Abstract
This report describes the fracture-scale mechanisms acting on solute transport in fractured aquifers under natural-flow conditions. It focuses on low-permeability rocks where advection in the matrix is negligible compared with that in fractures. The relevant transport mechanisms detailed have been identified by experimental and theoretical studies over the past 30 years: advection and hydrodynamic dispersion, channeling effects, matrix diffusion, and sorption reactions. This review is intended to emphasize the fundamental concepts and to draw up a reader's guide through an extensive bibliography by linking key problems to key papers. These concepts might be integrated into transport models, but their influence at the large scale, however, remains an open question that is not dealt with in this review.
Résumé
Ce rapport décrit les mécanismes agissant sur le transport de soluté dans les aquifères fissurés en régime d'écoulement naturel. L'accent est mis sur les roches peu perméables, où le transport par convection dans la matrice est négligeable devant la convection dans les fractures. Les mécanismes de transport sont analysés à l'échelle de la fracture: convection et dispersion hydrodynamique, chenalisation, diffusion dans la matrice et réactions de sorption. L'objectif de ce travail est double: d'une part, mettre en avant les concepts fondamentaux pouvant être intégrés dans les modèles de transport, et d'autre part, établir un "guide" permettant au lecteur de s'orienter à travers une bibliographie abondante, en reliant chaque sujet abordé à quelques articles clés. Notons que l'influence de ces mécanismes sur le transport à grande échelle reste un problème clé qui ne sera pas abordé ici.
Resumen
Este informe describe los mecanismos que actúan a escala de fractura en el transporte de solutos en acuíferos fracturados, bajo condiciones de flujo natural. Se centra en rocas de baja permeabilidad en las que la advección en la matriz es despreciable en relación con la advección en las fracturas. Los mecanismos de transporte relevantes han sido identificados mediante estudios experimentales y teóricos realizados en los últimos 30 años. Consisten en advección y dispersión hidrodinámica, influencia de los canales, difusión en la matriz y reacciones de sorción. Esta revisión pretende enfatizar en los conceptos fundamentales y generar una guía para el lector por medio de una bibliografía abundante que relaciona los problemas clave con artículos clave. Estos conceptos podrían ser integrados en modelos de transporte, pero su influencia a gran escala es todavía un tema no resuelto, el cual no se aborda en este trabajo.
Similar content being viewed by others
References
Abelin H, Birgersson L, Moreno L, Widen H, Agren T, Neretnieks I (1991) A large-scale flow and tracer experiment in granite. 2: Results and interpretation. Water Resour Res 27(12):3119–3135
Abelin H, Birgersson L, Widen H, Agren T, Moreno L, Neretnieks I (1994) Channeling experiments in crystalline fractured rocks. J Contam Hydrol 15(3):129–158
Adler PM, Thovert J-F (1999) Fractures and fracture networks. Kluwer, Dordrecht, The Netherlands, 429 pp
Amadei B, Illangasekare T (1994) A mathematical model for flow and solute transport in non-homogeneous rock fractures Int J Rock Mech Mineral Sci Geomech Abstr 31:719–731
Andersson P, Nordqvist R, Persson T, Eriksson CO, Gustafsson E, Ittner T (1993) Dipole tracer experiment in a low-angle fracture at Finnsjön: results and interpretation. The Fracture Zone Project—phase 3, SKB TR 93-26. Swed Nucl Fuel Waste Manage Co, Stockholm, Sweden
Aris R (1956) On the dispersion of a solute in a fluid flowing through a tube. Proc R Soc Lond Ser A 235:67–77
Aris R (1959) On the dispersion of a solute by diffusion, convection and exchange between phases Proc R Soc Lond Ser A 252:538–550
Autio J, Siitari-Kauppi M, Timonen J, Hartikainen K, Hartikainen J (1998) Determination of the porosity, permeability and diffusivity of rock in the excavation-disturbed zone around full-scale deposition holes using the 14C-PMMA and He-gas methods. J Contam Hydrol 35:19–29
Bear J, Tsang CH, de Marsily G (eds) (1993) Flow and contaminant transport in fractured rock. Academic Press, San Diego, CA, USA, 560 pp
Becker MW, Shapiro AM (2000) Tracer transport in fractured crystalline rock: evidence of nondiffusive breakthrough tailing. Water Resour Res 36(7):1677–1686
Berkowitz B, Scher H (1995) On characterization of anomalous dispersion in porous and fractured media. Water Resour Res 31(6):1461–1466
