Energy Fuels 2010, 24, 1164–1169 Published on Web 01/29/2010
: DOI:10.1021/ef901118n
Oil Production by Spontaneous Imbibition from Sandstone and Chalk Cylindrical Cores with Two Ends Open Geoffrey Mason,† Herbert Fischer,† Norman R. Morrow,† Else Johannesen,‡ A˚smund Haugen,‡ Arne Graue,‡ and Martin A. Fernø*,‡ †
Chemical and Petroleum Engineering, University of Wyoming, Laramie, Wyoming 82071 and ‡Department of Physics and Technology, University of Bergen, Bergen, Norway Received October 2, 2009. Revised Manuscript Received January 5, 2010
During spontaneous counter-current imbibition of brine into oil-filled porous rock, it is generally assumed that the flow rates of the brine and oil are equal and in opposite directions. However, significant scatter and inconsistent dimensionless times were observed in experiments using matched-viscosity fluids in two ends open (TEO) sandstone cores using an established correlation factor. In further TEO experiments, the oil production at each end face was measured separately and ranged from being equal and symmetrical to highly asymmetrical, with almost all of the mobile oil being produced from one end in nominally duplicate tests. The dimensionless time for scaled imbibition increased with increasing asymmetry in oil production. Thus, for imbibition into cores with the TEO boundary condition, although the overall flows of brine and oil have to be equal, the individual flows at each end face are not necessarily equal and opposite. The asymmetry in oil production during imbibition with the TEO boundary condition was further investigated by imaging the in situ fluid saturations during imbibition, this time using homogeneous chalk and fluids with differing viscosities. In all cases, the amount of brine imbibed at each end face was almost equal even though there was sometimes significant asymmetry in the oil production. This behavior was probably caused by most of the capillary pressure driving imbibition being dissipated in the brine. With only small pressure differences required to produce the oil, any inhomogeneities in the rock which change the production capillary back pressure at the open faces can have a disproportionate effect on the symmetry of oil production.
imbibition data2 and results for a high permeability aluminum silicate.3 The various boundary conditions to which the scaling function has been applied are shown in Figure 1. The twoends-open (TEO) geometry is a special case because it allows the possibility of recording recovery by imbibition separately from each of the producing end faces and can therefore be used to test the theory behind the characteristic length in eq 1, which assumes equal invasion and production at each end face. Berea 500 rock samples (with nominal permeabilities of 500 mD) used to develop the correlation given by eq 2 were once readily available1,4,5 and commonly used as a sandstone reservoir analogue. The available Berea sandstone used in the present work has consistently lower permeability (usually in the range of 60 to 150 mD) and will hereafter be termed LP Berea. The LP Berea gives consistently longer dimensionless times during imbibition when compared to earlier imbibition results using the Berea 500 sandstone6 and a range of other rock types.7 The large difference between scaled results for LP
Introduction Spontaneous counter-current imbibition into rock cores with different boundary conditions progresses at significantly different rates. One approach to scaling this behavior is based on the characteristic length,1 Lc, which is given by !0:5 n X Ai ð1Þ Lc ¼ Vb = l i ¼1 Ai where Vb is the bulk volume of the core, Ai is the area open to imbibition at the ith direction, lAi is the length from the open surface to the no-flow boundary, and n is the number of surfaces open to imbibition. A more complete semiempirical scaling function involving other variables as well as the core sample shape is sffiffiffiffi 1 K σ ð2Þ tD ¼ 2 pffiffiffiffiffiffiffiffiffiffiffiffiffit Lc j μw μnw where K is the rock permeability, j its porosity, σ is the interfacial tension between the phases, μw and μnw are the viscosities of the wetting and nonwetting phases, Lc is defined in eq 1, and t is the imbibition time in seconds. The scaling function1 gave satisfactory correlation for available data including previously reported sandstone and alundum
(2) Mattax, C. C.; Kyte, J. R. SPE J. 1962, 2 (2), 177–184. (3) Hamon, G.; Vidal, J. European Petroleum Conference, London, U.K., October 20-22, 1986. (4) Zhang, X.; Morrow, N. R.; Ma, S. SPE Res. Eng. 1996, 11 (4), 280–285. (5) Ma, S.; Morrow, N. R.; Zhang, X. J. Can. Pet. Technol. 1999, 28, 25–30. (6) Tong, Z.; Xie, X.; Morrow, N. R. SPWLA Petrophys. J. 2002, 43, 332–340. (7) Viksund, B. G.; Morrow, N. R.; Ma, S.; Wang, W.; Graue, A. International Symposium of Society of Core Analysts, The Hague, Holland, September 14-16, 1998.
