Correlation between capillary number and residual water saturation

Correlation between Capillary Number and Residual Water Saturation KHALID

A L - F O S S A I L *,1 AND L Y M A N

L. H A N D Y t

* K F U P M Box 1886, Dhahran 31261, Saudi Arabia and 4(University of Southern California Received October 21, 1988; accepted April 12, 1989

Displacement of a wetting phase by a nonwetting phase is controlled by the viscous as well as the capillary forces. The ratio of viscous forces to that of the capillary is called the capillary number. It is found that the residual water saturation was affected by increasing the viscosity of the displacing phase and by reducing the interfacial tension between oil and water. However, the effect of these two parameters will be observed after certain values of the viscosity and the interfacial tension. These values will be functions of absolute permeability of the core sample. It is expected that, for a higher permeability core sample, the residual water saturation will be lower than that of a lower permeability for the same displacing phase. Correlation between the residual water saturation and the capillary number resulted in two different curves when including viscosity and the interfacial tension effects. A new dimensionless number resulted in a unique correlation with the residual water saturation. © 1990AcademicPress,Inc.

KAp

INTRODUCTION

T h e forces acting in i m m i s c i b l e displacem e n t s are the capillary a n d viscous forces. Red u c i n g the capillary forces o r increasing the viscous forces m a y increase the recovery. T h e capillary forces are r e p r e s e n t e d b y the interfacial t e n s i o n b e t w e e n the i m m i s c i b l e phases, whereas the viscous forces are represented by the p r o d u c t o f the velocity m u l t i p l i e d by the viscosity o f the displacing phase or their e q u i v a l e n t f r o m D a r c y ' s law. T h e ratio o f the viscous to capillary forces is called the capillary n u m b e r . This capillary n u m b e r was c o r r e l a t e d with residual phases i n d i c a t i n g that the higher the capillary n u m ber, the lower the residual phases. H o w e v e r , this effect will n o t be shown until the capillary n u m b e r exceeds a certain value which depends o n the core s a m p l e s ' properties. CAPILLARY NUMBER

Nc - - a L cos O' where K Ae L a

permeability pressure d r o p across the s a m p l e length o f the s a m p l e interfacial tensions b e t w e e n the two samples 0 = c o n t a c t angle ( t a k e n as 180 ° for all cases).

= = = =

T h e capillary n u m b e r in Eq. [1] was m o d ified b y D o m b r o w s k i a n d Brownell ( 2 ) to include the gravity d r a i n a g e a n d the centrifugal force effects. A n o t h e r f o r m o f capillary n u m b e r was used extensively in literature ( 3 - 6 ) which has the form v#

CONCEPT

Nc = - - , ff

A n early study w h i c h relates the residual water s a t u r a t i o n with a capillary n u m b e r was d o n e by Brownell a n d K a t z ( 1 ) which h a d a f o r m e q u i v a l e n t to i To whom all correspondence should be addressed.

[ll

[2]

where v = d a r c y velocity # = viscosity o f the displacing phase a = interfacial tension.

256 0021-9797/90 $3.00 Copyright© 1990by AcademicPress, Inc. All rights of reproductionin any form reserved.

Journalof ColloMand InterfaceScience, Vol. 134,No. 1, January 1990

257

Nc AND Swr CORRELATION

In one of these studies (3), the average viscosity was used instead of the viscosity of the displacing phase. Figure 1 correlates the residual water saturation with capillary number for these studies. As shown, the higher the capillary number, the lower the residual water saturation. However, in most of these studies one variable was varied; either the interfacial tension or the flow rate. Therefore, the main objective of this paper is threefold:

for high tension systems or with the preequilibrated aqueous solution for low tension systems. In both cases, the core is flushed by many pore volumes until the pressure drop across the core stabilizes, and then the permeability can be measured. The displacement includes:

1. Run immiscible displacements using short cores of sandstone sample. The water will be displaced by the oil.

2. Displacement of the brine ( 1% NaC1) by different oils having different viscosities at a certain flow rate in high tension systems.

