SPE Effect of Initial Water Saturation on Spontaneous Water Imbibition Kewen Li, SPE, Kevin Chow, and Roland N. Horne, SPE, Stanford University

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1 SPE 7677 Effect of Initial Water Saturation on Spontaneous Water Imbibition Keen Li, SPE, Kevin Cho, and Roland N. Horne, SPE, Stanford University Copyright, Society of Petroleum Engineers Inc. This paper as prepared for presentation at the SPE Western Regional/AAPG Pacific Section Joint Meeting held in Anchorage, Alaska, U.S.A., May. This paper as selected for presentation by an SPE Program Committee folloing revie of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been revieed by the Society of Petroleum Engineers and are subject to 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 SPE meetings are subject to publication revie by Editorial Committees of the Society of Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes ithout the ritten consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 3 ords; illustrations may not be copied. The abstract must contain conspicuous acknoledgment of here and by hom the paper as presented. Write Librarian, SPE, P.O. Box , Richardson, TX , U.S.A., fax Abstract The effect of initial ater saturation on gas recovery by cocurrent spontaneous ater imbibition and imbibition rate as investigated both theoretically and experimentally. Equations correlating initial ater saturation, gas recovery, imbibition rate, rock/fluid properties, and imbibition time ere derived and used to conduct the theoretical analysis. These equations foresee that gas recovery and imbibition rate could increase, remain unchanged, or decrease ith increase in initial ater saturation, depending on rock properties, the quantity of residual gas saturation, the range of initial ater saturation, and the units used in the definitions of gas recovery and imbibition rate. The theoretical predictions ere verified experimentally by conducting spontaneous ater imbibition at five different initial ater saturations, ranging from to about 5%. Water phase relative permeabilities and capillary pressures ere calculated using the experimental data of spontaneous imbibition. The effects of initial ater saturation on residual gas saturation, ater phase relative permeability, and capillary pressure ere also studied experimentally. The results in different rocks ere compared. It as found that the residual gas saturation by spontaneous imbibition in a fired Berea sandstone sample (clay as removed by firing) as loer than in a natural Berea sandstone sample (clay as not removed). This demonstrates significant ettability alteration caused by firing. In other ords, there may be significant ettability differences among different gas-liquid-rock systems. Introduction Spontaneous ater imbibition is an important mechanism during ater injection. Prediction of recovery and imbibition rate by spontaneous ater imbibition is essential to evaluate the feasibility and the performance of ater injection. For example, is ater injection effective in the case of high initial ater saturation in reservoirs? Ansers to such a question may be found by investigating the effect of initial ater saturation on spontaneous ater imbibition. It has been observed experimentally that initial ater saturation affects recovery and production rate significantly 1-7. Hoever the experimental observations from different authors 1-7 are not consistent. On the other hand, fe studies have investigated the effect of initial ater saturation on recovery and imbibition rate theoretically, especially in gas reservoirs. Using numerical simulation techniques, Blair 1 found that the quantity and the rate of oil produced after a given period of imbibition increased ith decrease in initial ater saturation for countercurrent spontaneous imbibition. Zhou et al. studied the interrelationship of ettability, initial ater saturation, and oil recovery by countercurrent spontaneous imbibition and aterflooding in oil-ater-rock (Berea sandstone) systems. The porosity of the 41 core samples ranged from.5 to.6% and the permeability from 194 to 394 md. Experiments ere conducted at three values of initial ater saturation, around 15,, and 5% respectively. Zhou et al. found that both imbibition rate and final oil recovery in terms of oil originally in place (OOIP) increased ith increase in initial ater saturation, hereas oil recovery by aterflooding decreased. Viksund et al. 3, ho conducted 51 countercurrent spontaneous imbibition