### Abstract

Implementation of a Monte Carlo simulation for the solution of population balance equations (PBEs) requires choice of initial sample number (N_{0}), number of replicates (M), and number of bins for probability distribution reconstruction (n). It is found that Squared Hellinger Distance, H_{2}, is a useful measurement of the accuracy of Monte Carlo (MC) simulation, and can be related directly to N_{0}, M, and n. Asymptotic approximations of H^{2} 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= aMN*_{b0}, with the CPU cost index, b, indicating the weighting of N_{0 }in the total CPU cost. n must be chosen to balance accuracy and resolution. For fixed n, M × N_{0 }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 language | English |
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Pages (from-to) | 2394-2402 |

Number of pages | 9 |

Journal | AIChE Journal |

Volume | 61 |

Issue number | 8 |

Early online date | 22 Apr 2015 |

DOIs | |

Publication status | Published - 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 http://dx.doi.org/10.1002/aic.14837. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving### Keywords

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

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## Cite this

*AIChE Journal*,

*61*(8), 2394-2402. https://doi.org/10.1002/aic.14837