Accuracy and optimal sampling in Monte Carlo solution of population balance equations

Yu, Xi, Hounslow, Michael J. and Reynolds, Gavin K. (2015) Accuracy and optimal sampling in Monte Carlo solution of population balance equations. AIChE Journal, 61 (8), 2394-2402. (doi:10.1002/aic.14837).

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, C=aMN0b, 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.

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Contributors

Author: Xi Yu

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