tests in different rocks ith a ide range of porosity and permeability in oil-ater-rock systems, found that the final oil recovery (OOIP) by spontaneous ater imbibition in Berea sandstone shoed little variation ith change in initial ater saturation from to about 3%. The variation in final oil recovery obtained by Zhou et al. in Berea sandstone as great, as a comparison. Viksund et al. 3 reported that the final oil recovery (OOIP) by spontaneous imbibition in chalk shoed significant variation and decreased systematically ith increase in initial ater saturation ranging from to about 51%. The imbibition rate in Berea sandstone decreased ith increase in initial ater saturation from to 6%, reaching a minimum for the range 6 to 15%, and then increased ith increase in initial ater saturation from 15 to 3%. For the chalk samples tested by Viksund et al. 3, the imbibition rate first increased ith increase in initial ater saturation and then decreased slightly as initial ater

2 Keen Li, Kevin Cho, and Roland N. Horne 7677 saturation increased above 34%. The experimental observations ere quite complicated and even opposite in different rocks. Viksund et al. 3 speculated that the observed tendency might be attributed to the net effect of initial ater saturation and subsequent ater saturation history on imbibition capillary pressure and resistance to flo of oil and ater. Cil et al. 4 reported that the oil recovery (in terms of recoverable oil reserve) for zero and % initial ater saturation shoed insignificant differences in behavior. Hoever, the oil recovery for initial ater saturation above % increased ith increase in initial ater saturation. The countercurrent spontaneous imbibition experiments ere conducted in Berea sandstone. Tong et al. 5, ho also studied the effect of initial ater saturation on oil recovery in Berea sandstone ith air permeability ranged from 8 to 1 md, found that imbibition (countercurrent) rate as very sensitive to initial ater saturation. After scaling, the oil recovery (OOIP) at a specific imbibition time increased ith increase in initial ater saturation for the range from 1 to 8.%. Before scaling, the oil recovery did not vary systematically ith initial ater saturation. Li and Firoozabadi 6 performed spontaneous ater and oil imbibition (cocurrent) in gas-saturated rocks (Berea sandstone) at different initial ater saturations. The final gas recovery in the units of gas originally in place (GOIP) by spontaneous imbibition decreased ith increase in initial ater saturation in both gas-oil-rock and gas-ater-rock systems. The imbibition rate (GOIP/minute) increased ith increase in initial ater saturation at early time but decreased at later time. Li and Firoozabadi 6 also found that gas recovery by both spontaneous oil and ater imbibition in chalk as greater than that in Berea. Akin et al. 7, ho carried out spontaneous ater imbibition (cocurrent) in diatomite ith and ithout initial ater saturation, found that the oil recovery in the units of fraction of pore volume in diatomite ithout initial ater saturation as greater than that ith initial ater saturation (close to about 6%). The residual oil saturation as unaffected significantly by initial ater saturation. In this study, equations, derived theoretically, ere used to study the effect of initial ater saturation on gas recovery and imbibition rate. The equations correlate recovery, imbibition rate, initial ater saturation, rock/fluid properties, and other parameters, hich predict significant effect of initial ater saturation on recovery and imbibition rate in some cases but not in other cases. Experiments of spontaneous ater imbibition in gas-saturated rocks ere conducted to confirm the theoretical predictions. The initial ater saturation ranged from to about 5%. The effect of rock properties on gas recovery and imbibition rate as also studied. An X-ray CT scanner as used to monitor the distribution of the initial ater saturation to confirm that the initial distribution of the ater saturation as uniform. The experimental results ere compared to the data published in the literature. Mathematics Li and Horne 8 derived an equation to scale cocurrent spontaneous imbibition data in gas-liquid-rock systems based on a model developed previously 9. This equation constitutes the relationship beteen the normalized recovery, R *, by spontaneous imbibition and the dimensionless time, t d, ith initial ater saturation, relative permeability, capillary pressure, and gravity included. Using this equation, the