Articles | Volume 12, issue 10
https://doi.org/10.5194/se-12-2235-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/se-12-2235-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
05 Oct 2021
Research article |
| 05 Oct 2021
| 05 Oct 2021
Investigating the effects of intersection flow localization in equivalent-continuum-based upscaling of flow in discrete fracture networks
Maximilian O. Kottwitz
CORRESPONDING AUTHOR
Johannes Gutenberg University, Institute of Geosciences, Johann-Joachim-Becher-Weg 21, 55128 Mainz, Germany
Johannes Gutenberg University, M3ODEL – Mainz Institute of Multiscale Modeling, Staudingerweg 7, 55128 Mainz, Germany
Anton A. Popov
Johannes Gutenberg University, Institute of Geosciences, Johann-Joachim-Becher-Weg 21, 55128 Mainz, Germany
Johannes Gutenberg University, M3ODEL – Mainz Institute of Multiscale Modeling, Staudingerweg 7, 55128 Mainz, Germany
Steffen Abe
Igem, Institute for Geothermal Resource Management, Berlinstr. 107a, 55411 Bingen, Germany
Boris J. P. Kaus
Johannes Gutenberg University, Institute of Geosciences, Johann-Joachim-Becher-Weg 21, 55128 Mainz, Germany
Johannes Gutenberg University, M3ODEL – Mainz Institute of Multiscale Modeling, Staudingerweg 7, 55128 Mainz, Germany
Related authors
Philipp Eichheimer, Marcel Thielmann, Wakana Fujita, Gregor J. Golabek, Michihiko Nakamura, Satoshi Okumura, Takayuki Nakatani, and Maximilian O. Kottwitz
Solid Earth, 11, 1079–1095, https://doi.org/10.5194/se-11-1079-2020, https://doi.org/10.5194/se-11-1079-2020, 2020
Short summary
Short summary
To describe permeability, a key parameter controlling fluid flows in the Earth’s subsurface, an accurate determination of permeability on the pore scale is necessary. For this reason, we sinter artificial glass bead samples with various
porosities, determining the microstructure and permeability using both
experimental and numerical approaches. Based on this we provide
parameterizations of permeability, which can be used as input parameters for
large-scale numerical models.
Maximilian O. Kottwitz, Anton A. Popov, Tobias S. Baumann, and Boris J. P. Kaus
Solid Earth, 11, 947–957, https://doi.org/10.5194/se-11-947-2020, https://doi.org/10.5194/se-11-947-2020, 2020
Short summary
Short summary
In this study, we conducted 3-D numerical simulations of fluid flow in synthetically generated fractures that statistically reflect geometries of naturally occurring fractures. We introduced a non-dimensional characterization scheme to relate fracture permeabilities estimated from the numerical simulations to their geometries in a unique manner. By that, we refined the scaling law for fracture permeability, which can be easily integrated into discrete-fracture-network (DFN) modeling approaches.
Philipp Eichheimer, Marcel Thielmann, Anton Popov, Gregor J. Golabek, Wakana Fujita, Maximilian O. Kottwitz, and Boris J. P. Kaus
Solid Earth, 10, 1717–1731, https://doi.org/10.5194/se-10-1717-2019, https://doi.org/10.5194/se-10-1717-2019, 2019
Short summary
Short summary
Prediction of rock permeability is of crucial importance for several research areas in geoscience. In this study, we enhance the finite difference code LaMEM to compute fluid flow on the pore scale using Newtonian and non-Newtonian rheologies. The accuracy of the code is demonstrated using several analytical solutions as well as experimental data. Our results show good agreement with analytical solutions and recent numerical studies.
Nicolas Riel, Boris J. P. Kaus, Albert de Montserrat, Evangelos Moulas, Eleanor C. R. Green, and Hugo Dominguez
Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2024-197, https://doi.org/10.5194/gmd-2024-197, 2024
Preprint under review for GMD
Short summary
Short summary
Our research focuses on improving the way we predict mineral assemblage. Current methods, while accurate, are slowed by complex calculations. We developed a new approach that simplifies these calculations and speeds them up significantly using a technique called the BFGS algorithm. This breakthrough reduces computation time by more than five times, potentially unlocking new horizons in modeling reactive magmatic systems.
