(227d) Low-Dimensional Models for Real Time Simulations of Catalytic After-Treatment Systems
It is well known that the performance of the monolith reactors used in catalytic after-treatment systems (such as TWCs, DOCs, LNTs and SCRs) depends on the processes occurring at various length and time scales, e.g. complex chemistry and interactions between the various catalytic components at the crystallite (nanometer) scale, the diffusion of reactants and products thorough the porous washcoat (micrometer scale), the momentum, heat and mass transport processes in the monolith channels (millimeter scale) and the speed and width of various fronts along the monolith bricks (centimeter to meter scale). The design, optimization and control of these systems requires mathematical models that incorporate the processes occurring at all scales but simple enough so that they can simulated in real time or faster than real time. The focus of this talk will be on the development, validation and use of such low-dimensional models.
The low-D models are derived directly by averaging the governing partial differential equations and using the concepts of internal (intra-phase) and external (inter-phase) transfer coefficients. They are expressed in terms of multiple concentration and temperature modes (that are measurable in experiments) and include washcoat or intra-phase diffusional effects without using the concept of the effectiveness factor. The models are validated by simulating the steady state and transient behavior for various test cases and comparing the predictions with detailed solutions. It is shown that these new low-D models are robust, accurate with practically acceptable error, speed up the computations by orders of magnitude, and can be used with confidence for the real time simulation and control of various catalytic after-treatment systems. The application of these models to the transient operation of TWCs and LNTs will be illustrated. The use of the low-D models to estimate kinetic parameters using bench scale data as well as the determination of the controlling regimes as a function of various design and operating conditions will also be discussed.