*To whom correspondence should be addressed. Telephone: 4755582792. E-mail:
[email protected]. (1) Ma, S.; Morrow, N. R.; Zhang, X. J. Pet. Sci. Eng. 1997, 18 (3-4), 165–178. r 2010 American Chemical Society
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Energy Fuels 2010, 24, 1164–1169
: DOI:10.1021/ef901118n
Mason et al. Table 1. Berea Sandstone Rock with Matched Viscosities and Fluid Properties
Figure 1. Counter-current imbibition in cores with different boundary conditions. lAi is the distance traveled by an imbibition front from the open surface to the no-flow boundary.1
core ID
kg [mD]
Φ [%]
σ
μw [cP]
μo [cP]
B4cP-1 B4cP-2 B1cP-1 B14cP-2 B21cP B22cP B44cP B59cP B80cP B99cP B140cP-1 B140cP-2 B172cP
77.3 66.4 72.0 69.9 74.6 75.8 76.9 57.1 77.3 70.0 77.4 66.6 71.0
16.4 16.7 17.0 15.7 16.6 17.0 16.9 16.6 16.6 16.8 17.3 15.5 17.3
40.1 39.0 35.3 36.2 34.6 33.9 33.5 32.4 31.1 30.5 30.0 31.3 30.3
4.0 4.3 13.7 14.3 21.2 22.5 43.5 59.3 80.2 99.7 140.0 141.5 171.2
4.0 4.0 13.1 14.0 21.4 21.9 43.8 59.1 80.1 99.1 141.7 140.6 171.2
Table 2. Mineral Composition for Synthetic Seawater and Chalk Brine mineral
synthetic seawater [g/L]
chalk brine [wt %]
NaCl KCl MgCl2 CaCl2 NaN3 TDS
28.00 0.94 5.36 1.19 0.10 35.59
5.0 3.8 0.1
with a focus on wettability changes, were recently reported.10 The current work investigates the observed scatter in TEO imbibition results when compared to results for the AFO, TEC, and OEO boundary conditions. Experimental Procedures General Outline. The experimental program fell into three parts. Part one compares TEO imbibition results in LP Berea using matched viscosity fluids with the correlated data8 for the TEC, AFO, and particularly the OEO boundary conditions. Part two investigates the production of oil from each end face using LP Berea sandstone cores with the TEO boundary condition. Part three measures the development of the water saturation profiles during TEO imbibition and investigates the effect of initial water saturation and viscosity using long Rørdal chalk core samples. Core Material, Porosity, and Permeability. LP Berea sandstone cores with a nominal diameter of 3.81 cm and nominal length of 6.35 cm were cut from a single block. The cores were rinsed, dried at ambient temperature for 1 day, and then ovendried at 105 °C for 2 days. Nitrogen gas permeability, kg, was measured in a biaxial core holder at a confining pressure of 300 psi. The permeability of the cores to nitrogen ranged from 57 to 77 mD. The cores were saturated with oil, and the porosity was calculated from the increase in mass after oil saturation. Porosities ranged from 15.5 to 17.3%. The LP Berea core properties are summarized in Table 1. Chalk cores plugs were cut from larger samples of Rørdal chalk. The cores were evacuated and saturated with either mineral oils with different viscosities (see Table 3) or chalk brine (1.05 g/cm3, 1.09 cP, see Table 2 for mineral composition). The porosity was obtained from weight difference before and after saturation, and permeability to brine was calculated from the flow rate and pressure drop, see Table 3. Preparation of Matched-Viscosity Fluids. Oil phase viscosity was controlled by preparing mixtures of the mineral oil Soltrol 220 (3.9 cP) and a 172 cP mineral oil. Polar contaminants were removed by contact with alumina and silica gel by flow through packed columns. Aqueous phase viscosities were varied by using
Figure 2. General correlation curve for LP Berea imbibition (bold) using the OEO boundary condition (and taking into account results for TEC and AFO geometries) and scaled TEO data8 with matched oil and water viscosities. Viscosities are indicated in core name. The majority of the TEO imbibition results exhibit longer dimensionless times than the correlated curve, except for tD < 10.
