Characterizing flow and transport in fractured geological media: A review

Advances in Water Resources - Tập 25 Số 8-12 - Trang 861-884 - 2002
Brian Berkowitz1
1Department of Environmental Sciences and Energy Research, Weizmann Institute of Science, Rehovot 76100, Israel

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Bear, 1993

Sahimi, 1995

National Research Council. Rock fractures and fluid flow: contemporary understanding and applications. Washington, DC: National Academy Press; 1996

National Research Council. Conceptual models of flow and transport in the fractured vadose zone. Washington, DC: National Academy Press; 2001

Adler, 1999

2001, vol. 42

2000, vol. 122

Odling, 1999, Variations in fracture system geometry and their implications for fluid flow in fractured hydrocarbon reservoirs, Pet. Geosci., 5, 373, 10.1144/petgeo.5.4.373

Odling, 1997, Scaling and connectivity of joint systems in sandstone from western Norway, J. Struct. Geol., 19, 1257, 10.1016/S0191-8141(97)00041-2

Segall, 1983, Joint formation in granitic rock of the Sierra Nevada, Geol. Soc. Am. Bull., 94, 563, 10.1130/0016-7606(1983)94<563:JFIGRO>2.0.CO;2

Priest, 1976, Discontinuity spacings in rock, Int. J. Rock Mech. Min. Sci., 13, 135, 10.1016/0148-9062(76)90818-4

Winter, 1991, The new electrical potential logging tool, Sci. Drill., 2, 147

Jouanna, 1993, A summary of field test methods in fractured rocks, 437

Löw, 1999, Hydraulic borehole characterization through the application of moment methods to fluid conductivity logs, J. Appl. Geophys., 104, 17857

Hsieh, 1985, Field determination of the three-dimensional hydraulic conductivity tensor of anisotropic media, 2. Methodology and application to fractured rocks, Water Resour. Res., 21, 1667, 10.1029/WR021i011p01667

Neuman, 1988, Use of variable-scale pressure test data to estimate the log hydraulic conductivity and dispersivity of fractured granites near Oracle, Arizona, J. Hydrol., 102, 475, 10.1016/0022-1694(88)90112-6

Silliman, 1989, An interpretation of the difference between aperture estimates derived from hydraulic and tracer tests in a single fracture, Water Resour. Res., 25, 2275, 10.1029/WR025i010p02275

Novakowski, 1997, Borehole measurement of the hydraulic properties of low-permeability rock, Water Resour. Res., 33, 2509, 10.1029/97WR02189

Nativ, 1999, Designing a monitoring network for contaminated ground water in fractured chalk, Ground Water, 37, 38, 10.1111/j.1745-6584.1999.tb00956.x

Illman, 2001, Type curve interpretation of a cross-hole pneumatic injection test in unsaturated fractured tuff, Water Resour. Res., 37, 583, 10.1029/2000WR900273

Vesselinov, 2001, Three-dimensional numerical inversion of pneumatic cross-hole tests in unsaturated fractured tuff, 1. Methodology and borehole effects, Water Resour. Res., 37, 3001, 10.1029/2000WR000133

Brown, 1985, Broad bandwidth study of the topography of natural rock surfaces, J. Geophys. Res., 90, 12575, 10.1029/JB090iB14p12575

Poon, 1992, Surface measurement and fractal characterization of naturally fractured rocks, J. Phys. D, 25, 1269, 10.1088/0022-3727/25/8/019

Schmittbuhl, 1995, Scaling invariance of crack surfaces, J. Geophys. Res., 100, 5953, 10.1029/94JB02885

Brown, 1995, Simple mathematical model of a rough fracture, J. Geophys. Res., 100, 5941, 10.1029/94JB03262

Keller, 1985, Automatic, digital system for profiling rough surfaces, Rev. Sci. Instrum., 56, 330, 10.1063/1.1138299

Johns, 1993, Non-destructive measurements of fracture aperture in crystalline rock cores using X-ray computed tomography, J. Geophys. Res., 98, 1889, 10.1029/92JB02298

Feder, 1988

Power, 1991, Euclidean and fractal models for the description of rock surface roughness, J. Geophys. Res., 96, 415, 10.1029/90JB02107

Tsang, 1992, Usage of ‘equivalent apertures’ for rock fractures as derived from hydraulic and tracer tests, Water Resour. Res., 28, 1451, 10.1029/92WR00361

Bonnet, 2001, Scaling of fracture systems in geological media, Rev. Geophys., 39, 347, 10.1029/1999RG000074

Long, 1987, From field data to fracture network modeling: an example incorporating spatial structure, Water Resour. Res., 23, 1201, 10.1029/WR023i007p01201

Tsang, 1987, Channel model of flow through fractured media, Water Resour. Res., 23, 467, 10.1029/WR023i003p00467

Margolin, 1998, Structure, flow, and generalized conductivity scaling in fracture networks, Water Resour. Res., 34, 2103, 10.1029/98WR01648

Koudina, 1998, Permeability of three-dimensional fracture networks, Phys. Rev. E, 57, 4466, 10.1103/PhysRevE.57.4466

