多孔介质中不混溶粘性指进的起始与演化建模
Modelling the onset and evolution of immiscible viscous fingering in porous media
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中文总结 AI 辅助
本文针对多孔介质中不混溶粘性指进问题，基于线性稳定性分析与数值模拟，结合小尺度通道效应和弱油湿毛细管压力函数，成功匹配粘度比2000的实验结果，揭示了指进演化的关键机制。
中文摘要 AI 辅助
多孔介质中粘性指进的模拟与石油工程及水文地质中的驱替过程直接相关。基于近期针对极高粘度比下明确定义指形的建模方法研究，本文探究粘性指进背后的物理机制，以及捕捉实验中观测到的指形尺度和饱和度图案所需的建模要求。我们模拟并匹配了粘度比μₒ/μw=2000的粘性指进实验，讨论每个建模步骤的物理意义。采用线性稳定性分析表征驱替的早期不稳定性，后续数值模拟表明，为使模拟的指形尺度与实验匹配，起始阶段的最不稳定波长必须比目标指形宽度小数倍——以在考虑非线性阶段的屏蔽与合并后，指形仍保持较细。还需引入小尺度通道效应，以破坏近均质介质中粘性指进模拟常见的尾随稳定区域。最后，我们表明包含弱油湿毛细管压力函数可使模型捕捉实验中观测到的旁路原油。
英文摘要
The simulation of viscous fingering in porous media is of direct relevance to displacement processes in petroleum engineering and hydrogeology. Building on recent work proposing a modelling approach for well-defined fingers at very adverse viscosity ratios, we investigate the physical mechanisms behind viscous fingering and the modelling requirements for capturing the finger scales and saturation patterns observed in experiments. We simulate and match a viscous fingering experiment at a viscosity ratio of $μ_{o}/μ_{w}{=}2000$, discussing the physical significance of each modelling step. Linear stability analysis is used to characterize the early-stage instability of the displacement. Subsequent numerical simulations show that, for the simulated finger scales to match the experiment, the most unstable wavelength at onset must be several times smaller than the desired finger width---so that, after accounting for shielding and merging in the nonlinear regime, the fingers remain thin. Small-scale channelling effects are also required to disrupt the trailing stable region commonly observed in simulations of viscous fingering in nearly homogeneous media. Finally, we show that including a weakly oil-wet capillary pressure function enables our model to capture the bypassed oil observed in the experiment.
