Inertial forces affect fluid front displacement dynamics in a pore-throat network model

Asymmetric invasion in anisotropic porous media

We report and discuss, by means of pore-scale numerical simulations, the possibility of achieving a directional-dependent two-phase flow behavior during the process of invasion of a viscous fluid into anisotropic porous media with controlled design. By customising the pore-scale morphology and heterogeneities with the adoption of anisotropic triangular pillars distributed with quenched disorder, we observe a substantially different invasion dynamics according to the direction of fluid injection relative to the medium orientation, that is depending if the triangular pillars have their apex oriented (flow aligned) or opposed (flow opposing) to the main flow direction. Three flow regimes can be observed: (i) for low values of the ratio between the macroscopic pressure drop and the characteristic pore-scale capillary threshold, i.e., for Δp_{0}/p_{c}≤1, the fluid invasion dynamics is strongly impeded and the viscous fluid is unable to reach the outlet of the medium, irrespective of the direction of injection; (ii) for intermediate values, 1<Δp_{0}/p_{c}≤2, the viscous fluid reaches the outlet only when the triangular pillars are flow-opposing oriented; (iii) for larger values, i.e., for Δp_{0}/p_{c}>2, the outlet is again reached irrespective of the direction of injection. The porous medium anisotropy induces a lower effective resistance when the pillars are flow-opposing oriented, suppressing front roughening and capillary fingering. We thus argue that the invasion process occurs as long as the pressure drop is larger then the macroscopic capillary pressure determined by the front roughness, which in the case of flow-opposing pillars is halved. We present a simple approximated model, based on Darcy's assumptions, that links the macroscopic effective permeability with the directional-dependent front roughening, to predict the asymmetric invasion dynamics. This peculiar behavior opens up the possibility of fabrication of porous capillary valves to control the flow along certain specific directions.

Directional Water Wicking on a Metal Surface Patterned by Microchannels

This work focuses on the simulation and experimental study of directional wicking of water on a surface structured by open microchannels. Stainless steel was chosen as the material for the structure motivated by industrial applications as fuel cells. Inspired by nature and literature, we designed a fin type structure. Using Selective Laser Melting (SLM) the fin type structure was manufactured additively with a resolution down to about 30 μm. The geometry was manufactured with three different scalings and both the experiments and the simulation show that the efficiency of the water transport depends on dimensionless numbers such as Reynolds and Capillary numbers. Full 3D numerical simulations of the multiphase Navier-Stokes equations using Volume of Fluid (VOF) and Lattice-Boltzmann (LBM) methods reproduce qualitatively the experimental results and provide new insight into the details of dynamics at small space and time scales. The influence of the static contact angle on the directional wicking was also studied. The simulation enabled estimation of the contact angle threshold beyond which transport vanishes in addition to the optimal contact angle for transport.

Inertia Controlled Capillary Pressure at the Juncture between Converging and Uniform Channels

In this research, we reveal the transient behavior of capillary pressure as the fluid-fluid interface travels across the juncture between a converging and uniform capillary, via high-resolution CFD (Computational Fluid Dynamics) simulations. Simulations were performed at different wetting conditions (strong-wet and intermediate-wet) and capillary wall convergence angles. Our results demonstrate that as the angle of convergence increases, capillary pressure at the junction decreases commensurately. Moreover, in contrast to strong-wet conditions, the profile of capillary pressure at the converging-uniform capillary juncture under intermediate-wet conditions is highly non-monotonic, being characterized by a parabola-like form. This non-monotonic behavior is a manifestation of strong inertial forces governing dynamic fluid-fluid interface morphology. This yields conditions that promote the advancement of the fluid-fluid interface, as inertial forces partially nullify the capillary pressure required for the immiscible interface to enter the uniform capillary. In addition to numerical analysis detailed above, a novel theoretical stability criteria that is capable of distinguishing between stable (capillary dominated) and unstable (inertia dominated) interfacial regimes at the converging-uniform capillary juncture is also proposed. In summary, this fundamental study offers new insights into the interface invasion protocol, and paves the way for the re-evaluation of capillary junction controlled interfacial dynamics.

