References
- Barenblatt, G.I., Zheltov, Yu.P., Kochina, I.N.,1960. Prikl. Mat. Mekh, 24, 5, 1286–1303.
- Bear, J., Cheng, A.H.D., 2010. Modelling groundwater flow and contaminant transport. Springer, 834p.
- Benke, R., Painter, S., 2003. Modeling conservative tracer transport in fracture networks with a hybrid approach based on the Boltzmann transport equation. Water Resour. Res., 39, 11, 1324.
- Berrone, S., Borio, A., Fidelibus, C., Pieraccini, S., Scialò, S., Vicini, F., 2018. Advanced computation of steady-state fluid flow in discrete fracture-matrix models: FEM-BEM and VEM-VEM fracture-block coupling. GEM Int. J. Geomath., 9, 2, 377–399.
- Brebbia, C.A., Dominguez, J., 1992. Boundary Elements: An Introductory Course. WIT Press, Southampton, UK.
- Březina, J., Stebel, J., 2016. Analysis of Model Error for a Continuum-Fracture Model of Porous Media Flow. In: Kozubek, T., Blaheta, R., Šístek, J., Rozložník, M., Čermák, M. (eds), High Performance Computing in Science and Engineering 2015. Lecture Notes in Computer Science, vol 9611, Springer, Cham.
- Bruel, D., 2007. Using the migration of the induced seismicity as a constraint for fractured hot dry rock reservoir modelling. Int. J. Rock Mech. Min. Sci., 44, 1106–1117.
- Cacas, M.C., Ledoux, E., de Marsily, G., Barbreau, A., Calmels, P., Gaillard, B., Margrita, R., 1990. Modelling fracture flow with a stochastic discrete fracture network: calibration and validation - the transport model. Water Resour. Res., 26, 3, 491–500.
- Cacas, M.C., Ledoux, E., de Marsily, G., Tillie, B., Barbreau, A., Durand, E., Feuga, B., Paudecerf, P., 1990. Modeling fracture flow with a stochastic discrete fracture network: calibration and validation: 1. The flow model. Water Resour. Res., 26, 3, 479–489.
- Chen, Z., Liao, X., Sepehrnoori, K., Yu, W., 2018. A semianalytical model for pressure-transient analysis of fractured wells in unconventional plays with arbitrarily distributed discrete fractures. Soc. Pet. Eng. J., 23, 2041–2059.
- COMSOL AB, 2024. COMSOL Multiphysics® v. 6.3, Stockholm, Sweden.
- de Dreuzy, J.R., Davy, P., Bour, O., 2001. Hydraulic properties of two dimensional random networks following a power law length distribution: 1. Effective connectivity. Water Resour. Res., 37, 8, 2065–2078.
- Dershowitz, W.S., Einstein, H.H., 1988. Characterizing rock joint geometry with joint system models. Rock Mech. Rock. Eng., 21, 21–51.
- Dershowitz, W.S., Fidelibus, C., 1999. Derivation of equivalent pipe network analogues for three-dimensional discrete fracture networks by boundary element method. Water Resour. Res., 35, 9, 2685–2691.
- Huang, N., Jiang, Y., Liu, R., Li, B., 2017. Estimation of permeability of 3-D discrete fracture networks: an alternative possibility based on trace map analysis. Eng. Geol., 226, 12–19.
- Hyman, J.D., Dentz, M., Hagberg, A., Kang, P.K., 2019. Linking structural and transport properties in three-dimensional fracture networks. J. Geophys. Res. Solid Earth, 124, 1185–2104.
- Kang, P., Le Borgne, T., Dentz, M., Bour, O., Juanes, R., 2015. Impact of velocity correlation and distribution on transport in fractured media: field evidence and theoretical model. Water Resour. Res., 51, 940–959.
- Lee, S.H., Lough, M.F., Jensen, C.L., 2001. Hierarchical modelling of flow in naturally fractured formations with multiple length scales. Water Resour. Res., 37, 3, 443–355.
- Lenti, V., Fidelibus, C., 2003. A BEM solution of steady-state flow problems in discrete fracture networks with minimization of core storage. Comput. Geosci., 29, 9, 1183–1190.
- Li, P., Schanz, M., 2013. Time domain boundary element formulation for partially saturated poroelasticity. Eng. Anal. Bound. Elem., 37, 11, 1483–1498.
- Long, J.C.S., Remer, J.S., Wilson, C.R., Witherspoon, P.A., 1982. Porous media equivalents for networks of discontinuous fractures. Water Resour. Res., 18, 3, 645–658.
- Lough, M.F., Lee, S.H., Kamath, J., 1998. An efficient boundary integral formulation for flow through fractured porous media. J. Comput. Phys., 143, 462–483.
- Martin, V., Jaffré, J., Roberts, J.E., 2005. Modeling fractures and barriers as interfaces for flow in porous media, SIAM J. Sci. Comput., 26, 1667–1691.
- Neuman, S.P., 2005. Trends, prospects and challenges in quantifying flow and transport through fractured rocks. Hydrogeol. J., 13, 124–147.
