SCR-Filter Model Order Reduction (1): Development and Validation of the Base “High-Fidelity” Model

Abstract

Catalysed diesel particulate filters (c-DPF) have been described as multifunctional reactor systems. Integration of selective catalytic reduction (SCR) functionality in the DPF enhances filter performance to achieve nitrous oxides (NOx) treatment along with particulate matter (PM) collection. The physical and chemical aspects of the integrated SCR-filter make modelling difficult. The goal of this work is to develop a low-complexity model of the SCR-filter system with good fidelity. The first part of our work—presented in this paper—lays out the structure of the SCR-filter model and highlights a new approach to implement faster than real-time solution to the “full-order” or “high-complexity” model. The validated model was applied to evaluate the impact of diffusion on deNOx functionality of the SCR-filter system in a simulated characterisation exercise for the SCR-filter unit. We found that internal (pore) diffusion (effective diffusivity coefficient) and external channel to wall diffusion (mass transfer coefficient) orthogonal to the channel direction are significant for accurate characterisation of the deNOx performance of the SCR-coated filter system. System modelling can be used to select the geometric properties of the monolith (length and density of the SCR-coated filter system) and micro-properties of the washcoat (catalyst loading and zoning) to optimise the influence of diffusion on the system performance. The main contribution of this paper is the presentation of a different approach to implementing the solution to the cDPF model and in enough detail so that it can be easily replicated.

SCR-Filter Model Order Reduction (2): Proper Orthogonal Decomposition and Artificial Neural Network

“…The data can be obtained from experiments or from numerical simulation of the full-order model. The POD method in this work was applied using numerical data obtained from a validated high-fidelity model of the SCR-coated filter system [2]. For each of the cases considered, the numerical model is solved at the specified inlet conditions, to generate the system ensemble data for the POD basis.…”

“…The time-explicit component of the SCR-coated filter model equations [2] can be can be written compactly as…”

“…A model of the SCR-filter system has been developed and validated in [2]. The model was primarily validated against the published data in Schrade et al [3].…”

“…The model was primarily validated against the published data in Schrade et al [3]. The model describes the data well; details are provided in ' [2]. A new implementation of the model delivered faster than real-time solution times.…”

“…The alternative approach to model order reduction applied in this work is ANN. In this approach, data was obtained from the full-order model developed in [2] and a black-box function approximation is derived to represent the model performance.…”