effect of initial ater saturation on imbibition rate as investigated analytically in this section. The equation is expressed as follos: * R * ) td ( 1 R e = e (1) here the normalized recovery R * is calculated: * R = cr Here R is the gas recovery in terms of pore volume and is equal to N t /V p ( N t is the cumulative volume of ater imbibed into rocks and V p is the pore volume). c is a coefficient associated ith the ratio of the gravity force to the capillary force, c=b/a. The to constants, a and b, are calculated using the folloing expressions 9 : () Ak( Sf Si ) a = Pc (3) µ L Ak b = ρg µ (4) here A and L are the cross-section area and the length of the core respectively. µ is the viscosity of ater, the initial ater saturation, S f the ater saturation behind the imbibition front, k the effective permeability of ater phase at S f, P c the capillary pressure at S f ; ρ is the density difference beteen ater and gas, and g is the gravity constant. The dimensionless time t d is formulated as follos 8 : t kk P Sf S r c = c φ µ L d a i here k is the absolute permeability and k r the relative permeability of the core sample. L a is the characteristic length, hich is equal to the core length in our case, and t is the imbibition time. Li and Horne 8 pointed out that Eq. 1 could be reduced in some cases. For example, Eq. 1 can be reduced as follos hen gravity force is neglected: t (5)

3 7677 Effects of Initial Water Saturation on Spontaneous Water Imbibition 3 * ( R ) = t d (6) Eq. 6 can be deduced as follos using Eqs. 3, 4, and 5: coefficient first changes little ith initial ater saturation for less than a specific value (about 3% hen S gr is equal to 4%) and then decreases ith increase in initial ater saturation for greater (see Fig. 1). The final gas recovery by spontaneous imbibition in the units of GOIP, represented by R, is calculated as follos: N Pc kφ ( Sf Si A = t (7) µ ) t R 1 Si S = 1 S i gr (9) Note that Eq. 7 can be reduced to the Handy 1 equation hen the effect of initial ater saturation is not included. For convenience, Eq. 7, the reduced form of Eq. 1, as used in this study to analyze the effect of initial ater saturation on recovery (R) and imbibition rate, even though gravity force may not be neglected in some cases. Note that the same analysis could be made using Eq. 1 but it is more difficult to do so. According to Eq. 7, the gas recovery in the units of pore volume (or the amount of ater imbibed into rock) increases ith decrease in initial ater saturation, as long as S f, k, and P c do not vary ith initial ater saturation. Li and Horne 8 confirmed experimentally that there as little effect of initial ater saturation on S f, k, and P c in gas-liquid-rock (Berea sandstone) systems. This ill also be further proved in this paper and ill be discussed later in more detail. Considering that S f is closely equal to 1-S gr for spontaneous imbibition in gas-saturated rock, the gas recovery in the units of GOIP, defined as R GOIP = N t /(1- )V p, can be expressed as follos based on Eq. 7: We can see from Eq. 9 that the final gas recovery by spontaneous imbibition in the units of GOIP decreases ith increase in initial ater saturation if the residual gas saturation does not change ith initial ater saturation, hich is true in some cases 8. Imbibition rate q, defined as dn t /dt, can be obtained from Eq. 7: dn S S t f i Pc kφ q = = A t dt µ 1 (1) We can see from Eq. 1 that imbibition rate (in the units of ml/minute) increases ith decrease in initial ater saturation at the same imbibition time if S f, k, and P c are constant at different initial ater saturations, hich as already demonstrated experimentally by Li and Horne 8. Imbibition rate can also be expressed in a different ay, for example, in the units of fraction of GOIP/minute: R GOIP 1 Si Sgr Pc k = t (8) 1 S µ φl i 1 q GOIP 1 1 Si Sgr P ckφ 1 Si µ φl = t (11) The effect of initial ater saturation on the gas recovery in the 1 Si Sgr units of GOIP depends on, hich is referred 1 Si to as the saturation coefficient. The saturation coefficient may increase, decrease or even not change ith initial ater saturation, hich depends on the values of residual gas saturation and initial ater saturation. This ill be explained graphically in more detail. Fig. 1 shos the effect of initial ater saturation on the saturation coefficient at different values of residual gas saturation ranging from 1 to 5%. For residual gas saturation less than 3%, the saturation coefficient increases ith increase in initial ater