Steffen Abe and Hagen Deckert
Solid Earth, 12, 2407–2424, https://doi.org/10.5194/se-12-2407-2021, https://doi.org/10.5194/se-12-2407-2021, 2021
Short summary
Short summary
We use numerical simulations and laboratory experiments on rock samples to investigate how stress conditions influence the geometry and roughness of fracture surfaces. The roughness of the surfaces was analyzed in terms of absolute roughness and scaling properties. The results show that the surfaces are self-affine but with different scaling properties between the numerical models and the real rock samples. Results suggest that stress conditions have little influence on the surface roughness.
Philipp Eichheimer, Marcel Thielmann, Wakana Fujita, Gregor J. Golabek, Michihiko Nakamura, Satoshi Okumura, Takayuki Nakatani, and Maximilian O. Kottwitz
Solid Earth, 11, 1079–1095, https://doi.org/10.5194/se-11-1079-2020, https://doi.org/10.5194/se-11-1079-2020, 2020
Short summary
Short summary
To describe permeability, a key parameter controlling fluid flows in the Earth’s subsurface, an accurate determination of permeability on the pore scale is necessary. For this reason, we sinter artificial glass bead samples with various
porosities, determining the microstructure and permeability using both
experimental and numerical approaches. Based on this we provide
parameterizations of permeability, which can be used as input parameters for
large-scale numerical models.
Richard Spitz, Arthur Bauville, Jean-Luc Epard, Boris J. P. Kaus, Anton A. Popov, and Stefan M. Schmalholz
Solid Earth, 11, 999–1026, https://doi.org/10.5194/se-11-999-2020, https://doi.org/10.5194/se-11-999-2020, 2020
Short summary
Short summary
We apply three-dimensional (3D) thermo-mechanical numerical simulations of the shortening of the upper crustal region of a passive margin in order to investigate the control of 3D laterally variable inherited structures on fold-and-thrust belt evolution and associated nappe formation. The model is applied to the Helvetic nappe system of the Swiss Alps. Our results show a 3D reconstruction of the first-order tectonic evolution showing the fundamental importance of inherited geological structures.
Maximilian O. Kottwitz, Anton A. Popov, Tobias S. Baumann, and Boris J. P. Kaus
Solid Earth, 11, 947–957, https://doi.org/10.5194/se-11-947-2020, https://doi.org/10.5194/se-11-947-2020, 2020
Short summary
Short summary
In this study, we conducted 3-D numerical simulations of fluid flow in synthetically generated fractures that statistically reflect geometries of naturally occurring fractures. We introduced a non-dimensional characterization scheme to relate fracture permeabilities estimated from the numerical simulations to their geometries in a unique manner. By that, we refined the scaling law for fracture permeability, which can be easily integrated into discrete-fracture-network (DFN) modeling approaches.
Philipp Eichheimer, Marcel Thielmann, Anton Popov, Gregor J. Golabek, Wakana Fujita, Maximilian O. Kottwitz, and Boris J. P. Kaus
Solid Earth, 10, 1717–1731, https://doi.org/10.5194/se-10-1717-2019, https://doi.org/10.5194/se-10-1717-2019, 2019
Short summary
Short summary
Prediction of rock permeability is of crucial importance for several research areas in geoscience. In this study, we enhance the finite difference code LaMEM to compute fluid flow on the pore scale using Newtonian and non-Newtonian rheologies. The accuracy of the code is demonstrated using several analytical solutions as well as experimental data. Our results show good agreement with analytical solutions and recent numerical studies.
Anthony Osei Tutu, Bernhard Steinberger, Stephan V. Sobolev, Irina Rogozhina, and Anton A. Popov
Solid Earth, 9, 649–668, https://doi.org/10.5194/se-9-649-2018, https://doi.org/10.5194/se-9-649-2018, 2018
Short summary
Short summary
The Earth's surface is characterized by numerous geological processes, formed throughout the Earth's history to present day. The interior (mantle), on which plates rest, undergoes convection motion, generating stresses in the lithosphere plate and also causing the plate motion. This study shows that shallow density heterogeneities in the upper 300 km have a limited influence on the modeled horizontal stress field as opposed to the resulting topography, giving the importance depth sampling.
