New Experimental Approach for Measuring Drainage and

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Energy & Fuels 2009, 23, 260–271

New Experimental Approach for Measuring Drainage and Spontaneous Imbibition Capillary Pressure Osamah A. Al-Omair* Department of Petroleum Engineering, Kuwait UniVersity, Post Office Box 5969, Safat 13060, Kuwait ReceiVed May 25, 2008. ReVised Manuscript ReceiVed October 16, 2008

This research presents a visualizing method to estimate capillary pressure relationship from centrifuge experiments using spinning disk geometry. The visualizing method consists of continuously recording the local saturation variation by using a video camera while centrifuging at any given time. The experimental procedure consists of recording sample images and fluid production at any given time and then determines local saturation by a simple correlation between production and gray level. Thus, a modified core holder was designed to adopt the new approach. The core holder must be transparent for visual interpretation of the experiments and strong to account for the high pressure during experiments. The traditional geometry for the centrifuge method is well-established in the industry. However, the benefits of using the spinning disk approach consist of validity of zero capillary pressure at the outlet face, ability of measuring local saturation at any given time, possibility of estimating drainage and spontaneous imbibition capillary pressure, and consideration of radial effect. Results of 24 rock samples show a good agreement between the capillary pressure relationships obtained from the new approach and those obtained from the porous-plate method. Relative errors of the capillary pressure were less than 5% for most samples. Furthermore, the entry pressures and irreducible wetting phase saturations obtained by this approach were agreed with the porous plate method.

Introduction Capillary pressure exists when two immiscible phases are present in a porous rock. It is defined as the pressure differential between the wetting and nonwetting phases at the interface. Although the absolute magnitude of the capillary pressure in most petroleum reservoirs is usually not large, the effects are extremely important. Together with gravity, capillary pressure affects the original distribution of the fluid saturations within the reservoir, particularly the distribution of connate water. By virtue of their effects on the shapes of the fluid interfaces within the pore spaces, they control the relative freedom of movement of fluid present in the reservoir and are important factors in influencing the behavior and distribution of fluids in the production processes. Several methods are available for measuring capillary pressure as a function of water saturation in rocks. They consist of the mercury-injection method, the porous-plate methods, the standard centrifuge method, and the “spinning disk” centrifuge method. Methods for Measuring Capillary Pressure. Leverett1 was the first researcher that introduced the concept of capillary pressure for the oil industry. He presented general concepts on capillarity in porous media that are still valid today. Leverett’s concept was based on measuring water drainage from columns of unconsolidated sands. A number of other techniques for measuring drainage capillary pressure have been proposed since Leverett’s initial work. Hassler and Brunner2 presented the centrifuge technique and a methodology for converting the average saturation to the saturation at a given position in * To whom correspondence should be addressed. E-mail: dr-alomair@ hotmail.com. (1) Leverett, M. C. Trans. AIME 1941, 142, 152–169. (2) Hassler, G. L.; Brunner, E. Pet. Trans. AIME 1944, 160, 114–123.

the core sample. McCullough et al.3 developed the porous-plate technique for measuring capillary pressure of rocks. Purcell4 presented the mercury-injection technique as another method for rapidly obtaining drainage capillary pressure data. Mercury-Injection Method. In 1949, Purcell4 presented the mercury-injection method to obtain capillary pressure curves using the mercury as the nonwetting phase and nitrogen as the wetting phase. The core is inserted in the mercury chamber and then evacuated from air. Mercury is forced into the core under pressure. The volume of mercury injected at each pressure determines the nonwetting phase saturation. This procedure is continued until the core sample is filled with mercury or the injection pressure reaches some predetermined value. Important advantages are gained by this method: (1) the time for determination is reduced to a few minutes, (2) small, irregularly shaped pieces can be used, and (3) the range of pressure investigation is increased. Disadvantages of this method consist of the difference in wetting properties and the permanent destruction of the core sample; therefore, the method is limited to the study of the drainage curve. Porous-Plate Method. McCullough et al.3 introduced the porous-plate method. In this method, the rock sample is placed on a porous plate, which is permeable only to the wetting phase. First, the sample and the porous plate are fully saturated with the wetting liquid. Then, nonwetting liquid is forced into the rock, expelling the wetting liquid from the rock through the porous plate. The capillary pressure and wetting phase saturation are determined, respectively, from the difference in the pressure between the wetting and nonwetting phases and from the volume of wetting liquid that is expelled from the sample. The main advantage of the porous-plate method is its accuracy. However, (3) McCullough, J. J.; Allbaugh, F. W.; Jones, P. H. Drill. Prod. Pract. 1944, 180–188. (4) Purcell, W. R. Trans. AIME 1949, 186, 39–48.

