SPE 99763

Effect of Oil Viscosity on Heavy-Oil/Water Relative Permeability Curves

J. Wang, SPE, M. Dong, SPE, and K. Asghari, SPE, U. of Regina

Copyright 2006, Society of Petroleum Engineers

permeability is independent of fluid viscosities may be
This paper was prepared for presentation at the 2006 SPE/DOE Symposium on Improved Oil relatively appropriate for the systems of low to medium oil
Recovery held in Tulsa, Oklahoma, U.S.A., 22–26 April 2006.
viscosities. However, for heavy oil-water systems, to this
This paper was selected for presentation by an SPE Program Committee following review of
information contained in an abstract submitted by the author(s). Contents of the paper, as
point, there is no sound experimental evidence to support this
presented, have not been reviewed by the Society of Petroleum Engineers and are subject to assumption.
correction by the author(s). The material, as presented, does not necessarily reflect any
position of the Society of Petroleum Engineers, its officers, or members. Papers presented at The effect of fluid viscosity on relative permeability curves
SPE meetings are subject to publication review by Editorial Committees of the Society of
Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper
has been investigated extensively since the work of Leverett.1
for commercial purposes without the written consent of the Society of Petroleum Engineers is Dong and Dullien2 gave a review of the effect of viscosity
prohibited. Permission to reproduce in print is restricted to an abstract of not more than
300 words; illustrations may not be copied. The abstract must contain conspicuous ratio on two-phase relative permeabilities. Generally, there are
acknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O.
Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435.
two different observations reported in the literature. One is
that fluid viscosity has no effect on relative permeabilities.3–5
Abstract The other one is that the oil relative permeability is
For heavy oil reservoirs, the oil viscosity usually varies anomalously high at low water saturation for low permeability
dramatically during production processes, such as thermal media due to the lubricating effect of the moving water film,6,7
process or solvent injection. This paper presents an and that oil permeability shows an increasing trend with
investigation of the effect of oil viscosity on relative increasing oil/water viscosity ratio. So far, most of the
permeability curves for heavy oil-water systems. Unsteady- research on the effect of viscosity on relative permeability
state displacement tests were conducted in sandpacks under a curves has involved only a low range of oil viscosities.
typical injection flow rate in a heavy oil recovery process. A Dullien8 pointed out that, if one of the fluids is very viscous,
series of crude oils with a wide range of viscosities were used the viscosity ratio is evidently a very important parameter.
in the measurements. Large pore volumes of water were The study of temperature effect on relative permeability
injected to minimize the errors caused by the extrapolation of often involves the viscosity effect. Lo and Mungan9 measured
the recovery data. History matching was used to obtain the oil-water relative permeabilities using the steady-state
relative permeability curves, in which capillary pressure was technique for both oil-wet and water-wet core samples at room
included. It was found that, for the same injection flow rate, temperature and elevated temperatures. Their results showed
heavy oil-water relative permeability curves systematically that, with the increase in temperature, residual oil saturation
shifted with oil viscosity. With increasing oil viscosity, the decreased, irreducible water saturation increased, and oil
residual oil saturation increased and the oil and water relative relative permeability increased. They attributed the change in
permeabilities decreased at the higher water saturation range. oil relative permeability to the variation of viscosity and
Irreducible water saturation tended to decrease with increasing viscosity ratio.
oil viscosity. Micromodel experiments were conducted to The variation of residual oil saturation with increasing oil
visually investigate the difference in the flow behaviour viscosity also reveals the influence of fluid viscosity on
between heavy oil-water and light oil-water systems. relative permeabilities. Abrams10 conducted waterflood tests
Interacting capillary bundle models were used to analyze the on sandstone and limestone core samples, and his results
impact of oil viscosity on the residual oil saturation. This work showed that the viscosity ratio exerted an influence on the
aids in the laboratory measurement and determination of the residual oil saturation, which is larger for a higher oil/water
representative relative permeability curves for heavy oil-water viscosity ratio (μo/μw) flood. By using a two-layer glass
systems, as well as in the proper use of relative permeability micromodel, Tzimas et al.11 observed that the viscosity ratio
curves in reservoir simulation for heavy oil development. had a great influence on the residual oil saturation for a wide
range of capillary numbers. For the same capillary number, the
Introduction greater the oil/water viscosity ratio, the larger the residual oil
Heavy oil development is becoming increasingly important saturation.
due to the continuous decline in conventional oil production. The objective of this study was to investigate the viscosity
During improved heavy oil production processes, including effect on heavy oil-water relative permeability curves.
both thermal and solvent processes, the oil phase viscosity Unsteady-state tests were carried out with sandpacks. In order
usually varies because of temperature increase or dissolving of to minimize the error caused by the extrapolation of recovery
solvent in the oil. The common concept that the relative data, as discussed by Maini et al.,12 experiments were
terminated at very large pore volumes of water injection.
2 SPE 99763