saturation. So does the gas recovery in the units of GOIP. For residual gas saturation near 3%, the saturation coefficient varies very little ith initial ater saturation, hich implies that there is little effect of initial ater saturation on R GOIP. For residual gas saturation greater than 3%, the effect of initial ater saturation on the saturation coefficient is complicated. The saturation here q GOIP is the imbibition rate in the units of fraction of GOIP/minute, defined as dr GOIP /dt. Referring to Fig. 1 and Eq. 11, e can see that imbibition rate in the units of fraction of GOIP/minute can increase, stay constant, and decrease ith increase in initial ater saturation. Note that imbibition rate in the units of ml/minute alays increases ith decrease in initial ater saturation, as foreseen in Eq. 1. Eqs. 8 and 11 demonstrate that the effect of initial ater saturation on R GOIP and q GOIP may be different in different ranges of initial ater saturation and in different rocks in hich S gr may be different. This may be hy experimental observations from different researchers seem to be inconsistent. Similar analysis to the effect of initial ater saturation on gas recovery and imbibition rate can be made if units other than those discussed here are used. Note that Eq. 1 as derived from the folloing equation by Li and Horne 8 :

4 4 Keen Li, Kevin Cho, and Roland N. Horne 7677 dn t 1 q = = a b dt R (1) Using Eq. 1, the effective or relative permeability of the ater phase and the capillary pressure can be calculated simultaneously 8. The theoretical predictions regarding the effect of initial ater saturation on gas recovery (in the units of either pore volume or GOIP) and imbibition rate ill be compared to the experimental results and discussed later in more detail. Experiments Air as used as the gas phase and distilled ater as the liquid phase in this study. The natural Berea sandstone sample (clay as not removed by firing) had an air permeability of around 84 md and a porosity of about 1.%; its length and diameter ere 9.96 cm and 4.98 cm. The results from this core ere compared to the data obtained previously 8 from another Berea sandstone sample fired at a temperature of 6 o C to remove the clay. The fired Berea sandstone sample had a permeability of around 1 md and a porosity of about 4.5%; its length and diameter ere 43.5 cm and 5.6 cm. A schematic of the apparatus, similar to that used by Li and Horne 8, is shon in Fig.. The core sample as hung under a Mettler balance (Model PE 16), hich had an accuracy of 1g and a range from to 16 g. The ater imbibed into the core sample as recorded in time by the balance using an under-eighing method and the real-time data ere measured continuously by a computer through an RS-3 interface. Care as taken to keep the core vertical. Hoever, a bubble covered up part of the bottom surface of the core. The system as left standing for about three hours. The final ater saturation by spontaneous ater imbibition as measured by eighing after the imbibition test and as used to calibrate the initial experimental data. A modification to the imbibition test apparatus as made to remove the bubble. A stainless steel tubing ith an outside diameter of 1/8 inch as taped vertically to the side of the core; the end of the tubing as bent to the core bottom surface. Therefore, any air pockets could leave the inverted cup-like enclosure through the tubing. This modification as implemented at different initial ater saturations. There ere no bubbles trapped at the bottom of the core during the experiments ith this modification. The initial ater saturation in the core as established using the air injection method. The core as kept horizontal to attempt to lessen the effect of gravity on the ater distribution. The pressure used for air injection ranged from 3 to 7 psig, depending on the level of saturation and ho quickly the core appeared to dry. The air as injected from either outlet or inlet, sitching back and forth every 5 minutes or so. Care as also taken to inject the same air pressure at both ends of the core for maximum uniformity. The distribution of initial ater saturation as monitored using an X-ray CT method, hich ill be presented in the next section. The experimental procedure as similar to that used by Li and Horne. 