A fractal permeability model for the dual-porosity media of tight gas reservoirs

Hydraulic fracturing is a crucial method for the exploitation of tight gas reservoirs. The matrix permeability is a key factor influencing the fracturing result. This paper assumes that the matrix permeability is provided by a series of capillary bundles and tree-like networks, fully considering the stress sensitivity to establish a single-capillary (fracture) flow equation in terms of factors such as the water saturation, threshold pressure gradient (TPG), fracture width dynamic changes and real gas effect. The established permeability model after fracturing is generalized by Darcy's law with the fractal theory. The apparent permeability model shows that (1) the gas flow in capillaries and fractures is single-phase flow considering the connate water saturation, stress sensitivity, real gas effect, TPG, and fracture width dynamic changes. The fracture permeability is much higher than the capillary permeability. When the production pressure gradient is lower than the TPG, the flow rate is 0. As the formation pressure decreases, the dual-porosity medium permeability increases. (2) As the water saturation increases, the permeability decreases, and with increasing stress sensitivity and real gas effect, the permeability decreases. (3) The parameters of the tree-like fractal structure greatly affect the permeability. The larger the number and series of bifurcations are, the higher the permeability is. The fracture length ratio is K proportional to gamma, and the fracture width ratio is alpha proportional to K. The negative correlation becomes increasingly profound with increasing number and series of bifurcations. This fractal model fully considers TPG, stress sensitivity, and real gas effects, making the dual-porous medium reservoir permeability calculation model more complete, which can provide a more accurate calculation method for the permeability of the reservoir stimulation area after fracturing.