History matching was used to calculate the relative S w = S wi at t = 0 (6)

permeability curves with considering capillary pressure.

Calculation of relative permeability curves by history S w = 1 − S or at x = 0 and t ≥ 0 (7)

matching
From the recorded production and pressure differential data of where Swi is the initial water saturation and Sor is the residual
an unsteady-state displacement test, relative permeability oil saturation.
curves can be obtained by either explicit or implicit The following relative permeability functions are usually
calculation. The JBN (Johnson, Bossler, and Naumann) used in the simulation16–18:
technique,13 and its modified form developed by Jones and
Roszelle,14 are the most widely used explicit methods. Eo
⎛ 1 − S or − S w ⎞
However, these methods are based on the assumption that the K ro = K ro ( S wi )⎜⎜ ⎟⎟ (8)
effect of capillary pressure is negligible. Based on the scaling
criterion proposed by Rapoport and Leas,15 a high
⎝ 1 − S wi − S or ⎠
displacement velocity, usually 10 to 100 times the field value,
Ew
is commonly used to eliminate the effect of capillary pressure. ⎛ S w − S wi ⎞
However, the high injection rate may result in a ratio of K rw = K rw ( S or )⎜⎜ ⎟⎟ (9)
viscous to capillary force which is much higher than the ⎝ 1 − S wi − S or ⎠
typical value in the oil reservoir. The fluid distributions and
the residual oil saturation may not be representative of the where Kro(Swi) is the oil relative permeability at Swi; Krw(Sor) is
actual reservoir conditions. Therefore, the preferable unsteady- the water relative permeability at Sor; Eo is the oil relative-
state test method is to conduct the displacement at an injection permeability equation exponent; and Ew is the water relative-
velocity which reflects the field flow rate, taking account of permeability equation exponent.
the capillarity effect. Numerical calculation (implicit method) Exponents Eo and Ew are adjustable parameters in history
is usually used in this case. It is often called the history matching. In order to obtain a better matching result, a cubic
matching technique, in which the experimental production and spline function17 was used for the oil phase in this study, and
pressure drop data during the displacement process are Krw(Sor) was also taken as an adjustable parameter. The
matched by adjusting the relative permeability parameters.16–18 capillary pressure curve was measured independently in our
study.The IMPES (Implicit Pressure-Explicit Saturation)
For a linear, horizontal and one-dimensional two-phase method19 was used to solve the flow equations.
flow displacement in a porous sample, the following equations
are used: Experimental

