Abstract Two-phase water-steam flow conditions are frequently encountered in many engineering applications, including geothermal reservoirs. Although routine calculations are based on the multiphase Darcy’s law, the role of the topology of the flowing phases at the pore-scale is usually neglected in the estimation of relative permeabilities. Instead, the latter are frequently computed using empirical models like the Corey correlation. In this work, we first apply the model for relative permeabilities based on pore-scale flow regimes developed by Picchi and Battiato (2019), Relative permeability scaling from pore-scale flow regimes, Water Resour. Res. 55, 3215–3233, to scenarios typical of geothermal reservoirs and then extend it by deriving the scaling laws for the transmissibilities and the thermal properties as a function of temperature. First, we discuss the scaling behavior of normalized relative permeabilities in terms of viscosity ratio and capillary number of water-steam systems and, then, we provide a validation of the model against experimental data available in the literature. The model captures well the data trends collected in real 3D porous media. These results suggest that water-steam relative permeabilities follow the same scaling behavior of gas-liquid systems where the non-wetting phase is much less viscous than the wetting phase. Finally, we investigate the impact that relative permeabilities have on heat transfer rates at two-phase flow conditions and the scaling of mass and energy transmissibility and thermal properties of the mixture. An estimation of the exergy carried by the two-phase water-steam mixture is also included.

中文翻译：

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多孔介质中两相水蒸汽相对渗透率和热通量的标度

摘要 水汽两相流动条件在包括地热储层在内的许多工程应用中经常遇到。尽管常规计算基于多相达西定律，但在估计相对渗透率时通常会忽略孔隙尺度流动相拓扑结构的作用。相反，后者经常使用诸如 Corey 相关性之类的经验模型来计算。在这项工作中，我们首先应用基于由 Picchi 和 Battiato (2019) 开发的孔隙尺度流态的相对渗透率模型，从孔隙尺度流态的相对渗透率缩放，水资源。水库 55, 3215–3233，到典型地热储层的场景，然后通过推导作为温度函数的传输率和热特性的标度定律来扩展它。第一的，我们根据水-蒸汽系统的粘度比和毛细管数讨论归一化相对渗透率的标度行为，然后，我们根据文献中可用的实验数据对模型进行了验证。该模型很好地捕捉了在真实 3D 多孔介质中收集的数据趋势。这些结果表明，水-蒸汽的相对渗透率遵循与气-液系统相同的结垢行为，其中非润湿相的粘度远低于润湿相。最后，我们研究了相对渗透率对两相流动条件下的传热率以及混合物的质量和能量传输率和热性能的缩放的影响。还包括对由两相水-蒸汽混合物携带的火用的估计。