8 Results Experiments ere conducted at five different initial ater saturations,, 4, 35, 43, and 5%. The results and the analysis are described in this section. Distribution of initial ater saturation. It is important to have initial ater saturation distributed uniformly. The X-ray CT method as used to measure the distribution of porosity and the ater saturation in the core. Fig. 3 shos the distribution of CT values of the core hen it as dry, et (saturated ith ater completely), and after initial ater saturation as established (one example). CT dry in this figure represents the CT value of the core hen the sample is airsaturated; CT et represents the CT value of the core hen saturated ith ater completely and CT obj the CT value after initial ater saturation as established. Porosity and ater saturation at different positions in the core ere calculated using the CT values 11. The distribution of porosity and the initial ater saturation in the core are plotted in Fig. 4. It can be seen that this core, ith uniform distribution of initial ater saturation, as sufficiently homogeneous to be used to conduct ater imbibition tests. Effect of on gas recovery. The relationship beteen the gas recovery in the units of pore volume and the imbibition time is shon in Fig. 5 for five different values of :, 4, 35, 43, and 5%. Fig. 5 shos that the gas recovery in the units of pore volume increased ith decrease in at the same imbibition time above about one minute, hich is consistent ith the theoretical prediction made previously (see Eq. 7). If gas recovery is defined using different units (for example, in terms of pore volume and GOIP), the relationship beteen the gas recovery and the initial ater saturation can be different according to the theoretical analysis (see Eqs. 7 and 8). This phenomenon is demonstrated in Fig. 6 (also refer to Fig. 5). R GOIP increased ith increase in at the same imbibition time but not very significantly for from to about 3% and then decreased significantly for above about 4%. This experimental observation is remarkably consistent ith the theoretical prediction made previously (see Eq. 8 and Fig. 1; the residual gas saturation of the core as about 4%). Viksund et al. 3 also observed experimentally that the effect of on R GOIP as different in different ranges of for spontaneous ater imbibition in oil-saturated chalk and Berea sandstone. The effect of on the final gas recovery is shon in Fig. 7. We can see that the final gas recovery (GOIP) decreased ith increase in. This is consistent ith the theoretical analysis (see Eq. 9) and the observations by other authors 6,7. Also shon in Fig. 7 is the final gas recovery measured by Li and Horne 8 in a fired Berea sample. The final gas recovery (GOIP) also decreased ith increase in in the fired core but

5 7677 Effects of Initial Water Saturation on Spontaneous Water Imbibition 5 as significantly greater than that in the natural Berea sandstone. Only to parameters, permeability and ettability, are likely to have been altered significantly by firing. It is knon that gas recovery by spontaneous imbibition is not directly proportional to permeability. Therefore, the enhanced gas recovery in the fired Berea sandstone may demonstrate significant ettability alteration caused by firing in gas-liquid- Berea sandstone systems. In other ords, there may be significant differences beteen ettability properties of different gas-liquid-rock systems. This is interesting because it has been assumed for long time in the petroleum industry that the contact angle through the liquid phase is zero in gas-liquidrock systems, hich implies no significant differences beteen ettability properties of different gas-liquid-rock systems. Ho to determine the ettability in gas-liquid-rock systems is another important challenge. Li and Horne 1 discussed this in more detail. Effect of on residual gas saturation. Fig. 8 shos that the residual gas saturation by spontaneous ater imbibition is unaffected by initial ater saturation. This is consistent ith our previous observation in a fired Berea sandstone sample 8, hich is also plotted in Fig. 8. We can see from this figure that the residual gas saturation in the fired Berea sandstone is less than in the natural Berea sandstone. This may also be attributed to the ettability alteration by firing the rock, as analyzed previously for the effect of on the final gas recovery. Effect of on imbibition rate. The imbibition rate in the units of ml/minute decreased ith increase in at the same imbibition time, as shon in Fig. 9. This is also consistent ith our theoretical prediction (see Eq. 1). The effect of the initial ater saturation on the imbibition rate in the units of GOIP/minute is demonstrated in Fig. 1. For the