or to decrease transplant
rejections. The unit on atmospheric particles is started by ask-
ing the question, "Why do we care about particles in the at-
mosphere?", which leads to discussions of how particles in-
fluence global climate, the ozone hole, and human health.
Molecular self-assembly is explored as a process that can
create coatings for applications such as corrosion protection
of naval ships, chemical and biological sensors, biocompatible
medical devices, and water-resistant fabrics. The section on
semiconductor fabrication includes a discussion of how solid
state transistors work and an exercise that involves role play-
ing a process engineer evaluating a problem costing the com-
pany $250,000 per day. The role-playing exercise emphasizes
Winter 2003
the need for teamwork as well as the need to be informed
about how the unit processes of a production flow affect those
proceeding and following it.
The class meets for 75 minutes once a week for a total of
15 weeks. An outline of course topics from the fall 2001 semi-
nar is shown in Table 2. When the course was taught in fall
2000, the semiconductor fabrication unit was not included,
and the other research units were each expanded to four weeks.
The design of the course is such that different research units
can rotate or be replaced from year to year depending on fac-
ulty availability and interest.
Class sessions take a variety of forms. The "Chemical En-
gineering" and "Tying it All Together" sessions at the begin-
ning and end of the semester are taught by all of the profes-
sors. As part of the first class, small groups of three to four
students and a professor work to develop lists of chemical-
engineering-related products and companies. For the last class,
similar groups create lists of the research topics discussed
and match them up with the underlying chemical engineer-
ing principles (see Table 3).
Homework assignments are given out each week. They
contain a mixture of writing, data analysis and interpretation,
mathematical calculation, and experimental design. Students
are encouraged to collaborate on the homework but are re-
quired to submit individual assignments. The homework con-
tributes 70% to the course grade, with a comprehensive final
exam worth 30%.
The seminar enrolled 9 students in 1999, 11 students in
2000, and 13 students in 2001. Each year, approximately
half the students intended to major in chemical engineer-
ing, with the other half divided among the other engineer-
ing majors or undecided.
Research Units
The research units are taught by individual professors and
are structured to take advantage of their respective research
programs. Each of the units is described below. The semi-
conductor manufacturing and biopharmaceutical production
units are discussed in greater detail to illustrate the level at
which material is presented. While each research unit fo-
cuses on a specific research area, an important objective
is to illustrate the underlying chemical engineering prin-
ciples that are common to all areas. Table 3 summarizes
four of the main principles that are highlighted through-
out the course and examples of how they are presented in
the different research units.
For the atmospheric particles unit, students spend most of
the class period working in groups with a computer model
that simulates gas-particle equilibrium and growth. They use
the model to run simulated experiments and try to discover
how variables such as particle size, number concentration,
vapor pressure, temperature, and diffusivity influence par-
ticle growth. These computer exercises are supplemented
with discussions of student-selected current issues in at-
mospheric pollution such as global warming, the ozone
hole, and urban smog.
To teach students about molecular self-assembly, the in-
structor uses a hands-on demonstration involving the forma-
tion of a self-assembled monolayer to convey introductory
chemical engineering concepts in both thermodynamics and
kinetics. Since chemical engineers should ultimately develop
a molecular perspective, this unit also emphasizes how mo-
lecular-level effects can influence macroscopic surface prop-
erties. For example, the students find it extremely interesting
and intuitive that a hydroxyl-terminated self-assembled mono-
layer is wet by water while a methyl-terminated monolayer
repels water. The instructor also discusses the potential ap-
plications of these monolayer films to introduce students to
fundamental concepts in separations and mass transfer.
While studying semiconductor fabrication, students are
introduced to the unit operations of a typical process flow for
a complementary metal-oxide-semiconductor (CMOS) tran-
sistor. A video tape is used to help students visualize the clean-
room environment and the process equipment used in micro-
electronics manufacturing. After viewing the video, the class
participates in a group exercise focused on one of the process
steps. In 2001 we focused on chemical vapor deposition
(CVD). This exercise started with a brief lecture of the mecha-
nisms involved in CVD-transport of reactants into the re-
actor, diffusion of reactants to the substrate's surface, re-
action, surface diffusion of adatoms to form islands lead-
Course Topics
Week Tom
1 Chemical Engineering, Profession and Curriculum
Semiconductor Manufacturing
2 Microelectronic Device Processing
3 Silicon Oxidation
4 Chemical Vapor Deposition
Atmospheric Particles
5 Particles in the Atmosphere
6 Why do Particles Grow?
7 How Fast do Particles Grow?
Biopharmaceutical Production
8 Biotechnology and Cell Culture
9 Producing a Therapeutic Protein: Part I
10 Producing a Therapeutic Protein: Part II
Molecular Self-Assembly
11 Chemistry of the Kitchen Sink: An Introduction to Self-Assembly
12 Self-Assembled Monolayer Films
13 Use of Molecular Films in Corrosion Prevention
14 Tying it All Together
15 Final Exam
Chemical Engineering Education
ing to film formation, and desorption of reaction
byproducts. This lecture highlighted many chemical en-
gineering concepts, such as fluid dynamics, molecular
transport, and reaction kinetics.
Following the lecture the students broke up into groups to
discuss three questions related to CVD:
What process parameters might be important to CVD and
what might they :,i.- i
Whatproperties of thefilm that is formed might determine
how it is used in a device?
Sometimes the precursors exist as liquids at room tempera-
ture. How might they be introduced into the reactor in order
Examples of Chemical Engineering Principles
1. Material Balances
Atmospheric particles
when gases condense to form particles in the atmosphere,
the total mass in the system remains constant
Biopharmaceutical production
differential mole and cell balances for batch bioprocesses
cultivating mammalian cells
Semiconductor manufacturing
mass balances used in deriving models for silicon
oxidation and CVD
2. Mass Transfer
Atmospheric particles
particle growth depends on particle surface area, and the
concentration gradient between the particle surface and
bulk gas
Semiconductor manufacturing
reactants diffuse to the substrate surface in both CVD and
silicon oxidation processes
surface diffusion of adatoms in CVD
Molecular self-assembly
mass transfer of oxygen and water through a molecular
film to an underlying metal surface
3. Reaction Kinetics
Biopharmaceutical production
growth, death, and production rate constants are specified
as first order with respect to viable cell concentration
Semiconductor manufacturing
silicon oxidation described by first-order kinetics
Molecular self-assembly
how long will it take for a self-assembled monolayer to
4. Chemical and Phase Equilibrium
Molecular self-assembly
thermodynamic driving forces for molecular self-
assembly, i.e., when will a self-assembled monolayer
Atmospheric particles
particles form in the atmosphere when the gas phase
becomes supersaturated
the saturation concentration (vapor pressure) depends on
temperature and liquid phase composition (Raoult's law)
to participate in the reaction?
The intent of this exercise was to encourage the students to
think beyond what was presented in the video and brief lec-
ture and to incorporate basic concepts that they had been ex-
posed to in high school chemistry and physics.
Another class session is used to focus on a different pro-
cess step, silicon oxidation. Again, a brief lecture is used to
highlight some of the chemical engineering concepts involved
in the process, including oxidant transport to the surface,
oxidant transport through the growing oxide layer, and reac-
tion between the oxidant and silicon at the oxide/silicon in-
terface. The Deal-GroveE121 model of silicon oxidation is used
as the basis for this discussion. Development of the Deal-
Grove model was motivated by the lack of a comprehensive
model that could fit all published silicon oxidation data. Pre-
vious proposed models would only fit a small subset of the
published data. Therefore, we discussed how silicon oxi-
dation data could be used to validate proposed models.
Additionally, we discussed what experiments would be
used to collect these data.
As a homework assignment, the students are given pub-
lished silicon oxidation data and are asked to evaluate two
proposed models for this process. They are asked to deter-
mine parameters for the proposed models based on the data
they are given and are also asked to comment on how well
each model fits the experimental data. In addition to this as-
signment, the students are guided through an internet search
to learn more about the industry as well as the chemical engi-
neers who helped mold the industry into what it is today.
Specifically, they are given a list of terms related to semicon-
ductor processes to define. They are also asked to find out
who Andrew Grove is and what he, as a chemical engineer,
has done in the semiconductor processing arena.
During the biopharmaceutical production unit, the instruc-
tor introduces students to biotechnology and cell culture and
guides them through a discussion of the various factors that
influence the production of therapeutic proteins and their cost.
A lecture-based teaching method is enhanced by frequent
"break-out" sessions where students are asked to generate as
many possible explanations for a given effect or to calculate
a specific item for further discussion.
In the first class session of the unit, the terms biotechnol-
ogy, bioengineering, biochemical engineering, biomedical
engineering, and biomechanics are all defined. The chemical
engineering principles taught in each of the core chemical
engineering courses are highlighted and examples from bio-
tc'% il.1h -.\ are described (cell balances-material balances,
bioreactors-reactor design, solubility of oxygen in culture
medium-phase equilibria, control of pH-process control,
etc.). Biopharmaceutical production is then introduced as
a way to treat diseases such as diabetes or to decrease
transplant rejections. Several biotech companies, such as
Genentech, Genzyme, and Amgen, are listed as well as
Winter 2003
The challenge is in selecting and presenting the appropriate material to both
challenge and excite freshmen without scaring them with
concepts they are not prepared to learn.
some of their main prod-
ucts and applications.
As part of their first
biopharmaceutical assign-
ment, students do an
internet search to find ad-
ditional biotechnology
companies and products
that were not mentioned
during the lecture. They
are also asked to consider
engineering ethics by ex-
plaining which types of in-
therapeutic protein, adult
gene therapy (inserted
Figure 1. Student responses to end-of-course survey.
genes are not passed to the next generation), and embryonic
gene therapy (genes are presumably passed to their off-
spring)-they consider to be acceptable. Their viewpoints are
discussed in subsequent class sessions.
The remaining classes in the unit look at designing a pro-
cess to produce a therapeutic protein, such as one that could
dramatically reduce the symptoms of Alzheimer's disease.
Students are asked to estimate the demand, production re-
quirements, and cost to produce this protein. The amount of
product needed from an upstream batch process must be that
needed to meet the market plus the amount lost during sepa-
rations steps. Efficiency of separation is assumed to be 70%.
Reactor volume is then determined based on the estimated
market need for product (X kg/year) and assuming a given
achievable concentration of product at the end of a batch (1
g/L). Height and diameter of the vessel are determined given
a desired H:D ratio.
Material balances and kinetics are used to formulate dif-
ferential mole and cell balances for batch bioprocesses culti-
vating mammalian cells. "Accumulation = In Out + Gen-
eration Consumption" is formulated and translated to an
equation with appropriate nomenclature. Growth, death, and
production rate constants are specified as first order with re-
spect to viable cell concentration. Equations are integrated
and used to estimate final cell concentration and product given
growth, death, and production rate constants, or to determine
average rate constants given cell concentration and produc-
tion data. Students are shown how to use Excel for numerical
integration using the trapezoid rule.
Students use this model to determine how many days it
will take for the bioreactor to reach a maximum product con-
centration and to understand
the effect of the various re-
action rate parameters on
production time and cost.
The cost of biophar-
maceuticals is explained as
being high due to the low
yield from the primary pro-
cess batch and the high costs
of the elaborate separation
scheme needed to achieve
"ready-for-injection" purity.
Students estimate a reduc-
tion in cost associated with
increasing the product
yield by keeping cells
alive longer and/or genetically engineering them to pro-
duce more product per cell.
Course objectives, as defined by the professors, are sum-
marized in Table 1. Student-defined objectives for the course
are much more focused. In beginning- and end-of-course sur-
veys, in response to the question, "Why did you enroll in this
course?" students without exception stated two things: "To
learn about chemical engineering" and "To see if I wanted to
be a chemical engineer."
Achievement of these professor- and student-defined ob-
jectives was assessed with anonymous surveys at the begin-
ning and end of the semester. Responses to several questions
from the 1999 and 2000 end-of-course survey are shown in
Figure 1. The 2001 survey used different wording and, while
not directly comparable, showed similar results to the sur-
veys in the first two years. Virtually all students, whether
chemical engineering majors or non-majors, agreed or
strongly agreed that the course improved their understanding
of what chemical engineers do, with slightly higher ratings
from chemical engineering majors. This indicates that the first
objective of both professors and students-to learn about
chemical engineers and chemical engineering-is being met.
Much larger differences between majors and non-majors
were observed on questions regarding interest in chemical
engineering. After taking the course, chemical engineering
majors were more interested in both specific chemical engi-
neering research areas and in continuing to pursue a chemi-
cal engineering major. Non-majors had widely divergent re-
sponses to the question on chemical engineering research ar-
Chemical Engineering Education
This course improved my understanding of
what chemical engineers do.
This course increased my interest in
specific chemical engineering research
This course increased my interest in _
pursuing a chemical engineering major.
I enjoyed taking this course
[ChE Majors 1.0 2.0 30
]non-ChE Majors Strongly Disagree Neutral
40 5.0
Agree Strongly
eas, either strongly disagreeing or strongly agreeing that the
course increased their interest. Concerning pursuit of a chemi-
cal engineering major, the course tended to make non-majors
less interested. These results ,i- ili. 1% illic course has been
more effective at confirming students original selection of a
major rather than recruiting non-majors into chemical engi-
neering. Written student comments support this view, with
chemical engineering majors saying, "Now I am sure this is
what I want to major in," and non-majors saying "I found out
that I do not want to be a chemical engineer and that other
fields interest me more."
Both sets of students tended to agree or strongly agree that
they enjoyed taking the course, with exceptionally favorable
responses from the chemical engineering majors. That non-
majors, despite a demonstrated preference for other engineer-
ing majors, enjoyed the course is taken as a sign that the course
is providing the desired positive experience for freshman
engineering students.
Faculty response to the seminar has also been favorable.
We have appreciated the opportunity to get to know our stu-
dents early in their college careers. As we encounter them in
other courses, we find that we have already established a re-
lationship with them, which helps us connect better with the
entire class. Presumably, this experience is reciprocated, and
students also feel more comfortable interacting with us. An
additional benefit has been that several students have ex-
pressed interest in our individual research programs, and some
have begun working as undergraduate research assistants in
our research labs.
The overall time commitment for preparing and teaching
the seminar, particularly when divided among three or four
professors, is quite reasonable. But it was noted that prepara-
tion time for each class period was higher for this course com-
pared to semester-long courses. The challenge is in selecting
and presenting the appropriate material to both challenge and
excite freshmen without scaring them with concepts they are
not prepared to learn.
We have identified a few areas for improvement in upcom-
ing years. Greater coordination between the individual re-
search units is needed so that the seminar is a coherent, inte-
grated course and not merely a collection of unrelated mini-
seminars. Related to this, initially we noted a deficiency in
meeting the objective of introducing basic chemical engineer-
ing principles, so in 2001, greater emphasis was placed on com-
mon underlying ideas in each research unit to help tie the course
together and provide a better understanding of these principles.
Assessment surveys need to be refined to better measure
achievement of the stated course objectives. The progress of
past seminar students should be followed to determine what,
if any, impact the course may have had on their college expe-
rience. Unfortunately, due to the limited and voluntary en-
rollment, accurate comparison to a control group of students
who didn't take the seminar is not practical.
The first time the course was taught, we found two- or three-
week units to be too short. Three to four weeks for each re-
search area was better, because it allowed more time to ex-
plore the research topic. A certain amount of background
material is essential when introducing unfamiliar subjects,
but our goal is to achieve sufficient depth to intellectu-
ally challenge the students. Part of this challenge is in-
herent in making graduate-level research topics accessible
to a freshman audience.
Overall, we feel the course has been quite successful. Stu-
dents have learned more about chemical engineering, and by
exposure to our different research areas they have gained a
clearer view of the wide scope of opportunities available to
them. Perhaps most importantly, freshman engineering stu-
dents have had the opportunity to begin their college experi-
ence working closely with other engineering students and with
engineering faculty. The experience has proved enjoyable and
beneficial for all involved. The format of the course is flex-
ible and should be easily adaptable to other chemical engi-
neering departments.
Frank Bowman would like to thank the National Science
Foundation for supporting development of the educational
aerosol computer model under Grant ATM-9985108.
1. Ambrose, S.A., and C.H. Amon, "Systematic Design of a First-Year
Mechanical Engineering Course at Carnegie Mellon University," J.
Eng. Ed., 86, 173 (1997)
2. Carlson, B., et al., "A Motivational First-Year Electronics Lab Course,"
J. Eng. Ed., 86, 357 (1997)
3. Sheppard, S., and R. Jenison, "Examples of Freshman Design Educa-
tion," Int. J. Eng. Ed., 13, 248 (1997)
4. Burton, J.D., and D.M. White, "Selecting a Model for Freshman Engi-
neering Design," J. Eng. Ed., 88, 327 (1999)
5. Landis, R.B., "Improving Student Success Through a Model 'Intro-
duction to Engineering' Course," Proc. 1992 ASEE Ann. Conf., To-
ledo, OH (1992)
6. Hatton, D.M., PC. Wankat, and W.K. LeBold, "The Effects of an Ori-
entation Course on the Attitudes of Freshmen Engineering Students,"
J. Eng. Ed., 87, 23 (1998)
7. Porter, R.L., and H. Fuller, "A New 'Contact-Based' First Year Engi-
neering Course," J. Eng. Ed., 87, 399 (1998)
8. Budny, D., "The Freshman Seminar: Assisting the Freshman Engi-
neering Student's Transition from High School to College," Proc. 2001
ASEEAnn. Conf., Albuquerque, NM (2001)
9. Merritt, T.R., E.M. Murman, and D.L. Friedman, "Engaging Fresh-
men Through Advisor Seminars," J. Eng. Ed., 86, 29 (1997)
10. Richardson, C., "Freshman Retentionn Engineering Technology Pro-
grams at Rochester Institute of Technology," Proc. 1997 ASEE Ann.
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11. Overholser, K.A., "Engineering Freshman Seminars," Proc. 2001ASEE
Ann. Conf., Albuquerque, NM (2001)
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Winter 2003
Random Thoughts...
North Carolina State University Raleigh, NC 27695
Dear Engineering Student:
Don't take the title of this column literally. Despite the in-
comprehensible lectures, endless homework, and impossible
tests, studying engineering has rarely been fatal. Neverthe-
less, things may not always go quite the way you would like-
classes with absurd amounts of work and test averages in the
50s are facts of life in engineering. I had lots of classes like
that when I was where you are now, and I complained about
them just as loudly. Unfortunately, while complaining may
make you feel better, it won't do a thing for your grades.
I'd like to propose several better ways to help yourself.
First, though, let me i .-.c'l I.,i i. ilc ic.il problem may not be
that professor who's making your life miserable. It is that
over the years you may have unconsciously bought into a
message that goes like this: "My teachers know i. A iin... I
need to know to be an i,.;i,. Their job is to tell it to me in
lectures, and my job is to soak it up and then repeat it on
exams. If I can do that, I've learned it."
Wrong! That approach may have worked in high school
but it begins to fail in college, and once you get into the plant
or research lab, it stops working completely. Out there, there
are no professors, lectures, or texts with worked-out ex-
amples, and the problems don't come neatly packaged with
all the information needed to solve them. In fact, often
the hardest part of a real problem is figuring out exactly
what the problem is.
But you also need to remember this. Around the world,
hundreds of thousands of engineers-most no smarter than
you, many not as smart-who once struggled with their own
confusing instructors and unreadable texts and didn't under-
stand entropy any better than you do, are out there doing just
fine. Every day they figure out what they need to know to
solve their problems, and then they solve them. If they could
learn to do that, so can you. What I'd like to do here is give
you five simple tips to help you start learning it now. If you
find yourself struggling in classes, give the tips a try. If they
work (and I'm pretty sure that they will), you'll have an easier
time in school and hit the ground running in your first job.
Figure out what might make course
material clearer and try to get it in class.
Do you ever find yourself expressing one of these com-
mon complaints? "I need practical, real-world applications
before I can understand .. m". tiii,;.. but all we get in class is
theory." "I want to understand how i,;,,... work, but all we
get are facts to memorize and formulas to substitute into." "I
understand what I see-pictures, .!.i ., ,, ,.. demonstrations-
better than what I hear and read, but all we get are words
and formulas."
If you do, pay attention to yourself-identifying what
you're missing in a course is the first step toward getting it.
The obvious next step is to ask your professor, in or out of
class, for whatever it may be. Most professors genuinely want
their students to learn-that's why they became professors-
and often complain that their students rarely ask questions
except "Are we responsible for this on the test?" So if you
don't understand something, try asking for something that
Richard M. Felder is Hoechst Celanese Pro-
fessor Emeritus of Chemical Engineering at
North Carolina State University. He received
his BChE from City College of CUNY and his
PhD from Princeton. He is coauthor of the text
Elementary Principles of Chemical Processes
(Wiley, 2000) and codirector of the ASEE Na-
tional Effective Teaching Institute
Copyright ChE Division ofASEE 2003
Chemical Engineering Education
might clarify it. "Couldyou ...i an example ofhow you would
use that formula?" "Could you sketch what that (device, so-
lution, plot) might look like?" "Where did that equation you
just wrote come from ? Even if you're afraid a question may
sound stupid, ask it anyway. I guarantee that others in the
class are equally confused and will be grateful to you for
having the courage to speak up. And if you need more help,
go to the professor's office and ask for it.
Caution, however. Even instructors who really want to help
will get annoyed if they think you're trying to get them to do
your homework for you. Never ask your instructor for help
on a problem 'nuil you have made a serious t- i to solve it
by yourself When you ask, be prepared to show what you
tried and how far you got. Bring in your flow charts and free
body diagrams and calculations, including the ones that didn't
work. The more you bring in, the more likely you are to get
the help you need.
Some textbooks try to clarify difficult material by giving
practical illustrations and explanations. Check out those parts
of your text if you're having trouble rather than just search-
ing for solved examples that look like the homework prob-
lems. Another good strategy is to look at a second refer-
ence on the same subject-a different text, a handbook,
or a Web site. Even if you can't find the crystal-clear ex-
planations and examples you'd like, just reading about
the same topic in two different places can make a big dif-
ference in understanding.
Work with other students
When you work alone and get stuck on something, you
may be tempted to give up, where in a group someone can
usually find a way past the difficulty. Working with others
may also show you better ways to solve problems than the
way you have been using. Here are two ideas for making
groupwork effective.
Outline problem solutions by yourselffirst and then work
out the details in your.... *../ Someone in every group is gen-
erally fastest at figuring out how to start problem solutions
and does it for every problem. If that student isn't you, you
may have to figure it out for the first time on the test, which
is not a particularly good time to do it. Outlining the solu-
tions before meeting with the group is the way to avoid this
Get .-..'.*in, members-especially the weaker ones-to
explain all completed problem solutions before I,.i;,.. a
p.'I. 44. ,m...- ;ii .,r session. If everyone can do that, the ses-
sion worked.
Consult experts
Sometimes you'll run into a problem that completely stumps
you and everyone you're working with. When practicing en-
gineers run into such problems, as they all do occasionally,
they consult experts. You also have experts available to you.
Your course instructor is an obvious candidate, but that doesn't
always work out. Other potential consultants include gradu-
ate teaching assistants, other professors who teach the
same course, students who have previously taken the
course, smart classmates, and tutors. No matter whom you
go to, though, go early: waiting until two days before the
final exam probably won't cut it.
Believe that you have what it takes
to be a good engineer.
If this advice is hard for you to take now, you're probably
suffering from what psychologists refer to as the Impostor
Phenomenon, which is like a tape that plays inside people's
heads. If you're an engineering student looking around at your
classmates, the tape goes something like this: / I. .. people
are ... ...--hi. \ understand all this stuff They really '.. 1l..,.
here...but I don't. Over the years I've somehow mana,,Ied to
fool them all-my J,,/irl, my friends, my teachers. They all
think I'm smart ,,.,.*l1 to be here, but I know better...and
the very next hard test or hard question I get in class will
finally reveal me as the impostor I am." And what would
happen next is too horrible to contemplate, so at that point
you just rewind and replay the tape.
What you don't know is that almost everyone else in the
class is playing the same tape, and the student in the front
row with the straight-A average is playing it louder than any-
one else. Furthermore, the tape is usually wrong. If you sur-
vived your first year of engineering school, you almost cer-
tainly have what it takes to be an engineer. Just remember all
your predecessors who had the same self-doubts you have
now and did just fine. You do belong here, and you'll get
through it just like they did. Try to relax and enjoy the trip."1
Richard Felder
1. For more about student survival skills and the Impostor Phenomenon,
Winter 2003
All of the Random Thoughts columns are now available on the World Wide Web at
http://www.ncsu.edu/effectiveteaching and at http://che.ufl.edu/-cee/
Andrew L. Zydney
The Pennsylvania State University University Park, PA 16802
When I was an undergraduate studying chemical en-
gineering, there really was no significant membrane in-
dustry worth mentioning. That has certainly changed.
Today, the membrane industry has sales of several bil-
lion dollars a year. This includes major applications in
the treatment of kidney disease by hemodialysis, the
separation of commodity gases such as oxygen and ni-
trogen, the purification of therapeutic proteins and phar-
maceuticals, and the treatment and desalination of natu-
ral and industrial waters.
About two years ago, the North American Membrane
Society conducted a survey to determine the extent to
which membrane science and tci'lin, -., was covered
in the undergraduate chemical engineering curriculum.
This survey revealed a number of programs with sig-
nificant membrane-related material, including specific
laboratory experiments, open-ended design problems,
and significant sections in both core and elective ChE
courses. In most cases, however, the teaching was done
by only one or two "experts," typically faculty who had
significant personal experience in the membrane field.
Departments that had no faculty working on membranes
tended to have little if any coverage of membrane prob-
lems within their undergraduate programs.
Motivated in large part by the results of this survey,
the Membrane-Based Separations Area and the Educa-
tion Division of the AIChE decided to co-sponsor a ses-
sion on Membranes in the Chemical F,,.n i i ;, Cur-
riculum at the 2001 Annual Meeting. The session was
an enormous success, with a series of fascinating pre-
sentations covering a wide range of membrane problems
within the undergraduate curriculum. The papers pre-
sented in this issue of Chemical Fi,, .;n.. i in Education
are a direct result of this session, and I would like to
personally thank Tim Anderson for his encouragement
and support in putting this special issue together.