Wilke, 1985, Water penetration through fractured rocks: test of a tridimensional percolation description, Math. Geol., 17, 17, 10.1007/BF01030364

Stauffer, 1992

Balberg, 1991, Application of a percolation model to flow in fractured hard rocks, J. Geophys. Res., 96, 10015, 10.1029/91JB00681

Berkowitz, 1993, Percolation theory and its application to groundwater hydrology, Water Resour. Res., 29, 775, 10.1029/92WR02707

Bour, 1997, Connectivity of random fault networks following a power law fault length distribution, Water Resour. Res., 33, 1567, 10.1029/96WR00433

Bour, 1998, On the connectivity of three-dimensional fault networks, Water Resour. Res., 34, 2611, 10.1029/98WR01861

Bour, 1999, Clustering and size distributions of fault patterns: theory and measurements, Geophys. Res. Lett., 26, 2001, 10.1029/1999GL900419

Guéguen, 1991, Percolation and fluid transport in the crust, Geophys. Res. Lett., 18, 931, 10.1029/91GL00951

Chelidze, 1982, Percolation and fracture, Phys. Earth Planet Int., 28, 93, 10.1016/0031-9201(82)90075-9

Barton, 1995, Fractal analysis of scaling and spatial clustering of fractures, 141

Madden, 1983, Microcrack connectivity in rocks: a renormalization group approach to the critical phenomena of conduction and failure in crystalline rocks, J. Geophys. Res., 88, 585, 10.1029/JB088iB01p00585

Renshaw, 1996, Influence of subcritical fracture growth on the connectivity of fracture networks, Water Resour. Res., 32, 1519, 10.1029/96WR00711

Rouleau, 1985, Statistical characterization of the fracture system in the Stripa granite, Sweden, Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 22, 353, 10.1016/0148-9062(85)90001-4

Scholz, 1990, Determination of total strain from faulting using slip measurements, Nature, 346, 837, 10.1038/346837a0

Davy, 1993, On the frequency-length distribution of the San Andreas fault system, J. Geophys. Res., 98, 12141, 10.1029/93JB00372

Berkowitz, 2000, Scaling of fracture connectivity in geological formations, Geophys. Res. Lett., 27, 2061, 10.1029/1999GL011241

Bour O, Davy P, Darcel C, Odling NE. A statistical scaling model for fracture network geometry, with validation on a multi-scale mapping of a joint network (Hornelen Basin, Norway). J Geophys Res, in press

Davy, 1990, Some consequences of a proposed fractal nature of continental faulting, Nature, 348, 56, 10.1038/348056a0

DeHoff, 1968

Billaux, 1989, Three-dimensional statistical modelling of a fractured rock mass––An example from the Fanay-Augéres mine, Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 26, 281, 10.1016/0148-9062(89)91977-3

Cacas, 1990, Modeling fracture flow with a stochastic discrete fracture network: calibration and validation 1. The flow model, Water Resour. Res., 26, 479

Cacas, 1990, Modeling fracture flow with a stochastic discrete fracture network: calibration and validation 2. The transport model, Water Resour. Res., 26, 491

Warburton, 1980, A stereological interpretation of joint trace data, Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 17, 181, 10.1016/0148-9062(80)91084-0

Warburton, 1980, Stereological interpretation of joint trace data: influence of joint shape and implication for geological surveys, Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 17, 305, 10.1016/0148-9062(80)90513-6

Piggott, 1997, Fractal relations for the diameter and trace length of disc-shaped fractures, J. Geophys. Res., 102, 18121, 10.1029/97JB01202

Berkowitz, 1998, Stereological analysis of fracture network structure in geological formations, J. Geophys. Res., 103, 15339, 10.1029/98JB01072

Raven, 1985, Water flow in a natural rock fracture as a function of stress and sample size, Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 22, 251, 10.1016/0148-9062(85)92952-3

Pyrak-Nolte, 1987, Hydraulic and mechanical properties of natural fractures in low permeable rock, Proc. 6th Int. Cong. ProcRock Mech., 225

Durham, 1994, Self-propping and fluid flow in slightly offset joints at high effective pressures, J. Geophys. Res., 99, 9391, 10.1029/94JB00242

Keller, 1995, Prediction of single-phase transport parameters in a variable aperture fracture, Geophys. Res. Lett., 22, 1425, 10.1029/95GL01497

Vandergraaf, 1995, Radionuclide migration experiments under laboratory conditions, Geophys. Res. Lett., 22, 1409, 10.1029/95GL01492

Nolte, 1989, The fractal geometry of flow paths in natural fractures in rock and the approach to percolation, Pure Appl. Geophys., 131, 111, 10.1007/BF00874483

Rasmuson, 1986, Radionuclide transport in fast channels in crystalline rock, Water Resour. Res., 22, 1247, 10.1029/WR022i008p01247

Novakowski, 1985, A field example of measuring hydrodynamic dispersion in a single fracture, Water Resour. Res., 21, 1165, 10.1029/WR021i008p01165

