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Fuel

Manuscript Draft

Manuscript Number: JFUE-D-13-01836

Title: Gravity Stability Investigation of Low-Tension Surfactant Floods

Article Type: Original Research Paper

Keywords: chemical enhanced oil recovery (EOR), surfactant flood, gravity stability, microemulsion

Abstract: Classical stability theory can be used to estimate the critical velocity of a miscible flood

stabilized by gravity forces. However, stability theory for an ultra-low interfacial tension (IFT)

surfactant displacement is not well developed or validated. In this paper, a method for predicting the

critical velocity for a surfactant flood is proposed taking into account the microemulsion phase.

Vertical upward surfactant displacement experiments were performed and compared with stability

theory. The proposed theory and experimental results offer new insight into the behavior of surfactant

floods stabilized by gravity forces and how to optimize them by controlling the microemulsion

viscosity.

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Gravity stability theory was proposed for low-tension surfactant flood. Ultra-low IFT surfactant formulation was developed for the specific oil with results of phase

behavior, aqueous stability and microemulsion viscosity.

Surfactant floods were conduced to verify the proposed gravity stability theory, and alsocompared with the field test data.

The fractional flow theory was used to interpret lab data, and sensitivity studies wereperformed to show how to optimize gravity stable surfactant flood.

ghlights (for review)

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Gravity Stability Investigation of Low-Tension Surfactant FloodsJun Lu, Upali P. Weerasooriya, and Gary A. Pope, The University of Texas at Austin

AbstractClassical stability theory can be used to estimate the critical velocity of a miscible flood stabilized by gravity forces.

However, stability theory for an ultra-low interfacial tension (IFT) surfactant displacement is not well developed or validated.

In this paper, a method for predicting the critical velocity for a surfactant flood is proposed taking into account themicroemulsion phase. Vertical upward surfactant displacement experiments were performed and compared with stability

theory. The proposed theory and experimental results offer new insight into the behavior of surfactant floods stabilized by

gravity forces and how to optimize them by controlling the microemulsion viscosity.

IntroductionThe hydrodynamic stability of both miscible and immiscible displacements in porous media has been studied for many years.

Many investigators have reported both experimental and theoretical results for the effects of gravity and viscosity on the

stability of miscible displacements (Hill, 1952; Perrine, 1961 and 1963; Dumore, 1964; Tan and Homsy, 1987 and 1988;

Homsy, 1987; Hickernell and Yortsos, 1986; Manickam and Homsy, 1995) and immiscible displacements (Engelberts and

Klinkenberg, 1951; Chuoke et al., 1959; Terwilliger et al., 1951; Sheldon et al., 1959; Fayers and Sheldon, 1959; Raghavan

and Marsden, 1971; Nayfeh, 1972; Peters and Flock, 1981; Glass and Yarrington, 1996; Stephen et al., 2001; Meheust et al.,

2002; Ould-Amer and Chikh, 2003; Riaz and Tchelepi, 2004).

Surfactants can generate ultra-low IFT and displace almost all the residual oil after waterflooding a core (for recentexperimental examples, see Yang et al., 2010; Adkins et al., 2010; Barnes et al., 2012; Bataweel et al., 2012; Puerto et al.,

2012; Adkins et al., 2012; Lu et al., 2012; Tabary et al., 2013), but even at ultra-low IFT surfactant floods are still not

miscible displacements. Because understanding of the gravitational stability of surfactant floods is lacking, surfactant

displacement experiments were carried out to determine the critical velocity for a gravity stable surfactant flood.

Stability TheoryStability theory for water displacing oil in a homogeneous, uniform porous medium without a transition zone can be found in

Lake (1989). The critical velocity is given by Eq. 1.

0

0sin

1

rwc

w

gkkv

M

(1)

where

w o

and

00

0

rw o

w ro

kM

k

.

