A quadruple-porosity model for shale gas reservoirs with multiple migration mechanisms

• Proposed a quadruple-porosity model for multiple fractured horizontal well in shale gas reservoirs.
• Solubility capacity of organic matters and diffusion of dissolved gas are considered.
• Both organic matters and clay minerals have the ability to adsorb gas with different adsorption properties.
• Clay mineral content and TOC are introduced into this model.
• Sensitivity analysis of some key parameters and field application are conducted.

This paper presents a quadruple-porosity model for multi-stage fractured horizontal well (MFHW) with finite conductive hydraulic fractures in shale gas reservoirs. In this model, free gas, adsorbed gas and dissolved gas co-exist and gas migration in shale incorporates diffusion in kerogen bulk, desorption from the surface of organics and clays, slippage flow in porous kerogen and inorganic matrix, and Darcy flow in natural fractures. Bi-Langmuir theory was introduced to describe gas desorption from the surface of clays and organics. Continuous line source function, Laplace transform and numerical discrete method were employed to solve this new model. Gauss-Jordan elimination method and Stehfest numerical inversion algorithm were applied to calculate the pressure and production responses. Type curves were plotted and flow regimes were identified. Sensitivity analysis of solubility coefficient, diffusion coefficient, inter-porosity coefficient, TOC, clays content, hydraulic fracture conductivity and permeability correction coefficient was performed. Finally, the proposed model was validated by fitting actual production data of a field case and comparing with other models. The matching results showed that quadruple porosity model considering dissolved gas was closer to the actual situation than trilinear-flow model and dual-porosity radial-flow model. To sum up, this presented model considering some key mechanisms further expands the transient pressure models for MFHW in shale gas reservoirs and it can be utilized to analyze well performance in the production life of gas wells.