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Scaling Spontaneous Imbibition of Aqueous Surfactant Solution into Preferential Oil-Wet Carbonates Eli J. Høgnesen,† Dag C. Standnes,‡ and Tor Austad*,† Stavanger University College, Ullandhaug, Postbox 8002, 4068 Stavanger, Norway, and Centre for Integrated Petroleum Research (CIPR), University of Bergen, Norway Received March 12, 2004. Revised Manuscript Received July 8, 2004
Carbonate reservoirs are usually strongly fractured, with very high permeability contrasts between matrix blocks and fractures. Normally, a simulation of fluid flow with a dual porosity model is used, which is based on a fluid-exchange term where the dimensionless time is a key factor. Besides traditional reservoir rock and fluid parameters, the scaled dimensionless time must include the influence of capillary and gravitational forces. A very recent publication [Li and Horne, SPE Paper No. 77544, 2002] examined an “analytical” model that involved all these effects. In the present paper, we have tested the model for spontaneous imbibition of aqueous surfactant solution into preferential oil-wet carbonate cores. A chemical reaction occurs between the surfactant and adsorbed polar organic components/carboxylates at the carbonate surface, ahead of the fluid displacement process, as has been discussed previously [Standnes and Austad, J. Pet. Sci. Eng., 28, 123, 2000]. It was of great interest to determine if this new analytical model could handle such a process. The ranges for the scaling parameters were as follows: interfacial tension (IFT), 0.3-0.8 mN/m; permeability, 3-350 mD; initial water saturation (Swi), 0-0.5; core height, 5-30 cm (but with the same diameter); diameter, 2.5 and 3.5 cm (but with the same core height); temperature, 40-70 °C; and sulfate concentration, 0-1.7 g/L. Temperature change has a great influence on the imbibition rate, because of changes in IFT, critical micelle concentration, and fluid viscosity. Sulfate, being a potential-determining ion toward CaCO3 [according to Pierre et al., J. Dispersion Sci. Technol., 11, 611, 1990] was observed to have catalytic effects on the wettability alteration process in chalk at low temperature [according to Strand et al., Energy Fuels, 17, 1133, 2003]. When the characteristic length (La) is used as the shape factor of the cores, all the parameters scaled very well, except for the height of the core and the diameter of the core at low IFT (low temperature). However, when just the height of the cores was used as the shape factor, all the parameters scaled quite well when the normalized oil recovery was plotted versus dimensionless time. The fit of the scaling, using the height of the core as the shape factor, suggested that gravitational forces were very active in the oil recovery mechanism.
Introduction Imbibition has been described as a process by which a wetting fluid is drawn into a porous medium by capillary action. The process is important in oil production, and several papers in the literature, during a 50-year period, that address spontaneous imbibition have been tabulated and summarized.1 Very recently, Morrow and Mason2 gave a review about oil recovery by spontaneous imbibition that especially involved the influence of rock wettability and scaling of the imbibition process. Oil recovery from highly fractured carbonate reservoirs with low-permeability matrix blocks is an example where the spontaneous imbibition of water is an important improved oil recovery (IOR) technique.3 * Author to whom correspondence should be addressed. Telephone: +47 51832296. FAX: +47 51831750. E-mail:
[email protected]. † Stavanger University College. ‡ University of Bergen. (1) Zhou, X.; Morrow, N. R.; Ma, S. Presented at the 1996 SPE/DOE Tenth Symposium on Improved Oil Recovery, Tulsa, OK, April 2124, 1996, SPE/DOE Paper No. 35436, 1996. (2) Morrow, N. R.; Mason, G. Curr. Opin. Colloid Interface Sci. 2001, 6, 321-337.
