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Duo to different transport mechanisms and gas storage in organic and inorganic systems, a new triple-continuum model coupling Discrete Fracture Model (DFM) was established to investigate gas flow in shale gas reservoir. Considering the multi-scale and heterogeneity of shale matrix, fractal theory was used to calculate the apparent permeability of organic and inorganic systems while multiple gas transport mechanisms such as viscous flow, Knudsen diffusion, surface diffusion, gas absorption/desorption effect and real gas effect were incorporated. This coupled mathematical model was solved by Finite Element Method (FEM) and the presented fractal apparent permeability model was validated with the experimental data. The results show that fractal characteristics of shale matrix have great impact on gas reservoir performance. The model without considering the influence of fractal characteristics could lead to underestimate gas production by approximately 17%. Viscous flow is the dominate transport mechanisms of shale gas and Knudsen diffusion has an impact on gas flow when the pressure declines. Surface diffusion should be only considered in organic systems and can be ignored. Then the results of sensitivity analysis show that the characteristic parameters of inorganic matter have a greater impact than those of organic matter and establishing a triple-continuum model with considering comprehensive effect of organic and inorganic matter is necessary. In addition, gas production would decrease as the pore fractal dimension and tortuosity fractal dimension increase, which results from the increasing number of small pores and more tortuous path for gas flow.
The permeability of shale controls gas transport in shale gas reservoirs. The shale has a complex pore structure at the nanoscale and its permeability is affected by multiple transport and action mechanisms. In this study, a 3D fractal model for predicting the apparent gas permeability of shale matrix is presented, accounting for the effects of the transport mechanisms (bulk gas transport and adsorption gas diffusion) and action mechanisms (gas adsorption, real gas properties, water film, stress dependence, and total organic carbon (TOC) content). The proposed model is validated with the published experimental data. A series of sensitivity analyses are performed to investigate the influence of fractal characteristics and action mechanisms on the apparent permeability caused by each transport mechanism. The results show that the real gas properties, water film, and stress dependence cause different effects on the total apparent permeability of shale under different fractal characteristics. The maximum pore diameter is inversely proportional to the effects of these action mechanisms, and the porosity is positively proportional to the effects of real gas properties and water film but inversely proportional to the effects of stress dependence. An increase in TOC content can cause an improvement in the total apparent permeability. Furthermore, the effects of action mechanisms on the apparent permeability caused by different transport mechanisms are differently affected by the fractal characteristics. Changes in fractal characteristics mainly affect the apparent permeability caused by slip flow in the real gas effect, slip flow and Knudsen diffusion in the water film effect, and all transport mechanisms in the stress dependence effect.