An integrated unconventional reservoir model that accounts for known mechanisms and nonlinearities affecting modeling of hydraulically fractured wells is developed. In general, modeling and simulation of multi-fractured reservoirs are highly challenging due to the complexity attributed to the flow in this very low permeability and dense structured rock. Pressure- dependent phenomena in reservoir modeling are considered as combined hydraulic and natural fracture conductivity losses, desorption, Klinkenberg gas slippage effect and non-Darcy flow. Integrating these phenomena and analyzing the importance of each parameter in a reservoir model are essential.
The proposed model includes three zones, Rock Matrix (I), Induced-Fracture (II) and Hydraulic Fracture (III) that are defined with different characteristics. Pressure dependent permeability is considered for zone II and III, with an exponential relationship between permeability and reservoir pressure. Governing equations of gas flow are non-linear partial differential equations, for all three zones, due to incorporated pressure-dependent phenomena that are solved using the finite difference method. A synthetic case is defined in order to investigate the effect of each individual phenomenon on long-term production. Moreover, a history matching process with Marcellus Shale field production data is performed in order to obtain the most uncertain parameters in the model.
Results showed that combined effect of permeability losses of hydraulic and induced-fracture zones results in 15 percent gas production drop in 30 years. Also, it is observed that Klinkenberg effect and non-Darcy flow have insignificant effect on the modeling of shale gas reservoirs, whereas desorption has great contribution on long-term production. It is concluded that the minimum ingredients for an accurate shale reservoir modeling are considering gas desorption phenomena alongside with pressure-dependent permeability for the hydraulic and induced-fractures network. Our simple reservoir modeling approach helps in understanding complex behavior of flow mechanisms in shale plays. Also, this integrated model can be used during optimization of key factors in hydraulic fracturing process and fracture characterization by history matching of production.