Premium
Accuracy and optimal sampling in M onte C arlo solution of population balance equations
Author(s) -
Yu Xi,
Hounslow Michael J,
Reynolds Gavin K
Publication year - 2015
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.14837
Subject(s) - monte carlo method , hellinger distance , mathematics , weighting , population , sample size determination , statistics , replicate , coalescence (physics) , mathematical optimization , algorithm , combinatorics , physics , demography , sociology , acoustics , astrobiology
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 = a M N 0 b , 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. © 2015 American Institute of Chemical Engineers AIChE J , 61: 2394–2402, 2015