Berea and many other types of porous media is not fully understood but may be related to the effect of different pore size distributions on counter-current flow. Recent LP Berea imbibition data8 with matched aqueous and oil phase viscosities ranging from 4 to 171 cP demonstrated that the production curves differ slightly in shape for the one-end-open (OEO), the two-ends-closed (TEC), and all-faces-open (AFO) boundary conditions. A composite representative curve for the scaled OEO data is shown in Figure 2. Because the flow is linear, use of the OEO boundary condition gives the simplest example of counter-current imbibition to analyze. However, the smaller area open to imbibition tends to increase the scatter in results.9 According to eq 1, the characteristic length for TEO scales as if the process consisted of linear imbibition into two separate OEO cores with a length equal to half that of the TEO core. However, as will be seen, the two ends open data sometimes exhibits inconsistencies with dimensionless times often being longer than expected. Other TEO imbibition experiments, (8) Fischer, H.; Morrow, N. R. SPE ATCE, Dallas, TX, October 9-12, 2005. (9) Mason, G.; Fischer, H.; Morrow, N. R.; Ruth, D. W.; Wo, S. J. Pet. Sci. Eng. 2009, 66 (3-4), 83–97.
(10) Yu, L.; Evje, S.; Kleppe, H.; Karstad, T.; Fjelde, I.; Skjaeveland, S. M. J. Pet. Sci. Eng. 2009, 66 (3-4), 171–179.
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separately as a function of time for three LP Berea sandstone cores (see Table 4) in order to further investigate the variation in tD for TEO imbibition results. The total recoveryversus-time curves for all three cores were similar, but the amount of oil production from each end face turned out to be significantly different. Figure 3 shows results from nominally duplicate experiments where production from each side ranged from (i) equal and symmetrical, (ii) shifted to one side, and (iii) highly asymmetrical. The three distinctly different modes of oil production patterns given by only three duplicate tests was regarded as somewhat fortuitous. For linear imbibition into a uniform material, production is expected to vary as a square root of time and plots of recovery versus the square root of t should be straight lines. In all three cases, although oil production from each end showed different degrees of asymmetry, linearity was shown for about up to the first 90% of the production. Figure 4 shows the normalized total oil recovery as a function of tD (eq 2) for all three sandstone samples. It was observed that the core with equal production from each end face (S-equal) gave the lowest tD. The core with lop-sided production (S-shifted) was slightly shifted to the left with larger tD, whereas the core that gave the most asymmetric production (S-asym) had the highest tD. The asymmetric imbibition that was observed in these experiments was for the produced oil. Key questions were whether the brine imbibed symmetrically and what the distribution of fluids in the cores was. These questions could not be answered using short sandstone cores, and focus shifted to using longer chalk cores in which the spatial distribution of brine could be monitored. Measuring the Spatial Brine Saturation. Figure 5 shows the development in the water saturation profile during TEO imbibition into a long chalk core (C-0.8) with an oil/water viscosity ratio of 0.8. Core length is expressed in dimensionless length, XD = x/L. The initial water saturation of around 20% was uniformly distributed throughout the core at the start of