∂ ⎛ KK ro ∂Po ⎞ ∂ Porous Media and Test Fluids

⎜ ⎟ = (ΦS o )
∂x ⎜⎝ μ o ∂x ⎟⎠ ∂t
(1) The displacement tests were conducted using sandpacks
measuring 14.2 cm in length and 4.25 cm in diameter. Both
ends of the coreholder were equipped with flow distributors on
which 200-mesh stainless steel screens were spot-welded to
∂ ⎛ KK rw ∂Pw ⎞ ∂
⎜ ⎟ = (ΦS w ) prevent fine sand flow out and to provide more even
∂x ⎜⎝ μ w ∂x ⎟⎠ ∂t
(2)
distribution of injected fluid. Pure quartz Ottawa sand, of 60 to
100 meshe size distribution, was wet-packed in the coreholder.
For each test, fresh sand was packed to ensure the same
Pc = Po − Pw (3) wettability conditions. The porosity of the sandpacks was
approximately 35% and the absolute permeability was
So + S w = 1 (4) approximately 7.0 μm2.
The capillary pressure curve of the air/water system was
measured using the porous-plate method. The capillary
qt = q o + q w (5) pressure curve for the oil/water system was obtained by
considering the difference in the interfacial tensions between
where K and φ are the absolute permeability and porosity of the air/water and oil/water systems, assuming that both
the core sample, respectively; Kro and Krw are the relative systems are strongly water-wet (contact angles are the same
permeability to oil and water phase, respectively; Po and Pw and nearly zero). 16
are oil and water phase pressure; μo and μw are oil and water Four stock tank oils with viscosities ranging from 1,000 to
viscosity; x is the linear distance; Pc is capillary pressure; So 13,500 mPa.s were used in this study. Two additional oil
and Sw are oil and water phase saturations; qo and qw are the samples for the relative permeability tests were obtained by
flow rate of oil and water phase at the outlet face; and qt is the diluting two of the above stock tank oils with kerosene. Oil
total injection flow rate. viscosities were measured using the Brookfield DV-II+
The initial and boundary conditions are: Viscometer. The water phase for all of the tests was deionized
water with a viscosity of 1.0 mPa.s at room temperature.
SPE 99763 3

Procedure average water saturation to infinite throughput (1/Qi = 0) will

We followed the procedure suggested by Batychy and give the water saturation Swavg = 1−Sor. Table 1 lists the ranges
McCaffery16 in conducting the displacement tests. The of throughput for extrapolating residual oil saturations, the
absolute permeability was first measured by injecting single input and the estimated residual oil saturations and the
water phase through a 100% water-saturated sandpack. Then, corresponding errors. The required throughput for
initial water saturation was established by injecting oil until extrapolating residual oil saturation increases with increasing
water was no longer produced, which was followed by the oil viscosity. For the system with oil viscosity of 10, 000
determination of effective oil permeability at irreducible water mPa.s, the estimated residual oil saturations are acceptable
saturation. After this, the relative permeability test was using the production data of no more than 50PV of water
conducted at a constant water injection flow rate. For the injection.
purpose of comparison, the flow rates were the same for all the
experiments, at approximately 10 ml/h. After waterflooding, Results and Discussion
the average oil saturation in each sandpack was measured Fig. 2 shows the measured air/water capillary pressure curves
using a Dean Stark glass distillation assembly, which was of the sandpack. Considering the difference in the interfacial
applied to check the recorded production data. tension between the oil/water and the air/water systems, we
It is a great challenge to obtain precise residual oil used a factor of 0.35 to convert the measured capillary
saturation in a waterflooding test, especially for heavy oil pressure curve to the oil/water system. For the sake of
systems. For conventional oils, it is an accepted practice to simplicity, this conversion factor is used for all the oil/water
determine the residual oil saturation by the extrapolation systems in our simulation.
method, as shown by Jones and Roszelle.14 However, for Six oils were used to investigate the effect of oil viscosity
heavy oils, large pore volumes of throughput are required in on relative permeability curves. The viscosities of these oils,