Pore-scale characteristics of multiphase flow in heterogeneous porous media using the lattice Boltzmann method

This study provides a pore-scale investigation of two-phase flow dynamics during primary drainage in a realistic heterogeneous rock sample. Using the lattice Boltzmann (LB) method, a series of three-dimensional (3D) immiscible displacement simulations are conducted and three typical flow patterns are identified and mapped on the capillary number (Ca)-viscosity ratio(M) phase diagram. We then investigate the effect of the viscosity ratio and capillary number on fluid saturation patterns and displacement stability in Tuscaloosa sandstone, which is taken from the Cranfield site. The dependence of the evolution of saturation, location of the displacement front, 3D displacement patterns and length of the center of mass of the invading fluid on the viscosity ratio and capillary number have been delineated. To gain a quantitative insight into the characteristics of the invasion morphology in 3D porous media, the fractal dimension D_f of the non-wetting phase displacement patterns during drainage has been computed for various viscosity ratios and capillary numbers. The logarithmic dependence of D_f on invading phase saturation appears to be the same for various capillary numbers and viscosity ratios and follows a universal relation.

Non-Darcy interfacial dynamics of air-water two-phase flow in rough fractures under drainage conditions

Two-phase flow interfacial dynamics in rough fractures is fundamental to understanding fluid transport in fractured media. The Haines jump of non-Darcy flow in porous media has been investigated at pore scales, but its fundamental processes in rough fractures remain unclear. In this study, the micron-scale Haines jump of the air-water interface in rough fractures was investigated under drainage conditions, with the air-water interface tracked using dyed water and an imaging system. The results indicate that the interfacial velocities represent significant Haines jumps when the meniscus passes from a narrow "throat" to a wide "body", with jump velocities as high as five times the bulk drainage velocity. Locally, each velocity jump corresponds to a fracture aperture variation; statistically, the velocity variations follow an exponential function of the aperture variations at a length scale of ~100 µm to ~100 mm. This spatial-scale-invariant correlation may indicate that the high-speed local velocities during the Haines jump would not average out spatially for a bulk system. The results may help in understanding the origin of interface instabilities and the resulting non-uniform phase distribution, as well as the micron-scale essence of the spatial and temporal instability of two-phase flow in fractured media at the macroscopic scale.

The Role of Local Instabilities in Fluid Invasion into Permeable Media

Wettability is an important factor which controls the displacement of immiscible fluids in permeable media, with far reaching implications for storage of CO₂ in deep saline aquifers, fuel cells, oil recovery, and for the remediation of oil contaminated soils. Considering the paradigmatic case of random piles of spherical beads, fluid front morphologies emerging during slow immiscible displacement are investigated in real time by X-ray micro-tomography and quantitatively compared with model predictions. Controlled by the wettability of the bead matrix two distinct displacement patterns are found. A compact front morphology emerges if the invading fluid wets the beads while a fingered morphology is found for non-wetting invading fluids, causing the residual amount of defending fluid to differ by one order of magnitude. The corresponding crossover between these two regimes in terms of the advancing contact angle is governed by an interplay of wettability and pore geometry and can be predicted on the basis of a purely quasi-static consideration of local instabilities that control the progression of the invading interface.

Statistical mechanics of unsaturated porous media

We explore a mean-field theory of fluid imbibition and drainage through permeable porous solids. In the limit of vanishing inertial and viscous forces, the theory predicts the hysteretic "retention curves" relating the capillary pressure applied across a connected domain to its degree of saturation in wetting fluid in terms of known surface energies and void space geometry. To avoid complicated calculations, we adopt the simplest statistical mechanics, in which a pore interacts with its neighbors through narrow openings called "necks," while being either full or empty of wetting fluid. We show how the main retention curves can be calculated from the statistical distribution of two dimensionless parameters λ and α measuring the specific areas of, respectively, neck cross section and wettable pore surface relative to pore volume. The theory attributes hysteresis of these curves to collective first-order phase transitions. We illustrate predictions with a porous domain consisting of a random packing of spheres, show that hysteresis strength grows with λ and weakens as the distribution of α broadens, and reproduce the behavior of Haines jumps observed in recent experiments on an ordered pore network.