Research Areas

Multiphase flow in porous media

A wine stain spreading on tablecloth or oil percolating into wet sand are examples of a fluid displacing another in a porous material. The way by which fluids move and the associated enchanting invasion patterns are also scientifically and technologically important, controlling the efficiency of processes such as oil production, removal or storage of contaminant in the subsurface, or fluid mixing in microfluidics. Despite this importance and the great scientific and technological interest, modelling of how fluids flow in porous media remains elusive. A major challenge is that many of the processes occur at the scale of individual pores (sizes of the order of millimetres), whereas the phenomena of interest are often at the scale of meters and even kilometres.

Nonequilibrium flows

Multiphase and reactive fluid flow in porous media is often unstable, and highly heterogeneous: inevitable microstructural heterogeneity leads to the emergence of preferential pathways, where most of the flow is focused in a small portion of the medium. Furthermore, strong hysteresis and rate-dependence are frequently observed. This complex, out-of-equilibrium behavior is further corroborated by interactions between the fluids and the solid matrix, e.g. fracturing and dissolution. We combine experiments, simulations and theory to understand the pore-scale physics underlying nonequilibrium flows in porous media, and its implications on engineering problems, mainly in the field of energy and the environment.


Wetting-dewetting hysteresis

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.
Recent experiments expose that the capillary action of a single constriction in the fluid passage contains the key features of hysteresis. This insight forms the building block for an ab initio model that provides the quantitative link between the microscopic capillary physics, spatially-extended collective events (Haines jumps) and large-scale hysteresis. Read the paper in Nature Communications Physics (2020)

Soil hydrophobicity, flooding and erosion

Water repellency (hydrophobicity) is widespread in natural and agricultural soils. Hydrophobicity increases surface runoff and reduces soil cohesion, therefore promoting flooding and soil erosion. It also promotes the preferential flow of contaminants and nutrients into the groundwater, bypassing the plant root zone. Hydrophobicity and extreme weather have an intricate, two-way connection: hydrophobicity amplifies the consequences of extreme rainfall via flooding and soil erosion, while also being a consequence of global warming because excessive drying, wildfires, and greywater irrigation (due to shortage of freshwater) induce hydrophobicity.
We aim to provide the first proper representation of the underlying physics in watershed models. As such, it will improve our ability to predict and mitigate floods and soil erosion, reducing their impact on communities, agricultural and natural soil and water resources--a subject of increasing attention, e.g. see a recent news item.

Geological carbon sequestration

A promising technique for mitigation of the rising level of atmospheric CO2 and global warming is carbon capture and storage (CCS). This relies on subsurface storage of CO2, mainly in deep saline aquifers (but also in unminable coal seams or depleted oil and gas reservoirs). Following the injection of CO2 (in supercritical form) it undergoes several processes that control the rates and volume that could be safely stored, and the associated risk (e.g. of leakage or induced seismicity). However, these processes and their interplay with the medium microstructure and reactive transport mechanisms remain poorly understood.

One of the mechanisms that keeps the CO2 in place is dissolution trapping: the supercritical CO2 (scCO2) dissolves by diffusion into the brine to increase its density beyond that of the original brine, sinking deeper which makes it less prone to leakage. This process if often accelerated by a convective (gravitationally-driven) instability in the forms of fingers of denser CO2-rich brine sinking downwards, which in turn accelerates the rate of dissolution of further scCO2 into the brine at the top. Emmanuel Luther's PhD thesis addresses the onset of this instability and its impact on later stages via linear stability analyses (LSA) and reservoir simulations. Specifically, we are interested in the impact of the medium structure, in particular permeability variations in the form of layering which is prevalent in geological formations used for CCS. Our analysis shows that even a thin perturbation in permeability (Int. J. Greenh. Gas Control. 2021) and its inclination [in preparation] could greatly impact the onset of convective instability.

Another desired trapping mechanisms which also constitutes a fascinating open scientific problem is mixing-induced precipitation (MIP) of minerals, mainly carbonates. Particularly, the effects of small-scale heterogeneity (e.g. pore size variations), and the consequent non-uniform flow and precipitation at the km-scale of interest to CCS remain elusive. In a coming project, we will combine microfluidic experiments with pore network modelling to expose the underlying physics of MIP from the single pore to the sample level, including the effect of dimensionality (2D to 3D) and of the high pressures of real CCS conditions. We will then use reservoir modelling to upscale these insights to the field scale.

Wettability effects on invasion stability

Fluid displacement in porous media is often unstable, in the form of thin, convoluted fingers that penetrate only a small portion of the pore space. Instability associated with unfavourable viscosity ratio--when the invading fluid is less viscous than the one displaced, e.g. gas displacing liquid--has been thoroughly investigated since the seminal Saffman-Taylor experiment (1958). Yet, the fundamental effect of wettability (the relative affinity of the fluids to the solid), that is the remarkable difference between imbibition and drainage, exposed in the classic experiments of Stokes and coworkers (1986), remain largely unexplained. Stokes et al. showed that if the invading, less viscous fluid is non-wetting (drainage), the displacement occurs through preferential flow paths leaving much of the original fluid behind, whereas if the invading fluid is more wetting (imbibition), the front becomes more compact with a more efficient displacement. We explain these classical yet intriguing observations by computer simulations, showing that wettability changes the microscopic mechanisms of pore invasion, which in turn changes the global pattern, an effect which gets weaker as the flow rate increases.

