Simulations of an ASA flow crystallizer with a coupled stochastic-deterministic approach

Abstract A coupled solver for population balance systems is presented, where the flow, temperature, and concentration equations are solved with finite element methods, and the particle size distribution is simulated with a stochastic simulation algorithm, a so-called kinetic Monte-Carlo method. This novel approach is applied for the simulation of an axisymmetric model of a tubular flow crystallizer. The numerical results are compared with experimental data.

[1]  Eva Roblegg,et al.  Continuous Sonocrystallization of Acetylsalicylic Acid (ASA): Control of Crystal Size , 2012 .

[2]  Robert I. A. Patterson,et al.  A predictor-corrector algorithm for the coupling of stiff ODEs to a particle population balance , 2009, J. Comput. Phys..

[3]  Volker John,et al.  Direct discretizations of bi-variate population balance systems with finite difference schemes of different order , 2014 .

[4]  J. Khinast,et al.  Modeling a seeded continuous crystallizer for the production of active pharmaceutical ingredients , 2014 .

[5]  Daniele Marchisio,et al.  Solution of population balance equations using the direct quadrature method of moments , 2005 .

[6]  R. I. A. PATTERSON,et al.  The Linear Process Deferment Algorithm: A new technique for solving population balance equations , 2006, SIAM J. Sci. Comput..

[7]  Johannes G. Khinast,et al.  Continuous Crystallization of Proteins in a Tubular Plug-Flow Crystallizer , 2015, Crystal growth & design.

[8]  Naveed Ahmed,et al.  Finite element methods of an operator splitting applied to population balance equations , 2011, J. Comput. Appl. Math..

[9]  J. Akroyd,et al.  Numerical simulation and parametric sensitivity study of optical band gap in a laminar co-flow ethylene diffusion flame , 2016 .

[10]  Robert I. A. Patterson,et al.  Stochastic weighted particle methods for population balance equations with coagulation, fragmentation and spatial inhomogeneity , 2015, J. Comput. Phys..

[11]  Gunar Matthies,et al.  An Object Oriented Parallel Finite Element Scheme for Computations of PDEs: Design and Implementation , 2016, 2016 IEEE 23rd International Conference on High Performance Computing Workshops (HiPCW).

[12]  Volker John,et al.  A comparative study of a direct discretization and an operator-splitting solver for population balance systems , 2015, Comput. Chem. Eng..

[13]  R. Patterson.  Convergence of Stochastic Particle Systems Undergoing Advection and Coagulation , 2013 .

[14]  Volker John,et al.  On Finite Element Methods for 3D Time-Dependent Convection-Diffusion-Reaction Equations with Small Diffusion , 2008 .

[15]  S. Pratsinis,et al.  Particle size distributions and viscosity of suspensions undergoing shear-induced coagulation and fragmentation , 2003 .

[16]  Volker John,et al.  A numerical method for the simulation of an aggregation‐driven population balance system , 2012 .

[17]  Stefan Radl,et al.  Seed loading effects on the mean crystal size of acetylsalicylic acid in a continuous‐flow crystallization device , 2011 .

[18]  Y. Efendiev,et al.  Hybrid monte carlo method for simulation of two-component aerosol coagulation and phase segregation. , 2002, Journal of colloid and interface science.

[19]  Robert McGraw,et al.  Description of Aerosol Dynamics by the Quadrature Method of Moments , 1997 .

[20]  Daniel T. Gillespie,et al.  The Stochastic Coalescence Model for Cloud Droplet Growth. , 1972 .

[21]  Gregor Kotalczyk,et al.  A Monte Carlo method for the simulation of coagulation and nucleation based on weighted particles and the concepts of stochastic resolution and merging , 2017, J. Comput. Phys..

[22]  Dmitri Kuzmin,et al.  Explicit and implicit FEM-FCT algorithms with flux linearization , 2009, J. Comput. Phys..

[23]  Y. Tsuji,et al.  Discrete particle simulation of two-dimensional fluidized bed , 1993 .

[24]  Robert I. A. Patterson,et al.  Stochastic weighted particle methods for population balance equations with coagulation, fragmentation and spatial inhomogeneity , 2015, J. Comput. Phys..

[25]  Naveed Ahmed,et al.  ParMooN - A modernized program package based on mapped finite elements , 2016, Comput. Math. Appl..

[26]  Volker John,et al.  On (essentially) non-oscillatory discretizations of evolutionary convection-diffusion equations , 2012, J. Comput. Phys..

[27]  M. Kraft,et al.  A multidimensional population balance model to describe the aerosol synthesis of silica nanoparticles , 2012 .

[28]  Daniel T. Gillespie,et al.  An Exact Method for Numerically Simulating the Stochastic Coalescence Process in a Cloud , 1975 .

[29]  Volker John,et al.  Numerical methods for the simulation of a coalescence-driven droplet size distribution , 2013 .

[30]  D. Gillespie.  A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions , 1976 .

[31]  Graeme A. Bird,et al.  Direct Simulation and the Boltzmann Equation , 1970 .

[32]  D. Gillespie.  Exact Stochastic Simulation of Coupled Chemical Reactions , 1977 .

[33]  S. Friedlander,et al.  Bivariate population dynamics simulation of fractal aerosol aggregate coagulation and restructuring , 2006 .

[34]  Doraiswami Ramkrishna,et al.  Population Balances: Theory and Applications to Particulate Systems in Engineering , 2000 .

[35]  Timothy A. Davis,et al.  Algorithm 832: UMFPACK V4.3---an unsymmetric-pattern multifrontal method , 2004, TOMS.

[36]  Stefan Radl,et al.  Continuously Seeded, Continuously Operated Tubular Crystallizer for the Production of Active Pharmaceutical Ingredients , 2010 .

[37]  Henning Bockhorn,et al.  Calculation of the size distribution function of soot particles in turbulent diffusion flames , 2007 .

[38]  Volker John,et al.  Continuous Crystallization in a Helically Coiled Flow Tube: Analysis of Flow Field, Residence Time Behavior, and Crystal Growth , 2017 .

[39]  A. Yu,et al.  Discrete particle simulation of particulate systems: Theoretical developments , 2007 .

[40]  Chuguang Zheng,et al.  A population balance-Monte Carlo method for particle coagulation in spatially inhomogeneous systems , 2013 .

[41]  Jesse T. Pikturna,et al.  Quadrature method of moments for population‐balance equations , 2003 .

[42]  Marco Mazzotti,et al.  Design and Optimization of a Combined Cooling/Antisolvent Crystallization Process , 2009 .

[43]  Robert I. A. Patterson,et al.  A Stochastic Weighted Particle Method for Coagulation-Advection Problems , 2012, SIAM J. Sci. Comput..