2. Vary the flow rate, the viscosity of the oil phase, and the interfacial tension.

3. Displacement of the brine by the equilibrated oil at certain flow rate in low tension systems.

3. Correlate the residual water saturation with the capillary number.

1. Displacement of the brine ( 1% NaC1) by a known viscosity oil at different flow rates in high tension systems.

EXPERIMENTAL DESIGN

4. Displacement of the brine by preequilibrated oil using different flow rates in low tension systems.

Core samples used in this study ranged from 10 to 16 cm long and 2.54 cm in diameter of Berea sandstone. The core is mounted inside a Hassler sleeve type core holder with an overburden pressure of 400 psi. After the porosity is measured (7), the core is evacuated for a few hours, then saturated either with the brine

The influent fractions were collected in graduate tubes and the residual saturations were established by flowing about 30 pore volumes of oil or preequilibrated oil through the core. The viscous oils were obtained by mixing Chevron bolybutene with either kerosene or

5O

•

AMAEFULE 8, H A N D Y ~ ~ ~ L C H E R

# HARBERT

40 a_

30

E

~PREY

20

m~ lo

io-7

I(%5

i~ s

l o -1

CAPILLARY NUMBER, VAI O" FIG. l. Residual wetting phase versus capillary number. Journal of Colloid and Interface Science, Vol. 134,No. 1, January 1990

258

AL-FOSSAIL AND HANDY

m i n e r a l oil no. 9. Properties o f these oils are sho wn in Tab l e I. T h e low te n s i o n systems were o b t a i n e d by using Petrostep 450 with different salinities. T o reduce the effect o f core sample properties on the residual water saturation, the core sample was used several times. After each disp l a c e m e n t , the core s a m p l e was cleaned using s o m e isopropyl al c o h o l followed by distilled water. T h e n it was dried in a v a c u u m o v e n for several hours. C o n s t a m e t r i c H P L C I p u m p s were used in this study. Each p u m p is a single m o d u l e u n i t a n d gives a c o n s t a n t flow u n d e r

all pressure up to 5000 psig. T h e flow rate was varied f r o m 2.5 to 10 c c / m i n w h i c h was the m a x i m u m flow rate attainable by the p u m p s . T h e viscosity o f the oil was varied f r o m 1.38 to 143 cp while the interfacial tension between brine a n d kerosene was r e d u c e d to 0.01 an d 0.04 d y n / c m for b r i n e a n d m i n e r a l oil no. 9, respectively. O n e e x p e r i m e n t was repeated three t i m e s o n o n e o f the cores for kerosene displacing b r i n e to see the effect o f cleansing process o n the d i sp l acem en t . It was f o u n d that the residual w at er saturation was the same in all the runs.

TABLE I Physical Properties of Cores, Fluid Samples, and Displacement Data Run no.

ks md

L cm

~ %

t~

#o

cp

cp

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

605 605 300 405 385 832 1050 1067 1067 1067 1067 1100 840 840 835 875 1038 800 1038 1100 1038 930 892 870 685 840 444 844 920 625 824 840

15.3 15.3 15.4 12.1 15.3 15.2 15.4 15.4 15.4 15.4 15.4 15.4 10.2 10.2 15.2 15.35 15.4 15.3 15.4 15.4 15.4 15.4 15.5 14.7 15.2 15.4 15.1 15.3 15.2 15.2 15.5 15.2

22 22 20 22 22 22 22 22 22 22 22 22 22 22 21 22 22 21 22 22 21 22 22 22 22 22 21 22 22 22 22 22

1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.08 1.1 1.08 1.01 1.1 1.01 1.001 1.001

1.38 1.38 1.38 1.38 1.38 1.38 1.38 22.3 22.3 22.3 22.3 22.3 22.3 22.3 35.0 35.0 35.0 58.5 58.5 58.5 69.15 69.15 143 5.2 1.38 1.38 1.38 22.3 22.3 22.3 58.5 69.15

Journal of Colloid and Interface Science, Vol. 134, No. 1, January 1990

#~ g/cc

0.997 0.997 0.997 0.997 0.997 0.997 0.997 0.997 0.997 0.997 0.997 0.997 0.997 0.997 0.997 0.997 0.997 0.997 0.997 0.997 0.997 0.997 0.997 0.997 0.999 0.999 0.997 1.007 1.003 1.008 1.007 1.007

#o g/cc

0.7979 0.7979 0.7979 0.7979 0.7979 0.7979 0.7979 0.842 0.842 0.842 0.842 0.842 0.842 0.842 0.8428 0.8428 0.8428 0.844 0.8440 0.8440 0.8450 0.8450 0.8550 0.820 0.798 0.798 0.798 0.842 0.842 0.842 0.8428 0.8440

ao~ dyn/cm

qo cc/min

AP psia

S~ %

25.6 25.6 25.6 25.6 25.6 25.6 25.6 45.1 45.1 45.1 45.1 45.1 45.1 45.1 33.23 33.23 33.23 34.18 34.18 34.18 37.6 37.6 34.9 33.4 0.057 0.011 0.011 0.032 0.052 0.04 0.016 0.02

