Composition Routes for Three-Phase Partially Miscible Flow in Ternary Systems
- Tara C. LaForce (U. of Texas at Austin) | Russell T. Johns (U. of Texas at Austin)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- June 2005
- Document Type
- Journal Paper
- 161 - 174
- 2005. Society of Petroleum Engineers
- 5.4 Enhanced Recovery, 5.4.1 Waterflooding, 5.4.2 Gas Injection Methods, 4.1.2 Separation and Treating, 4.3.4 Scale, 5.3.1 Flow in Porous Media, 5.3.2 Multiphase Flow, 5.2.1 Phase Behavior and PVT Measurements, 4.1.5 Processing Equipment, 5.5 Reservoir Simulation, 5.4.7 Chemical Flooding Methods (e.g., Polymer, Solvent, Nitrogen, Immiscible CO2, Surfactant, Vapex), 1.6.9 Coring, Fishing, 4.5.7 Controls and Umbilicals, 5.6.4 Drillstem/Well Testing
- 0 in the last 30 days
- 555 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 5.00|
|SPE Non-Member Price:||USD 35.00|
Three-phase flow often occurs in reservoirs, particularly for secondary ortertiary oil recovery methods such as miscible gas or chemical flooding. Inthese cases, there is often significant mutual solubility of components in thephases. Unfortunately, there is insufficient understanding of how threepartially miscible phases can affect flow. Furthermore, there are currently nobenchmark analytical solutions available to validate numerical simulations forthis complex flow regime.
In this research, compositional solution routes are developed by the methodof characteristics (MOC) for 1D, dispersion-free flow wherein up to threepartially miscible flowing phases may be present. The method is applied to awater/alcohol/oil system that exhibits a large three-phase region in laboratoryexperiments. Unique solutions are found based on continuity arguments,shock-jump conditions, entropy constraints, and velocity constraints. Theanalytical solutions are compared to fine-grid finite-difference simulations toverify that they converge to the same dispersion-free limit.
The results show that composition routes within the three-phase region oftenexhibit one phase below its residual saturation so that only two phases areflowing. As miscibility is approached, cumulative oil recovery initiallydeclines because of the development of constant states in the solution, whichcause the leading shock to speed up. We show that multicontact miscibility isdeveloped at the critical point of one two-phase region and along the boundaryof the three-phase region where all shocks and waves flow at a dimensionlessvelocity of one. Last, we show that injectivity changes by a factor of two forthe specific relative permeabilities and injection compositions used.
Flow in a reservoir often consists of three or more flowing phases. Forexample, injection of CO 2 can form three hydrocarbon phases under realisticreservoir temperature and pressure conditions. 1 Three hydrocarbon phases arebelieved to occur in many west Texas CO 2 floods, and the numerous phases canhave an adverse effect on wellbore injectivity. 2 Although three-phase flow isbelieved to occur often, many fundamental questions remain about the effect ofthree-phase flow on oil recovery, particularly its effect on the miscible gasprocess.
Helfferich 3 first presented a general analytical theory using the MOC formulticomponent multiphase displacements. Construction of solutions to specificgas displacements has been ongoing ever since. For example, the analyticaltheory for two-phase partially miscible gas displacements has been studiedextensively for floods with an arbitrary number of components. 4--6
Many researchers have also studied immiscible three-phase three-componentMOC displacements. 7--14 In three-phase immiscible systems the mass-balanceequations governing flow may be elliptic, hyperbolic, or nonstrictly hyperbolicdepending on the relative permeability model used. 7 Gonzales and Araujo 11 andSahni et al. 12 have studied the effect of relative permeabilities oncomposition routes. Recently Juanes and Patzek 13,1.proposed new relativepermeabilities for which the mass-balance equation is hyperbolic at everyinterior point of the three-phase region. The elliptic and strictly hyperboliccases are beyond the scope of this paper; however, displacements with ellipticregions in the mass-balance equation have been studied extensively. 7
There has been considerable mathematical research dedicated to understandingnonunique solutions in three-phase immiscible flow. 15--18 Nonuniquenessresults from the introduction of transitional shocks when Lax and Liu entropyconditions fail to provide a composition route. 7 In the example cases studiedhere, no transitional shocks were encountered.
Several researchers have examined the numerical simulation of three-phasepartially miscible flow. Orr, 19 for example, outlined a numerical simulatorthat allows for partially miscible flow of up to four components and fourphases. Pongpitak 20 used this simulator to model three-phase waterflooding forcores saturated with the alcohol n-butanol (NBA) and C 16. The simulationssignificantly underestimated the oil recovery compared with core experiments.Fanchi 21 showed the relative unimportance of small three-phase regions using asimilar simulator on pseudoternary representations of CO 2 injection with crudeand synthetic oils. Gardner et al. 22 obtained an excellent match to slim-tubeexperiments with numerical simulation using pseudoternary representations of CO2 injected into Wasson crude. Moreover, Gardner et al. 22 showed that thenumerical composition route is dependent upon the level of numericaldispersion.
There is very little in the literature on the development of MOC solutionsto three-phase partially miscible flow. Giordano and Salter 23 comparednumerical simulations, corefloods, and one MOC solution for a partiallymiscible three-phase water/NPA/DMP system. The MOC and simulated compositionroutes agreed well, although the match to corefloods was only qualitative. Thedevelopment of this one MOC solution was not thoroughly explained in theirpaper.