Cited articles
Alghalandis, Y. F.: ADFNE: Open source software for discrete fracture network engineering, two and three dimensional applications, Comput. Geosci., 102, 1–11, https://doi.org/10.1016/j.cageo.2017.02.002, 2017. a, b, c, d
Andrä, H., Combaret, N., Dvorkin, J., Glatt, E., Han, J., Kabel, M., Keehm, Y., Krzikalla, F., Lee, M., Madonna, C., Marsh, M., Mukerji, T., Saenger, E. H., Sain, R., Saxena, N., Ricker, S., Wiegmann, A., and Zhan, X.: Digital rock physics benchmarks-Part I: Imaging and segmentation, Comput. Geosci., 50, 25–32, https://doi.org/10.1016/j.cageo.2012.09.005, 2013a. a
Andrä, H., Combaret, N., Dvorkin, J., Glatt, E., Han, J., Kabel, M., Keehm, Y., Krzikalla, F., Lee, M., Madonna, C., Marsh, M., Mukerji, T., Saenger, E. H., Sain, R., Saxena, N., Ricker, S., Wiegmann, A., and Zhan, X.: Digital rock physics benchmarks-part II: Computing effective properties, Comput. Geosci., 50, 33–43, https://doi.org/10.1016/j.cageo.2012.09.008, 2013b. a
Bai, T., Maerten, L., Gross, M. R., and Aydin, A.: Orthogonal cross joints: Do they imply a regional stress rotation?, J. Struct. Geol., 24, 77–88, https://doi.org/10.1016/S0191-8141(01)00050-5, 2002. a
Balay, S., Abhyankar, S., Adams, M., Brown, J., Brune, P., Buschelman, K., Dalcin, L., Dener, A., Eijkhout, V., Gropp, W., Karpeyev, D., Kaushik, D., Knepley, M.,
May, D., Curfman McInnes, L., Mills, R., Munson, T., Rupp, K., Sanan, P., Smith, B., Zampini, S., Zhang, H., and Zhang, H.: PETSc Users Manual: Revision 3.10, Tech. rep., Argonne National Lab.(ANL), Argonne, IL (US), 2018. a, b
Batchelor, G. K.: An Introduction to Fluid Dynamics, Cambridge Mathematical Library, Cambridge University Press, Cambridge, United Kingdom, https://doi.org/10.1017/CBO9780511800955, 1967. a
Berre, I., Doster, F., and Keilegavlen, E.: Flow in fractured porous media: A review of conceptual models and discretization approaches, Transport Porous Med., 130, 215–236, https://doi.org/10.1007/s11242-018-1171-6, 2019. a, b, c
Berre, I., Boon, W. M., Flemisch, B., Fumagalli, A., Gläser, D.,
Keilegavlen, E., Scotti, A., Stefansson, I., Tatomir, A., Brenner, K.,
Burbulla, S., Devloo, P., Duran, O., Favino, M., Hennicker, J., Lee, I.-H.,
Lipnikov, K., Masson, R., Mosthaf, K., Nestola, M. G. C., Ni, C.-F.,
Nikitin, K., Schädle, P., Svyatskiy, D., Yanbarisov, R., and Zulian, P.:
Verification benchmarks for single-phase flow in three-dimensional fractured porous media, Adv. Water Res., 147, 103759, https://doi.org/10.1016/j.advwatres.2020.103759, 2020. a, b
Boersma, Q., Hardebol, N., Barnhoorn, A., and Bertotti, G.: Mechanical Factors Controlling the Development of Orthogonal and Nested Fracture Network Geometries, Rock Mech. Rock Eng., 51, 3455–3469, https://doi.org/10.1007/s00603-018-1552-8, 2018. a
Bogdanov, I. I., Mourzenko, V. V., Thovert, J.-F., and Adler, P. M.: Effective permeability of fractured porous media in steady state flow, Water Resour. Res., 39, 1023, https://doi.org/10.1029/2001WR000756, 2003. a
Bonnet, E., Bour, O., Odling, N. E., Davy, P., Main, I., Cowie, P., and Berkowitz, B.: Scaling of fracture systems in geological media, Rev. Geophys., 39, 347–383, https://doi.org/10.1029/1999RG000074, 2001. a, b
Botros, F. E., Hassan, A. E., Reeves, D. M., and Pohll, G.: On mapping fracture networks onto continuum, Water Resour. Res., 44, W08435, https://doi.org/10.1029/2007WR006092, 2008. a, b, c
Brown, S. R.: Fluid flow through rock joints: the effect of surface roughness, J. Geophys. Res.-Sol. Ea., 92, 1337–1347, https://doi.org/10.1029/JB092iB02p01337, 1987. a, b
