Reduced Order Models with Local Property Dependent Transfer Coefficients for Real Time Simulations of Single and Dual Layered Monolith Reactors

Monolith reactors are widely used in catalytic aftertreatment systems. Detailed mathematical models of this reactor consist of a system of coupled nonlinear partial differential equations in three spatial dimensions and time. The numerical solution of these models with complex catalytic chemistry is demanding in terms of time and memory requirements. Therefore, the development of reduced order models for these systems is important for control and optimization algorithms related to fuel economy and real time implementation of emissions constraints. The objective of this work is to develop reduced order models by simplification of the problem of multicomponent diffusion and reaction in the catalytic layers. In the first part of this work, we present a novel method for computing washcoat diffusional effects with local property dependent internal mass transfer coefficient matrix. We present a method for computing this matrix for any arbitrary washcoat geometry as a function of the Thiele matrix, defined in terms of the Jacobian of the rate vector at the local concentrations. We illustrate this method with examples for single layered monolith reactors with global kinetics, and show that it leads to accurate solutions while speeding calculations by several orders of magnitude. In part II, we extend Thiele matrix approach to dual layered monolith reactors, where each layer may have different catalytic or transport properties. We determine the interfacial flux vectors and mass transfer coefficient matrices in terms of Thiele matrix of each layer. We illustrate the method using a dual layered system with first layer of selective catalytic reduction (SCR) and second layer of lean NOx trap (LNT) catalyst. We also investigate the mesh size dependency of the solution and note that the detailed model leads to sufficiently accurate solution only when the number of mesh points is about equal to or greater than the largest eigenvalue (in magnitude) of the Thiele matrix. We compare the speed and accuracy of the reduced order model solution and show that it is closer to detailed model which has sufficient mesh points. In part III, we extend the Thiele matrix approach to microkinetic models. First, we show that the short time scales associated with the adsorption/desorption steps requires the use of a large number of mesh points to obtain a mesh independent solution. We present a multimode coarse grained model using the internal mass transfer coefficient matrix. This matrix is shown to be diagonal for most microkinetic models of practical interest. We illustrate the method with H2/CO/C3H6 oxidation over a Pt/Al2O3 catalyst with a detailed microkinetic model. While the computation of the mesh independent solution of the detailed model is tedious, the reduced order model leads to an accurate solution while speeding up calculations by about three orders of magnitude.