Porous Medium Modeling of Catalytic Monoliths Using Volume Averaging

Catalytic monoliths are being explored in conventional catalytic processes for their ability to achieve process intensification. Scientific computing can play an essential role in this exploration. The high computational cost of the first-principles models has led to modeling these reactors as a porous medium. However, this modeling strategy is not performed in a mathematically rigorous manner. We use the volume averaging technique as a mathematical framework to convert the pointwise governing equations for a monolith into averaged equations for a porous domain. These averaged equations require the closure of several unclosed terms, which are neglected in the classical porous medium (CPM) assumption. We discuss these unclosed terms and their impact on model predictions. We show that except in the limit of negligible Damköhler number the treatment of the catalytic reactions in CPM leads to significant errors. We propose a technique to accurately calculate the catalytic reaction rates in the volume-averaging-based porous medium (VAPM) model developed here. This technique is valid for a wide range of Damköhler numbers for both linear and nonlinear kinetics. Moreover, to calculate the effective properties of the porous medium, such as thermal conductivity, we employ asymptotic averaging (numerical homogenization) that can be used for any arbitrary channel shape and size. Predictions of the proposed VAPM model are assessed against three-dimensional multichannel monolith simulations, resolving the solid and fluid phases, for elementary and complex kinetics. In addition, VAPM is validated against the experiments of steam methane reforming in a catalytic monolith. The developed methodology reduces the computational cost by 3 orders of magnitude while maintaining the accuracy of the detailed multichannel simulations.