Brown, S. R.: Simple mathematical model of a rough fracture, J. Geophys. Res.-Sol. Ea., 100, 5941–5952, https://doi.org/10.1029/94JB03262, 1995. a
Cacas, M. C., Ledoux, E., de Marsily, G., Tillie, B., Barbreau, A., Durand, E., Feuga, B., and Peaudecerf, P.: Modeling fracture flow with a stochastic discrete fracture network: calibration and validation: 1. The flow model, Water Resour. Res., 26, 479–489, https://doi.org/10.1029/WR026i003p00479, 1990. a, b
Cartwright, J. and Huuse, M.: 3D seismic technology: the geological “Hubble', Basin Res., 17, 1–20, https://doi.org/10.1111/j.1365-2117.2005.00252.x, 2005. a
Chen, M., Bai, M., and Roegiers, J.-C.: Permeability tensors of anisotropic fracture networks, Math. Geol., 31, 335–373, https://doi.org/10.1023/A:1007534523363, 1999. a, b, c
Chen, T., Clauser, C., Marquart, G., Willbrand, K., and Mottaghy, D.: A new upscaling method for fractured porous media, Adv. Water Resour., 80, 60–68, https://doi.org/10.1016/j.advwatres.2015.03.009, 2015. a
Cnudde, V. and Boone, M. N.: High-resolution X-ray computed tomography in geosciences: A review of the current technology and applications, Earth-Sci. Rev., 1–17, https://doi.org/10.1016/j.earscirev.2013.04.003, 2013. a
Darcel, C., Bour, O., Davy, P., and de Dreuzy, J. R.: Connectivity properties of two-dimensional fracture networks with stochastic fractal correlation, Water Resour. Res., 39, 1272, https://doi.org/10.1029/2002WR001628, 2003. a
Davy, P., Bour, O., De Dreuzy, J.-R., and Darcel, C.: Flow in multiscale fractal fracture networks, Geol. Soc. Sp., 261, 31–45, https://doi.org/10.1144/GSL.SP.2006.261.01.03, 2006. a, b
Davy, P., Le Goc, R., and Darcel, C.: A model of fracture nucleation, growth and arrest, and consequences for fracture density and scaling, J. Geophys. Res.-Sol. Ea., 118, 1393–1407, https://doi.org/10.1002/jgrb.50120, 2013. a
de Dreuzy, J.-R., Méheust, Y., and Pichot, G.: Influence of fracture scale heterogeneity on the flow properties of three-dimensional discrete fracture networks (DFN), J. Geophys. Res.-Sol. Ea., 117, B11207, https://doi.org/10.1029/2012JB009461, 2012. a, b, c
Dershowitz, W. S. and Einstein, H. H.: Characterizing rock joint geometry with joint system models, Rock Mech. Rock Eng., 21, 21–51, https://doi.org/10.1007/BF01019674, 1988. a, b
Eichheimer, P., Thielmann, M., Popov, A., Golabek, G. J., Fujita, W., Kottwitz, M. O., and Kaus, B. J. P.: Pore-scale permeability prediction for Newtonian and non-Newtonian fluids, Solid Earth, 10, 1717–1731, https://doi.org/10.5194/se-10-1717-2019, 2019. a, b
Eichheimer, P., Thielmann, M., Fujita, W., Golabek, G. J., Nakamura, M., Okumura, S., Nakatani, T., and Kottwitz, M. O.: Combined numerical and experimental study of microstructure and permeability in porous granular media, Solid Earth, 11, 1079–1095, https://doi.org/10.5194/se-11-1079-2020, 2020. a, b
Gross, M. R.: The origin and spacing of cross joints: examples from the Monterey Formation, Santa Barbara Coastline, California, J. Struct. Geol., 15, 737–751, https://doi.org/10.1016/0191-8141(93)90059-J, 1993. a
Hadgu, T., Karra, S., Kalinina, E., Makedonska, N., Hyman, J. D., Klise, K., Viswanathan, H. S., and 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, https://doi.org/10.1016/j.jhydrol.2017.07.046, 2017. a, b, c, d, e, f, g
Hauge, V. L., Lie, K.-A., and Natvig, J. R.: Flow-based coarsening for multiscale simulation of transport in porous media, Computat. Geosci., 16, 391–408, https://doi.org/10.1007/s10596-011-9230-x, 2012. a, b
