Improved Prediction of Oil Recovery From Waterflooded Fractured Reservoirs Using Homogenization
- Hamidreza Salimi (Delft University of Technology) | Johannes Bruining (Delft University of Technology)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- February 2010
- Document Type
- Journal Paper
- 44 - 55
- 2010. Society of Petroleum Engineers
- 5.5 Reservoir Simulation, 5.4.1 Waterflooding, 5.8.6 Naturally Fractured Reservoir, 4.3.4 Scale, 5.5.3 Scaling Methods, 4.1.5 Processing Equipment
- oil recovery, fractured reservoirs, homogenization, upscaling, waterflooding
- 3 in the last 30 days
- 903 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 12.00|
|SPE Non-Member Price:||USD 35.00|
Most simulations of waterflooding in fractured media are based on the Warren and Root (WR) approach, which uses an empirical transfer function between the fracture and matrix block. We use homogenization to obtain an improved flow model in fractured media, leading to an integro-differential equation; also called the boundary-condition (BC) approach. We formulate a well-posed numerical 3D model for the BC approach. This paper derives this numerical model to solve full 3D integro-differential equations in a field reservoir simulation. We compare the results of the upscaled model with ECLIPSE™ results. For the interpretation, it is useful to define three dimensionless parameters that characterize the oil production in fractured media. The most important of these parameters is a Peclet number, defined as the ratio between the time required to imbibe water into the matrix block and the travel time of water in the fracture system. The results of the WR approach and the BC approach are in good agreement when the travel time is of the same order of magnitude as the imbibition time. However, if the travel time is shorter or longer than the imbibition time, the approaches give different results. The BC approach allows the use of transfer functions based on fundamental principles (e.g., the use of a rate-dependent capillary pressure function). When implemented, it can be used to improve recovery predictions for waterflooded fractured reservoirs.
|File Size||863 KB||Number of Pages||12|
Arbogast, T. 1993a. Gravitational forces indual-porosity systems: I. Model derivation by homogenization. Transportin Porous Media 13 (2): 179-203. doi:10.1007/BF00654409.
Arbogast, T. 1993b. Gravitational forces indual-porosity systems: II. Computational validation of the homogenizedmodel. Transport in Porous Media 13 (2): 205-220.doi:10.1007/BF00654410.
Arbogast, T. 1997. Computational Aspects of Dual-Porosity Models. InHomogenization and Porous Media, ed. U. Hornung, Vol. 6, 203-223. NewYork: Interdisciplinary Applied Mathematics, Springer-Verlag.
Arbogast, T. and Lehr, H.L. 2006. Homogenization of aDarcy-Stokes system modeling vuggy porous media. ComputationalGeosciences 10 (3): 291-302.doi:10.1007/s10596-006-9024-8.
Barenblatt, G.I., Patzek, T.W., and Silin, D.B. 2002. The Mathematical Model ofNon-Equilibrium Effects in Water-Oil Displacement. Paper SPE 75169presented at the SPE/DOE Improved Oil Recovery Symposium, Tulsa, 13-17 April.doi: 10.2118/75169-MS.
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.
Bear, J. and Verruijt, A. 1987. Modeling Groundwater Flow andPollution. Dordrecht, The Netherlands: Kluwer Academic Publishers.
Bruining J. and Darwish, M.I.M. 2006. Homogenization for Fe2+ DepositionNear Drink Water Tube Wells During Arsenic Remediation. Paper P003 presented atthe 10th European Conference on the Mathematics of Oil Recovery (ECMOR X),Amsterdam, 4-7 September.
Douglas, J. and Arbogast, T. 1990. Dual-Porosity Models for Flow inNaturally Fractured Reservoirs. In Dynamics of Fluids in Hierarchical PorousMedia, ed. J.H. Cushman, 177-221. London: Academic Press.
Douglas, J. Jr., Arbogast, T., and Paes Leme, P.J. 1989. Two Models for Waterflooding ofNaturally Fractured Reservoirs. Paper SPE 18425 presented at the SPESymposium on Reservoir Simulation, Houston, 6-8 February. doi:10.2118/18425-MS.
Douglas, J. Jr., Hensley, J.L., and Arbogast, T. 1991. A dual-porosity model forwaterflooding in naturally fractured reservoirs. Computer Methods inApplied Mechanics and Engineering 87 (2-3): 157-174.doi:10.1016/0045-7825(91)90004-P.