data obtained before the imbibition front reached the top of the core, q GOIP changed very little ith increase in at the same imbibition time for from to about 3% and then decreased for above about 4% (see Fig. 1). The experimental observation is also remarkably consistent ith our theoretical prediction (see Eq. 11 and Fig. 1, referring to the curve ith the residual gas saturation of 4%). Note that Eq. 1 is appropriate for the data obtained before the imbibition front reached the top of the core. For the data obtained after the imbibition front reached the top of the core, q GOIP decreased ith increase in for all the values of studied. Effect of on relative permeability. Previously e reported that effective or relative permeability of the ater phase could be inferred from cocurrent spontaneous imbibition 8. The experimental data, in the form of imbibition rate versus the reciprocal of gas recovery in the units of pore volume, are plotted in Fig. 11. The relationships beteen imbibition rate and the reciprocal of gas recovery are satisfactorily linear at all the initial ater saturations studied, as foreseen by Eq. 1. Another interesting phenomenon observed in Fig. 11 is that all the straight lines do not go through the origin point, hich implies that the gravity force may not be neglected in the core ith a liquid permeability of about 5 md. The effective permeabilities of the ater phase calculated using Eq. 1 along ith Eq. 4 are almost unaffected by initial ater saturation, as shon in Fig. 1. Also shon in this figure are the effective permeabilities of the ater phase computed by Li and Horne 8 in a fired Berea sandstone core. Fig. 1 shos that there is little difference in the ater effective permeabilities beteen the natural and the fired Berea sandstone samples. Hoever the relative permeabilities of the ater phase are different, as shon in Fig. 13. The ater relative permeabilities in the fired Berea are less than in the natural Berea (this study), hich shos qualitatively that the rock ettability might be altered to more ater-et by firing. Effect of on capillary pressure. The capillary pressures at S f calculated using Eq. 1 along ith Eqs. 3 and 4 are shon in Fig. 14. The effect of initial ater saturation on capillary pressure is almost neglected, hich is consistent ith our previous observation in a fired Berea sample 8 (see Fig. 14). The capillary pressure in the fired Berea sandstone is greater than in the natural Berea core, hich may also demonstrate qualitatively that the rock ettability might be altered to more ater-et by firing. Gas recovery in different rocks. The experimental data of the final gas recovery in the units of GOIP by spontaneous imbibition in four different rocks, natural Berea, fired Berea, chalk, and grayacke are plotted in Fig. 15. R GOIP increases in the sequence of natural Berea, fired Berea, chalk, and grayacke. We can see from this figure that there is no correlation beteen R GOIP and permeability, as expected. Imbibition rates in different rocks. Fig. 16 shos the experimental data of imbibition rate (ml/minute) in four different rocks, natural Berea, fired Berea, chalk, and grayacke for the first 4 minutes. Apparently the imbibition rate increases ith increase in rock permeability. Although the ettability in different rocks may be different, the effect of permeability on imbibition rate seems to be dominated. Discussion The theoretical analysis in this study as based on Eq. 7, hich as derived by assuming that the cocurrent spontaneous imbibition in gas-saturated rock ould be a piston-like process. Another assumption as that the gas phase mobility as infinite, compared to the liquid phase. In such a simple case, the effect of initial ater saturation on gas recovery and imbibition rate is complicated according to the theoretical calculations and the experimental observations. In oil-aterrock systems, neither oil phase nor ater phase mobility can be infinite. Therefore the theoretical models governing spontaneous imbibition ill be more complicated than Eq. 7. The effect of initial ater saturation on oil recovery and

