Session BQ: Porous Media Flows II

Capillary rise of a liquid into a deformable porous material

We examine the effects of gravity in a model of one-dimensional imbibition of an incompressible liquid into an initially dry and deformable porous material. We obtain analytic results for steady state positions of the wet porous material--dry porous material interface as well as the liquid--wet material interface. The time-dependent free-boundary problem is solved numerically and the results compared to the steady state predictions. In the absence of gravity, the liquid rises to an infinite height and the porous material deforms to an infinite depth, following square-root in time scaling. In contrast, in the presence of gravity, the liquid rises to a finite height and porous material deforms to a finite depth. Dependence on model parameters such as the solid liquid density ratio is also explored.   

Primary and Secondary Spread of Wetting Droplet into Porous Medium

The spread of the wetting droplet into the porous medium is a two-step process where these two steps are referred as primary and secondary droplet spread. In the primary spread there is a free liquid present at the porous medium surface. The spread does not stop once all fluid from the surface is spread into porous medium, but it continues as a secondary spread due to the local medium heterogeneities that cause the gradient in the capillary pressure and liquid saturation. For both spreads, a capillary network model based on the micro-force balance is developed. The primary spread starts as single-phase (fully saturated), and as the liquid flows further into porous medium the multiphase flow can develop. As the spread progresses, the interface becomes irregular in shape and the immobile clusters of the originally present phase can be formed due to the entrapment. Besides the clusters of the originally present phase, regions filled with liquid phase at the interface can detach from the droplet main body forming insulated fluid ganglia. The secondary spread further increases the interface irregularity that causes the clusters of originally present phase to open and promotes ganglia formation. This leads to the reduction in ganglia size, and the liquid ganglia become immobile and the secondary spread is terminated. Finally, these are dynamic processes and the separation and coalescence of the fluid ganglia is governed with the force balance at the interface.   

Vertical Mobilization of a Residual Oil Phase in a Bead Pack Due to Flow of Discrete Gas Bubbles

Mobilization of trapped oil ganglia is of interest in soil and groundwater clean-up and enhanced oil recovery applications. In this work, experiments with glass beads and various oil phase compositions were performed to determine the volumetric fraction of the non-aqueous phase liquid that may be mobilized with rising discrete gas bubbles. Experiments were performed using 6 mm and 2 mm beads. The oil phase liquids included dodecane, perchloroethene, and trichloroethene representing both spreading and non-spreading oil phases. It was found that bubbles were quite effective in mobilizing all three oils including those with densities greater than that of the suspending water. The effectiveness of the mobilization was greater in bead packs with larger beads than in packs comprised of small beads. Volumetric fractional flows of the oil phase were up to 10{\%} of the bubble-droplet volumes, with volumetric fractions decreasing with decreasing oil phase saturations and bead size. The geometry of the oil ganglia/gas bubble combinatory body was also a function of the bead size with smaller beads producing larger, flatter gas bubbles, and the large beads producing bubbles and ganglia of similar size and geometries as the beads themselves.   

Characterization of Emulsion Flow through a Pore-Throat Capillary Model

Flow of emulsions in porous media is important in a number of industries, including oil recovery operations and clean up of non-aqueous phase liquids in soils. The impact of operating parameters and emulsions properties in flow in porous media is still under investigation. A detailed observation at microscopic scale of the flow phenomena involved is essential for the understanding of the flow of an emulsion in porous media. This would lead to the development of better simulation models. In this work, pressure drop - volumetric flow rate response for oil-in-water emulsions passing through constricted capillary systems was studied. Visualization under an optical microscope was carried out to understand the flow phenomena involved. Flow rates were in the 1 m/day to 60 m/day range, to reproduce injection rates used in reservoirs operations. At a set flow rate pressure drop of the flow of emulsions having the same viscosity but different average drop size distribution may be different due to constricion blocking phenomena. This findings show that a viscosity function for emulsions is not enough to fully characterize the flow response in porous media.   

Electrically driven flow of viscous liquids in a radial Hele-Shaw geometry

Viscous fluid flow control in confined geometries (at dimensions less than the capillary length, ranging from 500 to 100 $\mu$m) such as in porous media are of interest to emerging fields, such as micro (MEMS) and nano-electromechanical systems (NEMS). When fluids in these devices are driven by pressure, and/or motor driven constant flow-rate pumping then they lack a certain degree of control that is desirable for high precision and robust experiments. Recently, researchers have been studying the possibilities of driving fluid motion in porous media by using electrical phenomenon to overcome some of the shortcomings of there flow-rate and/or pressure driven flow counterparts. Here, a problem involving such a flow is presented to drive the motion of a very viscous non-conducting fluid, such as most common oils, in a Hele-Shaw geometry that is a model for flow in a porous media. The experiments are performed using varying viscosity fluid and the radial area versus time is recorded. The experiments are compared with theory and show good agreement.   