Now consider a vertical column of a homogeneous porous medium at residual oil saturation after waterflooding. An

aqueous surfactant solution is injected from the bottom of the column at a constant velocity. Neglect the in-situ generated

microemulsion phase. Only oil and aqueous phases flow through the porous medium. The aqueous phase containing

surfactant displaces the oil bank, so when applying Eq. 1 a modification is needed on the endpoint water-oil mobility ratio,

M0. The endpoint water to oil mobility ratio should be replaced by the water to oil bank mobility ratio. The total relative

mobility of the oil bank is defined as the total mobility of the flowing oil and water phases,

ro rwrtot ro rw

o w

k k

corresponding water to oil bank mobility ratio, M OB, is in the range of 10 to 20. Equation 1 is then changed to Eq. 2:

0

sin1

rw

w OB

gkkv

M

(2)

In reality, a microemulsion forms between the oil bank and the injected surfactant solution and should be taken into

account since its density and viscosity are different than the water and oil. Assume a uniform microemulsion at its optimum

salinity so the oil and water concentrations in the microemulsion are equal. Then the microemulsion density will be close to

the average of the water and oil densities. The microemulsion viscosity at optimum salinity is typically about ten times larger

nuscript

k here to view linked References

http://ees.elsevier.com/jfue/viewRCResults.aspx?pdf=1&docID=15491&rev=0&fileID=483520&msid={AB120568-66C2-4C31-AFA1-5AAA1108659D}http://ees.elsevier.com/jfue/viewRCResults.aspx?pdf=1&docID=15491&rev=0&fileID=483520&msid={AB120568-66C2-4C31-AFA1-5AAA1108659D}

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than the oil viscosity for a light oil, but must be measured under each specific condition. There are four regions in the

column: starting from the top and going down, there is water and oil at residual oil saturation, oil bank with both oil and

water flowing upward, microemulsion pushing the oil bank upward, and aqueous surfactant solution pushing the

microemulsion upward (Illustration shown in Fig. 1). Equation 1 can be applied at the interface between the microemulsion

and oil bank as follows:

sin1

me o rme

me OB

gkkv

M

(3)

where

rme

rme meOB

ro rwrtot

o w

k

Mk k

.

Similarly, the critical velocity at the interface between the microemulsion and the aqueous surfactant solution is:

sin

1

s me rs

s me

gkkv

M

(4)

where

rs meme

s rme

kM

k

.

The minimum of these two velocities is the critical velocity for a surfactant flood.

Experimental Materials and ProcedureSurfactant phase behavior tests were used to identify good surfactant formulations for this specific oil (Table 1) at reservoir

temperature. The detailed experimental procedure can be found in Levitt et al. (2006), Zhao et al. (2008) and Yang et al.

(2010). The surfactants that formed a low viscosity microemulsion in a few days and produced ultra-low IFT were selected

for further evaluation. The aqueous surfactant solution was observed for stability and clarity at both room temperature and

reservoir temperature to determine if it was stable up to at least optimum salinity.

Salinity scans were done to determine the optimum salinity and select microemulsion sample for viscosity measurement.

The sample was prepared in a tube of about 100 ml. The surfactant solution and oil were injected into the tube capped with arubber stopper, and then mixed and placed in the oven at reservoir temperature. When the sample was equilibrated, the rubber

stopper was removed and a syringe with a long needle was used to extract the microemulsion from the tube. An 8.5 ml

sample was required to complete a rheological test using an ARES LS-1 rheometer. The steady state viscosity was measured

in the shear rate range of 0.1 to 600 s -1.

Three column experiments were conducted in Kontes glass chromatography column of 4.8 cm inside diameter. The

column was packed with F-95 grade Ottawa sand. After packing, the column was vacuumed to remove the air from the

column. The column was then saturated with 0.75% NaCl brine. A tracer test was performed with 3% NaCl brine to estimate

the pore volume and determine the homogeneity of the sandpack. The tracer breakthrough data (Fig. 2) show that the

sandpack was nearly homogeneous. Then the column was inverted and several pore volumes of oil were injected from the top

of the column in a favorable direction with respect to gravity. The column was then flipped over to the original vertical

position, and 3% NaCl brine was injected to reach the residual oil saturation after waterflood, Sorw. Then the surfactant

solution at the optimum salinity was injected from the bottom continuously until the end of flood. After the chemical flood,

the column was then cleaned by injecting IPA and then NaCl brine until no surfactant was detected in the effluent. Then the

column was reused for next surfactant flood but at different interstitial velocities. The effluent samples during the surfactant

flood were collected in a fraction collector using volumetrically calibrated test tubes.

