Upscaling Reactive Transport Under Hydrodynamic Slip Conditions in Homogeneous Porous Media

Abstract

AbstractReactive transport of a dilute species in a Newtonian fluid saturating a homogeneous porous medium for slip flow is analyzed in this work. Incompressible Newtonian flow with a first‐order (Navier) slip boundary condition is considered together with a first‐order heterogeneous reaction. Kinetic numbers range up to unity while Knudsen numbers, characteristic of slip‐flow, are smaller than approximately 0.1. The pore‐scale problem is upscaled, using the volume averaging method, to obtain a macroscopic transport equation (referred to as the complete upscaled model) operating at the Darcy scale. Using order of magnitude estimates and an expansion in terms of the Kinetic number, simplifications in the expressions of the effective coefficients are explored. The conditions under which the effective convective velocity and the total dispersion tensor are independent of reaction are derived. Under such conditions, a simplified version of the macroscopic transport equation is obtained. This is referred to as the simplified model. Numerical results for a simple structure indicate that the longitudinal dispersion coefficient decreases with decreasing Knudsen number, while the opposite holds for the transverse component of the total dispersion tensor, the effective convective velocity, and the effective reaction rate coefficient. These effects are more evident when the Péclet number increases (i.e., in the convective‐favored regime) and when slip effects are more pronounced. Results predicted by the simplified and the complete versions of the upscaled model are validated with direct numerical simulations of the pore‐scale problem on a two‐dimensional model structure.