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MPACT VERIFICATION WITH MAGNOX REACTOR NEUTRONICS PROGRESSION PROBLEMS

MPACT is a state-of-the-art core simulator designed to perform high-fidelity analysis using whole-core, three-dimensional, pin-resolved neutron transport calculations on modern parallel computing hardware. MPACT was originally developed to model light water reactors, and its capabilities are being extended to simulate gas-cooled, graphite-moderated cores such as Magnox reactors. To verify MPACT’s performance in this new application, the code is being formally benchmarked using representative problems. Progression problems are a series of example models that increase in complexity designed to test a code’s performance. The progression problems include both beginning-of-cycle and depletion calculations. Reference solutions for each progression problem have been generated using Serpent 2, a continuous-energy Monte Carlo reactor physics burnup calculation code. Using the neutron multiplication eigenvalue keff as a metric, MPACT’s performance is assessed on each of the progression problems. Initial results showed that MPACT’s multigroup cross section libraries, originally developed for pressurized water reactor problems, were not sufficient to accurately solve Magnox problems. MPACT’s improved performance on the progression problems is demonstrated using this new optimized cross section library.


INTRODUCTION
MPACT is a state-of-the-art core simulator developed jointly at Oak Ridge National Laboratory and the University of Michigan to perform high-fidelity analysis using whole-core, three-dimensional (3D), pin-resolved neutron transport calculations on modern parallel computing hardware. MPACT was originally developed to model light water reactors (LWRs) [1], but the two-dimensional-onedimensional (2D-1D) neutron transport method [2] underlying the core simulator is agnostic to reactor type. Provided the core has a geometry extruded in the axial (z) dimension, as is the case for many reactors, a modified version of MPACT should be capable of performing neutronics calculations for non-LWR cores.
MPACT is being extended to simulate gas-cooled, graphite-moderated cores such as Magnox reactors. Several advanced reactor concepts depend on gas coolants or graphite moderators, and some concepts rely on both [3]. Magnox reactors were operated in the United Kingdom for nearly 60 years , so a large volume of operational data is potentially available for validation purposes. Before the modified MPACT code can be validated against operational data, it first should be verified using code-to-code comparisons.
The purpose of this work is to methodically benchmark MPACT's neutronic calculations for Magnox reactors against reference solutions computed using an independent code base and methodology. A series of progression problems have been created for Magnox reactors. A similar series of progression problems describing pressurized water reactor problems was prepared during the initial stages of the Consortium for Advanced Simulation of LWRs project [4]. These problems evolve from simple 2D pin-cells through more complicated geometries and conditions to a 3D full core. The reference solutions for these progression problems have been computed using Serpent 2, a continuous-energy Monte Carlo reactor physics burnup calculation code developed at VTT Technical Research Centre of Finland Ltd. [5]. Presented herein are the k eff results for the 2D progression problems; the results for the 3D core simulation are presented elsewhere in these proceedings [6].

