×

Upscaled discrete fracture matrix model (UDFM): an octree-refined continuum representation of fractured porous media. (English) Zbl 1434.86007

Summary: We develop a computational geometry-based upscaling approach to accurately capture the dynamic processes occurring within and between subsurface fracture networks and the surrounding porous matrix named the Upscaled Discrete Fracture Matrix model (UDFM). Fracture attributes (orientations and apertures) are upscaled and combined with matrix attributes (permeability and porosity) into properties of an unstructured spatially variable Delaunay tetrahedral continuum mesh. The resolution of the mesh depends on proximity to the fractures to preserve the geometric and topological integrity of the underlying fracture network as well as increasing the accuracy of gradients in the dynamics between the fractures and matrix. The UDFM Delaunay mesh and its dual Voronoi mesh can be used in existing multiphysics simulators for flow, solute/heat mass transport, and geomechanics, thereby eliminating the need for the additional development of numerical methods to couple processes in fracture/matrix systems. The model is verified by comparing flow, transport, and coupled heat-mass flow simulations on the provided meshes against analytical and numerical benchmarks. We also provide an additional example to demonstrate the applicability of the UDFM to complex heteregenous fractured media. Overall, the UDFM is accurate in all of the cases considered here and presents an attractive alternative to other modeling strategies that require novel numerical methods or multi-dimensional meshes.

MSC:

86-08 Computational methods for problems pertaining to geophysics
86A05 Hydrology, hydrography, oceanography
76M12 Finite volume methods applied to problems in fluid mechanics
76S05 Flows in porous media; filtration; seepage
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Los Alamos Grid Toolbox, LaGriT (2017). http://lagrit.lanl.gov
[2] Al-Hadhrami, H.; Blunt, M., Thermally induced wettability alteration to improve oil recovery in fractured resevoirs, SPE Reserv. Eval. Eng., 4, 3, 179-186 (2001)
[3] Berre, I., Doster, F., Keilegavlen, E.: Flow in fractured porous media: a review of conceptual models and discretization approaches. Transport. Porous Med. 10.1007/s11242-018-1171-6(2018)
[4] Berrone, S.; Pieraccini, S.; Scialò, S., A pde-constrained optimization formulation for discrete fracture network flows, SIAM J. Sci. Comput., 35, 2, B487-B510 (2013) · Zbl 1266.65188
[5] Bigi, S.; Battaglia, M.; Alemanni, A.; Lombardi, S.; Campana, A.; Borisova, E.; Loizzo, M., Co2 flow through a fractured rock volume: Insights from field data, 3d fractures representation and fluid flow modeling, Int. J. Greenh. Gas. Con., 18, 183-199 (2013)
[6] Botros, F.E., Hassan, A.E., Reeves, D.M., Pohll, G.: On mapping fracture networks onto continuum. Water Resour. Res., 44(8). 10.1029/2007WR006092 (2008)
[7] Bourret, S. M.; Kwicklis, E. M.; Miller, T. A.; Stauffer, P. H., Evaluating the Importance of Barometric Pumping for Subsurface Gas Transport Near an Underground Nuclear Test Site, Vadose Zone Journal, 18, 1, 1-17 (2019)
[8] Cacas, Mc; Ledoux, E.; De Marsily, G.; Tillie, B.; Barbreau, A.; Durand, E.; Feuga, B.; Peaudecerf, P., Modeling fracture flow with a stochastic discrete fracture network: calibration and validation: 1. The flow model, Water. Resour. Res., 26, 3, 479-489 (1990)
