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We have investigated experimentally the competition between viscous, capillary, and gravity forces during drainage in a two-dimensional synthetic porous medium. The displacement of a mixture of glycerol and water by air at constant withdrawal rate has been studied. The setup can be tilted to tune gravity, and pressure is recorded at the outlet of the model. Viscous forces tend to destabilize the displacement front into narrow fingers against the stabilizing effect of gravity. Subsequently, a viscous instability is observed for sufficiently large withdrawal speeds or sufficiently low gravity components on the model. We predict the scaling of the front width for stable situations and characterize it experimentally through analyses of the invasion front geometry and pressure recordings. The front width under stable displacement and the threshold for the instability are shown, both experimentally and theoretically, to be controlled by a dimensionless number F which is defined as the ratio of the effective fluid pressure drop (i.e., average hydrostatic pressure drop minus viscous pressure drop) at pore scale to the width of the fluctuations in the threshold capillary pressures.

We report on experimental studies of steady-state two-phase flow in a quasi-two-dimensional porous medium. The wetting and the nonwetting phases are injected simultaneously from alternating inlet points into a Hele-Shaw cell containing one layer of randomly distributed glass beads, initially saturated with wetting fluid. The high viscous wetting phase and the low viscous nonwetting phase give a low viscosity ratio M=10(-4). Transient behavior of this system is observed in time and space. However, we find that at a certain distance behind the initial front a "local" steady-state develops, sharing the same properties as the later "global" steady state. In this state the nonwetting phase is fragmented into clusters, whose size distribution is shown to obey a scaling law, and the cutoff cluster size is found to be inversely proportional to the capillary number. The steady state is dominated by bubble dynamics, and we measure a power-law relationship between the pressure gradient and the capillary number. In fact, we demonstrate that there is a characteristic length scale in the system, depending on the capillary number through the pressure gradient that controls the steady-state dynamics.

We present in this paper an experimental study of the invasion activity during unstable drainage in a two-dimensional random porous medium, when the (wetting) displaced fluid has a high viscosity with respect to that of the (nonwetting) displacing fluid, and for a range of almost two decades in capillary numbers corresponding to the transition between capillary and viscous fingering. We show that the invasion process takes place in an active zone within a characteristic screening length lambda from the tip of the most advanced finger. The invasion probability density is found to only depend on the distance z to the latter tip and to be independent of the value for the capillary number Ca. The mass density along the flow direction is related analytically to the invasion probability density, and the scaling with respect to the capillary number is consistent with a power law. Other quantities characteristic of the displacement process, such as the speed of the most advanced finger tip or the characteristic finger width, are also consistent with power laws of the capillary number. The link between the growth probability and the pressure field is studied analytically and an expression for the pressure in the defending fluid along the cluster is derived. The measured pressure is then compared with the corresponding simulated pressure field using this expression for the boundary condition on the cluster.