On the Constitutive Equations for Coupled Flow, Chemical Reaction, and Deformation of Porous Media

Abstract

Deformation, chemical reactions, fluid flow in geological formations, and many engineering materials are coupled processes. Most existing models of chemical reactions coupled with fluid transport assume the dissolution-precipitation process or mineral growth in rocks. However, these models have limitations, such as predicting restricted reaction extent due to pore clogging or disregarding porosity changes resulting from mineral growth. Recent studies indicate mineral replacement involves coupled dissolution-precipitation, maintaining porosity while altering the solid volume. This has multiple practical implications for natural geological processes and within petroleum and environmental engineering. We present a novel model for reaction-driven mineral expansion that preserves porosity and allows solid volume change. First, we look at fluid-rock interaction at the pore scale and derive effective rheology of a reacting porous media. On a larger scale, we adopt a two-phase continuum medium approach to investigate the coupling between reaction, deformation, and fluid flow. Our micromechanical model based on observations assumes that rock or cement consists of an assembly of solid reactive grains, initially composed of a single, pure phase. The reaction occurs at the fluid-solid contact and progresses into the solid grain material. We approximate the pores and surrounding solid material as an idealized cylindrical shell to simplify the problem and obtain tractable results. We derive macroscopic stress-strain constitute laws that account for chemical alteration and viscoelastic deformation of porous rocks. Our model explains the possibility of achieving a complete reaction, preservation of porosity during chemical reactions, and dependence of mechanical rock properties on fluid chemistry.