Modeling Fixed Bed Reactors of Open-Cell Foam Pellets as Porous Media

Traditional fixed-bed reactors use pellets that only allow species transport through diffusion, not convection. However, using highly porous pellets, such as open-cell foams, allows bulk gas to move through them. Such a fixed bed results in a lower pressure drop and intimate contact between the gas and solid phases, which is desirable for catalytic reactions and adsorption processes. A common strategy for modeling fixed beds is to use the porous medium assumption, where the gas and solid phases are represented as an effective porous medium. This approach necessitates several effective properties calculated using analytical relations for simple geometries and empirical correlations for complex geometries. However, such a representation for a fixed bed of highly porous pellets is unavailable. This study addresses this problem by developing a mathematical framework for a fixed bed reactor of open-cell foam pellets as a porous medium. To this end, the volume averaging and asymptotic averaging techniques are employed. The governing equations for the porous medium (continuum) model are developed based on the volume averaging technique, and the effective properties are calculated using the unit cell simulations. The developed mathematical framework is assessed against three-dimensional particle-resolved simulations for linear and nonlinear catalytic kinetics and CO₂ adsorption. For all the test cases, the developed framework can reproduce the pressure drop and species concentration predicted by the particle-resolved simulations with orders of magnitude reduction in the simulation time.