Observations and Correlations for Immiscible Viscous-Fingering Experiments

Abstract

Summary We studied immiscible two-phase flow instabilities in porous media underdrainage conditions. The objective of our experiments was to improve ourunderstanding of viscous fingering so that we could avoid it or at leastaccount for it in flow simulations. This paper first presents the moldingtechnique used to observe and measure viscous fingering in large, 3D, naturalconsolidated Porous samples. Moldings of 16 flows showed instabilities thatlooked like fingers and stable displacements behind the unstable front. Wecorrelated breakthrough recovery, mean local saturation, finger volume andwidth, pressure drop, and saturation profiles with dimensionless numbers. Threekinds of displacements occurred: stable displacements, with macroscopic viscousfingering, and displacements with both macroscopic and microscopic viscousfingering. Finally, we determined linear 1D relative permeabilities. Introduction Most EOR processes are based on the displacement of one fluid by another. The displacing fluid is frequently less viscous than the displaced one andviscous fingering appears. At present, various theoretical approaches to studyviscous fingering are proposed. Because experiments are required to testtheories or to proposed. Because experiments are required to test theories orto help in formulating them, a great deal of experimental work is being done. Most experiments to date, however, have been conducted on unconsolidated orartificial porous media, as the following literature survey and Table 1 show. Three observations about these media must be made. First, single-phasepermeabilities were very high. Second, in most, one dimension of the sampletested was on the order of a few pores. Consequently, the question arises ofwhether finger size is independent of pore size or should be scaled to it. Third, the sand or glass beads were sieved to get a narrow range of grain sizes(see Table 1). Hence, all the pores were of similar size and the derivative ofcapillary pressure with saturation was almost zero. Because this parametercontrols the dispersion caused by capillary pressure, the effect of dispersionon viscous fingering was not completely tested. To help understand viscousfingering in drainage displacements, we suggest developing and studyingexperiments that are as close as possible to reality. In the first part of thispaper, we describe 3D experiments on drainage displacements conducted innatural porous limestone. In the second part, we present observations and themain parameters that can be measured. We then propose correlations between themeasured parameters and relevant dimensionless numbers. The third and last partdeals with modeling. We show how viscous fingering can be integrated intorelative permeabilities, which become linear as a result. Literature Survey Engelberts and Klinnenberg coined the expression "viscous fingering" in 1951. They found that ultimate recovery after injection of numerous PV's wasalmost independent of displacement parameters and showed that breakthroughrecovery was high at low flow parameters and showed that breakthrough recoverywas high at low flow rates and also did not depend on displacement parameters. However, they proved that viscosity ratio was the most important vanable athigh flow rates. At a viscosity ratio above unity and high flow rates, a linearrelationship existed between breakthrough recovery and the logarithm of theviscosity ratio. In 1956, van Meurs used a transparent model to observe thedisplacement pattern. Viscous fingering did not occur at a viscosity ratio ofunity but did occur at a viscosity ratio of 80. Oil production rate decreasedslowly alter breakthrough at high viscosity production rate decreased slowlyalter breakthrough at high viscosity ratios. Chuoke et al. showed thatcapillary pressure may contribute to the enlargement of fingers. They foundthat fingers are small for high oil viscosity or low interfacial tension (IFT). Finger widths were larger in the presence of connate water saturation. de Haanshowed that water fingers in oil-wet media were on the order of the magnitudeof the pores, whereas in a water-wet medium the water phase was much morecontinuous. Nonetheless, viscous fingering occurred less readily in drainage. Benham and Olson confirmed the conclusions of van Meurs in 1963 by carrying outa number of elaborate experiments. In 1968, Croissant noted that the number offingers continuously decreased and that fingers grew with time in length andwidth. He found that every finger length was linear with time and that fingerwidth could be scaled with the square root of time. Perkins and Johnston showedthat distinct fingers broke up into a graded saturation zone early indisplacement in the presence of connate water. Gupta and Greenkorn found in1973 that numerous incipient fingers occurred at the very beginning ofdisplacement, and that they degenerated into a single finger at a later stage. Finger growth rate was linear with time. Peters and Flock visualized viscousfingering in long, cylindrical, 3D sandpacks. In fact, this was the firstattempt to visualize fingering in a 3D porous medium. Viscous fingering wasshown to reduce breakthrough recovery. The authors showed that fingers werealmost eight times wider in a water-wet medium than in an oil-wet medium.breathrough recovery decreased linearly with the logarithm of the flow rateuntil it reached a lower limit of 0.20. In 1987, Peters and Khataniardetermined relative permeabilities using production and pressure-drop data. They showed permeabilities using production and pressure-drop data. They showedthat relative permeability curves were affected by displacement stability. Ingeneral, oil relative permeability decreased with increasing instability, whilewater relative permeability increased. Bentsen and Saeedi used microwaveattenuation to measure mean local saturations. Saturation profiles presented bythe authors gave evidence of a stable 0.5 saturation zone at the inlet end. In1984, Paterson et al found that injection of water created more irregularfingers in the presence of connate water saturation. Two years later, Ni et alcarried out the first immiscible displacements in consolidated porous media. They used a radial plate of sintered glass beads. Breakthrough recovery vs. flow rate was very similar to the results already presented for the linearcase. In 1986, Stokes et al measured viscous finger width. They found thatfinger width was comparable with pore size in drainage. In imbibition, however, finger width was much larger than pore size and was found to scale with thesquare root of the capillary number. Nasr-El-Din et al studied radialdisplacements in consolidated porous media in 1987. They showed thatbreakthrough recovery was porous media in 1987. They showed that breakthroughrecovery was an almost linear, decreasing function of the logarithm of the flowrate. Sigmund et al presented cumulative saturation profiles that were almostlinear vs. the length of the sample. In profiles that were almost linear vs. the length of the sample. In addition, finger growth rates were linear withtime. Sarma measured both saturation and capillary pressure and determinedrelative permeabilities. Oil permeabilities changed more with instability thanwater permeabilities. Amiell showed that the number of fingers was almostindependent of flow rate, but that the shape of the finger was flow-ratedependent. SPERE P. 187