[9] Chen, M.; Bai, M.; Roegiers, Jc, Permeability tensors of anisotropic fracture networks, Math. Geol., 31, 4, 335-373 (1999)
[10] Davy, P.; Le Goc, R.; Darcel, C., A model of fracture nucleation, growth and arrest, and consequences for fracture density and scaling, J. Geophys. Res-Sol. Ea., 118, 4, 1393-1407 (2013)
[11] Davy, P., Le Goc, R., Darcel, C., Bour, O., de Dreuzy, J.R., Munier, R.: A likely universal model of fracture scaling and its consequence for crustal hydromechanics. J. Geophys. Res-Sol. Ea., 115(B10). 10.1029/2009JB007043 (2010)
[12] Delay, F.; Bodin, J., Time domain random walk method to simulate transport by advection-dispersion and matrix diffusion in fracture networks, Geophys. Res. Lett., 28, 21, 4051-4054 (2001)
[13] Dershowitz, W.S.: Fracman interactive discrete feature data analysis, geometric modeling and exploration simulation. User documentation (1998). https://ci.nii.ac.jp/naid/10018056647/en/
[14] de Dreuzy, J.R., Darcel, C., Davy, P., Bour, O.: Influence of spatial correlation of fracture centers on the permeability of two-dimensional fracture networks following a power law length distribution. Water Resour. Res. 40(1). 10.1029/2003WR002260 (2004)
[15] De Dreuzy, J.-R.; Méheust, Y.; Pichot, G., Influence of fracture scale heterogeneity on the flow properties of three-dimensional discrete fracture networks (DFN), Journal of Geophysical Research: Solid Earth, 117, B11, n/a-n/a (2012)
[16] Erhel, J.; De Dreuzy, J.; Poirriez, B., Flow simulation in three-dimensional discrete fracture networks, SIAM J. Sci. Comput., 31, 4, 2688-2705 (2009) · Zbl 1387.65124
[17] Flemisch, B.; Fumagalli, A.; Scotti, A., A Review of the XFEM-Based Approximation of Flow in Fractured Porous Media, 47-76 (2016), Cham: Springer International Publishing, Cham · Zbl 1371.76093
[18] Follin, S.; Hartley, L.; Rhén, I.; Jackson, P.; Joyce, S.; Roberts, D.; Swift, B., A methodology to constrain the parameters of a hydrogeological discrete fracture network model for sparsely fractured crystalline rock, exemplified by data from the proposed high-level nuclear waste repository site at Forsmark, Sweden, Hydrogeol. J, 22, 2, 313-331 (2014)
[19] Frampton, A., Cvetkovic, V.: Inference of field-scale fracture transmissivities in crystalline rock using flow log measurements. Water Resour. Res., 46(11) (2010)
[20] Fumagalli, A.; Scotti, A., A Reduced Model for Flow and Transport in Fractured Porous Media with Non-matching Grids, Numerical Mathematics and Advanced Applications 2011, 499-507 (2012), Berlin, Heidelberg: Springer Berlin Heidelberg, Berlin, Heidelberg · Zbl 1273.76398
[21] Gelet, R.; Loret, B.; Khalili, N., A thermo-hydro-mechanical coupled model in local thermal non-equilibrium for fractured HDR reservoir with double porosity, Journal of Geophysical Research: Solid Earth, 117, B7, n/a-n/a (2012)
[22] Hadgu, T.; Kalinina, E.; Lowry, Ts, Modeling of heat extraction from variably fractured porous media in enhanced geothermal systems, Geothermics, 61, 75-85 (2016)
[23] Hadgu, T.; Karra, S.; Kalinina, E.; Makedonska, N.; Hyman, Jd; Klise, K.; Viswanathan, Hs; Wang, Y., A comparative study of discrete fracture network and equivalent continuum models for simulating flow and transport in the far field of a hypothetical nuclear waste repository in crystalline host rock, J. Hydrol., 553, 59-70 (2017)