PROGRESSION PROBLEMS
The progression problems are organized primarily by geometry. Problem category 1 is the collection of all 2D pin-cell calculations. Although Magnox reactors use stackable fuel elements rather than fuel pins, a single fuel channel model is analogous to a single LWR fuel pin. Problem category 2 is the collection of problems that model slightly more complex 2D geometry-a collection of 16 fuel channels with a central control rod channel known as a charge pan. This problem category is analogous to an LWR fuel lattice, except Magnox cores do not employ variable enrichments and burnable absorbers in a charge pan. Problem category 3 is the collection of problems that model a 2D symmetric quarter core with graphite reflector geometry. The geometries for the three progression problem categories are shown in Figure 1.
Secondarily, the progression problems are organized by the type of calculation being performed. Problem type 1 calculations are single state point problems, such as those at beginning-of-cycle (BOC), middle-of-cycle (MOC), and end-of-cycle (EOC). Problem type 2 computations are depletion calculations. Depletion problems for MPACT and Serpent 2 use the same number and size of time steps, and the k eff values are compared at the same burnup. A burnup interval weighted rootmean discrepancy value is computed using Eqs. 1 and 2, where N is the total number of burnup steps, B i is the burnup at step i, k The ∆k value will always be positive regardless of the sign of the discrepancy at each burnup state point.
A nomenclature is now defined to describe the progression problems. All pin-cell problems are numbered 1.x with single state point problems are numbered 1.1, and depletion problems are numbered 1.2. Charge pan single state point problems are numbered 2.1, and charge pan problems depletion are numbered 2.1. Quarter core single state point problems are numbered 3.1, and quarter core depletion problems are numbered 3.2. Problems are further organized by minor modifications to geometry, temperature, burnup, enrichment, and the presence or absence of control rods. These modifications extend the nomenclature. For example, a BOC pin-cell problem using temperature profile I is problem 1.1.06, but a BOC pin-cell problem using a temperature profile II is problem 1.1.07.
The geometry variations in these progression problems are based on documentation for the Calder Hall 1 reactor at the Sellafield site near Seascale in the United Kingdom [7]. The core has three radial zones, each with a different coolant channel outer radius: zone A is 5.28 cm, zone B is 5.02 cm, and zone C is 4.58 cm. Each coolant channel radius is in its own case within pin cell and charge pan problems.
To test the full range of expected temperatures, five temperature profiles are used. The temperature profiles are shown in Table 1. Profile I corresponds to typical operating temperatures, and profile II corresponds to cold zero-power temperatures. Profiles III, IV, and V test a range of fuel temperatures while keeping the clad, coolant, and moderator temperatures constant. Serpent 2 uses The pin-cell problems also include variation due to burnup and enrichment ( 235 U wt%). Magnox reactors are typically fueled with natural uranium, but low-enriched fuel is used in some pin-cell progression problems to verify the robustness of the cross section library over the expected range of enrichments. Single state points include the following burnups: BOC at 0.0 MWd/MtU, MOC at 600.0 MWd/MtU, and EOC at 1200.0 MWd/MtU. Table 2 lists the enrichment and burnup variations for the pin-cell progression problems. An additional problem variation used is the presence of control rods for the charge pan and quarter core geometries. Control rods used in the Calder Hall reactor are axially heterogeneous, with steel composed of 3 wt% and steel composed of 4 wt% absorber regions and a stainless steel tip. The rodded charge pan problems use all 3 types of material, while the all-rods-in (ARI) quarter core problems use the steel composed of 3 wt%. The all-rods-out (ARO) problems use only coolant in the control rod channel. Table 3 lists control rod and other variations for the charge pan progression problems, and Table 4 lists the quarter core problems.  Reference solutions were computed using Serpent 2.1.31. Monte Carlo convergence of k eff eigenvalues varied by problem. The least converged problem had a standard error of 24 pcm, the most converged problem had a standard error of 7 pcm, and the average standard error of all problems is 20 pcm. Power normalization and fission heating terms are set in Serpent to be the same as those used by MPACT to ensure valid comparisons between the two codes throughout depletion.

COMPARISON OF MPACT RESULTS WITH REFERENCE SOLUTIONS
Initial MPACT calculations computed k eff eigenvalues using the multigroup cross section libraries with 47 and 51 energy groups developed for LWRs during the Consortium for Advanced Simulation of LWRs project. This proved inadequate as k eff eigenvalues were discrepant by > 1000 pcm (percent mille), i.e. a descrepancy of 1%, for even simple pin-cell calculations. This initiated development of a new 69-group cross section library designed specifically for Magnox reactors [8].
A comparison of MPACT's computed k eff eigenvalues with reference solutions computed by Serpent 2 is shown in Figure 2. These results were computed using the 69-group cross section library, and the agreement with the reference solutions is significantly better than values computed with the multigroup libraries developed for LWR analysis.

CONCLUSIONS AND FUTURE WORK
For the pin-cell problems, the greatest k eff discrepancies between MPACT and the reference solutions occur at the lower temperature profiles II (problems 1. For the quarter core unrodded BOC problems (3.1.1-3.1.3), all discrepancies are less than 125 pcm, with the greatest agreement (101 pcm) at temperature profile IV, which is near to nominal operating temperatures. The full core problem discrepancies are generally consistent with the charge pan and pin cell problems, and the biases are acceptably low.
These progression problems demonstrate that the MPACT and the newly developed 69-group library are generally excellent for unrodded Magnox reactor analysis over a range of operating conditions. They also demonstrate that computations using temperatures significantly lower than operating temperatures may have unacceptably large k eff biases. The rodded cases deviate from the reference solutions more than unrodded problems so further development of the 69-group crosssection library may be needed for rodded cases.
Further refinement of the cross section library for better agreement with the rodded problems is an area for future work. Additionally, other metrics, such as power distributions and isotopic concentrations during depletion, will be used to verify MPACT is accurate for Magnox reactor analysis. This verification effort only considered neutronic calculations, but MPACT is a core simulator capable of neutronic feedback from a coupled thermal code. A specially developed thermal code called AGREE has been developed for this purpose. Future work will include verification of a coupled MPACT-AGREE code for Magnox reactor analyses. After these verification efforts are complete, future work includes validation of MPACT-AGREE using operational cycle data from the Calder Hall 1 reactor.