Diffusion and Heterogeneous Reaction in Porous Media: The Macroscale Model Revisited

Abstract

Abstract Diffusion and reaction in porous media have been studied extensively due to the wide range of applications in which this transport phenomenon is involved. In particular, in chemical reactor engineering, reactive mass transfer is crucial to understand the performance of porous catalyst particles immersed in chemical reactors. Due to the disparity of characteristic lengths between the pores and the porous particles, this type of process is usually modeled by means of effective-medium equations, in which the solid and fluid phases are conceived as a pseudo-continuum. For conditions in which the pore-scale Thiele modulus (or Kinetic number) is much smaller than unity, it is reasonable to assume that the effective diffusivity involved in the effective-medium model is only a function of the porous medium geometry. However, a long debate has existed in the literature concerning the extensive use of this assumption for situations in which the Kinetic Number does not satisfy the above mentioned constraint. In addition, the functionality of the effective reaction rate coefficient with the Kinetic number has not been sufficiently studied. In this work we address these issues by means of the volume averaging method. Our analysis is focused on cases in which the Kinetic number can reach values up to 1. Interestingly, for this particular condition, the use of the intrinsic diffusivity tensor is justified. In addition, by means of Maclaurin series expansions, the effective reaction rate coefficient is shown to be acceptably approximated as a first-order function. These two conclusions for the effective medium coefficients constitute the major contributions from this work. In addition, the predictions from the upscaled model are validated by comparison with direct numerical simulations under steady and transient conditions.