A Sensitivity Analysis for Effective Parameters on 2D Fracture-Network Permeability
- Alireza Jafari (University of Alberta) | Tayfun Babadagli (University of Alberta)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- June 2009
- Document Type
- Journal Paper
- 455 - 469
- 2009. Society of Petroleum Engineers
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- 1,952 since 2007
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Fracture-network mapping and estimation of its permeability constitute two major steps in static-model preparation of naturally fractured reservoirs. Although several different analytical methods were proposed in the past for calculating fracture-network permeability (FNP), different approaches are still needed for practical use. We propose a new and practical approach to estimate FNP using statistical and fractal characteristics of fracture networks. We also provide a detailed sensitivity analysis to determine the relative importance of fracture-network parameters on the FNP in comparison to single-fracture conductivity using an experimental-design approach.
The FNP is controlled by many different fracture-network parameters such as fracture length, density, orientation, aperture, and single-fracture connectivity. Five different 2D fracture data sets were generated for random and systematic orientations. In each data set, 20 different combinations of fracture density and length for different orientations were tested. For each combination, 10 different realizations were generated. The length was considered as constant and variable. This yielded a total of 1,000 trials. The FNPs were computed through a commercial discrete-fracture-network (DFN) modeling simulator for all cases. Then, we correlated different statistical and fractal characteristics of the networks to the measured FNPs using multivariable-regression analysis. Twelve fractal (sandbox, box counting, and scanline fractal dimensions) and statistical (average length, density, orientation, and connectivity index) parameters were tested against the measured FNP for synthetically generated fracture networks for a wide range of fracture properties. All cases were above the percolation threshold to obtain a percolating network, and the matrix effect was neglected.
The correlation obtained through this analysis using four data sets was tested on the fifth one with known permeability for verification. High-quality match was obtained.
Finally, we adopted an experimental-design approach to identify the most-critical parameters on the FNP for different fracture-network types. The results are presented as Pareto charts.
It is believed that the new method and results presented in this paper will be useful for practitioners in static-model development of naturally fractured reservoirs and will shed light on further studies on modeling and understanding the transmissibility characteristics of fracture networks. It should be emphasized that this study was conducted on 2D fracture networks and could be extended to 3D models. This, however, requires further algorithm development to use 2D fractal characteristics for 3D systems and/or development of fractal measurement techniques for a 3D system. This study will provide a guideline for this type of research.
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Babadagli, T. 2001. Fractal analysis of 2-Dfracture networks of geothermal reservoirs in south-western Turkey. J.of Volcanology and Geothermal Research 112 (1-4): 83-103.doi:10.1016/S0377-0273(01)00236-0.
Barton, C.C. 1995. Fractal analysis of scaling and spatial clustering offractures. In Fractals in the Earth Sciences, ed. C.C. Barton and P.R.La Pointe, Chap. 8, 168. New York City: The Language of Science, PlenumPress.
Barton, C.C. and Hsieh, P.A. 1989. Physical and hydrologic-flowproperties of fractures, 28th International Geological Congress Field TripGuidebook T385. Washington, DC: American Geophysical Union.
Barton, C.C. and Larson, E. 1985. Fractal geometry of two dimensionalfracture networks at Yucca Mountain, southwestern Nevada. In Proceedings ofthe International Symposium on Fundamentals of Rock Joints, Bjorkliden,Sweden, 74-84. Lulea, Sweden: Centek Publishers.
Berkowitz, B. 1994. Modeling and contaminant transport in fractured media.In Advances in Porous Media, Volume 2, ed. Y. Corapcioglu, 397-451. NewYork City: Elsevier.
Berkowitz, B. and Hadad, A. 1997. Fractal and multifractal measures ofnatural and synthetic fracture networks. J. of Geophysical Research102 (B6): 12, 205-212, 218. doi:10.1029/97JB00304.
Bonnet, E., Bour, O., Odling, N.E., Davy, P., Main, I., Cowie, P., andBerkowitz, B. 2001. Scaling ofFracture Systems in Geological Media. Reviews of Geophysics39 (3): 347-383. doi:10.1029/1999RG000074.
Bourbiaux, B., Cacas, M.C., Sarda, S., and Sabathier, J.C. 1998. A rapid and efficient methodologyto convert fractured reservoir images into a dual-porosity model. Revuede l'institut Français du Pétrole 53 (6): 785-799. doi:10.2516/ogst:1998069.
