Multiple-Mixing-Cell Method for MMP Calculations
- Kaveh Ahmadi (University of Texas at Austin) | Russell T. Johns (Pennsylvania State University)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- December 2011
- Document Type
- Journal Paper
- 733 - 742
- 2011. Society of Petroleum Engineers
- 5.4.2 Gas Injection Methods, 5.2.2 Fluid Modeling, Equations of State
- Method of Characteristics, Mixing cell, Mixing-cell, Minimum Miscibility Pressure, MMP
- 28 in the last 30 days
- 1,422 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 12.00|
|SPE Non-Member Price:||USD 35.00|
The minimum miscibility pressure (MMP) is a key parameter governing the displacement efficiency of gasfloods. There are several methods to determine the MMP, but the most accurate methods are slim-tube experiments, analytical methods, and numerical-simulation/cell-to-cell methods. Slim-tube experiments are important to perform because they use actual crude oil, but they are costly and time consuming. Analytical methods that use the method of characteristics (MOC) are very fast and help to understand the structure of gasfloods. MOC, however, relies on finding the unique and correct set of key tie lines in the displacements, which can be difficult. Slim-tube simulation methods and their simplified cell-to-cell derivatives require tedious fluid and rock inputs, and their MMP estimates can be clouded by dispersion.
This paper presents a simple and accurate multiple-mixing-cell method for MMP calculations that corrects for dispersion, and is faster and less cumbersome than 1D simulation methods. Unlike previous mixing-cell methods, our cell-to-cell mixing model uses a variable number of cells, and is independent of gas/oil ratio, volume of the cells, excess oil volumes, and the amount of gas injected. The new method only relies on robust P/T flash calculations using any cubic equation-of-state (EOS). The calculations begin with only two cells and perform additional cell-to-cell contacts between resulting equilibrium-phase compositions based on equilibrium gas moving ahead of the equilibrium liquid phase. We show for a variety of oil and gas compositions that all key tie lines can be found to the desired accuracy, and that they are nearly identical to those found using analytical MOC methods. Our approach, however, is more accurate and robust than those from MOC because we do not make approximations regarding shocks along nontie-line paths, and the unique set of key tie lines converges automatically.
The MMP using our mixing-cell method can be calculated in minutes using an Excel spreadsheet and is estimated from a novel bisection method of the minimum tie-line lengths observed in the cells at four or five pressures. Our multiple-mixing-cell method can calculate either the MMP or the minimum miscibility for enrichment (MME) independent of the number of components in the gas or oil. Our approach further supports the notion that the MMP is independent of fractional flow because we obtain the same key tie lines independent of how much fluid is moved from one cell to another.
|File Size||1 MB||Number of Pages||10|
Christiansen, R.L. and Haines, H.K. 1987. Rapid Measurement ofMinimum Miscibility Pressure With the Rising-Bubble Apparatus. SPE ResEng 2 (4): 523-527; Trans., AIME, 283.SPE-13114-PA. http://dx.doi.org/10.2118/13114-PA.
Clancy, M., Stewart, G., Thomson, A., Todd, A.C., andVarotsis, N. 1986. Optimized Compositional Models for Simulation of EORProcess. Presented at the Third European Symposium on Improved Oil Recovery,Rome, 16-18 April.
Cook, A.B., Walker, C.J., and Spencer, G.B. 1969. Realistic KValues of C7+ Hydrocarbon for Calculating Oil Vaporization During Gas Cycle atHigh Pressures. J Pet Technol 21 (7): 901-915. SPE-2276-PA.http://dx.doi.org/10.2118/2276-PA.
Firoozabadi, A. and Aziz, K. 1986. Analysis and Correlation ofNitrogen and Lean-Gas Miscibility Pressure. SPE J. 1 (6):575-582. SPE-13669-PA. http://dx.doi.org/10.2118/13669-PA.
Hearn, C.L. and Whitson, C.H. 1995. Evaluating Miscible andImmiscible Gas Injection in the Safah Filed Oman. Paper SPE 29115 presented atthe SPE Reservoir Simulation Symposium, San Antonio, Texas, USA, 12-15February. http://dx.doi.org/10.2118/29115-MS.
Hutchinson, C. A. and Braun, P. H. 1961. Phase relations ofmiscible displacement in oil recovery. AIChE Journal 7 (1):64-72. http://dx.doi.org/10.1002/aic.
Jarrell, P., Fox, C., Stein, M., and Webb, S.L. 2002.Practical Aspects of CO2 Flooding. Monograph Series, SPE, Richardson,Texas 22.