10.1021/ef800394v CCC: $40.75  2009 American Chemical Society Published on Web 01/06/2009

Drainage and Imbibition Capillary Pressure

Energy & Fuels, Vol. 23, 2009 261

Figure 1. Side-view sketch of traditional and spinning disk centrifuge geometries. Table 1. Properties of Rock Samples sample ID 1B 3B 4B 5B 6B 10B 11B 12B 13B 14B 15B 16B 19B 20B 1D 2D 5D 6D 2L 5L 6L 8L 1R 5R

type

berea

dolomite

limestone reservoir rock

diameter (in.)

thickness (in.)

porosity (%)

permeability (mD)

4.0 3.6 3.7 4.0 3.9 4.0 3.8 4.0 4.0 3.8 4.0 3.7 4.0 3.8 4.0 3.8 4.0 3.6 3.6 4.0 3.8 4.0 3.5 3.5

0.50 0.50 0.48 0.45 0.50 0.50 0.48 0.50 0.45 0.50 0.48 0.50 0.50 0.45 0.48 0.45 0.50 0.46 0.46 0.48 0.48 0.50 0.45 0.50

20 17.4 22.6 23.1 16.3 24.5 15.5 21.2 21.4 20.5 21.7 20.3 19.6 18.7 9.8 23.9 19.9 12.7 12.9 18.5 23.7 22.3 20.5 22.1

200.0 560.1 147.3 883.5 322.9 958.2 66.3 133.6 162.5 147.7 133.4 119.4 93.7 288.4 70.2 657.5 111.6 235.0 90.0 231.7 947.3 318.9 145.6 232.4

the time required to obtain a curve is prohibitive, often a month or more. As a consequence, most of the data reported in the literature using this technique deal only with the drainage curve. Traditional Centrifuge Experiment for Measuring Capillary Pressure. The traditional centrifuge method of determining capillary pressure curves and rock saturations was initially developed by Hassler and Brunner in 1944.2 Since then, it has found a wide application in many aspects of core analysis. The centrifuge method entails increasing the centrifuge speed in steps and measuring at each step the amount of liquid produced from the core at equilibrium when all fluids have ceased. In the standard centrifuge experiments, the rock sample is placed in a cup or small bucket containing a calibrated tube, where fluid displaced from the rock sample by centrifugal force is collected. The cup or bucket is mounted on the centrifuge rotor. As the rotor spins at a constant speed, fluid drains from the rock. Measuring the volume of fluid drainage after sufficient time has been allowed to reach an end point at each of several centrifuge speeds can determine the capillary pressure relationship. The advantages of using the centrifuge method for estimating capillary pressure are rapid establishment of equilibrium, simple operation, and reasonable and reproducible results. However, the standard centrifuge methods do not directly measure the capillary pressure that pertains to a particular saturation. Rather, this relationship must be inferred from the average saturation in the core as a function of spin rate. In addition, two major problems, associated with fundamental assumptions, still complicate the proper application of the traditional centrifuge technique in obtaining accurate data. These

Figure 2. (A) Top-view sketch of the sample holder. (B) Side-view sketch of the sample holder.

problems are the radial effect, because of core width, and the gravity effect, because of low initial ramp-up speeds.5,15 Spinning Disk Approach for Measuring Capillary Pressure. For the last several decades, researchers have developed modifications to the centrifuge technique to overcome the limitations of the traditional centrifuge experiment. These modifications include modification of the core holder to account for end effects and to consider boundary effects.6-9 Other researchers have proposed techniques for measuring capillary pressure and relative permeability in a single centrifuge experiment. Among those researchers are O’Meara and Crump,10 King et al.,11 and Chardaire et al.12 However, all of those researchers focused on the modifications of the traditional centrifuge experiment. In 1987, Christiansen and Cerise6 presented a new centrifugal approach called the “spinning disk” approach using a thin disk-shaped sample of rock for measuring capillary pressure in a centrifuge. This differs significantly from the standard centrifuge geometry, in which a cylindrical sample of rock orbits at a short distance from the axis of the centrifuge. The two approaches are shown in Figure 1. The spinning disk approach was first demonstrated in 1998 at the Colorado School (5) Christiansen, R. L. SPE Form. EVal. 1992, 311–314. (6) Christiasen, R. L.; Cerise, K. S. Presented at the AIChE Annual Meeting, 1987; paper 47d. (7) O’Meara, D. J.; Hirasaki, G. J.; Rohan, J. A. SPE ReserVoir EVal. Eng. 1992, Feb, 133–142. (8) Bolas, B.; Torsaeter, O. International Symposium of the Society of Core Analysts Proceedings, 1995; paper 9533. (9) Al-Omair, O. A. M.S. Thesis, Colorado School of Mines, Golden, CO, 1997.