imbibition. The water saturation increased almost symmetrical around the middle of the core, L/2, (the no-flow boundary based on the characteristic length) but slightly shifted toward higher XD. At the end of spontaneous imbibition, the water saturation was fairly uniformly distributed, with slightly higher water saturation close to the ends. Figure 6 shows the amount of water imbibed at each end face for core C-0.8, calculated from the water saturation profiles, and the volumetrically measured oil production from each end face as a function of time. The oil production was highly asymmetric (left side, 18 mL; right side, 53 mL) at the same time as equal amounts (35.5 mL) of water imbibed from each side. This discrepancy showed that imbibition was accompanied by a flow of oil across the so-called no-flow boundary at the center of the cross-section of the core. Effect of Viscosity Ratio on Imbibition Fronts. Figure 7 shows the development in water saturation profiles during the TEO imbibition test in two 100% oil-saturated chalk cores (C-8.8, left and C-15.6, right) with oil/water viscosity ratios of 8.8 and 15.6. The movement of water imbibing from each end face was symmetrical about the center of the core, although slightly shifted to the right. Increased oil/ water viscosity ratios contributed to steeper imbibition fronts and increased the time to attain a uniform saturation distribution. Figure 8 shows the amount of water entering each side of the core and the corresponding oil produced for each
Table 3. Chalk Rock and Fluid Properties core ID
K [mD]
Φ [%]
μw [cP]
μo [cP]
viscosity o/w
μgm [cP]
C-0.8 C-8.8 C-15.6
3.6 4.0 4.2
47 52 53
1.09 1.09 1.09
0.92 9.6 17.0
0.84 8.81 15.60
1.00 3.23 4.30
Table 4. Sandstone Rock and Fluid Properties core
kg [mD]
Φ [%]
σ
μw [cP]
μo [cP]
S-equal S-shifted S-asym
100.8 155.8 117.9
18.3 18.8 18.5
38.5 38.5 38.5
9.3 9.4 9.3
4.0 4.0 4.0
mixtures of glycerol and synthetic seawater8,11 (1.02 g/cm3, 1.10 cP, see Table 2 for mineral composition). A total of 15 tests were run with LP Berea sandstone using liquid viscosities that were matched to give viscosity ratios very close to unity. Boundary Conditions. The cylindrical surface area of the core plugs was sealed with epoxy resin to obtain the TEO boundary condition, and the characteristic length for each core was calculated using eq 1. Figure 1 illustrates the different boundary conditions used in laboratory imbibition experiments. The most complex flow condition given by AFO is the most commonly used condition. Measurement of Oil Production and Advancing Imbibition Fronts. Three chalk and three sandstone core plugs were 100% saturated with oil with different viscosities, see Tables 3 and 4, respectively. The sandstone cores were placed horizontally in brine, and the volumetric production of oil was measured separately from each end face. For the chalk, the water front advance was monitored using the Nuclear Tracer Imaging (NTI) method12 or the nuclear magnetic resonance (NMR) T2 gradient method.13 Three oil/water viscosity ratios were studied: 0.8, 8.8, and 15.6, which is reflected in the name of the core (C-0.8, C-8.8, and C-15.6). The 1D water saturation profile was measured continuously in the NTI flow rig14 during the imbibition in C-0.8. In the NMR gradient method, the cores (C-8.8 and C-15.6) were removed from the brine at selected time steps to measure 1D water saturation profiles along the length of the core. The development in average water saturation was obtained by integrating each profile at selected time steps during imbibition.