Bunde, A. and Havlin, S. 1995. A Brief Introduction to Fractal Geometry. InFractals in Science, second edition, ed. A. Bunde and S. Havlin, Chap.1. Berlin: Springer-Verlag.
Cacas, M.-C., Sarda, S., Bourbiaux, B., and Sabathier, J.-C. 2000. Methodfor determining the equivalent fracture permeability of a fracture network in asubsurface multilayerd medium. US Patent No. 6,023,656.
Cox, D.R. and Reid, N. 2000. The Theory of the Design of Experiments,No. 86. Boca Raton, Florida: Monographs on Statistics and Applied Probability,CRC Press.
Dershowitz, B., LaPointe, P., Eiben, T., and Wei, L. 2000. Integration of Discrete FeatureNetwork Methods With Conventional Simulator Approaches. SPE Res Eval& Eng 3 (2): 165-170. SPE-62498-PA. doi:10.2118/62498-PA.
La Pointe, P.R. 1988. A method to characterizefracture density and connectivity through fractal geometry.International J. of Rock Mechanics and Mining Sciences 25(6): 421-429. doi:10.1016/0148-9062(88)90982-5.
La Pointe, P.R. 1997. Flow Compartmentalization and Effective Permeability in 3D Fractal FractureNetworks. International J. of Rock Mechanics and Mining Sciences34 (3): 390.http://www.ingentaconnect.com/content/els/01489062/1997/00000034/00000003/art00117.
Long, J.C.S. and Billaux, D.M. 1987. From field data to fracturenetwork modeling: An example incorporating spatial structure. WaterResources Research 23 (7): 1201-1216.doi:10.1029/WR023i007p01201.
Mandelbrot, B.B. 1982. The Fractal Geometry of Nature, 460. New YorkCity: W.H. Freeman.
Margolin, G., Berkowitz, B., and Scher, H. 1998. Structure, Flow and GeneralizedConductivity Scaling in Fracture Networks. Water Resources Research34 (9): 2103-2121. doi:10.1029/98WR01648.
Mason, R.L., Gunst, R.F., and Hess, J.L. 2003. Statistical Design andAnalysis of Experiments, With Applications to Engineering and Science,second edition. Hoboken, New Jersey: Wiley Series in Probability andStatistics, John Wiley & Sons.
Matsumoto, N., Yomogida, K., and Honda, S. 1992. Fractal Analysis of Fault Systems inJapan and the Philippines. Geophysical Research Letters19 (4): 357-360. doi:10.1029/92GL00202.
Montgomery, D.C. 2005. Design and Analysis of Experiments, sixthedition. Hoboken, New Jersey: John Wiley & Sons.
Mourzenko, V.V., Thovert, J.-F., and Adler, P.M. 2001. Permeability of Self-AffineFractures. Transport in Porous Media 45 (1):89-103.doi:10.1023/A:1011859722257.
Narr, W., Schechter, D.W., and Thompson, L.B. 2006. Naturally FracturedReservoir Characterization. Richardson, Texas: SPE.
Nelson, R.A. 2001. Geologic Analysis of Naturally FracturedReservoirs, second edition. Houston: Gulf Publishing Company.
Parney, P., Cladouhos, T., La Pointe, P., Dershowitz, W., and Curran, B.2000. Fracture and Production DataIntegration Using Discrete Fracture Network Models for Carbonate ReservoirManagement, South Oregon Basin Field, Wyoming. Paper SPE 60306 presented atthe SPE Rocky Mountain Regional/Low-Permeability Reservoirs Symposium andExhibition, Denver, 12-15 March. doi: 10.2118/60306-MS.
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.
Saxena, U. and Vjekoslav, P. 1971. Factorial Designs as an Effective Tool inMining and Petroleum Engineering. Paper SPE 3333 available from SPE,Richardson, Texas.
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.
Zhang, X., Sanderson, D.J., Harkness, R.M., and Last, N.C. 1996. Evaluation of the 2-Dpermeability tensor for fractured rock masses. International J. of RockMechanics and Mining Sciences 33 (1): 17-37.doi:10.1016/0148-9062(95)00042-9.