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«ABSTRACT Three-phase relative permeability has been calculated from unsteady state experiments. Gas or water were the injected phase in these ...»

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Arne Skauge and Johne A. Larsen

Norsk Hydro Research Center, Bergen, Norway


Three-phase relative permeability has been calculated from unsteady state experiments. Gas

or water were the injected phase in these displacements. The core material include both

outcrop and reservoir sandstones with different wettability.

The results show that the residual oil saturation can be significant lower by three-phase flow compared to two-phase waterflood or gas injection. The paper summarize the results of threephase relative permeability at different wettability for water-wet, intermediate and more oilwet cores. Relations for trapped gas from three-phase flow were investigated, and a new approach to model relative permeability hysteresis for WAG processes have been proposed.


For immiscible WAG processes, the microscopic displacement efficiency is usually regarded to be determined by gas residual oil saturation in gas invaded zones and by waterflood residual oil saturation in the water dominated zones. When hydrocarbon gas is the injected gas phase, vertical segregated zones with gas migrating to the top are dominant in reservoirs where vertical communication is good. The viscous-gravity ratio determines the extent of the zone of dispersed three-phase flow. Oil recovery is estimated by Sorg where gas flows, while in the water flooded parts the minimum oil saturation is determined by S o w. Under these assumptions, the oil recovery can be optimized depending on efficiency of gas and water (Sorg,Sorw). For such WAG processes three-phase relative permeabilities may be of less importance as the three-phase zone can be of negligible extent. However, the residual oil saturation in the three-phase zone may be reduced. Earlier results show that microscopic displacement efficiency by WAG is improved compared to waterflooding and gas injection1.

The mobility 'of the phases are in some cases reduced in a three-phase flow situation compared to two-phase flowly2. Both these arguments may lead to an extension of the threephase zone.

The objectives of the experimental studies reported in this paper has been to measure microscopic displacement by WAG and to compare to gas injection and waterflooding.

This paper tries to summarize the experience of measurements of relative permeabilities from a large number of unsteady-state experiments or displacements by injection of either gas or water. The oil recovery from some of the displacements reported here have been presented earlie8, but the relative permeability data from this large database have not been reported.

The most extensive experimental study of three-phase relative permeability have been the work of oak3. These steady-state relative permeability work have included different wettability and was recently summarized by ~ a k e r ~. relative permeability of the nonThe wetting phase can be susceptible.to dependence of saturation history. At intermediate wettability it is shown that it is important to maintain the capillary force equilibrium during di~placemen?.~. These arguments favours that the most representative relative permeability data are obtained by a saturation path similar to the process in the reservoir, i.e. unsteady state experiments at reservoir rates should be the best approach to respect the force balances and process path of any three-phase displacement process in a reservoir. An other question which arise is that three-phase relative permeabilities may be so sensitive to specific reservoir and process properties that little generalization can be made. If so the only approach is to do measurements in each case. The paper attempt to pursue these arguments.


The core material used in the core displacement experiments was sandstone cores either outcrop Berea or North Sea reservoir rock. Cores from four different oil reservoirs have been included and compared to displacement with Berea (B) and silanized Berea(TB). The reservoir rock material from the four reservoirs applied in the reported experiments had different permeabilities in the ranges as follows; R1 (100-500mD), R2 (30-300mD), R3 (800mD), and R4 (300-800mD).

The core length varied from 40 cm to 100 cm. the reservoir core models consist of several core pieces butted together in a tri-axial coreholder. Each core piece was carefully machined to ensure good capillary contact in the mounted core model. The core diameter was either

3.7 cm or 5.0 cm. The pore volume of the composite core models ranged from 70 to 470 ml.

The w;ttability-modified Berea core was treated by displacing 7 pore volumes of 5 wt% Drifilm (dimethyldichlorosilane)in hexane through the core. This procedure has earlier been reported to result in oil wet cores7. In other wettability studies silanized Berea have shown changing wettability upon fluid displacements8.

In the sequential flow experiments each displacement was continued until the oil production ceased. A minimum of 2-3 pore volumes were injected. The flow rates were generally defined to be lower than the critical velocity for stable flow. The flow rates for cores with diameter of about 3.7 cm were usually about 6 cc/h. Gas injection was performed on horizontal oriented cores for series B, TB, and R1 utilizing a constant differential pressure of

1.05 bar/m. All other gas injections were vertical gravity stable displacements.

The core was mounted in a triaxially core holder with confining pressure. Floating piston cylinders connected to a volumetric displacement pump were used to inject fluids at a constant volumetric rate. The injection fluids were stored in a thermostated oven, and all high pressure fluid lines were heat traced to avoid retrograde condensation of gas and possible wadasphalthene precipitation from the oil due to temperature gradients.

The reservoir cores were cleaned with toluene/methanol and dried. All cores were evacuated and initially saturated by brine before water permeability was measured. Then the cores were drained to irreducible water saturation by a high viscous paraffinic oil (Marc01 172).

The experimental conditions of the displacement experiments varied depending on the reservoir temperature and pressure. The experiments with reservoir cores have been performed at temperatures in the range of 100C and at pressure of about 300 bars. The fluids were recombined reservoir oil and gas, and all fluids including brine were equilibrated at the specific reservoir conditions. The core floods with outcrop cores were made with synthetic fluids. Equilibrated mixtures of methane and decane defined the gas and oil phase at the selected pressure. The experiment temperature was always at ambient conditions for all the outcrop core floods.

The reservoir fluids were either sampled at reservoir conditions or produced through a back pressure regulator into an atmospheric separator system. An automatic data acquisition system collected and stored the phase-volumes injected and produced, pressure, and temperature data. For the compositional studies, the produced gas and oil phases were sampled and analyzed to calculate correct phase composition at reservoir conditions.

