Permeability of fractured media plays an important role in many hydrogeologic applications. In this study, we propose an approach to quantify the equivalent permeability of fractal fractured media along with the fracture length direction, and both the laminar flow and nonlinear flow are considered according to the fracture features and critical Reynolds number. The analytical expression for equivalent permeability of fractured media is derived, which depends on fractal fracture properties and the applied conditions. The new approach is applicable for any Newtonian fluid. The effects of fractal dimension for aperture and length, maximum fracture aperture, ratio of minimum to maximum aperture, critical Reynolds number and pressure head loss across the fractures are explored and discussed. The fractal dimension for fracture aperture is positively correlated with the porosity of porous media, and a clear power-law correlation between the equivalent permeability and porosity can be observed in the results. The maximum aperture and the ratio of minimum to maximum aperture control the size of fracture apertures, and the increase in both parameters leads to high permeability. The larger fractal dimension for length causes more tortuous fractures, which reduce the equivalent permeability. A higher critical Reynolds number leads to a larger equivalent permeability. A larger pressure head loss results in a smaller equivalent permeability.

中文翻译：

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包含曲折和非线性流动的破裂介质的等效渗透率

裂缝介质的渗透性在许多水文地质应用中起着重要作用。在这项研究中，我们提出了一种量化分形裂缝介质等效渗透率和裂缝长度方向的方法，并根据裂缝特征和临界雷诺数考虑层流和非线性流。推导了裂缝介质等效渗透率的解析表达式，该表达式取决于分形裂缝性质和应用条件。新方法适用于任何牛顿流体。探讨和讨论了分形维数对孔径和长度、最大裂缝孔径、最小孔径与最大孔径之比、临界雷诺数和压头损失的影响。裂缝孔径的分形维数与多孔介质的孔隙度呈正相关，从结果中可以看出等效渗透率与孔隙度之间存在明显的幂律关系。最大孔径和最小孔径与最大孔径的比值控制着裂缝孔径的大小，这两个参数的增加导致高渗透率。长度分形维数越大，裂缝越曲折，从而降低等效渗透率。较高的临界雷诺数导致较大的等效渗透率。较大的压头损失导致较小的等效渗透率。最大孔径和最小孔径与最大孔径的比值控制着裂缝孔径的大小，这两个参数的增加导致高渗透率。长度分形维数越大，裂缝越曲折，从而降低等效渗透率。较高的临界雷诺数导致较大的等效渗透率。较大的压头损失导致较小的等效渗透率。最大孔径和最小孔径与最大孔径的比值控制着裂缝孔径的大小，这两个参数的增加导致高渗透率。长度分形维数越大，裂缝越曲折，从而降低等效渗透率。较高的临界雷诺数导致较大的等效渗透率。较大的压头损失导致较小的等效渗透率。