order to obtain a reliable extrapolation result. It is usually properties of the sandpacks, and main results are summarized
believed that the throughput would be too large (e.g., in Table 2. The cumulative injected pore volumes ranged from
thousands of pore volumes) to reach in an experiment. This 36 to 58, and each test had a water cut greater than 99.9%
concept is based on the assumption that relative permeability when terminated. Residual oil saturations were estimated by
curves are independent of the viscosity ratio. However, many extrapolating oil production curves as discussed in the
experimental results reported in the literature show that previous section. Although water phase relative permeability
residual oil saturation increases with increasing oil/water was measured at the end of each test, it was not the water
viscosity ratio. The required injection pore volumes would be relative permeability at residual oil saturation, Krw(Sor).
much lower than usually expected. In the following section, Therefore, it was not used as the end point of the water relative
the cumulative pore volumes required for extrapolation of permeability curve. The Krw(Sor) values listed in Table 2 were
residual oil saturation were investigated through simulation. obtained by history matching the measured data.
In Tests 2 to 6 (Table 2), it was observed that the oil
Pore volumes required for extrapolation of residual oil permeability at irreducible water saturation, Kro(Swi), was
saturation greater than the absolute permeability of the sandpack, which
In this section, Jones and Roszell’s method14 was used to was measured by flowing single water phase. This is attributed
extrapolate the residual oil saturation from the simulated oil to the lubricating effect of the water film as analyzed by
production data with a given set of relative permeability Yuster20 and experimentally observed by Templeton and
curves. The required pore volumes of injection to reach the Rushing21 and by Odeh.6 The measured Kro(Swi) value (see
assumed residual oil saturation in the given relative Table 2) increases with increasing oil viscosity, which is in
permeability curves were investigated for the systems with agreement with Odeh’s experimental results.6
different oil viscosities. The following parameters were used The history match of oil production and pressure drop and
in simulation: the generated relative permeability curves for Tests 1 and 3 are
The dimensions of the core sample used in the simulation shown in Figs. 3 and 4, respectively. Fig. 5 shows a
study were the same as in our experimental tests. The comparison of the relative permeability curves for all six
permeability of the sample was assumed to be 1.0μm2 and the oil/water systems.
porosity was assumed to be 35%. Relative permeability curves These figures show that oil viscosity does have an
are given in Equations (8) and (9) with the exponents for the influence on oil-water relative permeability curves. The
oil and water being assumed as 2 and 4, respectively. (In the general trend is that, with increasing oil viscosity, residual oil
process of actual production history matching to derive saturation increases while irreducible water saturation
relative permeability curves, these two exponents are decreases. Both oil and water relative permeability curves
adjustable parameters.) The same initial water saturation (Swi = shift to lower values with increasing oil viscosity.
10%) and water relative permeability curve were used for all In order to have a better understanding of the governing
of the systems. The water viscosity was 1.0 mPa.s, while the mechanism of the viscosity effect, a micromodel displacement
oil viscosity varied from 10 to 10,000 mPa.s, and the residual was conducted to visualize the residual oil distribution after
oil saturation varied from 20% to 50%. waterflooding. The micromodel consists only of doublets and
Fig. 1 shows the simulated average water saturation (Swavg) triplets. Fig. 6 shows the result for a heavy oil system with
vs. the reciprocal of injected pore volumes (1/Qi) for the viscosity of 1,088 mPa.s. The photograph shows that the
systems with different oil/water viscosity ratios and different residual oil exists mainly in larger pores and that the oil
residual oil saturation (Sor) values. Extrapolating the simulated ganglion is relative large, usually across several pores. For
4 SPE 99763

