(270f) Multi-Grid Monte Carlo Algorithm for the Simulation of Multi-Component Population Balance Models

In this work a new multi-grid strategy is utilized to accelerate the computational speed of the PEMC [1, 2] method for the case of multidimensional population balance models (PBM). The PEMC is a fast MC method to solve PBMs, increasing the simulation speed by order of magnitude without affecting accuracy (for 1D case).  This method is based on discretizing the internal variables to create a dual structure consisting of pseudospecies and subensembles. The advantages of this method are: (1) A reduced search space that allows very fast sampling for next event (thus fast simulation speed). (2) The “chemical structure” allows applying simulations techniques available in chemical kinetics (for example tau leap methods and multiscale methods [2]). (3) The ability to track individual particle/events history like the standard MC method. (4) The kernel structure is preserved and complex kernels can be compressed into a small matrix.

For multidimensional PBM, the discretization can generate a very large number of events reducing the computational speed of PEMC.  This problem is solved introducing a new multigrid strategy for the “next event” search. The multigrid strategy makes the computational speed of multidimensional PBM almost the same as a 1D case (orders of magnitude improvement in computational speed).  This is because in this “divide and conquer” type strategy the search scales linearly with dimensions instead of exponential. This new strategy makes the PEMC a very fast method for any type of PBM (single dimension or multidimensional).

The new method is discussed in details and tested with kernels of industrial relevance including wet granulation used in pharmaceutical industry. In this unit operation, the primary solid particles are mixed with a liquid binder. The physics of the process is governed by the aggregation kernel that is a function of the size and binder composition of the two colliding particles. A multidimensional population balance model is utilized to tracks the evolution of total granule size and binder size within granules.

[1] Irizarry R. (2007) Chem. Eng. Sci. 63,  7649-7664.

[2] Irizarry R. (2011)  Chem. Eng. Sci. 66, 4059–4069.