Berkowitz B, Zhou J (1996) Reactive solute transport in a single fracture. Water Resour Res 32(4):901–913
Bibby R (1981) Mass transport of solutes in dual-porosity media. Water Resour Res 17(4):1075–1081
Birgersson L, Neretnieks I (1990) Diffusion in the matrix of granitic rock: field tests in the Stripa mine. Water Resour Res 26(11):2833–2842
Bodin J, Delay F, de Marsily G (2003) Solute transport in a single fracture with negligible matrix permeability: 2. mathematical formalism. Hydrogeol J (in press)
Boving TB, Grathwohl P (2001) Tracer diffusion coefficients in sedimentary rocks: correlation to porosity and hydraulic conductivity. J Contam Hydrol 53:85–100
Bradbury MH, Green A (1985) Measurement of important parameters determining aqueous phase diffusion rates through crystalline rock matrices. J Hydrol 82:39–55
Bradbury MH, Green A (1986) Investigations into factors influencing long range matrix diffusion rates and pore space accessibility at depth in granite. J Hydrol 89, 123–139
Brandberg F, Skagius K (1991) Porosity, sorption and diffusivity data compiled for the SKB 91 study, SKB TR 91-16. Swed Nucl Fuel Waste Manage Co, Stockholm, Sweden
Brenner H (1980) A general theory of Taylor dispersion phenomena. PhysicoChem Hydrodynam 1:91–123
Broeck CVD (1990) Taylor dispersion revisited. Physica A 168(2):677–696
Brown SR (1987) Fluid flow through rock joints: the effect of surface roughness. J Geophys Res 92:1337–1347
Brown SR, Caprihan A, Hardy R (1998) Experimental observation of fluid flow channels in a single fracture. J Geophys Res 103:(B3):5125–5132
Brunauer MH, Emmet PH, Teller E (1938) Adsorption of gases in multimolecular layers. J Am Chem Soc 60:309–319
Byegard J, Johansson H, Skalberg M, Tullborg EL (1998) The interaction of sorbing tracers with different Äspö rock types: sorption and diffusion experiments in the laboratory scale, SKB TR 98-18. Swed Nucl Fuel Waste Manage Co, Stockholm, Sweden, 105 pp
Cacas MC, Ledoux E, de Marsily G, Barbreau A, Calmels P, Gaillard B, Margritta R (1990a) Modeling fracture flow with a stochastic discrete fracture network: calibration and validation, 2, the transport model. Water Resour Res 26(3):491–500
Cacas MC, Ledoux E, de Marsily G, Tillie B, Barbreau A, Calmels P, Durand E, Feuga B, Peaudecerf P (1990b) Modeling fracture flow with a stochastic discrete fracture network: calibration and validation. 1, The flow model. Water Resour Res 26(3):479–489
Cady CC, Silliman SE, Shaffern E (1993) Validation in aperture estimate ratios from hydraulic and tracer tests in a single fracture. Water Resour Res 29(9):2975–2982
Callahan TJ, Reimus PW, Bowman RS, Haga MJ (2000) Using multiple experimental methods to determine fracture/matrix interactions and dispersion of nonreactive solutes in saturated volcanic tuff. Water Resour Res 36(12):3547–3558
Carbol P, Engkvist I (1997) Compilation of radionuclide sorption coefficients for performance assessment, SKB R 97-13. Swed Nucl Fuel Waste Manage Co, Stockholm
Cvetkovic V, Selroos JO, Cheng H (1999) Transport of reactive tracers in rock fractures. J Fluid Mech 378:335–356
Dagan G (1989) Flow and transport in porous formation. Springer, Berlin Heidelberg New York, 465 pp
D'Alessandro M, Mousty F, Bidoglio G, Guimera J, Benet I, Vila XS, Gutierrez MG, Llano AYD (1997) Field tracer experiment in a low permeability fractured medium: results from el Berrocal site. J Contam Hydrol 26(1–4):189–201
Delay F, Porel G, Banton O (1998) An approach to transport in heterogeneous porous media using the truncated temporal moment equations: theory and numerical validation. Transport Porous Media 32(2):199–232
Dershowitz WS, Fidelibus C (1999) Derivation of equivalent pipe network analogues for three-dimensional discrete fracture networks by the boundary element method. Water Resour Res 35(9):2685–2691
Detwiler RL, Pringle SE, Glass RJ (1999) Measurement of fracture aperture fields using transmitted light: an evaluation of measurement errors and their influence on simulations of flow and transport through a single fracture. Water Resour Res 35(9):2605–2617
Detwiler RL, Rajaram H, Glass RJ (2000) Solute transport in variable-aperture fractures: an investigation of the relative importance of Taylor dispersion and macrodispersion. Water Resour Res 36(7):1611–1625
Dronfield DG, Silliman SE (1993) Velocity dependence of dispersion for transport through a single fracture of variable roughness. Water Resour Res 29(10):3477–3483