Novakowski, 1995, Preliminary interpretation of tracer experiments conducted in a discrete rock fracture under conditions of natural flow, Geophys. Res. Lett., 22, 1417, 10.1029/95GL00569

Raven, 1988, Interpretation of field tracer tests of a single fracture using a transient solute storage model, Water Resour. Res., 24, 2019, 10.1029/WR024i012p02019

Meheust, 2001, Geometrical heterogeneities and permeability anisotropy of rough fractures, J. Geophys. Res., 106, 2089, 10.1029/2000JB900306

Iwai K. Fundamental studies of fluid flow through a single fracture. Ph.D. Thesis, University of California, Berkeley, 1976

Brown, 1987, Fluid flow through rock joints: the effect of surface roughness, J. Geophys. Res., 92B, 1337, 10.1029/JB092iB02p01337

Moreno, 1988, Flow and tracer transport in a single fracture: a stochastic model and its relation to some field observations, Water Resour. Res., 24, 2033, 10.1029/WR024i012p02033

Thompson, 1991, The effect of anisotropic surface roughness on flow and transport in fractures, J. Geophys. Res., 96B, 21923, 10.1029/91JB02252

David, 1993, Geometry of flow paths for fluid transport in rocks, J. Geophys. Res., 98, 12267, 10.1029/93JB00522

Unger, 1993, Numerical study of the hydromechanical behavior of two rough fracture surfaces in contact, Water Resour. Res., 29, 2101, 10.1029/93WR00516

Amadei, 1994, A mathematical model for flow and solute transport in non-homogeneous and anisotropic rock fractures, Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 31, 719, 10.1016/0148-9062(94)90011-6

Zimmerman, 1991, Lubrication theory analysis of the permeability of rough-walled fractures, Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 28, 325, 10.1016/0148-9062(91)90597-F

Hasegawa, 1983, On steady flow through a channel consisting of an uneven wall and a plane wall, Part 1: case of no relative motion in two walls, Bull. Jpn. Soc. Mech. Eng., 26, 514, 10.1299/jsme1958.26.514

Mourzenko, 1995, Permeability of a single fracture: validity of the Reynolds equation, J. Phys. II Fr., 5, 465, 10.1051/jp2:1995133

Brown, 1995, Applicability of the Reynolds equation for modeling fluid flow between rough surfaces, Geophys. Res. Lett., 22, 2537, 10.1029/95GL02666

Ge, 1997, A governing equation for fluid flow in rough fractures, Water Resour. Res., 33, 53, 10.1029/96WR02588

Dijk, 1999, Investigation of flow in water-saturated rock fractures using nuclear magnetic resonance imaging (NMRI), Water Resour. Res., 35, 347, 10.1029/1998WR900044

Dijk, 1999, Three-dimensional flow measurements in rock fractures, Water Resour. Res., 35, 3955, 10.1029/1999WR900200

Oron, 1998, Flow in fractures: the local cubic law assumption reexamined, Water Resour. Res., 34, 2811, 10.1029/98WR02285

Hakami, 1996, Aperture measurements and flow experiments on a single natural fracture, Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 33, 395, 10.1016/0148-9062(95)00070-4

Berkowitz, 1989, Boundary conditions along permeable fracture walls: influence on flow and conductivity, Water Resour. Res., 25, 1919, 10.1029/WR025i008p01919

Neretnieks, 1982, Tracer movement in a single fissure in granitic rock: some experimental results and their interpretation, Water Resour. Res., 18, 849, 10.1029/WR018i004p00849

Neretnieks, 1993, Solute transport in fracture rock––Applications to radionuclide waste repositories, 39

Smith, 1984, An analysis of the influence of fracture geometry on mass transport in fractured media, Water Resour. Res., 20, 1241, 10.1029/WR020i009p01241

Tsang, 1987, Channel model of flow through fractured media, Water Resour. Res., 23, 467, 10.1029/WR023i003p00467

Tsang, 1988, Flow and tracer transport in fractured media: a variable aperture channel model and its properties, Water Resour. Res., 24, 2049, 10.1029/WR024i012p02049

1997

Barenblatt, 1960, Fundamental equations of filtration of homogeneous liquids in fissured rocks, Sov. Dokl. Akad. Nauk, 132, 545

Barenblatt, 1960, Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks, PMM (Sov. Appl. Math. Mech.), 24, 852

Warren, 1963, The behavior of naturally fractured reservoirs, J. Soc. Pet. Eng., September, 245, 10.2118/426-PA

Odeh, 1965, Unsteady-state behavior of naturally fractured reservoirs, J. Soc. Pet. Eng., 3, 60, 10.2118/966-PA

Kazemi, 1969, The interpretation of interference tests in naturally fractured reservoirs with uniform fracture distribution, J. Soc. Pet. Eng., 9, 463, 10.2118/2156-B

Da Prat, 1981, Decline curve analysis using type curve for two-porosity systems, Soc. Pet. Eng. J., June, 354, 10.2118/9292-PA

Crawford, 1976, Analysis of pressure build-up test in a naturally fractured reservoir, J. Pet. Tech., December, 1295, 10.2118/4558-PA