Results TEO Imbibition in LP Berea with Matched Viscosities. The results for TEO imbibition for a large range of matched viscosities (see Table 1) in LP Berea were compared to an average imbibition curve based on a large body of data for LP Berea, but particularly weighted toward the OEO boundary condition, because it also is linear imbibition (see Figure 2). The correlated imbibition curves for duplicate core plugs with the TEO boundary condition sometimes correlated with results for other boundary conditions but more usually exhibited larger dimensionless times than expected. In one instance (B4cP-1), the scaled imbibition time was shorter than the average curve. However, when this viscosity was repeated, the values of tD for the second test (B4cP-2) fell within the main body of the scattered TEO data (see Figure 2). Measurement of Oil Production from Each End Face. The production of oil from each end face was measured (11) Fischer, H.; Morrow, N. R. J. Pet. Sci. Eng. 2006, 52 (1-4), 35–53. (12) Graue, A.; Kolltveit, K.; Lien, J. R.; Skauge, A. SPE Form. Eval. 1990, 5 (4), 406–412. (13) Johannesen, E. B. Ph.D. Thesis, University of Bergen, Bergen, Norway, 2008. (14) Ramsdal, J. Can.Sient Thesis (in Norwegian), Bergen University, Bergen, Norway, 2000.
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Figure 3. Oil production from each end face during TEO spontaneous imbibition in sandstone cores for three nominally duplicate experiments: (i) core plug S-equal, almost equal production from each end; (ii) core plug S-shifted, significantly more production from end A than end B; (iii) core plug S-asym, highly asymmetric production with almost all the oil produced from end A. Total production was equal for all cores. The right column shows oil production vs square root of time.
Figure 4. Normalized correlation of TEO imbibition recovery curves in three nominally identical sandstone core plugs. The core with the greatest asymmetry in production imbibes the slowest.
Figure 5. The development of water saturation profiles versus time during TEO imbibition tests in a long chalk core (C-0.8). The imbibition fronts are almost symmetric around the middle of the core, L/2.
viscosity ratio. For a viscosity ratio of 8.8 (core plug C-8.8), the amount of brine imbibed and the amount of oil produced
from each end were closely matched. For the higher oil/water viscosity ratio of 15.6 (core plug C-15.6), the amount of brine 1167
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: DOI:10.1021/ef901118n
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Figure 6. TEO spontaneous imbibition results for chalk core plug C-0.8. Equal amounts of water imbibed at each open end face, but the corresponding oil production was highly asymmetric.
Figure 8. Water influx and oil production from each end face during TEO imbibition tests for oil/water viscosity ratios of 8.8 (upper, core C-8.8) and 15.6 (lower, core C-15.6). Equal volumes of water imbibed into each open end face in both cores, but the oil production was asymmetric for core C-15.6.
production was observed for both sandstone and chalk. This behavior does not seem to depend on the presence of initial water saturation because one of the chalk cores had initial water saturation whereas two of the chalk and all of the sandstone cores did not. In the experiments where the movement of water was monitored (chalk), the water imbibed relatively symmetrically even though the oil production was sometimes highly asymmetric. For the two viscosity ratios investigated using chalk, there is an indication that asymmetry may increase with viscosity ratio. However, asymmetry was also observed for nominally duplicate tests in sandstone cores. The time to reach maximum recovery increased with increased asymmetric oil production from each side. For three duplicate tests in sandstone cores, the time to reach maximum production varied between 115 h (symmetric production, core plug S-equal), 169 h (production shifted, core plug S-shift) to 217 h where the production was highly asymmetric (core plug S-asym). The pore space in a core is constant, and it can only be occupied by oil or water. It follows that any water that is imbibed displaces an equal volume of oil. The experiments show that, within the experimental error of the two techniques used, the rate of imbibition of water is equal at the two ends of the core. The experiments also show that in some cases there is clearly asymmetrical production of oil. For this to happen with equal water imbibition, some of the oil must flow between the two invasion fronts across the so-called no-flow boundary at the middle of the core. In some cases then between each front and its open face neither side corresponds
Figure 7. The development of water saturation profiles versus time (hours) during TEO imbibition tests in two long chalk cores with oil/ water viscosity ratios of 8.8 (upper) and 15.6 (lower). Increased oil viscosity in core C-15.6 produced slightly steeper water profiles during imbibition.