262 Energy & Fuels, Vol. 23, 2009

Al-Omair

Figure 3. Porous-plate apparatus (from Ruska’s manual).

Figure 4. Production profiles for sample 1B at different spin rates.

Figure 5. Production profiles for sample 5B at different spin rates.

of Mines by Al-Mudhi.13 Since that time, however, only a few researchers have considered this method and applied it.14 Limitations of the Traditional Centrifuge Experiment Several advances have been made in many aspects of the centrifuge technique, particularly in the area of data interpretation. However, researchers have realized in recent years that

Figure 6. Production profiles for sample 2L at different spin rates.

the centrifuge technique has not been perfected, and a number of problems associated with the fundamental assumptions made in the traditional Hassler-Brunner2 analysis remain to be clarified.15 In 2005, a survey on centrifuge capillary pressure measurements conducted by the Society of Core Analysts has shown that various problems exist with the experimental design, running, recording, data processing, and reporting of centrifuge experiments. The limitations of the traditional centrifuge experiment can be summarized as outflow boundary condition, local saturation, complete capillary pressure curves, and radial effect. Outflow Boundary Condition. The traditional HasslerBrunner2 interpretation of centrifuge capillary pressure data is based on several assumptions. One of these assumptions is that capillary pressure is zero at the outlet boundary of the rock sample. Thus, it is implicitly assumed that the bottom end-face is fully saturated with the phase being displaced out of the core sample. Wunderlich16 stated that the assumption of 100% saturation at the bottom end-face does not in fact hold in some (10) O’Meara, D. J., Jr.; Crump, G. J. SPE-14419, 1985. (11) King, M. J.; Flazone, A. J.; Cook, W. R.; Jennings, J. W.; Mills, W. H. SPE-5595, 1986. (12) Chadaire, C.; Forbes, P.; Chavent, G. SPE-24882, 1992. (13) Al-Modhi, S. M. M.S. Thesis, Colorado School of Mines, Golden, CO, 1998. (14) Al-Omair, O. A. Ph.D. Thesis, Colorado School of Mines, Golden, CO, 2001; pp 66-82. (15) Forbes, P. L.; Chen, Z. A. SPE-28182, 1994.



Figure 7. Saturation correlation for sample 1B. Figure 9. Saturation correlation for sample 2L.

Figure 8. Saturation correlation for sample 5B.

situations. O’Meara et al.7 stated that with the proper end piece to support the core sample, this boundary condition is valid in practically all circumstances. Melrose et al.17 showed that the failure of this assumption depends upon the magnitude of the displacement pressure for the particular rock sample being studied. Bolas and Toraeter8 presented the concept of a moving fluid/fluid level to overcome boundary assumption during the determination of capillary pressure versus saturation using centrifuge experiments. Al-Omair9,18 introduced a visualizing technique for measuring capillary pressure in a centrifuge and concluded that the assumption of 100% saturation at the outlet face of the rock in a centrifuge experiment might fail. Simon19 concluded that the outflow boundary condition can fail in some centrifuge experiments; when this occurs, it is possible to determine the capillary pressure curve using the centrifuge forward modeling technique. Failure of the outflow boundary condition appears to be one reason why many centrifuge capillary pressure experiments do not match porous-plate experiments. Local Saturation. In the traditional Hassler-Brunner2 technique for measuring capillary pressure, average saturation and not local saturation was reported. However, saturation may vary with the position; i.e., the Hassler-Brunner2 method of calculating the top-end saturation from the measured average saturation involves an approximation. Several researchers have studied this (16) Wunderlich, R. W. SPE-14422, 1985. (17) Melrose, J. C.; Dixon, J. R.; Mallinson, J. E. SPE-22690, 1994. (18) Al-Omair, O. A.; Christiansen, R. L. International Symposium of the Society of Core Analysis, 1998; paper 9838. (19) Simon, C. International Symposium of the Society of Core Analysis, 1998; paper 9810.