Results and DiscussionPhase Behavior Results and Microemulsion Viscosity. The surfactant formulation developed for this oil was a mixture of

0.5 wt% C13-13PO-Sulfate, 0.5 wt% C20-24 IOS, 2.0 wt % IBA, and 0.5 wt% Na2CO3 alkali. The large hydrophobe C20-

24 IOS is balanced by a more hydrophilic C13-13PO-sulfate. The co-solvent IBA improved aqueous stability and

microemulsion formation. The aqueous solutions were clear and stable up to 30,350 ppm TDS for more than 54 days at the

reservoir temperature of 38 C. This formulation equilibrates fast and shows a high optimum solubilization ratio of about 22

at the optimum salinity of about 21,000 ppm TDS as shown in Fig. 3. The estimated IFT at optimum salinity is about 6.2 10-

4dynes/cm based on the solubilization ratio of 22 (Huh, 1979). The trapping number (Pope et al., 2000) at this ultra-low IFT

is on the order of 0.01, which is sufficient to displace all of the oil from the sand. The trapping number is the sum of the

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capillary and Bond numbers for a vertical displacement. In these experiments, the capillary number was small compared to

the Bond number i.e. its value was dominated by the buoyancy term. The microemulsion sample at optimum salinity was

prepared, and the microemulsion viscosity was measured at 38 C. The in-situ shear rate of the surfactant floods was

estimated to be around 1 s-1. The microemulsion viscosity at 1 s-1with optimum salinity is about 24 cp or about 5 times the

oil viscosity.

Surfactant Flood Results. Figure 4 shows the photographs of all three sandpack floods at different times during the

surfactant flood. Four different sections and interfaces between them can be seen in the photographs. The four sections, fromthe top to the bottom of the column, are residual oil, oil bank, microemulsion, and aqueous surfactant solution, respectively.

The surfactant displacement is stable or nearly stable at a frontal velocity of 0.2 ft/day and unstable at 0.4 and 0.8 ft/day. For

each flood, the volume of microemulsion zone increases with injected pore volumes and is larger at higher velocity due to

more mixing of the unstable displacements. The interface between the oil bank and microemulsion and between the

microemulsion and aqueous surfactant solution at 0.2 ft/day are sharper and more horizontal compared to floods at 0.4 and

0.8 ft/day. The fingers for the high velocity floods are more pronounced at the lower interface because the viscosity of the

aqueous surfactant solution is nearly as low as brine and much lower than the viscosity of the microemulsion.

Figures 5 through 7 show the surfactant flood results including cumulative oil recovery, oil cut, and oil saturation at

velocities of 0.2, 0.4, and 0.8 ft/day, respectively. The surfactant floods displaced nearly all of the oil. The parameters and

details of the three sandpack experiments are summarized in Table 2.

At the stable velocity, 0.2 ft/day, the oil recovery at surfactant breakthrough and the average oil cut in the oil bank were

high. Both decreased as the velocity increased due to the viscous fingering and also less clean oil was recovered from the oil

bank and more from the produced microemulsion.

Calculation of Stable Velocity for Gravity Stable Surfactant Floods. The velocities required to achieve a gravity stable

surfactant flood in the sandpack were calculated using the models discussed in the stability theory section. The parameters

used in the calculations are listed in Table 3. The critical velocity calculated from Eq. 1 is 1.63 ft/day with k0rwassumed to be

1 since almost all of the oil was displaced by the surfactant solution. The critical velocity calculated by Eq. 2 with the

endpoint mobility ratio, M0, replaced by the oil bank mobility ratio, M OB, is 0.65 ft/day.

If the microemulsion phase is taken into account, there are three phases and two interfaces existing during the

displacement. Therefore, two velocities at two interfaces can be calculated, and the smaller one is the stable velocity. The

microemulsion viscosity at optimum salinity is estimated to be 24 cp. The relative permeability of both the microemulsion

and aqueous phase was assumed to be 1. In this case, M OBis calculated to be less than 1 with rtottaken as 0.05. This implies

a stable displacement at any velocity for the microemulsion phase displacing the oil bank. Next, the stable velocity between

the microemulsion phase and aqueous surfactant phase is calculated using Eq. 4 to be 0.18 ft/day. This is the predicted

velocity needed to achieve a gravity stable surfactant flood in this sandpack. This value is in much better agreement with the

experiments than the value calculated using either Eq. 1 or 2.Similar calculations were done for the White Castle field pilot described by Falls et al. (1994). The parameters of this

pilot are shown in Table 3. The critical velocity calculated by Eq. 1 is 0.30 ft/day. The critical velocity calculated from E q. 2

using an estimated oil bank mobility is 0.06 ft/day. The critical velocity calculated from Eq. 4 is 0.02 ft/day. Therefore, the

stable velocity to perform a gravity stable surfactant flood in this field is estimated to be 0.02 ft/day.