6 6 Keen Li, Kevin Cho, and Roland N. Horne 7677 imbibition rate in oil-ater-rock systems ould be very complicated, as has been already observed 1-5. Hoever, the tendency may be similar. The inconsistent experimental observations in different rock-fluid systems or from different researchers may be the representation of fluid flo mechanisms that govern the spontaneous imbibition in porous media. It is difficult to establish initial ater saturation ith uniform distribution at lo values. This is hy the experimental results at lo initial ater saturations ere absent in this study. It ill be interesting to have these data fulfilled and further confirm the theoretical predictions at lo initial ater saturations. There are many parameters that affect spontaneous imbibition. It is also interesting to identify hich parameter is the dominant one in a specific case. For example, permeability may be the dominant parameter to influence imbibition rate and ettability may be the dominant parameter to influence residual gas saturation. Initial ater saturation along ith ettability may be the major parameters that determine the final recovery. Conclusions Based on the present study, the folloing conclusions may be dran: 1. The gas recovery in the units of pore volume and the imbibition rate in the units of ml/minute decreased ith increase in initial ater saturation.. The gas recovery in the units of GOIP and the imbibition rate in the units of GOIP/minute increased slightly ith increase in initial ater saturation ranging from to about 3% but decreased for initial ater saturation above. 3. The final gas recovery decreased but the residual gas saturation as unchanged ith increase in initial ater saturation. The final gas recovery in the fired Berea sandstone as greater than in the natural Berea sandstone. Accordingly, the residual gas saturation in the fired Berea sandstone as less. 4. The ater phase relative permeability in the fired Berea as less than that in the natural Berea hile the capillary pressure in the fired Berea as greater than in the natural Berea. 5. There as little effect of initial ater saturation on residual gas saturation, ater phase relative permeability, and capillary pressure at S f. 6. The imbibition rate increased ith increase in permeability. The final gas recovery in different rocks as different and not correlated to permeability as expected. In general, most of the experimental observations are consistent ith our theoretical predictions. Acknoledgements This research as conducted ith financial support to the Stanford Geothermal Program from the Geothermal and Wind division of the US Department of Energy under grant DE- FG7-99ID13763, the contribution of hich is gratefully acknoledged. Nomenclature a = coefficient associated ith capillary forces, m/t A = cross-section area of the core, L b = coefficient associated ith gravity, m/t c = ratio of the gravity force to the capillary force g = gravity constant, L/t k = rock permeability, L k = effective permeability of ater, L k r = relative permeability of ater L = core length, L L a = characteristic length, L N t = volume of ater imbibed into the core, L 3 P c = capillary pressure, m/lt q = ater imbibition rate in the units of ml/minute, L 3 /t q GOIP = ater imbibition rate in the units of GOIP/minute, 1/t R = recovery by spontaneous ater imbibition in the units of fraction of pore volume R GOIP = gas recovery in the units of GOIP R = final gas recovery in the units of GOIP R * = normalized gas recovery S gr = residual gas saturation S f = ater saturation behind imbibition front = initial ater saturation t = imbibition time, t t d = dimensionless time V p = pore volume of the core sample, L 3 ρ = density difference beteen ater and gas, m/l 3 µ = viscosity of ater, m/lt φ = porosity References 1. Blair, P.M.: Calculation of Oil Displacement by Countercurrent Water Imbibition, SPEJ (September 1964), Zhou, X., Morro, N.R., and Ma, S.: "Interrelationship of Wettability, Initial Water Saturation, Aging Time, and Oil Recovery By Spontaneous Imbibition And Waterflooding," SPEJ (June ), 5 (), Viksund, B.G., Morro, N.R., Ma, S., Wang, W. and Graue, A.: Initial Water Saturation and Oil Recovery from Chalk and Sandstone by Spontaneous Imbibition, Proceedings of 1998 International Symposium of the Society of Core Analysts, The Hague, Netherlands, Sept Cil, M., Reis, J.C., Miller, M.A., and Misra, D.: An Examination of Countercurrent Capillary Imbibition Recovery from Single Matrix Blocks and Recovery Predictions by Analytical Matrix/Fracture Transfer Functions, paper SPE 495, presented at the 1998 SPE Annual Technical Conference and Exhibition, Ne Orleans, Louisiana, September 7-3, Tong, Z., Xie, X., and Morro, N. R.: "Scaling of Viscosity Ratio for Oil Recovery by Imbibition from Mixed-Wet Rocks," paper SCA 1-1, proceedings of the International Symposium of the Society of Core Analysts, Edinburgh, UK, September 17-19, 1.