approximation. Hoffman20 attempted to derive an exact equation to overcome this problem. Melrose21 presented an analysis to approximate centrifuge capillary pressure at low saturation. Ayappa et al.22 reported a method relating the average saturation of liquid in the porous medium to the capillary pressure at the end of the sample nearest the axis of rotation. Chadaire et al.12 presented a significant new improvement in the centrifuge method that continuously recording the local saturation using an ultrasonic device at different locations along the core while centrifuging at any given time. Forbes and Chen15 addressed the problem associated with the transformation of the centrifuge fluid production data into local saturation values. They proposed and tested two new methods for converting average saturation centrifuge data into drainage and imbibition capillary pressure curves. Al-Omair9 introduced a video-imaging technique for measuring local saturation in a centrifuge experiment. AlMudhi13 developed a visualizing method for measuring the local saturation in a centrifuge experiment using the spinning disk approach. Finally, Green et al.23 directly measured the water saturation of the rock sample in the centrifuge using magnetic resonance imaging (MRI) techniques. Complete Capillary Pressure Curves. The limitation of complete capillary pressure curves, including forced and spontaneous drainage and imbibition in the traditional centrifuge experiments, has been addressed by several researchers. Szabo24 stated that there is still no method known that can use the centrifuge to obtain the capillary pressure curve for the imbibition cycle. He proposed a new method for measuring imbibition capillary pressure by centrifuge. Oyno and Toraeter25 introduced a method in connection with their studies on the imbibition mechanism in fractured reservoirs. Bolas and Toraeter8 pointed out that a few authors have treated the problem of determining the spontaneous imbibition capillary pressure in standard centrifuge experiments. They used ultracentrifuge with standard core holders to determine both drainage and imbibition capillary pressure curves in the same experiment. Chen and Balcom26 proposed a single-shot method to measure the capillary pressure curve of a long rock core using single-speed centrifuge experiment and one-dimensional Centric Scan SPRITE MRI to determine the fluid saturation distribution along the length of the core. A full capillary pressure curve can be directly determined by the relation of saturation and the capillary pressure distribution along the length of the core. Jia et al.27 (20) Hoffman, R. N. SPR-555-PA, 1963. (21) Melrose, J. C. SPE-18331, 1990. (22) Ayappa, K. G.; Davis, H. T.; Davis, E. A.; Gordon, J. AIChE J. 1989, 35, 365–375.


Al-Omair

Figure 10. Capillary pressure saturation relationship for sample 1B at different spin rates.

Figure 13. Drainage and imbibition capillary pressure saturation relationship for sample 1B.

Figure 11. Capillary pressure saturation relationship for sample 5B at different spin rates.

Figure 14. Drainage and imbibition capillary pressure saturation relationship for sample 5B.

Figure 12. Capillary pressure saturation relationship for sample 2L at different spin rates.

developed an analytical approach to determine capillary pressure and relative permeability simultaneously by using experimental data of spontaneous water imbibition in gas-saturated rock. Radial Effect. As stated by Christiansen,5 accuracy of capillary pressure relationships obtained from centrifuge experiments is widely recognized to depend upon the quality of raw data, the homogeneity of the rock sample, and the methods used for data reduction. However, the systematic error caused by the radial nature of the centrifugal field is not widely recognized.

Figure 15. Drainage and imbibition capillary pressure saturation relationship for sample 2L.

His paper showed that this radial error could be greater than errors caused by poor data-reduction methods. The radial error can be estimated from the geometry of centrifuge rotors and rock sample dimensions. Careful experimental technique can minimize radial error. Furthermore, data-reduction methods can eliminate radial error by properly accounting for the radial nature of centrifugal fields. Forbes and Chen15 discussed the problems in the determination of the radial centrifugal field distribution inside a core sample. They presented a quantitative analysis of



Figure 16. Spinning disk versus porous-plate capillary pressure saturation relationships.

the radial field of the centrifugal field in core plugs for capillary pressure curves using a factor derived by Christiansen.5 The results showed that when the radial effect is taken into account, the capillary pressure curve is shifted to higher values than the traditional one-dimensional solution. Forbes and Chen15 stated that the most sophisticated techniques for deriving a capillary pressure curve from centrifuge data do not account for the fact that the centrifugal field is radial. Since 1945, radial effects have been considered negligible. However, in the past few years, several papers have questioned this approximation. Fleury and Porbes28 examined the radial effect experimentally by centrifuged homogeneous sandstone and carbonate outcrop samples at a large and small radius of rotation to generate low or high radial effect. Forbes29 quantitatively analyzed the effect of gravity, which is superimposed on the centrifuge pressure field (23) Green, D. P.; Gardner, J.; Balcom, B. J.; McAloon, M. J. SPE110518, 2008.

