Fluid flow through geological formations is often concentrated on distinct preferential flow paths owing to the presence of fractures or large-scale permeability structures. However, the existence of such structures is not a mandatory condition of preferential paths formation. Pore-scale spatial fluctuations of pore size and/or pore connectivity in statistically stationary porous media, if sufficiently large, can also lead to the concentration of fluid flow on distinct pathways. In this paper, we attempted to establish the conditions of formation of preferential flow paths in heterogeneous porous media in terms of pore-size heterogeneity and pore connectivity. We simulated steady-state flow through stochastically constructed two- and three-dimensional pore networks, in which the width of the pore radius distribution and the pore coordination number (a measure of pore connectivity) were varied. We developed new techniques based on graph theory to identify potential preferential flow paths and characterize them. We observed a gradual transition from approximately uniform flow fields in low heterogeneity/high connectivity networks to flow localization on preferential paths with increasing pore-size heterogeneity and decreasing connectivity. The transition occurred at lower heterogeneity levels in three-dimensional than in two-dimensional simulations and was less influenced by pore connectivity variations. These results were summarized in a phase diagram in pore-size heterogeneity/pore connectivity parameter space, which we found consistent with relevant real rocks data.

中文翻译：

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非均质多孔介质优先路径上的流体流动浓度：图论的应用

由于裂缝或大规模渗透结构的存在，通过地质地层的流体流动通常集中在不同的优先流动路径上。然而，这种结构的存在并不是优先路径形成的必要条件。统计稳定的多孔介质中孔径和/或孔连通性的孔尺度空间波动，如果足够大，也会导致不同路径上的流体流动集中。在本文中，我们试图从孔径异质性和孔隙连通性方面建立非均质多孔介质中优先流动路径的形成条件。我们通过随机构建的二维和三维孔隙网络模拟稳态流动，其中孔隙半径分布的宽度和孔隙配位数（孔隙连通性的度量）是不同的。我们开发了基于图论的新技术来识别潜在的优先流动路径并表征它们。我们观察到从低异质性/高连通性网络中的近似均匀流场逐渐过渡到优先路径上的流动定位，随着孔径异质性的增加和连通性的降低。与二维模拟相比，三维中的转变发生在较低的异质性水平，并且受孔隙连通性变化的影响较小。这些结果总结在孔径异质性/孔隙连通性参数空间的相图中，我们发现这与相关的真实岩石数据一致。