Fast Compartmental Monte Carlo Simulation of Population Balance Models: Application to Nanoparticle Formation in Nonhomogeneous Conditions

A new compartmental Monte Carlo (CMC) algorithm is introduced for the stochastic simulation of population balance models in spatially heterogeneous systems. The heterogeneities are modeled using a network of compartments. The algorithm is based on a new stochastic procedure called particle bundle flow (PBF) to model the stochastic transfer of particles between compartments in a given time interval (a time-driven algorithm). Different from other time-driven methods, the accuracy of the PBF is independent of the particle concentration. The validity of the PBF method is demonstrated by construction and confirmed with numerical experiments. A new strategy for time step control is developed to set bounds on the calculation of the time steps during the simulation. The CMC algorithm, based on the combination of the PBF algorithm with the τ point ensemble Monte Carlo algorithm, is a general-purpose methodology that can be applied to any network of compartments. The computational speed and the low computational lo...

[1]  Stephen A. Billings,et al.  A three-compartment model of the hemodynamic response and oxygen delivery to brain , 2005, NeuroImage.

[2]  D. Gillespie.  The chemical Langevin equation , 2000 .

[3]  J. Bourne,et al.  Calculation of micromixing in homogeneous stirred tank reactors , 1988 .

[4]  K. Burrage,et al.  Binomial leap methods for simulating stochastic chemical kinetics. , 2004, The Journal of chemical physics.

[5]  Model of Formation of Monodispersed Colloids , 2001, cond-mat/0102079.

[6]  R. Irizarry,et al.  Preparation and Formation Mechanism of Silver Particles with Spherical Open Structures , 2011 .

[7]  Bernt Lie,et al.  Validation of a compartmental population balance model of an industrial leaching process: The Silgrain® process , 2006 .

[8]  Milorad P. Dudukovic,et al.  CFD‐based compartmental modeling of single phase stirred‐tank reactors , 2006 .

[9]  W. Harmon Ray,et al.  Methodology for modeling detailed imperfect mixing effects in complex reactors , 2005 .

[10]  M. Vakili,et al.  CFD analysis of turbulence in a baffled stirred tank, a three-compartment model , 2009 .

[11]  Winfried Pippel,et al.  Utilization of markov chains for simulation of dynamics of chemical systems , 1977 .

[12]  R. Irizarry.  Simulated Dynamic Optical Response Strategy for Model Identification of Metal Colloid Synthesis , 2010 .

[13]  Fernando J. Muzzio,et al.  Hybrid DEM‐compartment modeling approach for granular mixing , 2007 .

[14]  Warren D. Seider,et al.  Model-predictive control of the Czochralski crystallization process. Part I. Conduction-dominated melt , 1997 .

[15]  Chuguang Zheng,et al.  Reducing Statistical Noise and Extending the Size Spectrum by Applying Weighted Simulation Particles in Monte Carlo Simulation of Coagulation , 2009 .

[16]  Linda R. Petzold,et al.  Improved leap-size selection for accelerated stochastic simulation , 2003 .

[17]  Satish J. Parulekar,et al.  Delivery of drug macromolecules from thermally responsive gel implants to the posterior eye , 2010 .

[18]  Paulette Clancy,et al.  Accurate implementation of leaping in space: the spatial partitioned-leaping algorithm. , 2010, The Journal of chemical physics.

[19]  Costas Kiparissides,et al.  CFD analysis of turbulence non-homogeneity in mixing vessels: A two-compartment model , 2002 .

[20]  Roberto Irizarry,et al.  Stochastic simulation of population balance models with disparate time scales: Hybrid strategies , 2011 .

[21]  Miguel E. Castro-Rosario,et al.  Nucleation and Growth of Silver Sulfide Nanoparticles , 2010 .

[22]  Alan Jones,et al.  On the influence of mixing on crystal precipitation processes—application of the segregated feed model , 2002 .

[23]  Warren D. Seider,et al.  Model-predictive control of the Czochralski crystallization process. Part II. Reduced-order convection model , 1997 .

[24]  F. Einar Kruis,et al.  Computational fluid dynamics based stochastic aerosol modeling: Combination of a cell-based weighted random walk method and a constant-number Monte-Carlo method for aerosol dynamics , 2012 .

[25]  Chao Yang,et al.  CFD-PBE simulation of premixed continuous precipitation incorporating nucleation, growth and aggregation in a stirred tank with multi-class method , 2012 .

[26]  Vadim Mizonov,et al.  Applications of Markov Chains in Particulate Process Engineering: A Review , 2004 .

[27]  D. Vlachos,et al.  Binomial distribution based tau-leap accelerated stochastic simulation. , 2005, The Journal of chemical physics.

[28]  Kurt Liffman,et al.  A direct simulation Monte-Carlo method for cluster coagulation , 1992 .

[29]  Alejandro L. Garcia,et al.  A Monte Carlo simulation of coagulation , 1987 .

[30]  Y. L. Moullec,et al.  Comparison of systemic, compartmental and CFD modelling approaches: Application to the simulation of a biological reactor of wastewater treatment , 2010 .