Braester, 1984, Influence of block size on the transition curve for a drawdown test in a naturally fractured reservoir, J. Soc. Pet. Eng., October, 498, 10.2118/10543-PA

Ahmadi A, Remazeilles V, Quintard M, Noetinger B. Direct calculation of large-scale properties for one-phase flow in random fractured systems. In: 5th European Conference on the Mathematics of Oil Recovery. Leoben, Austria, September 3–6, 1996

Bourbiaux, 1998, A rapid and efficient methodology to convert fractured reservoir images into a dual-porosity model, Revue de l’Institut Français du Pétrole, 53, 785, 10.2516/ogst:1998069

Bourbiaux B, Granet S, Landereau P, Noetinger B, Sarda S, Sabathier JC. Scaling up matrix-fracture transfers in dual-porosity models: Theory and application. SPE 56557, SPE Annual Technical Conference and Exhibition, Houston, USA, October 3–6, 1999

Henn N, Bourbiaux B, Quintard M, Sakthikumar S. Modelling conductive faults with a multiscale approach involving segregation concepts. Paper 2022, EAGE 10th European Symposium on Improved Oil Recovery, Brighton, UK, August 18–20, 1999

Gilman JR, Bowser JL, Rothkopf BW. Application of short-radius horizontal boreholes in the naturally fractured Yate field. Paper SPE 28568, Annual Technical Conference and Exhibition, New Orleans, September, 1994

Hearn, CL, Al-emadi IAA, Worley PLH, Taylor RD. Improved oil recovery in a tight reservoir with conductive faults. Paper SPE 38908, Annual Technical Conference and Exhibition, San Antonio, October, 1997

Narasimhan, 1987, MINC: An approach for analyzing transport in strongly heterogeneous systems

Kazemi, 1993, Multiphase flows in fractured petroleum reservoirs

Lee, 1993

Granet S, Fabrie P, Lemonnier P, Quintard M. A single-phase flow simulation of fractured reservoir using a discrete representation of fractures. In: 6th European Conference on the Mathematics of Oil Recovery (ECMOR VI). Peebles, Scotland, UK, September 8–11, 1998

Lenormand R, Le Romancer JF, Le Gallo Y, Bourbiaux B. Modeling the diffusion flux between matrix and fracture in a fissured reservoir, SPE 49007, Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, New Orleans, USA, September 27–30, 1998

Bernabé, 1995, The transport properties of networks of cracks and pores, J. Geophys. Res., 100, 4231, 10.1029/94JB02986

Friedman, 1998, Critical path analysis of the relationship between permeability and electrical conductivity of three-dimensional pore networks, Water Resour. Res., 34, 1703, 10.1029/98WR00939

Adler, 2000, Effective medium analysis of random lattices, Transp. Porous Media, 40, 145, 10.1023/A:1006611011600

Schwartz, 1983, A stochastic analysis of macroscopic dispersion in fractured media, Water Resour. Res., 19, 1253, 10.1029/WR019i005p01253

Charlaix, 1987, Permeability of a random array of fracture of widely varying apertures, Transp. Porous Media, 2, 31, 10.1007/BF00208535

Berkowitz, 1997, Anomalous transport in random fracture networks, Phys. Rev. Lett., 79, 4038, 10.1103/PhysRevLett.79.4038

Berkowitz, 1998, Theory of anomalous chemical transport in fracture networks, Phys. Rev. E, 57, 5858, 10.1103/PhysRevE.57.5858

Andersson, 1987, Conditional simulations of fluid flow in three-dimensional networks of discrete fractures, Water Resour. Res., 23, 1876, 10.1029/WR023i010p01876

Nordqvist, 1996, Effects of high variance of fracture transmissivity on transport and sorption at different scales in a discrete model for fractured rocks, J. Contam. Hydrol., 22, 39, 10.1016/0169-7722(95)00064-X

Moreno, 1993, Fluid flow and solute transport in a network of channels, J. Contam. Hydrol., 14, 163, 10.1016/0169-7722(93)90023-L

Englman, 1983, Fluid flow through a crack network in rocks, J. Appl. Mech., 50, 707, 10.1115/1.3167133

Robinson, 1983, Connectivity of fracture systems––a percolation theory approach, J. Phys. A, 16, 605, 10.1088/0305-4470/16/3/020

Robinson, 1984, Numerical calculations of critical densities for lines and planes, J. Phys. A, 17, 2823, 10.1088/0305-4470/17/14/025

Hestir, 1990, Analytical expressions for the permeability of random two-dimensional Poisson fracture networks based on regular lattice percolation and equivalent media theories, J. Geophys. Res., 95, 21565, 10.1029/JB095iB13p21565

Berkowitz, 1995, Analysis of fracture network connectivity using percolation theory, Math. Geol., 27, 467, 10.1007/BF02084422

Clauser, 1992, Permeability of crystalline rocks, EOS Trans. AGU, 73, 233, 10.1029/91EO00190

Gelhar, 1993

Barker, 1988, A generalized radial flow model for hydraulic tests in fractured rock, Water Resour. Res., 24, 1796, 10.1029/WR024i010p01796