comparison, another test was conducted on the same model residual oil saturation could be demonstrated. Trapping
using kerosene with a viscosity of 1.59 mPa.s. Because both occurred when the pressure differential over an oil slug was
the kerosene and water used in our test are transparent, we not sufficiently high to push it to flow into the smaller
could not obtain a clear full-view picture of the residual oil. capillary on its downstream side (Fig. 9). A model with six
However, under the microscope it was clearly observed that different tube radii (ranging from 20 μm to 35μm) was used to
the residual oil in this case was much less than in the simulate the residual oil saturation at the end of the imbibition
compared heavy oil system and that it existed mainly in the process for oils with different viscosities. The model length of
form of small oil drops. Fig. 7 shows microscopic images from 10 cm was divided into 25 equal segments. The oil/water
four different sections of the model. interfacial tension was 40 mN/m, and the contact angle was
For strongly water-wet systems, like the sandpacks in the assumed to be zero. The water injection flow rate was 0.0001
experiments of this study, the displacing water phase ml/s for this model. The viscosity of the water phase was 1.0
preferentially invades the small pores or narrow flow channels. mPa.s, while that of the oil phase ranged from 500 to 15,000
The higher the oil viscosity, the more serious the viscous mPa.s. Fig. 10 shows the simulated residual oil saturation as a
fingering and the more oil will be left in larger pores in the function of oil viscosity. The model-simulated result of the oil
process of waterflooding. On the other hand, larger oil viscosity effect on residual oil saturation is in good agreement
ganglions have more potential to plug larger throats. Because with our experimental results (Fig. 8). Although the model is a
the permeability of a porous medium is mainly determined by simplified porous medium, this agreement between the
the larger flow channels, the relative permeabilities to oil and simulated and the experimental results suggests that oil
water phases for more viscous oil systems tend to be lower at viscosity has an influence on residual oil saturation, providing
higher water saturation ranges. other conditions are the same.
The variation of irreducible water saturation with
increasing oil viscosity showed the same trend as seen in the Conclusion
results of Lo and Mungan.9 The higher oil/water viscosity ratio The effect of oil viscosity on oil/water relative permeability
makes the displacement more piston-like during the curves was investigated for heavy oil-water systems with oil
establishment of initial water saturation (Swi), which makes it viscosity ranging from 430 to 13,550 mPa.s. It was found that,
easier to arrive at low water saturation. When a constant flow under the same injection flow rate and with the same water
rate is used in this process, as in the experiments in this study, phase, relative permeabilities were a function of oil viscosity
the pressure gradient increases with increasing oil saturation in the oil viscosity range studied. The main results are
because oil viscosity is greater than that of water. The higher summarized as follows:
the oil viscosity, the greater the pressure gradient will be at the 1. Both the oil and water relative permeability curves shifted
last stage of Swi establishment. Therefore, the irreducible water to lower values with the increase in oil viscosity and the
saturation tends to decrease with increasing oil viscosity. difference was larger with increasing water saturation.
Fig. 8 shows changes in measured residual oil saturation 2. The residual oil saturation increased linearly with the log
(Sor) with respect to the oil viscosity which is plotted in log value of oil viscosity, while the irreducible water saturation
scale. The plot shows that residual oil saturation increases tended to decrease with increasing oil viscosity.
linearly with the log value of oil viscosity. Although this linear 3. For heavy oil systems, the oil permeability at irreducible
relationship needs to be verified by conducting more tests, the water saturation may be greater than the single-phase
appreciable increase of residual oil saturation with increasing permeability because of the lubricating effect of the water
oil viscosity strongly suggests that oil-water relative film.
permeability curves are not independent of oil viscosity.
Numerous studies have related the residual oil saturation to References
capillary number, a dimensionless parameter of the ratio of 1. Leverett, M.C.: “Flow of Oil-Water Mixtures through
viscous force to capillary force. Several researchers have also Unconsolidated Sands,” Trans., AIME (1939), 132, 149.
noted the effect of viscosity ratio on residual oil. Abrams10 2. Dong, M. and Dullien F.A.L.: “Porous Media Flows,” Multiphase
Flow Handbook, Crowe, C.T. (ed.), CRC Press, Taylor & Francis
provided experimental evidence of the influence of viscosity
Group, Boca Raton (2006) Chap. 10, 31–33.
ratio on the residual oil saturation and included the viscosity 3. Geffen, T.M., Owen, W.W., Parrish, D.R., and Morse, R.A.:
ratio in a dimensionless group, with which the residual oil “Experimental Investigation of Factors Affecting Laboratory
saturation can be correlated. Tzimas et al.11 and Vizika et al.22 Relative Permeability Measurements,” Trans., AIME (1951),
studied, both experimentally and theoretically, the important 192, 99–110.
role of viscosity ratio during forced imbibition in porous 4. Richardson, J.G.: “Calculation of Waterflood Recovery from
media. All the above research indicates that residual oil Steady-State Relative Permeability Data,” Trans., AIME (1957),
saturation increases with increasing oil viscosity. 210, 373–375.
In water-wet porous media, part of the oil in bigger pores 5. Sandberg, C.R., Gournay, L.S. and Sippel, R.F.: “The Effect of
Fluid-Flow Rate and Viscosity on Laboratory Determinations of
may be bypassed by water flowing through narrower channels
Oil-Water Relative Permeability,” Trans., AIME (1958), 213,
during the waterflood. On the basis of the interacting capillary 36–43.
bundle model proposed by Dong et al.,23–25 a serial type of 6. Odeh, A.S.: “Effect of Viscosity Ratio on Relative Permeability,”
interacting capillary bundle model26 was developed. In this Trans., AIME (1959), 216, 346–352.
model, capillary radii varied along their length and pressure
equilibration among capillaries was stipulated. With the
bypass trapping mechanism, the effect of oil viscosity on
 SPE 99763 5