Unfortunately, ∼90% of the carbonate reservoirs are neutral to oil-wet, which implies that spontaneous imbibition of water will not occur.4 Viscous flooding will normally give low sweep efficiency, because of the high permeability contrast between the fractures and the matrix blocks. Al-Hadhrami and Blunt5 discussed several IOR techniques (viscous forces, gravitational forces, reduced oil-water interfacial tension (IFT), gas injection, and wettability alteration) to overcome the capillary barrier to invade an oil-wet rock matrix and displace the oil in a secondary drainage process. Wettability alteration toward more water-wet conditions, which seems to be an actual method, can be obtained through the use of chemicals6,7 or steam.5 (3) Chen, H. L.; Lucas, L. R.; Nogaret, L. A. D.; Yang, H. D.; Kenyon, D. E. SPE Reservoir Eval. Eng. 2001, 3 (February), 16-25. (4) Rao, D. N. Wettability Effets in Thermal Heavy Oil Recovery Operations. Presented at the 1996 SPE/DOE Tenth Symposium on Improved Oil Recovery, Tulsa, OK, April 21-24, 1996, SPE/DOE Paper No. 35462. (5) Al-Hadhrami, H. S.; Blunt, M. J. SPE Reservoir Eval. Eng. 2001, 4, 179-186. (6) Standnes, D. C.; Nogaret, L. A. D.; Chen, H. L.; Austad, T. Energy Fuels 2002, 16, 1557-1564.
10.1021/ef040035a CCC: $27.50 © 2004 American Chemical Society Published on Web 09/04/2004
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Recently, we have shown that cationic surfactants of the type alkyltrimethylammonium bromide (CnTAB) are able to induce spontaneous imbibition of water into carbonate cores, showing an initially negative capillary pressure (i.e., they did not imbibe pure brine7). Based on a variety of experiments, using different surfactants and concentrations, temperatures, crude and model oils, and contact angle measurements on calcite surfaces, the mechanism for the wettability alteration process was described as a specific interaction between the monomer of the cationic surfactant and strongly adsorbed negatively charged carboxylic material from the crude oil. The strong electrostatic and hydrophobic interaction between the species forms a complex usually termed a “cat-anionic surfactant”.8 The complex is released from the surface and dissolved either in the oil phase or in the surfactant micelles in the aqueous phase. A positive capillary pressure is created, and spontaneous imbibition can occur. The fluid-flow mechanism of the spontaneous imbibition process can be either countercurrent, cocurrent, or a combination of the two, depending on the ratio between capillary forces and gravitational forces that are acting on the oil and water phases.9,10 When using surfactants, which decrease the impact of capillary forces sufficiently, the gravitational forces may dominate the fluid-flow mode. The oil recovery by spontaneous imbibition is dependent on crude oil/brine/rock (COBR) interactions, which surely are related to wetting conditions and multiphase flow. The COBR interaction is a complex interplay between the chemical and physical properties of the three elements. Thus, to cope with the variety of parameters involved, much effort has been spent on correlating spontaneous imbibition data, i.e., determining oil recovery versus time. Since the pioneering work by Mattax and Kyte,11 which scaled capillary forced imbibition under very specific conditions, several modifications of the scaling formula have appeared in the literature, as noted by Morrow and Mason.2 The scaling group defined by Ma et al.12 has been frequently used to scale capillary-forced imbibition:
td )
( ) xφkσ
x
µoµwL2a
t
(1)
where td is dimensionless time, k the rock permeability, φ the porosity, σ the interfacial tension between the wetting and nonwetting phases, µo the viscosity of oil, µw the viscosity of water, La the characteristic length (and is often called the shape factor), and t the actual time. Also, in this case, there are limitations concerning the wetting conditions and initial fluid saturation, and, of course, gravitational forces are neglected. Very (7) Standnes, D. C.; Austad, T. J. Pet. Sci. Eng. 2000, 28, 123-143. (8) Khan, A.; Marques, E. Catanionic Surfactants. In Specialist Surfactants; Robb, I. D., Ed.; Blackie Academic & Professional: London, 1997; Chapter 3. (9) Schechter, D. S.; Zhou, D.; Orr, F. M., Jr. J. Pet. Sci. Eng. 1994, 11, 283-300. (10) Standnes, D. C.; Austad, T. Colloids Surf., A 218, 2003, 161173. (11) Mattax, C. C.; Kyte, J. R. SPE J. 1962, 18 (June), 177-184. (12) Ma, S.; Zhang, X.; Morrow, N. R. J. Can. Pet. Technol. 1999, 38, 25-30.
