A Reactive-Chemo-Mechanical Model for Weak Acid-Assisted Cavity Expansion in Carbonate Rocks

Abstract

Cavity expansion due to internal pressurization is a fundamental problem encountered in many environmental, geotechnical, drilling, reservoir and geo-energy engineering problems. In these scenarios, cavity pressurization is often performed in a reactive chemical environment which can considerably influence the material behavior via chemical softening leading to unexpected failure. We propose a reactive-chemo-elasto-viscoplastic model to consider the problem of an instantaneously applied long-lasting dose of acid at the cavity. The cavity wall in plane strain is assumed under a constant subcritical uniformly distributed compressive traction. All the fields involved are axisymmetric. An extension of Perzyna’s overstress model into the chemical domain is proposed, based on the concept of reactive chemo-plasticity with a yield limit dependent on the mineral mass dissolved, inducing chemical softening. Mineral dissolution, via a rate equation, is described as a function of acid intensity and a variable specific surface area of solid–fluid interface. The latter is in turn assumed to be a function of irreversible deviatoric deformation. The presented constitutive formulation is the first cavity expansion theory to capture a combination of the effect of mineral dissolution on Young’s modulus, damage enhancement on chemical softening, and a chemical “ductilization” effect observed in the post-yield behavior of carbonate rocks. In the final set of governing equations, multiple cross-scale physio-chemo-mechanical processes, i.e., micro-cracking, chemical reactions, reactive-diffusion processes, delivery of acid, and the yielding of solid matrix, are fully coupled. Subcritical chemically driven yielding around the cavity and key influencing factors concerning acid environment, constitutive feedbacks and boundary conditions are numerically characterized.