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.