Skip to main content
Log in

Solute transport in a single fracture with negligible matrix permeability: 1. fundamental mechanisms

  • Paper
  • Published:
Hydrogeology Journal Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1.
Fig. 2.
Fig. 3.a
Fig. 4.
Fig. 5.

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

    CAS  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  CAS  Google Scholar 

  • 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

    Google Scholar 

  • Berkowitz B, Scher H (1995) On characterization of anomalous dispersion in porous and fractured media. Water Resour Res 31(6):1461–1466

    Google Scholar 

  • Berkowitz B, Zhou J (1996) Reactive solute transport in a single fracture. Water Resour Res 32(4):901–913

    CAS  Google Scholar 

  • Bibby R (1981) Mass transport of solutes in dual-porosity media. Water Resour Res 17(4):1075–1081

    Google Scholar 

  • 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

    Google Scholar 

  • 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)

    Google Scholar 

  • Boving TB, Grathwohl P (2001) Tracer diffusion coefficients in sedimentary rocks: correlation to porosity and hydraulic conductivity. J Contam Hydrol 53:85–100

    Article  CAS  PubMed  Google Scholar 

  • Bradbury MH, Green A (1985) Measurement of important parameters determining aqueous phase diffusion rates through crystalline rock matrices. J Hydrol 82:39–55

    CAS  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Broeck CVD (1990) Taylor dispersion revisited. Physica A 168(2):677–696

    Google Scholar 

  • Brown SR (1987) Fluid flow through rock joints: the effect of surface roughness. J Geophys Res 92:1337–1347

    Google Scholar 

  • Brown SR, Caprihan A, Hardy R (1998) Experimental observation of fluid flow channels in a single fracture. J Geophys Res 103:(B3):5125–5132

    Google Scholar 

  • Brunauer MH, Emmet PH, Teller E (1938) Adsorption of gases in multimolecular layers. J Am Chem Soc 60:309–319

    CAS  Google Scholar 

  • 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

    CAS  Google Scholar 

  • 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

    CAS  Google Scholar 

  • 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

    CAS  Google Scholar 

  • 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

    CAS  Google Scholar 

  • 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

    Article  CAS  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    CAS  Google Scholar 

  • 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

    CAS  Google Scholar 

  • Dykhuizen RC (1992) Diffusive matrix fracture coupling including the effects of flow channeling. Water Resour Res 28(9):2447–2450

    CAS  Google Scholar 

  • 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

    Google Scholar 

  • Ewing RP, Jaynes DB (1995) Issues in single-fracture transport modeling: scales, algorithms and grid types. Water Resour Res 31:303–312

    Google Scholar 

  • 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

    CAS  Google Scholar 

  • 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

    Google Scholar 

  • Foster SSD (1975) The chalk groundwater tritium anomaly: a possible explanation. J Hydrol 25:159–165

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    CAS  Google Scholar 

  • 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

    Google Scholar 

  • Glass RJ, Nicholl MJ (1995) Quantitative visualization of entrapped phase dissolution within a horizontal flowing fracture. Geophys Res Lett 22:1457–1460

    Google Scholar 

  • 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

    Google Scholar 

  • Grisak GE, Pickens JF (1980) Solute transport through fractured porous media, 1, the effect of matrix diffusion. Water Resour Res 16(4):719–730

    Google Scholar 

  • Grisak GE, Pickens JF (1981) An analytical solution for solute transport through fractured media with matrix diffusion. J Hydrol 52:47–57

    Google Scholar 

  • 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

    Google Scholar 

  • Guimera J, Carrera J (2000) A comparison of hydraulic and transport parameters measured in low-permeability fractured media. J Contam Hydrol 41:261–281

    Article  CAS  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  CAS  Google Scholar 

  • 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

    Google Scholar 

  • Hadermann J, Heer W (1996) The Grimsel (Switzerland) migration experiment: integrating field experiments, laboratory investigations and modelling. J Contam Hydrol 21:87–100

    Article  CAS  Google Scholar 

  • 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

    CAS  Google Scholar 

  • 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

    CAS  Google Scholar 

  • Harvey CF, Gorelick SM (1995) Temporal moment-generating equations: modeling transport and mass transfer in heterogeneous aquifers. Water Resour Res 31(8):1895–1911

    CAS  Google Scholar 

  • 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

    Google Scholar 

  • 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

    CAS  Google Scholar 

  • Hölttä P, Hautojärvi A, Hakanen M (1992) Transport and retardation of non-sorbing radionuclides in crystalline rock fractures. Radiochim Acta 58/59:285–290