Using data from the paper, the surfactant flood velocity in the pilot test was estimated to be about 0.24 ft/day, which is

much greater than the predicted critical velocity of 0.02 ft/day based on Eq. 4. Shell intended for the pilot to be stable, but

interpreted the results as unstable, which is consistent with these calculations.

Fractional Flow Theory and Sensitivity Studies. Fractional flow theory is a useful way to model first order effects of

immiscible displacements such as water floods and surfactant floods and in particular gravity stable surfactant floods. The

fractional flow curves using both oil and water Corey exponents of 4 for all three experiments are shown in Figures 8 through

10. Each figure shows the fractional flow curve for two-phase flow of oil and water at high interfacial tension (curve on left

of figure) and two-phase flow microemulsion and oil at low interfacial tension (curve on the right of figure). Where thetangent to the latter curve crosses the oil-water curve corresponds to the oil cut in the oil bank and is read on the right scale.

The oil cuts in the oil bank based on the fractional flow calculations including gravity are in reasonably good agreement with

the experimental values at 0.4 and 0.8 ft/D, but the oil cut for the flood at 0.2 ft/D is much higher than the fractional flow

value. This is most likely an experimental artifact of how the oil bank was collected.

The sensitivity of the critical velocity to both the microemulsion viscosity and aqueous surfactant phase viscosity was

investigated using Eqs. 3 and 4. Figure 11 shows the critical velocity for both interfaces. The critical velocity for the upper

interface between the oil bank and the microemulsion is v1. The critical velocity for the lower interface between the

microemulsion and the aqueous surfactant phase is v2. The displacement is stable when the velocity is less than the lower of

the two critical velocities. The highest or optimum critical velocity is when the two curves cross i.e. when v1=v2 which in

this case is at 0.45 ft/D for a microemulsion viscosity of ~10 cp. Thus, the microemulsion viscosity can be optimized to

maximize the velocity for a stable displacement. The experiments were done with an oil viscosity of 5.4 cp and a

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microemulsion viscosity of 24 cp. The surfactant flood can be done at a higher velocity and still be stable when the oil

viscosity decreases because the mobility of the oil bank increases.

Although the higher stable velocity with an optimized microemulsion viscosity is highly beneficial to the project

economics, the fractional flow curve is slightly less favorable. In the above example with a higher velocity of 0.45 ft/D,

Figure 12 shows the tangent to the fractional flow curve is less favorable than the one shown in Fig. 9. The tangent to the

microemulsion/oil curve is at a water saturation of about 0.9 compared to 0.95, which means a longer tail will exist for the

lower microemulsion viscosity case, but fortunately the displacement is still very efficient.

The calculations so far assume the viscosity of the aqueous surfactant solution is the same as water. If polymer is addedto the surfactant solution, then the critical velocity will increase for the lower interface between the aqueous surfactant

solution and the microemulsion as shown in Fig. 13 for the experimental case with a microemulsion viscosity of 24 cp. The

upper interface is unconditionally stable with such a viscous microemulsion. Figure 13 shows that adding polymer is not very

effective until the viscosity increases to nearly the value that would be stable even without gravity. These calculations show

that optimizing the microemulsion viscosity is a more effective method of increasing the critical velocity than adding

polymer.

ConclusionsA series of surfactant flood experiments in sandpacks without polymer for mobility control were performed at velocities of

0.2, 0.4, and 0.8 ft/day. The surfactant flood at 0.2 ft/day was a stable or nearly stable displacement whereas the floods at 0.4

and 0.8 ft/day were unstable with visually obvious fingers. The average oil cut and the oil recoveries at 1 PV injection

decreased with increasing velocities.

The critical velocity calculated from stability theory for a miscible displacement was optimistic. Surfactant floods are not

miscible. Furthermore, the formation of a microemulsion plays a significant role in the stability of the displacement because

its viscosity is much higher than the aqueous surfactant solution. The most important insight of this study is that the critical

velocity based on the displacement of the microemulsion by the aqueous surfactant solution is in good agreement with the

experimental results. These experiments have provided new insight into how a gravity stable low-tension surfactant

displacement behaves and in particular the importance of the microemulsion phase and its properties, especially its viscosity.

Higher microemulsion viscosity improves the stability of the oil bank displacement. However, it worsens the stability of the

aqueous surfactant phase displacement of the microemulsion phase and thus causes the critical velocity to decrease. Thus, it

is important to measure the microemulsion viscosity and account for its effect on the critical velocity. Furthermore, the

microemulsion viscosity can be optimized to increase the velocity for a stable displacement. The best way to change the

microemulsion viscosity will depend on the particular surfactant formulation, oil and temperature, but in general it is possible

to do so by optimizing the co-solvent or co-surfactant concentration in the formulation. This insight opens up a new pathway

for optimizing surfactant floods without mobility control.