Dutra, T.V. Jr. and Aziz, K. 1992. A New Double-Porosity Reservoir Modelfor Oil/Water Flow Problems. SPE Res Eng 7 (4):419-425. SPE-21248-PA. doi: 10.2118/21248-PA.
Gasem, F.H., Nashawi, I.S., Gharbi, R., and Mir, M.I. 2008. Recovery performance ofpartially fractured reservoirs by capillary imbibition. J. Pet. Sci.Eng. 60 (1): 39-50. doi:10.1016/j.petrol.2007.05.008.
Hassanizadeh, S.M., Celia, M.A., and Dahle, H.K. 2002. Dynamic Effect in theCapillary Pressure—Saturation Relationship and its Impacts on Unsaturated Flow.Vadose Zone J. 1: 38-57.
Kazemi, H., Gilman, J.R. and Elsharkawy, A.M. 1992. Analytical and Numerical Solution ofOil Recovery From Fractured Reservoirs With Empirical Transfer Functions.SPE Res Eng 7 (2): 219-227. SPE-19849-PA. doi:10.2118/19849-PA.
Kazemi, H., Seth, M.S., and Thomas, G.W. 1969. The Interpretation of InterferenceTests in Naturally Fractured Reservoirs with Uniform Fracture Distribution.SPE J. 9 (4): 463-472; Trans., AIME, 246.SPE-2156-PA. doi: 10.2118/2156-PA.
Lake, L.W. 1996. Enhanced Oil Recovery. Englewood Cliffs, New Jersey:Prentice Hall.
Leverett, M.C. 1941. Capillary Behavior in Porous Solids. Trans.,AIME, 142: 152-169.
Namdar Zanganeh, M., Salimi, H., and Bruining, J. 2007. Upscaling in Fractured ReservoirsUsing Homogenization. Paper SPE 107383 presented at the EUROPEC/EAGEConference and Exhibition, London, 11-14 June. doi: 10.2118/107383-MS.
Nelson, R.A. 1985. Geologic Analysis of Naturally FracturedReservoirs, Vol. 1. Houston, Texas: Contributions in Petroleum Geology andEngineering, Gulf Publishing Company.
Rossen, W.R., Gu, Y., and Lake, L.W. 2000. Connectivity and Permeability inFracture Networks Obeying Power-Law Statistics. Paper SPE 59720 presentedat the SPE Permian Basin Oil and Gas Recovery Conference, Midland, Texas, USA,21-23 March. doi: 10.2118/59720-MS.
Saidi, A.M. 1975. Mathematical simulation model describing Iranian fracturedreservoirs and its application to Haft-Kel field. Proc., 9th WorldPetroleum Congress, Tokyo, 209-219.
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.
Sarma, P. and Aziz, K. 2006. New Transfer Functions ForSimulations of Naturally Fractured Reservoirs with Dual-Porosity Models.SPE J. 11 (3): 328-340. SPE-90231-PA. doi:10.2118/90231-PA.
Shook, M., Lake, L.W., and Li, D. 1992. Scaling immiscible flow throughpermeable media by inspectional analysis. In Situ 16 (4):311-349.
Stearns, D.W. 1969. Fracture as a Mechanism of Flow in Naturally DeformedLayered Rocks. Proc., Conference on Research in Tectonics (Kink Bandsand Brittle Deformation), Ottawa, Canada, 14-15 March 1968, GSC Paper 68-52,79-96.
Stearns, D.W. and Friedman, M. 1972. Reservoirs in Fractured Rock. InAAPG Memoir 16, Stratigraphic Oil and Gas Fields--Classification,Exploration Methods, and Case Histories, 82-100. Tulsa, Oklahoma: AAPG.
van Duijn, C.J., Molenaar, J., and deNeef, M.J. 1995. The effect of capillary forces onimmiscible two-phase flow in heterogeneous porous media. Transport inPorous Media 21 (1): 71-93. doi:10.1007/BF00615335.
van Golf-Racht, T. 1982. Fundamentals of Fractured ReservoirEngineering, Vol 12. Oxford, UK: Elsevier Publishing Company.
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.
Wu, Y.-S., Liu, H.H., and Bodvarsson, G.S. 2004. A triple-continuumapproach for modeling flow and transport processes in fractured rock.Journal of Contaminant Hydrology 73 (1-4): 145-179.doi:10.1016/j.jconhyd.2004.01.002.