Accuracy and optimal sampling in Monte Carlo solution of population balance equations |
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| Authors: | Xi Yu Michael J Hounslow Gavin K Reynolds |
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| Affiliation: | 1. European Bioenergy Research Inst. (EBRI), School of Engineering and Applied Science, Aston University, Birmingham, U.K.;2. Dept. of Chemical and Biological Engineering, The University of Sheffield, Sheffield, U.K.;3. Pharmaceutical Development, Macclesfield, U.K. |
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| Abstract: | Implementation of a Monte Carlo simulation for the solution of population balance equations (PBEs) requires choice of initial sample number (N0), number of replicates (M), and number of bins for probability distribution reconstruction (n). It is found that Squared Hellinger Distance, H2, is a useful measurement of the accuracy of Monte Carlo (MC) simulation, and can be related directly to N0, M, and n. Asymptotic approximations of H2 are deduced and tested for both one‐dimensional (1‐D) and 2‐D PBEs with coalescence. The central processing unit (CPU) cost, C, is found in a power‐law relationship,  , with the CPU cost index, b, indicating the weighting of N0 in the total CPU cost. n must be chosen to balance accuracy and resolution. For fixed n, M × N0 determines the accuracy of MC prediction; if b > 1, then the optimal solution strategy uses multiple replications and small sample size. Conversely, if 0 < b < 1, one replicate and a large initial sample size is preferred. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2394–2402, 2015 |
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| Keywords: | Monte Carlo population balance model Hellinger distance optimal sampling accuracy coalescence |
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