Dverstorp B, Andersson J, Nordqvist W (1992) Discrete fracture network interpretation of field tracer migration in sparsely fractured rock. Water Resour Res 28(9):2327–2343
Dykhuizen RC (1992) Diffusive matrix fracture coupling including the effects of flow channeling. Water Resour Res 28(9):2447–2450
Endo HK, Long JCS, Wilson CR, Witherspoon PA (1984) A model for investigating mechanical transport in fracture networks. Water Resour Res 20(10):1390–1400
Ewing RP, Jaynes DB (1995) Issues in single-fracture transport modeling: scales, algorithms and grid types. Water Resour Res 31:303–312
Fahy MF (1997) Dual-porosity analysis of conservative tracer testing in saturated volcanic rocks at Yucca Mountain in Nye County, Nevada. Int J Rock Mech Mineral Sci Geomech Abstr 34(3/4):486–490
Faybishenko B, Witherspoon PA, Benson SM (eds) (2000) Dynamics of fluids in fractured rock. Am Geophys Union, Geophys Monogr 122:400
Feenstra S, Cherry JA, Sudicky EA, Haq Z (1984) Matrix diffusion effects on contaminant migration from an injection well in fractured sandstone. Ground Water 22(3):307–316
Folger PF, Poeter E, Wanty RB, Day W, Frishman D (1997) 222Rn transport in a fractured crystalline rock aquifer: results from numerical simulations. J Hydrol 195(1–4):45–77
Foster SSD (1975) The chalk groundwater tritium anomaly: a possible explanation. J Hydrol 25:159–165
Freeze RA, Cherry JA (1979) Groundwater. Prentice-Hall, Englewood Cliffs, NJ, USA, 604 pp
Garcia-Gutierrez ME, Guimera J, Llano AYD, Benitez HJH, Saltink M (1997) Tracer test at El Berrocal site. J Contam Hydrol 26(1–4):179–188
Garnier JM, Crampon N, Préaux C, Porel G, Vreulx M (1985) Traçages par 13C, 2H, I– et uranine dans la nappe de la craie sénonienne en écoulement radial convergent (Béthunes, France) [Tracing 13C, 2H, I– and uranine through the senonian chalk aquifer (Béthunes, France) using a two-well method]. J Hydrol 78:379–392
Gelhar LW (1993) Stochastic Subsurface Hydrology. Prentice Hall, Englewood Cliffs, NJ, USA, pp 184–194, 271–281
Gelhar LW, Axness CL (1983) Three-dimensional stochastic analysis of macrodispersion in aquifers. Water Resour Res 19(1):161–180
Gelhar LW, Welty C, Rehfeldt KR (1992) A critical review of data on field-scale dispersion in aquifers. Water Resour Res 28(7):1955–1974
Gelhar LW, Welty C, Rehfeldt KR (1993) Reply to comment on "A critical review of data on field-scale dispersion in aquifers" by Neuman (1993). Water Resour Res 29(6):1867–1869
Glass RJ, Nicholl MJ (1995) Quantitative visualization of entrapped phase dissolution within a horizontal flowing fracture. Geophys Res Lett 22:1457–1460
Grenier C, Mouche E, Tevissen E (1998) Influence of variable fracture aperture on transport of non-sorbing solutes in a fracture: a numerical investigation. J Contam Hydrol 35(1–3):305–315
Grisak GE, Pickens JF (1980) Solute transport through fractured porous media, 1, the effect of matrix diffusion. Water Resour Res 16(4):719–730
Grisak GE, Pickens JF (1981) An analytical solution for solute transport through fractured media with matrix diffusion. J Hydrol 52:47–57
Grisak GE, Pickens JF, Cherry JA (1980) Solute transport through fractured porous media, 2, column study of fractured till. Water Resour Res 16(4):731–739
Guimera J, Carrera J (2000) A comparison of hydraulic and transport parameters measured in low-permeability fractured media. J Contam Hydrol 41:261–281
Gutfraind R, Ippolito I, Hansen A (1995) Study of tracer dispersion in self-affine fractures using lattice-gas automata. Phys Fluids 7:(8):1938–1948
Gylling B, Birgersson L, Moreno L, Neretnieks I (1998) Analysis of a long-term pumping and tracer test using the Channel Network Model. J Contam Hydrol 32:203–222
Gylling B, Moreno L, Neretnieks I (1999) The channel network model—a tool for transport simulation in fractured media. Ground Water 37:(3):367–375
Hadermann J, Heer W (1996) The Grimsel (Switzerland) migration experiment: integrating field experiments, laboratory investigations and modelling. J Contam Hydrol 21:87–100
Haldeman WR, Chuang Y, Rasmussen TC, Evans DD (1991) Laboratory analysis of fluid flow and solute transport through a fracture embedded in porous tuff. Water Resour Res 27(1):53–65
Harrison B, Sudicky EA, Cherry JA (1992) Numerical analysis of solute migration through fractured clayey deposits into underlying aquifers. Water Resour Res 28:515–526
Harvey CF, Gorelick SM (1995) Temporal moment-generating equations: modeling transport and mass transfer in heterogeneous aquifers. Water Resour Res 31(8):1895–1911