Healy, D., Rizzo, R. E., Cornwell, D. G., Farrell, N. J. C., Watkins, H., Timms, N. E., Gomez-Rivas, E., and Smith, M.: FracPaQ: A MATLAB™ toolbox for the quantification of fracture patterns, J. Struct. Geol., 95, 1–16, https://doi.org/10.1016/j.jsg.2016.12.003, 2017. a
Hyman, J. D., Karra, S., Makedonska, N., Gable, C. W., Painter, S. L., and Viswanathan, H. S.: dfnWorks: A discrete fracture network framework for modeling subsurface flow and transport, Comput. Geosci., 84, 10–19, https://doi.org/10.1016/j.cageo.2015.08.001, 2015. a
Jing, L.: A review of techniques, advances and outstanding issues in numerical modelling for rock mechanics and rock engineering, Int. J. Rock Mech. Min., 40, 283–353, https://doi.org/10.1016/S1365-1609(03)00013-3, 2003. a
Kaus, B. J., Popov, A. A., Baumann, T., Pusok, A., Bauville, A., Fernandez, N., and Collignon, M.: Forward and inverse modelling of lithospheric deformation on geological timescales, in: Proceedings of NIC Symposium, available at: http://hdl.handle.net/2128/9842 (last access: 11 September 2021), 2016. a, b
Klimczak, C., Schultz, R. A., Parashar, R., and Reeves, D. M.: Cubic law with aperture-length correlation: implications for network scale fluid flow, Hydrogeol. J., 18, 851–862, https://doi.org/10.1007/s10040-009-0572-6, 2010. a, b
Kottwitz, M. O., Popov, A. A., Abe, S., Kaus, B. J. P.: LaMEM version used for finite-difference Stokes-flow computations in “Investigating the effects of intersection flow localization in equivalent continuum-based upscaling of flow in discrete fracture networks”, Zenodo [code], https://doi.org/10.5281/zenodo.5520927, last access: 22 September 2021. a
Kottwitz, M. O., Popov, A. A., Abe, S., Kaus, B. J. P.: LaMEM version used for finite-element Darcy-flow computations in “Investigating the effects of intersection flow localization in equivalent continuum-based upscaling of flow in discrete fracture networks”, Zenodo [code], https://doi.org/10.5281/zenodo.5521001, last access: 22 September 2021. a
La Pointe, P. R., Wallmann, P., and Follin, S.: Estimation of effective block conductivities based on discrete network analyses using data from the Äspö site (SKB-TR–95-15), Tech. rep., Swedish Nuclear Fuel and Waste Management Co., 1995. a
Lei, Q., Latham, J.-P., and Tsang, C.-F.: The use of discrete fracture networks for modelling coupled geomechanical and hydrological behaviour of fractured rocks, Comput. Geotech., 85, 151–176, https://doi.org/10.1016/j.compgeo.2016.12.024, 2017. a
Leung, C. T. O., Hoch, A. R., and Zimmerman, R. W.: Comparison of discrete fracture network and equivalent continuum simulations of fluid flow through two-dimensional fracture networks for the DECOVALEX–2011 project, Mineral. Mag., 76, 3179–3190, https://doi.org/10.1180/minmag.2012.076.8.31, 2012. a, b
Li, B., Mo, Y., Zou, L., Liu, R., and Cvetkovic, V.: Influence of surface roughness on fluid flow and solute transport through 3D crossed rock fractures, J. Hydrol., 582, 124284, https://doi.org/10.1016/j.jhydrol.2019.124284, 2020. a
Li, L. and Ji, S.: A new interpretation for formation of orthogonal joints in quartz sandstone, Journal of Rock Mechanics and Geotechnical Engineering, 13, 289–299, https://doi.org/10.1016/j.jrmge.2020.08.003, 2021. a
Lichtner, P. C., Hammond, G. E., Lu, C., Karra, S., Bisht, G., Andre, B.,
Mills, R., and Kumar, J.: PFLOTRAN User Manual: A Massively Parallel Reactive
Flow and Transport Model for Describing Surface and Subsurface Processes,
https://doi.org/10.2172/1168703, 2015. a