The experimental results presented in this paper and the simulation results presented in our companion paper (Tavassoli et

al., 2013) indicate that it should be possible to design an efficient surfactant flood without any mobility control if thesurfactant solution is injected at a low velocity in horizontal wells at the bottom of the geological zone and the oil captured in

horizontal wells at the top of the zone. This approach is practical only if the vertical permeability of the geological zone is

high. Under favorable reservoir conditions, gravity stable surfactant floods may be attractive alternatives to surfactant-

polymer floods. Some of the worlds largest oil reservoirs are deep, high-temperature, high-permeability, light-oil reservoirs

and thus candidates for gravity stable surfactant floods.

Nomenclature

g = gravitational acceleration constantk = permeability0

rok = endpoint oil relative permeability0

rwk = endpoint water relative permeabilityrok = oil relative permeabilityrwk = water relative permeabilityrsk = surfactant solution relative permeability

rmek = microemulsion relative permeabilityM

0= endpoint mobility ratio

MOB

= oil bank mobility ratio

Mme

= microemulsion mobility ratio

cv = critical interstitial velocity

v = interstitial velocity

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Greek symbols

= dip angleo = oil viscosityw = water viscositys = surfactant solution viscosity

me

= microemulsion viscosityro = oil relative mobilityrw = water relative mobility

rme = microemulsion relative mobilityrtot = total relative mobility

o = oil density

w = water density

s = surfactant solution density

me = microemulsion density

= porosity

AcknowledgmentsThe authors would like to thank the industrial affiliates of the Chemical Enhanced Oil Recovery project at The University of

Texas at Austin for their financial support of this research. We would also like to acknowledge the resources, staff and

undergraduate research assistants of the Center for Petroleum and Geosystems Engineering at The University of Texas at

Austin, and in particular we would like to thank Scott Hyde II, Richard Hernandez, Stephanie Adkins, Gayani P.

Arachchilage, Gayani Kennedy, Do Hoon Kim, and Christopher Britton for helping with the laboratory measurements.

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Large-Hydrophobe Alkoxy Carboxylate Surfactants, SPE 154256 presented at SPE IOR Symposium, Tulsa, OK, 14 -18 April, 2012.Adkins, S., Liyanage, P.J., Arachchilage, G.W., Mudiyanselage, T., Weerasooriya, U., and Pope, G.A. A New Process for Manufacturing

and Stablizing High-Performance EOR Surfactants at Low Cost for High Temperature, High Salinity Oil Reservoirs, SPE 129923,presented at the SPE Improved Recovery Symposium, Tulsa, Oklahoma, 25-28 April, 2010.

Barnes, J. R., Groen, K., On, A., Dubey, S., Reznik, C., Buijse, M.A., and Shepherd, A.G., Controlled Hydrophobe Branching to MatchSurfactant to Crude Oil Composition for Chemical EOR, SPE 154084, presented at SPE IOR Symposium, Tulsa, OK, 14-18 April,

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Cosurfactant-Enhanced Alkaline Flooding,SPERE, Aug. 1994, 217-223.Fayers, F.J. and Sheldon, J.W. The effect of capillary pressure and gravity on two-phase fluid flow in a porous medium,Petrol. Trans.

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Table 1Oil Properties

Temperature (C) 38

Total Acid Number (mg KOH/g oil) 0.15

Density (g/cm3) 0.80 (at 38 C)

Viscosity (cp) 5.4

Table 2Summary of Sandpack Floods

Experiment Number 1 2 3

Temperature (C) 38

Sand Name F95 Ottawa Sand

Length (cm) 24.4

Diameter (cm) 4.80

Pore Volume (ml) 160

Porosity 0.35

Brine Permeability (md) 5500

Initial Salinity (ppm) 30,000

Initial Oil Saturation, Soi(%) 82.89 84.70 83.17

Residual Oil Saturation After waterflood, Sorw(%) 16.16 12.58 14.02

Surfactant Solution

Surfactant Concentration (wt%) 1.0

Viscosity (cp) 0.7

Salinity (ppm) 21,000

Velocity (ft/day) 0.20 0.40 0.80

Results

Oil Recovery (%) 99.74 99.81 94.93

Final Oil Saturation, Sorc 0.0006 0.0003 0.0085

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Table 3Sandpack and White Castle Field Properties