Acuna, 1995, Application of fractal geometry to the study of networks of fractures and their pressure transient, Water Resour. Res., 31, 527, 10.1029/94WR02260

Becker, 2000, Tracer transport in fractured crystalline rock: evidence of nondiffusive breakthrough tailing, Water Resour. Res., 36, 1677, 10.1029/2000WR900080

OECD Nuclear Energy Agency. Proceedings of the 3rd NEA/SKB Symposium on In Situ Experiments Associated with the Disposal of Radioactive Waste. International Stripa Project, Stockholm, 3–4 October 1990. Paris: OECD Nuclear Energy Agency; 1990

Smellie JAT, Laaksoharju M. The Äspö hard rock laboratory: final evaluation of the hydrogeochemical pre-investigations in relation to existing geologic and hydraulic conditions. Stockholm, SKB (Swed. Nucl. Fuel Waste Handling Co.), Publ. No. TR 92-31, 1992

Hadermann, 1996, The Grimsel (Switzerland) migration experiment: integrating field experiments, laboratory investigations and modelling, J. Contam. Hydrol., 21, 87, 10.1016/0169-7722(95)00035-6

Köhl, 1997, Observation and simulation of non-Darcian flow transients in fractured rock, Water Resour. Res., 33, 407, 10.1029/96WR03495

Kosakowski, 1999, Flow pattern variability in natural fracture intersections, Geophys. Res. Lett., 26, 1765, 10.1029/1999GL900344

Gelhar, 1992, A critical review of data on field-scale dispersion in aquifers, Water Resour. Res., 28, 1955, 10.1029/92WR00607

Sidle, 1998, Spatially varying hydraulic and solute transport characteristics of a fractured till determined by field tracer tests, Funen, Denmark, Water Resour. Res., 34, 2515, 10.1029/98WR01735

McKay, 2000, Field-scale migration of colloidal tracers in a fractured shale saprolite, Ground Water, 38, 139, 10.1111/j.1745-6584.2000.tb00211.x

Kosakowski, 2001, Analysis of field observations of tracer transport in a fractured till, J. Contam. Hydrol., 47, 29, 10.1016/S0169-7722(00)00140-6

Margolin, 2000, Application of continuous time random walks to transport in porous media, J. Phys. Chem. B, 104, 3942, 10.1021/jp993721x

Berkowitz, 2001, The role of probabilistic approaches to transport theory in heterogeneous media, Transp. Porous Media, 42, 241, 10.1023/A:1006785018970

Berkowitz, 2001, Application of continuous time random walk theory to tracer test measurements in fractured and heterogeneous porous media, Ground Water, 39, 593, 10.1111/j.1745-6584.2001.tb02347.x

Berkowitz B, Klafter J, Metzler R, Scher H. Physical pictures of transport in heterogeneous media: Advection-dispersion, random walk and fractional derivative formulations. Water Resour Res, in press

Wilson, 1976, Flow interference effects at fracture intersections, Water Resour. Res., 12, 102, 10.1029/WR012i001p00102

Krizek RJ, Karadi GM, Socias E. Dispersion of a contaminant in fissured rock, Paper presented at Symposium on Percolation Through Fissured Rock, Int Soc Rock Mech, Stuttgart, Germany, 1972

Schwartz, 1983, A stochastic analysis of macroscopic dispersion in fractured media, Water Resour. Res., 19, 1253, 10.1029/WR019i005p01253

Schwartz, 1988, A continuum approach for modeling mass transport in fractured media, Water Resour. Res., 24, 1360, 10.1029/WR024i008p01360

Endo, 1984, A model for investigating mechanical transport in fracture networks, Water Resour. Res., 20, 1390, 10.1029/WR020i010p01390

Sahimi, 1986, Dispersion in flow through porous media-I. One phase flow, Chem. Eng. Sci., 41, 2103, 10.1016/0009-2509(86)87128-7

Hull, 1986, Streamline routing through fracture junctions, Water Resour. Res., 22, 1731, 10.1029/WR022i012p01731

Robinson, 1990, A laboratory and numerical investigation of solute transport in discontinuous fracture systems, Ground Water, 28, 25, 10.1111/j.1745-6584.1990.tb02226.x

Berkowitz, 1994, Mass transfer at fracture intersections: an evaluation of mixing models, Water Resour. Res., 30, 1765, 10.1029/94WR00432

Stockman, 1997, A lattice-gas and lattice Boltzmann study of mixing at continuous fracture junctions: importance of boundary conditions, Geophys. Res. Lett., 24, 1515, 10.1029/97GL51471

Park, 1999, Analytical solutions for solute transfer characteristics at continuous fracture junctions, Water Resour. Res., 35, 1531, 10.1029/1998WR900002

Park, 2001, Effects of junction transfer characteristics on transport in fracture networks, Water Resour. Res., 37, 909, 10.1029/2000WR900365

Park, 2001, Transport and intersection mixing in random fracture networks with power law length distributions, Water Resour. Res., 37, 2493, 10.1029/2000WR000131