The papers that follow have been organized "chrono-
logically," beginning with examples of how to introduce
membrane technology in the Introduction to Chemical
F, I,. ,. it i i. course and then moving through examples
in mass transfer, separations, the undergraduate labora-
tory, and senior design. The specific problems/examples
cover the full range of membrane applications, includ-
ing problems in
1) Design of appropriate hemodialysis therapy for the
treatment of kidney disease
2) Optimization of gas separations using hollow fiber
3) Removal of impurities from therapeutic proteins using
membrane ldiailtrir a' 'n
4) Desalination of salt water by reverse osmosis or
5) Recovery of precious metals from spent catalysts
6) Concentration of apple juice using ;ltailrridrririn
7) Production of ethylene in a ceramic membrane reactor
Our hope is that these papers will provide faculty with
examples that they can use in their classes so that all
chemical engineering undergraduates can be exposed to
some of the important principles and applications of
membrane tecdlll II i .'. The authors have tried, wherever
possible, to provide sufficient details and references so
that faculty can use these examples in their teaching. In
addition, all of the authors have indicated they would be
happy to answer questions about the problems, and sev-
eral of the papers contain URLs that provide links to
more detailed descriptions of the process simulators or
lab experiments.
The North American Membrane Society (NAMS) will
also be hosting an education section on its website
(www.membranes.org), and anyone who is using these
(or other) membrane problems within their courses is
strongly encouraged to contact NAMS so that this infor-
mation can be disseminated as effectively as possible
throughout the chemical engineering community.
Chemical Engineering Education
Membranes in ChE Education)
In the Introduction-to-ChE Course
University of Delaware Newark, DE 19716
he introductory course in most chemical engineering
departments is designed to meet a broad range of edu-
cational goals. They typically include: 1) providing
information that will enable students to determine if chemi-
cal engineering is the "correct" major for them; 2) providing
a foundation for subsequent courses in the curriculum; and
3) teaching significant chemical engineering principles, par-
ticularly in the area of mass balances.El Traditional introduc-
tory courses, e.g., those based on the classical book by Felder
and Rousseau,1[2 focus primarily on the use of steady-state
mass i. id ci i y) balances to describe the behavior of a wide
range of chemical processes. These courses often include a
small section on transient processes at the end of the semes-
ter, such as Chapter 11 in the Felder and RousseauE2] text or
Chapter 7 of Himmelblau.E31 Russell and DennE41 take a very
different approach, emphasizing transient balance equations
right from the beginning. This approach has the advantage of
allowing the instructor to focus on the key concepts of "rate"
and characteristic times, an aspect that is often lost in courses
that emphasize steady-state processes.
One of the challenges of introducing students to transient
mass balances is a lack of interesting and effective problems
that analyze the behavior of non-reacting systems (batch re-
actor problems provide a very effective introduction to time-
dependent reacting systems). Russell and DennE4' devote more
than an entire chapter to the analysis of draining and filling
tanks-a problem that illustrates the important concepts but
one that generates very little excitement and enthusiasm
among the students. HimmelblauE3' also uses the tank drain-
ing problem as a primary example, along with problems on
diluting a salt solution with water. Felder and RousseauE2" try
to make the tank draining problem a little more interesting
by examining the water level in a reservoir during a period of
drought and the water volume in a storage tank that has a
leak. But students often see these problems as artificial, in
part because of the seemingly arbitrary functions given
for the rate of inflow and outflow, and they provide little
opportunity for the students to think about process design
The University of Delaware uses the text by Russell and
DennE41 as the basis for its introductory chemical engineering
course, which is taught in the spring semester of the fresh-
man year. The course is divided into three main sections:
Transient mass balances in nonreacting systems
Transient mass balances in reacting systems, including the
analysis of batch reactors and CSTRs
Interfacial mass transfer
The traditional material in this course has been supplemented
with a series of membrane problems specifically designed to
illustrate the key concepts involved in the analysis of tran-
sient mass balances. These membrane problems are "real,"
they are easy for students to relate to, they tend to be much
more interesting than the traditional tank draining and filling
problem, they provide a much better introduction to the range
of problems and application areas of interest to chemical en-
gineers, and they give students an opportunity to think about
real design issues, even when they are freshmen.
Apple juice can be concentrated by a reverse osmosis system
Copyright ChE Division ofASEE 2003
Winter 2003
Andrew Zydney is currently Professor and
Endowed Chair in the Department of Chemi-
cal Engineering at The Pennsylvania State Uni-
versity. He received his PhD from MIT in 1985
and was a faculty member at the University of
Delaware from 1985 to 2001. He has been
actively involved in membrane research for
more than twenty years, with emphasis on bio-
technological and biomedical applications.
Membranes in ChE Education
using the fed-batch process shown in Figure 1. Fresh juice is
fed to a recycle tank, with the juice from the recycle tank
then passing through the reverse osmosis unit where water is
removed through the membrane. The concentrated juice is
returned to the recycle tank-the system is designed to oper-
ate so that the volume in the recycle tank remains constant
throughout the process. At the end of the process, a concen-
trated juice product is obtained in the recycle tank. It can be
frozen and sold as "apple juice concentrate" or the concen-
trated juice can be shipped and then reconstituted at a remote
site by simply adding water. This latter process can lead to
significant cost-savings since a much smaller volume of juice
needs to be shipped across the country. One of the concerns
with this process is that the membrane is never "perfect,"
meaning that there will be a small loss of flavor components
through the membrane during the concentration process. This
is why many juice companies will specifically advertise on
the label that their juice is "not from concentrate." Cheryan
and AlvarezE15 provide a more detailed discussion of mem-
brane processes for juice concentration.
The goal of the problem is to evaluate the fraction of flavor
components that are lost during a process designed to take
10,000 L of fresh juice and produce 500 L of apple juice con-
centrate. To simplify the analysis, we assume that the con-
centration of flavor components in the filtrate stream collected
through the membrane is equal to a certain fraction (S) of the
flavor concentration in the stream that enters the membrane
unit. This latter assumption is simply the definition of the
membrane sieving coefficient. This type of constitutive rela-
tion must be determined experimentally, playing a role analo-
gous to the rate expression in batch reactor problems.[14
The problem is solved by writing both total and compo-
nent mass balances around the recycle tank and the reverse
osmosis unit (shown by the dashed line in Figure 1):
d(pV) = PfeedQfeed PfiltrateQfiltrate (1)
d(- = QfeedCfeed SQfiltrateC (2)
where C is the concentration of the flavor components in the
feed tank. If we make the assumption of a constant (uniform)
density, then the total mass balance simply reduces to
Qf1rate=Qfeed since V is constant. This conclusion is also valid
for a juice in which the density is a linear function of the
flavor concentration.[4] The component mass balance is then
readily integrated to give
F Cfeed- SC
IL(- S)Cfeed j
_SQf edt
where the concentration of flavor components in the recycle
tank at the start of the process is equal to Cfeed. This equation
can be easily solved for the final concentration of flavor com-
ponents, with t evaluated as the time required to process
10,000 L of juice (or in this case, to add 9,500 L of juice to
the 500 L initially present in the recycle tank). The overall
flavor recovery is then evaluated as the ratio of the final mass
of flavor components in the juice (VCfnal) to the initial mass
of flavor components
Recovery C
VV(1- S) exp -SVtot- V]
where Vto, is the total amount of juice (in this case, 10,000
In addition to solving the mass balance equations, there are
a number of interesting design issues that the students can
begin to think about, such as what would happen to the final
concentration of flavor components in the recycle tank if it
were poorly mixed. For example, if the recycle stream is re-
turned to the top of the recycle tank, then the concentration
of flavor components will be lower in the bottom of the tank
(near the tank exit), which will reduce the amount of flavor
that is lost through the membrane. Although this situation
cannot be modeled quantitatively this early in the curricu-
lum, the qualitative behavior of the system is quite easy to
explain. The discussion of mixing provides a great opportu-
nity for the instructor to talk about the residence time in the
recycle tank and the different design approaches that can be
used to achieve good mixing in a large tank.
The students can also be asked to consider what (if any)
difference would occur if the juice concentration were ac-
complished using a batch process instead of the fed-batch
system shown in Figure 1. In this case, all of the juice is
placed in a single large tank, the feed stream entering the
fresh Recycle Stream
Pump Recycle
S Recycle
Pumn Membrane Unit
Figure 1. Fed-batch system for producing apple juice
Chemical Engineering Education
Membranes in ChE Education
tank is eliminated, and the volume in the tank decreases with
time as fluid is removed through the membrane. This prob-
lem can either be analyzed qualitatively based on physical
insights about the batch process, or the students can develop
and solve the mass balance equations for the batch system
(easily assigned as a homework problem after presenting the
fed-batch analysis in class). The final expression for the fla-
vor recovery in the batch system is simply
Recovery = Vfintial s (5)
SVinitial J
It is relatively easy to show that there is always less flavor
lost using the batch process. This is because the concentra-
tion of flavor components in the recycle tank in the fed-batch
process increases much more rapidly than that in the batch
system due to the smaller volume in the recycle tank, leading
to a greater passage of flavor components through the mem-
brane. Given that result, the students can think about why
one might still decide to use a fed-batch process for the juice
concentration. One practical reason is that it can be difficult
to maintain a well-mixed solution as one goes from an initial
volume of 10,000 L to a final volume of 500 L in the batch
process. The lack of mixing not only affects the flavor loss, it
also affects the filtrate flow rate that can be achieved in the
membrane unit. The batch process also requires the use of a
very large (and expensive) feed tank. In addition, the fed-
batch process provides greater design flexibility for use in
multiple processes in a single commercial facility.
The biotechnology industry now produces a wide range of
therapeutic proteins using recombinant gene technology. The
DNA of interest is cloned into an appropriate microorganism
or mammalian cell line, enabling those cells to produce the
desired protein using their natural metabolic processes. Cur-
rent commercial recombinant products include: insulin for
the treatment of diabetes, tissue plasminogen activator used
as an anti-clotting agent for the treatment of stroke and heart
attack, human growth hormone for the treatment of dwarf-
ism, and erythropoietin as a red blood cell stimulating agent
for the treatment of anemia. A nice review of recombinant
gene tcl'hnoi h -b, is provided by Glick and Pasternak.[6]
One of the critical issues in the production of therapeutic
proteins is the high degree of purification that must be
achieved, particularly since these molecules are typically
given directly into the bloodstream by intravenous injection.
The bulk of the purification is typically done using some com-
bination of affinity, ion exchange, and/or hydrophobic inter-
The traditional material in
this course has been supplemented with
a series of membrane problems specifically
designed to illustrate the key concepts
involved in the analysis of transient
mass balances.
action chromatography. Small impurities (e.g., buffer com-
ponents and excess salt), however, are generally removed
by membrane diafiltration. Van Reis and Zydney1[7 pro-
vide a nice review of the principles of diafiltration for
bioprocessing applications.
The diafiltration process looks very similar to the apple
juice concentration shown in Figure 1. The membrane is
nearly fully retentive to the protein of interest, but allows
relatively unhindered passage of the small impurity through
the membrane. The solution containing the therapeutic pro-
tein is contained in the recycle tank, and a protein- and impu-
rity-free buffer solution is continually added to the tank to
maintain a constant solution volume while the impurity is
washed through the membrane.
The transient mass balance for the constant volume
diafiltration process is
V = -SQfiltrateC (6)
where S, the membrane sieving coefficient, is equal to the
ratio of the impurity concentration in the filtrate solution to
that in the feed. Equation (6) can be integrated to give a simple
decaying exponential relating the impurity concentration at
time t to the initial concentration of the impurity in the pro-
tein solution. The results are more conveniently expressed in
terms of the total volume of protein-free buffer that must be
used to reduce the impurity concentration to a desired target
Final ( Sbuffer
initial = exp V (7)
C initial V
The membrane diafiltration can be used in combination with
an ultrafiltration process to achieve protein concentration and
impurity removal in a single processing step.E11
This same diafiltration process is also used as part of a vi-
ral inactivation step. For example, an appropriate solvent or
detergent is first added to the protein solution to achieve a
concentration that is sufficient to inactivate nearly all viruses.
The solvent/detergent is then removed by diafiltration, typi-
cally to a target of less than 10 ppm (parts per million). This
is an ideal opportunity to talk about product safety issues,
Winter 2003
Membranes in ChE Education
including the need to achieve essentially complete virus re-
moval/inactivation while at the same time avoiding denatur-
ation of the recombinant protein product and minimizing
potential complications from the presence of trace amounts
of any viral inactivation agents. It is important for students
to recognize that even though the membrane diafiltration
is very effective at removing residual solvents and deter-
gents, it is impossible to achieve 100% removal of these
components using a finite volume of diafiltration buffer-
the exponential decay provides an asymptotic approach
to zero concentration.
Another interesting membrane problem that is readily in-
corporated into the introductory mass balance course is analy-
sis of urea removal during hemodialysis.[81 Hemodialysis is
currently used to treat chronic kidney failure in more than
500,000 patients around the world-patients who would die
within about two weeks without the availability of this type
of artificial kidney. Urea removal in hemodialysis can first
be examined by analyzing a transient batch process for re-
moving urea from blood across a semi-permeable membrane
(top panel in Figure 2). The dialysate contains all the key
salts and sugars normally found in plasma to insure that
these components aren't removed during the dialysis. The
membrane is impermeable to all blood cells and proteins,
but it allows urea to be removed at a rate that is propor-
tional to the concentration difference between the blood
and the dialysate solution
transfer = kmA[Cblood -Cdialysate] (8)
where km is the membrane mass transfer coefficient (or per-
meability) and A is the membrane area. Component mass
balances are written for the urea concentration in the blood
and in the total system (blood plus dialysate)
Blood dC d kmA[Cblood Cdialysate]
dCblood dCdialysate
Blood d + Vdialysate dt-
dt dt
where we have assumed that the volumes of the blood and
dialysate compartments remain constant during the dialysis.
The system mass balance (Eq. 10) is directly integrated to
develop an expression for C ialysa in terms of Cbloo If pre-
sented in class, it is helpful to ask the student what will hap-
pen at long times before actually solving the equations. Many
students don't appreciate that the system will approach steady
state with Cblood = C alysate. The steady-state solution can eas-
ily be developed by setting the derivatives equal to zero and
solving the resulting algebraic equations. The full solution is
readily developed by integration of Eq. (9) to give
Sblood 1+ Vblood
Cblood,0 Vdialysate
1 1
Vblood Vdialysate
where C b is the urea concentration in the blood at the start
of the dialysis. It is easy to show that Eq. (11) approaches the
steady-state solution in the limit of t -> as required.
After analyzing the transient hemodialysis system, the stu-
dents can think about why this isn't the way hemodialysis is
actually performed clinically. Most students recognize the
problem of having a large portion of the patient's blood out-
side of the body, and some will even appreciate the logistical
challenge of insuring that the right blood is returned to the
right patient. It thus becomes relatively easy to motivate the
need for using a continuous-flow system for hemodialysis
(bottom panel of Figure 2). A simple solution for this prob-
lem can be developed by assuming that the urea concentra-
tions are at steady state and that the blood and dialysate solu-
tions are both well-mixed. The steady-state assumption can
often be confusing since the urea concentration in the
patient's blood clearly decreases with time during the
hemodialysis. But the time constant for concentration
changes in the dialyzer is so much shorter than the time
constant for the body due to the small extracorporeal vol-
ume, that it is appropriate to use this type of pseudo-
S membrane
a) Batch hemodialysis system
Q Blood I(return to patient)
QB I Blood
(from patient) .-.. .i
Dialysate I QD
b) Continuous flow hemodialysis system
Figure 2. Hemodialysis systems for urea removal.
Top panel shows a batch system; bottom panel
shows continuous-flow process.
Chemical Engineering Education
Membranes in ChE Education
steady-state approximation. The final result is
CBout QB+D
CBin kmA +kA
QB 1+ km
where CBout and CBn are the urea concentrations in the blood
leaving and entering the dialyzer, and QB and QD are the
blood and dialysate flow rates. More sophisticated solu-
tions can be developed for countercurrent flow if the stu-
dents are able to handle the concepts and mathematics
required for analysis of the position-dependent differen-
tial mass balances in this system.?8]
Although the well-mixed analysis provides a simple ana-
lytical expression, most students don't immediately appreci-
ate the implications of the final result. For example, the analy-
sis clearly shows that the outlet urea concentration in the blood
doesn't go to zero as the membrane area becomes infinite. In
addition, this equation seems to imply that increasing the
blood flow rate is detrimental since it increases the urea con-
centration in the blood stream that is returned to the patient
(although it also increases the rate of urea removal from the
body). This leads nicely into a discussion of the key design
criteria for the dialyzer.
It is also relatively easy to couple analysis of the
hemodialyzer with the transient mass balances describing the
urea concentration within the body (treated as a well-mixed
"tank"). The resulting equations can be used to examine the
performance of a clinical dialysis session at reducing the urea
concentration to a safe level. Current clinical practice is for
patients with complete kidnez*[ailure to undergo four-hour
dialysis sessions three times a week, 52 weeks a year. The
total cost of providing hemodialysis in the United States is
approximately $15 billion per year, essentially all of which
is paid by the Federal government. This is a great opportu-
nity for a discussion about some of the ethical and economic
issues involved in the development and delivery of expen-
sive new medical technologies, an issue that is likely to be-
come even more important in the coming years.
Another hemodialysis design issue that can be worth dis-
cussing is the importance of minimizing the extracorporeal
blood volume while maintaining a large surface area for mass
transfer. Current clinical dialyzers use a parallel array of more
than 10,000 narrow hollow fiber membranes (inner diameter
of about 200 pm) to achieve a surface area of close to two
square meters. Smaller diameter fibers, approaching the 6-8
pm diameter of the blood capillaries within the kidney, would
further increase the ratio of surface area to blood volume.
Blood clotting becomes a major problem in these very nar-
row fibers, however, even in the presence of a strong anti-
coagulant like heparin. This leads nicely into a discussion of
biomaterials and some of the issues involved in the develop-
ment of truly biocompatible polymeric materials that still
maintain the desired mechanical and mass transport charac-
teristics needed for this type of biomedical device.
The membrane problems described in this paper provide
an attractive set of examples for introducing students to key
concepts in the analysis of transient material balances in non-
reacting systems. Related problems can also be developed
for the analysis of gas separation membrane processes (e.g.,
the production of oxygen from air) and on the behavior of
membrane reactors (e.g., the use of palladium membranes to
remove hydrogen and thereby improve product yield in equi-
librium-limited dehydrogenation reactions).
All of these membrane problems are of real commercial
interest, they provide students some exposure to new appli-
cation areas of chemical engineering, and they give the in-
structor an opportunity to introduce basic concepts of pro-
cess design at a very early stage in the curriculum.
Student response to these problems in the Introduction to
Chemical Engineering course at the University of Delaware
has been outstanding. They definitely appreciate being able
to analyze real-world problems even as freshmen, and they
clearly enjoy the opportunity to begin thinking about process
design issues. In addition, these membrane examples give
students a perspective into the kinds of problems and pro-
cesses that they will encounter throughout their undergradu-
ate chemical engineering education.
1. Solen, K.A., and J. Harb, "An Introductory ChE Course for First-Year
Students," Chem. Eng. Ed., 32(1), 52 (1998)
2. Felder, R.M., and R.W. Rousseau, Elementary Principles i ... .'
Processes, 3rd ed., John Wiley & Sons, Inc., New York, NY (2000)
3. Himmelblau, D.M., Basic Principles and Calculations in Chemical
Engineering, 6th ed., Prentice Hall, Upper Saddle River, NJ (1996)
4. Russell, T.W.F., and M.M. Denn, Introduction to ( .... i. .. r-
ing Analysis, John Wiley & Sons, Inc., New York, NY (1972)
5. Cheryan, M., and J. Alvarez, "Food and Beverage Industry Applica-
tions," in Membrane Separations Technology: Principles and Appli-
cations, R.D. Noble and S. A. Sterns, eds., Elsevier, Amsterdam (1995)
6. Glock, B.R., and J.J. Pasternak, Molecular Biotechnology: Principles
and Applications ofRecombinant DNA, 2nd ed., American Society for
Microbiology Press, Washington, DC (1998)
7. van Reis, R., and A.L. Zydney, "Protein Ultrafiltration," in Encyclo-
pedia of Bioprocess Technology: Fermentation, Biocatalysis, and
Bioseparation, M.C. Flickinger and S.W. Drew, eds., pp 2197-2214,
John Wiley & Sons, Inc., New York, NY (1999)
8. Galletti, P.M., C.K. Colton, and M.J. Lysaght, "Artificial Kidney," in
The ... i .. .... i ,.. book, Vol. II, 2nd ed., J.D. Bronzino,
ed., CRC Press, Boca Raton, FL (2000) 1
Winter 2003
Membranes in ChE Education
An Interdisciplinary Reverse Osmosis Project
for First-Year Engineering Students
S. SCOTT MooR, EDMOND P. SALIKLIS, SCOTT R.
Lafayette College Easton, PA 18042
Attempting to create a project that includes chemical,
civil, electrical, and mechanical engineering is a chal-
lenging task. At Lafayette College we try to include
such a project in our Introduction to Engineering course.
While finding electro-mechanical projects is relatively easy,
it is difficult to include the process nature of chemical engi-
neering in projects that are typically product oriented.
Among engineering programs that use an introduction-to-
engineering course, a wide range of projects and laboratories
is used. At the 2002 ASEE annual meeting, several mechani-
cal or electro-mechanical projects were described, including
a sundial, wind power for a ski resort public-transit system,
and an orbital sander.E'-3] At Rowan University, the Freshman
Clinic provides a year-long lab experience with
multidisciplinary experiments that use measurement as the
theme.E4 51 They use a wide range of approaches and projects,
including reverse engineering, engineering analysis of the
human body,[6] and the production of beer.E7 Recently, they
included a project that involves using a membrane fuel cell
to charge batteries for a LEGO Mindstorms robot.E81
Many programs rotate through several different labs that
illustrate different disciplines in order to include chemical
engineering. At Notre Dame, a year-long introductory course
uses four projects with the LEGO Mindstorms brick-con-
trol of pH is one of these four projects.E9' North Carolina State
uses a series of laboratories, one of which is a reverse osmo-
sis experiment.E10o At Virginia Tech several laboratories and
projects are used with one laboratory being focused on a
simple mass balance,E11 while Drexel University's E4 program
uses a laboratory focused on measurements to introduce stu-
dents to engineering.E12' The environmental engineering pro-
gram at the University of Dayton uses a sand-and-charcoal
filter where students analyze both the filtration process and
HUMMEL, YIH-CHOUNG Yu
the support structure."13 In very few cases does one project
include concepts from both chemical engineering and other
branches of engineering.
For many years, C.S. Slater (Rowan University) has devel-
oped and advocated several reverse osmosis experiments
based on PUR brand portable RO systems.5 141 Both the Uni-
versity of Minnesota at Duluth and Manhattan College have
also developed laboratories based on the PUR systems. 1,161
We have developed a project based on a simple dead-end
reverse osmosis (RO) test system at Lafayette College. The
equipment consists of a cylindrical vessel with a small pis-
ton-and-lever arm used to create the pressure. Each disci-
pline examines different issues with the device: in the chemi-
S. Scott Moor isAssistant Professor of Chemical Engineering at Lafayette
College. He received a BS and MS in Chemical Engineering from M.I. T
in 1978. After a decade in industry he returned to academia at the Uni-
versity of California, Berkeley, where he received a PhD in Chemical En-
gineering and an MA in Statistics in 1995. His current research focuses
on educational materials development and on the visualization of fluid
and transport dynamics in Wurstercoating, in fluidized beds, and in spray
Edmond Saliklis is Assistant Professor in the Department of Civil and
Environmental Engineering at Lafayette College. He received his BS from
the University of Illinois-Chicago in 1984, his MS from Syracuse Univer-
sity in 1988, and his PhD from the University of Wisconsin-Madison in
1992, all in Civil Engineering. His current research focuses on the me-
chanics of thin wood-based plates and thin concrete and masonry shells.
Scott Hummel is Assistant Professor of Mechanical Engineering at
Lafayette College. He earned a BS at the University of Hartford in 1988,
an MS at Stevens Institute of Technology in 1996, and a PhD at Lehigh
University in 1998. His current research focuses on the wear properties
of nonlubricated stainless steel components and on the LENS rapid
prototyping process.
Yih-Choung Yu is Assistant Professor of Electrical and Computer Engi-
neering at Lafayette College. He received a BSEE degree from Chinese
Culture University in Taipei, Taiwan, in 1987, an MSEE degree from the
State University of New York at Binghamton in 1992, and a PhD degree
from the University of Pittsburgh. His research interests include control
applications for bioengineering and medical device development.
Copyright ChE Division ofASEE 2003
Chemical Engineering Education
Membranes in ChE Education
cal engineering portion of the course, we study the theory
and practice of reverse osmosis; in the civil engineering por-
tion, the focus is on the hoop stresses in our cylindrical pres-
sure vessel and the use of RO in water treating; in the me-
chanical engineering portion, students examine the mechani-
cal advantage needed to create the necessary pressure for RO;
and in the electrical engineering portion, students study and
construct the circuit to monitor the strains on the surface of
the vessel.
The "Introduction to Engineering" course, where we use
this project, is a complex interdisciplinary course. It consists
of five segments, or blocks, covering 1) engineering econom-
ics and management, 2) chemical engineering, 3) civil engi-
neering, 4) electrical and computer engineering, and 5) me-
chanical engineering. Figure 1 diagrams the structure of the
course. Engineering economics and management are covered
in the first and last weeks of the class. During the middle
weeks of the term, students rotate through four three-week
Intro Week Project Planning o
^Ch m.: Eng
v E I I
Eletr.cal Ern.