Parameter Sandpack Flood White Castle Pilot

k (md) 5500 1000

0.35 0.31

90 45

o(g/cm3) 0.80 0.88

s(g/cm3

) 1.0 1.0me(g/cm

3) 0.9 0.94

o(cp) 5.4 2.8

w(cp) 0.7 0.64

s(cp) 0.7 0.64

me(cp) 24 10 (estimated)

ko

rw 1.0 1.0

ko

ro 0.93 0.9 (estimated)

krs 1.0 1.0

krme 1.0 1.0

rtot 0.05 0.05

MOB 20 (estimated) 20 (estimated)

v (ft/day) by Eq. 1 1.63 0.30

v (ft/day) by Eq. 2 0.65 0.06

v (ft/day) by Eq. 3 infinite 0.59

v (ft/day) by Eq. 4 0.18 0.02

Actual v (ft/day) 0.2 0.24 (estimated)

Fig. 1Illustration of Four Idealized Flow Regions.

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0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

Pore Volumes

DimensionlessConcentration

Fig. 2Tracer breakthrough data in sandpack.

0

10

20

30

40

5000 10000 15000 20000 25000 30000 35000

Salinity (ppm TDS)

Solubiliza

tionRatio(cc/cc)

Oil

Water

Aqueous Stability = 30,350 ppm

Fig. 3Phase behavior of 0.5 wt% C13-13PO-Sulfate, 0.5 wt% C20-24 IOS, and 2.0 wt% IBA.

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Fig. 4Photographs of surfactant floods in sandpacks at 0.2 ft/D (left), 0.4 ft/D (middle) and 0.8 ft/D (right).

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0%

20%

40%

60%

80%

100%

0.0 0.5 1.0 1.5Pore Volumes

CumulativeOilRecover

ed(%)

OilCut(%)

0%

10%

20%

30%

OilSaturation(%)

Oil Cut

Cumulative Oil

Oil Saturation

Fig. 5Measured oil recovery, oil cut, and oil saturation from surfactant flood at 0.2 ft/day and 38 C.

0%

20%

40%

60%

80%

100%

0.0 0.5 1.0 1.5 2.0Pore Volumes

CumulativeOilRecovered(%)

OilCut(%)

0%

5%

10%

15%

20%

25%

OilSaturation(%)

Oil Cut

Cumulative Oil

Oil Saturation

Fig. 6Measured oil recovery, oil cut, and oil saturation from surfactant flood at 0.4 ft/day and 38 C.

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0%

20%

40%

60%

80%

100%

0.0 0.5 1.0 1.5 2.0Pore Volumes

CumulativeOilRecovered(%)

OilCut(%)

0%

5%

10%

15%

20%

25%

OilSaturation(%)

Oil Cut

Cumulative Oil

Oil Saturation

Fig. 7Measured oil recovery, oil cut, and oil saturation from surfactant flood at 0.8 ft/day and 38 C.

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Water Saturation, Sw

FractionalFlowofWater,fw

Oil Saturation, So

Fractionalflow

ofoil,fo

Fig. 8Fractional flow curves for experiment # 1 at 0.2 ft/D.

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-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Water Saturation, Sw

FractionalFlowofWater,f

w

Oil Saturation, So

Fractionalflow

ofoil,fo

Fig. 9Fractional flow curves for experiment # 2 at 0.4 ft/D.

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Water Saturation, Sw

FractionalFlowofWater,fw

Oil Saturation, So

Fractionalflow

ofoil,fo

Fig. 10Fractional flow curves for experiment # 3 at 0.8 ft/D.

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0. 0

0. 1

0. 2

0. 3

0. 4

0. 5

0. 6

0. 7

0. 8

0. 9

1 . 0

0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 20

Microemulsion Viscosity (cp)

CriticalVelocity(ft/D)

v1

v2

Fig. 11Critical velocity of upper interface (v1) and lower interface (v2) for a fixed aqueous phase viscosity of 0.7 cp.

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Water Saturation, Sw

FractionalFlowofWater,fw

Oil Saturation, So

Fractionalflow

ofoil,fo

Fig. 12Fractional flow curves for optimized microemulsion viscosity of 10 cp at 0.45 ft/D.

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0

1

2

3

4

5

0 4 8 12 16 20 24 28

Aqueous Viscosity (cp)

CriticalVelocity(ft

/D)

v2

Fig. 13Critical velocity of lower interface for a fixed microemulsion viscosity of 24 cp.