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An Efficient Implicit-Pressure/Explicit-Saturation-Method-Based Shifting-Matrix Algorithm To Simulate Two-Phase, Immiscible Flow in Porous Media With Application to CO2 Sequestration in the Subsurface
- Amgad Salama (King Abdullah University of Science and Technology) | Shuyu Sun (King Abdullah University of Science and Technology) | Mohamed El-Amin (King Abdullah University of Science and Technology)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- July 2013
- Document Type
- Journal Paper
- 1,092 - 1,100
- 2013. Society of Petroleum Engineers
- 0 in the last 30 days
- 145 since 2007
- Show more detail
The flow of two or more immiscible fluids in porous media is widespread, particularly in the oil industry. This includes secondary and tertiary oil recovery and carbon dioxide (CO2) sequestration. Accurate predictions of the development of these processes are important in estimating the benefits and consequences of the use of certain technologies. However, this accurate prediction depends--to a large extent--on two things. The first is related to our ability to correctly characterize the reservoir with all its complexities; the second depends on our ability to develop robust techniques that solve the governing equations efficiently and accurately. In this work, we introduce a new robust and efficient numerical technique for solving the conservation laws that govern the movement of two immiscible fluids in the subsurface. As an example, this work is applied to the problem of CO2 sequestration in deep saline aquifers; however, it can also be extended to incorporate more scenarios. The traditional solution algorithms to this problem are modeled after discretizing the governing laws on a generic cell and then proceed to the other cells within loops. Therefore, it is expected that calling and iterating these loops multiple times can take a significant amount of computer time. Furthermore, if this process is performed with programming languages that require repeated interpretation each time a loop is called, such as Matlab, Python, and others, much longer time is expected, particularly for larger systems. In this new algorithm, the solution is performed for all the nodes at once and not within loops. The solution methodology involves manipulating all the variables as column vectors. By use of shifting matrices, these vectors are shifted in such a way that subtracting relevant vectors produces the corresponding difference algorithm. It has been found that this technique significantly reduces the amount of central-processing-unit (CPU) time compared with a traditional technique implemented within the framework of Matlab.
Alavian, S.A. and Whitson, C. 2009. Modeling CO2 Injection in aFractured Chalk Experiment. Paper SPE 125362 presented at the SPE/EAGEReservoir Characterization and Simulation Conference, Abu Dhabi, UAE, 19-21October. http://dx.doi.org/10.2118/125362-MS.
Altundas, Y. B., Ramakrishnan, T. S., Chugunov, N., et al. 2010. Retardationof CO2 Migration due to Capillary Pressure Hysteresis: a New CO2Trapping Mechanism. Paper SPE 139641 presented at the SPE InternationalConference on CO2 Capture, Storage, and Utilization, New Orleans, Louisiana,10-12 November. http://dx.doi.org/10.2118/139641-MS.
Bachu, S. 2002. Sequestration of CO2 in Geological Media inResponse to Climate Change: Road Map for Site Selection Using the Transform ofthe Geological Space into the CO2 Phase Space. Energ. Converg.Manag. 43 (1): 87-102. http://dx.doi.org/10.1016/S0196-8904(01)00009-7.
Bielinski, A. 2007. Numerical Simulation of CO2 Sequestration inGeological Formations. PhD dissertation, Universität Stuttgart, Stuttgart,Germany (2007).
Blunt, M., Fayers, F.J., and Orr, F.M. Jr. 1993. Carbon Dioxide in EnhancedOil Recovery. Energ. Converg. Manag. 34 (9-11): 1197-1204.http://dx.doi.org/10.1016/0196-8904(93)90069-M.
Burruss, R.C., Brennan, S.T., Freeman, P.A., et al. 2009. Development of aProbabilistic Assessment Methodology for Evaluation of Carbon Dioxide Storage.U.S. Geological Survey Open-File Report 2009-1035, http://pubs.usgs.gov/of/2009/1035/ofr2009-1035.pdf.
Carneiro, J.F. 2009. Numerical Simulations on the Influence of MatrixDiffusion to Carbon Sequestration in Double Porosity Fissured Aquifers. Int.J. Greenh. Gas Con. 3 (4): 431-443. http://dx.doi.org/10.1016/j.ijggc.2009.02.006.
Chen, Z., Huan, G., and Li, B. 2004. An Improved IMPES Method for Two-PhaseFlow in Porous Media. Transport Porous Med. 54 (3):361-376. http://dx.doi.org/10.1023/B:TIPM.0000003667.86625.15.
Chen, Z., Huan, G. and Ma, Y. 2006. Computational Methods for MultiphaseFlows in Porous Media. Philadelphia: Society for Industrial and AppliedMathematics.
Doughty, C. 2007. Modeling Geologic Storage of Carbon Dioxide: Comparison ofNon-Hysteretic and Hysteretic Characteristic Curves. Energ. Converg.Manag. 48 (6): 1768-1781. http://dx.doi.org/10.1016/j.enconman.2007.01.022.
