The solution to the Buckley–Leverett problem in fractured porous media is investigated by applying the dual-porosity dual-permeability model. It is shown that the dual-permeability medium is equivalent to an upscaled homogenized medium at long injection times when local capillary equilibrium is established. Simple analytical relationships for the petrophysical properties and saturation functions of the equivalent medium are derived. The upscaled relative permeability and the fractional flow function can exhibit kinks, resulting in more complicated solutions to the Buckley–Leverett problem as compared to the classical case. It is found that immiscible displacement in fractured porous media leads to the appearance of saturation profiles with several displacement fronts and rarefaction waves. Up to four solution types are possible, which are constrained in a solution map constructed in the space of the dimensionless parameters of the problem. It is shown that, for particular parameters, the displacing fluid moves faster through the matrix than through the fractures.

中文翻译：

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具有局部毛细管平衡的双渗透介质中的流体置换

通过应用双孔隙度双渗透率模型研究了裂缝多孔介质中 Buckley-Leverett 问题的解决方案。结果表明，当建立局部毛细管平衡时，双渗透介质在较长的注射时间内等效于放大的均质介质。导出了等效介质的岩石物理特性和饱和度函数的简单解析关系。与经典情况相比，放大的相对渗透率和分数流函数可能会出现扭结，从而导致巴克利-莱维特问题的解决方案更加复杂。研究发现，裂缝性多孔介质中的不混溶位移导致出现具有多个位移前沿和稀疏波的饱和剖面。多达四种解决方案类型是可能的，它们被约束在问题的无量纲参数空间中构建的解映射中。结果表明，对于特定参数，驱替流体通过基质的速度比通过裂缝的速度要快。