We employ the semi-analytical approach in modeling of coupled flow and geomechanics, where flow is solved numerically and geomechanics is solved analytically. We first model a PKN hydraulic fracture geometry numerically and incorporate the fluid compressibility term in order to investigate the effect of the fluid compressibility on hydraulic fracture geometry evolution. The results show that as the fluid becomes compressible, the fracture propagation is delayed because it takes time for pressure to be built up to extend the fracture. In a multi-phase flow system, we model a hydraulic fracturing process in a gas reservoir by solving flow numerically and geomechanics analytically. The fracture propagates slowly when water saturation of the reservoir is low. This implies high initial gas saturation, resulting in high total compressibility of reservoir fluid. We observe the gas concentration near the fracture tip, caused by (1) the movement of initial gas within the fracture to the fracture tip and (2) the possibility of the leakage of gas from the formation to the hydraulic fracture. The existence of gas is another factor that can lead fluid flow within the hydraulic fracture to be compressible