Heath M, Montoto M, Rodrigues RA, Argadona VGR, Menendez B (1992) Rock matrix diffusion as a mechanism of radionuclide retardation: a natural analogue study of El Berrocal granite, Spain. Radiochim Acta 58–59:379–384
Hellmuth KH, Siitari-Kauppi M, Lindberg A (1993) Study of porosity and migration pathways in crystalline rock by impregnation with 14C-polymethylmethacrylate. J Contam Hydrol 13:403–418
Hölttä P, Hautojärvi A, Hakanen M (1992) Transport and retardation of non-sorbing radionuclides in crystalline rock fractures. Radiochim Acta 58/59:285–290
Hölttä P, Hakanen M, Hautojärvi A, Timonen J, Väätäinen K (1996) The effects of matrix diffusion on radionuclide migration in rock column experiments. J Contam Hydrol 21(1–4):165–173
Hölttä P, Siitari-Kauppi M, Hakanen M, Huitti T, Hautojärvi A, Lindberg A (1997) Radionuclide transport and retardation in rock fracture and crushed rock column experiments. J Contam Hydrol 26(1–4):135–145
Hölttä P, Siitari-Kauppi M, Lindberg A, Hautojärvi A (1998) Na, Ca, Sr retardation on crushed crystalline rock. Radiochim Acta 82:279–285
Hölttä P, Siitari-Kauppi M, Hakanen M, Tukiainen V (2001) Attempt to model laboratory-scale diffusion and retardation data. J Contam Hydrol 47:139–148
Ibaraki M (2001) A simplified technique for measuring diffusion coefficients in rock blocks. Water Resour Res 37(5):1519–1523
Ippolito I, Hinch EJ, Daccord G, Hulin JP (1993) Tracer dispersion in 2-D fractures with flat and rough walls in a radial flow geometry. Physics Fluids A, Fluid Dynam 5(8):1952–1962
Ippolito I, Daccord G, Hinch EJ, Hulin JP (1994) Echo tracer dispersion in model fractures with a rectangular geometry. J Contam Hydrol 16(1):87–108
Isakov E, Ogilvie SR, Taylor CW, Glover PWJ (2001) Fluid flow through rough fractures in rocks I: high resolution aperture determinations. Earth Planet Sci Lett 191:267–282
Jardine PM, Sanford WE, Gwo JP, Reedy OC, Hicks DS, Riggs JS, Bailey W (1999) Quantifying diffusive mass transfer in fractured shale bedrock. Water Resour Res 35(7):2015–2030
Johansson H, Siitari-Kauppi M, Skalberg M, Tullborg EL (1998) Diffusion pathways in crystalline rock: examples from Äspö-diorite and fine-grained granite. J Contam Hydrol 35:41–53
Johns RA, Roberts PV (1991) A solute transport model for channelized flow in a fracture. Water Resour Res 27(8):1797–1808
Jorgensen PR, McKay LD, Spliid NH (1998) Evaluation of chloride and pesticide transport in a fractured clayey till using large undisturbed columns and numerical modeling. Water Resour Res 34(4):539–553
Jussel P, Stauffer F, Dracos T (1994) Transport modeling in heterogeneous aquifers, 2, three-dimensional transport model and stochastic numerical tracer experiments. Water Resour Res 30(6):1819–1831
Kapoor V, Gelhar LW (1994a) Transport in three-dimensionally heterogeneous aquifers, 1, dynamics of concentration fluctuations. Water Resour Res 30(6):1775–1788
Kapoor V, Gelhar LW (1994b) Transport in three-dimensionally heterogeneous aquifers, 2, predictions and observations of concentration fluctuations. Water Resour Res 30(6):1789–1801
Keller AA, Roberts PV, Kitanidis PK (1995) Prediction of single phase transport parameters in a variable aperture fracture. Geophys Res Lett 22(11):1425–1428
Keller AA, Roberts PV, Blunt MJ (1999) Effect of fracture aperture variations on the dispersion of contaminants. Water Resour Res 35(1):55–63
Koplik J, Ippolito I, Hulin JP (1993) Tracer dispersion in rough channels: a two-dimensional numerical study. Phys Fluids A, Fluid Dynam 5(6):1333–1343
Kovscek AR, Tretheway DC, Persoff P, Radke CJ (1995) Foam flow through a transparent rough-walled rock fracture. J Petrol Sci Eng 13(2):75–86
Kunstmann H, Kinzelbach W, Marschall P, Li G (1997) Joint inversion of tracer tests using reversed flow fields. J Contam Hydrol 26(1–4):215–226
Landström O, Tullborg EL (2001) Alteration and diffusion profiles in two drill cores from Äspö. In: First TRUE stage—transport of solutes in an interpreted single fracture. Proceedings from the 4th Int. Seminar Äspö, 9–11 September 2000, SKB TR 01-24. Swed Nucl Fuel Waste Manage Co, Stockholm, Sweden, pp 15–18
Lapcevic PA, Novakowski KS, Sudicky EA (1999) The interpretation of a tracer experiment conducted in a single fracture under conditions of natural groundwater flow. Water Resour Res 35(8):2301–2312
Lessof SC, Konikow LF (1997) Ambiguity in measuring matrix diffusion with single-well injection/recovery tracer tests. Ground Water 35(1):166–176