Lie, K.-A.: Upscaling Petrophysical Properties, in: An Introduction to Reservoir Simulation Using MATLAB/GNU Octave: User Guide for the MATLAB Reservoir Simulation Toolbox (MRST), edited by: Lie, K.-A., pp. 558–596, Cambridge University Press, Cambridge, https://doi.org/10.1017/9781108591416.020, 2019. a
Lin, G., Liu, J., Mu, L., and Ye, X.: Weak Galerkin finite element methods for Darcy flow: Anisotropy and heterogeneity, J. Comput. Phys., 276, 422–437, https://doi.org/10.1016/j.jcp.2014.07.001, 2014. a, b
Maillot, J., Davy, P., Le Goc, R., Darcel, C., and de Dreuzy, J. R.: Connectivity, permeability, and channeling in randomly distributed and kinematically defined discrete fracture network models, Water Resour. Res., 52, 8526–8545, https://doi.org/10.1002/2016WR018973, 2016. a, b
Makedonska, N., Hyman, J. D., Karra, S., Painter, S. L., Gable, C. W., and Viswanathan, H. S.: Evaluating the effect of internal aperture variability on transport in kilometer scale discrete fracture networks, Adv. Water Resour., 94, 486–497, https://doi.org/10.1016/j.advwatres.2016.06.010, 2016. a
Malehmir, A., Bellefleur, G., Koivista, E., and Juhlin, C.: Pros and cons of 2D vs 3D seismic mineral exploration surveys, First Break, 35, 8, https://doi.org/10.3997/1365-2397.35.8.89805, 2017. a
McDonald, M. G. and Harbaugh, A. W.: A modular three-dimensional finite-difference ground-water flow model, US Geological Survey, United States, 1988. a
Méheust, Y. and Schmittbuhl, J.: Flow enhancement of a rough fracture, Geophys. Res. Lett., 27, 2989–2992, https://doi.org/10.1029/1999GL008464, 2000. a
Méheust, Y. and Schmittbuhl, J.: Scale effects related to flow in rough fractures, Pure Appl. Geophys., 160, 1023–1050, https://doi.org/10.1007/PL00012559, 2003. a, b
Mourzenko, V. V., Thovert, J.-F., and Adler, P. M.: Conductivity and Transmissivity of a Single Fracture, Transport Porous Med., 123, 235–256, https://doi.org/10.1007/s11242-018-1037-y, 2018. a
Neuman, S. P.: Trends, prospects and challenges in quantifying flow and transport through fractured rocks, Hydrogeol. J., 13, 124–147, https://doi.org/10.1007/s10040-004-0397-2, 2005. a
Oda, M.: Permeability tensor for discontinuous rock masses, Géotechnique, 35, 483–495, https://doi.org/10.1680/geot.1985.35.4.483, 1985. a, b, c
Odling, N. E., Gillespie, P., Bourgine, B., Castaing, C., Chiles, J. P., Christensen, N. P., Fillion, E., Genter, A., Olsen, C., Thrane, L., Trice, R., Aarseth, E., Walsh, J. J., and Watterson, J.: Variations in fracture system geometry and their implications for fluid flow in fractures hydrocarbon reservoirs, Petrol. Geosci., 5, 373–384, https://doi.org/10.1144/petgeo.5.4.373, 1999. a, b
Olson, J. E.: Sublinear scaling of fracture aperture versus length: An exception or the rule?, J. Geophys. Res.-Sol. Ea., 108, 2413, https://doi.org/10.1029/2001JB000419, 2003. a, b
Oron, A. P. and Berkowitz, B.: Flow in rock fractures: The local cubic law assumption reexamined, Water Resour. Res., 34, 2811–2825, https://doi.org/10.1029/98WR02285, 1998. a
Ortega, O. J., Marrett, R. A., and Laubach, S. E.: A scale-independent approach to fracture intensity and average spacing measurement, AAPG Bull., 90, 193–208, https://doi.org/10.1306/08250505059, 2006. a
Osorno, M., Uribe, D., Ruiz, O. E., and Steeb, H.: Finite difference calculations of permeability in large domains in a wide porosity range, Arch. Appl. Mech., 85, 1043–1054, https://doi.org/10.1007/s00419-015-1025-4, 2015. a, b
Patir, N. and Cheng, H. S.: An average flow model for determining effects of three-dimensional roughness on partial hydrodynamic lubrication, J. Lubr. Tech., 100, 12–17, https://doi.org/10.1115/1.3453103, 1978. a, b