Electrically driven flow and instability in a vertical Hele-Shaw geometry

The electrohydrostatic capillary flow of a viscous Newtonian fluid flowing between vertically oriented conducting parallel plates is studied both theoretically and experimentally. The dimensionless parameters governing the flow are the electric Bond and electric Reynolds numbers. At low electric Reynolds ($<1$) and electric Bond numbers ($<1$) the displaced fluid interface remains flat. At high electric Reynolds ($\gg 1$) and electric Bonds ($>1$) numbers the interface develops a instability. The experimental results for the interface displacement as a function of time elapsed are compared with the theoretical predictions which are analogous to those derived by Washburn (1921) for the flow of a fluid in cylindrical capillaries. Despite the instability the theory and experiments for the trends in the static rise height show good agreement. The flow dynamics show similar trends to the theoretically predicted flow but deviate at higher electric Reynolds numbers due to a convective instability.   

Lubrication theory for a random fibrous medium

In the classical theory for a slipper bearing one examines the relative motion of an inclined planar surface and a horizontal planar surface. The solution for the pressure distribution and lift force are independent of which boundary is moving and there is an optimum tilt $k=h1/h2=2.2$ for maximum lift. This symmetry is lost if the intervening space is filled with a soft porous fibrous material. In this paper the generalized Reynolds equation derived in Feng and Weinbaum (2000) J. Fluid Mech. 422:281 is extended to treat a random fiber matrix satisfying the widely used Carman-Kozeny equation. We show that the solutions are strikingly different depending on whether a) the inclined upper boundary moves or b) the upper boundary is stationary and the horizontal lower boundary moves beneath it. The behavior depends critically on the value of the dimensionless fiber interaction layer thickness $\alpha =H/\sqrt {K_p } $. In a) the pressure and lift force increase as $\alpha^2$ and asymptotically approach a limiting behavior for large values of $\alpha $ since the fluid is pushed forward by the tilt of the upper boundary. In b) the pressure and lift force decay as $\alpha^{-2}$ since the fiber interaction layer thickness decreases and the amount of fluid dragged though the fluid gap decreases as $\alpha$ increases and vanishes for $\alpha >> 1$.   

Flow characteristics in dynamically compacted soft porous materials

The dynamic behavior of soft compressible porous media undergoing uniform axial compaction was investigated experimentally in our unique cylinder-piston apparatus that has been used successfully in our previous work with snow compaction. Several synthetic porous materials have been tested and characterized under compression time scales below 0.2 sec. Excess pore pressure has been generated during dynamic compaction which is due to the substantial increase in hydraulic resistance that the fluid encounters as it tries to vent from the confining boundaries through the thin compressed layer. The contributions from the solid phase force have been decoupled from those of the air phase by measuring the total force with miniature load cells first and then subtracting the air pressure force measured by pressure transducers. Static strain-stress measurements showed that the axial compression of the solid phase is accompanied by the generation of significant radial stresses at the cylinder wall which introduce frictional force opposing the piston motion. A dramatic reduction in permeability of the porous media has been found with increased compaction. A 50 per cent compression ratio results in a 60 percent decrease in permeability.   

Irregular Deposition of Colloidal Particles in Fibrous Media during Capillary Spreading

When a drop of liquid is placed on a dry fibrous medium (e.g., paper or clothing), capillary suction induces the liquid to spread radially. Sufficiently small colloidal particles are entrained in the flow, and eventually deposit onto the fibers, forming a stain. Here we investigate the colloidal deposition patterns, and we report that under many conditions the highest concentration of particles is found at the periphery of the stain. This nonmonotonic radial distribution is qualitatively different from the exponential decay predicted in standard filtration theory. We explain the experimental observations in terms of a competition between capillary flow and colloidal-scale interactions. The results have implications for many processes in fibrous media, including stain removal, thin-layer chromatography, and bacterial growth in porous environments.   

Stability of two-phase vertical flow in homogeneous porous media

Immiscible two-phase flow in porous media, that results from the downward injection of a heavier fluid or upward injection of a lighter fluid, is characterized by two shocks, one at each end of a rarefaction wave. The specific details of the saturation profile, such as the shock speeds and the shock saturations, are determined by the fractional flow function for given values of the mobility ratio and the gravity number. We employ a normal mode, matched asymptotic expansion analysis to obtain analytical expressions governing the stability behavior of such flows. Instability occurs at both ends of the 1-D base saturation profile with unique characteristics such that, the maximum growth rate decreases both when the mobility ratio is increased at the front end and decreased at the back end. This unusual behavior is explained in terms of vorticity eigenfunctions related to non-monotonic mobility profiles.