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

Project overview

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.

Project objectives

Wetting-dewetting hysteresis, and the corresponding multivaluedness and history dependence, are of primary concern in various applications. Notably, hysteresis is key in water and energy resources, including soil moisture, contamination and remediation, enhanced energy recovery, and carbon geosequestration (CGS). The primary aim of this project is to develop a physically-sound model of wetting-dewetting in disordered porous or fractured media, capable of predicting the observed hysteretic capillary pressure-saturation (PS) response, and assess its implications in large-scale applications, notably CGS. This in turn, requires a fundamental understanding of the underlying (microscopic) mechanisms for hysteresis. Considering the complexity and richness of this problem, we will: (1) develop a model starting from a simple scenario (quasi-static, single defect case), and gradually add complexity (disorder and dynamics); (2) use the model to explore the key factors controlling hysteresis and its manifestation in terms of interfacial instabilities; and (3) integrate the small-scale physics into large-scale continuum simulations, to assess the impact of wetting hysteresis on CGS. The first two objectives are concerned with understanding mechanisms, hence are of significant theoretical value, whereas the third aims at implementing these insights into an engineering application and therefore is more geared towards impact. These objectives are summarised below.

Objective 1: To develop a physically-based working model for hysteresis, which--in contrast with state-of-the-art models-only uses meaningful and measurable parameters. We first wish to quantify an elementary mechanism for hysteresis that does not rely on sample-scale heterogeneity (a single ``mesa-defect''), for exceedingly slow (quasi-static) displacements. Next we aim to upscale the model to consider the effect of microstructural heterogeneity, i.e. disordered media with multiple defects of varying properties. Eventually we will seek to generalise the model beyond the quasi-static limit to include dynamic effects of viscous pressure dissipation (relevant to rapid flows).

Objective 2: To gain further understanding by revealing the relationships between pore-size heterogeneity, interfacial jumps dissipating energy, and hysteresis. We will examine how heterogeneity is manifested in the (macroscopic) PS hysteresis as well as its (microscopic) signature in the form of avalanches. As hysteresis is the result of irreversible energy losses, these analyses will allow us to make the connection between the microscopic physics (pore structure and microscopic jumps) and the large-scale hysteresis manifested in the PS relationship.

Objective 3: To implement the gained knowledge of the physics of wetting hysteresis in CGS, i.e. making the link between the hysteresis observed at the sample scale (emanating from microscopic mechanisms) and the field scale, through quantitative representation of PS hysteresis in volume-averaged, continuum models of flow in porous and fractured media. We will use the PS relationships generated by our model for different type of microstructures (representing different types of rocks) in a commercial reservoir simulator. Together with our project partners at the British Geological Survey, we will explore the effect of hysteresis on the injected CO2 plume spreading using data from a CGS site. Discussions with potential stakeholders (using the UK Fluids Network Special Interest Group meetings) to identify other potential applications will further enhance the project's longer-term (organisational) impact, whereas training of early career researchers will promote the shorter-term (individual) impact.

Impact statement

Wetting hysteresis in porous and fractured media has been the subject of intensive interdisciplinary scientific research in several research areas strongly supported by EPSRC; these include fundamental areas e.g. Fluid Dynamics, Soft Matter Physics, Continuum Mechanics, Non-Linear Systems and Complexity Science, as well as more applied areas of Water Engineering, Ground Engineering, Manufacturing Technology and Carbon Capture and Storage.

The computational platform developed in this project will quantify the link between microscopic capillary instabilities (jumps) and to hysteresis at larger (continuum) scales, all the way to the field scale. The latter would be achieved through reservoir simulations---the standard tool for modelling subsurface flow in energy and environmental applications---in which pressure-saturation (PS) relationships appear as a constitutive equation. 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.

Outputs

Conference presentations:

Oral:

(i) Holtzman, R., Dentz, M., Planet, R., Ortin, J., Memory, energy dissipation and hysteresis of two-phase flows. 13th International Conference on Porous Media (Interpore), 2022 (online).

(ii) Dentz, M., Holtzman, R., Planet, R., Ortin, J., Energy dissipated through Haines jumps in disordered media. XXXII IUPAP Conference on Computational Physics, 2021 (online).

(iii) Holtzman, R., Dentz, M., Planet, R., Ortin, J., Energy dissipated through Haines jumps in disordered media. 12th International Conference on Porous Media (Interpore), 2021 (online).

Poster:

Holtzman, R., Planet, R., Ortin, J., Dentz, M., Memory and energy dissipation of two-phase flows in disordered media. Gordon Research Conference on Flow and Transport in Permeable Media, Les Diablerets, Switzerland, 2022.

Article Collection on “Nonequilibrium Multiphase and Reactive Flows in Porous and Granular Materials”, Frontiers in Water & Frontiers in Physics (PI is Lead Associate Guest Editor).

Publications:

Ran Holtzman, Marco Dentz, Ramon Planet, Jordi Ortin. The relation between dissipation and memory in two-fluid displacements in disordered media. Authorea, 2023.