Freeze, 1979

Wels, 1994, Retardation of sorbing solutes in fracture media, Water Resour. Res., 30, 2547, 10.1029/94WR01128

Rubin, 1983, Transport of reacting solutes in porous media: relation between mathematical nature of problem formulation and chemical nature of reactions, Water Resour. Res., 19, 1231, 10.1029/WR019i005p01231

Brusseau, 1994, Transport of reactive contaminants in heterogeneous porous media, Rev. Geophys., 32, 285, 10.1029/94RG00624

Berkowitz, 1996, Reactive solute transport in a single fracture, Water Resour. Res., 32, 901, 10.1029/95WR03615

Ibaraki, 1995, Colloid-facilitated contaminant transport in discretely fractured porous media 1. Numerical formulation and sensitivity analysis, Water Resour. Res., 31, 2945, 10.1029/95WR02180

Ibaraki, 1995, Colloid-facilitated contaminant transport in discretely fractured porous media 2. Fracture network examples, Water Resour. Res., 31, 2961, 10.1029/95WR02181

Ryder, 1993, A cave system in Permian gypsum at Houtsay Quarry, Newbiggin, Cumbria, England, Cave Science, 20, 23

Johnson, 1981, Dissolution of salt on the east flank of the Permian Basin in the southwestern USA, J. Hydrol., 54, 75, 10.1016/0022-1694(81)90153-0

Johnson, 1992, Evaporite karst in the Permian Blaine Formation and associated strata in Western Oklahoma, USA, Int. Contribut. Hydrogeol., 13, 405

Cooper, 1986, Subsidence and foundering of strata caused by the dissolution of Permian gypsum in the Ripon and Bedale areas, North Yorkshire, vol. 22, 127

Cooper AH. Subsidence hazards caused by the dissolution of Permian gypsum in England: geology, investigation and remediation. in: Maund JG, Eddleston M. (Eds.), Geohazards in engineering geology, Engineering geology special publication. vol. 15, London: Geological Society; 1998, p. 265–275

James, 1978, Gypsum and anhydrite in foundations of hydraulic structures, Geotechnique, 28, 249, 10.1680/geot.1978.28.3.249

Vaughan, 1986, Role of cracks in progressive permeability reduction during flow of heated aqueous fluids through granite, J. Geophys. Res., 91, 7517, 10.1029/JB091iB07p07517

Turpault, 1992, Dissolution-precipitation process induced by hot water in a fractured granite; Part 1: wall-rock alteration and vein deposition process, Eur. J. Mineral., 4, 1457, 10.1127/ejm/4/6/1457

Turpault, 1992, Analysis of hot fluid infiltration in fractured granite by fluid inclusions study, Appl. Geochem., 1, 269, 10.1016/S0883-2927(09)80081-4

Blanpied, 1992, An earthquake mechanism based on rapid sealing of faults, Nature, 358, 574, 10.1038/358574a0

Moore, 1994, Reduction of permeability in granite at elevated temperatures, Science, 265, 1558, 10.1126/science.265.5178.1558

Gong, 1998, A new model of acid fracture conductivity based on deformation of surface asperities, vol. 39431, 133

Durham, 2001, Direct observation of reactive flow in a single fracture, Water Resour. Res., 37, 1, 10.1029/2000WR900228

Dijk, 2000, Buoyancy-driven dissolution enhancement in rock fractures, Geology, 28, 1051, 10.1130/0091-7613(2000)28<1051:BDEIRF>2.0.CO;2

Dijk, 2002, Measurement and analysis of dissolution patterns in rock fractures, Water Resour Res, 38, 10.1029/2001WR000246

Anderson, 1980, Dissolution of salt deposits by brine density, Geology, 8, 66, 10.1130/0091-7613(1980)8<66:DOSDBB>2.0.CO;2

Berger, 1992, Dissolution-precipitation processes induced by hot water in a fractured granite, Part 2: modelling of water-rock interaction, Eur. J. Mineral., 4, 1477, 10.1127/ejm/4/6/1477

Lowell, 1993, Silica precipitation in fractures and the evolution of permeability in hydrothermal upflow zones, Science, 260, 192, 10.1126/science.260.5105.192

Mourzenko, 1996, Deposition in fractures, Chem. Eng. Commun., 148, 431, 10.1080/00986449608936530

Dreybrodt, 1990, The role of dissolution kinetics in the development of karst aquifers in limestone: a model simulation of karst evolution, J. Geol., 98, 639, 10.1086/629431

Dreybrodt, 1996, Principles of early development of karst conduits under natural and man-made conditions revealed by mathematical analysis of numerical models, Water Resour. Res., 32, 2923, 10.1029/96WR01332

Békri, 1997, Dissolution and precipitation in fractures, Eng. Geol., 48, 283, 10.1016/S0013-7952(97)00044-6

Dijk, 1998, Precipitation and dissolution of reactive solutes in fractures, Water Resour. Res., 34, 457, 10.1029/97WR03238

