Pore-Network Modeling of Isothermal Drying in Porous Media

In this paper we present numerical results obtained with a pore-network model for the drying of porous media that accounts for various processes at the pore scale. These include mass transfer by advection and diffusion in the gas phase, viscous flow in the liquid and gas phases and capillary effects at the liquid--gas interface. We extend our work by studying the effect of capillarity-induced flow in macroscopic liquid films that form at the pore walls as the liquid--gas interface recedes. A mathematical model that accounts for the effect of films on the drying rates and phase distribution patterns is presented. It is shown that film flow is a major transport mechanism in the drying of porous materials, its effect being dominant when capillarity controls the process, which is the case in typical applications.     

The Shape of a Gravity Finger in a Rectangular Channel in Homogeneous Porous Media

Using conformal mapping techniques, we derive analytical expressions for the shape of a propagating finger in a rectangular channel in homogeneous porous media, in the absence of interfacial tension, but in the presence of gravity, acting in a direction transverse to the direction of displacement. The gravity finger propagates either along the top or the bottom boundaries of the channel, depending on the density contrast between displacing and displaced fluids. Thus, the model describes the respective cases of gravity override or gravity underrunning, which occur when a lighter fluid phase displaces a heavier one and vice-versa. The solution is expressed in terms of the finger thickness, which is a free parameter in this model. When gravity is neglected, the solution reduces to the classical solution of the Saffman–Taylor finger. Numerical illustrations are provided to examine the sensitivity of the finger geometry to the various parameters, following the scaling theory of Brener et al. (1991).     

Viscous coupling in a model porous medium geometry: Effect of fluid contact area

We study the effect of fluid contact area on viscous coupling in the parallel flow of immiscible fluids in a porous media geometry. We consider flow on opposite sides of a planar interface, consisting of alternating solid and open (slit) segments. We use the analytical solution of Tio and Sadhal [15] to derive explicit expressions for viscous coupling in terms of the fractional area of contact between the fluids and the viscosity ratio,M. ForM=1, the coefficient matrix obtained is symmetric showing that Onsager's relations are satisfied. In this case, the resulting viscous coupling is typically very small, in agreement with recent experimental results. Lattice gas simulations forM=1 using theBGK model support the theoretical results and show that viscous coupling further diminishes as the wall thickness increases. Assuming the same configuration, analytical results are next derived forM1. The results confirm an existing reciprocity relation between the off-diagonal terms. Viscous coupling remains small.     

The critical gas saturation in a porous medium in the presence of gravity

The critical gas saturation, S(gc), denotes the volume fraction of the gas phase at the onset of bulk gas flow during the depressurization of a supersaturated liquid in a porous medium. In the absence of gradients due to viscous or gravity forces, S(gc) is controlled by nucleation, capillary forces, and the rate of decline of the supersaturation. In this paper we address one important additional effect, that of buoyancy. We use 2-D pore-network simulations, based on invasion percolation in a gradient (IPG), and corresponding scaling relations to obtain the dependence of S(gc) on the gravity Bond number, B, under conditions of slow growth, namely when mass transfer is sufficiently fast. The critical gas saturation approaches two plateau values at low and high Bond numbers. In the in-between region it scales as a power law of B, which for a 2-D lattice is S(gc) approximately B(-0.91).     

Water removal from porous media by gas injection: experiments and simulation

The flow of a saturated gas through a porous medium, partially occupied by a liquid phase, causes evaporation due to gas expansion. This process, referred to as flow-through drying, is important in a wide variety of natural and industrial applications, such as natural gas production, convective drying of paper, catalysts, fuel cells and membranes. X-ray imaging experiments were performed to study the flow-through drying of water-saturated porous media during gas injection. The results show that the liquid saturation profile and the rate of drying are dependent on the viscous pressure drop, the state of saturation of the gas and the capillary characteristics of the porous medium. During the injection of a completely saturated gas, drying occurs only due to gas expansion. Capillary-driven flow from regions of high saturation to regions of low saturation lead to more uniform saturation profiles. During the injection of a dry gas, a drying front develops at the inlet and propagates through the porous medium. The experimental results are compared with numerical results from a continuum model. A good agreement is found for the case of sandstone. The comparison is less satisfactory for the experiments with limestone.     

Capillary effects in steady-state flow in heterogeneous cores

Effects of capillary heterogeneity at the macroscopic scale have previously been analyzed for static conditions or in the context of outflow end-effects. This paper presents a systematic study for the case of one-dimensional, steady-state flow, that complements recent work on transient displacement. We consider the saturation response to various forms of heterogeneity. Included are analytical results for certain model cases, some general results, and numerical solutions for variously correlated spatial variations. The sensitivity to process parameters, such as rate, heterogeneity length scale and correlation, is studied. Physical interpretations are offered and potential applications in the estimation of heterogeneity are discussed.     

The Spreading of Immiscible Fluids in Porous Media under the Influence of Gravity

We use an approach based on invasion percolation in a gradient (IPG) to describe the displacement patterns that develop when a fluid spreads on an impermeable boundary in a porous medium under the influence of gravity (buoyancy) forces in a drainage process. The approach is intended to simulate applications, such as the spreading of a DNAPL in the saturated zone and of a NAPL in the vadose zone on top of an impermeable layer, or the classical problems of gravity underruning and gravity override in reservoir engineering. As gravity acts in a direction transverse to the main displacement direction, a novel form of IPG develops. We study numerically the resulting patterns for a combination of transverse and parallel Bond numbers and interpret the results using the concepts of gradient percolation. A physical interpretation in terms of the capillary number, the viscosity ratio and the gravity Bond number is also provided. In particular, we consider the scaling of the thickness of the spreading gravity tongue, for the cases of gravitydominated and viscousunstable displacements, and of the propagating front in the case of stabilized displacement at relatively high rates. It is found that the patterns have percolation (namely fractallike) characteristics, which cannot be captured by conventional continuum equations. These characteristics will affect, for example, mass transfer and must be considered in the design of remediation processes.