Final Week Engineering Economics
Figure 1. Structure of Introduction to Engineering course
at Lafayette College.
Figure 2. A cut-away view of the press RO system
(dimensions are in cm).
blocks covering each of the main engineering disciplines.
These blocks include both lecture and laboratory experiences.
Concurrently throughout the term, students are learning com-
puter-aided drafting (CAD) and working in teams on the RO
project. One laboratory period in each disciplinary block is
devoted to RO experiments.
The learning objectives are that upon completion of this
course, students will have
1) An ability to apply engineering equations to solve a variety
of practical engineering problems
2) An ability to design and conduct experiments as well as an
ability to analyze, interpret, and document experimental
3) An introduction to the various aspects of engineering
design that include initial sizing or planning of a compo-
nent or system, modeling, drawing, testing, cost-estimat-
ing, and redesigning the component or system
4) A firm introduction to engineering graphics and proper
protocol on engineering drawings
5) An ability to function on multidisciplinary teams
6) Experience in communicating technical information
7) A knowledge of the engineering departments at Lafayette
College and possible career tracks upon graduation
Figure 2 is a diagram of the basic design of our system. An
approximately 5-cm diameter membrane is held in the bot-
tom of the device by a clamp ring with two O-rings for seal-
ing. One O-ring seals the clamp ring to the bottom of the
device and the other seals the clamp ring to the top of the
membrane. There is a small chamber above the clamp ring
that holds the salt water that we are purifying. A 1.9-cm di-
ameter piston is used to pressurize the water reservoir with a
lever arm to amplify the force applied. The small piston area
combined with the lever arm produces a mechanical advan-
tage of approximately 14 to 1. Weights are hung from the
lever arm to apply a constant load. The product water flows
out the bottom of the unit. The major components of the sys-
tem are constructed of aluminum. The material cost is ap-
proximately $35/unit. A picture of the ready-to-run press RO
system is shown in Figure 3. While a cross-flow configura-
tion is the norm for RO systems, we chose to use a dead-end
system because of the engineering principles it allowed us to
illustrate. This configuration allows us to create the neces-
sary pressure using simple and understandable lever and hy-
draulic principles. The cylindrical shape of the pump allows
for simple structural strain calculations.
The project addresses all of the course goals listed in the
previous section. It is particularly important in addressing
experimentation (goal 2), design (goal 3), working in
multidisciplinary teams (goal 5), and communication (goal
Winter 2003
Membranes in ChE Education
6). It also provides concrete examples of the application of
each of the engineering disciplines (goal 7). It is hoped that
the project will be interesting, enjoyable, and accessible to
our first-year students.
This project provides a wealth of chemical engineering top-
ics, including osmotic pressure, equilibrium, flux, rate based
separation, and fluid processing. The general concepts of os-
motic pressure and solution equilibrium are discussed. The
van't Hoff equation is used to estimate osmotic pressure
where II is the osmotic pressure, C is the molar concentra-
tion of ions, R is the universal gas constant, and T is the ab-
solute temperature. This equation assumes a dilute ideal so-
lution that follows Raoult's law. For the solutions, we are
using (0-14 g/1 NaC1), the van't Hoff equation predicts 3-5%
high and is adequate for our needs.171 Wankat presents the
theory for more accurate estimations of osmotic pressure for
other situations. 181
There is some disagreement on the exact mechanism for
reverse osmosis, but the solution-diffusion theory is the most
widely accepted.[18,191 In this picture of membrane function,
the membrane has no true pores. Rather, the membrane is
treated as a separate phase. The solvent and solute dissolve
in and diffuse through the membrane.
Students are then introduced to the concept of flux and its
proportionality to driving force. We present the simplified
case of the driving force as the pressure above osmotic. The
resulting equation for flux is
Jw = A(AP-oAII) (2)
where Jw is the volumetric flux of water through the mem-
brane, q is the total flow through the membrane, A is the wa-
ter permeability constant, o is the Staverman coefficient, S
is the membrane area, and AP is the applied pressure across
the membrane.[191 Assuming that the Staverman coefficient
equals one in Eq. (2) implies that the solute is perfectly ex-
cluded. This is a simplification of the real case, but it is fre-
quently used.[5,17,18'20]
Equation (3) shows a simple and common model for the
solute (salt) flux through the membrane under a concentra-
tion gradient:
S= B(Cfeed Cproduct) (3)
where J. is the molar flux of solvent, B is the salt permeabil-
ity constant, and the driving force (Cfeed Cprodc) is the salt
concentration difference across the membrane. Again, a more
complete version of the theory would include a second re-
flection coefficient.1191 Using the first two equations, students
are able to complete a design problem determining a pres-
sure drop and membrane area that will meet a given purifica-
tion need. For these simple first-pass sizing problems, we
assume that the solute flux will be negligible.
The concepts behind these equations and their simplifica-
tions are explained to the students. We then ask them to evalu-
ate how well these concepts (particularly the simplifications)
are playing out in our experimental system. A short section
in Perry's on reverse osmosis and nanofiltration provides some
helpful conceptual background in a brief presentation.[20' The
issues considered include the nature of membranes, recov-
ery, concentration polarization, pretreatment, rate-based sepa-
rations, and cartridge configurations.
Concentration polarization is a particularly important is-
sue. The salt concentration near the membrane is increased
because salt is being transported to the membrane by bulk
flow, but then it is being retained by the membrane. This in-
crease in concentration near the membrane affects the os-
motic pressure and the potential flux of solute. A mass diffu-
sion model is required to estimate this effect.[18,21-23]
Students experiment on the press RO system, examining
the impact of pressure and salt concentration on the purified
water flow rate. They determine the water permeability con-
Figure 3. A press RO system ready to run.
Chemical Engineering Education
Membranes in ChE Education
stant in these experiments.
Figures 4 and 5 show experimental sets of data. The first
series is a nice linear relationship-a reliable upper-class stu-
dent assistant prepared this series. The second series, which
is not so nicely linear, was the initial attempt of some first-
year students. The difference in results arises from how care-
fully the apparatus was assembled and how consistently it
was operated. The students soon realized that they must have
disciplined laboratory procedures in order to get the best re-
sults. With a "good" set of data, such as the first series, it is
possible to use the x-intercept to estimate the experimental
osmotic pressure. For poor results such as those in the sec-
ond series, the results of this extrapolation are too variable
and the students must calculate the osmotic pressure, fix
the x-intercept, and then simply estimate the slope of the
line. This procedure yields reasonable results even for poor
data. In both approaches, the slope is the water perme-
ability constant, A.
The biggest weakness of these RO devices is their dead-
end configuration and the likelihood of significant concen-
tration polarization. In fact, plots of flux versus time show
Example data 5 g/I NaCI
0.25 -------------
0.15- I Data1
S, Data 2
S0.1 -Model Fit
0 1 2 3 4
Pressure (psi)
Figure 4. Example flux data for 5 g/1 sodium chloride. An
upper-class laboratory assistant took the data labeled data
1. An inexperienced first-year team took the data labeled
data 2. See the text for an explanation of how the model fit
line was generated.
Example Data 10 g/I
0.140 -
0.100 --
S0.080 Data 1
E A Data 2
S0.060-- -Model Fit
0.020 -
0.00 0.50 1.00 1.50 2.00 2.50 3.00
Pressure (MPa)
Figure 5. Example flux data for 10 g/l sodium chloride.
The series labels have the same meaning as in Figure 4.
steadily decreasing flux rates throughout our experiments.
To allow some standardization, students take flux data from
20 to 40 minutes during their experiments and calculate an
average flux during this period. Students are also able to
measure the conductivity of the salt solution before and after
passing through the membrane. In our dead-end unit, a 75%
reduction in salt concentration is typically achieved. This
concentration reduction is substantial, but not perfect, and
leads to a discussion of the rate-based nature of the RO sepa-
ration. Finally, we can also address the practical issues of
how membranes are implemented, including the use of cross-
flow filtration and spiral-wound cartridges. Throughout,
we provide practical examples of RO implementation,
from emergency RO water purifiers[24] to a new two-mil-
lion-gallon per day RO desalination plant recently in-
stalled in Cape May, New Jersey.[251
Two civil engineering lab exercises familiarize the students
with elementary pressure vessel design. The equation describ-
ing hoop stress for thick-walled pressure vessels is
Thick -2 2 (4)
where Othick is the thick-walled hoop stress at any given ra-
dius, r is the specific radius, runner and routr are the inner and
outer diameters respectively, p is the vessel internal pressure,
and k is the ratio rouer/rnner. During the first lab, students pro-
gram this equation in Mathematica and perform parametric
studies of the influence of changing wall thickness. They
compare the results of the thick-walled equation to those of
the simpler thin-walled equation
Gthin P(roer (5)
where Othin is the thin-walled hoop stress and t is the wall
thickness. Finally, in the first lab they are given Hooke's Law,
which relates stress to strain.
In the second lab, the students are given the opportunity to
quantify experimentally the strains on the outer surface of
our RO system cylinder by means of strain gages. The outer
diameter of several RO system cylinders has been reduced,
creating vessels of several wall thicknesses. The students plot
vessel pressure versus hoop strain. They then calculate the
stress by means of the previously presented Hooke's Law
formulation and are thus able to compare theoretical strains
to experimental strains.
Another exercise requires them to analyze the stress and
the deflection in the lever arm of the pump. Experimental
Winter 2003
Membranes in ChE Education
investigations of the bent arm are compared to theoretical
predictions. This exercise provides an opportunity to discuss
structural design strategies and specific design codes in gen-
eral terms. Finally, one civil engineering lecture is devoted
to hydrology. During this lecture, RO systems are discussed.
BLOCK A dea
system i
One of the mechanical design consider- basis J
nations of the reverse osmosis unit is generat- basi
ing a high pressure, 10 to 20 bar, across the
membrane with a relatively low applied load, project t
5 to 10 kg, on the input handle. The design a w
problem is solved through the use of a me- probj
chanical linkage and a piston-cylinder ar- example
rangement. This enables low forces applied differed
to the piston to generate relatively large pres- of engi
sure inside the chamber. In addition, the pis- connect[
ton is made part of a slider-crank mechanism court
to further increase the pressure inside the engi
chamber for a given applied load. The pivot
points of the mechanism are determined by
the students as part of their design recommen-
dations for the project. Students examine hy-
drostatics, lever arm mechanical advantage, and the use of a
load cell to measure force.
During the electrical engineering block, students use lab
time to construct and experiment with a Wheatstone bridge
to read the strain gauges used in the civil engineering block.
Their lab experience includes bread boarding and calibrating
a basic circuit. From their experiments and circuit analysis,
they are expected to select appropriate resistance values for
their bridge. In these labs they learn practical skills in con-
structing electrical circuits and are required to make some
circuit design decisions. In lectures, students learn the
basic circuit principles that allow them to understand how
the circuit works.
During the first week of the term, students are introduced
to some basic scheduling concepts and asked to apply them
to planning their work on the project. They need to schedule
experimentation, analysis, and report preparation. During the
final week of the term they learn basic engineering econom-
ics and are given a problem to analyze on the economics of
RO desalination.
In our apparatus, the volume pushed through the membrane
is small relative to the total volume of salt water feed (less
than 5%). This allows us to assume the concentration of salt
is essentially constant. If, however, the vol-
ume change is allowed to be significant and
the separation assumed to be perfect (i.e., no
salt passes the membrane), a mass balance
yields the following interesting differential
equation for flow through the membrane:
dx CoVoRT
d = A AP (6)
dt VO-X
where x is the volume of pure water produced,
Co is the initial concentration of the salt feed,
and Vo is the initial volume of salt solution in
the device. This equation is complex but still
separable. It is being used as an example prob-
lem in our Calculus 2 class. The basic differ-
ential equation and its derivation are pre-
sented in class, and students are asked to solve
the equation analytically as a homework prob-
lem. Then they come to a computer lab ses-
sion where they use Mathematica to explore
this differential equation and make some design trade-offs.
This is part of an institutional effort to connect our calcu-
lus classes to applications in other courses. Students who
have advanced placement in calculus are in this Calculus
2 class at the same time that they are taking Introduction
to Engineering.
Groups of 4 to 5 students each work on the RO project
throughout the semester in four phases. The first phase is an
orientation to the project and reverse osmosis. The project
nature, structure, and expectations are introduced. During the
second phase, students carry out their first experiments with
the press RO system. They learn assembly and operation of
the pumps and complete an initial trial and data analysis.
During the third phase, they learn how to install the mem-
branes in their pumps and complete another set of trials. Dur-
ing this phase, each group runs a different condition and posts
their data to the course website. The groups are expected to
download and analyze the complete data set. From this data,
students must determine what the flux coefficient is for the
membrane they have been using.
The final phase of the project is a time for student-directed
open-ended trials and design work. Students are expected to
extend the work they have done so far. Many options are
Chemical Engineering Education
provides the
for a truly
health of
lems and
es for many
nt branches
s] a calculus
se to the
Membranes in ChE Education
given for this extension: they can take additional data to an-
swer questions arising from their earlier analysis; they can
run experiments with a different membrane, different
seals, or a different technique; they can vary the salt used.
Students are asked to consider how they would improve
the test apparatus.
In addition, each group is given a unique RO sizing prob-
lem. An example problem is
A small and exclusive island resort requires an improved water
supply for the roughly 150 people who are there at any given time.
The resort estimates it will need 30 gallons/person each day. There
is a large brackish water supply on the island with a salt concen-
tration of 13 g/l as NaC1.
Students are expected to use the water permeability constant
that they determined from their experiments to calculate pos-
sible pressures and membrane areas. They are expected to
consider the economic ramifications of their choices. In this
simplified analysis, the operating costs are considered to be
the cost of creating pressure. This cost is determined by cal-
culating the energy required for pumping. We use the basic
power = (7)
to determine the power required. Students assume that they
are using a cross-flow configuration and that they are able to
recover the pressure energy of the waste stream. AP is the
pressure increase across the pump, Q is the volumetric flow
rate, iT is the pump efficiency (we use 0.80), and power is
the power required. The capital cost of the plant is consid-
ered to be a function of membrane area. Students are given
the following scale-up formula to estimate the capital cost:
C = (4500$ / m15)AO75 (8)
where C is the estimated capital cost (in $), andA is the mem-
brane area (in m2). In their economic sections they have
been taught to calculate net present value and are expected
to consider the optimum trade-off between capital and op-
erating costs.
The project was evaluated based on re-examining final
project reports from half of the student groups involved in
the class (16 out of 32 groups) and based on instructors' ob-
servations. Reports were re-examined with a particular
focus on the students' demonstration of experimentation
skills (goal 2) and design skills (goal 3). Throughout this
analysis it is difficult to separate the project impact from
the course as a whole.
The chance for students to experiment with the system
throughout the term was one of the strengths of this project.
The final reports included an analysis of flux experiments at
different concentrations and pressures, plus student-designed
studies. In reviewing the final reports, 88% of the groups
analyzed flux experiments completely and correctly. A re-
view of the student-designed studies showed that 79% met
our expectation of solid creative experiments that fit the time
and equipment constraints. Students completed a wide range
of additional experiments, including testing an alternative
membrane; using calcium chloride instead of sodium chlo-
ride; examining variations in flux decline with time and
concentration; studying an alternative clamping mecha-
nism that has a longer back diffusion path; and examin-
ing hold-up volume by comparing piston stroke move-
ment to volume collected.
Reports included two different engineering design sections:
the specific RO sizing problem and suggested design improve-
ments for the RO press. As pertains to the sizing problem, in
80% of the cases, the basic RO analysis was correct, but as
we move to more advanced analysis, the number of student
groups mastering the concepts drops off. The idea of an eco-
nomic trade off between pressure and membrane area was
clearly understood by 63% of the groups. A majority (56%)
completed the expected economic estimates, but only a third
included an analysis of the time value of money. All of the
percentages were a bit lower than we had hoped.
The students' work on design improvements to the test
pumps showed mixed results. In almost all cases (fourteen
reports), the students had solid initial proposals for how to
improve our apparatus, but the detailing of their designs was
weak. In only five cases did the students complete detailed
design calculations and make their designs specific. Suggested
improvements included
1 I.., in the lever arm to reduce 1.. li.. i,. -, (change the
material and/or dimensions
Increasing the piston stroke to increase the volume of water
pumped per stroke
Implementing a cross. ..', ( ,r fi. iru trin
Adding agitation to the system to reduce concentration
Adding additional instrumentation to the units
This project was designed from the beginning to be
multidisciplinary. Almost all student reports mention aspects
from all four BS engineering disciplines. The instructors found
that they needed each other's skills to design and understand
this project. We freely pointed this out to the students.
A dead-end RO system provides the basis for a truly inter-
disciplinary project that provides a wealth of problems and
Winter 2003
examples for many different branches of engineering. In ad-
dition, it is used to connect a calculus course to the engineer-
ing curriculum. The project provided a particularly good in-
troduction to engineering experimentation. Student design
work on the project was good, but could be strengthened-
particularly in the details of full design calculations and eco-
nomic analysis.
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17. Baker, R.W., E.L. Cussler, W. Eykamp. W.J. Koros, R.L. Riley, and H.
Strathman, Membrane Separation Systems: Research and Develop-
ment Needs Assessment, Final Report, Contract Number DE-AC01-
88ER30133, U.S. Department of Energy (1990)
18. Wankat, PC., "Membranes," Part III in Rate Controlled Separations,
Klawer, Amsterdam (1990)
19. Cussler, E.L., "Membranes," Chapter 17 in Diffusion: Mass Transfer
in Fluid Systems, 2nd ed., Cambridge University Press (1997)
20. Eykamp, W., "Reverse Osmosis and Nanofiltration," in Perry's Chemi-
cal Engineers' Handbook, 7th ed., R.H. Perry, D.W. Green, and J.O.
Maloney, eds., pp. 22-48 thru 22-52, McGraw-Hill (1997)
21. McCabe, W.L., J.C. Smith, and P Harriott, "Membrane Separation
Processes," Chapter 26 in Unit Operations of Chemical Engineering,
6th ed., McGraw-Hill, 857 (2001)
22. Mahlab, D., N. Ben Joseph, and G. Belfort, "Interferometric Measure-
ment of Concentration Polarization Profile for Dissolved Species in
Unstirred Batch Hyperfiltration (Reverse Osmosis)," Chem. Eng.
Comm., 6, 225 (1980)
23. Ho, W.S.W., and K.K. Sirkar, Membrane Handbook, Van Nostrand
Reinhold (1992)
24. Proctor & Gamble, PUR Survivor 06, at http://www.purwater.com/
L3_marend_06.shtml, retrieved 7/2002
25. Avedissian, E., Cape May's Desalination Plant's No Albatross!, at http:/
/www.capemay.com/Desalination.html, retrieved 7/2002 1
Modeling of Chemical Kinetics and
Reactor Design
by A. Kayode Coker
2nd edition; 1095 pages plus CD-ROM; US $195. ISBN 0-88415-481-5 (2001)
Published by Butterworth-Heinemann, 225 Wildwood Avenue,
This book is intended as a reference volume by the au-
thor. Educators will find the book useful for several top-
ics that are not covered by textbooks or other reference
In addition to standard chapters on residence time dis-
tribution and reactor models for non-ideal flow, there is
an extensive chapter (91 pages) on mixing in tanks, mix-
ing by static elements, and heat transfer in agitated tanks.
There is also a chapter (47 pages) that introduces the
use of computational fluid dynamic simulators for study-
ing mixing and flow in reactors. That chapter discusses
examples of mixing and reaction in a stirred tank and flow
in a radial flow catalyst bed. On the CD, there are beauti-
ful and informative color images of transient mixing and
Chemical Engineering Education
reaction of a competitive-consecutive reaction in a stirred
Other chapters in the book, which aren't covered or are
covered only briefly by other books, include a chapter
(80 pages) on biochemical reactions and reactors. There
is an extensive chapter (134 pages) on safety, including
descriptions of calorimeters used to characterize reactions,
calculations of vent sizes, and a brief discussion of
HAZOP analysis. Scale-up of reactors is considered in a
chapter (47 pages) that discusses the use of dimensional
similitude in combination with reactor models.
Another strong point of the book is the numerous ex-
amples that are worked in detail. Many of these example
problems are supplemented by Excel spreadsheets and
computer programs on the CD.
The CD also has a unit conversion program and PDF
files with explanations of numerical methods and a cross-
reference between examples in the book and supporting
material on the CD. Source code (Fortran 77) for all of
the software programs on the CD is included along with
the executables. Unfortunately, temporary files produced
during compilation (object, make, compiler interface) are
also included, which (in addition to the lack of sub-fold-
ers in each chapter's folder) makes finding the file needed
to run the program harder than necessary. A DOS pro-
gram is available for calculating heats of reaction at reac-
tion temperature with input of stoichiometry, standard
heats of formation, and heat capacity formula coefficients.
Other programs are Windows double-clickable
executables that display text output in the output window
and write output files to disk. A recommendation for fu-
ture editions is to change the file extensions to "txt" from
those used for the input ("dat") and output ("res") so that
they can be accessed easily by double-clicking.
There are several topics that are not covered by the book.
Other than brief mention and sketches in a chapter men-
tioning types of reactors, there is nothing on multiple-
phase reaction systems. There is nothing on reaction-dif-
fusion in porous catalysts or non-catalytic solids. There
is brief discussion on pressure drop but none on the effect
of pressure drop of gases on reaction rate. There are a
couple brief discussions of selectivity and yield in two-
reaction systems, but nothing on more complex multiple-
reaction systems. The thermodynamics section would ben-
efit from a worked example on reaction equilibrium com-
position. There are no end-of-chapter problems that can
be used for student assignments.
Other chapters in the book cover standard material such
as reaction mechanisms, analysis of kinetic data, design
and comparison of the "ideal" reactor types, thermal ef-
fects, and residence time distribution.
Richard K. Herz
Chemical E,,.;i,.. i in.: Program and
Mechanical & Aerospace Eng. Dept.
University of California, San Diego
letter to the editor
To the Editor:
Reference is made to the article by Ang and Braatz,
"Experimental Projects for the Process Control Labo-
ratory" [CEE, 36(3), p. 182, 2002]. The exercise that
has to do with "dye concentration" can also be done
with the control of a hot-water stream instead of a
dye stream flowing into the tank. Just as a colori-
meter indicates the amount of dye stream, so too can
thermocoupling indicate the amount of hot-water
stream; otherwise the experimental apparatus would
be the same.
We find a convenience in not needing to deal with
a dye stream disposal problem at the "Drain" indi-
cated in their figure. Our water stream is collected
and reused.
Dale L. Schruben
Texas A&M Kin;' %i ille
Author's Response
We agree that control of temperature using a hot-water stream is
safe, with no waste disposal issues-which is why this is used in
many control apparatuses (e.g., as in apparatuses 5, 7, and 10 de-
scribed in the article). An advantage of the dye concentration control
experiment is that students can directly visualize the open- and closed-
loop dynamics and the extent of nonideal mixing, as they observe the
color changes in the tank.
Before constructing any apparatus, Materials Safety Data Sheets
should be consulted for safety and disposal considerations for all
chemicals that are intended for use in the experiments. The instructional
value of a particular apparatus with particular chemicals should be
weighed against capital and operating costs and any safety or dis-
posal issues. There are many internet resources for viewing MSDSs
(e.g., see
Richard D. Braatz
University of Illinois
Winter 2003
Membranes in ChE Education
University of Toledo Toledo, OH 43606-3390
Membrane separation processes have infiltrated both
the academic and industrial worlds. Commercial
successes have engendered a wealth of research
activity and collaboration on projects ranging from nitrogen
production to hemodialysis. Coverage of membrane topics
in the undergraduate curriculum has lagged, however, as
authors and educators wait to see if membrane processes
are "for real."
In this paper we present three design projects that have been
used in chemical engineering classes to introduce membrane
processes. The first project requires students to specify a treat-
ment plan for individuals undergoing hemodialysis. The sec-
ond and third projects highlight the manufacturing process
used to produce hollow fiber membranes. One requires the
design of a water distribution system for spinline quench
baths, while the other seeks to recover solvent from the di-
lute, aqueous waste stream produced by the process. These
projects do not require extensive knowledge of membrane
transport phenomena, modules, or processes, but they do re-
quire application of fundamental chemical engineering prin-
ciples for design purposes while simultaneously providing
an introduction to the manufacture and use of membranes.
Hemodialysis Treatment
(Mass and Energy Balances)
This design problem, given to freshmen and sophomores
in mass and energy balances classes, builds upon the hemo-
dialysis problem in Felder and Rousseau.1" Instructors might
encourage students to look up the dialysis process on the
equipment CD that accompanies Felder and Rousseau or in
the Membrane Handbook.2 Hemodialysis replaces kidney
function for individuals who have experienced total or par-
tial kidney failure. The preferred treatment is a kidney trans-
plant, but hemodialysis (or other replacement therapy such
as peritoneal dialysis) is required when a donor is not avail-
able or the failure is expected to be temporary.
Hemodialysis only partially replaces kidney function. The
primary goals are removal of cell metabolism waste products
and maintenance of the body's water balance. Typically, three
times per week a patient will spend three to four hours in a
clinic connected to a dialysis machine. Blood is taken from
the patient and passed through an artificial kidney
(hemodialyzer) where water and wastes are removed before
being returned to the patient.
Within the hemodialyzer, the patient's blood flows through
the lumen of 10,000 to 15,000 hollow fiber membranes while
simultaneously dialysate is pumped around the exterior of
the fibers. The dialysate serves as a reservoir for accumula-
tion of metabolism wastes as they diffuse across the porous
fiber wall. The incoming dialysate stream possesses a com-
position similar to blood plasma, excluding the wastes, to
minimize loss of electrolytes and other low molecular weight
plasma components. Large components such as red blood cells
and albumin cannot diffuse or flow across the wall because
the pores are too small.
For the design problem, students are asked to specify a treat-
ment schedule (the time required for treatment, td, and the
time interval between treatments, tb) for a patient weighing
G. Glenn Lipscomb is Professor of Chemical
and Environmental Engineering at the Univer-
sity of Toledo. After graduating from the Uni-
versity of California at Berkeley, he worked for
three years in Dow Chemical's Western Divi-
sion Applied Science and Technology Labora-
tory in Walnut Creek, CA. He was part of the
team that developed Dow's second-generation
oxygen/nitrogen membrane separation system.