Lin B-S, Lee C-H (1998) An explanation of distance-dependent dispersion of mass transport in fractured rock. J Chinese Inst Eng 21(3):365–372
Long JCS, Witherspoon PA (1985) The relationship of the degree of interconnection to permeability in fracture networks. J Geophys Res 90(B4):3087–3098
Maloszewski P, Zuber A (1985) On the theory of tracer experiments in fissured rock with a porosity matrix. J Hydrol 79:333–358
Maloszewski P, Zuber A (1990) Mathematical modeling of tracer behaviour in short-term experiments in fissured rocks. Water Resour Res 26(7):1517–1528
Maloszewski P, Zuber A (1992) On the calibration and validation of mathematical models for the interpretation of tracer experiments in groundwater. Advance Water Res 15(1):47–62
Maloszewski P, Zuber A (1993) Tracer experiments in fissured rocks: matrix diffusion and the validity of models. Water Resour Res 29(8):2723–2735
Mazurek M, Alexander WR, Mackenzie AB (1996) Contaminant retardation in fractured shales: matrix diffusion and redox front entrapment. J Contam Hydrol 21(1–4):71–84
McKay LD, Gillham RW, Cherry JA (1993) Field experiments in a fractured clay till, 2, solute and colloid transport. Water Resour Res 29(12):3879–3890
Moreno L, Neretnieks I (1993a) Flow and nuclide transport in fractured media: the importance of the flow-wetted surface for radionuclide migration. J Contam Hydrol 13(1–4):49–71
Moreno L, Neretnieks I (1993b) Fluid flow and solute transport in a network of channels. J Contam Hydrol 14(3–4):163–192
Moreno L, Tsang CF (1991) Multiple-peak response to tracer injection tests in single fractures: a numerical study. Water Resour Res 27(8):2143–2150
Moreno L, Neretnieks I, Eriksen T (1985) Analysis of some laboratory tracer runs in natural fissures. Water Resour Res 21(7):951–958
Moreno L, Tsang YW, Tsang CF, Hale FV, Neretnieks I (1988) Flow and tracer transport in a single fracture: a stochastic model and its relation to some field observations. Water Resour Res 24(12):2033–2048
Moridis GJ (1999) Semianalytical solutions for parameter estimation in diffusion cell experiments. Water Resour Res 35(6):1729–1740
National Research Council (1996) Rock fractures and fluid flow: contemporary understanding and applications. National Academy Press, Washington, DC, 551 pp
Neretnieks I (1980) Diffusion in the rock matrix: an important factor in radionuclide retardation? J Geophys Res 85(B8):4379–4397
Neretnieks I (1983) A note on fracture flow dispersion mechanisms in the ground. Water Resour Res 19(2):364–370
Neretnieks I (1993) Solute transport in fractured rock: applications to radionuclide waste repositories. In: Bear J, Tsang CF, de Marsily G (eds) Flow and contaminant transport in fractured rock. Academic Press, San Diego, CA, USA, pp 39–127
Neretnieks I, Eriksen T, Tahtinen P (1982) Tracer movement in a single fissure in granitic rock: some experimental results and their interpretation. Water Resour Res 18(4):849–858
Neuman SP (1990) Universal scaling of hydraulic conductivities and dispersivities in geologic media. Water Resour Res 26(8):1749–1758
Neuman SP (1993) Comment on "A critical review of data on field-scale dispersion in aquifers" by Gelhar LW, Welty C, Rehfeldt KR. Water Resour Res 29(6):1863–1865
Nordqvist AW, Tsang YW, Tsang C-F, Dverstorp B, Andersson J (1992) A variable aperture fracture network model for flow and transport in fractured rocks. Water Resour Res 28(6):1703–1713
Nordqvist AW, Tsang YW, Tsang C-F, Dverstorp B, Andersson J (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(1–2):39–66
Novakowski KS (1992) The analysis of tracer experiments conducted in divergent radial flow fields. Water Resour Res 28(12):3215–3225
Novakowski KS, Bogan JD (1999) A semi-analytical model for the simulation of solute transport in a network of fractures having random orientations. Int J Numerical Anal Methods Geomech 23(4):317–333
Novakowski KS, Lapcevic PA (1994) Field measurement of radial solute transport in fractured rock. Water Resour Res 30(1):37–44
Novakowski KS, van der Kamp G (1996) The radial diffusion method: 2, a semianalytical model for the determination of effective diffusion coefficients, porosity and adsorption. Water Resour Res 32(6):1823–1830
Novakowski KS, Evans GV, Lever DA, Raven KG (1985) A field example of measuring hydrodynamic dispersion in a single fracture. Water Resour Res 21(8):1165–1174