and founded to be significant. Simon19 presented the centrifuge forward modeling technique, which accounts for the radial effect. Scope of This Paper Until now, no technique has been developed to account for all of the traditional centrifuge limitations using a single experiment. Most researchers focused on part of these limitations: O’Meara et al.7 resolved outflow boundary conditions; Forbes and Chen15 and Chardaire et al.12 computed local saturation values from total fluid recovery; Longeron et al.30 and Bolas and Toraeter8 developed modified techniques using micropore membranes to produce complete sets of capillary pressure curves. Christiansen and Cerise6 and Christiansen5 investigated the radial centrifugal field distribution. Ayappa et al.22 also discussed models for arbitrary-shaped core samples, and they derived the relevant equations. Forbes15,31 re-evaluated this problem and provided a semi-analytical solution to quan-


Al-Omair


titatively account for the radial effect in practical applications. Therefore, the scope of this paper is to use a modified spinning disk approach for measuring capillary pressure saturation profiles, to account for all of the limitations of the traditional centrifuge experiment. Capillary pressure saturation profiles generated with the modified spinning disk approach will be validated with porous-plate technique measurements. Experimental Specifications The spinning-disk geometry is particularly suited for video measurement of saturation profiles because the cylindrical rock sample spins on its axis. Thus, a standard video camera can capture images of the spinning sample without concern for synchronization that would be needed in the conventional centrifuge geometry. (24) Szabo, M. T. SPE-3038, 1974. (25) Oyno, L.; Torsaeter, O. Presented at the North Sea Chalk Symposium, 1990. (26) Chen, Q.; Balcom, B. J. SPE-100059, 2006. (27) Jia, F.; Zhou, K.; Yangtze, U.; Li, K SPE-99893, 2006.

Modified spinning disk combined with a visualization approach in centrifuge experiments were conducted for 24 disk-shaped rock samples. Table 1 shows properties of each sample. The modified spinning disk is different from the one used by Al-Omair.14 In this study, the produced fluid is collected at the edges of the rock rather than at the top of the rock. Parts A and B of Figure 2 show top and side views of the rock holder. The interface between wetting (mixed with dye) and nonwetting phases for samples was deduced using the image technique. This technique consists of recording and processing the video images of a rock sample and produced fluid at every spin rate. From these images, the local saturation at any location on the sample can be obtained at any time using a correlation that relates the gray level to saturation. Then, capillary pressure values are calculated at any position in the rock sample. Therefore, at any selected point on the top face of the rock sample, the capillary pressure relationship can be determined by the visualizing technique.9 Experiment Setup. The apparatus consists of a centrifuge, a modified rotor, a modified core holder for containing disk-shaped rock samples, and video and computer for data collection. The




centrifuge used in this research is modified Bekman J6B with a new rotor to carry the specially designed core holder and high spin rates. The modified core holder, shown in parts A and B of Figure 2, is made of a transparent plastic material (Lexan) to facilitate video recording of sample images and to hold disk-shaped rock samples. The core holder consists of a chamber that can carry out a rock sample up to 4 in. in diameter by 0.5 in. in thickness. Attached to the chamber, four cylindrical fluid collectors of the same size are placed evenly across the chamber. The fluid collectors are tilted upward with a small angel toward outer edges as shown in Figure 2B; in this way, the collected fluid can imbibe into the rock as the spin rate is reduced (spontaneous imbibition). Each fluid collector is graduated to accurately measure the fluid volume. These collectors are connected with each other by a groove at the bottom end to guarantee a uniform fluid level at any spin rate. The top cover of the centrifuge was re-assembled with a window at the center to allow for viewing the rock sample enclosed in the holder and to identify the fluid level in the collector. A video camera is

centered above the window and connected to a computer for processing the sample and collector images. The rock samples saturated with brine as the wetting phase and then span in the spinning disk. Air is used here as the nonwetting phase. Therefore, the air-water capillary pressure results are reported in the study. To validate the spinning disk capillary pressure relationships, a porous-plate apparatus was used to measure capillary pressure relationships for the same samples. A Ruska capillary pressure cell was used in this research to measure the capillary pressure for rock samples as shown in Figure 3. In this method, the rock sample is placed on a porous plate. At the start of an experiment, the sample and the porous plate are fully saturated with the wetting phase (28) Fleury, M.; Porbes, P. International Symposium of the Society of Core Analysis, 1995; paper 9534. (29) Forbes, P. International Symposium of the Society of Core Analysis, 1997; paper 9734. (30) Longeron, D.; Hammervold, W. L.; Skjaeveland, S. M. International Symposium of the Society of Core Analysis, 1994; paper 9426.


