IPTC 12227 A New Three-Phase Oil Relative Permeability imulation Tuned by Experimental Data Bevan Yuen, Alan iu, hamsuddin henawi, Nader Bukhamseen, ti Lynra, and Ali Al-Turki; PE / audi Aramco Copyriht 2008, International Petroleum Technoloy Conference This paper was prepared for presentation at the International Petroleum Technoloy Conference held in Kuala Lumpur, Malaysia, 3 5 December 2008. This paper was selected for presentation by an IPTC Proramme Cmittee followin review of information contained in an abstract submitted by the author(s. Contents of the paper, as presented, have not been reviewed by the International Petroleum Technoloy Conference and are subject to correction by the author(s. The material, as presented, does not necessarily reflect any position of the International Petroleum Technoloy Conference, its officers, or members. Papers presented at IPTC are subject to publication review by ponsor ociety Cmittees of IPTC. Electronic reproduction, distribution, or storae of any part of this paper for cmercial purposes without the written consent of the International Petroleum Technoloy Conference is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledment of where and by wh the paper was presented. Write Librarian, IPTC, P.O. Box 833836, Richardson, TX 75083-3836, U..A., fax +1-972-952-9435. Abstract The measurement of three-phase displacement involves varyin two independent saturations. Therefore, recordin the relative permeability for all possible three-phase displacement cbinations in the reservoir beces impractical. A cmon practice utilizes two-phase data to estimate three-phase relative permeability in the reservoir simulator. Most three-phase oil relative permeability models used in cmercial simulators do not contain the flexibility of tunin with measured experimental data. In this paper, a new empirical three-phase oil relative permeability model is proposed to offer a tunin flexibility to improve the simulator prediction. The new model is based on saturation-weihted interpolation between the two-phase values, similar to the Baker model, but with a simple tunin coefficient that allows adjustment to match the experimental measurements. The paper discusses factors that are essential for accurate reservoir simulation modelin. The presented experimental data shows the inter-relationship between phase relative permeability, trapped as and residual oil saturation. Also, a cparison of this new three-phase oil relative permeability model with standard industry models is iven. Introduction The laboratory measurements of three-phase flow experiments are costly and time consumin, which have limited the number of these experiments actually reported. In most reservoir enineerin calculations, particularly in reservoir simulation code, the processes involvin three-phase flow are approximated by the three-phase relative permeability models or correlations based upon two-phase oil-water, oil-as and/or water-as relative permeability laboratory measurements. Three-phase permeability core floodin data exist for se of the iant carbonate fields in audi Arabia. Due to unreasonable prediction results provided by several three-phase reservoir simulation studies in audi Aramco, a further investiation of the industry standard three-phase relative permeability models based on two-phase data was performed. This work concluded that none of the available industry standard correlations provided three-phase results close to laboratory results measured on the audi Aramco core samples. As a result, an alternative model was developed to provide three-phase relative permeability curves that closely match the available three-phase relative permeability data; thus, providin sinificantly improved reservoir simulation predictions in three-phase flow situations. Review of Three-Phase Oil Relative Permeability Correlations used in Cmercial imulators The most cmonly used three-phase oil relative permeability correlations are the tone 1,2 models. The tone I model was introduced in 1970 based on the channel flow theory that assumes in any flow channel there is mostly one mobile fluid. The water and as relative permeability will be a function of its own saturation. The oil relative permeability depends on the twophase oil / water and as/oil relative permeability correspondin to the effective water and as saturations: oekrowkro k = ro k (1 (1 (1 ro max we e The tone I model effective phase saturations ( oe, e and we are calculated fr the followin equations:
2 IPTC 12227 oe o = (2 1 we w = (3 1 e = 1 (4 A correlation was proposed by Fayers and Matthews 3 to estimate residual oil saturation after water and as flood: = λ + ( 1 λ (5 orw orw or = 0. 5 (with trapped as (6 λ (7 = 1 or Due to the difficulty in estimatin the three-phase residual oil saturation (, the modified tone II model by Aziz and ettari 4 is more cmonly used in the industry: k = k + k k ( k + k k k ( k + k (8 ro ( row ro max rw ro ro max r ro max rw A saturation-weihted interpolation between oil-water and oil-as two-phase relative permeability data was proposed by Baker (1988 5. It assumes that the end-points of two-phase data are the same as in the three-phase system. The ereated model in Eclipse TM and Line model in Chears TM are also variations of this saturation-weihted approach: k ( k + ( k w row r ro ro = (9 ( w + ( r In these models, k row and k ro are calculated as a function of the rid cell oil saturations. Heiba 6 suested the Line model where the oil iso-permeabilities can be approximated by straiht lines connectin between the two-phase relative permeability at irreducible water saturation. The as and water saturations would be proportional to the as and water saturations at the three-phase oil relative permeability. The (k ro and w (k ro are found by iteration to