3.5 5.2 10.0 10.0 7.5 3,4 3.4 2.5 5.0 7.0 9.3 3.4 4.0 8.0 5.0 3.4 3.3 3.3 3.4 3.4 3.4 2.9 2.08 3.3 3.2 3.4 4.1 3.3 3.4 3.4 3.2 3.25

8 12.7 35.0 28.5 21.3 7.2 5.6 67.0 133.0 193 218 83 67 125 208 119 120 247 215 198 253 203 283 16.0 7.0 6.8 17.0 95 87 110 234 319

33.0 33.0 33.0 33.0 33.0 31.0 31.0 22.4 21.5 21.0 21.0 21.0 21.2 17.2 18.0 20.6 20.3 19.0 18.0 19.5 15.0 16.6 12.5 29.0 26.3 20.3 24.5 18.6 19.7 20.0 11.5 9.4

259

Nc A N D Swr C O R R E L A T I O N

KEROSENE AND BRINE o •

HIGH TENSION SYSTEMS LOW TENSION SYSTEMS

50 40 0

- - 0

30

O

0

20 10

I 1

%

I 2

I 3

I 4

I 5

1 6

FLOW

I 7

RATE,

I 8

I 9

I

10

CC/min

FIG. 2. Effect of flow rate on the water saturation in high and low tension kerosene-brine systems.

E X P E R I M E N T A L R E S U L T A N D DISCUSSION

The effect of flow rate was carried out using kerosene with a flow rate increased from 2.5 to 10 c c / m i n with no considerable changes in the residual water saturation for both high and low tension systems (see Fig. 2). Viscous oils could not be used to investigate the effect of flow rate due to the resultant pressure drop

across the core which exceeded the overburden pressure. However, the viscosity of the displacing phase (oil viscosity) decreases the residual water saturation as shown in Fig. 3. In this figure, the residual water saturation was reduced from 32% to about 12%, A similar result was obtained by Ehrlich and Crane (8) from displacements of a brine (2% NaC1) by one of several oils. The displacements were

---¢z 50-

o

o

20

8

10

I 10

I

I

I t ILl[

I

I

I

I I Illl

10 1 OIL

I 10 2

VISCOSITY

I

I

11111 10 3

, cp

FIG. 3. Viscosity effect on the residual water saturation (viscosity ranges: 1.38-143 ). Journal of Colloid and Interface Science, Vol.

134, N o . 1, J a n u a r y 1990

260

AL-FOSSAIL AND H A N D Y

performed using 2 in. diameter, 28 in. long Berea sandstone core samples. The reduction in water saturation is due to the pressure exerted by the viscous oil, which allows the oil to penetrate the smaller pores. Also the water (wetting phase) is considered to be continuous which can be determined by the capillary pressure saturation (9); a lower residual water saturation requires more pressure to be obtained. The reduction in the residual water saturation was due to the viscous forces rather than to wettability alteration, which can be seen clearly by comparing run n u m b e r 24 in Table I with run n u m b e r 13 since the viscosity of run 24 was obtained by adding kerosene to mineral oil no. 9. This viscosity reduction resulted in lower viscous forces and consequently in higher residual water saturation. Also the effect of viscous forces can be seen by comparing runs 13 and 14 when the viscous forces were varied by changing only the flow rate. Reducing the intert~acial tension results in a lower residual water saturation; it was reduced from 32 to 16% for a reduction in the

interfacial tension from 26 to 0.011 d y n / c m in kerosene-brine systems. Also it was reduced from 22 to 17% for a reduction in the interfacial tension from 45 to .04 d y n / c m in mineral oil no. 9-brine systems (see Fig. 4). It was observed that the absolute permeability affects the residual water saturation especially if it is reduced to 50% of its original value and the effect will be more pronounced with the viscous oil. Therefore, the absolute permeability and the pressure drop across the core should be included in the capillary number to have the form Ks2xp Lo-ow '

N~-

[3]

where Ks = absolute permeability of the core sample Ap = pressure drop across the core sample L = length of the core sample aow = interfacial tension between the oleic phase and the aqueous phase.

