Effective rheology of (de)compacting reactive porous media

Deformation, chemical reactions, fluid flow in geological formations, and many engineering materials, such as cement, are coupled processes. Most existing models of chemical reactions coupled with fluid transport assume the dissolution-precipitation process or mineral growth in rocks. However, dissolution-precipitation models predict a very limited extent of reaction hampered by pore clogging and blocking reactive surfaces, which will stop reaction progress due to limited fluid supply to reactive surfaces. Yet, field observations report that natural rocks can undergo 100% hydration/carbonation. Mineral growth models, on the other hand, preserve solid volume but do not consider its feedback on porosity evolution. In addition, they predict an unrealistically high force of crystallization on the order of several GPa that must be developed in minerals during the reaction. Yet, experiments designed to measure the force of crystallization consistently report values on the order of hundreds of MPa, which is close to the failure limits for most rock types. Recent experimental and observational studies suggest that mineral replacement is a coupled dissolution-precipitation process that preserves porosity and is associated with the change in the solid volume. Volume change associated with chemical reactions has multiple practical implications. It might be hazardous, causing damage to building materials or deterioration of caprock permeability and leakage of waste fluids, at least along the injection wellbore. Or it might be useful. For example, reaction-driven mineral expansion associated with the hydration of some solid additives may be utilized in plugging and abandonment of old petroleum wells to prevent leakage between plug and caprock or between plug and casing. In a geological context, mineral expansion plays an important role in pseudomorphic replacement and vein formation. Here, we propose a new model for reaction-driven mineral expansion, which preserves porosity and limits unrealistically high build-up of the force of crystallization by allowing inelastic failure processes at the pore scale. First, we look at fluid-rock interaction at the pore scale and derive effective rheology of a reacting porous media. We use a two-phase continuum medium approach to investigate the coupling between reaction, deformation, and fluid flow on a larger scale. 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 poroviscoelastic stress-strain constitute laws that account for chemical alteration and viscoelastoplastic deformation of porous rocks. Our model explains many experimental observations on natural and engineering geomaterials, such as the possibility of achieving a complete reaction, preservation of porosity during chemical reactions, moderate values of the force of crystallization, and dependence of mechanical rock properties on fluid chemistry.