We present simulations of two-phase flow using the Rothman and Keller colour gradient Lattice Boltzmann method to study viscous fingering when a “red fluid” invades a porous model initially filled with a “blue” fluid with different viscosity. We conducted eleven suites of 81 numerical experiments totalling 891 simulations, where each suite had a different random realization of the porous model and spanned viscosity ratios in the range \(M\in [0.01,100]\) and wetting angles in the range \(\theta _w\in [180^\circ ,0^\circ ]\) to allow us to study the effect of these parameters on the fluid-displacement morphology and saturation at breakthrough (sweep). Although sweep often increased with wettability, this was not always so and the sweep phase space landscape, defined as the difference in saturation at a given wetting angle relative to saturation for the non-wetting case, had hills, ridges and valleys. At low viscosity ratios, flow at breakthrough is localized through narrow fingers that span the model. After breakthrough, the flow field continues to evolve and the saturation continues to increase albeit at a reduced rate, and eventually exceeds 90% for both non-wetting and wetting cases. The existence of a complicated sweep phase space at breakthrough, and continued post-breakthrough evolution suggests the hydrodynamics and sweep is a complicated function of wetting angle, viscosity ratio and time, which has major potential implications to Enhanced Oil Recovery by water flooding, and hence, on estimates of global oil reserves. Validation of these results via experiments is required to ensure they translate to field studies.

我们使用 Rothman 和 Keller 颜色梯度 Lattice Boltzmann 方法展示了两相流的模拟，以研究当“红色流体”侵入最初充满具有不同粘度的“蓝色”流体的多孔模型时的粘性指法。我们进行了 11 套 81 次数值实验，共 891 次模拟，其中每套都有不同的多孔模型随机实现，跨度粘度比在范围\(M\in [0.01,100]\)和范围内的润湿角\ (\theta _w\in [180^\circ ,0^\circ ]\)使我们能够研究这些参数对突破（扫掠）时流体置换形态和饱和度的影响。尽管扫掠通常随着润湿性而增加，但并非总是如此，并且扫掠相空间景观（定义为给定润湿角下饱和度相对于非润湿情况下的饱和度的差异）具有山丘、山脊和山谷。在低粘度比下，突破处的流动通过横跨模型的窄指定位。突破后，流场继续演变，饱和度继续增加，尽管速率降低，最终在非润湿和润湿情况下均超过 90%。突破时存在复杂的扫掠相空间，突破后的持续演化表明流体动力学和波及是润湿角、粘度比和时间的复杂函数，这对通过水驱提高石油采收率具有重大潜在影响，因此对全球石油储量的估计具有重要意义。需要通过实验验证这些结果，以确保它们转化为实地研究。