imbibed into each end remained equal. However, the production of oil was asymmetric. Discussion The TEO imbibition curves, even for the matched viscosity results, presented in Figure 2 did not scale satisfactorily. Although the decrease in the characteristic length from OEO to TEO predicts a 4-fold increase in imbibition rate, the bulk of the data indicated that the rate was only about doubled. When the oil production from the open end faces was monitored separately, asymmetric oil production was observed on some but not all occasions. Asymmetric oil 1168
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to pure counter-current flow; there is a net outward flow of oil on one side of the core and a net inward flow of water at the opposite side. Between the invasion fronts, in the central oil-filled part of the core, the relative permeability to oil will be very high, allowing oil, particularly if its viscosity is low, to flow without much differential pressure. Furthermore, as the two fronts approach each other, the distance oil has to travel between the two fronts decreases and this reduces the pressure required even further. The expectation is that initially imbibition will be purely counter-current and then progressively deviates from equal invasion and production at each end of the core. This idea is consistent with the results shown in Figure 3. When these results are plotted against time squared (see Figure 3, right column), the rates of production from each end of the core start symmetrically and it is only after imbibition has progressed some way that oil production becomes asymmetric. Behind each imbibition front, there is partial saturation of both phases and the relative permeabilities to each phase will be significantly less than unity. In all of the reported experiments, the oil/water viscosity ratio ranged from 1 to about 15. Because the path lengths for both fronts are the same, it is primarily the magnitudes of the relative permeabilities that decide the pressure drop within each phase. Since the measured water influx in chalk was symmetric, the implication is that most of the pressure drop occurs in the water phase and, consequently, behind the front. The relative permeability to water has to be much lower than the relative permeability to oil, a conclusion similar to that of Nguyen et al.15 If there is very little pressure drop actually driving the flow of the nonwetting phase, then the pressure in the nonwetting phase at the fronts is predominantly set by the capillary back pressures at the two open faces. These two capillary back pressures are the pressures required to force oil out of the open faces of the core and into the brine and they will depend on the largest pore sizes at the open faces. The capillary back pressure can be significant and was estimated to be about a fifth of the
capillary pressure driving imbibition. Any inhomogeneity in the rock, such as a small gradation in permeability, will give, because pore size is related to permeability, a small difference in capillary back pressure between the ends of the core. Even subtle differences in the pore sizes that control oil production from the end faces will have the same effect. This difference in the capillary back pressures would be a relatively small percentage of the full capillary back pressure. However, it could be a significant percentage of the pressure difference required to drive the flow of oil and this would account for the significant asymmetric production of oil. If most of the capillary pressure driving imbibition is dissipated in driving the water flow, then the water flows would be less affected by the small differences in oil pressure caused by the different capillary back pressures and therefore the advance of the water fronts would be expected to be symmetrical. It is concluded that, for all experiments conducted so far, the rate of imbibition of the brine is the ratelimiting step because it consumes almost all of the capillary driving pressure at the front. Only a small pressure is required to drive the oil out of the cores, and this means that small nonuniformities in the core properties can have a disproportionate effect.
(15) Nguyen, V. H.; Sheppard, A. P.; Knackstedt, M. A.; Pinczewski, W. V. J. Pet Sci. Eng. 2006, 52 (1-4), 54–70.
(16) Li, Y.; Ruth, D.; Mason, G.; Morrow, N. R. J. Pet. Sci. Eng. 2006, 52 (1-4), 87–99.
Conclusions During spontaneous imbibition into oil-filled cores with two ends open boundary condition, the oil production measured from each core end can be significantly different. The asymmetric production of oil does not depend on rock type or the presence or absence of initial water saturation for the conditions investigated in this work. The brine imbibed evenly from each end even though the production of oil is often asymmetric. This could be related to a much lower relative permeability to brine compared to the relative permeability to oil behind the invasion front. Increase in oil/water viscosity ratios above unity appears to dampen the asymmetry in oil production, but it slows the imbibition process dramatically.
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