Jaubert, J.-N., Arras, L., Neau, E., and Avaullée, L. 1998b. ProperlyDefining the Classical Vaporizing and Condensing Mechanisms When a Gas IsInjected into a Crude Oil. Ind. Eng. Chem. Res. 37 (12):4860-4869. http://dx.doi.org/10.1021/ie9803016.
Jaubert, J.-N., Wolff, L., Neau, E., and Avaullée, L. 1998a. A Very SimpleMultiple Mixing Cell Calculation to Compute the Minimum Miscibility PressureWhatever the Displacement Mechanism. Ind. Eng. Chem. Res. 37 (12): 4854-4859. http://dx.doi.org/10.1021/ie980348r.
Jensen, F. and Michelsen, M.L. 1990. Calculation of FirstContact and Multiple Contact Minimum Miscibility Pressures. In Situ:Oil-Coal-Shale-Minerals 14 (1): 1-17.
Jessen, K. and Orr, F.M. Jr. 2008. On Interfacial-TensionMeasurements To Estimate Minimum Miscibility Pressures. SPE Res Eval &Eng 11 (5): 933-939. SPE-110725-PA. http://dx.doi.org/10.2118/110725-PA.
Jessen, K., Michelsen, M., and Stenby, E.H. 1998. Globalapproach for calculating minimum miscibility pressure. Fluid PhaseEquilibria 153 (2): 251-263. http://dx.doi.org/10.1016/S0378-3812(98)00414-2.
Johns, R.T. and Orr, F.M. Jr. 1996. Miscible Gas Displacementof Multicomponent Oils. SPE J. 1 (1): 39-50. SPE-30798-PA. http://dx.doi.org/10.2118/30798-PA.
Johns, R.T., Dindoruk, B., and Orr, F.M. Jr. 1993. AnalyticalTheory of Combined Condensing/Vaporizing Gas Drives. SPE Advanced TechnologySeries 1 (2): 7-16. SPE-24112-PA. http://dx.doi.org/10.2118/24112-PA.
Johns, R.T., Sah, P., and Solano, R. 2002. Effect of dispersionon local displacement efficiency for multicomponent enriched-gas floods abovethe minimum miscibility enrichment. SPE Res Eval & Eng 5 (1): 4-10. SPE-75806-PA. http://dx.doi.org/10.2118/75806-PA.
LaForce, T. and Johns, R.T. 2005. Composition Routes forThree-Phase Partially Miscible Flow in Ternary Systems. SPE J. 10 (2): 161-174. SPE-89438-PA. http://dx.doi.org/10.2118/89438-PA.
Lake, L.W. 1989. Enhanced Oil Recovery. EnglewoodCliffs, New Jersey: Prentice Hall.
Li, Y. and Johns, R.T. 2007. A Rapid and Robust Method toReplace Rachford-Rice in Flash Calculations. Paper SPE 106080 presented at theSPE Reservoir Simulation Symposium, Houston, 26-28 February. http://dx.doi.org/10.2118/106080-MS.
Metcalfe, R.S., Fussell, D.D., and Shelton, J.L. 1973. AMulticell Equilibrium Separation Model for the Study of Multiple ContactMiscibility in Rich-Gas Drives. SPE J. 13 (3): 147-155.SPE-3995-PA. http://dx.doi.org/10.2118/3995-PA.
MMPz user manual, Ver. 1.3 (November). 2002. Portland,Oregon: Zick Technologies.
Monroe, W.W., Silva, M.K., Larson, L.L., and Orr, F.M. Jr.1990. Composition Paths in Four-Component Systems: Effect of DissolvedMethane on 1D CO2 Flood Performance. SPE Res Eng 5 (3):423-432. SPE-16712-PA. http://dx.doi.org/10.2118/16712-PA.
Neau, E., Avaullée, L., and Jaubert, J.N. 1996. A new algorithm for enhancedoil recovery calculations. Fluid Phase Equilibria 119(1-2): 265-272. http://dx.doi.org/10.1016/0378-3812(95)02962-1.
Orr, F.M. Jr. 2007. Theory of Gas Injection Processes.Copenhagen, Denmark: Tie-Line Publications.
Orr, F.M. Jr., Johns, R.T., and Dindoruk, B. 1993. Developmentof Miscibility in Four-Component CO2 Floods. SPE Res Eng 8(2): 135-142. SPE-22637-PA. http://dx.doi.org/10.2118/22637-PA.
