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∝γ, and the fracture width ratio is α∝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.

中文翻译：

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致密气藏双孔隙介质的分形渗透率模型

水力压裂是致密气藏开发的重要手段。基质渗透率是影响压裂效果的关键因素。本文假设基质渗透率由一系列毛细管束和树状网络提供，充分考虑应力敏感性，根据含水饱和度、临界压力梯度等因素建立单毛细管（裂缝）流动方程。 (TPG)、裂缝宽度动态变化和真实气体效应。压裂后建立的渗透率模型由达西定律和分形理论推广。表观渗透率模型表明：（1）考虑固有水饱和度、应力敏感性、真实气体效应、TPG、裂缝宽度动态变化，毛细管和裂缝中的气流为单相流。裂缝渗透率远高于毛细管渗透率。当生产压力梯度低于TPG时，流量为0。随着地层压力的降低，双孔介质渗透率增加。(2) 随着含水饱和度的增加，渗透率降低，随着应力敏感性和真实气效应的增加，渗透率降低。(3) 树状分形结构参数对渗透率影响较大。分叉的数量和级数越大，渗透率越高。裂缝长度比为K∝γ，裂缝宽度比为α∝K。随着分叉的数量和系列的增加，负相关变得越来越深刻。这个分形模型充分考虑了TPG、应力敏感性和真实气体的影响，