Al-Omair


(brine). Then, nonwetting (air) is forced into the rock, expelling the wetting liquid from the rock through the porous plate. The capillary pressure is indicated from the difference in pressure between the wetting and nonwetting phases. The Ruska capillary pressure cell is mainly made of plastic and metal components, permitting operation at pressure up to 100 psig. In this research, four cells were mounted on a stand. Each cell can accommodate a core specimen to 2.5 in. long, having a maximum cross-sectional dimension of 1.125 in. on the contact end. The inside diameter of the cell chamber is 1.625 in. The Ruska capillary pressure cell is composed of five main parts: the core chamber, the assembly block, the diaphragm assembly, the base, and the support stand. The porous disk is the most important part of the porous-plate apparatus, which is usually constructed of a ceramic material. If the pores of this disk are sufficiently small and if it saturated with the wetting fluid, it will remain impermeable to the nonwetting fluid for all pressures encountered during the test. The minimum pressure (31) Forbes, P. The Centrifuge Capillary Pressure Workshop at Society of Core Analysis Annual Technical Conference, 1993.

required to force nonwetting fluid into the disk is called the “threshold pressure” or “breakdown pressure” of the disk. The porous disk used in the porous-plate experiment usually has a relatively low permeability because of its small pores.

Results and Discussion A total of 24 core samples were tested using a spinning disk approach to measure capillary pressure relationships. Using this approach, both the fluid production and core sample were analyzed to develop a local saturation correlation for each sample. Then, the drainage and spontaneous imbibition capillary pressures were developed. After that, the capillary pressurewetting phase saturation relationships developed by the new approach were compared to those performed by the porousplate technique for the same rock samples. Finally, capillary pressure error analysis between this approach and the porousplate method was performed.


Energy & Fuels, Vol. 23, 2009 269 Table 2. Error Results Summary

entry pressure (psi)

capillary pressure relationship

irreducible brine saturation (Sbr) (%)

sample number

porous plate

current method

porous plate

current method

absolute error (psi)

relative error (%)

1B 3B 4B 5B 6B 10B 11B 12B 13B 14B 15B 16B 19B 20B 1D 2D 5D 6D 2L 5L 6L 8L 1R 5R

0 1.4 2 0.025 0.65 0.91 1.33 1.5 1.8 3.4 0.9 1.0 1.0 1.0 1.0 1.0 2.6 2.5 0.52 3.0 1.0 1.7 1.0 5.0

0 1.3 1.9 0.019 0.64 0.88 1.52 1.5 2.1 3.2 0.65 1.0 0.8 1.2 0.8 0.8 2.5 2.0 0.49 2.5 0.7 0.3 1.0 5.0

13 19 14 23 18 17.9 21.2 14 22 14 19 22 20 17.4 34.1 12 11.7 11.7 54.7 60 11 13 21 36

13.3 19.35 14.62 22 18 18.24 21 12.56 23 19.67 19.21 22.13 19.9 16.7 30.7 10.92 10.48 10.14 54 60.84 10.58 11.64 18.54 33

0.168 0.667 0.117 0.101 0.248 0.265 0.575 1.220 1.670 1.870 1.910 0.842 1.655 1.569 1.180 0.1625 0.6167 0.503 2.404 3.401 1.014 0.300 1.243 1.68

2.11 3.64 3.34 3.96 2.06 3.56 4.61 9.59 5.05 5.02 4.75 2.23 4.97 4.96 4.92 4.85 4.98 4.72 3.93 4.06 4.37 4.82 6.918 5.189

Fluid Production Measurement. The collectors were carefully machined to have constant dimensions (e.g., diameter and length) by titling the whole collection chamber upward and not only the base. As a result, the effect of the slope of the water interface at the inner side of the chamber will be offset by the one at the outer interface. Therefore, consideration of the slope in the calculation of the collected volume is not required. The volume of fluid produced at any time is calculated from the volume inside the fluid collectors. The following expressions were used to calculate the fluid volume in each collector: Vf ) Ac(Rco - Rci)

(1)

