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Simplification of Mathematical Models of Chemical Reaction Systems.

Detailed modeling of complex reaction systems is becoming increasingly important in the development, analysis, design, and control of chemical reaction processes. For industrial processes, complete incorporation of the chemistry into process models facilitates the minimization of byproduct and pollutant formation, increased efficiency, and improved product quality. Processes that involve complex reaction networks include a variety of noncatalytic and homogeneous or heterogeneous catalytic processes (such as fluid catalytic cracking, combustion, chemical vapor deposition, and alkylation). For some systems, large sets of relevant reactions have been identified for use in simulations.1-3 For others, the availability of advanced computing environments has enabled the automated generation of reaction networks and their models, based on computational descriptions of the reaction types occurring in the system.4-6 The use of such complex models is hindered by two obstacles. First, because of their sheer size and the presence of multiple time scales, these models are difficult to solve. Second, the models contain large numbers of uncertain (and sometimes unknown) kinetic parameters; regression to determine the parameters of complex nonlinear models is both difficult and unreliable, and the sensitivity of simulations to parameter uncertainties cannot be easily ascertained. Furthermore, for the purpose of gaining insights into the reaction system’s behavior, it is usually preferable to obtain simpler models that bring out the key features and components of the system. For these reasons, model simplification and order reduction are becoming central problems in the study of complex reaction systems. The simulation, monitoring, and control of a complex chemical process benefit from the derivation of accurate and reliable reduced models tailored to particular process modeling tasks. Model simplification is directly linked to identification of key reactions and sets of species that give valuable insights into the behavior of the network and how it may be influenced. Advanced control schemes such as model predictive control7 or multiple model adaptive control8 must be based on selecting appropriate reduced models and tracking key sets of species. Ideally, a model order reduction algorithm should have broad applicability, enable analysis at several levels of detail, and provide an assessment of the modeling error.