Mesoscale and Hybrid Models of Fluid Flow and Solute Transport

Abstract

Fluid flow and reactive transport is relevant to many subsurface applications including CO2 sequestration, miscible/immiscible displacements in enhanced oil recovery, wellbore acidization, pollutant transport, and leakage/remediation of nuclear waste repositories. In all these scenarios, one or more fluid phases flow through the complicated geometry of the pore space, while advecting one or more chemical species along their flow streamlines. Simultaneously, the chemical species undergo molecular diffusion, due to their Brownian motion, allowing them to randomly jump from one streamline to the next. In the case of fluid–fluid or fluid–mineral reactions, chemical species may be transformed, potentially leading to precipitation and/or dissolution of solid minerals that alter the geometry/topology of the pore space. This in turn affects the velocity field of flow, and thus transport via advection/diffusion. Such complicated feedback between these pore-scale processes could give rise to “emergent” manifestations at larger scales. These manifestations are referred to as “emergent” because they cannot be foreseen from the behavior of the individual pore-scale mechanisms involved. In order to make reliable predictions of flow and transport at any scale of interest, accurate models need to be developed. Two spatial scales are commonly identified with a porous medium: the “micro/pore scale” (1–100 μm) and the “macro/continuum scale” (>1 m). The former is the fundamental scale in which physical processes (flow, transport, and geochemistry) take place, and the porous medium is regarded as discrete in nature (void space vs. grain space). The latter is a more practical scale, where we would ultimately like to have a reliable description of flow and reactive transport, and the porous medium is regarded as a continuum. The macroscopic parameters appearing in the description of continuum models, such as permeability or dispersion coefficient, are typically extracted from experiments or stand-alone pore-scale simulations. While such a “hierarchical” upscaling approach is …