Two-phase transport with simultaneous component adsorption and mechanical entrapment occurs in numerous suspension and nano-colloidal flows in porous media, including polymer flooding in oilfields. To the contrary of one-dimensional (1D) self-similar solution for polymer flooding that ignores the mechanical entrapment, accounting for this phenomenon breaks self-similarity. However, this non-self-similar problem allows for an exact integration. For the first time, the present work derives an exact solution for polymer injection into a rock saturated by oil and water with simultaneous adsorption and mechanical entrapment. The splitting method that uses Lagrangian coordinate as an independent variable instead of time, splits the 3 × 3 governing system into 2 × 2 auxiliary system that determines suspended and captured polymer concentrations, and the scalar equation for unknown phase saturation. The exact solution reveals two fingerprints of the component entrapment under small entrapped concentrations: stabilisation of the breakthrough concentration at the value below the injected one, and non-stabilised pressure drop growth. Three sets of laboratory polymer core-floodings exhibit a close match by the analytical model.

中文翻译：

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使用聚合物机械截留和吸附的三次聚合物驱的精确解决方案

在多孔介质中的大量悬浮液和纳米胶体流中，包括油田中的聚合物驱，发生了同时发生组分吸附和机械截留的两相输运。与忽略机械截留的聚合物驱一维 (1D) 自相似解决方案相反，解释了这种现象打破了自相似性。然而，这个非自相似问题允许精确积分。本工作首次推导出将聚合物注入被油和水饱和的岩石中同时吸附和机械截留的精确解决方案。使用拉格朗日坐标作为自变量而不是时间的分裂方法，将 3×3 控制系统分裂为 2×2 辅助系统，决定悬浮和捕获的聚合物浓度，以及未知相位饱和度的标量方程。精确的解决方案揭示了在小截留浓度下组分截留的两个指纹：突破浓度稳定在低于注入浓度的值，以及不稳定的压降增长。三组实验室聚合物岩心驱油表现出与分析模型的密切匹配。