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

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.