Ferguson, R.C., Kuuskraa, V.A., Van Leeuwen, T.S. 2010. StoringCO2 with Next-Generation CO2-EOR Technology. Paper SPE139717 presented at the SPE International Conference on CO2 Capture,Storage, and Utilization, New Orleans, Louisiana, 10-12 November. http://dx.doi.org/10.2118/139717-MS.
Gaspar Ravagnani, A., Ligero, E., and Suslick, S. 2009. CO2Sequestration through Enhanced Oil Recovery in a Mature Oil Field. J.Petrol. Sci. Eng. 65 (3-4): 129-138. http://dx.doi.org/10.1016/j.petrol.2008.12.015.
Hayek, M., Mouche, E., and Mügler, C. 2009. Modeling Vertical Stratificationof CO2 Injected into a Deep Layered Aquifer. Adv. WaterResour. 32 (3): 450-462. http://dx.doi.org/10.1016/j.advwatres.2008.12.009.
Holt, T., Jensen, J.I., and Lindeberg, E. 1995. Underground Storage ofCO2 in Aquifers and Oil Reservoirs. Energ. Converg. Manag. 36 (6-9): 535-538. http://dx.doi.org/10.1016/0196-8904(95)00061-H.
Holt, T., Lindeberg, E., and Taber, J. 2000. Technologies and Possibilitiesfor Larger-Scale CO2 Separation and Underground Storage. Paper SPE63103, presented at the SPE Annual Technical Conference and Exhibition, Dallas,Texas, 1-4 October. http://dx.doi.org/10.2118/63103-MS.
Hoteit, H. and Firoozabadi, A. 2008. Numerical Modeling of Two-Phase Flow inHeterogeneous Permeable Media with Different Capillarity Pressures. Adv.Water Resour. 31 (1): 56-73. http://dx.doi.org/10.1016/j.advwatres.2007.06.006.
Izgec, O. and Demiral, B. 2005. Experimental and Numerical Investigation ofCarbon Sequestration in Saline Aquifers. Paper SPE 94697 presented at theSPE/EPA/DOE Exploration and Production Environmental Conference, Galveston,Texas, 7-9 March. http://dx.doi.org/10.2118/94697-STU.
Jahangiri, H.R. and Zhang, D. 2010. Optimization of Carbon DioxideSequestration and Enhanced Oil Recovery in Oil Reservoir. Paper SPE 133594presented at the SPE Western Regional Meeting, Anaheim, California, 27-29 May.http://dx.doi.org/10.2118/133594-MS.
Jessen, K., Kovscek, A.R., and Orr, F.M. Jr. 2005. Increasing CO2Storage in Oil Recovery. Energ. Converg. Manag. 46 (2):293-311. http://dx.doi.org/10.1016/j.enconman.2004.02.019.
Kou, J. and Sun, S. 2010a. A New Treatment of Capillarity to Improve theStability of IMPES Two-Phase Flow Formulation. Comput. Fluids 39 (10): 1923-1931. http://dx.doi.org/10.1016/j.compfluid.2010.06.022.
Kou, J. and Sun, S. 2010b. On Iterative IMPES Formulation for Two-Phase Flowwith Capillarity in Heterogeneous Porous Media. Int. J. Numer. Anal.Mod. Series B 1 (1): 20-40.
Law, D.H.S. and Bachu, S. (1996). Hydrogeological and Numerical Analysis ofCO2 Disposal in Deep Aquifers in the Alberta Sedimentary Basin.Energ. Converg. Manag. 37 (6-8): 1167-1174. http://dx.doi.org/10.1016/0196-8904(95)00315-0.
Liu, X., Gong, B., and Huo, D. 2010. Numerical Simulation on CO2Sequestration in Saline Formations with Natural or Hydraulic Fractures Using aDiscrete Modeling Approach. Paper SPE 137621 presented at the CanadianUnconventional Resources and International Petroleum Conference, Calgary,Alberta, Canada, 19-21 October. http://dx.doi.org/10.2118/137621-MS.
Martin, D. and Taber, J. 1992. Carbon Dioxide Flooding. J. Pet Tech 44 (4): 396-400. http://dx.doi.org/10.2118/23564-PA.
Metz, B., Davidson, O., de Coninck, H., et al., eds. 2005. IPCC SpecialReport on Carbon Dioxide Capture and Storage. Cambridge: CambridgeUniversity Press.
Moortgat, J., Firoozabadi, A., Li, Z., et al. 2010. A Detailed Experimentaland Numerical Study of Gravitational Effects on CO2 EnhancedRecovery. Paper SPE 135563 presented at the SPE Annual Technical Conference andExhibition, Florence, Italy, 19-22 September. http://dx.doi.org/10.2118/135563-MS.
