ABSTRACT This article presents a model for the hydration of periclase into brucite during water infiltration into a dry, pure periclase core. The hydration process proceeds in two stages. In Phase I, an infiltration front advances through the core while simultaneously triggering the hydration reaction. Phase II begins once the front reaches the downstream end of the core and continues until hydration is complete. Asymptotic analysis shows that, at early times, the infiltration front advances proportionally to the square root of time. This behavior breaks down at intermediate times. At sufficiently large times, however, and provided that the Damköhler number—defined as the ratio of hydraulic to reaction timescales—is large and the infiltration front has not yet traversed the core, the front again exhibits a square‐root‐of‐time scaling. In this late‐stage Phase I regime, the hydration reaction becomes increasingly localized in a narrowing zone immediately behind the advancing infiltration front, accompanied by a sharpening gradient in the degree of reaction. A numerical solution of the governing equations confirms and quantifies the asymptotic predictions. The numerical method combines a finite difference scheme with a weak formulation of the balance condition at the moving front. Because the extent of reaction serves as a proxy for the eigenstrain associated with the volumetric expansion of the hydrated mineral, and because gradients in eigenstrain at the hydration/infiltration front control the magnitude of induced tensile stresses, the model provides a key theoretical framework for interpreting experimental observations that core damage intensifies with increasing Damköhler number.
Detournay et al. (Thu,) studied this question.