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Hölttä P, Siitari-Kauppi M, Lindberg A, Hautojärvi A (1998) Na, Ca, Sr retardation on crushed crystalline rock. Radiochim Acta 82:279–285

    Google Scholar 

  • 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

    Article  PubMed  Google Scholar 

  • Ibaraki M (2001) A simplified technique for measuring diffusion coefficients in rock blocks. Water Resour Res 37(5):1519–1523

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  CAS  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  CAS  Google Scholar 

  • Johns RA, Roberts PV (1991) A solute transport model for channelized flow in a fracture. Water Resour Res 27(8):1797–1808

    CAS  Google Scholar 

  • 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

    CAS  Google Scholar 

  • 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

    CAS  Google Scholar 

  • Kapoor V, Gelhar LW (1994a) Transport in three-dimensionally heterogeneous aquifers, 1, dynamics of concentration fluctuations. Water Resour Res 30(6):1775–1788

    CAS  Google Scholar 

  • 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

    CAS  Google Scholar 

  • 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

    Google Scholar 

  • Keller AA, Roberts PV, Blunt MJ (1999) Effect of fracture aperture variations on the dispersion of contaminants. Water Resour Res 35(1):55–63

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  CAS  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Lessof SC, Konikow LF (1997) Ambiguity in measuring matrix diffusion with single-well injection/recovery tracer tests. Ground Water 35(1):166–176

    Google Scholar 

  • 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

    Google Scholar 

  • Long JCS, Witherspoon PA (1985) The relationship of the degree of interconnection to permeability in fracture networks. J Geophys Res 90(B4):3087–3098

    Google Scholar 

  • Maloszewski P, Zuber A (1985) On the theory of tracer experiments in fissured rock with a porosity matrix. J Hydrol 79:333–358

    CAS  Google Scholar 

  • Maloszewski P, Zuber A (1990) Mathematical modeling of tracer behaviour in short-term experiments in fissured rocks. Water Resour Res 26(7):1517–1528

    CAS  Google Scholar 

  • 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

    Google Scholar 

  • Maloszewski P, Zuber A (1993) Tracer experiments in fissured rocks: matrix diffusion and the validity of models. Water Resour Res 29(8):2723–2735

    CAS  Google Scholar 

  • 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

    Google Scholar 

  • 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

    CAS  Google Scholar 

  • 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

    Google Scholar 

  • Moreno L, Neretnieks I (1993b) Fluid flow and solute transport in a network of channels. J Contam Hydrol 14(3–4):163–192

    Google Scholar 

  • 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

    Google Scholar 

  • Moreno L, Neretnieks I, Eriksen T (1985) Analysis of some laboratory tracer runs in natural fissures. Water Resour Res 21(7):951–958

    Google Scholar 

  • 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

    CAS  Google Scholar 

  • Moridis GJ (1999) Semianalytical solutions for parameter estimation in diffusion cell experiments. Water Resour Res 35(6):1729–1740

    Article  Google Scholar 

  • National Research Council (1996) Rock fractures and fluid flow: contemporary understanding and applications. National Academy Press, Washington, DC, 551 pp

    Google Scholar 

  • Neretnieks I (1980) Diffusion in the rock matrix: an important factor in radionuclide retardation? J Geophys Res 85(B8):4379–4397

    Google Scholar 

  • Neretnieks I (1983) A note on fracture flow dispersion mechanisms in the ground. Water Resour Res 19(2):364–370

    Google Scholar 

  • 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

    CAS  Google Scholar 

  • Neuman SP (1990) Universal scaling of hydraulic conductivities and dispersivities in geologic media. Water Resour Res 26(8):1749–1758

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    CAS  Google Scholar 

  • 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

    Google Scholar 

  • Novakowski KS (1992) The analysis of tracer experiments conducted in divergent radial flow fields. Water Resour Res 28(12):3215–3225

    Google Scholar 

  • 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

    Google Scholar 

  • Novakowski KS, Lapcevic PA (1994) Field measurement of radial solute transport in fractured rock. Water Resour Res 30(1):37–44

    Google Scholar 

  • 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

    CAS  Google Scholar 

  • 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

    CAS  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Ohlsson Y, Neretnieks I (1998) Some evidence for surface ion mobility in rock. J Contam Hydrol 35(1–3):91–100

    Google Scholar 

  • Ohlsson Y, Löfgren M, Neretnieks I (2001) Rock matrix diffusivity determinations by in-situ electrical conductivity measurements. J Contam Hydrol 47:117–125

