Modeling of subcritical cracking in acidized carbonate rocks via coupled chemo-elasticity
Injection of acidized water into the crack process area has been known for long to induce subcritical crack propagation. Acid rain or vegetation decomposition can cause activation or reactivation of landslides at subcritical stress, while acid injection is used to enhance oil and gas reservoir stimulation. Equally promising is acid enhancement of crack propagation in geothermal field stimulation. To quantify the above mentioned processes, crack propagation is simulated using a chemo-elasticity model in which a chemically controlled strain is added to linear elastic strain, in analogy to thermal strain. That strain is proportional to accumulated mass removal, controlled by a chemical reaction. The coefficient of chemical shrinkage is either constant, or is postulated to depend on the level of straining of rock using various scalar measures of either volumetric or shear strain to simulate the dependence of mineral dissolution on micro-cracking. With that formulation an Airy stress function, as in classical linear elasticity solution, has been for the first time, to our knowledge, used for solving chemo-elasticity problem, by employing an additional particular potential term. The results suggest that a constant chemically induced shrinkage alone is not sufficient to produce any significant enhancement of the crack tip displacement. However, making the coefficient of chemical shrinkage dependent on a shear strain invariant (and hence making the constitutive law implicit), leads to an enhancement of crack propagation velocity at a desired level. Yet, the obtained crack propagation acceleration appears to be too modest. That suggests that to obtain realistic results, in addition to diffusive transport, the advective–reactive transport process (especially, permeability) should be as well coupled to deformation.
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