Ac ) rc2

(2)

where Vf and Ac are the volume of fluid and the cross-sectional area of the cylindrical fluid collector, respectively, Rco is the radius from the center of the spin to the outer face of the collector, Rci is the radius form the center of the spin to the level of the fluid inside the collector, and rc is the radius of the cylindrical fluid collector. The total volume of the produced fluid is calculated as follows: Vt ) nVf + Vd

(3)

where Vt is the total volume of produced fluid, n is the number of collectors (here, n ) 4), and Vd is the dead volume of fluid inside the groove, which is measured at the beginning of each experiment. At each spin rate, the produced volume of the wetting phase is recorded with time. When production stops, the spin rate is increased. This method is repeated until the difference between volumes produced is less than 1%. Figures 4, 5, and 6 show production profiles for samples 1B, 5B, and 2 L, respectively. The production profiles are used for local saturation determination as discussed below. The total volume produced from sample 1B is 17.8 cm3, which is about 85% of the pore volume. While the total volume produced from samples 5B and 2L are 16.9 and 4.6 cm3, respectively, which are equivalent to 76 and 46% of the pore volume. In the case of samples 1B and 5B, the final spin rates are reported as 3000 and 4000 rpm. However, it reached 10 000 rpm for sample 2L because of the low permeability and porosity.

In this case, safety consideration has been taken while operating the modified centrifuge at 10 000 rpm. Local Saturation Determination. One of the advantages of using the modified core holder is the possibility of developing a saturation profile. Thus, at any time, local saturation can be estimated. In this technique, the average gray levels of the images collected at each step in a centrifuge experiment are corrected directly with the average saturation in the sample. The important advantage of this method is that it uses the results of a centrifuge experiment to develop the local saturation correlation. Therefore, a separate effort to develop a correlation is not needed. At selected times, the images of the rock samples and the fluid collectors are analyzed to develop a local saturation expression. From the images of the core sample, the average gray level is determined using image software. While, from the images of the fluid collectors, the produced volume is calculated using eq 3. The average saturation of the wetting phase is calculated from the produced volume using the following equation: Sj )

Vp - Vt Vp

(4)

where Vp is the pore volume. As a result, for each selected image, two variables are reported: average gray level and average saturation. Then, these points are plotted (gray level versus average saturation) as shown in Figures 7-9. Therefore, for each sample, a saturation correlation is developed during the test. From this correlation, local saturations are calculated at any position in the rock samples. Adsorption of the dye on the solid surface could greatly complicate interpretation of the results. While it is likely that some of the dye is adsorbed, the depletion of the gray level from its maximum when the media is fully saturated toward the minimum of completely dry media indicates that adsorption was not an issue in these experiments. For applications with oils that are naturally colored, adsorption is probably a minor concern. Spinning Disk Drainage/Imbibition Capillary Pressure Relationship. The capillary pressure relationship for each


Al-Omair

Figure 20. Capillary pressure error analysis between the porous-plate method and the modified spinning disk approach using cross-plots.

sample was developed using the visualization method. At a given spin rate, an infinite number of points on the sample images can be analyzed to obtain this relationship. On each image, several points or cross-sectional areas are selected. From each selection, the local saturation is determined using saturation correlation developed during test and the radius from the center of the spin to the center of the selection is identified to calculate the capillary pressure. The capillary pressure can be calculated using the measured average distance from the center of the spin to the location of the local saturation measurement. The capillary pressure at any point in the sample can be calculated using the following equation: 1 (5) Pc(r) ) ∆Fω2(R2 - r2) 2 where, Pc is the capillary pressure (psia), ∆F is the fluid mass density difference (g/cm3), ω is the centrifuge angular velocity (rad/s), R is the radius of the sample (cm), and r is the radius at any point in the sample (cm).

The capillary pressure relationships at different spin rates for samples 1B, 5B, and 2L are shown in Figures 10, 11, and 12, respectively. Using this new approach, an infinite number of capillary pressure points can be measured. The figures show that the entry pressures for samples 1B, 5B, and 2L are 0, 0.019, and 0.49 psi, respectively. In addition, the irreducible brine saturations are 13.3, 22, and 54%, respectively. After reaching the final spin rate at which no more fluid is produced, the rate is reduced in steps and the produced fluid started to imbibe into the rock because fluid collectors are attached with the rock sample and tilted upward. At each step, the imbibition capillary pressure relationship is determined using the same process used for the drainage cycle. Figures 13-15 show drainage and imbibition capillary pressure curves for samples 1B, 5B, and 2L. The primary drainage and spontaneous imbibition curves constitute a closed hysteresis loop as observed for the samples. Porous-Plate Capillary Pressure Relationship. One of the main objectives for developing this approach is to develop a