recently, Li and Horne13 “analytically” derived a general scaling model for spontaneous imbibition that incorporated both capillary and gravitational forces in addition to general parameters such as mobility and capillary pressure. The authors tested the scaling model on experimental imbibition data previously published by Schechter et al.9 Model solvent systems were used as fluid phases, and the IFT was varied using the corresponding fluids along different tie lines (0.10-38.1 mN/ m). Also, the permeability of the porous medium was varied using different types of core materials (15-500 mD). The fit was surprisingly good when the normalized oil recovery was plotted versus the new dimensionless time. Note that the dimension of the cores was not included as a scaling parameter. The objective of the present paper is to verify if the data from spontaneous imbibition processes that involve surface-active materials to change the wettability of carbonates do fit with this new dimensionless time formula that has been suggested by Li and Horne.13 Correlations of imbibition data are of special importance to reservoir simulation. Dual-porosity models usually contain a fluid-exchange term, which describes the amount of oil that has been depleted from the specific matrix blocks at certain times. The fluid-exchange factor is often written in terms of dimensionless time, and, therefore, it is very important to make reliable correlations that can be used.14 Furthermore, the computational efficiency of the simulators could be drastically increased by including the imbibition rate as scaled dimensionless time in the fluid-transfer functions. Some key equations in developing the scaling model of Li and Horne13 are listed below. The volume rate of water (qw) flowing into an oil-saturated core can be expressed as
(R1 ) - b
qw ) a0
0
(2)
where R is the oil recovery factor, in the units of pore volume (PV), and
a0 )
AM/e(Swf - Swi) / Pc L
(3)
b0 ) AM/e∆Fg
(4)
where A is the cross section area of the core, M/e the effective mobility at the water front, Swf the water saturation at the water front, Swi the initial water saturation, L the length of the core, P/c the capillary pressure at the water front, ∆F the density difference between water and oil, and g the gravitational acceleration constant. Thus, by plotting qw versus 1/R and using a linear regression technique, the values of a0 and b0 are determined. From eqs 3 and 4, the values of P/c and (13) Li, K.; Horne, R. N. A General Scaling Method for Spontaneous Imbibition. Presented at the 2002 SPE Annual Technical Conference and Exhibition, San Antonio, TX, September 29-October 2, 2002, SPE Paper No. 77544. (14) Kazemi, H.; Gilman, J. R.; Eisharkawy, A. M. SPE Reservoir Eng. 1992, 7 (May), 219-227.
Imbibition of Aqueous Surfactants into Carbonates
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Table 1. Brine Composition component
concentration [g/L]
Na+ Ca2+ Mg2+ ClHCO3SO42-
10.35 0.43 0.75 17.49 0.12 2.31
total
31.85
M/e are then calculated. A parameter c was also defined,
c)
b0 a0
(5)
which is, in fact, the ratio of the gravitational force to the capillary force (the Bond number). The characteristic length/shape factor, La, is defined as
La )
x
Vb
(6)
Ai
∑d
Results and Discussion
i
where Vb is the bulk volume, Ai represents the different surface areas exposed for spontaneous imbibition, and di represents the corresponding distances to the no-flow boundary. The dimensionless time td was finally defined as
td ) c
[
2
]
M/eP/c (Swf - Swi) φL2a
oil that was used, and, finally, ∼2 mm of the core surface was shaved off, to remove nonrepresentative organic materials that had been deposited on the core surface during the aging process. Limestone. Outcrop rock samples from Faxe near Copenhagen, Denmark, were used as the porous medium. The air permeability of the core material was ∼73 mD, and the porosity was in the range of 35%-37%. In the long-core experiment, four different cores, with a length of ∼6 cm, from the same block were placed on top of each other to form a composite core with capillary contact in the vertical direction. Chalk. Outcrop rock samples from Stevns Klint near Copenhagen, Denmark, were used as the porous medium. The air permeability of the core material was ∼1-3 mD, and the porosity was in the range of 44%-49%. Oil. An acidic crude oil from the North Sea diluted with n-heptane was used (with a crude oil:n-heptane ratio of 60: 40, by volume). The resulting oil had an acid number (AN) that was equal to 1.7 mg KOH/g oil. No precipitation of asphaltenes was noticed on storage. Brine. The composition of the brine is given in Table 1. Surfactant. The cationic surfactant n-C12-N(CH3)3Br, abbreviated as C12TAB and diluted to 1.0 wt % in brine, was used in the imbibition tests.