    Article  CAS  PubMed  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Google Scholar 

  • Rasmuson A (1985) Analysis of hydrodynamic dispersion in discrete fracture networks using the method of moments. Water Resour Res 21(11):1677–1683

    Google Scholar 

  • 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

    CAS  Google Scholar 

  • Rasmuson A, Neretnieks I (1986) Radionuclide transport in fast channels in crystalline rock. Water Resour Res 22(8):1247–1256

    CAS  Google Scholar 

  • 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

    CAS  Google Scholar 

  • 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

    Article  CAS  Google Scholar 

  • 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

    CAS  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Roux S, Plouraboué F, Hulin JP (1998) Tracer dispersion in rough open cracks. Transport Porous Media 32(1):97–116

    Article  Google Scholar 

  • 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

    CAS  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    CAS  Google Scholar 

  • Schwartz FW, Smith L, Crowe AS (1983) A stochastic analysis of macroscopic dispersion in fractured media. Water Resour Res 19(5):1253–1265

    Google Scholar 

  • Shapiro AM (2001) Effective matrix diffusion in kilometer-scale transport in fractured crystalline rock. Water Resour Res 37(3):507–522

    Google Scholar 

  • 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

    CAS  Google Scholar 

  • 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

    CAS  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    CAS  Google Scholar 

  • Skagius K, Neretnieks I (1986b) Porosities and diffusivities of some nonsorbing species in crystalline rocks. Water Resour Res 22(3):389–398

    CAS  Google Scholar 

  • Smellie JAT, Karlsson F (1999) The use of natural analogues to assess radionuclide transport. Eng Geol 52:193–220

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  CAS  Google Scholar 

  • 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

    Google Scholar 

  • Stephenson D, Paling WAJ, Jesus ASMD (1989) Radiotracer dispersion tests in a fissured aquifer. J Hydrol 110(1–2):153–164

    Google Scholar 

  • Streltsova TD (1976) Hydrodynamics of groundwater flow in a fractured formation. Water Resour Res 12:405–413

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    CAS  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Taylor SG (1953) Dispersion of soluble matter in solvent flowing slowly through a tube. Proc R Soc Lond Ser A 219:186–203

    Google Scholar 

  • 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

    Article  CAS  Google Scholar 

  • Thompson ME, Brown SR (1991) The effect of anisotropic surface roughness on flow and transport in fractures. J Geophys Res 96(B13):21923–21932

    Google Scholar 

  • 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

    Google Scholar 

  • Toran L, Sjoreen A, Morris M (1995) Sensitivity analysis of solute transport in fractured porous media. Geophys Res Lett 22(11):1433–1436

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Tsang YW (1984) The effect of tortuosity of fluid flow through a single fracture. Water Resour Res 20(9):1209–1215

    Google Scholar 

  • Tsang YW (1992) Usage of "equivalent apertures" for rock fractures as derived from hydraulic and tracer tests. Water Resour Res 28(5):1451–1455

    Google Scholar 

  • Tsang YW (1995) Study of alternative tracer tests in characterizing transport in fractured rocks. Geophys Res Lett 22(11):1421–1424

    Google Scholar 

  • Tsang YW, Tsang CF (1987) Channel model of flow through fractured media. Water Resour Res 23(3):467–479

    CAS  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    CAS  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Williams MMR (1996) Radionuclide transport in fractured rock. Progr Nuclear Energy 30(3):243–253

    Article  CAS  Google Scholar 

  • 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

    Article  CAS  Google Scholar 

  • Wooding RA (1960) Instability of a viscous fluid of variable density in a vertical Hele-Shaw cell. J Fluid Mech 7(501–515)

    Google Scholar 

  • Xu S, Wörman A (1999) Implications of sorption kinetics to radionuclide migration in fractured rocks. Water Resour Res 35(11):3429–3440

    Google Scholar 

  • 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

    Article  CAS  PubMed  Google Scholar 

  • 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

    Article  CAS  Google Scholar 

  • Yamaguchi T, Sakamoto Y, Senoo M (1993) Consideration on effective diffusivity of strontium in granite. J Nucl Sci Technol 30(8):796–803

    CAS  Google Scholar 

  • 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

    Article  CAS  Google Scholar 

  • 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

    CAS  Google Scholar 

  • 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

    Google Scholar 

Download references

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

Authors

Corresponding author

Correspondence to J. Bodin.

Rights and permissions

Reprints 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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10040-003-0268-2

Keywords

Navigation