Recovery and Sweep Efficiency in a Cross-Sectional Problem of Immiscible Displacement with Gravity Override and Capillary Imbibition

We consider a cross-sectional study of immiscible displacement under the influence of gravity, anisotropic permeability, and capillary effects. We propose the similarity criteria characterizing the relative role of these effects and qualitatively different flows. We present a classification of the flow regimes in four limiting cases of the displacement. The recovery and sweep efficiencies in such cases can be compromised by the gravity override, channeling, and coning effects. In the phase plane, we constrain the parameter ranges at which these effects become relevant. We then aim at evaluating the range of the similarity criteria characterized by the maximum efficiencies and describe the placements of horizontal wells allowing to reach these maxima. We show that the placement of the producing well is generally more relevant. In the limiting cases, the variety of placements can be merged in groups by their efficiencies. We eventually come up with the maps of the maximal efficiencies and associated placements allowing for a quick assessment of the optimal injection scenarios. The proposed classification of the flow regimes and the calculated maps can be useful in evaluating various scenarios of waterflooding and gas injection.