convincingly accurate measurement of drainage and spontaneous imbibition capillary pressure curves. This accuracy is verified by comparing the spinning disk capillary pressure data to porousplate capillary pressure data for the same rock sample. Figures 16-19 provide examples of comparisons between spinning disk and porous plate. In practice, the difference appears to be small, even for low levels of capillary pressure. The comparison of the 24 core samples are shown in Figures 16-19. Capillary pressure error analyses show small differences in capillary pressure curves of porous plate and this approach. The relative error for most of the core samples is less the 5%, except for sample 12B (9.89%) and reservoir samples (5.2-7%), as shown in Table 2. All capillary pressure points obtained from the porous plate were compared to the same points obtained from the modified spinning disk approach. An irreducible brine saturation comparison indicated that 62.5% of the samples (15 samples) produced less than 5% error, 33% of the samples (8 samples) produced error between 5 and 13%, and one sample (14B) reached 40% error. Finally, cross-plots of porous-plate capillary pressure versus spinning disk capillary pressure are shown in Figure 20. Here, at given saturations, porous-plate capillary pressure is potted against the one obtained from the modified spinning disk approach. Most of the samples show reasonable agreements. Summary Interpreting centrifuge measurements, in terms of capillary pressure curves, requires a number of assumptions regarding core homogeneity and boundary conditions. In addition, accounting for the exact pressure field within the sample is an issue for reliable capillary pressure curve determinations. Therefore, techniques for capillary pressure measurement with fluids similar to reservoir fluids vary in accuracy. The centrifuge method is the most common method and is the main subject of this investigation. Many fundamental questions about centrifuge experiments need further clarification. These questions include the definition of boundary condition on both end faces of a cylindrical core plug, the gravity degradation effect at low speeds, the characterization of core sample heterogeneity, and the effect of radial centrifugal field distribution inside a core sample. On the basis of the literature review of capillary pressure measurement in the centrifuge, most of the researchers focused on improving the Hassler-Brunner technique for measuring capillary pressure. They addressed Hassler-Brunner’s assumptions and how to eliminate some of them. These assumptions are capillary pressure at the outlet face of the rock sample is zero; the heterogeneity of the core sample can be neglected; and the radial


character of the centrifugal field inside the rock sample is neglected. In this research, these assumptions were considered, except the assumption of rock homogeneity. A modified spinning disk approach for measuring capillary pressure saturation profiles has been used in this research. The new approach minimized the radial effects and allowed for the measurement of the wetting-phase saturation at any cross-section as a function of time. This novel approach has been used to generate the capillary pressure saturation profiles of 24 core samples with permeability varying from 9.8 to 24.5%. The 24 core samples span the three types of reservoir lithologyies: sandstone, dolomite, and limestone. Capillary pressure-wetting phase saturation profiles have been generated for the same rock samples using the porous-plate technique as well. Air and brine have been used with both experiments. Both drainage and imbibition cycles have been generated. Experiments using visualizing techniques show relatively good agreement between modified spinning disk and porousplate methods in terms of the value of threshold pressure and excellent agreement in term of shape of capillary pressure curve. Local saturation correlation can be developed easily during the experiment from the production and the sample images without additional effort. Measurements for the 24 rock samples tested using the modified spinning disk approach have been validated in this research with capillary pressure saturation profiles measured with the porous-plate technique. The relative error in capillary pressure data was less that 5% for most rock samples. Acknowledgment. This work was supported by Kuwait University, Research Grant EP 02/05.

Nomenclature Ac ) cross-sectional area of the cylindrical collector, cm2 Pc ) capillary pressure, psia r ) radius at any point in the sample, cm R ) radius of the sample, cm rc ) radius of the cylindrical fluid collector Rci ) radius from the center of the spin to the level of the fluid inside the collector, cm Rco ) radius from the center of the spin to the outer face of the collector, cm Sj ) wetting phase average saturation Vd ) dead volume of fluid inside the groove Vf ) volume of fluid, cm3 Vp ) pore volume Vt ) total volume of the produced fluid Greek Symbols ∆F ) fluid mass density difference, g/cm3 ω ) centrifuge angular velocity, rad/s EF800394V

New Experimental Approach for Measuring Drainage and

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