Novakowski KS, Lapcevic PA, Voralek J, Bickerton G (1995) Preliminary interpretation of tracer experiments conducted in a discrete rock fracture under conditions of natural flow. Geophys Res Lett 22(11):1417–1420
Novakowski KS, Lapcevic PA, Voralek JW, Sudicky EA (1998) A note on a method for measurement of the transport properties of a formation using a single well. Water Resour Res 34(5):1351–1356
Ohlsson Y, Neretnieks I (1995) Literature survey of matrix diffusion theory and of experiments and data including natural analogues, SKB TR 95-12. Swed Nucl Fuel Waste Manage Co, Stockholm, Sweden, 89 pp
Ohlsson Y, Neretnieks I (1997) Diffusion data in granite: Recommended values, SKB TR 97-20. Swed Nucl Fuel Waste Manage Co, Stockholm, Sweden, 13 pp
Ohlsson Y, Neretnieks I (1998) Some evidence for surface ion mobility in rock. J Contam Hydrol 35(1–3):91–100
Ohlsson Y, Löfgren M, Neretnieks I (2001) Rock matrix diffusivity determinations by in-situ electrical conductivity measurements. J Contam Hydrol 47:117–125
Park CK, Vandergraaf TT, Drew DJ, Hahn PS (1997) Analysis of the migration of nonsorbing tracers in a natural fracture in granite using a variable aperture channel model. J Contam Hydrol 26(1–4):97–108
Persoff P, Pruess K (1995) Two-phase visualization and relative permeability measurements in natural rough-walled rock fractures. Water Resour Res 31(5):1175–1186
Plouraboué F, Hulin JP, Roux S, Koplik J (1998) Numerical study of geometrical dispersion in self-affine rough fractures. Phys Rev E 58(3):3334–3346
Pruess K, Faybishenko B, Bodvarsson GS (1999) Alternative concepts and approaches for modeling flow and transport in thick unsaturated zones of fractured rocks. J Contam Hydrol 38(1–3):281–322
Rasmuson A (1985) Analysis of hydrodynamic dispersion in discrete fracture networks using the method of moments. Water Resour Res 21(11):1677–1683
Rasmuson A, Neretnieks I (1981) Migration of radionuclides in fissured rock: the influence of micropore diffusion and longitudinal dispersion. J Geophys Res 86(B5):3749–3758
Rasmuson A, Neretnieks I (1986) Radionuclide transport in fast channels in crystalline rock. Water Resour Res 22(8):1247–1256
Raven KG, Novakowski KS, Lapcevic PA (1988) Interpretation of field tracer tests of a single fracture using a transient solute storage model. Water Resour Res 24(12):2019–2032
Rebour V, Billiotte J, Deveughele M, Jambon A, Guen CI (1997) Molecular diffusion in water-saturated rocks: a new experimental method. J Contam Hydrol 28:71–93
Reedy OC, Jardine PM, Wilson GV, Selim HM (1996) Quantifying the diffusive mass transfer of nonreactive solutes in columns of fractured saprolite using flow interruption. Soil Sci Soc Am J 60(5):1376–1384
Robinson BA, Tester JW (1984) Dispersed fluid flow in fractured reservoirs: an analysis of tracer-determined residence time distributions. J Geophys Res 89(B12):10374–10384
Robinson NI, Sharp JM, Kreisel I (1998) Contaminant transport in sets of parallel finite fractures with fracture skins. J Contam Hydrol 31(1–2):83–109
Roux S, Plouraboué F, Hulin JP (1998) Tracer dispersion in rough open cracks. Transport Porous Media 32(1):97–116
Rubin Y, Cushey MA, Wilson A (1997) The moments of the breakthrough curves of instantaneously and kinetically sorbing solutes in heterogeneous geologic media: prediction and parameter inference from field measurements. Water Resour Res 33(11):2465–2481
Sahimi M (1993) Flow, dispersion, displacement processes in porous media and fractured rocks: from continuum models to fractals, percolation, cellular automata and simulated annealing. Rev Model Phys 65(4):1393–1534
Sahimi M (1995) Flow and transport in porous media and fractured rock, from classical methods to modern approaches. VCH, Weinheim, Germany, 482 pp
Sato H (1999) Matrix diffusion of simple cations, anions, neutral species in fractured crystalline rocks. Nucl Technol 127(2):199–211
Schwartz FW, Smith L, Crowe AS (1983) A stochastic analysis of macroscopic dispersion in fractured media. Water Resour Res 19(5):1253–1265
Shapiro AM (2001) Effective matrix diffusion in kilometer-scale transport in fractured crystalline rock. Water Resour Res 37(3):507–522
Shapiro AM, Nicholas J (1989) Assessing the validity of the channel model of fracture apertures under field conditions. Water Resour Res 25(5):817–828
Sidle RC, Nilsson B, Hansen M, Fredericia J (1998) Spatially varying hydraulic and solute transport characteristics of a fractured till determined by field tracer tests, Funen, Denmark. Water Resour Res 34(10):2515–2527
