Abstract: In view of the great difficulty of simulating the shale gas seepage process, fractal theory is applied to describe the microstructure of shale gas reservoir. Based on the multi-layer adsorption phenomenon of adsorption layer, the pressure sensitive effect and the real gas effect are taken into account, the mass flow expression of micro-nano shale gas is derived, and the micro-nano fractal apparent permeability model of shale gas is also established. The accuracy of the model is verified by comparing the numerical simulation with the actual production data of Well A1 in Zhaotong shale gas field. The result shows that the number of adsorbed gas layers on the pore surface is more sensitive to pressure change, but less sensitive to temperature change. Due to the pressure sensitive effect, as the diffusion resistance of shale gas increases, the apparent permeability decreases. With the increase of gas compression factor, the thickness of the adsorption layer increases and the section area ratio of the adsorption zone increases. Moreover, the pressure sensitive effect of the shale pore decreases the pore diameter, and the induced flow of the adsorbed gas decreases first and then tends to be gentle, thus reducing the overall apparent permeability of shale gas. The research results can provide part of the theoretical basis for the numerical simulation of shale gas and improve the recovery efficiency of shale gas fracturing by controlling the main control elements that affect the fractal permeability of shale gas.

Key words: multi-layer absorption, micro-nano, pressure sensitive effect, real gas effect, induced flow of absorbed gas, fractal