Reduced-Order Models with Local Property Dependent Transfer Coefficients for Real Time Simulation of Monolith Reactors

Mingjie  Tu, University of Houston

Reduced-Order Models with Local Property Dependent Transfer Coefficients for Real Time Simulation of Monolith Reactors

Mingjie Tu, Prof. V. Balakotaiah, and Dr. R. Ratnakar*

Department, University of Houston, Houston, TX 77204

* Shell International Exploration and Production Inc, Houston

The monolith reactor is the most widely used reactor in catalytic after-treatment systems (e.g. TWC, DOC, LNT, etc). The detailed mathematical models of a monolith reactor consist of a system of coupled nonlinear partial differential equations (PDEs) in at least two spatial dimensions (axial and radial/transverse) and time. Although the numerical solution of such detailed models with complex catalytic chemistry is possible with the present day computers, it may be demanding in terms of time and memory requirements, especially for real time simulations that may be needed in the control and optimization schemes. Therefore, the development of low-dimensional (reduced order) models for these systems is important for various control and optimization algorithms related to fuel economy and real time implementation of emissions constraints. There are several simplified approaches proposed in the literature for the solution of diffusion-reaction equations in the washcoat to avoid the computational demand of the full numerical solution.

In this work, we first review and evaluate the accuracy of various simplified approaches (reduced order models) for treating the external and internal diffusion problem in monolith reactors. Next, we present a new approach with local property dependent internal and external transfer coefficients for real time simulation of monolith reactors. We illustrate the application of the reduced order models with position dependent transfer coefficients to three-way catalytic converters (TWCs) and Lean NOx trap catalyst (LNT) with both macro and micro kinetics to determine the steady-state as well as transient behavior in real time. We also compare the solutions obtained using various reduced order models with detailed model to assess the accuracy. We show that totally ignoring washcoat diffusion which has been commonly applied to recent publications will lead to a large error and the use of local property dependent transfer coefficients in terms of the Jacobian of reaction rate vector leads to the best match with detailed model followed by its diagonal approximation followed by the asymptotic values, especially in the washcoat diffusion controlled regime.

Keywords: Pore diffusion; Low-dimensional models; Internal mass transfer coefficients; External mass transfer coefficients; Real time simulations; Thiele matrix; Sherwood matrix.