satisfy the proportional function. Proposed Modified Baker When the Baker correlation was used to estimate the three-phase oil relative permeability in this study, it was found that its estimates were lower than k ro and the laboratory measured k ro. In order to attain a hiher k ro, the k ro was evaluated at rather than o and k row is evaluated at oil saturation. In addition, it is proposed to introduce a matchin parameter (α to match the laboratory data. As suested by Blunt 7, the weihtin function of k ro is also set to decrease at the second order of threephase mobile oil saturation ( on. If it is not determined experimentally, interpolates linearly between orw and or. The followin modified Baker correlation is proposed: r k ro ( = w ( w k row + + 2 on 2 on α( α( r r k ro (10 The mobile oil saturation ( on is calculated by the relationship: on ( o = (11 (1 The three-phase residual oil saturation ( used for calculatin on is determined by the expression: + w orw or = (12 w +
IPTC 12227 3 Testin of New Modified Baker with Published Data The data sets of Donaldson 8 / Dean and Oak 9 were selected for the testin of the proposed modified Baker correlation. The cparisons and iso-permeabilities were reported by Delshad 10 and Pejic 11, respectively. The error of deviation was calculated accordin to the followin equation: DEV = n i= 1 2 ( k ro k (13 exp, i rocalc, i The modified Baker correlation performs better than all the other four correlations mentioned above as shown in Table 1. The three-phase iso-permeabilities are shown in Fiures 1 and 2. Three-Phase Relative Permeability Flow Effects Core laboratory experiments were conducted to obtain three-phase relative permeability data. The experimental data indicates four major flow effects that should be considered in order to realistically simulate oil and as recovery processes. Those are: (a as relative permeability hysteresis, (b effect of trapped as saturation on residual oil saturation, (c oil relative permeability in presence of trapped as, and (d water relative permeability in the presence of trapped as. (a Gas Relative Permeability Hysteresis The injected as in the oil drainae cycle displaced the oriinal oil leavin irreducible oil saturation after as floodin ( or in the laboratory core samples. ubsequently, an oil imbibition cycle will take place as oil displaces the as. The laboratory experiments show that a trapped as saturation remains in the core plus followin the oil imbibition cycle. This trapped as needs to be modeled by a as hysteresis correlation to simulate the reduction in as movement and recovery (Fiure 3. Gas drainae relative permeability data fr three as flood experiments were fitted with equations, as shown in Fiure 4. Gas imbibition relative permeability was derived based on the conceptual hysteresis model by Carlson 12 since no experimental measurements are available. Carlson s model assumes that the total as in the core durin displacement of as by oil can be separated into immobile (trapped as and mobile free as. Land 13,14 empirically demonstrated a relationship between the maximum non-wettin phase (as saturation and the value of the trapped as saturation. Based on the experimental data fr this study, a trapped as model was developed ( t = max, as shown in Fiure 5. The drainae curve at free flowin as saturation can be utilized to enerate the imbibition boundary curve. Most cmercial simulators possess the option to model as hysteresis with drainae and imbibition curves. (b Effect of Trapped Gas on Residual Oil aturation The residual oil saturation is less in the presence of trapped as than in the absence of trapped as as observed in ten waterflood experiments. The reduction can be correlated by the equation Δ or = 8 t (Fiure 6. In the three-phase laboratory experiments, it was observed that residual oil saturation in the presence of trapped as followin waterfloodin was hiher than residual oil saturation after as displacement ( or. Both these residual oil saturations were less than residual oil saturation ( orw after waterfloodin the oil column without introduction of as. (c Oil Relative Permeability in Presence of Trapped Gas Laboratory data indicates that the presence of trapped as usually increases the oil relative permeability, which can positively impact oil mobility, but it may not increase the ultimate oil recovery (Fiure 7. Oil relative permeabilities by waterfloodin with trapped as were measured under reservoir and pseudo reservoir conditions. The effect of hysteresis on the oil relative permeability is shown in Fiure 8. Both oil drainae (Fiure 9 and imbibition (Fiure 10 relative permeabilities can be determined fr laboratory measurements fr as flood / centrifue and as displacements by oil. The oil-as hysteresis can be modeled with drainae and imbibition k ro curves. (d Water Relative Permeability in the Presence of Trapped Gas The experimental data presented in Fiure 11 shows a consistent trend in the reduction of relative permeability to water by waterfloodin in the presence of trapped as. Laboratory measurements fr four cposite cores under reservoir conditions usin reservoir fluids indicate that the water relative permeability depends on trapped as saturation as well as water saturation. The presence of trapped as sinificantly reduces water relative permeability, which positively impacts oil recovery by slowin down the water front velocity. The water relative permeability (k rw with presence of trapped as can be modeled by shiftin t in the normalized water saturation ( wn : wn w A t = (14 1 orw It is obvious that three-phase relative permeability correlations are needed to simulate these cplex recovery processes. The accuracy of the residual oil saturation modeled in the reservoir simulator stronly affects the ultimate oil recovery.
