Abstract
Based on fractal geometry theory, the Hagen–Poiseuille law, and the Langmuir adsorption law, this paper established a mathematical model of gas flow in nano-pores of shale, and deduced a new shale apparent permeability model. This model considers such flow mechanisms as pore size distribution, tortuosity, slippage effect, Knudsen diffusion, and surface extension of shale matrix. This model is closely related to the pore structure and size parameters of shale, and can better reflect the distribution characteristics of nano-pores in shale. The correctness of the model is verified by comparison with the classical experimental data. Finally, the influences of pressure, temperature, integral shape dimension of pore surface and tortuous fractal dimension on apparent permeability, slip flow, Knudsen diffusion and surface diffusion of shale gas transport mechanism on shale gas transport capacity are analyzed, and gas transport behaviors and rules in multi-scale shale pores are revealed. The proposed model is conducive to a more profound and clear understanding of the flow mechanism of shale gas nanopores.
Highlights
Shale gas reservoirs have different reservoir formation modes and reservoir physical properties from conventional gas reservoirs, which leads to the complexity and multi-scale characteristics of shale gas percolation
A new shale gas apparent permeability model is established based on fractal geometry theory, Hagen–Poiseuille law, and Langmuir adsorption law, which can be well matched with experimental data
Gas migration mechanism in nanoscale pores of shale matrix includes free gas slip flow, Knudsen diffusion and surface diffusion of adsorbed gas, so the total mass flow rate of gas flowing through nanoscale pores of shale matrix is
Summary
Shale gas reservoirs have different reservoir formation modes and reservoir physical properties from conventional gas reservoirs, which leads to the complexity and multi-scale characteristics of shale gas percolation. Based on the research results of Javadpour and Swami and Settari established a single-tube flow model of shale gas in nanoscale pores by considering multiple seepage mechanisms such as Darcy flow, Knudsen diffusion and slippage effect. In previous studies on apparent permeability model in nano-pores of shale gas, the influences of pore structure, slippage effect, Knudsen diffusion and surface expansion on pore flow of shale matrix have not been comprehensively considered [29,30,31]. As shale reservoirs are different from conventional reservoirs in physical characteristics and gas occurrence characteristics, it is necessary to comprehensively consider each influencing factor when establishing flow mechanism To achieve this goal, a new shale gas apparent permeability model is established based on fractal geometry theory, Hagen–Poiseuille law, and Langmuir adsorption law, which can be well matched with experimental data. This model can be a good reference for scientific research and engineering application
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