Core wettability The wettability of the five different types of core material have been compared by determination of the Amott wettability index. The Amott index for the Berea cores were 0.7while the silanized Berea core also changed to water wet condition after the series of displacements were completed, WI = 0.85. Initial displacements just after the silane treatment showed a more oil wet behavior, the end point water relative permeability at Sorw was 0.4 compared to 0.07 for the water wet Berea cores. The silanized Berea clearly changed wettability during displacement, which indicate that the silane adsorption on the surface of the rock is reversible. The reservoir cores show wettability indices of 0.3-0.5 for R1, 0.2-0.4 for R2, 0.3 for R3 and 0.3 for R4. The wettability index measurements were performed at ambient conditions and changes in wettability may occur for the displacements at reservoir conditions.

The oil production after water breakthrough during waterflood is an other indication of the wettability. Both Berea, R1 and R4 show very little oil production after breakthrough, about 2% of the pore volume. The other core material TB, R2 and R3 show destingtly more oil produced after breakthrough of water, in the range of 5-7 %PV. The R1 cores also gave a low krw at Sor 0.13, compared to more oil wet behavior of the R2 and R3 core material with krw(Sor) equal to 0.4.

Three-phase relative permeabilities All relative permeability data were measured by displacement (unsteady-state) experiments.

The three-phase relative permeability was calculated by the standard approach described andlor used in several paper^(^-'^). The figures attached presenting the relative permeability data are plotted against normalized total mobil phase saturation The displacement process was defined by G for gas injection and W for water flooding. The number behind the letter refers to either primary, secondary or tertiary injection sequence, as an example W3 refers to a tertiary waterflood.' The oil phase saturation is always decreasing in all the displacement, either water or gas was the injected (increasing) phase. The kr data were tried to visualized in different geometric realisations, but we found the best representation of the data to be standard graphs when only a few figures could be presented.

Saturation estimations and displacement front stability The gas injection sequences were conducted in two different ways to reduce effects of front instability problems. Either the gas was injected at a constant pressure gradient of 1.05 barlm, or the gas injection was done gravity stable at constant rate. Figure 1 shows the changes in average saturation between start- and endpoint of each displacement for a water wet case.

Analogous, Figure 2, shows the estimated saturation at x=L from the same core material, this is also the position where the relative permeabilities were estimated. The start- and end-point of the trajectories should be the same as in Figure 1. The agreement was reasonable remembering that relative permeability were estimated when two or three phases flow simultaneously. Viscous fingering of gas will only influence the saturation on a local level, but because of mass balances the saturation at the outflow end will be on average correctly estimated with the standard Buckley/Leverett and Welge method.

Water wet cores The water wet cores used were either Berea outcrop cores or sandstone reservoir cores R1 and R4. Gas is regarded as the non-wetting phase for water-wet, intermediate-wet and oil-wet cores. The liquid phases, water and oil, are regarded as wetting phase and intermediate wetting phase depending on the wettability of the core.

The water wet cores show a slight tendency to hysteresis in the water relative permeability curves, Figure 3. The water k seems only to depend on the water saturation. The results r from steady state gas-oil-water relative permeability studies in ref. 4 show similar conclusions as the relative permeability of a wetting phase depends most strongly on the saturation of that phase, and hysteresis were only a minor factor for the wetting phase.

The oil relative permeabilities were all obtained from experiments where oil saturation was decreasing. Therefore this study cannot conclude on the possible hysteresis in the oil relative permeability. As the experiments were sequences of waterfloods and gas injection a dependence on the saturation history may occur. The data show very little tendency to systematically changes with injected phase or saturation history, Figure 4. The trend in the oil isoperms were a curvature of concave towards oil for the water wet cores, as also has been concluded by others4.

The shape of the gas relative permeability curves from constant pressure gradient experiments could indicate a functional representation independent of saturation. Secondly, the gas relative permeability does not go to zero continuously. One explanation of this unusual behavior could be viscous fingering, i.e. gas bypassing a resident fluid (in this case oil and water). The gas would prefer to flow in the channels already occupied by gas, and the estimated relative permeability may become larger than "true" values, due to reduced pressure gradients after gas breakthrough. The gas kr remains constant due to insignificant pressure drop by gas and nearly constant fractional flow after breakthrough.

The gas relative permeabilities show a strong dependence on process path i.e. increasing or decreasing saturation change. However, there were little changes between primary and tertiary gas injection. An observed variationlspread of the relative permeabilities data can be due to dependence on more than one phase saturation, Figure 5. Also steady state data4 observe hysteresis for the non-wetting phase.

Oil wet The,Berea cores were silanized to make the surface of the rock oil wet. As reported earlier the wettability altered during stages of several experiments. After a total of seven flooding sequences the core was showing water wet properties when water flooded and core plugs used for wettability study show water wet wettability index. The saturation changes and endpoint relative permeabilities of the displacement experiments are shown in Table 1.

The water kr show hysteresis especially when comparing secondary water flood with tertiary gas injection, Figure 6. The more oil wet cores generally show stronger hysteresis in krw, and also show a dependence on the saturation history. However, the influence of varying wettability on the silanized Berea makes it hard to draw conclusions from these experiments.

The oil kr show only minor change with saturation history, but the last few displacements show some deviation, Figure 7. These changes is most likely due to changes in the wetting properties during continuous flooding experiments. The oil relative permeabilities seems to primary be a function of oil saturation only for the more oil wet cores. The gas kr show very reduced permeability for tertiary gas injection compared to primary gas injection, Figure 8.

Intermediate wettability The R2 cores have shown wetting behavior in the range of intermediate or mixed wettability.

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