7 7677 Effects of Initial Water Saturation on Spontaneous Water Imbibition 7 6. Li, K. and Firoozabadi, A.: Experimental Study of Wettability Alteration to Preferential Gas-Wetness in Porous Media and its Effect, SPEREE (April ), 3(), Akin, S., Schembre, J.M., Bhat, S.K., and Kovscek, A.R.: Spontaneous Imbibition Characteristics of Diatomite, J. of Petroleum Science and Engineering (), 5, Li, K. and Horne, R.N.: Scaling of Spontaneous Imbibition in Gas-Liquid Systems, SPE 75167, presented at the SPE/DOE Thirteenth Symposium on Improved Oil Recovery held in Tulsa, Oklahoma, April 13 17,. 9. Li, K. and Horne, R.N.: Characterization of Spontaneous Water Imbibition into Gas-Saturated Rocks, SPEJ (December 1), Handy, L.L.: Determination of Effective Capillary Pressures for Porous Media from Imbibition Data, Petroleum Transactions AIME, 19, 196, Li, K. and Horne, R.N.: An Experimental Method of Measuring Steam-Water and Air-Water Capillary Pressures, paper 1-84, presented at the Petroleum Society s Canadian International Petroleum Conference 1, Calgary, Alberta, Canada, June 1 14, Li, K. and Horne, R.N.: Wettability of Steam-Water- Rock Systems, presented at the 7 th International Symposium on Reservoir Wettability, Freycinet, Tasmania, Australia, March 1-15,. Saturation Coefficient S gr =1% S gr =% S gr =3% S gr =4% S gr =5% CT Value CT dry CT et CT obj Position, cm Fig. 3: Distribution of CT values in the core hen the core is dry, saturated ith ater, and displaced by gas. Porosity, fraction. Porosity Saturation Position, cm 1 Fig. 4: Distribution of porosity and initial ater saturation in the core Water Saturation, % Fig. 1: Effect of initial ater saturation on saturation coefficient, hich is directly proportional to recovery (GOIP) and imbibition rate (GOIP/minute). Gas Recovery, PV. =% =4% =35% =43% =5% Fig. : Schematic of apparatus for ater imbibition test. Fig. 5: Effect of initial ater saturation on gas recovery in the units of pore volume in natural Berea sandstone.

8 8 Keen Li, Kevin Cho, and Roland N. Horne 7677 Recovery, GOIP. =% =4% =35% =43% =5% Fig. 6: Effect of initial ater saturation on gas recovery in the units of GOIP in natural Berea sandstone. Gas Recovery, GOIP Fig. 7: Effect of initial ater saturation on final gas recovery in the units of GOIP in natural and fired Berea. Imbibition Rate, ml/minute 1 =% =4% =35% =43% =5% Fig. 9: Effect of initial ater saturation on imbibition rate in the units of ml/minute in natural Berea sandstone. Imbibition Rate, GOIP/minute.1 1 =% =4% =35% =43% =5% Fig. 1: Effect of initial ater saturation on imbibition rate in the units of GOIP/ minute in natural Berea sandstone. Residual Gas Saturation, % Imbibition Rate, ml/minute =% =4% =35% =43% =5% /Recovery, 1/PV Fig. 8: Effect of initial ater saturation on residual gas saturation in natural and fired Berea. Fig. 11: Relationship beteen imbibition rate and the reciprocal of gas recovery at different initial ater saturations in natural Berea.

9 7677 Effects of Initial Water Saturation on Spontaneous Water Imbibition 9 Effective Permeability, md Fig. 1: Effect of initial ater saturation on effective permeability of the ater phase in natural and fired Berea. Relative Permeability Fig. 13: Effect of initial ater saturation on relative permeability of the ater phase in natural and fired Berea. Final Gas Recovery, GOIP. 5 md 1 md 5 md Chalk Grayacke Fig. 15: Final gas recovery (GOIP) in different rocks. Imbibition Rate, ml/minute md chalk Grayacke Fig. 16: Imbibition rate in the units of ml/minute in different rocks. P c, cm Water Column Fig. 14: Effect of initial ater saturation on capillary pressure in natural and fired Berea.