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

Xi Yu*, Michael J. Hounslow, Gavin K. Reynolds

*Corresponding author for this work

Research output: Contribution to journalArticle


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= aMNb0, 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.

Original languageEnglish
Pages (from-to)2394-2402
Number of pages9
JournalAIChE Journal
Issue number8
Early online date22 Apr 2015
Publication statusPublished - Aug 2015


Bibliographical note

This is the peer reviewed version of the following article: Yu, X., Hounslow, M. J., & Reynolds, G. K. (2015). Accuracy and optimal sampling in Monte Carlo solution of population balance equations. AIChE Journal, 61(8), 2394-2402, which has been published in final form at This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving


  • accuracy
  • coalescence
  • hellinger distance
  • Monte Carlo
  • optimal sampling
  • population balance model

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