High Ca, strong drainage High Ca, weak imbibition Low Ca, strong drainage Low Ca, weak imbibition
Viscous fingering: destabilization of the entire interface, where high defending fluid pressure in the “gulfs” between fingers allows only the finger tips to advance (screening) Capillary fingering driven by disorder. Quasi-static (IP-like) advancement by invasion into the largest accesible pore along the interface Compact displacement resulting from dominance of non-local, cooperative pore-filling events ("overlaps")

For further information, see:
  • Phys. Rev. Lett. 2015 for a presentation of our novel pore-scale model, explaining the transition between the different displacement regimes.
  • Nature Sci. Rep. 2016 showing how wettability effects interacts with those of rate and pore size heterogeneity.
  • PNAS 2019 for a comprehensive comparison of pore-scale models for multiphase flow in porous media.

Microstructural heterogeneity

The microstructure of a porous medium, characterized by both the distribution and the spatial arrangement of pores of various sizes, has a substantial impact on fluid displacement patterns. We combine pore-scale simulations with microfluidic experiments to quantify the impact of pore-scale heterogeneity on fluid displacement. We explain how quenched disorder (pore sizes which are spatially uncorrleated) and its interplay with rate affects drainage patterns in dedformable porous media such as bead packs (Phys. Rev. E 2010), as well as the cross-coupling with wettability (Nature Sci. Rep. 2016).

An important feature of the microstructure of many types of porous media such as soils and rocks is the existence of spatial correlations in pore sizes, such as when pores of similar size are clustered together, creating distinct regions with different hydraulic properties. We study how spatially-correlated heterogeneity affects both forced displacement in partially-wettable medium (Adv. Water Resour. 2019). We also investigated how spatial correlations in pore sizes affects isothrmal drying, where fluid displacement is driven by evaporation, numerically (Water Resour. Res. 2017) and experimentally (Nature Sci. Rep. 2017). We have used our data together with an invasion-percolation model to explain the link between microstructure and the temporal stochastic statistics (avalanches) of the pressure signal (Phys. Rev. Fluids 2018).

Fluid displacement in deformable granular media

Opening of fracture-like conduits in wet particulate materials is a phenomenon we encounter on a daily basis, for instance in drying paints or soils. It also plays a crucial role in many processes in which gas flows in the subsurface, including methane venting from lakes and marine sediments and enhanced oil recovery. We demonstrate experimentally, and explain by pore-scale simulations and scaling analysis, the emergence of fracturing as a mode of gas invasion in granular media, for both forced injection (Phys. Rev. E 2010; Phys. Rev. Lett. 2012; see also Synopsis) and evaporative drying (Int. J. Heat Mass Tran. 2020). We denote this regime 'capillary fracturing' because it is distinctly different from other types of fracturing. In contrast with hydraulic fracturing, which is the result of single-phase flow at high injection rates, capillary fracturing relies on interfacial phenomena (the presence of a fluid-fluid interface) and can occur at vanishingly small injection rates. Capillary fracturing allows fast exchange of mass and heat and is therefore critical to the water, carbon and energy budgets in the biosphere.

One dramatic example is gas seepage and the creation of pockmarks in submarine sediments. The video shows our experimental reconstruction of pockmark formation in the laboratory, providing crucial insights into the unerlying mechanisms.

Reactive transport

We seek fundamental understanding of the intricate coupling between reactive dissolution of a porous media, its hydraulic and reactive properties, e.g. its permeability and bulk rate of reaction.

Reactive transport under stress: We developed a novel pore-scale model that captures coupling of dissolution and weakening-induced compaction during injection of a reactive fluid into porous media. We use numerical simulations to demonstrate how chemo-mechanical deformation of stressed rocks, namely the coupling of pore opening by dissolution with weakening-induced compaction, inhibits permeability evolution. We show that the underlying mechanism is stress concentration at the undissolved (hence stiffer) downstream region, resulting in a bottleneck effect. At high Damköhler number (Da), stress acts to reduce transport heterogeneity, promoting wormhole competition (see video).
Read more in Earth Planet. Sci. Lett. 2018.

Impact of medium anisotropy on dissolution: We develop a pore network model to expose the evolution of heterogeneous and anisotropic media during dissolution.
In the uniform dissolution regime (flow faster than reaction, low Damkӧhler number), we show that the dissolution extensively homogenizes the medium and therefore the flow field; this is further enhanced when the surface reaction is transport-controlled—-i.e. when slow diffusion of dissolved ions away from the mineral surface leads to the reduction of the global dissolution rate. Under these conditions, diffusive transport is more effective in narrow channels, which selectively enlarge, leading to an initial steep rise of the permeability which later slows down due to a decrease in reaction rate (Water Resour. Res. 2020).
In the wormholing regime (high Damkӧhler), we find that anisotropy controls wormhole competition and their characteristic spacing. It also affects the flow through the individual wormholes and their shapes, and consequently, shifts the optimum injection rate at which breakthrough is achieved at a minimal expense of reactant. For anisotropic media with low transverse pore conductivities, wormhole distribution ceases to be scale-invariant and pronounced side-branches develop. Wormholing is further compared to viscous fingering in an anisotropic network, and other unstable growth processes of similar underlying dynamics (Geophys. Res. Lett. 2021).