t
(7)
where t is the actual imbibition time. Li and Horne13 found that variations in IFT and permeability scaled quite well when normalized oil recovery was plotted versus td, using cores of the same dimension. The normalized oil recovery (R*) could be defined as
R* ) cR
(8)
The type of shape factor used in eq 7 is surely related to the relative contribution of capillary and gravitational forces acting on the fluids. If capillary forces are dominating the fluid flow, a shape factor describing the surface area of the sample, as defined by eq 7, seemed to scale the core dimension quite well. If, however, gravitational forces are dominating, which may be the case at low IFT, the core dimension is scaled using just the height of the sample as the characteristic length. Experimental Section Most of the experimental data used in this paper has been published previously, as noted in Table 2. To extend the scaling area to include the core dimension/shape, some additional experiments were conducted, using limestone chalk cores. Prior to imbibition, the cores were handled in the same way as described previously, in regard to fluid saturation, aging, shaving, etc.15 To obtain homogeneous wetting conditions, the water-saturated cores were flooded with at least 2 PV of oil in each direction and aged at 90 °C for 4 weeks (for cores without initial water, the aging time was 5 days at 50 °C) in the crude (15) Standnes, D. C.; Austad, T. J. Pet. Sci. Eng. 2000, 28, 111121.
General Considerations. It is important to note that the analytical model proposed by Li and Horne13 assumes that the contribution of capillary and gravitational forces is constant during the imbibing process. If the fluid flow changes drastically during the oil expulsion, because of changes in the relative contribution of capillary and gravitational forces, it is hard to believe that the relationship between qw and 1/R will be a linear function: i.e., the parameter c ) b0/a0 is not constant. Furthermore, at the plateau recovery, R ) Rmax and qw ) 0. Thus, the linear correlation between qw and 1/R should cross the x-axis at 1/Rmax, and the value must be >1. In most of the cases, the imbibition has proceeded long enough to obtain a good approximation of Rmax; however, in some cases, the plateau of the oil production was not reached. In these cases, the value of Rmax is estimated based on closely related experiments using similar core materials. In most cases, when plotting qw vs 1/R, a reasonably linear correlation was obtained when discarding points below 10% oil recovery. The value of a0 was then determined as the slope of the line. In most cases, however, the line crossed the x-axis below a value of 1, which indicates an oil recovery of >100%. This is obviously wrong. Therefore, a more-correct value of 1/Rmax was estimated, based on plateau oil recovery from the imbibition curves. To obtain a probably morecorrect value of b0, a line with a slope of a0 passing through this estimated experimental value of 1/Rmax on the x-axis was constructed, as illustrated in Figure 1, using test 6 as an example. The experimental estimated values used to calculate b0 are listed in Table 2. Another reason for an inaccurate linear correlation between qw and 1/R may be inhomogeneous wetting conditions for cores that have initial water present. The cores were prepared to Swr at room temperature and then left in the corresponding oil at 90 °C for 4 weeks. Because of expansion of the fluids inside the core, oil and water will move toward the core surfaces. Oil will escape from the core into the surrounding oil phase, whereas water is held close to the core surface, resulting
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Table 2. Core Data for the Different Imbibition Tests core typea 1 2 3 4 5 6 7 8 9 10 11 12 13 14 a
D D C D D D L L C C C C C C
k temp diameter PV HCPV Swi salinity sulfate IFT [mD] [°C] L [cm] [cm] φ [%] [cm3] [cm3] [%] [g/L] [g/L] 1/Rmax [mN/m] 352 101 ∼3 352 101 162 ∼73 ∼73 ∼3 ∼3 ∼3 ∼3 ∼3 ∼3
40 40 40 40 40 40 40 40 70 40 40 40 40 70
5.86 5.64 4.60 5.86 5.64 29.90 6.42 25.65 5.03 4.63 4.33 4.25 4.92 4.64
3.75 3.80 3.48 3.75 3.80 3.17 3.73 3.73 3.61 3.51 3.51 3.51 2.51 2.50
25.5 22.5 44.8 26.2 23.2 21.1 34.0 34.0 45.4 48.3 47.8 48.1 47.6 48.0
16.49 14.42 19.60 16.91 14.84 49.79 24.04 93.98 23.37 21.64 20.03 19.78 11.58 10.99
9.500 7.500 19.601 9.000 7.490 34.904 24.040 93.983 23.374 15.54 14.50 14.50 11.58 10.99
42.4 48.0 0.0 46.8 49.5 29.9 0.0 0.0 0.0 28.2 27.6 26.7 0.0 0.0
9.25 9.25 44.94 9.25 9.25 9.25 33.39 33.39 44.94 43.59 43.59 43.59 33.39 33.39
0.16 0.16 1.56 0.16 0.16 0.16 2.31 2.31 1.56 0.07 0.4 1.7 2.31 2.31
2.10 2.20 1.55 2.10 2.20 2.19 1.29 1.59 1.41 9.74 3.58 1.49 1.83 1.53
0.3 0.3 0.8 1.0 1.0 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8
reference Standnes and Austad,10 test 7 Standnes and Austad,10 test 8 Standnes and Austad,7 test 1 Standnes and Austad,10 test 5 Standnes and Austad,10 test 6 Standnes et al.,6 test YL1 present work present work Standnes and Austad,7 test 26 Strand et al.,16 test 18 Strand et al.,16 test 19 Strand et al.,16 test 20 present work present work
D, dolomite; C, chalk; and L, limestone. Table 3. Calculated Data from the Scaling Process test
Figure 1. Example of how to determine a0 and b0 for the scaling process.
