×

An extended finite element model for fluid flow in fractured porous media. (English) Zbl 1394.76126

Summary: This paper proposes a numerical model for the fluid flow in fractured porous media with the extended finite element method. The governing equations account for the fluid flow in the porous medium and the discrete natural fractures, as well as the fluid exchange between the fracture and the porous medium surrounding the fracture. The pore fluid pressure is continuous, while its derivatives are discontinuous on both sides of these high conductivity fractures. The pressure field is enriched by the absolute signed distance and appropriate asymptotic functions to capture the discontinuities in derivatives. The most important advantage of this method is that the domain can be partitioned as nonmatching grid without considering the presence of fractures. Arbitrarily multiple, kinking, branching, and intersecting fractures can be treated with the new approach. In particular, for propagating fractures, such as hydraulic fracturing or network volume fracturing in fissured reservoirs, this method can process the complex fluid leak-off behavior without remeshing. Numerical examples are presented to demonstrate the capability of the proposed method in saturated fractured porous media.

MSC:

76S05 Flows in porous media; filtration; seepage
76M10 Finite element methods applied to problems in fluid mechanics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Berkowitz, B.; Bear, J.; Braester, C., Continuum models for contaminant transport in fractured porous formations, Water Resources Research, 24, 8, 1225-1236, (1988) · doi:10.1029/wr024i008p01225
[2] Barenblatt, G. I.; Zheltov, I. P.; Kochina, I. N., Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks [strata], Journal of Applied Mathematics and Mechanics, 24, 5, 1286-1303, (1960) · Zbl 0104.21702 · doi:10.1016/0021-8928(60)90107-6
[3] Karimi-Fard, M.; Durlofsky, L. J.; Aziz, K., An efficient discrete-fracture model applicable for general-purpose reservoir simulators, SPE Journal, 9, 2, 227-236, (2004) · doi:10.2118/88812-PA
[4] Lee, J.; Choi, S.-U.; Cho, W., A comparative study of dual-porosity model and discrete fracture network model, KSCE Journal of Civil Engineering, 3, 2, 171-180, (1999) · doi:10.1007/bf02829057
[5] Lee, S. H.; Lough, M. F.; Jensen, C. L., Hierarchical modeling of flow in naturally fractured formations with multiple length scales, Water Resources Research, 37, 3, 443-455, (2001) · doi:10.1029/2000wr900340
[6] Chen, B. G.; Song, E. X.; Cheng, X. H., A numerical method for discrete fracture network model for flow and heat transfer in two-dimensional fractured rocks, Chinese Journal of Rock Mechanics and Engineering, 33, 1, 43-51, (2014)
[7] Warren, J. E.; Root, P. J., The behavior of naturally fractured reservoirs, Old SPE Journal, 3, 3, 245-255, (1963)
[8] Pruess, K.; Narasimhan, T. N., A practical method for modeling fluid and heat flow in fractured porous media, Society of Petroleum Engineers journal, 25, 1, 14-26, (1985) · doi:10.2118/10509-pa
[9] Kolditz, O., Modelling flow and heat transfer in fractured rocks: conceptual model of a 3-D deterministic fracture network, Geothermics, 24, 3, 451-470, (1995) · doi:10.1016/0375-6505(95)00020-q
[10] Yao, J.; Wang, Z. S.; Zhang, Y.; Huang, Z. Q., Numerical simulation method of discrete fracture network for naturally fractured reservoirs, Acta Petrolei Sinica, 31, 2, 284-288, (2010)
[11] Karihaloo, B. L.; Xiao, Q. Z., Modelling of stationary and growing cracks in FE framework without remeshing: a state-of-the-art review, Computers & Structures, 81, 3, 119-129, (2003) · doi:10.1016/s0045-7949(02)00431-5
[12] Moës, N.; Dolbow, J.; Belytschko, T., A finite element method for crack growth without remeshing, International Journal for Numerical Methods in Engineering, 46, 1, 131-150, (1999) · Zbl 0955.74066 · doi:10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J
[13] Li, L. X.; Wang, T. J., The extended finite element method and its applications: a review, Advances in Mechanics, 35, 1, 5-20, (2005)
[14] Yu, T. T., The Extended Finite Element Method: Theory, Application and Program, (2014), Beijing, China: Science Press, Beijing, China
[15] Khoei, A. R.; Moallemi, S.; Haghighat, E., Thermo-hydro-mechanical modeling of impermeable discontinuity in saturated porous media with X-FEM technique, Engineering Fracture Mechanics, 96, 701-723, (2012) · doi:10.1016/j.engfracmech.2012.10.003
[16] Mohammadnejad, T.; Khoei, A. R., An extended finite element method for hydraulic fracture propagation in deformable porous media with the cohesive crack model, Finite Elements in Analysis and Design, 73, 77-95, (2013) · Zbl 1302.74167 · doi:10.1016/j.finel.2013.05.005
[17] Lamb, A. R., Coupled Deformation, Fluid Flow and Fracture Propagation in Porous Media, (2011), London, UK: Imperial College, London, UK
[18] Lamb, A. R.; Gorman, G. J.; Elsworth, D., A fracture mapping and extended finite element scheme for coupled deformation and fluid flow in fractured porous media, International Journal for Numerical and Analytical Methods in Geomechanics, 37, 17, 2916-2936, (2013) · doi:10.1002/nag.2168
[19] Watanabe, N.; Wang, W.; Taron, J.; Görke, U. J.; Kolditz, O., Lower-dimensional interface elements with local enrichment: application to coupled hydro-mechanical problems in discretely fractured porous media, International Journal for Numerical Methods in Engineering, 90, 8, 1010-1034, (2012) · Zbl 1242.74172 · doi:10.1002/nme.3353
[20] Witherspoon, P. A.; Wang, J. S. Y.; Iwai, K.; Gale, J. E., Validity of cubic law for fluid flow in a deformable rock fracture, Water Resources Research, 16, 6, 1016-1024, (1980) · doi:10.1029/wr016i006p01016
[21] Belytschko, T.; Moes, N.; Usui, S.; Parimi, C., Arbitrary discontinuities in finite elements, International Journal for Numerical Methods in Engineering, 50, 4, 993-1013, (2001) · Zbl 0981.74062
[22] Lewis, R. W.; Schrefler, B. A., The Finite Element Mothod in the Static and Dynamic Deformation and Consolidation of Porous Media, (1998), John Wiley & Sons · Zbl 0935.74004
[23] Yu, T. T.; Gong, Z. W., Determination of enrichment type of node in extended finite element method, Rock and Soil Mechanics, 34, 11, 3284-3290, (2013)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.