[24] Hartley, L.; Joyce, S., Approaches and algorithms for groundwater flow modeling in support of site investigations and safety assessment of the Forsmark site, Sweden, J. Hydrol., 500, 200-216 (2013)
[25] Hyman, Jd; Gable, Cw; Painter, Sl; Makedonska, N., Conforming Delaunay triangulation of stochastically generated three dimensional discrete fracture networks: A feature rejection algorithm for meshing strategy, SIAM J. Sci. Comput., 36, 4, A1871-A1894 (2014) · Zbl 1305.74082
[26] Hyman, Jd; Jiménez-Martínez, J.; Viswanathan, Hs; Carey, Jw; Porter, Ml; Rougier, E.; Karra, S.; Kang, Q.; Frash, L.; Chen, L.; Lei, Z.; O’Malley, D.; Makedonska, N., Understanding hydraulic fracturing: a multi-scale problem, Philos. T R Soc. A, 374, 2078, 20150426 (2016)
[27] Hyman, Jd; Karra, S.; Makedonska, N.; Gable, Cw; Painter, Sl; Viswanathan, Hs, dfnworks: A discrete fracture network framework for modeling subsurface flow and transport, Comput. Geosci., 84, 10-19 (2015)
[28] Hyman, Jeffrey D.; Rajaram, Harihar; Srinivasan, Shriram; Makedonska, Nataliia; Karra, Satish; Viswanathan, Hari; Srinivasan, Gowri, Matrix Diffusion in Fractured Media: New Insights Into Power Law Scaling of Breakthrough Curves, Geophysical Research Letters, 46, 23, 13785-13795 (2019)
[29] Jackson, Cp; Hoch, Ar; Todman, S., Self-consistency of a heterogeneous continuum porous medium representation of a fractured medium, Water. Resour. Res., 36, 1, 189-202 (2000)
[30] Jenkins, C.; Chadwick, A.; Hovorka, Sd, The state of the art in monitoring and verification—ten years on, Int. J. Greenh. Gas. Con., 40, 312-349 (2015)
[31] Jordon, A.B., Stauffer, P.H., Knight, E.E., Rougier, E., Anderson, D.N.: Radionuclide gas transport through nuclear explosion-generated fracture networks. Sci Rep-UK., 5(18383). 10.1038/srep18383(2015)
[32] Kalinina, Ea; Klise, Ka; Mckenna, Sa; Hadgu, T.; Lowry, Ts, Applications of fractured continuum model to enhanced geothermal system heat extraction problems, SpringerPlus, 3, 1, 110 (2014)
[33] Karra, S.; Makedonska, N.; Viswanathan, H.; Painter, S.; Hyman, J., Effect of advective flow in fractures and matrix diffusion on natural gas production, Water. Resour. Res., 51, 10, 8646-8657 (2015)
[34] Köppel, M.; Martin, V.; Jaffré, J.; Roberts, Je, A lagrange multiplier method for a discrete fracture model for flow in porous media, Computat. Geosci., 23, 2, 239-253 (2019) · Zbl 1414.76059
[35] Lauwerier, Ha, The transport of heat in an oil layer caused by the injection of hot fluid, Appl. Sci. Res., 5, 2, 145-150 (1955)
[36] Li, L.; Lee, Sh, SPE-103901-MS, chap. Efficient Field-Scale Simulation for Black Oil in a Naturally Fractured Reservoir via Discrete Fracture Networks and Homogenized Media, 12-12 (2006), Beijing, China: Society of Petroleum Engineers, Beijing, China
[37] Lichtner, P.C., Hammond, G.E., Lu, C., Karra, S., Bisht, G., Andre, B., Mills, R., Kumar, J.: Pflotran user manual: A massively parallel reactive flow and transport model for describing surface and subsurface processes. 10.2172/1168703 (2015)
[38] Makedonska, N.; Painter, Sl; Bui, Qm; Gable, Cw; Karra, S., Particle tracking approach for transport in three-dimensional discrete fracture networks, Computat. Geosci., 19, 5, 1123-1137 (2015) · Zbl 1391.76735