Nasrabadi, H., Firoozabadi, A., and Ahmed, T. 2009. Complex Flow andComposition Path in CO2 Injection Schemes from Density Effects in 2and 3D. Paper SPE 124803 presented at the SPE Annual Technical Conference andExhibition, New Orleans, Louisiana, 4-7 October. http://dx.doi.org/10.2118/124803-MS.
Negara, A. 2011. Simulation of CO2 Injection in Porous Media withStructural Deformation Effect. MSc thesis, King Abdullah University of Scienceand Technology, Thuwal, Saudi Arabia (June 2011).
Neuzil, C.E. 1986. Groundwater Flow in Low-Permeability Environments.Water Resour. Res. 22 (8): 1163-1195. http://dx.doi.org/10.1029/WR022i008p01163.
Nghiem, L., Shrivastava, V., Kohse, B., et al. 2010. Simulation andOptimization of Trapping Processes for CO2 Storage in SalineAquifers. J Cdn. Pet. Tech. 49 (8): 15-22. http://dx.doi.org/10.2118/139429-PA.
Nordbotten, J.M., Celia, M.A., and Bachu, S. 2005. Injection and Storage ofCO2 in Deep Saline Aquifers: Analytical Solution for CO2Plume Evolution during Injection. Transport Porous Med. 58(3): 339-360. http://dx.doi.org/10.1007/s11242-004-0670-9.
Pruess, K. 2004. Numerical Simulation of CO2 Leakage from aGeologic Disposal Reservoir, Including Transitions from Super- to SubcriticalConditions, and Boiling of Liquid CO2. SPE J. 9(2): 237-248. http://dx.doi.org/10.2118/86098-PA.
Salama, A. and Van Geel, P. J. 2008a. Flow and Solute Transport in SaturatedPorous Media: 1. The Continuum Hypothesis. J. Porous Media 11 (4): 403-413. http://dx.doi.org/10.1615/JPorMedia.v11.i4.
Salama, A. and Van Geel, P. J. 2008b. Flow and Solute Transport in SaturatedPorous. Media: 2. Violating the Continuum Hypothesis. J. Porous Media 11 (5) 421-441. http://dx.doi.org/10.1615/JPorMedia.v11.i5.
Sasaki, K., Fujii, T., Niibori, Y., et al. 2008. Numerical Simulation ofSupercritical CO2 Injection into Subsurface Rock Masses. Energ.Converg. Manag. 49 (1): 54-61. http://dx.doi.org/10.1016/j.enconman.2007.05.015.
Sbai, M. and Azaroual, M. 2010. Numerical Modeling of Formation Damage byTwo-Phase Particulate Transport Processes during CO2 Injection inDeep Heterogeneous Porous Media. Adv. Water Resour. 34 (1):62-82. http://dx.doi.org/10.1016/j.advwatres.2010.09.009.
Sifuentes, W., Giddins, M., and Blunt, M. 2009. Modeling CO2Storage in Aquifers: Assessing the Key Contributors to Uncertainty. Paper SPE123582 presented at Offshore Europe, Aberdeen, UK, 8-11 September. http://dx.doi.org/10.2118/123582-MS.
Span, R. and Wagner, W. 1996. A New Equation of State for Carbon DioxideCovering the Fluid Region from the Triple-Point Temperature to 1100 K atPressures Up to 88 MPa. J. Phys. Chem. Ref. Data 25 (6):1509-1595. http://dx.doi.org/10.1063/1.555991.
Sun, S. and Firoozabadi, A. 2009. Compositional Modeling in Three-Phase Flowfor CO2 and Other Fluid Injections Using Higher-Order Finite ElementMethods. Paper SPE 124907 presented at the SPE Annual Technical Conference andExhibition, New Orleans, Louisiana, 4-7 October. http://dx.doi.org/10.2118/124907-MS.
Sun, S., Salama, A., and El-Amin, M.F. 2012. Matrix-Oriented Implementationfor the Numerical Solution of the Partial Differential Equations GoverningFlows in Porous Media. Comput. Fluids 68: 38-46. http://dx.doi.org/10.1016/j.compfluid.2012.07.027.
Taber, J., Martin, F., and Seright, R. 1997. EOR Screening CriteriaRevisited—Part 2: Applications and Impact of Oil Prices. SPE Res Eval &Eng 12 (3): 199-206. http://dx.doi.org/10.2118/39234-PA.
Thomas, S. and Wheeler, M. 2011. Multiblock Methods for CoupledFlow-Transport and Compositional Flow Through Porous Media - Applications tothe Simulation of Transport of Reactive Species and Carbon Sequestration. PaperSPE 141824 presented at the SPE Reservoir Simulation Symposium, Woodlands,Texas, 21-23 February. http://dx.doi.org/10.2118/141824-MS.
Todd, M. and Grand, G. 1993. Enhanced Oil Recovery Using Carbon Dioxide.Energ. Converg. Manag. 34 (9-11): 1157-1164. http://dx.doi.org/10.1016/0196-8904(93)90065-I.
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