Wettability Stabilizes Fluid Invasion into Porous Media via Nonlocal, Cooperative Pore Filling

We study the impact of the wetting properties on the immiscible displacement of a viscous fluid in disordered porous media. We present a novel pore-scale model that captures wettability and dynamic effects, including the spatiotemporal nonlocality associated with interface readjustments. Our simulations show that increasing the wettability of the invading fluid (the contact angle) promotes cooperative pore filling that stabilizes the invasion, and that this effect is suppressed as the flow rate increases, due to viscous instabilities. We use scaling analysis to derive two dimensionless numbers that predict the mode of displacement. By elucidating the underlying mechanisms, we explain classical yet intriguing experimental observations. These insights could be used to improve technologies such as hydraulic fracturing, CO$_{2}$ geo-sequestration, and microfluidics.Comment: In review, Physics Review Letter

The origin of hysteresis and memory of two-phase flow in disordered media

Cyclic fluid-fluid displacements in disordered media feature hysteresis, multivaluedness, and memory properties in the pressure-saturation relationship. Quantitative understanding of the underlying pore-scale mechanisms and their extrapolation across scales constitutes a major challenge. Here we find 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. The mechanisms identified here apply to a broad range of problems in hydrology, geophysics and engineering

Onset of convective instability in an inclined porous medium

The diffusion of a solute from a concentrated source into a horizontal, stationary, fluid-saturated porous medium can lead to a convective motion when a gravitationally unstable density stratification evolves. In an inclined porous medium, the convective flow becomes intricate as it originates from a combination of diffusion and lateral flow, which is dominant near the source of the solute. Here, we investigate the role of inclination on the onset of convective instability by linear stability analyses of Darcy's law and mass conservation for the flow and the concentration field. We find that the onset time increases with the angle of inclination ($\theta$) until it reaches a cut-off angle beyond which the system remains stable. The cut-off angle increases with the Rayleigh number, $Ra$. The evolving wavenumber at the onset exhibits a lateral velocity that depends non-monotonically on $\theta$ and linearly on $Ra$. Instabilities are observed in gravitationally stable configurations ($\theta \geq 90^{\circ}$) solely due to the non-uniform base flow generating a velocity shear commonly associated with Kelvin-Helmholtz instability. These results quantify the role of medium tilt on convective instabilities, which is of great importance to geological CO$_2$ sequestration.Comment: 18 pages, 7 figure

Emergence of dissipation and hysteresis from interactions among reversible, non-dissipative units:The case of fluid-fluid interfaces

We examine the nonequilibrium nature of two-phase fluid displacements in a quasi-two-dimensional medium (a model open fracture), in the presence of localized constrictions ("defects"), from a theoretical and numerical standpoint. Our analysis predicts the capillary energy dissipated in abrupt interfacial displacements (jumps) across defects, and relates it to the corresponding hysteresis cycle, e.g. in pressure-saturation. We distinguish between "weak" (reversible interface displacement, exhibiting no hysteresis and dissipation) and "strong" (irreversible) defects. We expose the emergence of dissipation and irreversibility caused by spatial interactions, mediated by interfacial tension, among otherwise weak defects. We exemplify this cooperative behavior for a pair of weak defects and establish a critical separation distance, analytically and numerically, verified by a proof-of-concept experiment

The Interplay Between Pore‐Scale Heterogeneity, Surface Roughness, and Wettability Controls Trapping in Two‐Phase Fluid Displacement in Porous Media

Predicting the compactness of the invasion front and the amount of trapped fluid left behind is of crucial importance to applications ranging from microfluidics and fuel cells to subsurface storage of carbon and hydrogen. We examine the interplay of wettability, macro‐ and pore scale heterogeneity (pore angularity and pore wall roughness), and its influence on flow patterns formation and trapping efficiency in porous media by a combination of 3D micro‐CT imaging with 2D direct visualization of micromodels. We observe various phase transitions between the following capillary flow regimes (phases): (a) compact advance, (b) wetting and drainage Invasion percolation, (c) Ordinary percolation

Effect of spatially correlated disorder on solute dispersion and mixing in partially saturated porous media

The transport of solute particles is common in many natural and engineering processes, such as nutrition/contamination transport in subsurface systems or underground carbon dioxide sequestration. While most of the available investigations concentrate on single-phase scenarios, more often, multiple fluids coexist, denoted frequently as unsaturated conditions. Here, and by means of direct numerical simulation, the effect of spatially correlated disorder in pore size is examined for two-phase displacement in viscous fingering regime. Following the stabilisation of fluids interface (steady-state condition), the solute solution is introduced into the invading phase with lower viscosity. Simulation results indicate that the spatial disorder impacts solute migration through the invading phase saturation and tortuosity of velocity streamlines. A bimodal variation can be seen from the histogram of probability of pore-scale Peclet number with zones being mostly dominated by either advection or diffusion. In addition, there exists a transition region with an interplay between both advective and diffusive mechanisms. The creation of trapped regions focuses the flow into preferential pathways, resulting in a higher dispersion coefficient. This, on the other side, forms a concentration gradient transverse to the direction of flow, directing solute solution through diffusivity from preferential pathways to low-velocity zones