Verification and Proper Use of Water-Oil Transfer Function for Dual-Porosity and Dual-Permeability Reservoirs
- Adetayo S. Balogun (Shell E&P) | Hossein Kazemi (Colorado School of Mines) | Erdal Ozkan (Colorado School of Mines) | Mohammed Al-kobaisi (Colorado School of Mines) | Benjamin Ramirez (Colorado School of Mines)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- April 2009
- Document Type
- Journal Paper
- 189 - 199
- 2009. Society of Petroleum Engineers
- 2 in the last 30 days
- 1,203 since 2007
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Accurate calculation of multiphase fluid transfer between the fracture and matrix in naturally fractured reservoirs is a very crucial issue. In this paper, we will present the viability of the use of a simple transfer function to accurately account for fluid exchange resulting from capillary and gravity forces between fracture and matrix in dual-porosity and dual-permeability numerical models. With this approach, fracture- and matrix-flow calculations can be decoupled and solved sequentially, improving the speed and ease of computation. In fact, the transfer-function equations can be used easily to calculate the expected oil recovery from a matrix block of any dimension without the use of a simulator or oil-recovery correlations.
The study was accomplished by conducting a 3-D fine-grid simulation of a typical matrix block and comparing the results with those obtained through the use of a single-node simple transfer function for a water-oil system. This study was similar to a previous study (Alkandari 2002) we had conducted for a 1D gas-oil system.
The transfer functions of this paper are specifically for the sugar-cube idealization of a matrix block, which can be extended to simulation of a match-stick idealization in reservoir modeling. The basic data required are: matrix capillary-pressure curves, densities of the flowing fluids, and matrix block dimensions.
Naturally fractured reservoirs contain a significant amount of the known petroleum hydrocarbons worldwide and, hence, are an important source of energy fuels. However, the oil recovery from these reservoirs has been rather low. For example, the Circle Ridge Field in Wind River Reservation, Wyoming, has been producing for 50 years, but the oil recovery is less than 15% (Golder Associates 2004). This low level of oil recovery points to the need for accurate reservoir characterization, realistic geological modeling, and accurate flow simulation of naturally fractured reservoirs to determine the locations of bypassed oil.
Reservoir simulation is the most practical method of studying flow problems in porous media when dealing with heterogeneity and the simultaneous flow of different fluids. In modeling fractured systems, a dual-porosity or dual-permeability concept typically is used to idealize the reservoir on the global scale. In the dual-porosity concept, fluids transfer between the matrix and fractures in the grid-cells while flowing through the fracture network to the wellbore. Furthermore, the bulk of the fluids are stored in the matrix. On the other hand, in the dual-permeability concept, fluids flow through the fracture network and between matrix blocks.
In both the dual-porosity and dual-permeability formulations, the fractures and matrices are linked by transfer functions. The transfer functions account for fluid exchanges between both media. To understand the details of this fluid exchange, an elaborate method is used in this study to model flow in a single matrix block with fractures as boundaries. Our goal is to develop a technique to produce accurate results for use in large-scale modeling work.
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Al-Kandari, H.A., Kazemi, H., and Van Kirk, C.W. 2002. Gas InjectionEnhanced Oil Recovery in High Relief Naturally Fractured Reservoirs. Presentedat the 2002 Kuwait International Petroleum Conference and Exhibition, KuwaitCity, State of Kuwait, November.
Barenblatt, G.I., Zheltov, Iu.P., and Kochina, I.N. 1960. Basic concepts in thetheory of seepage of homogeneous liquids in fissured rocks. Journal ofApplied Mathematics and Mechanics 24 (5): 1286-1303.DOI:10.1016/0021-8928(60)90107-6.
Beliveau, D. 1989. PressureTransients Characterize Fractured Midale Unit. J. Pet Tech41 (12): 1354-1362; Trans., AIME, 287. SPE-15635-PA.DOI: 10.2118/15635-PA.
Blair, P.M. 1964. Calculation ofOil Displacement by Countercurrent Water Imbibition. SPE J.4 (3): 195-202; Trans., AIME, 231. SPE-873-PA. DOI:10.2118/873-PA.
Chang, M-M. 1993. NIPER-696:Deriving the shape factor of a fractured rock matrix. Technical report,Contract No. DE93000170, US DOE, Washington, DC (September 1993). DOI:10.2172/10192737.
Civan, F. and Rasmussen, M.L. 2002. Analytical Hindered-Matrix-FractureTransfer Models for Naturally Fractured Petroleum Reservoirs. Paper SPE74364 presented at the SPE International Petroleum Conference and Exhibition inMexico, Villahermosa, Mexico, 10-12 February. DOI: 10.2118/74364-MS.
Fung, L.S.K. 1991. Simulationof Block-to-Block Processes in Naturally Fractured Reservoirs. SPE ResEng6 (4): 477-484. SPE-20019-PA. DOI:10.2118/20019-PA.
Gilman, J.R. 1986. An EfficientFinite-Difference Method for Simulating Phase Segregation in the Matrix Blocksin Double-Porosity Reservoirs. SPE Res Eng 1 (4):403-413; Trans., AIME, 281. SPE-12271-PA. DOI:10.2118/12271-PA.
Gilman, J.R. 2003. Practical aspects of simulation of fractured reservoirs.Presented at the International Forum on Reservoir Simulation, Buhl,Baden-Baden, Germany, 23-27 June.
Gilman, J.R. and Kazemi, H. 1988. Improved Calculations for Viscous andGravity Displacement in Matrix Blocks in Dual-Porosity Simulators. J.Pet Tech 40 (1): 60-70; Trans., AIME, 285.SPE-16010-PA. DOI: 10.2118/16010-PA.
