Thermodynamic Characterization of Chemical Damage in Variably Saturated Water-Active Shales

Abstract

A constitutive framework is developed for variably saturated water-active swelling rocks undergoing chemical damage using modified mixture theory and continuum damage mechanics. The Helmholtzian thermodynamic potential for the skeletal system is derived as a function of the state variables including deformation, damage, two-phase fluid pressures, and chemical potential. Using this, in addition to chemo-poroelastic constitutive equations, a thermodynamically consistent first-order estimation of the damage variable is developed. The working of the theory is shown through the numerical example of water uptake in clay-rich shale rocks solved by the finite element method. The numerical results portray the significance of including variably saturated conditions in constitutive equations as a unique damage-dependent poroelastic behavior was observed for wet and dry regions. The theoretical-based damage estimation corroborated by previous experimental observations illustrates that the rock strength is dominantly controlled by the time of exposure to water rather than the level of water saturation. Contrary to what was perceived, the results show that poroelastic and chemo-poroelastic responses do not coincide even in less reactive shales due to the time-dependent water-induced microstructural deterioration of the rock. The microstructural deterioration increases the storage and flow capacity in the water-saturated region giving rise to substantive spatio-temporal changes in matrix stresses. The research findings provide valuable insights to understand how poromechanics plays a role in causing water uptake in water-sensitive rocks and how such behavior is coupled with associated microstructural chemical damage.