A multiscale approach in modeling of chemically reactive porous media

Chemical reactions occur in geotechnical, biological and synthetic porous media. Swelling and shrinkage phenomena can be observed in clays, shales and gels, when they are in close contact with water. In petroleum engineering, wellbore-stability problems are caused by swelling or shrinking of the wellbore. Thus, it is significant to model the Chemo-Hydro-Mechanical (CHM) processes in porous media that include different physical and geometrical heterogeneities. In this paper, a multiscale computational homogenization approach is developed for the analysis of CHM problems. In this manner, the first-order homogenization technique is adopted for the two-scale formulation. The heterogeneities are assumed in the microscale level and a homogeneous domain is considered for the macroscale level, where the constitutive behavior is derived from the microscopic level. The governing equations and constitutive equations of the CHM processes are presented in the coupled manner. The primary variables are taken as the displacement, pore pressure, and solute concentration fields. Moreover, the transient terms are included in the microscale level to increase the accuracy of computations. Consequently, a generalized form of Hill-Mandel principle of macro-homogeneity is defined between the two scales. Appropriate microscopic boundary conditions, i.e. the linear and periodic boundary conditions, are employed to satisfy the averaging constraints. Finally, the accuracy and efficiency of the proposed computational multiscale method are illustrated through several numerical examples.