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

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(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 x 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. (c) 2015 American Institute of Chemical Engineers AIChE J, 61: 2394-2402, 2015