Reduced Order Models with Local Property Dependent Transfer Coefficients for Real Time Simulations of Single and Dual Layered Monolith Reactors
Mingjie Tu, University of Houston
Mingjie Tu, Dr. R. Ratnakar* and Prof. V. Balakotaiah
Department of Chemical and Biomolecular Engineering, University of Houston, Houston, TX 77204
* Shell International Exploration and Production Inc, Houston
In a previous paper , we presented a novel method for computing washcoat diffusional effects in reduced order models with local property dependent internal and external transfer coefficients for real time simulations of monolith reactors. The method includes washcoat diffusional effects by computing the internal Sherwood matrix which depends on the local Thiele matrix, defined in terms of the Jacobian of the rate vector at the local concentrations. The accuracy and speed-up of the method was illustrated for single layered monolith reactors with global kinetics, and it was also compared with other existing methods in literature. It was shown that this method leads to the best match with detailed model while speeding calculations by orders of magnitude. In this work, we extend Thiele matrix approach further to include dual-layered washcoats and/or micro kinetics.
For the case of dual-layered monolith reactors, we integrate the Thiele matrix approach with the multi-scale averaging technique , and vector form of the internal, external and cross Sherwood number matrices for multi-component systems. We illustrate the method using a dual layered LNT-SCR model. We also investigate the mesh size dependency in the transverse direction on detailed model accuracy and note that the detailed model has sufficient accuracy when the number of mesh points is about equal to the magnitude of the largest eigenvalue of the Thiele matrix Φ². We also compare the speed and accuracy of the reduced order model solution with the detailed model and show that Thiele matrix solution is closer to detailed model which has sufficient mesh points. The asymptotic solution also shows good approximation because the reactions are not stiff in SCR layer or at lower temperatures or when washcoat layers are thin.
Although asymptotic solution has acceptable accuracy and is faster compared to the Thiele matrix in the case of dual-layer monolith at lower temperatures or slow kinetics in one of the layers, this is not the case at higher temperatures or thicker washcoats or more active layers. Further, it is found that for single layered washcoat with micro-kinetics, the Thiele matrix solution is as fast as and much more accurate than asymptotic solution, because of the fact that the Thiele matrix becomes diagonal which leads to an easier calculation of the Sherwood matrix.
Keywords: Pore diffusion; Mesh size dependency; Low-dimensional models; Dual-layer monolith; Micro kinetics; Thiele matrix; Sherwood matrix; Lean NOx trap; Selective catalytic reduction.
- M. Tu, R. R. Ratnakar, V. Balakotaiah, 2018. Reduced order models with local property dependent transfer coefficients for real time simulations of monolith reactors. Chemical Engineering Journal 383 (2020) 123074.
- R. R. Ratnakar, R. K. Dadi, and V. Balakotaiah. Multi-scale reduced order models for transient simulation of multi-layered monolith reactors, Chemical Engineering Journal 352 (2018) 293–305