modeling of hydraulic fracture problem in partially saturated porous media using cohesive zone model

in this paper, a finite element model is developed for the fully hydro-mechanical analysis of hydraulic fracturing in partially saturated porous media. the model is derived from the framework of generalized biot theory. the fracture propagation is governed by a cohesive fracture model. the flow within the fracture zone is modeled by the lubrication equation. the displacement of solid phase, and the pressure of wetting and non-wetting phases are considered as the main unknown parameters. other variables are incorporated into the model using empirical relationships between saturation, permeability and capillary pressure. zero-thickness element and conventional bulk element are used for propagating fracture and the surrounding media, respectively. the model is validated with respect to analytical solution of hydraulic fracture propagation problem in saturated media and then the problem is solved in semi-saturated media, considering the wetting and non-wetting pore fluid.