His research interests lie primarily in module
design and membrane formation.
Copyright ChE Division ofASEE 2003
Chemical Engineering Education
Membranes in ChE Education
135 lbm. They are given the above background information
on kidney function, hollow fiber hemodialyzers, and the di-
alysis process. They are also given the following informa-
tion for the specific hemodialyzers and treatment processes
they are to consider:
During treatment, blood and dialysateflow rates are held
The inlet bloodflow rate equals the outlet bloodflow rate
Blood cannot be withdrawn from the body at a rate greater
than 400 ml/min
Dialysate cannot be introduced into the ,rrifil ial kidney at
a rate greater than 800 ml/min
The available .i, ii. l;.: kidneys possess I m2 of membrane
area and a mass transfer ( ffl( icnt of 0.010 cm/min
To simplify the analysis, urea is taken as a model waste
solute-the only one for which mass balances are required to
determine dialysis efficacy. Urea is produced by the body at
a rate roughly given by r = 0.11*M g/day, where M is the
body mass in kilograms.13] The goal of treatment is to keep
urea levels below 3 g/L-normal concentrations are approxi-
mately 0.5 g/L.
Students are instructed to treat urea-containing fluid within
the body like fluid within a single, well-stirred tank (CSTR).
The fluid volume in liters is related to mass by V = 0.58*M.E31
They are also encouraged to consider what happens when a
patient is undergoing therapy (Figure 1 shows a schematic of
the treatment process) separately from what happens between
treatments. During treatment, urea is removed (students are
told to neglect urea generation during treatment) while urea
is produced by the body between treatments. Finally, students
are given the following equation to describe the performance
of the hemodialyzer:[2]
S, 1 exp[-N(1- Z)]1
Qb(Cb -Cbo) =QbCb __ (1)
S1 Z exp[-N(l Z)j
where Qb is the blood flow rate, cb is the inlet blood urea
concentration, cb, is the outlet concentration, N = (kA)/Qb,
Dialysate out Dialysate in
Artificial Kidney
Blood in > Blood out
Body fluid
Figure 1. Schematic of hemodialysis treatment process.
Z = Qb/Q, k is the mass transfer coefficient, A is the mem-
brane area in the module, and Qd is the dialysate flow rate.
Equation (1) provides the relationship between cb and Cb. in
terms of membrane properties and process conditions that is
required in mass balances.
The analysis requires application of transient mass balances.
These projects do not require
extensive knowledge of membrane transport
phenomena, modules, or processes, but they
do require application offundamental
chemical engineering principles
for design purposes ...
A urea mass balance around the body (tank) during the treat-
ment time leads to the differential equation
d(cbV) Qbb, ) (2)
where cb is the blood urea concentration leaving the body
(which equals the concentration entering the hemodialyzer),
V is the urea distribution volume of the body (body fluid
volume), Qb is the rate at which blood is withdrawn from the
body (which equals the rate it enters the artificial kidney),
and cbo is the blood urea concentration entering the body
(which equals the concentration leaving the hemodialyzer).
Assuming k, A, Qb' Qd, and V do not change with time,
substituting Eq. (1) into Eq. (2) gives a differential equation
that can be readily integrated to give
cb = Cb,d exp(-t/ T) (3)
where cb,d is the blood concentration at the beginning of treat-
ment and T is given by
(V 1- Z exp[-N(1- Z)]]
Qb 1 exp[-N(1- Z)]
In between dialysis treatments, the material balance for urea
in the body is given by
= r (5)
which one can readily integrate, assuming r is constant, to
Cb bb = -(6)
where cbb is the blood concentration at the beginning of the
period between treatments. Therefore, the design equations
Winter 2003
Membranes in ChE Education
that relate concentration to treatment time, td, and time be-
tween treatments, tb, are
Cb,b = Cb,d exp(-td /i) (7)
Cb,d = Cb,b +rtb /V (8)
Given values for M, kA, Qb, and Qd' these two equations in-
volve four unknowns: cb,b, b,d td. and tb. Therefore, one must
specify two more variables before the problem is fully speci-
fied and the remaining dependent variables can be calculated.
A spreadsheet can be used to rapidly solve the equations for
a range of values for each variable. A typical solution is illus-
trated in Figure 2.
With this analysis, students are asked to answer the fol-
lowing questions:
How long should each dialysis treatment last?
What are the desiredflow rates of blood and dialysate?
What is the bodyfluid urea concentration at the beginning
of treatment? At the end of treatment?
How much dialysate is used during each treatment?
How long can a person wait between treatments? \t... ; a
practical treatment schedule; for example, it is not
practicalfor a patient to visit the clinic every 2.3 days, so
patients typically are scheduled at the same time on
\~pc ifii days during the week.
Is the assumption of no urea generation during dialysis a
good one?
Students are encouraged to minimize the time required for
each treatment (to reduce treatment costs and improve pa-
tient well being), maximize the time between treatments (also
to reduce treatment costs and improve patient well being),
and minimize the amount of dialysate used (to reduce di-
alysate costs). One cannot achieve all of these goals si-
Past experiences with this problem have been positive. The
subject intrigues students-the problem also challenges them.
The challenge comes not from the mathematics involved but
from setting up the equations from the problem statement
and identifying the constants, independent variables, and de-
pendent variables in each. This is often their first experience
with an unstructured, open-ended design problem-one that
requires arbitrarily specifying some variables to calculate
others and to synthesize a solution from information presented
not in order of use and in a variety of unit systems.
Additionally, the problem involves processes and concepts
that may not be familiar to them. With a little guidance and
encouragement, though, they can obtain a solution. The pri-
mary negative feedback is that the students didn't want to
work in groups and be assigned a group grade despite at-
tempts to address these issues using approaches described in
the literature.[41 We believe such criticism is common to group
projects in classes across the curriculum and is not related to
the membrane content of the problem.
Hollow Fiber Spinning Plant
Water Distribution System Design
(Fluid Mechanics)
Polymeric membranes in the form of fine hollow fibers are
used almost exclusively to form modules for gas separations
and hemodialysis. The fibers are produced in a spinning pro-
cess similar to that used to produce textile and structural fibers.
In this process, the polymer is mixed with one or more
solvents to form a "spin dope." The spin dope is pumped
through a spinneret to form a hollow liquid cylinder; a single
extruder may feed multiple spinnerets while a single spin-
neret may produce from 10 to over 100 filaments. A second
liquid or gas stream is fed to the spinneret to fill the cylinders
and keep them from collapsing. The filaments pass through
an air gap ("draw zone") and then one or more liquid baths
("quench baths") to induce a desired wall structure and ex-
tract solvent. The most commonly used liquid is water. The
filaments produced by a single spinneret travel through
the process in a group referred to as a "tow." Figure 3
illustrates the process.
The membranes produced by this process commonly pos-
sess a porous wall in which pore size depends on position in
the wall. Typically, the smallest pores are adjacent to one wall
Figure 2. Urea concentration changes during treatment and
between treatments for Qb = 400 ml/min, Qd = 800 ml/min,
cb,d = 1.5 g/L, and t = 240 min. For these conditions, cb,b
0.85 g/L and tb = 4900 min (3.4 days).
Chemical Engineering Education
Time (min)
Membranes in ChE Education
and the largest adjacent to the other wall. Fibers range in size
from approximately 100 to 400 microns outer diameter and
75 to 300 microns inner diameter, while pore sizes range from
Angstroms (molecular size) to microns.
Students in fluid mechanics classes were asked to design a
water distribution system for the water baths. The circulation
loop contains an adsorption column to remove solvent since
Figure 3. Schematic of a typical fiber spinning plant with
a single quench bath.
20m >T T
distribution manifold 2 m, between
Storage Tank each bath
Figure 4. Water distribution system in a fiber spinning
Multiple fiber 'tow'
0.5 mwide
0 r water r
0.5 m
S// M overflow
water inlet/// //-
Figure 5. Bath schematic.
the solvent concentration in the baths must be kept below
some critical level to produce "good" fiber. Figure 4 illus-
trates the water distribution system, while Figure 5 illustrates
the dimensions of each water bath.
For the analysis, a range of water flows was specified that
would ensure the solvent concentration remains below the
maximum allowable value. Simplified packed bed perfor-
mance and design guidelines were given for sizing purposes.
Additionally, constraints on the piping, pumps, pump loca-
tion, and the storage tank were specified. These are summa-
rized in Table 1.
The students were asked to provide
A p/ ,nt ,i .1, ,l,*i..,i,,it
Pump placement and horsepower
Packed bed dimensions and 1,, .;. i i, requirements
An inventory of required equipment
The analysis consists primarily of application of macroscopic
momentum balances (i.e., the Bernoulli equation), basic pump
sizing principles, and mass balances. The equipment inven-
tory for a typical design is provided in Table 2 (next page).
Student response to the problem was positive. Unsolicited
Design Constraints for Water Distribution System
[ Water flow rates range from 1 2 m3/hr and solvent concentra-
tion cannot exceed 1% by weight.
I Centrifugal pumps are available in integral horsepower ratings
from 1 to 10 hp and increments of 5 hp above 10 hp. Assume
80% efficiency and NPSH = 2 m.
I Use 12-gauge stainless steel tubing and at most two sizes: one
for the supply and one for the return.
[I Minimum working distance between pump and tank is 0.5 m.
[ Neglect pressure changes in the distribution manifold.
I Account for entrance and exit losses for all tanks.
[ All fitting losses may be approximated by an increase in the
required straight pipe length of 10% except for the specific ones
mentioned above.
I The water stream is always near 25 C.
[ The viscosity and density of the water stream do not change until
the solvent concentration exceeds 10%.
I The packed beds are mounted vertically and flow is upward. The
bottom of each bed is 0.5 m off the ground. The stream exiting
from the packed bed empties into the top of the storage tanks.
[ Packing is 1-cm diameter spheres (p = 2000 kg/m3), bed void
fraction ranges from 0.45 to 0.55, packing adsorbs 1 kg solvent/
kg packing, and exiting water stream is solvent free until packing
is saturated.
I Cylindrical beds are available in 0.5 m, 1 m, 1.5 m, and 2 m
diameters. Use an aspect ratio of 3.
Winter 2003
Quen h Bath
Melt Spinneret
Pump u I
Tows to
Draw Zone
Membranes in ChE Education
comments on course evaluation forms included "I liked the
group project" and "The design project was a good idea ex-
cept for the whole group work thing." As with the previous
problem, students were not comfortable working in groups
despite attempts to address their concerns.
0 1
Hollow Fiber Spinning Plant Solvent Recovery
(Senior Design)
In the senior design class, students were asked to design c
separation system to recover solvent from the water leaving
the quench baths for recycle within the process. The econom-
ics of membrane manufacture can be very sensitive to sol-
vent losses and environmental costs associated with waste
disposal. Consequently, this problem might be used as a pol-
lution prevention example in the design course.
The spinning process for this problem is illustrated in Fig-
ure 6. The primary difference between this process and the
process illustrated in Figure 3 is that two quench baths ir
series are used to remove the solvent. Students were giver
essential process specifications (see Table 3) and asked tc
design the recovery process. A fiber spinning process witt
similar characteristics is described in the patent literature.151
Each student group had to provide the following design
What is the required makeup waterflow rate for each
bath? At what rate is water removed from each bath
for treatment?
What are the .l.I. -.;.,ii, spcifictihiifor each unit
operation in the solvent recovery process ?
Provide a complete PFDfor the process, i,1, ./. 1;in : a
table of stream and unit operation properties.
Estimate process costs and compare to the cost of
simply ,. i, ,; in:' the wastewater to the city sewer
system at a concentration of less than 0.1 -i. ;..t
percent *,i.., ,
As one might expect, most groups considered dis-
tillation processes. Common process simulators
(e.g., ChemCAD) can be used for the design of in- Solid
dividual columns and column trains. Consideration
of other unit operations such as reverse osmosis,
pervaporation, or adsorption requires hand calcula-
tions and contact with potential vendors.
The separation process design is complicated by
the tight requirements on the water effluent from
the first bath -total solvent concentration less than
1% by weight. For the given process specifications,
a minimum of approximately 120 Ibm/min of water
Fiber Spinning Process Specifications
E[ The spin dope consists of 32.5 weight percent N-methyl
pyrrolidone (C i i \i 15.5 weight percent ethylene glycol, and
the balance polycarbonate.
E The spin dope is extruded at a rate of 5 lbm/min. This is fed to three
spinnerets that each produce 60 fibers.
E The 180 liquid filaments enter into a water bath maintained at 5C
and spend approximately 5 seconds in the bath.
E[ Upon exiting from the first bath, approximately 65% of the
ethylene glycol is removed and 45% of the N-methyl pyrrolidone.
An equal volume of water replaces the organic solvents.
E[ The total solvent composition of the first bath must be kept below
one weight percent.
E[ The fiber enters a second bath maintained at a temperature of 85C
and spends approximately 10 minutes in the bath.
E[ Upon exiting from the second bath, virtually all of the organic
solvents have been removed and replaced by an equal volume of
E[ The total solvent composition of the second bath must be kept
below 10 weight percent.
E[ Makeup water for the baths comes from city water lines but must
be distilled to purify it.
E[ Makeup water should be returned at the temperature of the bath.
However, you do not have to provide temperature control for either
E[ To reuse the solvents, the water content must be less than one
weight percent.
Melt Spinneret 5 CBath 85 C Bath
Polymer I P
Extruder Fiber
Tows to
-: -- -I ------ -- Drying
Draw Zone
Figure 6. Schematic of a typical fiber spinning plant with
two quench baths.
Chemical Engineering Education
Typical Equipment Inventory for
Water Distribution System
E[ 5-hp centrifugal pump (160 psig discharge) for water supply to
baths from storage tank
E[ 6-hp centrifugal pump (210 psig discharge) for water return to
storage tank from baths
E 230 ft 7/8 in OD 12-gauge stainless steel tubing
[I Four stainless steel 7/8-in tees
[I Ten globe valves
E[ Two vessels (Im x 3m) for packed beds
E[ 2 m3 packing for packed beds
E[ One vessel (2m x 2m) for the storage tank (illustrated in Figure 4)
[I Four water baths (illustrated in Figure 5)
Membranes in ChE Education
must be fed to the first bath. Some of the effluent from the
first bath can be used as the feed water to the second, but the
water flow through the second bath is an order of magnitude
less (about 12 lb/min), so most of the dilute effluent from
the first bath must be sent to the separation process.
One can recover solvent from the combined bath effluents
at sufficiently high purity (less than 1 weight percent water)
to permit reuse with a single modest column (five stages and
reflux ratio of 2). Water recovery to permit reuse in the first
bath is more problematic. Large columns with high reflux
ratios are required to increase water purity above 99%, the
maximum allowed concentration of the effluent from the first
bath; use of multiple columns is undesirable since water (the
highest concentration component) goes overhead in each col-
umn. Therefore, most designs send some water to waste treat-
ment and replace it with fresh water. The trade-offs between
the cost of water disposal, cost of solvent lost in the waste-
water, and column energy and capital costs dictate the final
design. Instructors may use cost information from standard
design texts (e.g., Turton, et al.6) to evaluate the trade-off.
Other configurations that students have considered include
sending the effluent from each bath to separate columns and
sending only the effluent from the second bath (with the high-
est solvent concentration) to a column. In the latter configu-
ration, all of the effluent from the first bath is sent to waste
[TRV1 stirred pots
Three design problems that illustrate hollow fiber mem-
brane manufacturing processes and use of membranes in sepa-
ration processes are described. The problems have been used
in classes that range from the freshman/sophomore to senior
years in the curriculum. These problems are unique in their
emphasis on membrane manufacture. Upon request, detailed
problem statements and sample solutions can be provided.
1. Felder, R.M., and R.W. Rousseau, Elementary Principles i. ...
Processes, 3rd ed., John Wiley & Sons, New York, NY (2000)
2. Kessler, S.B., and E. Klein, "Dialysis," in Membrane Handbook, W.S.
Ho and K.K. Sirkar, eds., Van Nostrand Reinhold, New York NY (1992)
3. Galletti, P.M., C.K. Colton, and M.J. Lysaght, "Artificial Kidney," in
I... i. *.. ..' i ...... .. ii .. book, J.D. Bronzino, ed., CRC Press,
Boca Raton, FL (1995)
4. Felder, R.M., and R. Brent, "Cooperative Learning in Technical
Courses: Procedures, Pitfalls, and Payoffs," ERIC Document Repro-
duction Service, ED 377038 (1994) Available on-line at
5. Sanders, E.S., D.O. Clark, J.A. Jensvold, H.N. Beck, G.G. Lipscomb,
and F.L. Coan, Process for Preparing POWADIR Membranes from
Tetrahalobisphenol A Polycarbonates, US Patent 4,772,392, issued
Sept. 20, 1988.
6. Turton, R., R.C. Bailie, W.B. Whiting, and J.A. Shaeiwitz, Analysis,
Synthesis, and Design of Chemical Processes, Prentice Hall, Upper
Saddle River, NJ (1998) 1
After reading David Lindley's book Boltzmann'sAtom, Professor Robert R. Hudgins (University of Waterloo) was
inspired to pen his thoughts on two subjects very familiar to chemical engineers. He shares those thoughts here...
Ludwig Boltzmann's Disorder
Herr Doktor Boltzmann has a vision rare
Of gases as a flight of tiny balls
In random 3-D motion that would dare
Allow him to explain their force on walls.
Ernst Mach insists that physics must be strict
And not be mocked, since atoms are not real.
Observables alone cannot be tricked;
Thereby, vague theories shall be brought to heel.
But Boltzmann's disarray achieves a feat-
Bold inf'rences drawn from how atoms fly.
He reinterprets what is meant by heat,
And temperature and pressure by the bye.
At length, chaotic motion proves its worth,
As entropy's conceived and has its birth.
Gibbs' Phase Rule
J. Willard Gibbs, the pedant in this tale,
Reflecting on an elemental state
Of matter at his alma mater, Yale,
Took to his books and never sought a mate.
In love with equilibrium he stayed
(No doubt both metaphorical and real).
When do P phases coexist? He played
With arguments with consecrated zeal.
As countrymen pursued uncivil war
'Round F degrees of freedom for their slaves,
Gibbs solved, with C components of savoir,
A theorem that, when understood, draws raves.
Robust and brief wouldud make a fine tatoo),
Proclaims F equals C less P plus two.
Winter 2003
Membranes in ChE Education
Rowan University Glassboro, NJ 08028
Electrodialysis is an electrochemical membrane sepa-
ration technique for ionic solutions that has been used
in industry for several decades.'1 It can be used in
the separation and concentration of salts, acids, and bases
from aqueous solutions, the separation of monovalent ions
from multivalent ions, and the separation of ionic compounds
from uncharged molecules. It can be used for either electro-
lyte reduction in feed streams or recovery of ions from dilute
streams.E2-41 Industrial applications encompass several indus-
tries and include the production of potable water from
brackish water, removal of metals from wastewater, dem-
ineralization of whey, deacidification of fruit juices, and
the removal of organic acids from fermentation broth.E12-
5] Additional examples of the applications of electrodi-
alysis are given in Table 1.
As a selective transport technique, electrodialysis uses an
ion-selective membrane as a physical barrier through which
ions are transported away from a feed solution. An energy-
intensive phase change is unnecessary, in contrast to the com-
mon separation techniques of distillation and freezing.[61 The
use of an organic solvent, as is often required with other se-
lective transport techniques such as liquid extraction, is
avoided with electrodialysis. In addition, electrodialysis is
typically performed under mild temperature conditions, mak-
ing it particularly attractive for food, beverage, and pharma-
ceutical applications that deal with heat liable substances.
In typical chemical engineering undergraduate curricula,
students are exposed to traditional separations methods with
a heavy emphasis on operations such as distillation, extrac-
tion, and absorption. The need for incorporation of membrane
tcilin 'l h -.1 into the chemical engineering curriculum has at-
tracted recent attention.E7-91
The membrane separation processes mentioned above em-
ploy "traditional" driving forces such as concentration and
pressure gradients, in contrast to electrodialysis, which uses
electrical potential to drive the separation. The first treatment
of electrodialysis in the educational literature appeared in
1931. 110 In this work, Kendall and Gebauer-Fuelnegg present
three reasons why electrodialysis remains among the "ne-
glected methods" of organic chemistry: 1) its treatment in
textbooks is inadequate, 2) its advantages and applicability
are not generally recognized, and 3) simple and efficient types
of electrodialyzers are not generally available. While bench-
scale electrodialysis equipment is now readily available from
various manufacturers, electrodialysis is not commonly ad-
dressed in chemical engineering curricula, due primarily to
the first two reasons presented above. Several reference books
include excellent treatment of electrodialysis theory and ap-
plications,[E13-5 1 but this material is not easily "distilled" into
material that can be introduced in the undergraduate class-
room or laboratory, particularly if the professor has limited
experience with membrane separations.
Increasing interest in electrochemical education is reflected
by recent publications that address electrochemical reactors
for synthesis and pollution control.12 171 Kendall and Gebauer-
Stephanie Farrell is Associate Professor of Chemical Engineering at
Rowan University. She received her BS in 1986 from the University of
Pennsylvania, her MS in 1992 from Stevens Institute of Technology, and
her PhD in 1996 from New Jersey Institute of Technology. Her teaching
and research interests are in controlled drug delivery and biomedical en-
Robert Hesketh is Professor of Chemical Engineering at Rowan Univer-
sity. He received his BS in 1982 from the University of Illinois and his PhD
from the University of Delaware in 1987. His research is in the areas of
reaction engineering, novel separations, and green engineering.
C. Stewart Slater is Chair of the Chemical Engineering Department at
Rowan University. He is a two-time recipient of the Martin Award, and
otherawards include the Westinghouse, Carlson, and Dow He is the found-
ing chair of the innovative, hands-on undergraduate-focused chemical
engineering program at Rowan. He is on the editorial board of Chemical
Engineering Education andThe International Journal of Engineering Edu-
Copyright ChE Division ofASEE 2003
Chemical Engineering Education
Membranes in ChE Education
Fuelneggo101 made a strong case for inclusion of electrodialy-
sis in the chemistry curriculum and described inexpensive
laboratory set-ups for simple and rapid laboratory investiga-
tions. Literature that specifically explores electrodialysis in
chemical engineering and chemistry education is scarce,
however. Garcia-Garcia, et al., have developed an excit-
ing experiment for the desalting of an amino acid solu-
Industrial Applications of Electrodialysis
Electrolyte reduction Potable water from brackish water
Nitrate removal for drinking water
Boiler water, cooling tower water, effluent
steam desalting
Cheese whey demineralization
Fruit juice deacidification
Sugar and molasses desalting
Potassium tartrate removal from wine
Blood plasma protein recovery
Demineralization of amino acid solutions in
the food industry
Acid removal from organic products
Electrolyte recovery Edible salt production from seawater
Ag(I) salts from photographic waste
Zn(II) from galvanizing rinse water
Organic salts from fermentation broth
Amino acids from protein hydrolysates
Salts, acids, and alkali from industrial rinse
Miscellaneous Conversion of organic salts into acid and base
(bipolar membrane ED)
Salt splitting
Ion-rich Con-
Ion-depleted centrate
Cathode A-j Anode
c' c
Catholyte Anolyte
Rinse Rinse
Feed C+A
Figure 1. The principles of electrodialysis.
tion using electrodialysis as an alternative to precipita-
tion using organic solvents."181
This paper describes a hands-on investigation of electrodi-
alysis that introduces the basic principles and applications of
electrodialysis tccl iilh ::,. The effects of various process
operating conditions on the system performance are explored
experimentally. Emphasis is given to data analysis and engi-
neering calculations related to rate of ion transfer, Faraday's
law, efficiency, energy consumption, and separation perfor-
mance. These experiments can be implemented in core chemi-
cal engineering courses such as unit operations and separa-
tion processes, or in elective or graduate-level courses in
green/environmental engineering, wastewater treatment, elec-
trochemical engineering, pharmaceutical engineering, and
food engineering. Through these experiments, students are
not only exposed to an innovative membrane separation ex-
periment, but they also gain a greater knowledge of experi-
mental skills and calculations relevant to the membrane field.
The principle that governs electrodialysis is an electrical
potential difference across an alternating series of cation and
anion exchange membranes between an anode and a cath-
ode. The feed solution containing both positive and negative
ions enters the membrane stack to which a voltage is applied,
thus causing the migration of the ions toward their respective
electrodes. The cation exchange membranes allow the trans-
fer of cations but inhibit the transfer of anions. Conversely,
anion exchange membranes allow the transfer of anions but
inhibit the transfer of cations. The result is alternating com-
partments containing streams of dilute ion concentration
(diluate) and streams rich in ion concentration (concentrate)
exiting the stack. An ionic rinse solution is circulated past
the electrodes to maintain conductivity of the membrane stack
while preventing potentially corrosive ions from the feed
solution from contacting the electrodes. This concept is
illustrated in Figure 1 with a feed solution of a salt (CA-
) in aqueous solution.
The electrodialysis membrane stack comprises electrodes
and membranes separated by gaskets and spacers. The spac-
ers are turbulence-promoting support mesh used to create the
compartments through which the solutions flow. Uniform flow
distribution and prevention of internal leakage through spacer
and gasket design are critical to system performance. Stack
design is discussed by Strathmann.J31
Material balances can be written for streams entering and
exiting the membrane stack, as ions are transported from the
feed stream to the concentrate stream. The molar rate of trans-
fer of an ionic species to a stream passing through the mem-
Winter 2003
Membranes in ChE Education
brane stack is
m1 = F2C2 FiCC (1)
where the subscript 2 is the stream exiting the stack and 1 is
the stream entering the stack, superscript i represents either
the feed or concentrate stream, F is volumetric flowrate, and
The electrodialysis system is easy to operate
and the students can perform the suggested
experiments in a typical undergraduate
laboratory period. The experiments can
be used in a variety of undergraduate
classes, including a unit operations
laboratory or separations course.