4 IPTC 12227 Testin of Oil Three-Phase Relative Permeability Correlations with Recent Laboratory Data The recent laboratory measurements of three-phase oil relative permeability under reservoir conditions with trapped as saturation of 81 were used to calibrate the three-phase relative permeability correlations. The three-phase oil relative permeability starts fr two-phase oil-as k ro (Fiure 12 and terminates at the model calculated residual oil saturation. The tone I, ereated, Baker, and Line correlations calculate very similar oil relative permeabilitites; however, these correlations do not match the available experimental data. The modified Baker correlation introduces a matchin parameter that can be used to obtain a reasonable match with the laboratory data, as demonstrated in Fiure 12. The tone II alorithm provided a hih residual oil saturation of 0.56 in presence of the trapped as saturation of 81, as depicted in Fiure 13. Consequently, at oil saturations lower than 0.56 in the oil flooded as area, the oil will be immobile in the reservoir simulator. Oil will move and accumulate near the as area to the threshold oil saturation of 0.56. After that oil can start to move into the as flooded area aain. The tone II model yields pessimistic and unrealistic simulation results. The Baker and ereated models use the minimum of either the residual oil saturation after as flood ( or or residual oil saturation after waterflood ( orw. The Line model residual oil saturation is a linear interpretation of or and orw. The residual oil saturation ( in tone I and modified Baker can match either the laboratory measurements or as a weihted function of orw and or. Fiure 13 presents a cparison of the residual oil saturation ( at trapped as saturation ( t of 81 for the different three-phase models. Conclusions 1 In three-phase recovery processes, four major relative permeability effects are identified. The two most important of these four factors are three-phase oil relative permeability and the three-phase residual oil saturation. 2 The proposed modified Baker model can be calibrated with laboratory measurements and it also yields better predictability than available three-phase oil relative permeability correlations in cmercial reservoir simulators. 3 In this study, the tone II three-phase relative permeability correlation produced unreasonable and unreliable residual oil saturations. Acknowledement The authors would like to thank audi Aramco manaement for the permission to publish this paper. ymbols, Abbreviations and Units A tunin parameter for krw with trapped as to match laboratory data, A= ~ (dimensionless k r two-phase as relative permeability in oil/as (dimensionless k ro three-phase oil relative permeability (dimensionless k ro two-phase oil relative permeability in oil/as (dimensionless k row two-phase oil relative permeability in oil/water (dimensionless k rax two-phase oil relative permeability measured at connate water saturation (dimensionless k rw two-phase water relative permeability in oil/water (dimensionless as saturation (fraction e effective as saturation used in tone I model (fraction max maximum as saturation in rid cell (fraction r residual as saturation (fraction t trapped as saturation (fraction o oil saturation (fraction oe effective oil saturation used in tone I model (fraction three-phase residual oil saturation (fraction on three-phase mobile oil saturation (fraction or two-phase residual oil saturation in oil/as (fraction orw two-phase residual oil saturation in oil/water (fraction w water saturation (fraction connate water saturation (fraction we effective water saturation used in tone I model (fraction wn normalized water saturation (fraction Δ or reduction in residual oil saturation at a iven trapped as saturation cpared to or at t = 0 (fraction α matchin parameter for modified Baker (dimensionless λ averain weihtin factor (dimensionless
