A rigorous and efficient numerical method for simulation of shale gas production considering complex hydraulic and natural fracture geometries and multiple gas transport mechanisms in nanopores is very important to evaluate stimulation effectiveness. In this study, we present an innovative EDFM (Embedded Discrete Fracture Model) method in conjunction with the third-party compositional reservoir simulator to simulate shale gas production considering all these complexities. Through the EDFM method, complex hydraulic and natural fractures can be directly and explicitly embedded in the matrix blocks. The complex fracture geometries can easily be handled without using local grid refinement near fractures or using unstructured gridding technique. In addition, gas transport mechanisms such as non-Darcy flow, gas desorption, gas slippage and pressure-dependent matrix permeability and fracture conductivity are included in the model. The LBM (lattice Boltzmann method) was used to model gas slippage phenomenon in nanopores. We verified the EDFM method against the LGR (local grid refinement) method for dealing with simple bi-wing fractures and the computational efficiency was also compared. After validation, we applied the EDFM method to perform history matching and production forecasting for an actual shale-gas well from Marcellus shale formation. Both simple and complex fracture geometries were considered and compared. Complex fracture geometry was predicted by a fracture propagation model considering natural fractures. Through history matching, conductivities of hydraulic fractures, active and non-active natural fractures were determined. The complex fracture geometry performs better in terms of productivity than the simple fracture geometry due to a larger amount of conductive fracture surface area. The simulation results based on an actual shale-gas well show that gas desorption and gas slippage significantly affects ultimate gas recovery, which can increase gas recovery after 30 years by 46.8%. Pressure-dependent matrix permeability and fracture conductivity play a negative impact on well productivity, which can reduce gas recovery after 30 years by 14%. Hence, complex fracture geometries and gas transport mechanisms should be properly accounted for in the numerical model in order to achieve more accurate long-term production forecasting of shale-gas wells.

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