Hierarchical multi-scale model reduction in the simulation of catalytic converters

Abstract This paper presents a methodology for multi-scale modelling using pre-computed data for the small scales. By pre-computing the required data at the micro- and meso-scales and storing them in a look-up table, these small-scale effects can be captured in a macro-scale model that executes with practicable execution times. The methodology is presented in the context of modelling a washcoated monolith reactor for the catalytic combustion of methane using a detailed multistep mechanistic model. The modelling is illustrated as a sequence of steps of increasing model simplification. In the first instance, only the reaction rates are pre-computed. Then the washcoat diffusion is included using a 2D axisymmetric model with a washcoat of uniform thickness, then with a non-symmetrical channel with a washcoat of non-uniform thickness. It is shown how a simple 1D single channel model can accurately account for the presence of a non-uniform washcoat. Finally, the external transport resistance is included in the pre-computation step, and it is shown that a simple one dimensional pseudo-homogeneous single channel model can be used provided the effective average rates are appropriately calculated. Execution times are shown to decrease by several orders of magnitude at minimal loss of solution accuracy. The use of pre-computed data allows for the inclusion of complex heat and mass transfer phenomena, as well as complex kinetics in full scale converter models at relatively small computational cost. The implementation of look-up tables into full scale CFD models is described, and optimal strategies proposed.

[1]  William S. Meisel,et al.  Repro-Modeling: An Approach to Efficient Model Utilization and Interpretation , 1973, IEEE Trans. Syst. Man Cybern..

[2]  Tamás Turányi,et al.  Parameterization of Reaction Mechanisms Using Orthonormal Polynomials , 1994, Comput. Chem..

[3]  Robert E. Hayes,et al.  Transient experiments and modeling of the catalytic combustion of methane in a monolith reactor , 1996 .

[4]  J. P. Mmbaga,et al.  Three dimensional modelling of methane ignition in a reverse flow catalytic converter , 2007, Comput. Chem. Eng..

[5]  Robert E. Hayes,et al.  Modelling the three-way catalytic converter with mechanistic kinetics using the Newton–Krylov method on a parallel computer , 2002 .

[6]  M. Votsmeier.  Efficient implementation of detailed surface chemistry into reactor models using mapped rate data , 2009 .

[7]  F. Bracco,et al.  Two dimensional, transient catalytic combustion of CO-air on platinum , 1985 .

[8]  J. T’ien.  Transient Catalytic Combustor Model , 1981 .

[9]  Enrico Tronconi,et al.  Continuous vs. discrete models of nonadiabatic monolith catalysts , 1996 .

[10]  Stephen B. Pope,et al.  Computationally efficient implementation of combustion chemistry using in situ adaptive tabulation , 1997 .

[11]  Yiyu Cheng,et al.  Surface B-splines fitting for speeding up the simulation of adsorption processes with IAS model , 2011, Comput. Chem. Eng..

[12]  Steffen Tischer,et al.  Transient three-dimensional simulations of a catalytic combustion monolith using detailed models for heterogeneous and homogeneous reactions and transport phenomena , 2001 .

[13]  R. Hayes,et al.  A fast approximation method for computing effectiveness factors with non-linear kinetics , 2007 .

[14]  R. Hayes,et al.  CFD modelling of the automotive catalytic converter , 2012 .

[15]  Martin Votsmeier,et al.  Runtime efficient simulation of monolith catalysts with a dual-layer washcoat , 2012 .

[16]  Tamás Turányi,et al.  Application of repro-modeling for the reduction of combustion mechanisms , 1994 .

[17]  R. Hayes,et al.  Efficient simulation of an ammonia oxidation reactor using a solution mapping approach , 2011 .

[18]  Carl de Boor,et al.  A Practical Guide to Splines , 1978, Applied Mathematical Sciences.

[19]  Frank Behrendt,et al.  NUMERICAL MODELING OF CATALYTIC IGNITION , 1996 .

[20]  Robert E. Hayes,et al.  MASS AND HEAT TRANSFER EFFECTS IN CATALYTIC MONOLITH REACTORS , 1994 .

[21]  R. E. Hayes,et al.  Introduction to Catalytic Combustion , 1998 .

[22]  R. Hayes,et al.  A study of Nusselt and Sherwood numbers in a monolith reactor , 1999 .

[23]  J. Mantzaras,et al.  Numerical investigation on the start-up of methane-fueled catalytic microreactors , 2010 .

[24]  Robert E. Hayes,et al.  Finite-element model for a catalytic monolith reactor , 1992 .

[25]  R. Hayes,et al.  Calculating effectiveness factors in non-uniform washcoat shapes , 2005 .

[26]  R. Hayes,et al.  The effect of washcoat geometry on mass transfer in monolith reactors , 2004 .

[27]  Ankan Kumar,et al.  Adaptation and application of the In Situ Adaptive Tabulation (ISAT) procedure to reacting flow calculations with complex surface chemistry , 2011, Comput. Chem. Eng..

[28]  R. Hayes,et al.  The effective thermal conductivity of monolith honeycomb structures , 2009 .

[29]  M. D. Checkel,et al.  The Effect of Catalytic Washcoat Geometry on Light-off in Monolith Reactors , 2006 .

[30]  R. Hayes,et al.  Towards the simulation of the catalytic monolith converter using discrete channel-scale models , 2012 .

[31]  J. Gieshoff,et al.  Simulation of automotive NH3 oxidation catalysts based on pre-computed rate data from mechanistic surface kinetics , 2010 .

[32]  Vladimír Novák,et al.  Multi-scale modelling of reaction and transport in porous catalysts , 2010 .

[33]  Pio Forzatti,et al.  A comparison of lumped and distributed models of monolith catalytic combustors , 1995 .

[34]  Laxminarayan L. Raja,et al.  A critical evaluation of Navier–Stokes, boundary-layer, and plug-flow models of the flow and chemistry in a catalytic-combustion monolith , 2000 .

[35]  Robert E. Hayes,et al.  Diffusion limitation effects in the washcoat of a catalytic monolith reactor , 1996 .

[36]  R. Hayes,et al.  On the use of mechanistic CO oxidation models with a platinum monolith catalyst , 2007 .

[37]  Nikunj Gupta,et al.  Heat and mass transfer coefficients in catalytic monoliths , 2001 .