Kaufmann, 1999, Karst aquifer evolution in fractured rocks, Water Resour. Res., 35, 3223, 10.1029/1999WR900169

Steefel, 1994, Diffusion and reaction in rock matrix bordering a hyperalkine fluid-filled fracture, Geochim. Cosmochim. Acta, 58, 3595, 10.1016/0016-7037(94)90152-X

Savage, 1993, Modeling reactions between cement pore fluids and rock––implications for porosity change, J. Contam. Hydrol., 13, 365, 10.1016/0169-7722(93)90071-Y

Groves, 1994, Early development of karst systems, 1. Preferential flow path enlargement under laminar flow, Water Resour. Res., 30, 2837, 10.1029/94WR01303

Howard, 1995, Early development of karst systems, 2. Turbulent flow, Water Resour. Res., 31, 19, 10.1029/94WR01964

Groves, 1994, Minimum hydrochemical conditions allowing limestone cave development, Water Resour. Res., 30, 607, 10.1029/93WR02945

Shikaze, 1998, Density-dependent solute transport in discretely-fractured geologic media: is prediction possible?, J. Contam. Hydrol., 34, 273, 10.1016/S0169-7722(98)00080-1

Mukhopadhyay S, Sahimi M. Heat transfer and two-phase flow in fractured reservoirs, Soc Pet Eng Paper 24043, Proceedings of Society of Petroleum Engineers Western Regional Meeting, Bakersfield, California, 1992

Fourar M, Lenormand R. A viscous coupling model for relative permeabilities in fractures, SPE 49006, Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, New Orleans, USA, Septembner 27–30, 1998

Nicholl MJ, Glass RJ, Nguyen HA. Gravity-driven fingering in unsaturated fractures. In: Proceedings of the High Level Radioactive Waste Manag. Conference, Las Vegas, NV, 1992

Nicholl MJ, Glass RJ, Nguyen HA. Small-scale behavior of single gravity-driven fingers in an initially dry fracture. In: Proceedings High Level Radioactive Waste Manag. Conference, Las Vegas, NV, 1993

Nicholl, 2000, Factors controlling satiated relative permeability in a partially-saturated horizontal fracture, Geophys. Res. Lett., 27, 393, 10.1029/1999GL006083

Rasmussen, 1991, Steady fluid flow and travel times in partially saturated fractures using a discrete air-water interface, Water Resour. Res., 27, 67, 10.1029/90WR01901

Rasmussen, 1993, Water infiltration into exposed fractured rock surfaces, Soil Sci. Soc. Am. J., 57, 324, 10.2136/sssaj1993.03615995005700020006x

Tokunaga, 1997, Water film flow along fracture surfaces of porous rock, Water Resour. Res., 33, 1287, 10.1029/97WR00473

Su, 1999, Experimental studies of water seepage and intermittent flow in unsaturated, rough-walled fractures, Water Resour. Res., 35, 1019, 10.1029/1998WR900127

Wang, 1985, Hydrologic mechanisms governing fluid flow in a partially saturated, fractured, porous medium, Water Resour. Res., 21, 1861, 10.1029/WR021i012p01861

Peters, 1988, A continuum model for water movement in unsaturated fractured rock, Water Resour. Res., 96, 415

Liu, 1998, An active fracture model for unsaturated flow and transport in fractured rocks, Water Resour. Res., 34, 2633, 10.1029/98WR02040

Pruess, 1999, A mechanistic model for water seepage through thick unsaturated zones in fractured rocks of low matrix permeability, Water Resour. Res., 35, 1039, 10.1029/1998WR900100

Kwicklis, 1993, Numerical investigation of steady liquid water flow in a variably saturated fractured network, Water Resour. Res., 29, 4091, 10.1029/93WR02348

Komor, 1994, Movement of water, solute and stable isotopes in unsaturated zones of two sand plains in the upper Midwest, Water Resour. Res., 30, 253, 10.1029/93WR03099

Nativ, 1995, Water percolation and solute transport through the vadose zone of fractured chalk under desert conditions, Water Resour. Res., 31, 253, 10.1029/94WR02536

Scanlon, 1991, Evaluation of moisture flux from chloride data in desert soils, J. Hydrol., 128, 137, 10.1016/0022-1694(91)90135-5

Scanlon, 1992, Evaluation of liquid vapor water flow in desert soils based on chlorine-36 and tritium tracers and nonisothermal flow simulations, Water Resour. Res., 28, 285, 10.1029/91WR02200

Pruess, 1999, Alternative concepts and approaches for modeling flow and transport in thick unsaturated zones of fractured rocks, J. Contam. Hydrol., 38, 281, 10.1016/S0169-7722(99)00018-2

McLaren, 2000, Flow and transport in fractured tuff at Yucca Mountain: numerical experiments on fast preferential flow mechanisms, J. Contam. Hydrol., 43, 211, 10.1016/S0169-7722(00)00085-1

Doe, 2001, What do drops do? Surface wetting and network geometry effects on vadose-zone fracture flow, 243

Foster, 1980, The infiltration of tritium in the chalk unsaturated zone, J. Hydrol., 46, 343, 10.1016/0022-1694(80)90086-4

