We perform steady-state simulations with a dynamic pore network model, corresponding to a large span in viscosity ratios and capillary numbers. From these simulations, dimensionless steady-state time-averaged quantities such as relative permeabilities, residual saturations, mobility ratios and fractional flows are computed. These quantities are found to depend on three dimensionless variables, the wetting fluid saturation, the viscosity ratio and a dimensionless pressure gradient. Relative permeabilities and residual saturations show many of the same qualitative features observed in other experimental and modeling studies. The relative permeabilities do not approach straight lines at high capillary numbers for viscosity ratios different from 1. Our conclusion is that this is because the fluids are not in the highly miscible near-critical region. Instead they have a viscosity disparity and intermix rather than forming decoupled, similar flow channels. Ratios of average mobility to their high capillary number limit values are also considered. Roughly, these vary between 0 and 1, although values larger than 1 are also observed. For a given saturation, the mobilities are not always monotonically increasing with the pressure gradient. While increasing the pressure gradient mobilizes more fluid and activates more flow paths, when the mobilized fluid is more viscous, a reduction in average mobility may occur.

中文翻译：

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粘度比和压力梯度对多孔介质中稳态不可压缩两相流影响的孔隙网络建模

我们使用动态孔隙网络模型执行稳态模拟，对应于粘度比和毛细管数的大跨度。通过这些模拟，可以计算无量纲稳态时间平均量，例如相对渗透率、残余饱和度、迁移率和分流。发现这些量取决于三个无量纲变量，润湿流体饱和度、粘度比和无量纲压力梯度。相对渗透率和残余饱和度显示了许多在其他实验和建模研究中观察到的相同定性特征。对于不同于 1 的粘度比，相对渗透率在高毛细管数下不会接近直线。我们的结论是，这是因为流体不在高度混溶的近临界区域。相反，它们具有粘度差异和混合，而不是形成分离的、相似的流动通道。还考虑了平均流动性与其高毛细管数限制值的比率。粗略地说，这些值在 0 和 1 之间变化，但也观察到大于 1 的值。对于给定的饱和度，迁移率并不总是随压力梯度单调增加。虽然增加压力梯度会使更多的流体流动并激活更多的流动路径，但当流动的流体更粘稠时，平均流动性可能会降低。对于给定的饱和度，迁移率并不总是随压力梯度单调增加。虽然增加压力梯度会使更多的流体流动并激活更多的流动路径，但当流动的流体更粘稠时，平均流动性可能会降低。对于给定的饱和度，迁移率并不总是随压力梯度单调增加。虽然增加压力梯度会使更多的流体流动并激活更多的流动路径，但当流动的流体更粘稠时，平均流动性可能会降低。