C is concentration of the species being transported. In batch
recirculation mode, the streams exiting the stack are returned
directly to the well-mixed reservoir vessels. The solutions in
the reservoir vessels are then fed to the stack. The unsteady-
state material balance on the reservoir vessel is
SV'C' Fi'C-FC 2 (2)
Equating Eqs. (1) and (2) yields an expression for the molar
rate of change in the reservoir vessels in terms of measured
reservoir volume V' and concentration
m = d(i) (3)
Transfer of ions to and from the rinse solutions does take
place, and this rate of transfer is found by an overall balance
on the three streams (feed, rinse, and concentrate):
mr'i + mi + mf = 0 (4)
Electrodialysis is commonly performed in either constant-
voltage or constant-current mode. Calculations relating volt-
age and current to power consumption and efficiency are of
critical interest, and basic equations that will be used for pro-
cess evaluation are presented here.
The cell voltage and current within a membrane stack are
related through Ohm's Law
V =IxR (5)
where V is the voltage (V), I is the current (A), and R is the
resistance of the membrane stack ( ). The resistance of the
membrane stack is due to the friction of the ions with the
membranes and the aqueous solution while being transferred
from one solution to another.E51 At high voltages, the system
does not follow Ohm's Law, and the interested reader is re-
ferred to standard texts such as MulderE'1 for the description
of other regimes.
The power consumption necessary for the removal of ions
from the feed solution is proportional to the current and the
stack resistance. The necessary power, P(J/s), is represented
This equation does not account for power necessary to pump
the feed, rinse, or diluate streams.[1
Combination of Eqs. (5) and (6) results in a power expres-
sion in terms of measured variables voltage and current, and
the number of membrane pairs in the stack, n,
P =V nI (7)
Current is the rate of charge passed through the stack
where c = charge passed (Coul) and t is time (s). For a system
operated at constant voltage, the power consumption will
change throughout the run as the current changes. The power
is defined as the rate of energy consumption
To determine the total energy consumed in time t, Eqs. (7)
and (8) are substituted into Eq. (9), which is integrated from
time 0 to t to obtain
E = nT c
The efficiency of the membrane stack is a measure of the
system's ability to use the current effectively in the removal
of ions. The minimum (theoretical) charge, cmnn, required to
transfer m moles of ions through the membrane stack is ex-
pressed by Faraday's Law
Cm = zm (11)
where z is the valence and 3 is Faraday's Constant (96,500
c/mol). The efficiency, T1, of the stack compares the mini-
mum theoretical charge to the actual charge required to trans-
port ions through a stack having n membrane pairsE31
1 Cmin (12)
An efficiency of less than one indicates that not all of the
charge passed by the electrodialysis system was used to trans-
fer ions from one stream to another. Potential causes of a
less-than-perfect efficiency include less-than-perfect ion se-
lectivity of the membranes, the potential of parallel current
paths within the membrane stack, and the transfer of water
Chemical Engineering Education
Membranes in ChE Education
molecules by osmosis and ion hydration.J61 The efficiency will
change with feed and concentrate solution concentrations
throughout a batch run, since the rates of water transfer by
osmosis and ion hydration are concentration-dependent.E31
In an electrodialysis system with the feed stream contain-
ing monovalent and divalent ions, the selectivity of a spe-
cific membrane of one ion over another can be calculated.
The selectivity, a, is taken to be the ratio of the number of
moles transferred from the feed vessel of each ionj and k, mi
and mk.[19]
Basic Features of the Electrodialysis System
Cell body Polypropylene
Number of membranes 10 pairs
Individual effective membrane area 0.1 m2
Spacers Polypropylene mesh, 0.75 mm intermembrane gap, 2.0 mm
electrode chamber gap
Gaskets Epoxy-Cured EPDM
Anode Platinized titanium
Cathode 316 stainless steel
Reservoir Custon 2-L glass
Conductivity/Temperature measurement Amel K-1 glass,
polypropylene probes with Amel SIRIO meters
Charge, Current, Voltage, Temperature, Flow measurement/
display The Boss electrochemical process control system
Pumps March model BC-3CP-MD centrifugal, polypropylene and
ceramic with viton o-rings
Flow sensors Teflon impeller style, Cole-Parmer Model U-33110-05
Tubing, compression fittings, valves Polypropylene, 1/2-inch
Figure 2. Scheme of the experimental electrodialysis sys-
tem employed for the separation runs. T C, Fare Tempera-
ture, Conductivity, and Flowrate on-line analyzers.
Equation (13) is applicable when the ion species j and k are
equal in the feed vessel. In a batch electrodialysis system, the
feed concentrations change with time, and Eq. (13) for over-
all selectivity throughout the run is used to quantify the se-
lective transport of ions.
There is a wide range of important theoretical concepts and
practical issues related to electrodialysis that are beyond the
scope of this paper. Selective transport theory is presented in
various referencesE3,5 6] and StrathmanE15 offers a practical treat-
ment of design and cost estimates that would allow estima-
tion of membrane area and required energy for a desired plant
capacity. Additional practical considerations of electrodialy-
sis operations include limiting current density, boundary layer
effects, and concentration polarization, osmosis, and elec-
troosmosis effects. For treatment of these topics, the reader
should consult references 1,3,4,5,6, and 11.
The laboratory-scale electrodialysis system in our experi-
ments was purchased from Electrosynthesis Corporation in
Lancaster, New York. The major components of the system
are the electrodialysis cell, an electrochemical process con-
trol unit, and system instrumentation. The basic features of
the electrodialysis system in our laboratory are summarized
in Table 2. The entire system was purchased for approximately
$30,000. A perfectly adequate electrodialysis system could
be constructed for well under $10,000 by purchasing a fabri-
cated electrodialysis cell for about $3,200 (electrodes, cell
body, membranes, gaskets, and spacers) and assembling the
other components and instrumentation in-house.
The Electrosynthesis Model ED-1 electrodialysis cell fea-
tures a platinum-on-titanium anode and 316 stainless steel
cathode, polypropylene cell body, and individual membrane
area of 0.01 m2. Multiple pairs of membranes allow a total
membrane area up to 0.2 m2. The cell stack includes turbu-
lence-promoting mesh spacers and gaskets. A photograph of
the electrodialysis cell is shown in Farrell, et a1.,E20 in this
issue of CEE (Figure 2b).
The Boss Model 710 electrochemical process control sys-
tem features a digital coulometer, digital temperature moni-
tor, four independent pump and flow control loops, and digi-
tal indicators for temperature, cell potential, current, pro-
cess charge, and setpoints. Safety features include pro-
cess shutdown for exceeding flow, voltage, temperature,
or charge limits.
The system is fully instrumented with in-line conductivity/
Winter 2003
Membranes in ChE Education
temperature probes (K-1, AMEL, Milan, Italy), programmable
microprocessor conductivity/resistivity indicator (model
SIRIO, AMEL s.r.l., Milan, Italy), Teflon impeller flow sen-
sor (model U-33110-05, Cole Parmer, Vernon Hills, IL) with
ratemeter/totalizer (model DP78A, Omega Engineering, Inc.,
Stamford, CT). Determination of cation concentrations for
mixed monovalent-divalent cation solutions was made using
ion selective electrodes divalentt cation electrode Model 93-
32 and ammonium electrode model 93-18 with sensing mod-
ule, Thermo Orion, Beverly, MA).
The electrodialysis process is shown schematically in Fig-
ure 2, and a photograph of the system is shown in the com-
panion paper by Farrell, et al., (Figure 2a).[20] The system is
operated in batch recirculation mode. Continuous and batch
modes of operation, along with their relative advantages and
disadvantages, are described by Shaffer and Mintz.[6]
The performance of ion-permeable membranes used in elec-
trochemical processes depends on several properties. The
desirable characteristics of membranes used in electrodialy-
sis applications include[5,21] selectivity between ions of oppo-
site charge, high ionic conductivity, low electrical conduc-
tion, long-term chemical stability, mechanical strength, and
resistance to fouling. These characteristics are determined by
the membrj,,i matrix polymer and the fixed ionic moiety that
effects the ion selectivity of the membrane. StrathmannE51
describes the challenges of optimization of these properties.
Polymer materials such as polystyrene, polyethylene, and
polysulfone are often chosen for the membrane matrix and
are often cross-linked to ensure stability. Fixed ionic moi-
eties such as SO3-, COO-, PO32-, HPO2-, AsO32-, and SeOe3 are
commonly used for cation exchange membranes, and NH3+,
RNH2+, R3N+, R2N+, R3P+, R2S+, are common choices for an-
ion-exchange membranes. 51
There are several manufacturers of ion-selective membranes
for a variety of electrochemical process applications. Table 3
provides information on the materials and features of several
ion exchange membranes used in electrodialysis applications.
Detailed information on membrane manufacturers and mem-
brane characteristics is provided in reference books[3,21] and
directly from the manufacturers. Membrane replacement costs
are on the order of $100/m2.
Tokuyama Soda Nc% ,'cpi.i ion-exchange membranes are
used in our experiments. Two Neosepta cation exchange
membanes, CMX and CMS, were investigated, while the same
anion exchange membranes, Neosepta AMX, were used in
all experiments. Neosepta AMX and CMX membranes are
standard grade, general-purpose polystyrene-based ion ex-
change membranes. Neosepta CMS membranes have a thin
cationic charged layer on the membrane surface that increases
the selectivity between monovalent cations (i.e., NH4+) and
multivalent cations (i.e., Mg2+). Neosepta membranes have
high ionic selectivity, low electric resistance, and a low dif-
fusion coefficient for solute or solvent. They exhibit high me-
chanical strength and high dimensional stability, and are
highly resistant to chemical attack.
Ammonium cations and chloride anions are contaminating
Ion Exchange Membranes Used in Electrodialysis Applications
(Information from References 3, 21, and Membrane Manufacturers)
Manufacturer Tradename Material Special Features Location
Solvay Perfluorinated film with fixed pyridine (anion-permeable) or France
sulfonic acid (cation-permeable)
FuMA-Tech Polyetherketones, polysulfone, polyphenylene oxide Germany
Tokuyama Soda Neosepta Styrene-divinyl benzene Robust high mechanical strength; Japan
Moderate electrical resistance
Asahi Glass Selemiom Polystyrene-based Very low electrical resistance Japan
Asahi Chemical Aciplex Styrene-divinyl benzene/PVC backing Japan
Ionics, Inc. Heterogeneous polystyrene-based/acrylic fabric, with fixed Rugged, low resistance, high select- MA, USA
sulfonate (cation-permeable) and quarternary ammonium cations ivity, chemically stable, low fouling
Dupont Co. Nafion Perflourinated sulfuric acid polymer Cation permeable NC, USA
Sybron lonac Heterogeneous resin-PVDF/fabric High mechanical strength NJ, USA
Chemical Engineering Education
Membranes in ChE Education
species that are commonly present in industrial process
streams. In this investigation, we considered removal of am-
monium chloride from an aqueous stream. Experiments were
performed to study the effect of the following parameters in
the removal of NH4Cl from water: the initial concentration
of the concentrate vessel, the applied cell voltage, and the
selection of the membranes. Additional experiments could
be conducted to investigate other process parameters such as
number of membrane pairs, flow rate, feed concentration, and
temperature (within the limits of the membranes). The sys-
tem performance was evaluated using efficiency, selectivity,
power, and energy consumption calculations.
The membrane stack was constructed with five pairs of
cation and anion exchange membranes, with a cation ex-
change membrane adjacent to each electrode as described
above. A solution of 0.5 M ammonium sulfate was used as
0 5 10 15 20 25 30
Time minutes )
Figure 3. Effect of initial concentrate concentration at
constant voltage. Process operating conditions: 13 V 1 M
feed (initial), AMX/CMX membranes.
c 0.7
8 0.4
- 0.3
0 10 20 30 40 50 60 70 80
Time (minutes)
Figure 4. Effect of voltage on the feed concentration. Process
operating conditions: 1 M feed (initial), 0.1 concentrate (initial),
and AMX/CMX membranes.
the anolyte/catholyte rinse solution in order to prevent gen-
eration of chlorine or hypochlorite, which would be hazard-
ous. The feed solution was aqueous NH4Cl or NH4Cl/MgC12
with a total initial salt concentration of approximately 1.0 M.
The concentrate stream was an aqueous NH4C1 with an ini-
tial concentration between 0.05 and 0.2 M (specified for each
run). At the anode, the expected predominant reaction in this
system with a neutral solution is the formation of oxygen
2H20) > O() + 4 H+ + 4e (14)
At the cathode, the formation of hydrogen gas is the pre-
dominant reaction in neutral solution
2H20() + 2e- H2(g) + 2Ha) (15)
The system was operated in a constant voltage, batch recir-
culation mode. Flowrates were 0.5 L/min for the feed and
concentrate streams, and 0.7 L/min for the combined anolyte
and catholyte streams. The following data were collected at
regular intervals of ten minutes or less: liquid volume in each
vessel, conductivity of each stream, current, charge passed,
and temperature. Completion of experiments took between
70 and 90 minutes, depending on the applied voltage and
other operating parameters. The experiment was consid-
ered complete when the current dropped to approximately
1.0 A. The ion concentrations were determined using con-
ductivity measurements.
Initial concentration of the concentrate vessel is important
because it is a key parameter in the resistance of the mem-
brane stack. If the concentrate stream initially has an ex-
tremely low ion concentration, water splitting may occur in
order to provide the ions necessary to carry the current. (Wa-
ter splitting generates hydrogen ions and hydroxyl ions, which
are capable of migrating through the cation- or anion-
selective membranes, respectively; this may result in
pH changes in the diluate and concentrate compart-
ments.) Thus, the concentrate stream is usually
"primed" with a low electrolyte concentration to fa-
cilitate transport of the desired ions from the feed
stream. To illustrate this, the system performance is
compared using different initial concentrate vessel con-
centrations. The effect of the initial ion concentration
in the concentrate stream is shown in Figure 3.
These runs were performed at a constant voltage of
13 V using a 1.0 M NH4C1 feed and 0.5 M (NH),SO4
rinse, and the initial concentrate concentration was
varied from 0.05 M to 0.2 M NH4C1. The figure shows
the decline in the feed ion concentration throughout
the course of the runs. The rate of ion transport increases
with increasing initial concentrate concentration. At
Winter 2003
Membranes in ChE Education
higher concentrate concentrations, the ionic conductivity of
the membrane increases, effecting a higher current for a given
voltage drop across the cell stack and thus resulting in a higher
rate of transport of the ionic species.
Applied cell voltage is a critical operating condition in elec-
trodialysis processes. As the cell voltage is increased, the ion
concentration in the feed vessel is depleted more rapidly, thus
reducing the duration of the experiments. Increasing the cell
voltage, however, increases the energy consumption of the
unit according to Eq. (10). An interesting investigation can
be performed by varying the voltage and comparing the sys-
tem performance and energy consumption.
To study the effect of voltage, the voltage was varied be-
tween 8 and 13 volts, based on manufacturer recommenda-
tions.E221 The system operated in the Ohmic region within this
voltage range. The results of ammonium chloride removal at
different voltages are shown in Figure 4, which plots the feed
ion concentration throughout the run. This figure shows that
at higher cell voltages, the feed ion concentration is depleted
more rapidly than at lower cell voltages. As the concentrate
concentration increases at the start of the run, the current in-
creases and a higher ion transport rate is observed. This can
be observed through the change in the slope of the curves in
Figure 4 (about 5-10 minutes into the run).
Using Eqs. (11) and (12), students can calculate the effi-
ciency of the membrane stack in the removal of ions at the
various cell voltages. At the conditions shown in Figure 4,
overall efficiencies of close to 100% were obtained for the 8
V and 10V runs, while the efficiency of the 13 V run was
approximately 85%. The lower efficiency of the 13 V run
was accompanied by an increase in temperature due to finite
membrane resistance, which could damage the ion-selective
membranes if cooling is not provided. Similarly, the calcu-
lated energy consumption for the 13 V run was significantly
higher than that for the 8 V or 10 V run, as shown in Table 4.
The experimental results for efficiency and energy con-
sumption could be used to estimate the energy require-
ments and membrane area necessary to achieve this
deionization task for a given plant capacity and to obtain
a rough estimation of process costs.
A third parameter for students to investigate is the type of
membrane used in the stack. There are numerous types of
specialized membranes available for a variety of separation
applications. Some general features of available commercial
membranes include size selective, charge selective, and spe-
cific-ion selective membranes. The objective of this experi-
ment is to compare the selectivities of two types of cation
exchange membranes-a general-purpose membrane (CMX)
and a monocation-selective membrane (CMS).
For the purpose of this experiment, divalent cations (Mg2+)
and monocations (NH4+) were provided in a feed solution of
0.55 M MgCl2 and 0.55 M NH C1. The initial concentrate
concentration was 0.2 M NH4C1 and the system was oper-
ated at 10 V. Samples were extracted from the feed and con-
centrate vessels initially and at ten-minute intervals. They
were stored for analysis with ion selective probes.
The monocation-selective membranes reduce the migra-
tion of the divalent magnesium ions from the feed vessel to
the concentrate vessel. The concentration of the ammonium
ions and magnesium ions in the feed vessel can be plotted as
a function of time for either set of membranes. Figure 5 shows
the slow decline of magnesium ions in the feed vessel in com-
parison with the rapid decline of the ammonium ions in an
experiment with the CMS membranes. Comparing the per-
formance of CMS membranes to CMX membranes, the en-
hanced retention of magnesium in the feed using the CMS
membranes is also shown in Figure 5. (At early times, the
expected difference in magnesium ion removal rates for the
two membranes is not apparent. This is probably due to sys-
Comparison of Total Energy
Consumption for Runs at Three
Different Applied Voltages
Time Voltage Energy Consumption
(min) (V) (kJ)
68 8 722
38 10 816
25 13 962
0 500
0 300
o so
*Mg2+, CMS
*Mg2+, CMX
* *
0 10 20
Time (min)
50 0 7
50 60 70
Figure 5. Removal of ammonium and magnesium ions us-
ing CMX and CMS cation exchange membranes. Process
operating conditions: 10 V 0.5 M MgC1,, and 0.5 M NH4Cl
feed (initial), 0.2 M concentrate (initial).
Chemical Engineering Education
Membranes in ChE Education
tem equilibration and run-to-run variations that are most ap-
parent at start-up. The difference in removal rates for the two
runs is evident after 20 minutes.)
The overall selectivity throughout the run, for ammonium
relative to magnesium, is calculated using Eq. (13), using the
total number moles of each ion removed from the feed at the
completion of a 70-minute run. The total number of moles of
each ion transferred from the feed is determined by integrat-
ing Eq. (3) for the duration of the run.
For the general-purpose CMX membrane, the overall se-
lectivity was 1.04, indicating that the average removal rates
of ammonium and magnesium are approximately equal. For
the monocation-selective membrane, the overall selectiv-
ity was 2.8, indicating that the CMS membrane selectively
enhances the removal of monovalent ammonium ions from
the feed.
We have developed an experimental investigation of the
practical engineering aspects of electrodialysis. Students in-
vestigate the effects of operating parameters such as concen-
trate concentration and applied voltage. Membrane selection
is explored through comparison of two cation exchange mem-
branes for the selective removal of competing cations.
Additional experiments could be conducted to investigate
other process parameters such as the number of membrane
pairs, flow rate, feed concentration, and temperature (within
the limits of the membranes). Data analysis and calculations
emphasize practical engineering considerations such as en-
ergy consumption, efficiency, and selectivity.
The electrodialysis system is easy to operate and the stu-
dents can perform the suggested experiments in a typical
undergraduate laboratory period. These experiments can be
used in a variety of undergraduate classes, including a unit
operations laboratory or separations course. Advanced courses
that would be enhanced with electrodialysis experiments are
specialized topics courses such as green/environmental en-
gineering, wastewater treatment, electrochemical engineer-
ing, pharmaceutical engineering, and food engineering.
Support for the laboratory development activity described
in this paper was provided for by Johnson Matthey, Inc., a
grant (DUE 9850535) from the National Science Founda-
tion, and the Chemical Engineering Department at Rowan
University. The authors gratefully acknowledge the work of
Rowan engineering students, particularly Natalie Deflece and
Craig Rogers, in conducting experiments.
1. Mulder, M., Basic Principles ofMembrane Technology, 2nd ed., Kluwer
Academic Publishers, Dordrecht, Holland (1996)
2. Electrosynthesis Company promotional literature at
accessed May 6, 2001
3. Strathmann, H., "Electrodialysis" in Synthetic Membranes: Science,
Engineering, and Applications, P.M. Bungay, H.K. Lonsdale, and
M.N.D. de Pinho, eds., Reidel Publishing Company, Dordrecht, Hol-
land (1986)
4. Davis, T.A., "Electrodialysis," in Handbook of Industrial Membrane
Technology, M.C. Porter, ed., Noyes Publications, Park Ridge, NJ
5. Strathmann, H. "Electrodialysis," in Membrane Handbook, W.S. Ho
and K.K. Sirkar, eds., Van Nostrand Reinhold, New York, NY (1992)
6. Shaffer, L.H., and M.S. Mintz, Principles of Desalination, Academic
Press, Inc., New York, NY (1980)
7. Slater, C.S., "Teaching the Engineering Aspects of Membrane Process
Technology," J. Membr. Sci., 62, 239 (1991)
8. Slater, C.S., and H.C. Hollein, "Educational Initiatives in Teaching
Membrane Technology," Desal., 90, 291 (1993)
9. Slater, C.S., "Education on Membrane Science and Technology" in
Membrane Processes in Separation and Purification, J.G. Crespo and
K.W. Boddeker, eds., Kluwer Academic Publishers, Dordrecht, Neth-
erlands, pg. 479 (1994)
10. Kendall, A.I., and E. Gebauer-Fuelnegg, "Electrodialysis with Simple
Apparatus," J. Chem. Ed., 8, 1634 (1931)
11. Lacey, R.E., "Basis of Electromembrane Processes" in Industrial Pro-
cessing with Membranes, R.E. Lacey and S. Loeb, eds., John Wiley
and Sons, New York, NY (1972)
12. Ottewill, G., and F. Walsh, "Education Topics Number 2: The Speed
of Metal Deposition and Dissolution," Trans. Inst. Met. Finish, 77(5),
209 (1999)
13. Walsh, E, and G. Ottewill, "Education Topic Number 3: Electrochemi-
cal Cell Reactions," Trans. Inst. Met. Finish, 77(4), 169 (1999)
14. Walsh. F, and D. Robinson, "Electrochemical Filter-Press Reactors:
Technology Designed for Versatility and Efficiency," Electrochemi-
cal Soc. Interface, 7(2), 40 (1998)
15. Walsh, F, and G. Ottewill, "Electrochemical Cells," Chem. Rev., 5(4),
2 (1996)
16. Trinidad, P., and F. Walsh, "Conversion Expressions for Electrochemi-
cal Reactors Which Operate Under Mass Transport Controlled Reac-
tion Conditions: Part 1. Batch Reactor, PFR, and CSTR," Int. J. Eng.
Ed., 14(6), 431 (1998)
17. Exp6sito, E., M.J. Ingls, J. Iniesta, J. Gonzalez-Garcia, P. Bonete, V
Garcia-Garcia, and V. Montiel, "Removal of Heavy Metals in Waste-
water by Electrochemical Treatment," Chem. Eng. Ed., 33(2), 172
18. Garcia-Garcia, V., V. Montiel, J. Gonzalez-Garcia, E. Exp6sito, J.
Iniesta, P. Bonete, and E.M. Ingles, "The Application of Electrodialy-
sis to Desalting an Amino Acid Solution," J. Chem. Ed., 77(11), 1477
19. Wankat, P.C., Rate Controlled Separations, Kluwer, Amsterdam (1990)
20. Farrell, S., R.P. Hesketh, M.J. Savelski, K.D. Dahm, and C.S. Slater,
"Membrane Projects with an Industrial Focus in the Curriculum,"
Chem. Eng. Ed., 37(1), 68 (2003)
21. Davis, T.A., J.D. Genders, and D. Pletcher, A First Course in Ion Per-
meable Membranes, The Electrochemical Consultancy, Hants, England
22. Personal communication with Duane Mazur, Electrosynthesis Com-
pany, June 9, 1999 J
Winter 2003
SMembranes in ChE Education
Tools for Teaching
Research Triangle Institute Research Triangle Park, NC 27709-2194
as separation with polymer membranes is rapidly be-
coming a mainstream separation tcl'iiinlh-b.,. The
most widely practiced separations are enriched ni-
trogen production from air, hydrogen separation in ammonia
plants and refineries, removal of carbon dioxide from natural
gas, removal of volatile organic compounds (e.g., ethylene
or propylene) from mixures with light gases (e.g., nitrogen)
in polyolefin purge gas purification, and water vapor removal
from air.[1-3] Relative to conventional separation technologies,
membranes are low-energy unit operations, since no phase
change is required for separation. Additionally, membranes
have a small footprint, making them ideal for use in applica-
tions on offshore platforms, aboard aircraft, and on refriger-
ated shipping containers, where space is at a premium or
where portability is important. They have no moving parts,
making them mechanically robust and increasing their suitabil-
ity for use in remote locations where reliability is critical.[31
Gas separation membranes are often packaged in hollow-
fiber modules-a cartoon of such a module is presented in
Figure 1. A full-scale industrial module for air separation may
contain from 300,000 to 500,000 individual fibers in a tubu-
lar housing that is 6 to 12 inches in diameter and approxi-
mately 40 inches long. Each fiber will have inside and out-
side diameters on the order of 150 and 300 micrometers, re-
spectively. For a typical case, the fiber wall, approximately
75 micrometers thick, consists of a very thin, dense separa-
tion membrane layer on the order of 500 to 1000 A (0.05 to
0.1 micrometers) thick, on the outside of the fiber. This thin
layer provides, ideally, all of the mass transfer resistance and
separation ability of the hollow fiber. The remaining 74.9 to
74.95 micrometers of the fiber wall comprise a porous poly-
mer layer that provides mechanical support for the thin mem-
brane, but offers little or no mass transfer resistance. (To put
fiber dimensions in perspective, the diameter of a typical
human hair is about 100 micrometers.)