Heinemann, Z.E. and Mittermeir, M.G. 2006. Rigorous derivation of theKazemi-Gilman-Elsharkawy generalized dual-porosity shape factor. Paper B044presented at the 10th European Conference on the Mathematics of Oil Recovery,Amsterdam, 4-7 September.
Horie, T., Firoozabadi, A., and Ishimoto, K. 1990. Laboratory Studies of CapillaryInteraction in Fracture/Matrix Systems. SPE Res Eng 5(3): 353-360. SPE-18282-PA. DOI: 10.2118/18282-PA.
Hoteit, H. and Firoozabadi, A. 2006. Numerical Modeling of Diffusion inFractured Media for Gas Injection and Recycling Schemes. Paper SPE 103292presented at the SPE Annual Technical Conference and Exhibition, San Antonio,Texas, USA, 24-27 September. DOI: 10.2118/103292-MS.
Iffly, R., Rousselet, D.C., and Vermeulen, J. L. 1972. Fundamental Study of Imbibition inFissured Oil Fields. Paper SPE 4102 presented at the Fall Meeting of theSociety of Petroleum Engineers of AIME, San Antonio, Texas, USA, 8-11 October.DOI: 10.2118/4102-MS.
Kazemi, H. and Gilman, J.R. 1993. Multiphase flow in fractured petroleumreservoirs. In Flow and Contaminant Transport in Fractured Rock, ed. J.Bear, C.-F. Tsang, G. de Marsily, 267-323. San Diego, California: AcademicPress.
Kazemi, H., Merrill, J.R, Porterfield, K.L., and Zeman, P.R. 1976. Numerical Simulation of Water-Oil Flowin Naturally Fractured Reservoirs. SPE J. 16 (6):317-326; Trans., AIME, 261. SPE-5719-PA. DOI:10.2118/5719-PA.
Kleppe, J. and Morse, R.A. 1974. Oil Production From FracturedReservoirs by Water Displacement. Paper SPE 5084 presented at the FallMeeting of the Society of Petroleum Engineers of AIME, Houston, 6-9 October.DOI: 10.2118/5084-MS.
Kyte, J.R. 1970. A CentrifugeMethod To Predict Matrix-Block Recovery in Fractured Reservoirs. SPEJ. 10 (2): 161-170; Trans., AIME, 249.SPE-2729-PA. DOI: 10.2118/2729-PA.
Lim, K.T. and Aziz, K. 1995. Matrix-fracture transferfunctions for dual porosity simulators. J. Pet. Sci. Eng.13 (3-4): 169-178. DOI: 10.1016/0920-4105(95)00010-F.
Litvak, B.L. 1985. Simulation and characterization of naturally fracturedreservoirs. Proc., Reservoir Characterization Technical Conference,Dallas, 561-583.
Lu, H., Di Donato, G., and Blunt, M.J. 2006. General Transfer Functions forMulti-Phase Flow. Paper SPE 102542 presented at the SPE Annual TechnicalConference and Exhibition, San Antonio, Texas, USA, 24-27 September. DOI:10.2118/102542-MS.
Mattax, C.C. and Kyte, J.R. 1962. Imbibition Oil Recovery From Fractured,Water-Drive Reservoir. SPE J. 2 (2): 177-184;Trans., AIME, 225. SPE-187-PA. DOI: 10.2118/187-PA.
Moreno, J., Kazemi, H., and Gilman, J.R. 2004. Streamline Simulation ofCountercurrent Water-Oil and Gas-Oil Flow in Naturally Fractured Dual-PorosityReservoirs. Paper SPE 89880 presented at the SPE Annual TechnicalConference and Exhibition, Houston, 26-29 September. DOI: 10.2118/89880-MS.
Rangel-German, E.R. and Kovscek, A.R. 2003. Time-Dependent Matrix-Fracture ShapeFactors for Partially and Completely Immersed Fractures. Paper SPE 84411presented at the SPE Annual Technical Conference and Exhibition, Denver, 5-8October. DOI: 10.2118/84411-MS.
Saidi, A.M. 1983. Simulation ofNaturally Fractured Reservoirs. Paper SPE 12270 presented at the SPEReservoir Simulation Symposium, San Francisco, 15-18 November. DOI:10.2118/12270-MS.
Sonier, F., Souillard, P, and Blaskovich, F.T. 1988. Numerical Simulation of NaturallyFractured Reservoirs. SPE Res Eng 3 (4): 1114-1122;Trans., AIME, 285. SPE-15627-PA. DOI: 10.2118/15627-PA.
Uleberg, K. and Kleppe, J. 1996. Dual porosity, dual permeabilityformulation for fractured reservoir simulation. Presented at the NorwegianUniversity of Science and Technology (NTNU), Trondheim RUTH Seminar,Stavanger.
Warren, J.E. and Root, P.J. 1963. The Behavior of Naturally FracturedReservoirs. SPE J. 3 (3): 245-255; Trans., AIME,228. SPE-426-PA. DOI: 10.2118/426-PA.
Yamamoto, R.H., Padgett, J.B., Ford, W.T., and Boubeguira, A. 1971. Compositional Reservoir Simulation forFissured Systems--The Single-Block Model. SPE J. 11(2): 113-128. SPE-2666-PA. DOI: 10.2118/2666-PA.
Zhang, X., Morrow, N.R., and Ma, S. 1996. Experimental Verification of aModified Scaling Group for Spontaneous Imbibition. SPE Res Eng11 (4): 280-285. SPE-30762-PA. DOI: 10.2118/30762-PA.