Siitari-Kauppi M, Hellmuth KH, Lindberg A, Huitti T (1994) Diffusion in homogeneous and heterogeneous rock matrices. A comparison of different experimental approaches. Radiochim Acta 66/67:409–414
Siitari-Kauppi M, Lindberg A, Hellmuth KH, Timonen J, Väätäinen K, Hartikainen J, Hartikainen K (1997) The effect of microscale pore structure on matrix diffusion—a site-specific study on tonalite. J Contam Hydrol 26(1–4):147–158
Silliman SE (1989) An interpretation of the difference between aperture estimates derived from hydraulic and tracer tests in a single fracture. Water Resour Res 25(10):2275–2283
Skagius K (1986) Diffusion of dissolved species in the matrix of some Swedish crystalline rocks. PhD Thesis, Royal Institute of Technology, Stockholm, Suède
Skagius K, Neretnieks I (1986a) Diffusivity measurements and electrical resistivity in rock samples under mechanical stress. Water Resour Res 22(4):570–580
Skagius K, Neretnieks I (1986b) Porosities and diffusivities of some nonsorbing species in crystalline rocks. Water Resour Res 22(3):389–398
Smellie JAT, Karlsson F (1999) The use of natural analogues to assess radionuclide transport. Eng Geol 52:193–220
Smith L, Schwartz FW (1984) An analysis of the influence of fracture geometry on mass transport in fractured media. Water Resour Res 20(9):1241–1252
Smith PA, Gautschi A, Vomvoris S, Zuidema P, Mazurek M (1997) The development of a safety assessment model of the geosphere for a repository sited in the crystalline basement of northern Switzerland. J Contam Hydrol 26:309–324
Stafford P, Toran L, McKay L (1998) Hydrology influence of fracture truncation on dispersion: a dual permeability model. J Contam Hydrol 30(1–2):79–100
Stephenson D, Paling WAJ, Jesus ASMD (1989) Radiotracer dispersion tests in a fissured aquifer. J Hydrol 110(1–2):153–164
Streltsova TD (1976) Hydrodynamics of groundwater flow in a fractured formation. Water Resour Res 12:405–413
Sudicky EA, Frind EO (1982) Contaminant transport in fractured porous media: analytical solutions for a system of parallel fractures. Water Resour Res 18(6):1634–1642
Sudicky EA, McLaren RG (1992) The Laplace Transform Galerkin Technique for large-scale simulation of mass transport in discretely fractured porous formations. Water Resour Res 28(2):499–514
Suksi J, Ruskeeniemi T, Rasilainen K (1992) Matrix diffusion—evidences from natural analogue studies at Palmottu in SW Finland. Radiochim Acta 58/59:385–393
Tang DH, Frind EO, Sudicky EA (1981) Contaminant transport in fractured porous media: analytical solution for a single fracture. Water Resour Res 17(3):555–564
Taylor SG (1953) Dispersion of soluble matter in solvent flowing slowly through a tube. Proc R Soc Lond Ser A 219:186–203
Therrien R, Sudicky EA (1996) Three-dimensional analysis of variably-saturated flow and solute transport in discretely-fractured porous media. J Contam Hydrol 23:1–44
Thompson ME, Brown SR (1991) The effect of anisotropic surface roughness on flow and transport in fractures. J Geophys Res 96(B13):21923–21932
Tidwell VC, Meigs LC, Christian-Frear T, Boney CM (2000) Effects of spatially heterogeneous porosity on matrix diffusion as investigated by X-ray absorption imaging. J Contam Hydrol 42(2–4):285–302
Toran L, Sjoreen A, Morris M (1995) Sensitivity analysis of solute transport in fractured porous media. Geophys Res Lett 22(11):1433–1436
Tsang CF (1993) Tracer transport in fracture systems. In: Bear J, Tsang CF, de Marsily G (eds) Flow and contaminant transport in fractured rock. Academic Press, San Diego, CA, USA, pp 237–266
Tsang CF, Neretnieks I (1998) Flow channeling in heterogeneous fractured rocks. Rev Geophys 36(2):275–298
Tsang CF, Tsang YW, Hale FV (1991) Tracer transport in fractures: analysis of field data based on a variable-aperture channel model. Water Resour Res 27(12):3095–3106
Tsang YW (1984) The effect of tortuosity of fluid flow through a single fracture. Water Resour Res 20(9):1209–1215
Tsang YW (1992) Usage of "equivalent apertures" for rock fractures as derived from hydraulic and tracer tests. Water Resour Res 28(5):1451–1455
Tsang YW (1995) Study of alternative tracer tests in characterizing transport in fractured rocks. Geophys Res Lett 22(11):1421–1424
Tsang YW, Tsang CF (1987) Channel model of flow through fractured media. Water Resour Res 23(3):467–479
Tsang YW, Tsang CF (1989) Flow channeling in a single fracture as a two-dimensional strongly heterogeneous permeable medium. Water Resour Res 25(9):2076–2080
