Competition of gravity, capillary and viscous forces during drainage in a two-dimensional porous medium, a pore scale study

We have studied experimentally and numerically the displacement of a highly viscous wetting fluid by a non-wetting fluid with low viscosity in a random two-dimensional porous medium under stabilizing gravity. In situations where the magnitudes of the viscous-, capillary- and gravity forces are comparable, we observe a transition from a capillary fingering behavior to a viscous fingering behavior, when decreasing apparent gravity. In the former configuration, the vertical extension of the displacement front saturates; in the latter, thin branched fingers develop and rapidly reach breakthrough. From pressure measurements and picture analyzes, we experimentally determine the threshold for the instability, a value that we also predict using percolation theory. Percolation theory further allows us to predict that the vertical extension of the invasion fronts undergoing stable displacement scales as a power law of the generalized Bond number Bo∗=Bo−Ca, where Bo and Ca are the Bond and capillary numbers, respectively. Our experimental findings are compared to the results of a numerical modeling that takes local viscous forces into account. Theoretical, experimental and numerical approaches appear to be consistent.