IPTC 12227 5 References 1. tone, H.L.: Probability for Estimatin Three-Phase Relative Permeability, PE 2116, Journal of Petroleum Technoloy, PE Feb. 1970, p. 1428-36 2. tone, H.L.: Estimation of Three-Phase Relative Permeability and Residual Oil Data, Journal of Canadian Petroleum Technoloy, Oct.-Dec. 1973, p. 53-61. 3. Fayers, F.J. & Matthews, J.D.: Evaluation of Normalized tone s Methods for Estimatin Three-Phase Relative Permeabilites, PE 11277, PEJ Vol. 24 No.2, 1984. 4. Aziz, K. & ettari, T.: Petroleum Reservoir imulation, Applied cience Publishers, London, 1979. 5. Baker, L.E.: Three-Phase Relative Permeability Correlations, PE 17369, PE/DOE EOR ymposium, Tulsa, Apr. 17-20, 1988. 6. Heiba, A. A., Davis, H. T., & criven, L.E.: tatistical Network Theory of Three-Phase Relative Permeabilities, PE 12690, PE/DOE Enhanced Oil Recovery, Tulsa, Apr. 15-18, 1984. 7. Blunt, M.J.: An Empirical for Three-Phase Relative Permeability, PE 56474, PE Annual Technical Conference and Exhibition, Houston, Oct. 3-5, 1999. 8. Donaldson, E.C.: Two and Three-Phase Relative Permeability tudies, U.. Dep. of the Interior, Bureau of Mines, Report 6826, 1966. 9. Oak, M.J., Three-Phase Relative Permeability of Intermediate-Wet Berea andstone, PE 22599, PE Annual Technical Conference and Exhibition. Dallas, Oct. 6-9, 1991. 10. Delshad, M. & Pope, G.A.: Cparison of the Three-Phase Oil Relative Permeability s, Transport in Porous Media, 4:5, 1989. 11. Pejic, D. & Maini, B.: Three-Phase Relative Permeability of Petroleum Reservoirs, PE 81021, PE Latin American and Caribbean Petroleum Enineerin Conference, Port-of-pain, Trinidad, Apr. 27-30, 2003. 12. Carlson, F.M.: imulation of Relative Permeability Hysteresis to the Nonwettin Phase, PE 10157, PE Annual Technical Conference and Exhibition, an Antonio, Texas, UA, 4-7 Oct., 1981. 13. Land, C..: Calculation of Imbibition Relative Permeability for Two- and Three-Phase Flow fr Rock Properties, PE 1942, PE Journal Vol. 8 No. 2, Jun. 1968, Trans. AIME, vol. 243, p. 149-156. 14. Land, C..: Cparison of Calculated with Experimental Imbibition Relative Permeability, PE 3360, PE Journal Vol. 11 No. 4, Dec. 1971, Trans. AIME, vol. 251, p. 419-425. Table 1: Deviation ( DEV of oil relative permeability models Correlation Donaldson & Dean Oak 1966 1991 tone I 0632 6746 tone II 9949 7085 ereated 2932 6860 Baker 2932 6804 Line 4378 6810 Modified Baker 8850 6271 Fiure 1 Modified Baker model (α=2.7 prediction of Donaldson & Dean experiment 0.8 k r, fraction 0.6 Drainae Imbibition 0.6 0.8, fraction Fiure 2 - Modified Baker model (α=-0.3 prediction of Oak experiment Fiure 3 Gas relative permeability hysteresis model
6 IPTC 12227 k r, fraction 1 Well 1 * Well 2 Well 3 t, fraction 0.5 0.3 Rock Group 2 * Rock Group 3 01 0.6 0.8 n = ( c /(1 c wi or, fraction Fiure 4 - Gas drainae relative permeability 0.6 0.8 max, fraction Fiure 5 - Trapped as saturation ( t versus maximum as saturation ( max 0.3 Rock Group 2 * Rock Group 3 D or, fraction k ro, fraction 1 t = 11 t = 0.3 t, fraction 01 0.6 0.8 o, fraction Fiure 6 - Reduction in or (after 5 PV injections versus trapped as saturations Fiure 7 - Oil relative permeability by waterfood with and without t k ro, fraction 0.8 0.6 k ro, fraction 1 Well 1 * Well 2 Well 3 Well 4 0.6 0.8, fraction 0.6 0.8 on = (1 - wi - or /(1 wi or, fraction Fiure 8 - Oil relative permeability k ro hysterisis Fiure 9 - Drainae oil relative permeability (k ro
IPTC 12227 7 Well 1 * Well 2 t = k ro, fraction 1 k rw, fraction 1 t = 7 0.6 0.8 on = (1 - lr /(1 lr, fraction 01 0.6 0.8 w, fraction Fiure 10 - Imbibition oil relative permeability (k ro Fiure 11 - Water relative permeability by waterflood with and without t Oil Relative Permeability, frac. 0 0 G tone II tone I 2-Phases Lab Data Baker Modified Baker Line 0 0.3 0.5 0.6 0.7 0.8 Oil aturation, frac. Fiure 12 - Cparison of calculated k ro by three-phase models with laboratory measurements 0.7 (=8 Residual Oil aturation 0.6 0.5 0.3 Line MB Baker G (ECL tone II 0.3 0.5 0.6 0.7 0.8 0.9 Gas aturation, frac. Fiure 13 - Cparison of residual oil saturations calculated by three-phase models