Reeves, D. M., Benson, D. A., and Meerschaert, M. M.: Transport of conservative solutes in simulated fracture networks: 1. Synthetic data generation, Water Resour. Res., 44, W05404, https://doi.org/10.1029/2007WR006069, 2008. a, b
Renshaw, C. E.: On the relationship between mechanical and hydraulic apertures in rough-walled fractures, J. Geophys. Res.-Sol. Ea., 100, 24629–24636, https://doi.org/10.1029/95JB02159, 1995. a, b
Rodrigues, O.: Des lois géométriques qui régissent les déplacements d'un système solide dans l'espace: et de la variation des cordonnées provenant de ces déplacements considérés indépendamment des causes qui peuvent les produire, Journal de mathématiques pures et appliquées 1re série, tome 5, pp. 380–440, 1840. a
Ruf, J. C., Rust, K. A., and Engelder, T.: Investigating the effect of mechanical discontinuities on joint spacing, Tectonophysics, 295, 245–257, https://doi.org/10.1016/S0040-1951(98)00123-1, 1998.
a
Rutqvist, J., Leung, C., Hoch, A., Wang, Y., and Wang, Z.: Linked multicontinuum and crack tensor approach for modeling of coupled geomechanics, fluid flow and transport in fractured rock, Journal of Rock Mechanics and Geotechnical Engineering, 5, 18–31, https://doi.org/10.1016/j.jrmge.2012.08.001, 2013. a
SKB: Data report for the safety assessment SR-Site, Technical Report SKB TR-10-52, Technical Report TR-10-52, Swedish Nuclear Fuel and Waste Management Co., Stockholm, Sweden, 2010. a
Snow, D. T.: Anisotropie permeability of fractured media, Water Resour. Res., 5, 1273–1289, https://doi.org/10.1029/WR005i006p01273, 1969. a, b
Sweeney, M. R., Gable, C. W., Karra, S., Stauffer, P. H., Pawar, R. J., and Hyman, J. D.: Upscaled discrete fracture matrix model (UDFM): an octree-refined continuum representation of fractured porous media, Computat. Geosci., 24, 293–310, https://doi.org/10.1007/s10596-019-09921-9, 2020.
a, b, c
Witherspoon, P. A., Wang, J. S. Y., Iwai, K., and Gale, J. E.: Validity of cubic law for fluid flow in a deformable rock fracture, Water Resour. Res., 16, 1016–1024, https://doi.org/10.1029/WR016i006p01016, 1980. a
Xu, C. and Dowd, P.: A new computer code for discrete fracture network modelling, Comput. Geosci., 36, 292–301, https://doi.org/10.1016/j.cageo.2009.05.012, 2010. a
Zhou, H., Li, L., and Jaime Gómez-Hernández, J.: Three-dimensional hydraulic conductivity upscaling in groundwater modeling, Comput. Geosci., 36, 1224–1235, https://doi.org/10.1016/j.cageo.2010.03.008, 2010. a, b
Zimmerman, R. W. and Bodvarsson, G. S.: Hydraulic conductivity of rock fractures, Transport Porous Med., 23, 1–30, https://doi.org/10.1007/BF00145263, 1996. a, b, c, d
Zou, L., Jing, L., and Cvetkovic, V.: Modeling of flow and mixing in 3D rough-walled rock fracture intersections, Adv. Water Resour., 107, 1–9, https://doi.org/10.1016/j.advwatres.2017.06.003, 2017. a
Short summary
Upscaling fluid flow in fractured reservoirs is an important practice in subsurface resource utilization. In this study, we first conduct numerical simulations of direct fluid flow at locations where fractures intersect to analyze the arising hydraulic complexities. Next, we develop a model that integrates these effects into larger-scale continuum models of fracture networks to investigate their impact on the upscaling. For intensively fractured systems, these effects become important.
Upscaling fluid flow in fractured reservoirs is an important practice in subsurface resource...