In this paper, the analytical theory using MOC is extended tothree-component, three-phase partially miscible flow for a variety of injectioncompositions. Unique solutions are found for a three-phase partially miscibleflow problem with a large three-phase region. The MOC solutions are comparedwith fine-grid finite-difference solutions. Changes in injectivity andcumulative oil recovery with alcohol enrichment are also studied.
|File Size||1 MB||Number of Pages||14|
1. Turek, E.A., Metcalfe, R.S., and Fishback, R.E.: "Phase Behav-ior of SeveralCO2/West-Texas-Reservoir-Oil Systems," SPERE (May 1988) 505.
2. Jarrell, P.M. et al.: Practical Aspects of CO2 Flooding, SPE Henry L.Doherty Series, Monograph Series, SPE, Richardson, Texas (2002) 22, 13-32.
3. Helfferich, F.G.: "Theory ofMulticomponent, Multiphase Dis-placement in Porous Media," SPEJ (February1981) 51.
4. Johns, R.T.: "Analytical Theory of Multicomponent Gas Drives withTwo-Phase Mass Transfer," PhD dissertation, Stanford U., Stanford, California(1992).
5. Jessen, K. et al.: "Fast,Approximate Solutions for 1D Multi-component Gas Injection Problems ,"paper SPE 56608 pre-sented at the 1999 SPE Annual Technical Conference andEx-hibition, Houston, 3-6 October.
6. Yuan, H.: "Application of Miscibility Calculations to Gas Floods," PhDdissertation, U. of Texas at Austin, Austin, Texas (2003).
7. Guzman, R.E.: "Mathematics of Three-Phase Flow," PhD dis-sertation,Stanford U., Stanford, California (1995).
8. Falls, A.H. and Schulte, W.M.: "Theory of Three-Component,Three-Phase Displacement in Porous Media," SPERE (August 1992) 377; Trans.,AIME, 293.
9. Falls, A.H. and Schulte, W.M.: "Features of Three-Component,Three-Phase Displacement in Porous Media," SPERE (Novem-ber 1992) 426;Trans., AIME, 293.
10. Lake, L.W.: Enhanced Oil Recovery, first edition, Prentice Hall,Engelwood Cliffs, New Jersey (1989).
11. González, M. and Araujo, M.: "Use of the Method of Charac-teristicsto Study Three-Phase Flow," paper SPE 75168 pre-sented at the 2002 SPE/DOEImproved Oil Recovery Sympo-sium, Tulsa, 13-17 April.
12. Sahni, A., Guzman, R., and Blunt, M.: "Theoretical Analysis of Three-PhaseFlow Experiments in Porous Media," paper SPE 36664 presented at the 1996SPE Annual Technical Conference and Exhibition, Denver, 6-9 October.
13. Juanes, R. and Patzek, T.W.: "Three-Phase Displacement The-ory: AnImproved Description of Relative Permeabilities," pa-per SPE 77539presented at the 2002 SPE Annual Technical Conference and Exhibition, SanAntonio, Texas, 29 Septem-ber-2 October.
14. Juanes, R. and Patzek, T.W.: "Relative Permeabilities in Co-CurrentThree-Phase Displacements With Gravity ," paper SPE 83445 presented at the2003 SPE Western Regional/AAPG Pa-cific Section Joint Meeting, Long Beach,California, 19-24 May.
15. Isaacson, E., Marchesin, D., and Plohr, B.: "Transitional Waves forConservation Laws," SIAM J. Math. Anal. (July 1990) 837.
16. Schecter, S.: "Structurally Stable Riemann Solutions," J. ofDifferential Eq. (1996) 126, 303.
17. Azevedo, A.V. et al.: "Nonuniqueness of Riemann Problems," Zeitschriftfur angewandte Mathematik und Physik (1997) 47, 977.
18. Marchesin, D., Plohr, B., and Schecter, S.: "An Organizing Center forWave Bifurcation in Multiphase Flow Models," SIAM J. Appl. Math (October 1997)57, 1189.
19. Orr, F.M. Jr.: "Simulation of the One-Dimensional Convection ofFour-Phase, Four-Component Mixtures," Report 80-3, New Mexico PetroleumRecovery Research Center, Socorro, New Mexico (June 1980).
20. Pongpitak, S.: "Interaction of Phase Behavior with Multiphase Flow inPorous Media," MS thesis, New Mexico Inst. of Min-ing and Technology, Socorro,New Mexico (1980).
21. Fanchi, J.R.: "Effect ofComplex Fluid Phase Behavior on CO2 Flood Simulation," paper SPE 16711presented at the 1987 SPE Annual Technical Conference and Exhibition, Dallas,27-30 September.
22. Gardner, J.W, Orr, F.M., and Patel, P.D.: "The Effect of Phase Behavior onCO2-Flood Displacement Efficiency," JPT (No-vember 1981) 2067.
23. Giordano, R.M. and Salter, S.J.: "Comparison of Simulation andExperiments for Compositionally Well-Defined Core-floods," paper SPE/DOE12697 presented at the 1984 SPE/DOE Enhanced Oil Recovery Symposium, Tulsa,15-18 April.
24. Seto, C.J., Jessen, K., and Orr F.M. Jr.: "Compositional Streamline Simulationof Field Scale Condensate Vaporization by Gas Injection," paper SPE 79690presented at the 2003 SPE Reservoir Simulation Symposium, Houston, 3-5February.
25. Torres-Roldán, R.L., García-Casco, A., and García-Sanchez, P.A.: CSpace:An Integrated Workplace for the Graphical and Algebraic Analysis of PhaseAssemblages on 32-Bit Wintel Platforms, http://www.ugr.es/~cspace/, Computersand Geo-sciences (1999).
26. Chemical Properties Handbook, C.L. Yaws (ed.), McGraw-Hill, New YorkCity (1999).
27. Henry, R.L. and Metcalfe, R.S.: "Multiple-Phase Generation DuringCarbon Dioxide Flooding," SPEJ (August 1983) 595.