Current hydraulic fracture conductivity evolution models fail to incorporate the fractures microscopic petrophysical properties, and notable discrepancies consequently exist between predictions and observations. We present a new conductivity model considering the irregular fracture undulation and channel roughness in propped fractures. The propped fracture networks are treated as bundles of tortuous capillaries with a fractal distribution of sizes with the size of a single capillary calculated using a constitutive model representing contacting rock surfaces under normal cyclic loading. The capillaries tortuosity is described by the effective inclination angle, and the fracture closure is calculated by the history of the in situ stress distribution and rock property changes. The fracture surface roughness, number of capillaries per unit width of the hydraulic fracture, and total cross-sectional area are obtained using fractal theory. The proposed model is validated by comparison with experimental data and other analytical solutions. The results indicate that the apparent permeability and conductivity of the fracture significantly decrease to 58.0% and 48.2% within 2 years of production, respectively, and then remain steady for the remainder of the well life. Compared with fixed fracture conductivity, the temporal variability in conductivity leads to a lower formation pressure drop and reduction in final production. Furthermore, the influences of the effective inclination angle, relative roughness of micro-channel, fracture porosity, and microchannel fractal dimension on the conductivity are investigated and the conductivity proves to be largely controlled by the fracture porosity, while the influence of the relative roughness ratio on the conductivity is least significant.

中文翻译：

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支撑裂缝分形时间导流模型及其在致密油藏中的应用

目前的水力裂缝导流能力演化模型未能结合裂缝微观岩石物理特性，因此预测和观测之间存在显着差异。我们提出了一种考虑支撑裂缝中不规则裂缝起伏和通道粗糙度的新导流模型。支撑的裂缝网络被视为具有分形大小分布的曲折毛细管束，使用表示在正常循环载荷下接触岩石表面的本构模型计算单个毛细管的大小。毛细管弯曲度用有效倾角描述，裂缝闭合度通过地应力分布历史和岩石性质变化计算。断面粗糙度，水力裂缝单位宽度的毛细血管数量和总横截面积是利用分形理论获得的。通过与实验数据和其他分析解决方案的比较来验证所提出的模型。结果表明，裂缝的表观渗透率和导流能力在生产后 2 年内分别显着下降至 58.0% 和 48.2%，然后在剩余的井寿命内保持稳定。与固定裂缝导流能力相比，导流能力的时间变化导致较低的地层压降和最终产量的减少。此外，有效倾角、微通道相对粗糙度、裂缝孔隙度、