7. Danis, M. and Jacquin, C.: “Influence du contraste de viscosité 18. MacMillan, D.J.: “Automatic History Matching of Laboratory
sur les perméabilltés relatives lors du drainage: Experimentation Corefloods to Obtain Relative-Permeability Curves,” SPE
et modélisation,” Rev. dl’IFT (1983) 38. Reservoir Engineering (February 1987) 85–91.
8. Porous Media: Fluid Transport and Pore Structure, second 19. Petroleum Reservoir Simulation, Aziz, K. and Settari, A.,
edition, Dullien, F.A.L., Academic Press, San Diego (1992) 355. Blitzprint Ltd., Calgary (2002) 135–137.
9. Lo, H.Y. and Mungan, N.: “Effect of Temperature on Water-Oil 20. Yuster, S. T.: “Theoretical Considerations of Multiphase Flow in
Relative Permeabilities in Oil-Wet and Water-Wet Systems,” Idealized Capillary Systems,” Proc., Third World Pet. Cong., The
paper SPE 4505 presented at 1973 SPE Annual Meeting, Las Hague (1951) Section II, 437–445.
Vegas, 30 September–3 October. 21. Templeton, C.C. and Rushing, Jr., S.S.: “Oil-Water
10. Abrams: “The Influence of Fluid Viscosity, Interfacial Tension, Displacements in Microscopic Capillaries,” Trans., AIME
and Flow Velocity on Residual Oil Saturation Left by (1956), 207, 211–214.
Waterflood,” SPEJ (October 1975) 437–447. 22. Vizika, O., Avraam, D.G., and Payatakes, A.C.: “On the Role of
11. Tzimas, G.C., Matsuura, T., Avraam, D.G., Van Der Brugghen, the Viscosity Ratio during Low-Capillary-Number Forced
W., Constantinides, G.N., and Payatakes, A.C.: “The Combined Imbibition in Porous Media,” J. Colloid Interface Sci. (1994),
Effect of the Viscosity Ratio and the Wettability during Forced 165, 386–401.
Imbibition through Nonplanar Porous Media,” J. Colloid 23. Dong, M., Dullien, F. A. L., and Zhou. J.: “Characterization of
Interface Sci. (1997), 189, 27–36. Waterflood Saturation Profile Histories by the ‘Complete’
12. Maini, B.B. and Okazawa, T.: “Effect of Temperature on Heavy Capillary Number,” Transport in Porous Media (1998), 31, 213–
Oil-Water Relative Permeability of Sand,” J. Can. Pet. Tech. 237.
(May–June 1987) 33–41. 24. Dong, M., Dullien, F. A. L., Dai, L., and Li, D.: “Immiscible
13. Johnson, E.F., Bossler, D.P., and Naumann, V.O.: “Calculation of Displacement in the Interacting Capillary Bundle Model, Part I.
Relative Permeability From Displacement Experiments,” Trans., Development of Interacting Capillary Bundle Model,” Transport
AIME (1959), 216, 370–372. in Porous media (2005), 59, 1–18.
14. Jones, S.C., and Roszelle, W.O.: “Graphical Techniques for 25. Dong, M., Dullien, F. A. L., Dai, L., and Li, D.: “Immiscible
Determining Relative Permeability from Displacement Displacement in the Interacting Capillary Bundle Model, Part II.
Experiments,” JPT (May 1978) 807–817. Applications of Model and Comparison of Interacting and Non-
15. Rapoport, L.A. and Leas, W.J.: “Properties of Linear Interacting Capillary Bundle Models,” Transport in Porous
Waterfloods,” Trans., AIME (1953), 198, 139–148. Media (2005), in press.
16. Batycky, J.P., McCaffery, F.G., Hodgins, P.K., and Fisher, D.B.: 26. Wang, J., Dong M., and Dullien, F. A. L.: “Trapping in the Serial
“Interpreting Relative Permeability and Wettability From Type Interacting Tube Bundle Model,” paper submitted to
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From Displacement Experiments: An Error Analysis,” SPE
Reservoir Engineering (March 1986) 175–182.
6 SPE 99763