Faybishenko, 2000, Conceptual model of the geometry and physics of water flow in a fractured basalt vadose zone, Water Resour. Res., 36, 3499, 10.1029/2000WR900144

Dahan, 1998, A measurement system to determine water flux and solute transport through fractures in the unsaturated zone, Ground Water, 36, 444, 10.1111/j.1745-6584.1998.tb02815.x

Dahan, 1999, Field observation of flow in a fracture intersecting unsaturated chalk, Water Resour. Res., 35, 3315, 10.1029/1999WR900198

Dahan, 2000, On fracture structure and preferential flow in unsaturated chalk, Ground Water, 38, 444, 10.1111/j.1745-6584.2000.tb00231.x

Weisbrod, 1998, On the variability of fracture surfaces in unsaturated chalk, Water Resour. Res., 34, 1881, 10.1029/98WR01447

Weisbrod, 1999, The impact of intermittent flow of rainwater and wastewater on coated and uncoated fractures in chalk, Water Resour. Res., 35, 3211, 10.1029/1999WR900194

Therrien, 1996, Three-dimensional analysis of variably-saturated flow and solute transport in discretely-fractured porous media, J. Contam. Hydrol., 23, 1, 10.1016/0169-7722(95)00088-7

Kueper, 1991, The behavior of dense, nonaqueous phase liquids in fractured clay and rock, Ground Water, 29, 716, 10.1111/j.1745-6584.1991.tb00563.x

Mercer, 1990, A review of immiscible fluids in the subsurface: properties, models, characterization and remediation, J. Contam. Hydrol., 6, 107, 10.1016/0169-7722(90)90043-G

Abriola, 1985, A multiphase approach to the modeling of porous media contamination by organic compounds, 1. Equation development, Water Resour. Res., 21, 11, 10.1029/WR021i001p00011

Abriola, 1985, A multiphase approach to the modeling of porous media contamination by organic compounds, 2. Numerical simulation, Water Resour. Res., 21, 19, 10.1029/WR021i001p00019

Kueper, 1991, Two-phase flow in heterogeneous porous media 1. Model development, Water Resour. Res., 27, 1049, 10.1029/91WR00266

Kueper, 1991, Two-phase flow in heterogeneous porous media 2. Model application, Water Resour. Res., 27, 1059, 10.1029/91WR00267

Kueper, 1995, Variability of point source infiltration rates for two-phase flow in heterogeneous porous media, Water Resour. Res., 31, 2971, 10.1029/95WR02329

LeRomancer J-F, Defives D, Fernandes G. Mechanism of oil recovery by gas diffusion in fractured reservoir in presence of water, SPE/DOE 27746, Symposium on Improved Oil Recovery SPE/DOE, Tulsa, USA, April 1994

Le Gallo Y, Le Romancer J-F, Bourbiaux B, Fernandes G. Mass transfer in fractured reservoirs during gas injection: Experimental and numerical modeling, SPE 38924, SPE Annual Technical Conference and Exhibition, San Antonio, USA, October 5–8, 1997

Paterson, 1984, Diffusion-limited aggregation and two-fluid displacements in porous media, Phys. Rev. Lett., 52, 1621, 10.1103/PhysRevLett.52.1621

Lenormand, 1988, Numerical models and experiments on immiscible displacements in porous media, J. Fluid Mech., 189, 165, 10.1017/S0022112088000953

Wilkinson, 1983, Invasion percolation: a new form of percolation theory, J. Phys. A, 16, 3365, 10.1088/0305-4470/16/14/028

Meakin, 1992, Invasion percolation in a destabilizing gradient, Phys. Rev. A, 46, 3357, 10.1103/PhysRevA.46.3357

Glass, 1996, Simulation of gravity fingering in porous media using a modified invasion percolation model, Geoderma, 70, 231, 10.1016/0016-7061(95)00087-9

Ewing, 2001, Stochastic pore-scale growth models of DNAPL migration in porous media, Adv. Water Resour., 24, 309, 10.1016/S0309-1708(00)00059-2

Glass, 2000, Gravity-destabilized nonwetting phase invasion in macroheterogeneous porous media: experimental observations of invasion dynamics and scale analysis, Water Resour. Res., 36, 3121, 10.1029/2000WR900152

Keller, 2000, Behavior of nonaqueous phase liquids in fractured porous media under two-phase flow conditions, Trans. Porous Media, 38, 189, 10.1023/A:1006619402305

Parker, 1994, Diffusive disappearance of immiscible-phase organic liquids in fractured geologic media, Ground Water, 32, 805, 10.1111/j.1745-6584.1994.tb00922.x

VanderKwaak, 1996, Dissolution of non-aqueous-phase liquids and aqueous-phase contaminant transport in discretely-fractured porous media, J. Contam. Hydrol., 23, 45, 10.1016/0169-7722(95)00087-9

Slough, 1999, Importance of rock matrix entry pressure on DNAPL migration in fractured geologic materials, Ground Water, 37, 237, 10.1111/j.1745-6584.1999.tb00979.x