Gas (air in this example) flows under pressure into the
module, where it is distributed to the bores of the fibers. In
air separation, feed pressures of approximately 10 to 15 bar
* University of Texas at Austin, Austin, TX 78758
are typical. The air gases permeate through the wall of the
fibers into the shell of the hollow-fiber module, which is
maintained at essentially atmospheric pressure. The gas per-
meating through the fibers and into the shell is collected and
leaves the module as the permeate stream.
Because oxygen, water, and carbon dioxide are more per-
meable than nitrogen and argon, the gas in the fiber bore is
enriched in N2 and Ar as it moves through the fiber lumens
from the feed to the residue end of the module. This process
can produce 99+% N2 in the residue stream.
Such purified nitrogen is widely used for blanketing or
inerting applications in, for example, the aviation (fuel tank
bl.11 ikci ill.- shipping (food container/packaging bl.11 ike illi-
and chemical industries (storage tank and line blanketing or
Per me ie
I N ,+Ar
c Pco
Feed A
Figure 1. Cartoon of hollow-fiber module used for air
separation. From
and Ref. 4.
David T. Coker provides engineering software services for Research Tri-
angle Institute. He holds a BS in Chemical Engineering (1997) from North
Carolina State University.
Rajeev Prabhakar is currently working toward his PhD in chemical engi-
neering at the University of Texas at Austin. His research relates to the
development of membrane-based systems for removal of carbon dioxide
from natural gas streams. He received his BTech in chemical engineering
from the Indian Institute of Technology (Kharagpur) and his MS from North
Carolina State University.
Benny D. Freeman is the Matthew van Winkle Professor of Chemical En-
gineering at the University of Texas atAustin. His research is in polymers,
particularly the sorption, diffusion, and permeation of small molecules
through polymers and polymer-based composites.
Copyright ChE Division ofASEE 2003
Chemical Engineering Education
Membranes in ChE Education )
pmlii-i-ii 'l(,
for further examples).
This paper presents a brief background section describing
the fundamentals of gas transport in polymer membranes and
then discusses models of mass transfer in gas separation mod-
ules. First, an analytical model for binary gas separation will
be described, and it can be used to rapidly develop intuition
regarding the effect of membrane process variables on sepa-
ration performance. Then, a more rigorous model, which is
available on the Internet, will be described-this model can
be used to perform more realistic simulations and address
more complex situations (e.g., multicomponent separations,
use of sweep streams to enhance separation efficiency, stag-
ing membrane units, recycle, etc.).
L > pV XA, pL
Figure 2. Schematic of a gas separation membrane of thick-
ness t being used to separate a gas mixture of components
A and B (0, and N,, for example). The upstream pressure,
PL is greater than the downstream pressure, Pv, and the mol
fractions of component A on the upstream and downstream
sides of the membrane arexA and yA, respectively. The steady
state fluxes of components A and B through the membrane
are NA and N,, respectively. By convention, component A is
selected so that the permeability of the membrane to com-
ponent A, PA, is greater than the permeability of the mem-
brane to component B, P,
Oxygen and Nitrogen Permeability in Selected Polymers
Oxygen Permeability
Poly(phenylene oxide)
Ethyl cellulose
6FDA-DAF (polyimide)
The fundamental mechanism for gas transport across a
polymer membrane was described by Sir Thomas Graham
more than a century ago."1 (This classic article, along with a
number of other seminal papers in membrane science, are
reproduced in the 100th volume of the Journal of Membrane
Science. [6) This mechanism, known as the solution/diffusion
model, postulates a three-step process for gas transport
through a polymer: 1) dissolution of the gas into the high-
pressure (or high chemical potential) upstream face of the
polymer, 2) diffusion of the gas through the polymer, and 3)
desorption from the low-pressure (i.e., low chemical poten-
tial) downstream face of the polymer. Steps 1 and 3 are very
fast relative to step 2, so diffusion through the polymer is the
rate-limiting step in mass transport across a membrane.
Figure 2 depicts a dense polymer film (or membrane) of
thickness t exposed to a binary mixture of gases A and B. The
mole fraction of A on the upstream, or high pressure, side of
the membrane is xA, and the mole fraction of A on the down-
stream, or low pressure, side of the membrane is yA. The up-
stream pressure, PL, is greater than the downstream pressure,
Pv. Because separation membranes are so thin (500-1000A),
the characteristic timescale for gas molecule diffusion through
the membrane is very fast, and as a result, industrial gas sepa-
ration membranes typically operate at steady state. The flux
of A across the film, N is 21
where PA is the permeability of the polymer to component A.
The ratio of permeability to membrane thickness is called
the permeance of the membrane to gas A, and this ratio can
be viewed as a mass transfer coefficient that con-
nects the flux (often expressed in cm3[STP] of
,,...,, Permeability Oxygen/Nitrogen
(Barrer) Selectivity
Polyaramid 3.1 0.46 6.8
Tetrabromo his polycarbonate 1.4 0.18 7.8
*These data are from Baker.3J The unit for gas permeability, the Barrer is named after
Professor Barrer, one of the pioneers in this area.7J
1 Barrer = 10- cm2(STP)cm/(cm3s cmHg). Forpermeability values, standard temperature
and pressure (STP) are O0C and I atm, respectively.
gas permeated through the membrane per cm2
of membrane area per second) with the driving
force for transport, which is the partial pressure
difference between the upstream and downstream
sides of the membrane. (Standard temperature
and pressure for permeance are 0C and 1 atm,
respectively.) A similar expression can be writ-
ten for component B as
NB = -[(- XA)PL -(l- yA)P] (2)
For a given gas molecule, every polymer has a
different permeability coefficient. Based on the
data in Table 1, oxygen permeability, for ex-
ample, varies by orders of magnitude from one
polymer to another. Moreover, in a given poly-
mer, the permeability coefficient will vary from
Winter 2003
Membranes in ChE Education
one gas to the next, and it is this property that allows the polymer
to separate gas mixtures. The data in Table 1 indicate that oxygen
is always more permeable than nitrogen in all polymers, and the
ratio of 02 to N2 permeability, the selectivity, varies from 1.6 to
7.8 in the materials shown. Typically, as the permeability of a
polymer to oxygen increases, its selectivity decreases, and vice
versa.E8 9] In the most widely used gas separation membranes, per-
meability coefficients often decrease with increasing gas mol-
ecule size, so most gas separation membranes are more perme-
able to small molecules (e.g., H2) than to larger molecules (e.g.,
CH4). There are interesting exceptions to this general rule, and
membranes based on such materials may become more common-
place in the near future.[10-12]
The mole fraction of gas A on the permeate or downstream side
of the membrane is given by the flux of component A through the
membrane divided by the total gas flux through the membrane
PA( pL yApV)
t A
PA p _VAPV _+q[fh A }PL _\ _VA Apv
This expression can be reorganized as follows to permit a direct
calculation of permeate purity:
1+(U-1) +XA 4 1- XAx
-(1-u) [ 1 1) __
where the selectivity, c, is defined as the ratio of permeability
coefficients ( =PA/PB) and the pressure ratio, R, is defined as the
ratio of feed to permeate pressure (R=P/PV). Equation 4 can be
used to determine the effect of feed composition, pressure ratio,
and membrane selectivity on the mole fraction of gas produced
by a membrane.
There are two limits of Eq. (4) that provide insight into the
factors that govern the ultimate separation performance of mem-
branes. It is easier to see these two limits if, instead of using Eq.
(4) directly, we use the following equivalent reorganized form of
Eq. (3):
YA RxA YA
Figure 3 presents the permeate purity as a function of membrane
selectivity, and the two limits of interest are shown. The first limit
to be discussed is the pressure ratio limit. As membrane
selectivity increases, the permeate mole fraction, A', will
increase, but YA can only increase up to the point that the
partial pressure of component A on the upstream side (xAPL)
of the membrane equals that on the downstream side (yPV).
At this point, the driving force for transport of A across the
membrane is zero, the flux of component A goes to zero,
and there can be no further increase in the mole fraction of
component A in the permeate. Therefore, in the limit of very
high selectivity (i.e., as a o in Eq. 5 and, therefore, Eq
4), Eq. (5) reduces to
That is, at high selectivity, the purity of gas produced is
limited by the pressure ratio. Of course, the value of YA can
never be greater than unity.
This limit has industrial significance in situations were
selectivity is very high and process conditions dictate a small
pressure ratio between permeate and feed streams. An ex-
ample is the removal of hydrogen from mixtures with hy-
drocarbons in hydrotreaters in refineries.J31 The hydrocar-
bons in such a mixture would be methane and higher hy-
drocarbons, all of which are less permeable than methane
in the membranes used for such separations. Typically, H2
is hundreds of times more permeable than CH4 and other
components in such a mixture.E21 But typical upstream and
downstream pressures would be 120 and 30 bar, respec-
tively,E31 so the pressure ratio would only be 4. In such a
case, having very high selectivity does not result in much
1 10 100 1000
Figure 3. Permeate purity as a function of mem-
brane selectivityfor a feed composition, XA, of 1 mole
percent A (99 mol percent B) and a pressure ratio
of 20.
Chemical Engineering Education
selectivity limit
Membranes in ChE Education
higher-purity H2 in the permeate because the H2 permea
is at or near the limit where its partial pressure upstream
downstream are almost equal.
Another example is dehydration of gas streams such as
Typically, water is much more permeable than air gase
polymers used for gas separation, so the amount of w
that can be removed from a gas stream is often limited b)
ability to keep the partial pressure of water very low in
permeate gas. This is often done by recycling some of
dry residue gas product back across the permeate side of
membrane to dilute the concentration of water being prodi
in the membrane. Such so-called purge or permeate sw
strategies can markedly reduce the dew point of air prodi
by dehydration membranes.[]
At the other extreme, if the membrane is operated wi
vacuum on the permeate side of the membrane (i.e., R -
then Eq. 5 becomes
l + ( l)xA
and permeate purity is limited by polymer selectivity. As
meate pressure, PV, decreases toward zero (or, equivalei
as the ratio of feed to permeate pressure increases to the p
that the partial pressures of components A and B in the
meate become very small relative to their partial pressure
the feed), the flux of components A and B approach m
mum values based on membrane permeability, thickn
composition, and upstream pressure
NA A pL
and NB ( XA)PL
Figure 4. Permeate purity as a function of pressure
ratio for a feed composition, XA, of 1 mole percent
A (99 mol percent B) and a selectivity of 30.
Winter 2003
s in
When the expressions in Eq. (8) are used to evaluate perme-
ate purity based on yA = NA/(NA+NB), Eq. (7) is obtained. In
this case, the mole fraction of component A in the permeate
is then limited by the ability of the membrane to prevent trans-
port of component B across the membrane; that is to say,
permeate purity is limited by membrane selectivity. This limit
is shown in Figure 3 and also in Figure 4, which presents
permeate mole fraction as a function of pressure ratio. This
limit is reached when the pressure ratio is very high or the
membrane selectivity is low.
uced An example of practical importance is the separation of N2
ieep from CH4 in natural gas wells, a separation that is currently
iced not practiced industrially using membranes because of this
issue.[3] Many natural gas wells are contaminated with nitro-
th a gen, which would need to be removed to bring the heating
S value of the natural gas to pipeline specifications.[31 But poly-
mer membranes rarely have an N2/CH4 selectivity greater than
2. In this case, even for large pressure ratios, the separation
(7) of this gas mixture is not good using membranes. For ex-
ample, when the feed mole fraction of N2 is 2%, the perme-
per- ate mole fraction of N2 is only 3.9%, and at a feed mole frac-
ntly, tion of 20%, the permeate mole fraction is only 33%. There
point is little separation, and most of the low-pressure permeate
per- waste gas is methane. That is (because the separation is poor),
es in there is a large loss of methane into the low-pressure perme-
axi- ate stream with little removal of N2 from the feed gas.
The analytical model described above is applicable to sepa-
(8) ration of binary mixtures only. Moreover, it does not account
for the fact that as the feed gas travels through the hollow
fibers, its composition changes as selective permeation strips
the more permeable components from the feed-gas mixture.
A classic extension of this model, due to Weller and Steiner,
takes this factor into account.[13' This model, however, is no
longer strictly an analytical solution, Moreover, it cannot
simulate the countercurrent flow patterns that are used in-
dustrially in gas-separation modules. As indicated qualita-
tively in Figure 1, typical industrial permeators are designed
to allow the feed gas and permeate gas to flow countercur-
rent to one another. Moreover, this model does not allow for
separation of multicomponent mixtures of gases, which is a
major practical limitation.
The simple model described above has been extended to
account for multicomponent gas separation and to simulate
countercurrent flow.[4,14] In this case, the governing mass bal-
ance equations are coupled differential equations, and no
analytical solution is available. Numerical solutions to this
model are available for public use at
selectivity lmit
Pressure ratio
limit /
0.15 Equation 5
yA //
1 10 100 1000
Feed Pressure/Permeate Pressure, PL/pV
Membranes in ChE Education
The basic notion underlying the multicomponent, counter-
current simulator developed by Coker, et al., is presented in
Figure 5, which shows a diagram of the hollow-fiber module
from Figure 1 divided axially into N slices or stages. In a
typical simulation, N ranges from a few hundred to several
thousand, depending on how rapidly the concentration of the
most permeable species changes with axial position along
the module. Inside each stage of the membrane, mass trans-
fer occurs according to Eq. (1), which is written analogously
for each component.
Using an approach originally developed for staged unit
operations such as distillation,l151 the flow of each compo-
nent from stage to stage is linked by a mass balance. The set
of mass balances for each component on each stage can be
written in the form of a family of tridiagonal matrices, which
are solved using the Thomas algorithm.[161 The mass balances
are nonlinear, so an iterative solution is required. Moreover,
the model allows for pressure in the bore of the hollow fi-
bers to change according to the Hagen-Poiseuille equa-
tion, and this introduces another source of nonlinearity
into the problem. The details of the solution are provided
in the literature.[4]
The simulation is organized to perform analysis calcula-
tions. That is, the membrane permeation characteristics, thick-
ness, fiber inner and outer diameter, fiber length, and num-
ber of fibers are all specified via a graphical user interface,
shown in Figure 6. The user may select bore-side or shell-
side feed. It should be noted that the model is based on plug
flow of gas through the module and fibers, so effects associ-
ated with gas maldistribution in the module are not captured.
The reader is directed to the work of Lipscomb and colleagues
for a more detailed description of these effects.[17
The so-called "pot length" of the fibers must be specified
in the simulation. When membrane fibers are assembled into
a module, the membrane bundle is glued or "potted" on both
ends in epoxy to provide a leak-free connection between the
fiber bundle and the module housing. Gas can travel down
the bore of the fibers in the potted region of the module, which
leads to a pressure drop along the bore of the fibers, but be-
cause the fibers are covered with epoxy, there is no gas trans-
port across the fiber wall. Typical values of pot length would
be 10 cm on each end of a fiber 100 cm long. So, in the case,
the "active" length of a fiber (i.e., the length of fiber that is
active for mass transfer via permeation) would be 100 cm -
2x10 cm (since the fiber is potted on both ends) = 80 cm.
An on-line databank is available with permeation proper-
ties of a few common polymers, such as polysulfone, or the
users can supply their own permeation properties. The feed
pressure, feed flowrate, feed composition, and permeate pres-
sure are specified by the user. With these inputs, the simula-
tor calculates the concentration, flow and pressure profiles in
the module, the residue and permeate composition and
flowrate, and the residue pressure. The concentration and flow
profiles can be viewed as graphs built into the simulator. A
user can establish an account where membrane fiber and mod-
ule data are stored, so that simulation conditions can be en-
tered and stored for later use. Several example simulations
can be downloaded as pdf files.
Two examples of the use of the model are presented. Other
examples are given in the literature.[4,141 The first case involves
a membrane for air drying. The objective is to remove water
from air and produce dry air as the residue stream. In con-
ventional gas-separation membranes, water is typically more
permeable (by a factor of 50 or more) than air gases such as
N2 and 0,, so H2O/N2 and H2O/02 selectivities are very high.
Additionally, the mol fraction of water in air is low. For ex-
ample, air at 400C and 10 atmospheres total pressure (condi-
tions that are common for feeding a gas-separation module
for air separations), the mole fraction of water at saturation is
Feed -Residue
F LN+1 LN Lk+2 Lk+1 Lk Lk-1 L2 L1
Xj,N+1 Xj,N / j,k+2 Xj,k+1 Xj,k x),k-l xj,2 Xjl
Permeate Purge
VN rfij V N-1 Vk+1k ijk 1-1 mj,k| Vk.2 V1 mV,1 V
Yj,N YjN-1/ N Yj,k+ Yj,k j,k- Yk-2 Yo
N k+1 k k-1 1
Figure 5. Schematic of hollow-fiber module divided into N stages. In analogy with labeling conventions used in distillation,
the flow rate of gas leaving the upstream (i.e., residue) side of stage k is labeled Lk, and the flow rate of gas leaving the
downstream (i.e., permeate) side of stage k is labeled V,. The flow rate of gas of component j that permeates from the
upstream to the downstream side of stage k is m k The mole fractions of component j leaving stage k on the upstream and
downstream sides of the membrane are xk and Yjk respectively. Adapted from the literature.4'
Chemical Engineering Education
Membranes in ChE Education
0.72%.[18] These conditions (high selectivity, low feed con-
centration) lead to pressure-ratio-limited separation, and the
amount of water removed from the gas stream is strongly
dependent on the downstream partial pressure of water.
If one could lower the downstream partial pressure of wa-
ter or otherwise accelerate the removal of water from the per-
meate side of the membrane, then the amount of water that
could be removed from the air fed to the module would be
enhanced. In practice, this is most often achieved by recycling
a small fraction of the dry residue gas to the permeate side of
the membrane, as illustrated in Figure 7. This has the benefit of
sweeping or purging the permeate of components (i.e., water)
that have been preferentially removed by the membrane-this
Edit Help
Module Streams
Plots I
-Module Options
Flow Direction i:outer-Ciiutnt
Feed Location Bore-Side
Update I Reset I Simulate
Figure 6. Graphical user interface of the on-line
membrane simulator at
Figure 7. Gas flow configuration in which a portion of the
residue stream, P is returned to the permeate side of the
membrane as a sweep or purge stream to increase the driv-
ing force for removal of water. Adapted from Coker, et al.4'
The feed gas flow rate is F, the permeate flow rate is V, and
the final residue flow rate of product gas is R'.
recycle stream is often called a purge or sweep stream.
An interesting calculation is to determine the effect of
changes in the fraction of the residue stream that is recycled
on the water concentration in the product residue gas, usu-
ally expressed as the dew point of the residue gas. The gen-
eral trend, shown in Figure 8, is that using more gas to purge
the permeate results in better water removal from the residue
(i.e., lower dew point). This results in a smaller amount of
the dry product gas being available for use, however, so there
is a trade-off between gas dryness and production rate.
Other problems that could be envisioned include replacing
the polymer (which is polysulfone in the case of the results
presented in Figure 8) with other polymers having different
selectivities for water and determining the impact of separa-
tion factor on the fraction of residue purge gas needed to
achieve a given dewpoint using a standard-size module. A
good first approximation of the reduction in the amount of
residue gas available for use is the flowrate of residue gas in
the absence of purging times the fraction of residue gas re-
moved for purging. This rule-of-thumb is not exact, how-
2 3
Purge (% of residue)
Figure 8. The effect of permeate purge on the dew point of
the residue gas obtained by feeding air to a module at 400C
and 10 atm. The permeate pressure is 1 atm, and the per-
meance of the membrane to water is 1,000x10-6 cm3(STP)/
(cm2 s cmHg). Standard temperature and pressure for per-
meance, like permeability, are O0C and 1 atm. The feed air
flowrate is 8,000 ft3(60 F, 1 atm)/hr. Specifying gas flowrates
at 600F and 1 atm (rather than at STP) is standard in some
process simulators. Other parameters (number and length
of fibers, permeance to all other components, etc.) are given
in the literature.4' The water mole fraction data in the resi-
due stream were converted to dew points using a web-based
psychometric calculator at
Winter 2003
Membranes in ChE Education
ever, and it is of interest to allow students to figure out
what other factors (i.e., driving force for other compo-
nents in the feed gas, etc.) might also influence the resi-
due-gas flow rate for such problems.
The second example is hydrogen recovery from a
hydrotreatment unit in a refinery. In hydrotreatment, petro-
leum intermediates are contacted with hydrogen to reduce
sulfur, nitrogen, metals, asphaltene, and carbon residue con-
tent. This process requires substantial amounts of hydrogen
gas, and much of the excess hydrogen can be recycled. Mem-
branes are often used to purify the recycled hydrogen. The
major impurities are light hydrocarbons. A typical stream
might contain 65 mol % H,, 21 mol % CH4, and the balance
will be other hydrocarbons, such as C2 and C3. 41
In the conventional membranes used in this process, hy-
drogen is by far the most permeable component in the mix-
ture, followed by methane and then by the other hydrocar-
bons. H/CH4 selectivity values can be of the order of several
hundred in commercially used membrane materials.
The objective of this separation is to generate highly puri-
fied hydrogen for recycle to the process. Because this is a
high-pressure process and because the H2 product appears in
the permeate stream, permeate pressure must be kept as close
to the feed pressure as possible to minimize recompression
costs. So the pressure ratio is typically not very high. At fixed
feed and permeate pressure, the more feed gas that is allowed
to permeate through the membrane (by having lower flow
rates or larger membrane area, or both), the higher is the re-
covery of hydrogen in the permeate, but the purity of the per-
meate stream is lower. So it is instructive to construct so-
called purity/recovery curves for this separation.
One example is shown in Figure 9. The curves in this fig-
ure were generated by varying the feed flow rate to a module
and noting the permeate H2 purity and flowrate. That is, at
very high flow rates, one can produce relatively pure H,,
but the amount of H, recovered in the permeate stream is very
low. At the opposite extreme, at very low flow rates, most of
the H2 and CH2 gas permeates through the membrane, so H2
recovery is very high, but the purity is quite low. The ideal situ-
ation would be to have both high recovery and high purity, but
these factors typically work against one another.
Figure 9 also illustrates the impact of pressure ratio on the
results. Two pressure scenarios are presented. In both cases,
the difference between feed and permeate pressure is identi-
cal. The case with lower feed pressure and higher pressure
ratio yields superior membrane separation performance, how-
ever. Such sensitivity of purity/recovery curves is an indica-
tion that the separation is being performed in a pressure-ra-
tio-limited regime.
Other interesting problems include calculating purity/re-
covery curves for other polymers to understand how the choice
of polymer material influences the separation. In this regard,
there is a large database of permeability values in the Poly-
mer Handbook. 119] Also, the hydrotreater example as well as
the air separation example involve multicomponent mixtures,
and one could track the distribution of each of the other com-
ponents as polymer selectivity, flowrate, feed, or permeate
pressure changes. We have used the analytical simulator as
well as the Internet version of the simulator in the senior-
level design course, and it should be suitable for an under-
graduate unit operations course as well.
The Internet simulator allows exploration of the effects of
operating the module with bore-side feed or shell-side feed.
It is of interest to compare the same separation (e.g., air sepa-
ration) using bore- and shell-side feed and to explain differ-
ences in the separation results. Basically, when the membrane
module is fed on the bore side, the permeate gas is collected
on the shell side of the module and experiences essentially no
pressure drop traveling from one end of the module to the other.
There is a slight decrease in pressure along the bore of the fi-
bers, but this decrease is typically small relative to the feed
pressure and has a small impact on separation performance.
With shell-side feed, however, the permeate gas flows in
the bore of the fibers, and pressures are much lower in the
permeate stream than in the residue stream. Small pressure
changes along the bore of the fibers, estimated according to
the Hagen-Poisseulle relation, can lead to decreases in sepa-
Figure 9. Effect of pressure ratio on H, purity and recovery
in a hydrotreater application. The membrane properties
and module conditions as well as the feed composition are
given in Coker, et al.4' H, recovery in the permeate is the
molar flowrate of hydrogen in the permeate divided by the
molar flowrate of hydrogen fed to the module.
Chemical Engineering Education
100 -----------i
90 L =42.4 bar
p=7.9 bar --
o R=5.3
SpL = 76.9 bar
75 pV = 42.4 bar
0 20 40 60 80 100
H2 Recovery (%)
Membranes in ChE Education
ration efficiency (lower product purity, less gas permeated
per unit area of membrane) relative to bore-side feed.
Additionally, the Internet simulator allows connection of
the outlet stream (e.g., residue) from one module as the feed
stream to a second module. This feature allows exploration
of the effect of connecting modules in series on product gas
purity and flowrate. Similarly, the Internet simulator is orga-
nized to allow the product gas from one module to be re-
cycled to the feed side of a previous module. Downloadable
example files illustrate the use of these features.
If students have access to process simulation tools, com-
parison with other separation technologies can be interest-
ing. For example, large-scale air separation is currently per-
formed using cryogenic distillation. If one requires only 98%
nitrogen for an application (rather than pure nitrogen), cur-
rent membranes with an 02/N2 selectivity of 7 or 8 can readily
produce gas at this purity level.
An interesting calculation is to compare capital and oper-
ating costs for a cryogenic air-separation plant and a mem-
brane-separation plant to produce nitrogen at such purities.
Some variables that could be studied include required prod-
uct gas flowrate, purity, and pressure. For such rough eco-
nomic analyses, the installed costs of membranes have been
estimated as $54/m2 of membrane surface area.t201 For a mem-
brane process, the process operating cost is the energy input
required to compress air from one atmosphere to the 10-15
atmosphere range normally used for air-separation membranes.
Therefore, the higher the purity of the product required, the
lower the product recovery and the greater the energy waste
due to loss of nitrogen into the low-pressure permeate stream.
