Porous Medium Modeling of Catalytic Monoliths Using Volume Averaging

Catalytic monoliths are being explored in conventionalcatalyticprocesses for their ability to achieve process intensification. Scientificcomputing can play an essential role in this exploration. The highcomputational cost of the first-principles models has led to modelingthese reactors as a porous medium. However, this modeling strategyis not performed in a mathematically rigorous manner. We use the volumeaveraging technique as a mathematical framework to convert the pointwisegoverning equations for a monolith into averaged equations for a porousdomain. These averaged equations require the closure of several unclosedterms, 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 Damko''hler numberthe treatment of the catalytic reactions in CPM leads to significanterrors. We propose a technique to accurately calculate the catalyticreaction rates in the volume-averaging-based porous medium (VAPM)model developed here. This technique is valid for a wide range ofDamko''hler numbers for both linear and nonlinear kinetics. Moreover,to calculate the effective properties of the porous medium, such asthermal conductivity, we employ asymptotic averaging (numerical homogenization)that can be used for any arbitrary channel shape and size. Predictionsof the proposed VAPM model are assessed against three-dimensionalmultichannel monolith simulations, resolving the solid and fluid phases,for elementary and complex kinetics. In addition, VAPM is validatedagainst the experiments of steam methane reforming in a catalyticmonolith. The developed methodology reduces the computational costby 3 orders of magnitude while maintaining the accuracy of the detailedmultichannel simulations.