Simulation of (bio)chemical processes with distributed parameters using Matlab

Abstract Nowadays, simulations have become indispensable for the analysis and optimisation of (bio)chemical processes. However, as a lot of these processes are distributed in nature (i.e., the properties vary both in time and space), their simulation requires the solution of non-linear convection–reaction–diffusion partial differential equations (PDEs). Therefore, this paper compares different solution methods in a comprehensible way in order to provide practical guidelines. Moreover, to stimulate their usage in practice, all techniques have been implemented in Matlab ® , and all test examples have been made available ( www.matmol.org ). This allows practitioners to rapidly evaluate different methods when setting-up their own process simulation code. Finally, a complex reverse flow reactor case illustrates how these methods can be successfully combined with optimisation approaches.

[1]  G. Eigenberger,et al.  On the efficient simulation and analysis of regenerative processes in cyclic operation , 1997 .

[2]  Ilse Smets,et al.  Optimal design of dispersive tubular reactors at steady-state using optimal control theory , 2009 .

[3]  Lawrence F. Shampine,et al.  Solving Index-1 DAEs in MATLAB and Simulink , 1999, SIAM Rev..

[4]  S. Thompson,et al.  A MATLAB implementation of upwind finite differences and adaptive grids in the method of lines , 2005 .

[5]  Denis Dochain,et al.  Optimal temperature control of a steady‐state exothermic plug‐flow reactor , 2000 .

[6]  Filip Logist,et al.  Optimal temperature profiles for tubular reactors implemented through a flow reversal strategy , 2007 .

[7]  Lawrence F. Shampine,et al.  The MATLAB ODE Suite , 1997, SIAM J. Sci. Comput..

[8]  Ilse Smets,et al.  Optimal control of dispersive tubular chemical reactors: Part I , 2005 .

[9]  Pablo Marín,et al.  Procedures for heat recovery in the catalytic combustion of lean methane―air mixtures in a reverse flow reactor , 2009 .

[10]  J. Verwer,et al.  Analysis of operator splitting for advection-diffusion-reaction problems from air pollution modelling , 1999 .

[11]  William E. Schiesser The numerical method of lines , 1991 .

[12]  I. Queinnec,et al.  Development and calibration of a nitrification PDE model based on experimental data issued from biofilter treating drinking water , 2006, Biotechnology and bioengineering.

[13]  Krzysztof Gosiewski Effective approach to cyclic steady state in the catalytic reverse-flow combustion of methane , 2004 .

[14]  J. Verwer,et al.  Numerical solution of time-dependent advection-diffusion-reaction equations , 2003 .

[15]  Khalid Alhumaizi,et al.  Comparison of finite difference methods for the numerical simulation of reacting flow , 2004, Comput. Chem. Eng..

[16]  Paul A. Zegeling,et al.  Algorithm 731: A moving-grid interface for systems of one-dimensional time-dependent partial differential equations , 1994, TOMS.

[17]  T. Prabhakar Clement,et al.  Assessment of a non-traditional operator split algorithm for simulation of reactive transport , 2005, Math. Comput. Simul..

[18]  A. Wouwer,et al.  Adaptive Method of Lines , 2001 .

[19]  Alírio E. Rodrigues,et al.  Applications of a moving finite element method , 2001 .

[20]  Denis Dochain,et al.  Solution of the convection-dispersion-reaction equation by a sequencing method , 2003, Comput. Chem. Eng..

[21]  A. R. Mitchell,et al.  The Finite Difference Method in Partial Differential Equations , 1980 .

[22]  M. E. Achhab,et al.  Dynamical Analysis of a Tubular Biochemical Reactor Infinite-Dimensional Nonlinear Model , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[23]  Samir Hamdi,et al.  Method of lines , 2007, Scholarpedia.

[24]  Khalid Alhumaizi,et al.  Numerical analysis of a reaction-diffusion-convection system , 2003, Comput. Chem. Eng..

[25]  A. Vande Wouwer,et al.  Settler dynamic modeling and MATLAB simulation of the activated sludge process , 2009 .

[26]  S. E. Buckley,et al.  Mechanism of Fluid Displacement in Sands , 1942 .

[27]  Bengt Fornberg,et al.  Classroom Note: Calculation of Weights in Finite Difference Formulas , 1998, SIAM Rev..

[28]  P. V. Danckwerts Continuous flow systems , 1953 .

[29]  Filip Logist,et al.  Derivation of generic optimal reference temperature profiles for steady-state exothermic jacketed tubular reactors , 2008 .

[30]  A. Wouwer,et al.  Simulation of distributed parameter systems using a matlab-based method of lines toolbox: Chemical engineering applications , 2004 .

[31]  P. Sweby High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws , 1984 .