Currently, membrane processes do not scale as well as con-
ventional separation technologies. That is, to double the
amount of gas being processed by a membrane plant, one
needs to install twice as much membrane area, so the capital
cost scales linearly with gas flowrate. Processes depending
on column-based tc'hniiin i%, such as distillation, exhibit
much slower increases in capital costs with increasing flow
rate, and this factor has led to membranes being used for lower
flowrate applications and distillation being used for high-
flowrate situations.E21 One could also explore the effect of new
membrane materials development on such a separation. If
the 02/N2 selectivity of today's membranes could be raised
from 7 to 14, how would this influence the capital and oper-
ating costs associated with nitrogen production?
We have described some basic issues related to the use of
polymeric membranes as separation agents, and we have pro-
vided two types of tools-one analytical and one Internet-
based-to assist students in gaining intuition into the perfor-
mance of gas separation membranes. Examples provide some
basis for homework or class project activities. Some extensions
to the problems discussed in this manuscript would have a sig-
nificant design component, which might increase their utility.
1. Zolandz, R.R., and G.K. I ....... "Gas Permeation" in Membrane
Handbook, W.S.W. Ho and K.K. Sirkar, eds, Van Nostrand Reinhold,
New York, NY, p. 17 (1992)
2. Ghosal, K., and B.D. Freeman, "Gas Separation Using Polymer Mem-
branes: An Overview," Polym. Adv. Tech., 5(11), 673 (1994)
3. Baker, R.W., Membrane Technology andApplications, McGraw-Hill
Book Co., New York, NY (2000)
4. Coker, D.T., B.D. Freeman, and G.K. l ....... "Modeling Multi-
component Gas Separation Using Hollow-Fiber Membrane
Contactors," AIChE J., 44(6), 1289 (1998)
5. Graham. T., "On the Absorption and Dialytic Separation of Gases by
Colloid Septa. Part I. Action of a Septum of Caoutchouc," I .' II .
32 401 (1866)
6. Graham, T., "On the Absorption and Dialytic Separation of Gases by
Colloid Septa. Part I. Action of a Septum of Caoutchouc," J. Mem-
brane Sci., 100, 27 (1995)
7. Michaels, A.S., "A Sixty-Year Love Affair with Membranes: Recol-
lections of Richard M. Barrer, Edited and Annotated by Alan S.
Michaels," J. Membrane Sci., 109(1), 1 (1996)
8. Robeson, L.M., "Correlation of Separation Factor Versus Permeability
for Polymeric Membranes, J. Membrane Sci., 62, 165 (1991)
9. Freeman, B.D., "Basis of Permeability/Selectivity Tradeoff Relations
in Polymeric Gas Separation Membranes," Macromolecules, 32, 375
10. Baker, R.W., and J.G. Wijmans, "Membrane Separation of Organic
Vapors from Gas Streams," in Polymeric Gas Separation Membranes,
D.R. Paul and Y.P. Yampol'skii, eds., CRC Press, Boca Raton, FL
11. Freeman, B.D., and I. Pinnau, "Separation of Gases Usoing Solubil-
ity-Selective Polymers," Trends in Poly. Sci., 5(5), 167 (1997)
12. Freeman, B.D., and I. Pinnau, "Polymeric Materials for Gas Separa-
tions," in Polymeric Membranes for Gas and Vapor Separations:
( ,... .... and Materials Science, ACS Symposium Series Number
733, B.D. Freeman and I. Pinnau, eds., American Chemical Society,
Washington, DC (1999)
13. Weller, S., and W.A. Steiner, "Fractional Permeation Through Mem-
branes," Chem. Eng. Prog., 46(11), 585 (1950)
14. Coker, D.T., T. Allen, B.D. Freeman, and G.K. Fl ....
"Nonisothermal Model for Gas Separation Hollow-Fiber Mem-
branes," AIChE J., 45(7), 1451 (1999)
15. Stichlmair, J., and J.R. Fair, Distillation: Principles and Practices,
John Wiley & Sons, New York, NY (1998)
16. King, C.J., Separation Processes, McGraw-Hill, New York, NY
17. Lemanski, J., and G.G. Lipscomb, "Effect of Shell-Side Flows on
Hollow-Fiber Membrane Device Performance," AIChE J., 41(10),
2322 (1995)
18. Felder, R.M., and R.W. Rousseau, Elementary Principles of Chemi-
cal Processes, John Wiley & Sons, New York, NY (1986)
19. Pauly, S., "Permeability and Diffusion Data," in Polymer Handbook,
4th ed., J. Brandrup, E.H. Immergut, and E.A. Grulke, eds., John
Wiley and Sons, New York, NY (1999)
20. Baker, R.W., "Future Directions of Membrane Gas Separation Tech-
nology," Ind. Eng. Chem. Res., 41, 1393 (2002) 1
Winter 2003
Membranes in ChE Education
In The Curriculum
Rowan University Glassboro, NJ 08028
Educational initiatives are crucial to the continued tech-
nical growth and wide-scale commercialization of
membrane processes. This paper discusses innovative
use of membrane tcilhiiil .1 .:, in a project-oriented curricu-
lum, building on the prior work of Slater, et al., who devel-
oped membrane experiments in a conventional chemical engi-
neering laboratory setting.[1-7 At Rowan University, the authors
have integrated membrane technology throughout the engineer-
ing curriculum and involved student teams in a unique
multidisciplinary laboratory project experience-the clinics.[8]
Chemical engineering education is traditionally a process-
or systems-oriented curriculum, producing graduates who can
apply their process expertise in many industries. Some ver-
satility has been lost over the last several decades due to the
overwhelming emphasis on unit operations and design prob-
lems pertaining to the petroleum industry. Separation-pro-
cess needs exist both in the traditional process industries and
in emerging areas such as biochemical engineering, specialty
chemical manufacture, hazardous waste management, food
and beverage processing, microelectronics production, and
biomedical engineering.[9,10] Growth in these technologies will
depend on engineers who are well-educated in the field and
have a working knowledge of membrane applications in these
areas. Education should have a multidisciplinary perspective
where students from other fields can apply their expertise to
solving membrane-related process problems.[111
The need for more instruction in membrane tichi l 11 ,i and
in many other advanced separation processes has been previ-
ously addressed. 12,13] Many schools have graduate courses in
advanced mass transfer and some have courses in membrane
tcclil II -.,, but introducing it to the undergraduate chemical
engineering curriculum is rare. A 1995 studyE14" revealed that
only 2.6% of lecture time in an undergraduate mass transfer
course is on the subject of membrane processes. ABET's Cri-
teria 2000 specifies many of the outcomes that are included
in this curriculum development: an ability to function in multi-
disciplinary teams, designing and conducting experiments,
understanding safety and environmental issues, analyzing and
interpreting data, and using modem engineering tools.J1
Rowan University is a comprehensive regional state uni-
versity with six colleges: Business Administration, Commu-
nications, Education, Engineering, Fine and Performing Arts,
and Liberal Arts and Sciences. The College of Engineering
was initiated using a major gift in 1992 from the Rowan Foun-
dation.[161 The engineering program is taking a leadership role
by using innovative methods of teaching and learning, as rec-
ommended by ASEE,1171 to prepare students for entry into a
Stephanie Farrell is Associate Professor of Chemical Engineering at
Rowan University. She received her BS in 1986 from the University of
Pennsylvania, her MS in 1992 from Stevens Institute of Technology, and
her PhD in 1996 from New Jersey Institute of Technology Her teaching
and research interests are in controlled drug delivery and biomedical en-
Robert Hesketh is Professor of Chemical Engineering at Rowan Univer-
sity. He received his BS in 1982 from the University of Illinois and his PhD
from the University of Delaware in 1987. His research is in the areas of
reaction engineering, novel separations, and green engineering.
Mariano J. Savelski is Assistant Professor of Chemical Engineering at
Rowan University He received his BS in 1991 from the University of Buenos
Aires, his ME in 1994 from the University of Tulsa, and his PhD in 1999
from the University of Oklahoma. His technical research is in the area of
process design and optimization with over seven years of industrial expe-
Kevin Dahm is Assistant Professor of Chemical Engineering at Rowan
University He received his PhD in 1998 from Massachusetts Institute of
Technology His primary technical expertise is in chemical kinetics and
mechanisms, and his recent educational scholarship focuses on incorpo-
rating computing and simulation into the curriculum.
C. Stewart Slater is Professor and Chair of the Department of Chemical
Engineering at Rowan University. He received his BS, MS, and PhD from
Rutgers University. His research and teaching interests are in separation
and purification technology, laboratory development, and investigating
novel processes for fields such as bio/pharmaceutical/food engineering
and specialty chemical manufacture.
Copyright ChE Division ofASEE 2003
Chemical Engineering Education
Membranes in ChE Education
rapidly changing and highly competitive marketplace.
To meet these objectives, the four engineering programs of
chemical, civil/environmental, electrical/computer, and me-
chanical engineering have a common engineering "clinic"
throughout their programs of study. At the freshman level,
students conduct engineering measurements and reverse en-
gineer a process. The sophomore engineering clinic is com-
munications-intensive and also introduces students to the de-
sign process of each discipline
and to related topics of product/
process function. The junior and
senior clinics provide an oppor-
tunity for the most ambitious
part of our project-intensive cur-
riculum-team projects employ-
ing modern technologies that tie
together many engineering and
scientific principles. Institutions
that have similarly named engi-
neering "clinics" are Harvey
Mudd College and California
State Polytechnic University,
Pomona.['18 Our flexible clinic
model allows departmental and Figure 1. Student coi
interdepartmental initiatives separation study of vegt
that satisfy programmatic and
faculty/student/university de-
velopmental needs. These clinics also provide an opportu-
nity for industrial involvement in the sponsoring and
mentoring of projects.[8]
This ambitious program takes a leading-edge tc'li 11'l -,
such as membrane processes and uses it as the focal point of
curricular innovation in our College of Engineering. We have
involved teams of engineering students in process research,
development, design, and analysis of experimental systems.
Students have gained an understanding of the fundamental
aspects of membrane tcchlin l .1.,, process design, and appli-
cation to new and emerging fields. Our curriculum is consid-
ered to be project-intensive and industrially oriented, with a
strong hands-on component. One of the most important at-
tributes obtained through this type of activity is a focus on
"soft skills." Students working on designing, fabricating, and
starting up an experimental system have a much richer envi-
ronment of interacting in a team setting. Team dynamics im-
prove and management skills are incorporated into the project.
Students' informal and formal communication skills are also
enhanced. Our Chemical Engineering Industrial Advisory
Board has endorsed this concept from the technical side and
in preparing students in other areas such as teamwork and
communication skills.
The major focus of the innovative aspects of this project is
the junior and senior engineering clinics where
multidisciplinary teams (3-4 students/team) work on open-
ended projects in various areas, many linked to industry or a
faculty grant from a state or federal agency. These projects
emanate from a particular discipline, are led by that
department's faculty, and typically involve an industrial men-
tor. The teams are matched by the fac-
ulty Project Manager (PM) to achieve
the best results in the individual
projects. Teams may combine various
fields of expertise within a classic dis-
cipline (environmental, water re-
sources, and structural in CEE; bio-
chemical and polymer in ChE; science
with engineering in Chem and ChE)
as recommended by the recent report
of the NRC.e8] In some cases, student
"consultants" from other disciplines
assist on a limited basis, representing
the realistic role found in industry. Stu-
dents are required to produce a writ-
ting membrane ten report or paper/j journal publication
e product stream, and present an oral report at the end
of the semester.
Several selected membrane-oriented clinic projects are sum-
marized below. A full listing of Rowan clinic projects can be
obtained at
Advanced Vegetable Processing Technology
In a project sponsored by Campbell Soup Company, a team
of students researched cutting-edge technologies, such as
novel membrane processes, for processing soups and juices.
The multidisciplinary team consisted of two undergraduate
chemical engineering students, one civil engineering student,
and one biology student. In addition, one master's student
served as PM. Campbell Soup has its corporate R&D facili-
ties in nearby Camden, New Jersey, facilitating frequent
progress meetings with the project sponsors.
Through this project, students investigated advanced mem-
brane separation techniques as well as enzymatic, thermal,
and physical/mechanical treatment techniques applied to veg-
etable processing. Their responsibility included HAZOP
analysis, project planning, budget formulation and manage-
ment, literature and patent reviews, experimental design, and
development of a proposal for a second phase of the clinic
project (see Figure 1). In addition to the engineering exper-
tise the students acquired through this project, they gained
Winter 2003
Membranes in ChE Education
familiarity with Food and Drug Administration regulations,
good manufacturing practices, and labeling requirements.
Engineers from Campbell's demonstrated a high level of
commitment to the project by attending monthly progress
meetings where the students gave oral presentations on their
progress. This was followed by brainstorming and discus-
sion sessions where the industrial representatives and faculty
refocused and fine-tuned the project. This industrial interac-
tion helped maintain a high level of motivation among the
students and maintained the focus and a fast pace of produc-
tivity. In addition to the progress meetings, the student team
also conducted a "lunch-and-leam" seminar at Campbell's to
share their research with engineers, scientists, and marketing
representatives from the company. The enthusiastic response
of the audience at Campbell's reaffirmed the industrial rel-
evance and impact of the team's clinic research project.
Campbell Soup Company is a strong supporter of our pro-
gram, not only by supporting the clinic project mentioned
above, but also by employing both full-time and internship
students from our program. In the summer following the veg-
etable processing project, two undergraduate students ac-
cepted summer internships at Campbell's. The students had
the rewarding experience of successfully implementing two
of the technologies developed at Rowan into Campbell's pro-
cessing facilities in California and New Jersey.
Metals Purification Processes
Various metals purification projects have been sponsored
by Johnson Matthey, Inc. A precious metals "refinery" is op-
erated at West Deptford, New Jersey, which is less than ten
minutes from our campus. This close proximity facilitates
numerous interactions and projects that we have with Johnson
Matthey. The company has sponsored three years of engi-
neering clinic projects with the objective of investigating
novel techniques that have the potential to replace current
"traditional" refinery process units.
At the refinery, precious metals such as Pt, Pd, and Rh are
purified from feed streams containing many unwanted metal
species and other impurities. The feed streams are made up
of spent catalysts from which precious metals are recovered
and recycled to feed stream from mines. In the refinery, there
are many dissolution, selective-precipitation, and filtration
steps. Using innovative membrane processes, the plant ca-
pacity, product purity, and processing costs have the poten-
tial to be improved. In essence, students have an opportunity
in the engineering clinic to conduct engineering projects that
are equivalent in scope to those done by engineers in the plant.
Our most successful project resulted in Johnson Matthey add-
ing several new processing units to their refinery.
One of the Johnson Matthey projects involving membranes
was electrodialysis process development for separation of a
precious metal chloride salt solution that was contaminated
with unwanted acids and salts. The traditional separation and
purification steps used in the production of these metal com-
pound solutions include multiple precipitation and dilution steps
that are time-consuming and labor intensive and result in a sig-
nificant loss of product. Development of an alternative separa-
tion and purification technique was the aim of this project.
The specific objectives of the projects were
To design and build an electrodialysis unit for the separa-
tion and pu'rii iatrin of the desired process stream
To investigate the performance of electrodialysis in the
removal of the salt contaminant from the product on a
laboratory scale
Figure 2. (a) Electrodialysis process system used in pre-
cious metals separation clinic project. (b) Electrodialysis
cell used in the process system.
Chemical Engineering Education
Membranes in ChE Education
To perform an economic analysis of the proposed process in
comparison with the traditional technique
To scale up the process to pilot scale
The potential outcomes include reduction of operating costs,
increased product yield, and increased product output by an
order of magnitude.
The first phase of the project involved the design and as-
sembly of a laboratory-scale electrodialysis unit and prelimi-
nary benchmark testing (see Figures 2a and 2b). The second
phase of the project involved investigation of process param-
eters on the yield and selectivity of the product. Typical stu-
dent results for the removal of an ammonium chloride con-
taminant are shown in Figure 3. Subsequent experiments were
conducted to investigate the impact of size-selective and
charge-selective ion exchange membranes on the retention
of desired product. Based on the experimental results, the pro-
cess was scaled up to pilot scale and an economic investigation
was conducted to examine the trade-off between capital costs
and operating costs as well as the overall economic feasibility
of the process. The process demonstrates the potential for re-
duced operating costs and increased product yield and selectiv-
ity and is currently being evaluated
further by Johnson Matthey. Ammonium Chloride RE
Johnson Matthey has provided
significant support to our chemical 1
engineering department and was a 09
"charter member" of the PRIDE 08
program (Partners with Rowan in 7 S 0
Developing Engineers). They have 06
employed Rowan chemical engi- 5
neering students both as interns and 0
as permanent employees. o3
Ceramic Membrane
Reactor System 0
In this project, a ceramic mem- 0 10 20 30
brane reactor has been designed and
constructed by a team of three Figure 3. Typical stude
undergraduate students. The reactor, voltage on the remove
contaminant from a pr
used for the production of ethylene contaminantfom a
from the dehydrogenation of
ethane, is modeled after that of T. S Gas
Champagnie and colleagues.[19,20] F P uartReaorwth
Equilibrium as a reaction constraint camincmembrne
and methods to shift equilibrium in
favor of desired products are taught
in chemistry and chemical reaction Pn d
and Ethane
engineering courses, but a student
rarely uses these techniques in ex-
periments. This reactor, when in- Figure 4. Process flo
tegrated into an undergraduate membrane
Winter 2003
Time (m
'nt do
w di
course on reaction engineering, demonstrates the advantages
of using advanced membrane tc'l 1 i1h ,I- in combination with
reaction kinetics. The basic operational principle behind the
ceramic membrane reactor is that removal of a reaction prod-
uct (hydrogen) through the membrane drives the reaction
beyond the equilibrium constraints set by the feed composi-
tion and reaction temperature and pressure.
Ethane dehydrogenation was chosen as an example for a
number of reasons. The most compelling was that ethylene is
a chemical that is familiar to the students, and at over 50
billion pounds per year it is one of the top five chemicals in
annual worldwide sales, -'iim.kil-i the problem recognizable
as a practical one. Another point is that the reaction is very
endothermic, and temperatures in excess of 1000 K are needed
for the reaction to approach completion. The student team
first explored the feasibility of the membrane reactor con-
cept through modeling studies, using the assumption that
Knudsen diffusion describes the operation of the membrane.
Students modeled the system in HYSYS, using an alternat-
ing series of equilibrium reactors and separators to approxi-
mate a simultaneous reaction/separation. These studies sug-
gest that the membrane reactor
Using Electrdialysis should be able to achieve a given
I Using Electrodialysis
conversion at temperatures hun-
dreds of degrees Kelvin lower than
_--8 v needed in a conventional plug flow
-- ov reactor of the same volume. Stu-
dents readily appreciate the desir-
ability of operating at lower tem-
peratures, both in terms of cost and
safety. Thus, this project integrates
many process design concepts. The
process flow diagram of the system
is shown in Figure 4.
The reactor consists of a quartz
50 60 70 80 shell surrounding a platinum-
coated ceramic membrane tube.
tta showing the effect of The ceramic membrane was ob-
n ammonium chloride trained from US Filter and has a
is metal feed solution.
____ ______ pore size of 5nm. Students worked
in conjunction with Johnson
V tion Matthey and students and faculty
from the Department of Chemis-
S try to devise and carry out a work-
GCMS able plan for coating the catalyst
tubes using a choroplatinic acid
process. The reactant and product
concentrations are measured using
an HP 6890 GC/MS. The only
agram of the ceramic other equipment required included
tor project. Fisher heating tapes, temperature
Membranes in ChE Education
controllers, and mass flow meters. The total cost of the sys-
tem, including reactor and catalyst (but excluding the GC/
MS, which was previously on site) was less than $2000.
In addition to illustrating important chemical engineering
concepts, this setup also demonstrates some interesting prac-
tical issues to the students. One point is that although "iso-
thermal reactors" are routinely posed in problems and mod-
eled by undergraduate students, students do not necessarily
appreciate the difficulty involved in carrying out a reaction
that is truly isothermal. In this case, the reaction is very en-
dothermic and is carried out well above room temperature-
both factors that complicate maintaining an isothermal reac-
tion. Another issue is the difficulty of creating gas-tight seals
when working with materials (such as the ceramic membrane)
that expand significantly with increasing temperature. Work-
ing with the chemical engineering lab technician, the students
devised a procedure for sealing the reactor after it had al-
ready been brought to temperature. After the experiment is
complete, the temperature is maintained and the system is
purged with nitrogen before the seal is broken. Throughout
the "design-and-build" phase of this project, the student team
worked with various technicians in the college, from machin-
ing parts to electronic controls.
Of significant importance to chemical engineering educa-
tors is satisfying the new EC2000 requirements of ABET, the
most vexing of which are the "soft skills" represented by
Criterion 3, f-i. The projects mentioned above can effectively
satisfy these criteria, and the outcomes can be effectively as-
sessed in a sustainable way. Our program has firsthand expe-
rience with this and has used various assessment instruments
to verify the results. Table 1 indicates how the membrane
projects meet the EC2000 requirements.
ABET Criterion 3 (a-k) in the Membrane Projects
Membrane Proiect Implementation
a Apply math, science and engineering
b Design/conduct experiments and analyze data
c Design process
d Function of multidisciplinary teams
e Formulate/solve engineering problems
f Professional and ethical responsibility
g Communicate effectively
h Impact of engineering on society
i Life-long learning
j Contemporary issues
k Modern engineering tools
1 University-specific criteria: Undergraduate
research/emerging fields
* Projects apply basic mathematics such as in calculating fluxes. Chemistry is applied in understand-
ing the nature of the solutions to be separated and membrane structure.
* Chemical engineering is applied from membrane mass transfer to process transport analysis.
* The membrane projects involve experimentation-students must design the studies to be conducted
and collect, correlate, and analyze their experimental results. Modern software tools are used.
* In most of the projects, the students design the bench-scale process unit to be used. In some of the
projects, students present a final scale-up "paper" design for plant implementation that may include
multiple sequential processes.
* Inherent in the Rowan clinic program is that students perform the project in multidisciplinary or
multifunctional teams. Each students has a role simulating actual industrial membrane project
*While many of the projects have their original problem statements formulated by industry, the
student teams may refine the problem and obviously will be the ones solving the process problem.
* Students learn about many aspects, such as safe handling and disposal of chemicals, safety, and
process responsibility.
* All students must give an oral report and submit a final written report at the end of each semester.
* Additionally, students engage in meetings with industrial representatives and present/defend their
* Senior Clinic counts as the "writing intensive" part of our curriculum.
* Through these projects, students learn the impact of membrane technology on society, such as in
waste management, water reuse, purification of pharmaceuticals, and energy conservation.
* The membrane projects have stimulated students to consider continuing their education, and many
of them have gone on to pursue Masters or Doctoral degrees.
* Membrane processes are used in many contemporary problems facing society, such as environmen-
tal management, health care, and the production of potable water.
* Membranes are indeed a modern engineering process and therefore satisfies this broad category.
Other modern engineering tools used in the membrane projects include analytical instrumentation,
computer data acquisition/control, and computer hardware and software.
* A unique criteria added at Rowan University was to engage undergraduate students in research in
emerging fields, which these membrane projects effectively do.
Chemical Engineering Education
Membranes in ChE Education
Student feedback from the clinic projects mentioned above
has been extremely positive. The experiential outcomes of
our clinic projects have been assessed in several ways. We
have conducted student focus groups, and representative com-
ments from students on the membrane projects include: "The
clinics gave me industrial hands-on experience that has helped
me understand chemical engineering better." "I liked work-
ing in a team and having an industrial focus to my project."
"I learned project management and research skills through
the clinic and was more excited because it was a real indus-
trial problem our group was solving.
Senior exit interviews have also been conducted. The re-
sponses from several questions related to the curriculum de-
velopment described in this paper from twelve graduating
seniors involved in the projects are:
In the area of experimental research methods, can you write
literature reviews, design experiments, and present research results?
91.7% Yes; 8.3% Maybe
In the laboratory, can you make appropriate measurements, record
information in a meaningful format, perform necessary analysis, and
convey an interpretation of the results to an appropriate audience?
91.7% Yes; 8.3% Maybe
Can you select a process component based on chemical engineering
principles that is of an appropriate size and type to meet desired
needs? 91.7% Yes; 8.3% Maybe
Can you conduct experiments in a safe manner and understand safe
practices and hazards? 100% Yes
Can you interact synergistically with students from other disciplines,
backgrounds, and cultures to achieve a common goal? 100% Yes
In Classroom, design, and laboratory activities, can you identify
known variables, formulate key relationships between them, solve
engineering problems, and assess the reasonableness of their
problem solutions? 100% Yes
Can you write effective documents, including memos, e-mails,
business letters, technical reports, operations manuals, and
descriptions of systems, processes, or components? 100% Yes
Can you give effective oral presentations? 100% Yes
Are the Junior/Senior Clinic projects a valuable experience in your
preparation as a chemical engineer? 100% Yes
Through the support of NSF and several industries,
multidisciplinary student projects were initiated that chal-
lenged student teams to solve realistic industrial problems.
These projects are versatile and can be modified slightly for
use as laboratory experiments to provide the curricular de-
velopment. The clinic projects help the forward-looking
EC2000 curriculum by providing a focal point for ability to
function in multidisciplinary teams, ability to design and con-
duct experiments, understand safety and environmental is-
sues, analyze and interpret data, and use modern engineering
tools. In a primarily undergraduate institution such as Rowan
University, these projects provide an opportunity for faculty/
student scholarship.
Support for the industrial projects mentioned above has been pro-
vided by the sponsors, Johnson Matthey, Inc., and Campbell Soup
Company, to which our department is grateful. Some support for
membrane equipment purchased for these projects was provided by
a grant (DUE-9850535) from the National Science Foundation
through the Division for Undergraduate Education.