30

o o

20

(/~

t0 0

KEROSENE

D MINERAL

0

iiii 2 10

I i

I

AND OIL

IIIIII 1 10

BRINE

NO. 9

I

i

i

SYSTEMS

AND

BRINE

IIllll 0 10

i i

SYSTEMS

i

|ltlll -1

i

i

10

INTERFACIAL TENSION, DYNE /

i

Iiiiii -2 t0

t

i

I -3 10

em

FiG. 4. Interfacial tension effect on the residual water saturation for kerosene and mineral oil no. 9-brine systems. Journal of Colloid and Interface Science, Vol. 134, No. 1, January 1990

Nc AND Swr CORRELATION

261

40' E] INTERFACIAL TENSION EFFECT O VISCOSITY EFFECT

30

0

20

8 0 o

oo

I

1100-7

10-6

i

10- 5

10-4

10-3

10-2

10 -1

10 0

kAP Nc = L o-

FIG. 5. Residual water saturation against the capillarynumber.

Using the data in Table I with this form yields two curves as shown in Fig. 5 where the residual water saturation was plotted versus the capillary number. One curve represents the effect of the interfacial tension only, while the other curve shows the effect of increasing the viscosity of the displacing phase. Both curves show that the higher the capillary number, the

lower the residual water saturation. However, the reduction in residual water saturation due to the viscosity effect was more pronounced than that due to the interfacial tension effect. But the objective is to have one curve rather than two; therefore, the capillary number used in this study should be modified to fit our need. One approach to modifying the capillary

30

20

~

O

Ca0 10

L

0166

165

I

164.

I

Id 3

I

162 VAJO ~10 .4 N o = -~--~w ( pJw )

I

101

I

I(~0

FIG. 6. Residualwater saturation againstthe dimensionlessgroup (after A. Abrams, (10)). Journal of Colloid and Interface Science, Vol.134,No. 1,January1990

262

AL-FOSSAIL A N D H A N D Y

3(

0

0

20

0~

o D.

0

0

10

0

I 16 4

16 5

I t~ 3

I 1(~2 A.IO

0"2

NC. ( -~--~- - "-'~-~- )

I 10-1

t6 °

.65

FIG. 7. Residual water saturation as correlated with the new dimensionless n u m b e r .

n u m b e r was done by correlating the data with A b r a m s ' dimensionless group (10) which has the forms

N~'(#°]" \#w/ "

[4]

Several values of n were used and all the correlations yield two curves. Figure 6 correlates the data of this study for n = .4 as suggested by Abrams. This approach is good only if the viscosity ratios for low tension systems are small such as brine-kerosene systems. Therefore, the viscosity ratio as well as the ratio of the interfacial for high tension systems to that for low tension systems should be included with the capillary n u m b e r raised to a certain power " n " to have the form (N°°dr2]

n,

[5]

al = interfacial tension value for high tension system a2 = interfacial tension value for low tension system. Several values of n (n less than 1.0) were used. The best fit is shown in Fig. 7 for n = 0.65. APPENDIX:

A core cross-sectional area, cm 2 Ks= absolute permeability of the core ~_

Z N~= qo = Swr = Ap = flow

where Nc = capillary n u m b e r #o/#w = viscosity ratio of oil/water Journal of Colloid and Interface Science, Vol. 134, No. 1, January 1990

NOMENCLATURE

O-1

sample, m d length of the core sample, cm capillary n u m b e r oil flow rate, cm 3 / min residual water saturation pressure drop across core sample at irreducible water saturation, psi interfacial tension between the oleic phase and the aqueous phase, dyn/cm interfacial tension value for high tension system

Nc AND Swr CORRELATION 0" 2 =

Uo = Uw = uo/Uw = Po = pw = q~ =

interfacial tension value for l o w tension system oil viscosity, cp water viscosity, cp viscosity ratio o f o i l / w a t e r oil density, g / c c water density, g / c c porosity, d i m e n s i o n l e s s REFERENCES

Brownell, L. E., and Katz, D. L., Chem. Eng. Prog. 43, 601 (1947).

263

2. Dombrowski, H. S., and Brownell, L. E., Ind. Eng. Chem. 46, 1207 (1954). 3. Harbert, L. W., SPE paper no. 12171, 1983. 4. Fulcher, R. A., Ertekin, T., and Stahl, C. D., SPE paper no. 12170, 1983. 5. Amaefule, J., and Handy, L., SPE J. 376 (1982). 6. Gupta, S. P., and Trushenski, S. P., SPEJ. 116 (1979). 7. A1-Fossail, K., Ph.D. dissertation, 1986. 8. Ehrlich, R., and Crane, F. E., S P E J . 221 (1969). 9. Shah, D. O., and Schechter, R. S., "Improved Oil Recovery by Surfactant and Polymer Flooding," p. 55. Academic Press, New York, 1977. 10. Abrams, A., S P E J . 437 (1975).

Journal of Colloid and Interface Science, Vol. 134,No. 1,January 1990