Tsang YW, Tsang CF, Hale FV, Dverstorp B (1996) Tracer transport in a stochastic continuum model of fractured media. Water Resour Res 32(10):3077–3092
Vandergraaf TT, Drew DJ, Masuda S (1996) Radionuclide migration experiments in a natural fracture in a quarried block of granite. J Contam Hydrol 21(1–4):153–164
Vandergraaf TT, Drew DJ, Archambault D, Ticknor KV (1997) Transport of radionuclides in natural fractures: some aspects of laboratory migration experiments. J Contam Hydrol 26(1–4):83–95
Wan J, Tokunaga TK, Tsang C-F, Bodvarsson GS (1996) Improved glass micromodel methods for studies of flow and transport in fractured porous media. Water Resour Res 32(7):1955–1964
Wan J, Tokunaga TK, Orr TR, O'Neill J, Connors RW (2000) Glass casts of rock fracture surfaces: a new tool for studying flow and transport. Water Resour Res 36(1):355–360
Weber WJJ, McGinley PM, Katz LE (1991) Sorption phenomena in subsurface systems: concepts, models and effects on contaminant fate and transport. Water Res 25(5):499–528
Wels C, Smith L, Vandergraaf T (1996) Influence of specific surface area on transport of sorbing solutes in fractures: an experimental analysis. Water Resour Res 32(7):1943–1954
Wels C, Smith L, Beckie R (1997) The influence of surface sorption on dispersion in parallel plate fractures. J Contam Hydrol 28(1–2):95–114
Wendland E, Himmelsbach T (2002) Transport simulation with stochastic aperture for a single fracture, comparison with a laboratory experiment. Advance Water Res 25(1):19–32
Williams MMR (1996) Radionuclide transport in fractured rock. Progr Nuclear Energy 30(3):243–253
Wood WW, Shapiro AM, Hsieh PA, Councell TB (1993) Observational, experimental and inferred evidence for solute diffusion in fractured granite aquifers—examples from the Mirror Lake watershed, Grafton County, New Hampshire. In: Morganwalp DW, Aronson DA (eds) US Geological Survey toxic substances hydrology program—Proceedings of the Technical Meeting, Colorado Springs, Colorado, 20–24 September 1993: US Geological Survey Water-Resources Investigations Report 94-4015, vol 1, pp 167–170
Woodbury AD (1997) A probabilistic fracture transport model: application to contaminant transport in a fractured clay deposit. Can Geotech J 34(5):784–798
Wooding RA (1960) Instability of a viscous fluid of variable density in a vertical Hele-Shaw cell. J Fluid Mech 7(501–515)
Xu S, Wörman A (1999) Implications of sorption kinetics to radionuclide migration in fractured rocks. Water Resour Res 35(11):3429–3440
Xu S, Wörman A, Dverstorp B (2001) Heterogeneous matrix diffusion in crystalline rock—implications for geosphere retardation of migrating radionuclides. J Contam Hydrol 47:365–378
Yamaguchi T, Nakayama S (1998) Diffusivity of U, Pu and Am carbonate complexes in a granite from Inada, Ibaraki, Japan studied by through diffusion. J Contam Hydrol 35:55–65
Yamaguchi T, Sakamoto Y, Senoo M (1993) Consideration on effective diffusivity of strontium in granite. J Nucl Sci Technol 30(8):796–803
Yamaguchi T, Sakamoto Y, Nakayama S, Vandergraaf TT (1997) Effective diffusivity of the uranyl ion in a granite from Inada, Ibaraki, Japan. J Contam Hydrol 26:109–117
Yu JW, Neretnieks I (1997) Diffusion and sorption properties of radionuclides in compacted bentonite, SKB TR 97-12. Swed Nucl Fuel Waste Manage Co, Stockholm, Sweden
Zimmerman RW, Bodvarsson GS (1996) Hydraulic conductivity of rock fractures. Transport Porous Media 23(1):1–30
Zimmerman RW, Yeo IW (2000) Fluid flow in rock fractures: from the Navier–Stokes equations to the cubic law. In: Faybishenko B, Witherspoon PA, Benson SM (eds) Dynamics of fluids in fractured rock. Am Geophys Union, Geophys Monogr 122:213–224
Zuber A, Motyka J (1994) Matrix porosity as the most important parameter of fissured rocks for solute transport at large scales. J Hydrol 158(1–2):19–46
Acknowledgements
This work was partly funded by the "Programme National de Recherche en Hydrologie" (PNRH). We are grateful to Dr. R. Therrien and Dr. W.S. Dershowitz for their constructive comments on the manuscript. We are also grateful to M.C. Ferré (UMR 6532 Hydrasa, Université de Poitiers) for helping us in seeking reprints of the references cited in this article.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bodin, J., Delay, F. & de Marsily, G. Solute transport in a single fracture with negligible matrix permeability: 1. fundamental mechanisms. Hydrogeology Journal 11, 418–433 (2003). https://doi.org/10.1007/s10040-003-0268-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10040-003-0268-2