Table 1 Summary of the extrapolation of simulated data

Input Qi range (PV) for Extrapolated Swavg, % Extrapolated Extrapolation
μo/μw 1 / Qi
Sor, % extrapolation at 1/Qi = 0 Sor, % Error (%)
10 20.00 6–20 0.167–0.050 79.84 20.16 0.8
100 30.00 16–30 0.062–0.033 69.51 30.49 1.6
1,000 40.00 26–40 0.038–0.025 59.07 40.93 2.3
10,000 50.00 28–50 0.036–0.020 48.79 51.21 2.4

Table 2. Summary of unsteady-state displacement tests

No. μo, mPa.s φ, % Ka, μm
2
Swi, % Kro(Swi) Qi, PV Sor, % Krw(Sor)
1 430 35.6 6.5 10.5 0.95 36.7 32.5 0.033
2 1,088 36.0 7.3 7.8 1.10 43.4 38.9 0.024
3 1,450 35.8 7.1 7.3 1.15 36.4 40.5 0.019
4 1,860 35.7 7.5 6.9 1.25 41.7 41.3 0.015
5 5,410 35.9 7.1 4.9 1.40 42.3 43.6 0.006
6 13,550 35.8 7.2 3.8 1.60 58.4 48.2 0.0025

80.0 70.0

μ o / μ w=10 μ o / μ w=100
79.0 69.0
Simulated
Extrapo lated Simulated
Swavg

Swavg

78.0 68.0 Extrapo lated

77.0 67.0

76.0 66.0
0 0.05 0.1 0.15 0.2 0 0.02 0.04 0.06 0.08
1/Qi, 1/PV 1/Qi, 1/PV

60.0 49.0
μ o / μ w=10,000
59.0 μ o / μ w=1,000
48.9
Simulated
58.0
Simulated 48.8 Extrapo lated
Swavg
Swavg

57.0 Extrapo lated

48.7
56.0
48.6
55.0

54.0
48.5
0 0.01 0.02 0.03 0.04 0.05 0 0.01 0.02 0.03 0.04

1/Qi, 1/PV 1/Qi, 1/PV

Fig. 1 Extrapolation of the water saturation for different oil-water systems.

SPE 99763 7

10.0

Drainage
Imbibitio n
8.0

6.0
Pc, kPa

4.0

2.0

0.0
0 20 40 60 80 100

S w, %

Fig. 2 Capillary pressure curve of the sandpack for water/air system.

1.0 10.0 1

Experimental Data
Histo ry M atch
0.8 8.0
Exterimental Data
Histo ry M atch
Pressure Drop, kPa
Oil Produced, PV

0.1
0.6 6.0
Kr

0.4 4.0

0.01

0.2 2.0

0.0 0.0
0.001
0 10 20 30 40
0 20 40 60 80
Pore Volum es Injected S w, %

Fig. 3 History matches of oil production and pressure drop data and the derived relative permeability curves. Oil viscosity: 430 mPa.s.
8 SPE 99763

1.0 20.0
10

Experimental Data
Histo ry M atch
0.8 Experimental Data
Histo ry M atch 15.0

Pressure Drop, kPa

1
Oil Produced, PV

0.6

10.0

Kr
0.1
0.4

5.0
0.2 0.01

0.0 0.0
0 10 20 30 40 0.001
Pore Volum es Injected 0 20 40 60 80
S w, %

Fig. 4 History matches of oil production and pressure drop data and the derived relative permeability curves. Oil viscosity: 1,450 mPa.s.

10

0.1
Kr

0.01

0.001

0.0001
0 20 40 60 80
S w, %
μ o = 430 mP a.s μ o =1,088 mP a.s
μ o =1,450 mP a.s μ o =1,860 mP a.s
μ o =5,410 mP a.s μ o =13,550 mP a.s
Fig. 5 Effect of viscosity ratio on relative permeability curves.
SPE 99763 9

60

50

40

S or, %
30

20

Fig. 6 Residual oil in micromodel for heavy oil-water system. 10

0
100 1,000 10,000 100,000
μ o, m Pa.s
Fig. 10 Simulated residual oil saturation vs. oil viscosity with a
serial type interacting capillary bundle model.

Fig. 7 Residual oil (Kerosene) in micromodel.

60

50

40
S or, %

30

20

10

0
100 1,000 10,000 100,000

μ o, m Pa.s
Fig. 8 Measured residual oil saturation vs. oil viscosity.

r4 r1 Oil

r3 r2
Water
r2 r4

r1 r3

Trapped Oil
Fig. 9 Schematic of trapping in a serial type interacting capillary
bundle model. Tube radii r1 > r2 > r3 > r4.