in higher water saturation in this area, compared to the rest of the core. Thus, a higher water saturation results in a lower oil saturation, which means that the core surface has decreased access to surface-active materials from the oil phase. Consequently, the core becomes more water-wet in a region close to the core surface. Although ∼2 mm of the cores were shaved off on all surfaces, we normally noticed a fast spontaneous production of oil, corresponding to ∼5%-7% of the initial oil present, depending on the initial water saturation.7,15 In the following sections, the scaling of actual reservoir parameters is performed using the model of Li and Horne.13 Note that the polar components in the oil, especially the carboxylic material, are important for the wetting conditions of the carbonate rock. Therefore, in all experiments, the same oil was used to obtain preferential oil-wet carbonate materials, (dolomite, chalk, and limestone). Permeability. Tests 1-3 from Table 2 were used, i.e., two dolomite cores and one chalk core. The permeability varied between 3 mD and 350 mD. The dimensions of the cores are comparable; however, it is noticed that the porosity varied between 22% and 45%. It was also noticed that the IFT for the two dolomite cores was 0.3 mN/m, and for the low-permeability chalk test, the IFT was 0.8 mN/m, because of different modifications of the surfactant systems used. The initial water saturation also was quite different. The dolomite cores had a Swi value of 42%-48%, whereas the chalk core did not contain initial water at all. Previous experiments have shown that initial water in chalk had minor effects on the imbibition process.7 It was also noticed that the sulfate concentration was higher for test 3, compared to the dolomite tests. Previous studies have shown that the catalytic effects of sulfate, when using dolomite, had
1 2 3 4 5 6 7 8 9 10 11 12 13 14 a
a0 [m3/s] 10-13
7.33 × 2.41 × 10-13 7.57 × 10-13 5.76 × 10-12 2.42 × 10-12 4.79 × 10-12 8.57 × 10-12 1.01 × 10-11 5.07 × 10-12 1.58 × 10-14 5.7 × 10-14 4.88 × 10-13 9.96 × 10-13 1.04 × 10-12
b0 [m3/s] 10-12
1.54 × 5.31 × 10-13 1.17 × 10-12 1.21 × 10-11 5.33 × 10-12 1.05 × 10-11 1.10 × 10-11 1.60 × 10-11 7.16 × 10-12 1.54 × 10-13 2.04 × 10-13 7.28 × 10-13 1.82 × 10-12 1.59 × 10-12
ca 2.10 2.20 1.55 2.10 2.20 2.18 1.29 1.59 1.41 9.74 3.58 1.49 1.83 1.53
M*e [m3 s/kg] P*c [Pa] 7.37 × 10-13 3.63 × 10-13 5.85 × 10-13 5.89 × 10-12 2.52 × 10-12 1.02 × 10-11 4.80 × 10-12 6.97 × 10-12 3.32 × 10-12 7.54 × 10-14 1.00 × 10-13 3.57 × 10-13 1.75 × 10-12 1.53 × 10-12
109 105 97 109 105 386 135 541 106 98 91 90 104 98
c ) b0/a0.
a minor effect on the imbibition process.16 The results from the scaling are shown in Figure 2. The plateau production for test 3 was ∼65%, which is consistent with similar experiments using the same system (see Figure 2a). For the two dolomite cores (tests 1 and 2), the final oil recovery was suggested to be ∼90%, which was observed in similar tests using the same core materials. The relationship between qw and 1/R was quite linear for test 1; however, the correlation was worse for test 3, as indicated by Figure 2b and c. The observed slope is listed as a0 values in Table 3. In both cases, the lines cross the x-axis at values of