1. Slater, C.S., "A Manually Operated Reverse Osmosis Experiment," Int.
J. Eng. Ed., 10, 195 (1994)
2. Slater,C.S.,"Educationon\! ., .. 1... .I. ,. I .. ,,....."inMem-
brane Processes in Separation andt I .: K.W. Boddeker and
J.G. Crespo, eds., Kluwer Academic Publishers, Boston MA (1994)
3. Slater, C.S., and H.C. Hollein, "Educational Initiatives in Teaching Mem-
brane Technology," Desalination, 90, 291 (1993)
4. Slater, C.S., C. Vega, and M. Boegel, "Experiments in Gas Permeation
Membrane Processes," Int. J. Eng. Ed., 7, 368 (1992)
5. Slater, C.S., and J.D. Paccione, "A Reverse Osmosis System for an Ad-
vanced Separation Process Laboratory," ( ....- -i .- i 22,138 (1987)
6. Slater, C.S., H.C. Hollein, P.O. Antonecchia, L.S. Mazzella, and J.D.
Paccione, "Laboratory Experiences in Membrane Separation Processes,"
Int. J. Eng. Ed., 5, 369 (1989)
7. Hollein, H.C., C.S. Slater, R.L. D'Aquino, and A.L. Witt, "Bioseparation
via Cross Flow Membrane Filtration," Chem. Eng. Ed., 29, 86 (1995)
8. Newell, J.A., S. Farrell, R.P. Hesketh, C.S. Slater, "Introducing Emerg-
ing Technologies into the Curriculum Through a Multidisciplinary Re-
search Experience," Chem. Eng. Ed., 35, 296 (2001)
9. Garside, J., and S. Furusaki, The I ... World of Chemical Engi-
neering, Gordon and Breach Science Publishers, Amsterdam, The Neth-
erlands (1994)
10. Hegedus, L.L. (National Research Council, Committee on Critical Tech-
nologies), Critical Technologies: The Role of( ,... .-- :. and Chemical
Engineering, National Academy Press, Washington, DC (1992)
11. American Chemical Soc. '. .... .... ... ii.. ..11 hemicalEngineers,
The Chemical Manufacturers Association, The Council for Chemical
Research, The Synthetic Organic Chemical Manufacturers Association,
Technology Vision 2020, American Chemical Society, Washington, DC
12. Wankat, PC., R.P Hesketh, K.H. Schulz, and C.S. Slater "Separations:
What to Teach Undergraduates," Chem. Eng. Ed., 28, 12 (1994)
13. King, C.J. (National Research Council, Committee on Separation Sci-
... .... I I ..i,,.. Separationand I ..: Critical Needs and
Opportunities, National Academy Press, Washington, DC (1987)
14. Griffith, J.D., "The Teaching of Undergraduate Mass Transfer," AIChE
Annual Meeting Paper 245a, Miami Beach, FL (1995)
15. Engineering Accreditation Commission of the Accreditation Board for
Engineering -,. I I ..i..i.... "Engineering Criteria 2000," Dec. (1995)
16. Rowan, H.M., and J.C. Smith, The Fire Within, Penton Publishers, Cleve-
land, OH (1995)
17. "Engineering Education for a Changing World," joint project report by
the Engineering Deans Council and Corporate Roundtable of the Ameri-
can Society for Engineering Education, Washington, DC (1994)
18. Annon., "The Engineers Are In! The Cal Poly Pomona Engineering In-
terdisciplinary Clinic," Chem. Eng. Prog., S5, November (1995)
19. Champagnie, A.M., T.T. Tsotsis, R.G. Minet, and I.A. Webster, "A High
Temperature Catalytic Membrane Reactor for Ethane Dehydrogenation,"
Chem. Eng. Sci., 45, 2423 (1990)
20. Champagnie, A.M., T.T. Tsotsis, R.G. Minet, and E. Wagner, "The Study
of Ethane Dehydrogenation in a Catalytic Membrane Reactor," J Catal.,
134, 713 (1992)
21. http://www.chemexpo.com/news/ 1
Winter 2003
Membranes in ChE Education
A Simple Analysis For
University of Minnesota Duluth Duluth, MN 55812
embrane applications for gas separations have made rapid ad-
vances over the past decde.J11 In some cases, membrane tech-
nologies have been used to enhance or replace more traditional
methods of gas purification. The need for educating undergraduate chemi-
cal engineering students about membrane-based separations has not gone
unnoticed. Newer editions of popular separations textbooks have added
chapters on membranes with sections on gas permeation.[2-4]
Earlier, Davis and Sandall"51 described an undergraduate laboratory mem-
brane experiment and analysis for separating the components of air. It
remains relevant today as one approach to providing students with hands-
on experience with this important tc%~'ihn .1 The experimental objec-
tives included an inverse mass transfer analysis of experimental data for
key membrane transport parameters. The original analysis involved solv-
ing a set of differential species balances and fitting the results to experi-
mental data by iterative, trial-and-error techniques. They found that the
numerical methods required to implement their analysis were beyond the
scope of the undergraduate chemical engineering laboratory experience.
Consequently, they provided students with True BASIC programs that
were used to solve the model equations. Unfortunately, the programs were
limited to the specific membrane configuration in the laboratory. Stu-
dents were unable to explore alternative designs using the validated mod-
els without modifying the programs. In the meantime, several popular,
modem, computational software applications (such as Excel, Mathcad,
Matlab, or Polymath) have emerged that provide readily accessible tools Figure 1. Prism hollow-fiber membrane
for solving complex problems that involve nonlinear algebraic and dif- apparatus.
ferential equations. The drawbacks in the original analysis, along with
developments in computational tools, have led to a simpler alternative RichardA. Davis isAssociate Professor in the Department of
Chemical Engineering at the University of Minnesota Duluth.
analysis described in this paper. He earned his BS in Chemical Engineering from Brigham Young
University and his PhD from the University of California, Santa
EXPERIlME NT Barbara. He teaches a variety of courses in transport phenom-
ena and separations, and his current research interests include
Davis and Sandall[f provided specific details of the experimental ob- process modeling and optimization.
Orville C. Sandall is Professor of Chemical Engineering at
jectives, apparatus, and procedure for a commercial hollow-fiber mem- the Universityof California, Santa Barbara. He is a graduate of
brane unit for air separation. The Prism separator developed by Permea the University of Alberta (BSc and MSc) and the University of
California, Berkeley (PhD). His teaching and research inter-
* University of( Santa Barbara, CA 93106 ests are in the areas of mass transferandseparation processes.
Copyright ChE Division ofASEE 2003
Chemical Engineering Education
Membranes in ChE Education
Corporation, shown in Figure 1, consists of four hollow-fi-
ber membrane modules arranged in a series of columns. Each
module is a shell-and-tube arrangement of a bundle of hol-
low-fiber membranes that are capped at the top. High-pres-
sure feed air is introduced to the shell side of the fibers. The
permeating gas flows through the hollow-fiber bores and is
collected in a manifold at the open end. The pressure drop
across the shell side of the membrane unit was found to be
negligible.515 The permeate streams are open to the atmosphere.
The pressure at the closed end of the fiber bores is not di-
rectly measurable in the current module arrangements. Infor-
mation about fiber length, fiber inside diameter, and the num-
ber of fibers in the Prism separator bundle is not available,
but a conservative estimate of the pressure build-up in the
fiber bore was calculated to increase by less than nine per-
cent above atmospheric pressure for the range of experimen-
tal operating conditions. For most of the experiments, the
pressure build-up was estimated to be less than three percent.
Figure 2. Schematic of single, countercurrent flow
column or four columns with alternating flow patterns.
y -- d(yn) Permeate
\Ie Inhrjl, _____
Feed -x P x-- n x" + d(xn) Retentate
XF,nF X___R,nR
Figure 3. Ideal cocurrent flow pattern
Permeate d(yn) --
yp,np=npF +
xF,npF dA XR,nR
Figure 4. Ideal countercurrent flow pattern.
Winter 2003
Modem gas-separation membrane modules introduce the
high-pressure feed to the bore side of the fibers to eliminate
channeling and maintain a more uniform flow distribution.
High-pressure feed to the fiber bores can result in a signifi-
cant axial pressure drop in the fibers. Although not required
for this membrane module, the effects of pressure are included
in the analysis for completeness.
As shown in the schematic of Figure 2, the air-flow pattern
consists of alternating countercurrent and cocurrent flow
through the columns. The composition of the retentate and
permeate streams was measured with oxygen analyzers. The
flow rate of the retentate stream was measured with a volu-
metric flow meter. The feed and permeate flow rates may be
calculated by mass balances.
The membrane separator may be operated as four columns
in series, or as a single column by closing a valve on the tube
connecting the retentate and feed streams between the first
two columns. The first column operates in countercurrent flow
and was used to calibrate the membrane models from a series
of runs performed at various feed-flow rates and pressures.
The calibrated model was confirmed by favorable compari-
sons of model predictions with experimental results from the
four-column configuration.
A differential model of binary gas separation in the mem-
brane experiment was validated by Davis and Sandall and is
summarized next. For the conditions of the experiment, it
can be shown that a simplification to the equations permits
an algebraic solution.
The mathematical model of membrane gas separation was
based on several key assumptions. First, the temperature was
assumed to be constant. Further, it was assumed that all
streams through the shell and permeate sides of the fibers
were in plug flow. The air fed to the unit was assumed to be a
binary mixture of 79% N2 and 21% 0,. All four columns were
assumed to have the same dimensions and specific area for
mass transfer. Finally, axial pressure drop was ignored for
the fiber bore. This assumption is valid for low permeate flow
or large transmembrane pressure differences where small
changes in permeate pressure are negligible relative to the
high feed pressure.
* Differential Model
Walawender and Stemr61 derived the differential equations
for a binary gas system in countercurrent and cocurrent plug
flow patterns, shown ideally in Figures 3 and 4. Details of
the derivation are available in several references. 3,561 For a
binary gas system, the total mole and 02 species balances
around the separator are
Retentate (Single Column)
1 2
r1rf fif r
Membranes in ChE Education
nF =nR + p (1)
xFnF = xRR + ypnp (2)
where nF, nR, and n are the molar flow rates of the feed,
retentate, and permeate streams, respectively, and xF, xR, and
x are the feed, retentate, and permeate 02 mole fractions,
respectively. The species balances around a differential vol-
ume element in the membrane give
d(xn) = Qo, (xP yp)dA (3)
d[(1 x)n] = QN [(1 x)P (1- y)p]dA (4)
where Q is the permeance of species j, A is the membrane
surface area, and P and p are the average retentate and per-
meate side pressures, respectively.
For convenience in the analysis, Eqs. (1) to (4) were com-
bined into the following dimensionless equations for coun-
tercurrent flow:
KR dx -- y (1-x)(xr-y)-x[(1-x)r-(1-y)]}
dA* xR iY
KR d= 1x-_{*(-y)(xr-y)-y[(1-x)r-(1-y)]}
K dy (x ( y) I
KR =*(xr y)+(1- x)r -(1- y) (7)
where yl is the mole fraction in the permeate at the closed
end of the fibers. The dimensionless transport parameters are
defined as
A*=A/Am (8)
r=P/p (9)
KR =nR/QN2Amp (10)
S= Qo2 /QN, (11)
n* = n / nR (12)
where Am is the total membrane area. The ideal separa-
tion factor, x*, was assumed constant, but the dimensionless
transport parameter, KR, was defined as a function of the
retentate molar flow rate. The solution to Eq. (7) was used to
check the assumptions leading to the algebraic model of
the next section. The countercurrent flow equations are
integrated from the retentate end of the membrane, sub-
ject to the initial conditions
=Y i atA*=0 (13)
n =1
Note the discontinuity in Eq. (6) at x = xR requires
application of l'H6pital's rule.[6]
The dimensionless cocurrent flow model equations are
KF d, = f -1{)*(1 x)(xr y) -x[(1 x)r (1 y)]}
dA NyXF
KF dy x y{*(1 -y)(xr -y) y[(1 -x)r -(1 -y)]}
dA x xF
KF nF (16)
QN2 A p
The cocurrent model equations are integrated from the feed
end, subject to the initial conditions
S I at A = 0 (17)
Y =Yij
The permeate composition at the capped end of the hollow
fibers is calculated from the ratio of Eqs. (3) and (4)
Yi "*[xr -yi]
1-i [(1-x)r-(1 )](
where, for countercurrent flow, x = xR. For cocurrent flow, x
= xF. Equation (18) is quadratic in y. Note that there is an
error in the denominators of Eqs. (17) and (22) of the paper
by Davis and Sandall. 51 The correct solution to the quadratic
equation is
(a* -1)(xr+l)+r- [(* -1)(xr+1)+r]2 4(
2(a 1)
Davis and Sandall successfully used the differential model
in their analysis of 02/N2 separation in the membrane mod-
ule. At the time, they found that the background required to
solve the model equations for a* and KR was beyond the
scope of an undergraduate student in their laboratory course.
Consequently, they developed True BASIC programs that
were provided to the students to solve the model equations.
Since then, advances in computational software (such as
Mathcad) have simplified the process of solving the model
Chemical Engineering Education
Membranes in ChE Education
equations. Undergraduate students are now able to develop
their own solutions using standard numerical methods for
solving systems of nonlinear equations or differential equa-
tions that are readily available in these computer tools.
Nevertheless, students are still required to set up a stan-
dard method such as Euler's or Runge-Kutta for the initial-
value problems in order to find the values for a* and KR by
inverse analysis of the first column in countercurrent flow.
For example, Mathcad and Polymath do not permit their in-
trinsic capabilities for solving systems of first-order differ-
ential equations to be treated as part of another function. An
example of programming required in Mathcad for the inverse
mass transfer is shown in Figure 5. This type of solution may
be intimidating for undergraduate students, depending on their
level of experience. This realization, along with the observa-
tion that the composition profiles along the membrane were
approximately linear, led to the following alternative analy-
sis that avoids the initial-value problem solution requirements
xF:= 0.21 R :=0.16 yp:= 0.48 r:= 6.465 Ct:=6 KR := 50
Y i (a : l).(r.R + )+ r- [(a -l).(rxR + ) + r2 4 a-r-xR-(a 1)
2.(a 1)
dxx,y,KR,a) := -1. x y y[(1 x ( ) x.[r.(l -x) -- y))
KR Y xR
dy(x,y,KR,a):= if = xR
Yin Yi(a)
(xR yin).[- yin(a 1)]
(xR yin).(a l).(2-yin rxR 1) -r]
KR dx(R, Yin,KR,a)
.- .[(1 y).a.(rx- y) -y.[r-(l x) -(1- y)]] otherwise
KR x- xR
dn(x,y,KR,a) := a.(x.r y)+(l-x) (- y)
f(KR,a) := z0~-
YO Yi(a)
n0o- 1
for je 1..m
S<- z. + Az
x _, + Azdx(jl,yj_,,KR,a)
YJ Yj-I + Az'dy (x-1.Yj-I.KR,')
nj n + Az.dn(xjl, ,KR,a)
s, x
s2 -- y
53 -- n
<-- Euler's method
m 100 Az-
Solve forv and KR
(f(KR, a))= XF
(f(KR.)2) Yp
Find(Ka) 49.032
Figure 5. Example of Mathcad programming for inverse
mass transfer analysis for a* and K.
0 Algebraic Model
Boucif, et al.,El presented a series solution to the binary
component differential model Eqs. (5), (6), (14), and (15)
that requires a numerical solution to a pair of third-order poly-
nomial equations. The solution to the series equations agrees
with numerical solutions to the differential model when the
cut is less than 50%. The series solution does not include
axial pressure effects in the feed or permeate gas, however.
Hundyil and KorosE8' presented a more complete analysis of
hollow-fiber membrane modules for multicomponent gas
separation that includes pressure effects. Their approach is
based on a finite-volume element model that requires itera-
tive solutions to a large system of nonlinear algebraic equa-
tions. The finite-element approach is recommended when de-
tailed information of pressure, temperature, and composition
effects is required.
A simpler, alternative analysis of the membrane unit described
here was developed that involves only the solution to a small
system of nonlinear algebraic equations and includes pres-
sure effects when necessary. The simpler-model equations
are analogous to the shell-and-tube heat-exchanger design
equations that are familiar to undergraduate chemical engi-
neering students. The following analysis assumes laminar
flow and constant species permeances that are independent
of the pressure and composition of the feed or permeate gas.
The Hagen-Poisseuille equation is commonly used to calcu-
late axial pressure effectsE91
dp 128 RTn (20)
dz prdfNNf
where R is the ideal gas constant, T is the gas temperature, 1
is the gas viscosity, n is the variable molar flow rate of per-
meate gas, df is the inside fiber bore diameter, and Nf is the
number of fibers in a bundle. Other expressions derived from
the Hagen-Poisseuille equation have been developed to ac-
count for compressibility and flow in porous channels when
It has been observed that when the change in the feed mole
fraction of oxygen is less than 50%, the differential balances
may be replaced with algebraic expressions involving the
logarithmic mean of the transmembrane partial-pressure dif-
ference.'131 In Eq. (3), let
A = xP yp (21)
The driving force for diffusion across the membrane, A, is
assumed to be a linear function of the change in the molar
flow on the feed side of the membrane
d(xn) (xn)R (xn)F (22)
dA AR AF
Combine eqs. (2), (3), and (22), separate variables and inte-
Winter 2003
Membranes in ChE Education
ypnp =Q2 (AR AF)dA
ypnp = Qo2 (xP yp)mAm (24)
where the log-mean difference in 02 partial pressure across
the membrane is defined as
(xP y) (xP -YP)R (xP F (25)
(xP-YP, YP (25)
m n[(xP- YP)R/(xP- YP)F
A similar result is found for a N2 flux expression
(- yp)np = QN2 [(1 x)P -(1- y)p]mAm (26)
The steady-state binary-gas membrane equations can be writ-
ten in dimensionless form using the average pressures
xF = XR(1- )+ yp0 (27)
ypKR = (1- )a* (xr Y)m (28)
( yp)KR = (1- )[( x)r- (1 y)]m (29)
where the cut is defined here as the ratio of permeate-to-feed
flow rates
S= np / nf (30)
Alternative forms of Eqs. (28) and (29) in terms of KF are
ypKF = a*(xr Y)m (31)
(1-yp)KF= [( -x)r- (1 -y)] (32)
The permeate composition at the closed end of the hollow-
fiber membranes is calculated from Eq. (19).
The experimental separation factor was calculated from the
measured compositions of the permeate and retentate streams
a =y- XR) (33
XR(- Yp)
Under conditions where the change in the feed composi-
tion exceeds 50%, the log-mean model can be applied two or
more times as necessary across a module such that each cut
does not exceed a 50% change in xF from the previous step.
The pressure at the closed end of the fiber bore can be calcu-
lated by assuming that the permeate flow rate is a linear func-
tion of distance along the fiber
n = (34)
where L is the fiber length. Equation (20) can be integrated
with substitution from Eq. (34) to give an estimate for the
permeate pressure at the closed end of the fibers[9]
PC= 2 128RTpLnp
Pc =p2 + dfNf (35)
lTdf Nf
Solution Method
The algebraic model Eqs. (19) and (27-29) represent a sys-
tem with four degrees of freedom, or four equations in eight
variables: xF, XR, p y, Y a K*, KR, and r. The model was ini-
tially calibrated by fixing xF and r and measuring xR and yp,
leaving y, 0, a*, and KR as unknowns in the solution.
The solution of the system of nonlinear algebraic equa-
tions requires an iterative, trial-and-error technique, such as
Newton's method. The log-mean approximation of the par-
tial-pressure driving force is notoriously difficult to converge
under these circumstances. Fortunately, there are good ap-
proximations to the log-mean that avoid problems of diver-
gence in the solution. The following form of the Chen ap-
proximation was used:[141
tn(A2 /A1) L 2
Floudas noted that the Chen approximation to the log-mean
has the advantage that it becomes zero if either the feed or
exit partial-pressure driving forces become zero.151
The four-column configuration requires sequential solution
to the countercurrent and cocurrent models. Note that n2F =
nlR and K2F = K1R between the first and second columns, and
that n4F = nBR and K4F = KBR between the third and fourth col-
umns. The feed flow rates to each column are calculated from
the cut for the previous column.
The experimental data of Davis and Sandalls51 were used to
illustrate the analysis procedure. The assumption of Eq. (22)
for the log-mean approximation was evaluated by plotting a
) representative numerical solution to Eq. (7), shown in Figure
6. A linear least-squares regression of the numerical results
Figure 6.
results to
support the
assumptions for
and K,=4900.
Chemical Engineering Education
0.23 --
0.22 /
5 0.19
0. 15 a .
06 065 07 0.75 0.8 0.85 0.9
Membranes in ChE Education
shows that the assumption of a linear function for A is valid
for the conditions of this laboratory experiment.
A sample calculation of the single countercurrent flow
model calibration using Mathcad is shown in Figure 7. The
experimental data and results of the algebraic model are com-
pared with the results from the differential model in Table 1
for a* and KR. There are no significant differences in the
results between these models.
XF:=0.21 xR:=0.16 yp:= 0.48 r:= 6.465
KR:=50 a:=6 yi:=0.5 := 0.2
( l+ A23
x= xR(1 ) + yp-e
Yi a.(xRr-yi)
1 yi= 1 xR- (1 Yi)
yp.KR.0 = (1 0).-c.AlxF-r yp, R.r yi)
(1 yp).KR.O = (1 6).Al1( XF).r- ( yp),(l xR).r- ( y)]
Find(KR,a,yi, ) =0426
Figure 7. Example of Mathcad calculation for inverse
mass transfer analysis using the log-mean model.
Calibration Data[51 and Results for Single Countercurrent Column
Experimental Data Differential Model Algebraic Model
P(kPa) (gmol/s) XR yp KR a KR
377 0.73 0.18 0.43 5.81 31.1 5.82 31.1
377 0.74 0.18 0.43 5.81 31.1 5.82 31.1
377 1.03 0.19 0.44 5.98 49.6 5.98 49.6
377 1.32 0.19 0.44 5.98 49.6 5.98 49.6
377 2.54 0.20 0.44 5.71 98.7 5.71 98.6
515 0.62 0.15 0.45 5.93 26.2 5.97 26.1
515 0.73 0.16 0.46 6.02 33.3 6.05 33.2
515 0.95 0.17 0.47 6.12 43.9 6.14 43.9
515 1.51 0.18 0.47 5.85 58.2 5.86 58.2
515 2.25 0.19 0.48 5.96 92.1 5.96 92.1
653 0.74 0.14 0.46 5.78 31.5 5.84 31.4
653 0.95 0.15 0.47 5.84 38.8 5.88 38.7
653 1.32 0.16 0.48 5.90 49.1 5.93 49.0
653 2.18 0.18 0.49 5.73 85.7 5.74 85.6
653 3.44 0.19 0.5 5.81 135 5.81 135
Average 5.88 5.90
A linear relationship between the retentate flow rate and
KR is calculated for use in the remaining three column pre-
dictions. The linear function is plotted with the results in Fig-
ure 5. The result of a linear least-squares regression gives
KR = 4.0 x 103nR (37)
The average value of ca was calculated to be 5.9 assuming
atmospheric pressure in the fiber bore. An increase in fiber-
bore pressure would cause the experimentally determined
species permeances to decrease. The axial pressure drop has
been found to vary linearly with flow rate, however.El61 Thus,
the slope in Eq. (37) is not affected by the small pressure
build-up in the permeate stream.
Separation factors for the four-column configuration were
predicted from the sequential calculations of the model for a
range of feed pressures and flow rates. The results plotted in
Figure 9 show good agreement with the experimental values
calculated from the data of Davis and Sandall.
All of these results lend confidence in the algebraic model.
Students are able to quickly design alternative configurations
and explore the potential performance of competing designs.
Figure 8.
Correlation of
with n,
for a
3 3.5 4 4.5 5 55
Figure 9.
results for air
in the four-
0=515 kPa,
A=653 kPa.
Winter 2003
, 80
20 ----
0.5 1 1.5 2 2.5
n X 10 gmols
3 3.5
Membranes in ChE Education
For example, students usually start by comparing the perfor-
mance of cocurrent and countercurrent flow. This leads to a
design for one column operating in countercurrent flow with
the same membrane surface area as the four columns. The
single column design gives a predicted increase of 10% N,
recovery when compared to the modular design. Students may
use the models to predict a dimensionless membrane area,
1/K, to recover a desired fraction of oxygen fed to the
permeator. Other designs include four columns operating in
parallel with countercurrent flow or four columns with the
feed side in series and the permeate side in parallel.
The Mathcad files used in the analysis are available at
A membrane experiment for investigating gas separation
has been in use for over ten years in the undergraduate labo-
ratory at the University of California, Santa Barbara. A simple
analysis method was presented that requires only the solu-
tion to a system of four algebraic equations. The simpler analy-
sis is equally applicable to newer membrane configurations
that introduce the high-pressure feed to the fiber bores in or-
der to maintain better flow patterns in the membrane mod-
ule. The experimental apparatus was designed to permit
single- and four-column investigations of air separation. The
single column was used to calibrate the models for binary
gas separation. Comparing results for the four-column op-
eration validated the calibrated model. Good model and ex-
perimental agreement lend confidence in the model and vali-
date the model assumptions. Students are then able to use the
model to develop competing designs for gas separation and
optimize their designs for maximizing efficiency of separa-
tion. The advantages of the simpler approach are that stu-
dents can readily set up and solve the model equations
without complicated programming. Students are also able
to explore alternative designs by building models and
comparing the results.
A membrane area, m2
d diameter, m
K dimensionless membrane transport parameter
L fiber length, m
n molar flow rate, gmol/s
N number of fibers in a bundle
p permeate side pressure, kPa
P feed side pressure, kPa
Q' permeance, gmol/(s-kPa-m2)
R ideal gas constant, kPa-m3/gmol-K
T temperature, K
x feed stream mole fraction of oxygen
y permeate stream mole fraction of oxygen
z variable fiber length, m
Greek Symbols
a experimental separation factor
A transmembrane partial pressure, kPa
p viscosity, N-m/s
o cut of feed to permeate stream
c closed end of fiber bore
e experimental
f fiber
F feed
i closed end of permeate stream
Im log-mean result
m membrane
N, nitrogen
0, oxygen
p predicted
R retentate
dimensionless or ideal parameter
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Chemical Engineering Education
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