- Nieber, J.L., Sidle, R.C., 2010. How do disconnected macropores in sloping soils facilitate preferential flow? Hydrol. Process. 24, 1582–1594.
- Pan, J.B., Lee, C.C., Lee, C.H., Yeh, H.F., Lin, H.I., 2010. Application of fracture network model with crack permeability tensor on flow and transport in fractured rock. Eng. Geol., 116, 166–177.
- Pichot, G., Erhel, J., De Dreuzy, J., 2012. A generalized mixed hybrid mortar method for solving flow in stochastic discrete fracture networks. SIAM J. Sci. Comput., 34, 1, B86–B105.
- Priest, S.D., 1993. Discontinuity Analysis for Rock Engineering. Chapman and Hall, London
- Pruess, K., Narasimhan, T., 1985. Practical method for modelling fluid and heat flow in porous media. Soc. Pet. Eng. J., 25, 14–26.
- Rasmussen, T.C., 1991. Steady fluid flow and travel times in partially saturated fractures using a discrete air-water interface. Water Resour. Res., 27, 1, 67–76.
- Rasmussen, T.C., Yeh, T.C.J., Evans, D.D., 1989. Effect of variable fracture permeability/matrix permeability ratios on three-dimensional fractured rock hydraulic conductivity. Battelle Columbus Division, OH, pp. 337–358.
- Reeves, D.M., Parashar, R., Pohlmann, K., Russell, C., Chapman, J., 2014. Development and calibration of dual-permeability models with discontinuous fault networks. Vadose Zone J., 13, 8.
- Reichenberger, V., Jakobs, H., Bastian, P., Helmig, R., 2006. A mixed-dimensional finite volume method for two-phase flow in fractured porous media, Adv. Water Resour., 29, 1020–1036.
- Ren, F., Ma, G., Fan, L., Wang, Y., Zhu, H., 2017. Equivalent discrete fracture networks for modelling fluid flow in highly fractured rock mass. Eng. Geol., 229, 21–30.
- Renshaw, C.E., 1999. Connectivity of joint networks with power law length distributions. Water Resour. Res., 35, 9, 2661–2670.
- Ronayne, M.J., Gorelick, S.M., 2006. Effective permeability of porous media containing branching channel networks. Phys. Rev. E, 73, 026305.
- Samardzioska, T., Popov, V., 2005. Numerical comparison of the equivalent continuum, non-homogeneous and dual porosity models for flow and transport in fractured porous media. Adv. Water Resour., 28, 235–255.
- Sandve T.H., Berre I., Nordbotten, J.M., 2012. An efficient multi-point flux approximation method for discrete fracture– matrix simulations. J. Comput. Phys., 231, 3784–3800.
- Shapiro, A. M., Andersson, J., 1983. Steady state fluid response in fractured rock: A boundary element solution for a coupled, discrete fracture continuum model. Water Resour. Res., 19, 4, 959–969.
- Shapiro, A.M., Andersson, J., 1985. Simulation of steady-state flow in three-dimensional fracture networks using the boundary element method. Adv. Water Resour., 8, 3, 106–110.
- Therrien, R., Sudicky, E.A., 1996. Three-dimensional analysis of variably-saturated flow and solute transport in discretely-fractured porous media. J. Contam. Hydrol., 23, 1–44.
- Wang, B., Feng, Y., Zhou, X., Pieraccini, S., Scialò, S., Fidelibus, C., 2022. Discontinuous boundary elements for steady-state fluid flow problems in discrete fracture networks. Adv. Water Resour., 161, 104125.
- Xu, C., Dowd, P.A., 2014. Stochastic fracture propagation modelling for enhanced geothermal systems. Math. Geosci., 46, 665–690.
- Xu, C., Dowd, P.A., Nguyen, N., Wang, W. J., 2020. Non-parametric three-dimensional fracture modelling from fracture mapping data, in special issue: “Statistical analysis and modelling of fractures and fracture networks in rock masses” of Boletín Geológico y Minero, 131 (3): 401–422.
- Xu, C., Dowd, P.A., Wyborn, D., 2013. Optimisation of a stochastic rock fracture model using Markov Chain Monte Carlo simulation. Min. Tech. Trans. Inst. Min. Metall. A, 122, 3, 153–158.
- Xu, C., Fidelibus, C., Dowd, P., Wang, Z., Tian, Z., 2018. An iterative procedure for the simulation of the steady-state fluid flow in rock fracture networks. Eng. Geol., 242, 160–168.
- Xu, C., Fidelibus, C., Dowd, P.A., 2014. Realistic pipe models for flow modelling in discrete fracture networks. Proceedings of DFNE2014, Vancouver, Canada.
- Yang, R., Huang, Z., Yu, W., Li, G., Ren, W., Zuo, L., Tan, X., Sepehrnoori, K., Tian, S., Sheng, M., 2016. A comprehensive model for real gas transport in shale formations with complex non-planar fracture networks. Sci. Rep., 6, 36673.