Hysteresis of two-phase flows in porous and fractured media: From micro-scale Haines jumps to macro-scale pressure-saturation curves

铺在桌布上的酒渍或从破裂的岩石中渗出的油都是流体在多孔和破裂的材料中取代另一种流体的例子。流体驱替在广泛的应用中起着关键作用，包括农业和水文学、生物、能源和环境工程，以及水泥和食品的印刷和固化等工业过程。许多这些过程是循环驱动的，湿润性较弱的流体被湿润性较强的流体驱替（称为“吸胀”），反之亦然（“排水”）；例如，土壤中的降雨和蒸发循环，以及碳地质封存（CGS）中二氧化碳注入停止后的流动逆转。值得注意的是，这些循环表现出明显的滞后或路径依赖性。这在压力-饱和度（PS）关系中表现得很明显，在排液中达到给定饱和度（一种流体的相对量）所需的压力与在吸胀中不同。滞后及其相关的多值性和历史依赖性使得CGS的预测和控制，以及提高石油采收率和土壤修复具有很高的挑战性。润湿迟滞是一个具有重大实际意义的迷人科学问题，物理学家、地球科学家和工程师对它进行了近一个世纪的深入研究。尽管如此，我们对潜在机制的理解仍然是片面的。这种知识差距的主要来源是，大规模的滞后是微观毛细管不稳定性（间歇性钉住和流体-流体界面的“跳跃”）之间相互作用的结果。因此，现有的模型要么是启发式的——使用可调的、非物理参数，要么是难以处理的——需要的细节实际上是实验上甚至是数字上无法实现的；四肢的用处有限，而且会产生严重的误差。润湿滞后在我们今天面临的一些环境挑战中所起的作用，使得物理合理的预测模型的制定非常及时。拟议的项目通过制定第一个严格的润湿滞后模型来解决上述缺点，与现有模型相比，该模型仅基于清晰，可识别的物理参数。我们通过融合不同学科的数值、实验和理论方法来实现这一目标——统计物理学、流体力学、水文学和地球物理学，并利用最新的计算和实验进展。该模型将用于定量解释微观毛细管不稳定性（跳跃）如何在更大（连续）尺度上导致滞后，这对更大的多孔介质科学界（工程师、物理学家和地球科学家）有巨大的好处。该模型还将用于通过油藏模拟（能源和环境应用中模拟地下流体的标准工具）评估迟滞对现场工程实践的影响，其中PS关系表现为本构方程。与我们在英国地质调查局的项目合作伙伴一起，我们将使用我们的模型生成的物理健全的PS关系进行油藏模拟，旨在改善对英国具有巨大经济潜力的CGS操作。

A wine stain spreading on a tablecloth or oil percolating through a fractured rock are examples of a fluid displacing another in porous and fractured materials. Fluid displacement plays a key role in a wide range of applications, including agriculture and hydrology, biology, energy and environmental engineering, and industrial processes such as printing and curing of cement and foods. Many of these processes are driven in cycles, alternating between displacement of the less wetting fluid by the more wetting one (called "imbibition"), and vice versa ("drainage"); for example rain and evaporation cycles in soils, and flow reversal after CO2 injection stops in carbon geosequestration (CGS). Remarkably, these cycles exhibit significant hysteresis or path-dependency. This is evident in the pressure-saturation (PS) relationship, where the pressure required to achieve a given saturation (relative amount of one fluid) in drainage differs from that in imbibition. Hysteresis and the associated multivaluedness and history dependence make prediction and control of CGS, as well as enhanced oil recovery and soil remediation, highly challenging.A fascinating scientific problem of huge practical importance, wetting hysteresis has been intensely studied for almost a century by physicists, geoscientists and engineers. Nonetheless, our understanding of the underlying mechanisms remains partial. The main source of this knowledge gap is that large-scale hysteresis is the result of interactions between microscopic capillary instabilities (intermittent pinning and "jumps" of the fluid-fluid interface). Consequently, existing models are either heuristic--use tunable, non-physical parameters, or intractable--requiring details which are practically unattainable experimentally or even numerically; both extremities are of limited usefulness, and can produce significant errors. The role wetting hysteresis plays in some of the environmental challenges we face today, makes formulation of a physically-sound, predictive model highly timely.The proposed project addresses the aforementioned shortcomings, by formulating the first rigorous model of wetting hysteresis, which, in contrast to existing models, is based only on clear, identifiable physical parameters. We achieve this by blending numerical, experimental and theoretical approaches from various disciplines--statistical physics, fluid mechanics, hydrology and geophysics, and exploiting recent computational and experimental advancements. The model will be used to quantitatively explain how the microscopic capillary instabilities (jumps) contribute to hysteresis at larger (continuum) scales, of huge benefit to the greater porous media scientific community (engineers, physicists and geoscientists). The model will also be used to assess the implications of hysteresis for engineering practice at the field scale through reservoir simulations--the standard tool for modelling subsurface flow in energy and environmental applications--in which PS relationships appear as a constitutive equation. Together with our project partners in the British Geological Survey we will conduct reservoir simulations using physically-sound PS relationships generated by our model, aiming to improve CGS operations which are of enormous economic potential to the UK.