Relative Permeability Hysteresis: Laboratory Measurements and a Conceptual Model

Abstract

Relative permeability hysteresis has been measured for a water-wet outcrop rock sample and a mixed-wet reservoir core. For the oil phase, imbibition and drainage relative permeability curves differed significantly. The difference was much less pronounced for the water phase. Scanning curves, which characterize transitions between imbibition and drainage curves, were also measured. A notable characteristic of the oil relative permeability scanning curves is their reversibility; along most of the length of a scanning curve, oil relative permeability exhibits no hysteresis. A proposed mechanism for the reversible behavior is pinning of water-oil interfaces on surfaces of rock grains. Pinned interfaces remain anchored at fixed positions on grains despite changes in interface curvature and contact angle. In water-wet samples, pinning can occur as a result of contact angle hysteresis. In mixed-wet rock, pinning can occur at the boundaries between water-wet and oil-wet grain surfaces. As long as interfaces remain pinned, pore-level fluid geometry is a function of saturation only, and does not depend on the direction of saturation change. Introduction Relative permeability curves, which characterize simultaneous multi-phase flow in porous rock, are important in understanding and predicting the performance of immiscible displacement processes in oil and gas reservoirs. Hysteresis in both relative permeability and contact angle has long been recognized. In the case of relative permeability, two-phase flow properties of a porous medium depend on which phase is increasing in saturation, For contact angle, measured values depend on which phase is advancing over a solid surface, Numerous studies have reported hysteresis data for either relative permeability or contact angle, but little work has been done to link the two phenomena. This paper attempts to make such a linkage by showing that relative permeability data exhibit a hysteresis pattern that would be expected if fluid geometries are controlled by contact angle hysteresis. For the two water-oil systems investigated here, relative permeability scanning curves, which describe flow when the direction of saturation change is reversed, are shown to be reversible over limited saturation ranges. Under these conditions, we propose that contact angles will change between maximum and minimum values while water-oil interfaces remain pinned at fixed positions on grain surfaces. As long as the interfaces remain pinned, changes in fluid geometry are reversible. Outside the range of reversibility, contact angles are at their limiting values, interfaces move along grain surfaces, and fluid geometries are controlled by processes that result in hysteresis. Terminology Processes in porous media that involve decreases in the saturation of the wetting phase are commonly referred to as "drainage". We use that term here to refer to decreases in water saturation for a water-oil system regardless of rock wettability. "Primary drainage" relative permeability curves are those measured while decreasing the water saturation from 100%, while "secondary drainage" curves involve a decrease from the high water saturation occurring when immobile oil is present.

Compositional Three-Phase Relative Permeability and Capillary Pressure Models Using Gibbs Free Energy

“…Comparison of relative permeability data with curves calculate from model during first increasing, first decreasing and second increasing displacements. Experimental data reported by Braun and Holland (1995).…”

“…To verify the validity of the above assumptions in deriving bounding and scanning relative permeability curves, a set of empirical data reported by Braun and Holland (1995) was used. They performed a series of two-phase measurements on a water-saturated Berea sandstone Eq.…”

Relative Permeability Correlation for Mixed-Wet Reservoirs

“…The scan from S w [2] back to S w [1] is now interrupted by the third reversal at S w [3], the first reversal point shown in the figure. The imbibition scan p ci [3] from S w [3] is aimed back at S w [2], but is interrupted at S w [4] with a drainage process p cd [4] that aims back at S w [3]. Two more reversals occur, at S w [5] and S w [6].…”

“…4 • The hysteresis loops of the capillary pressure and the relative permeabilities form a consistent set. 5,6 • Imbibition oil relative permeability curves may exhibit a characteristic inverted "S" shape.…”

“…5,6 • Imbibition oil relative permeability curves may exhibit a characteristic inverted "S" shape. [7][8][9][10][11][12][13] • The validity of the relative permeability correlation and the hysteresis scheme is tested on published relative permeability measurements 4 and simultaneously measured hysteretic relative permeability and capillary pressure curves. 5 The hysteresis scheme is easy to program and could replace the Killough 14 scheme in numerical reservoir simulators.…”