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The Impact of Pore-Scale Flow Regimes on Upscaling of Immiscible Two-Phase Flow in Porous Media

机译：孔尺度流型对多孔介质中不相溶的两相流放大的影响

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摘要

Empirical or theoretical extensions of Darcy's law for immiscible two-phase flow have shown significant limitations in properly modeling the flow at the continuum scale. We tackle this problem by proposing a set of upscaled equations based on pore-scale flow regimes, that is, the topology of flowing phases. The incompressible Navier-Stokes equation is upscaled by means of multiple-scale expansions and its closures derived from the mechanical energy balance for different flow regimes at the pore scale. We also derive the applicability conditions of the upscaled equations based on the order of magnitude of relevant dimensionless numbers, that is, Eotvos, Reynolds, capillary, Froude numbers, and the viscosity and density ratio of the system, as well as a set of closures valid for the basic flow regimes of low Eotvos number systems, that is, core-annular and plug and drop traffic flows. We provide analytical expressions for the relative permeability of the wetting and nonwetting phases in different flow regimes and demonstrate that the effect of the flowing-phases topology on the relative permeabilities is significant. Finally, we show that the classical two-phase Darcy law is recovered for a limited range of operative conditions, while specific terms accounting for interfacial and wall interactions should be incorporated to accurately model ganglia or drop traffic flow.
机译：对于不相溶的两相流，达西定律的经验或理论扩展已经显示出在连续流规模上对流进行正确建模的显着局限性。我们通过提出一组基于孔尺度流态的扩展方程组（即流动相的拓扑结构）来解决此问题。不可压缩的Navier-Stokes方程是通过多尺度扩展而放大的，并且其闭合是根据孔尺度上不同流态下的机械能平衡得出的。我们还根据相关的无量纲数的数量级（即Eotvos，Reynolds，毛细管，Froude数，系统的粘度和密度比以及一组封闭量）推导了高级方程的适用条件。适用于低Eotvos号码系统的基本流机制，即核心环流和即插即用流量。我们提供了在不同流动状态下润湿相和非润湿相的相对渗透率的解析表达式，并证明了流动相拓扑对相对渗透率的影响是显着的。最后，我们表明可以在有限的操作条件范围内恢复经典的两阶段达西定律，同时应考虑到界面和壁相互作用的特定术语，以准确地模拟神经节或交通流量。

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  • 来源
    《Water resources research》 |2018年第9期|6683-6707|共25页
  • 作者

    Picchi D.; Battiato I.;

  • 作者单位

    Stanford Univ, Dept Energy Resources Engn, Stanford, CA 94305 USA;

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