Pedersen, K.S., Fjellerup, J., Thomassen, P. and Fredenslund,A. 1986. Studies of Gas Injected Into Oil Reserves by Cell-to-Cell SimulationModel. Paper SPE 15599 presented at the SPE Annual Technical Conference andExhibition, New Orleans, 5-8 October. http://dx.doi.org/10.2118/15599-MS.
Peng, D.-Y. and Robinson, D.B. 1978. The characterization ofthe heptanes and heavier fractions for the GPA Peng-Robinson programs. GPAResearch Report RR-28, Project 756, University of Alberta, Edmonton, Alberta(March 1978).
PennPVT 3.9. 2010. Gas Flooding Joint Industry Project,Pennsylvania State University, University Park, Pennsylvania (formerly at theUniversity of Texas at Austin).
Pires, A.P. and Bedrikovetsky, P.G. 2005. Analytical Modelingof 1-D n-Component Miscible Displacement of Ideal Fluid. Paper SPE 94855presented at the SPE Latin American and Caribbean Petroleum EngineeringConference, Rio de Janeiro, Brazil, 20-23 June. http://dx.doi.org/10.2118/94855-MS.
Rao, D.N. 1997. A new technique of vanishing interfacialtension for miscibility determination. Fluid Phase Equilibria 139 (1-2): 311-324. http://dx.doi.org/10.1016/S0378-3812(97)00180-5.
Seto, C.J, Jessen, K. and Orr, F.M. Jr. 2006. AFour-Component, Two-Phase Flow Model for CO2 Storage and Enhanced CoalbedMethane Recovery. Paper SPE 102376 presented at the SPE Annual TechnicalConference and Exhibition, San Antonio, 24-27 September. http://dx.doi.org/10.2118/102376-MS.
Seto, C.J. and Orr, F.M. 2008. Analytical Solutions forMulticomponent, Two-Phase Flow in Porous Media with Double ContactDiscontinuities. Transport in Porous Media 78 (2): 161-183.http://dx.doi.org/10.1007/s11242-008-9292-y.
Stalkup, F.I. 1987. Displacement Behavior of theCondensing/Vaporizing Gas Drive Process. Paper SPE 16715 presented at SPEAnnual Technical Conference and Exhibition, Dallas, 27-30 September. http://dx.doi.org/10.2118/16715-MS.
Wang, Y. 1998. Analytical calculation of minimum miscibilitypressure. PhD dissertation, Stanford University, Stanford,California.
Wang, Y. and Orr, F.M. Jr. 1997. Analytical calculation ofminimum miscibility pressure. Fluid Phase Equilibria 139(1-2): 101-124. http://dx.doi.org/10.1016/S0378-3812(97)00179-9.
Whitson, C.H. and Michelsen, M.L. 1989. The negative flash.Fluid Phase Equilibria 53 (2): 51-71. http://dx.doi.org/10.1016/0378-3812(89)80072-X.
Yellig, W.F. and Metcalfe, R.S. 1980. Determination andPrediction of CO2 Minimum Miscibility Pressures. J Pet Technol 32 (1): 160-168. SPE-7477-PA. http://dx.doi.org/10.2118/7477-PA.
Yuan, H. and Johns, R.T. 2005. Simplified Method forCalculation of Minimum Miscibility Pressure or Enrichment. SPE J. 10 (4): 416-425. SPE-77381-PA. http://dx.doi.org/10.2118/77381-PA.
Zhao, G.-B., Adidharama, H., Towler, B., and Radosz, M. 2006b. Using aMultiple-Mixing-Cell Model to Study Minimum Miscibility Pressure Controlled byThermodynamic Equilibrium Tie Lines. Ind. Eng. Chem. Res. 45 (23): 7913-7923. http://dx.doi.org/10.1021/ie0606237.
Zhao, G.B., Adidharma, H., Towler, B., and Radosz, M. 2006a.Minimum Miscibility Pressure Prediction Using Statistical Associating FluidTheory: Two- and Three-Phase System. Paper SPE 102501 presented at the SPEAnnual Technical Conference and Exhibition, San Antonio, Texas, USA, 24-27September. http://dx.doi.org/10.2118/102501-MS.
Zick, A.A. 1986. A Combined Condensing/Vaporizing Mechanism in theDisplacement of Oil by Enriched Gases. Paper SPE 15493 presented at the AnnualTechnical Conference and Exhibition, New Orleans, 5-8 October. http://dx.doi.org/10.2118/15493-MS.