Dimensionless groups for three-phase gravity drainage flow in porous media

Abstract

The downward displacement of oil by gas (either through gas cap expansion or by gas injection) at the crest of the reservoir is an attractive method of oil recovery. The drainage of oil under gravity forces is a potentially efficient method as it can reduce the remaining oil saturation to below that obtained after waterflooding. This paper describes a series of experiments of gas invasion under gravity-dominated conditions with special attention to the effects of wettability and water saturation on three-phase flow. The experiments were performed in bead-pack models by spontaneous gas invasion at both low and high water saturations with a spreading oil. Different oil recovery rates were observed depending on the wettability of the beads and initial water saturation. At irreducible water saturation, the process appeared to be less efficient for the oil-wet conditions, while similar oil recoveries are observed for both oil-wet and water-wet media at residual oil saturation. Different recovery rates occur with different fluid morphology, which depend on the matrix wettability and the balance between gravity, viscous and capillary forces. The results have been analysed using dimensionless groups. The Bond ( N B) and capillary numbers ( N C) were modified to include the 3-phase effects of gas, oil and water. However, for these cases the Bond and capillary numbers alone were insufficient to fully describe the dynamics of oil recovery by gravity drainage. Therefore, a new dimensionless group combining the effects of gravity and viscous forces to capillary forces was defined as: N= N B+ A( μ d/ μ g) N C, where A is a scaling factor (in all our experiments A=−17225) and ( μ d/ μ g) is the viscosity ratio between the displaced and displacing phase. A linear relationship was found between this new group and the total recovery for all the scenarios tested. The slope was approximately 40 for three cases, i.e., water-wet case at irreducible water saturation, and water-wet and oil-wet cases at residual oil saturation. The oil-wet case at irreducible water saturation has a larger slope, probably due to the blocking effect of water. These experimental results may be used as a benchmark to test theoretical models of three-phase flow under gravity dominated conditions. The new dimensionless group should improve the understanding of the pore scale mechanisms so that these processes can be included in the development of network models and in the processes of upscaling laboratory results.