[39] Moinfar, A., Varavei, A., Sepehrnoori, K., Johns, R.: Development of a coupled dual continuum and discrete fracture model for the simulation of unconventional reservoirs. Society of Petroleum Engineers. 10.2118/163647-MS (2013)
[40] Moinfar, A.; Varavei, A.; Sepehrnoori, K.; Johns, Rt, Development of an efficient embedded discrete fracture model for 3d compositional reservoir simulation in fractured reservoirs, Soc. Petrol. Eng. J, 19, 2, 289-303 (2014)
[41] Mustapha, H.; Mustapha, K., A new approach to simulating flow in discrete fracture networks with an optimized mesh, SIAM J. Sci. Comput., 29, 4, 1439-1459 (2007) · Zbl 1251.76056
[42] National Research Council: Rock Fractures and Fluid Flow: Contemporary Understanding and Applications. National Academy Press (1996)
[43] Neuman, Sp, Trends, prospects and challenges in quantifying flow and transport through fractured rocks, Hydrogeol. J, 13, 1, 124-147 (2005)
[44] Oda, M., Permeability tensor for discontinuous rock masses, Géotechnique, 35, 4, 483-495 (1985)
[45] Odsæter, Lh; Kvamsdal, T.; Larson, Mg, A simple embedded discrete fracture-matrix model for a coupled flow and transport problem in porous media, Comput. Method. Appl. M, 343, 572-601 (2019)
[46] Okabe, A.; Boots, B.; Sugihara, K., Spatial Tessellations: Concepts and Applications of Voronoi Diagrams (1992), New York: Wiley, New York · Zbl 0877.52010
[47] Painter, S., Cvetkovic, V., Mancillas, J., Pensado, O.: Time domain particle tracking methods for simulating transport with retention and first-order transformation. Water Resour. Res., 44(1). 10.1029/2007WR005944 (2008)
[48] Pichot, G.; Erhel, J.; De Dreuzy, J., A mixed hybrid mortar method for solving flow in discrete fracture networks, Appl. Anal., 89, 10, 1629-1643 (2010) · Zbl 1387.65122
[49] Pichot, G.; Erhel, J.; De Dreuzy, J., A generalized mixed hybrid mortar method for solving flow in stochastic discrete fracture networks, SIAM J. Sci. Comput., 34, 1, B86-B105 (2012) · Zbl 1387.65121
[50] Reeves, D.M., Benson, D.A., Meerschaert, M.M.: Transport of conservative solutes in simulated fracture networks: 1. synthetic data generation. Water Resour. Res., 44(5). 10.1029/2007WR006069 (2008)
[51] Schwenck, N.; Flemisch, B.; Helmig, R.; Wohlmuth, Bi, Dimensionally reduced flow models in fractured porous media: crossings and boundaries, Computat. Geosci., 19, 6, 1219-1230 (2015) · Zbl 1391.76747
[52] Tsang, Yw; Tsang, Cf; Hale, Fv; Dverstorp, B., Tracer transport in a stochastic continuum model of fractured media, Water. Resour. Res., 32, 10, 3077-3092 (1996)
[53] Vanderkwaak, J.; Sudicky, E., Dissolution of non-aqueous-phase liquids and aqueous-phase contaminant transport in discretely-fractured porous media, J. Contam. Hydrol., 23, 1-2, 45-68 (1996)
[54] Willis-Richards, J.; Watanabe, K.; Takahashi, H., Progress toward a stochastic rock mechanics model of engineered geothermal systems, J. Geophys. Res-Sol. Ea., 101, B8, 17481-17496 (1996)
[55] Xu, C.; Dowd, Pa; Mardia, Kv; Fowell, Rj, A connectivity index for discrete fracture networks, Math. Geol., 38, 5, 611-634 (2006) · Zbl 1323.74055
[56] Zyvoloski, G., Robinson, B., Z.V., D., Kelkar, S., Viswanathan, H., Pawar, R., Stauffer, P., Miller, T., Chu, S.: Software users manual (um) for the fehm application version 3.1-3.x. Los Alamos National Laboratory Repository, LA-UR-12-24493
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.