Backflow is a typical flow phenomena in two-phase displacement, but it is rarely studied in the forced imbibition and it remains unknown if the backflow occurs in forced imbibition into a porous medium. In this paper, we focus on the forced imbibition and investigate the backflow behavior in pore doublet (PD) models and in dual-permeability pore networks. Inspired by Gu et al. (2021) and Shan et al. (2023), a general mathematical model is first developed to predict the evolution of the penetration length of wetting fluid in a PD with arbitrary initial interface locations. Based on the analytical predictions and numerical simulations, we then study the influence of initial interface location, capillary number, viscosity ratio, and channel width ratio on the backflow. Results show that the backflow in a PD is mainly attributed to high flow rate in narrow channel, driven by the dominant capillary force. To supplement the insufficiency of inlet flow rate, the fluid in wide channel has to flow backwards to fill the narrow channel. The backflow strengthens with the decrease of capillary number or viscosity ratio, but it exhibits non-monotonic variation with initial interface location and channel width ratio. Moreover, the phase diagrams showing the critical conditions for the occurrence of backflow are established in terms of capillary number, viscosity ratio and channel width ratio. Finally, numerical simulations are conducted to explore the occurrence of backflow in three different dual-permeability pore networks. It is found that the backflow does not occur in dual-permeability pore networks due to the low flow rate caused by overlap event and pronounced tortuosity in the low permeability zone, or occurs only in the early stage when the capillary valve effect does not work.

中文翻译：

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强制吸入双渗透孔隙网络时是否会发生回流？

回流是两相驱中的一种典型流动现象，但在强制渗吸过程中的研究却很少，且在强制渗吸多孔介质中是否会发生回流仍不清楚。在本文中，我们重点关注强制渗吸，并研究双孔 (PD) 模型和双渗透孔隙网络中的回流行为。受到顾等人的启发。 (2021) 和 Shan 等人。 (2023)，首先开发了一个通用数学模型来预测具有任意初始界面位置的 PD 中润湿液的渗透长度的演变。基于分析预测和数值模拟，我们研究了初始界面位置、毛细管数、粘度比和通道宽度比对回流的影响。结果表明，PD 中的回流主要归因于狭窄通道中的高流速，由主导毛细管力驱动。为了补充入口流量的不足，宽通道中的流体必须向后流动以填充窄通道。回流随着毛细管数或粘度比的减小而增强，但随初始界面位置和通道宽度比呈现非单调变化。此外，还根据毛细管数、粘度比和通道宽度比建立了显示回流发生的临界条件的相图。最后，进行数值模拟来探讨三种不同的双渗透孔隙网络中回流的发生。研究发现，由于低渗透带重叠事件和明显的迂曲造成流速较低，双渗透孔隙网络中不会发生回流，或者仅在毛细管阀效应不起作用的早期阶段发生回流。