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

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.RésuméCe 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.ResumenEste 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.

[1]  P. Jardine,et al.  Quantifying diffusive mass transfer in fractured shale bedrock , 1999 .

[2]  Tetsuji Yamaguchi,et al.  Diffusivity of U, Pu and Am carbonate complexes in a granite from Inada, Ibaraki, Japan studied by through diffusion , 1998 .

[3]  K. Novakowski.  The analysis of tracer experiments conducted in divergent radial flow fields , 1992 .

[4]  O. Banton,et al.  An Approach to Transport in Heterogeneous Porous Media Using the Truncated Temporal Moment Equations: Theory and Numerical Validation , 1998 .

[5]  E. Sudicky,et al.  Three-dimensional analysis of variably-saturated flow and solute transport in discretely-fractured porous media , 1996 .

[6]  E. A. Sudicky,et al.  The Laplace Transform Galerkin Technique for large-scale simulation of mass transport in discretely fractured porous formations , 1992 .

[7]  Brian Berkowitz,et al.  On Characterization of Anomalous Dispersion in Porous and Fractured Media , 1995 .

[8]  R. Aris.  On the dispersion of a solute in a fluid flowing through a tube , 1956, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[9]  Ivars Neretnieks,et al.  Diffusion in the rock matrix: An important factor in radionuclide retardation? , 1980 .

[10]  John A. Cherry,et al.  Solute transport through fractured media: 2. Column study of fractured till , 1980 .

[11]  G. Marsily,et al.  Modeling fracture flow with a stochastic discrete fracture network: calibration and validation: 1. The flow model , 1990 .

[12]  S. Roux,et al.  Tracer Dispersion in Rough Open Cracks , 1998 .

[13]  C. Tsang.  5 – Tracer Transport in Fracture Systems , 1993 .

[14]  Paul A. Witherspoon,et al.  A Model for Investigating Mechanical Transport in Fracture Networks , 1984 .

[15]  A. Rasmuson.  Analysis of Hydrodynamic Dispersion in Discrete Fracture Networks Using the Method of Moments , 1985 .

[16]  S. Nakayama,et al.  Effective diffusivity of the uranyl ion in a granite from Inada, Ibaraki, Japan , 1997 .

[17]  G. Taylor.  Dispersion of soluble matter in solvent flowing slowly through a tube , 1953, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[18]  Gudmundur S. Bodvarsson,et al.  Hydraulic conductivity of rock fractures , 1996 .

[19]  Diffusive matrix fracture coupling including the effects of flow channeling , 1992 .

[20]  A. Shapiro.  Effective matrix diffusion in kilometer‐scale transport in fractured crystalline rock , 2001 .

[21]  H. Johansson,et al.  Diffusion pathways in crystalline rock—examples from Äspö-diorite and fine-grained granite , 1998 .

[22]  A. Lindberg,et al.  Study of porosity and migration pathways in crystalline rock by impregnation with 14C-polymethylmethacrylate , 1993 .

[23]  Ivars Neretnieks,et al.  2 – Solute Transport in Fractured Rock — Applications to Radionuclide Waste Repositories , 1993 .

[24]  K. Novakowski,et al.  2. A Semianalytical model for the determination of effective diffusion coefficients, porosity, and adsorption , 1996 .

[25]  Radiotracer dispersion tests in a fissured aquifer , 1989 .

[26]  P. Reimus,et al.  Using multiple experimental methods to determine fracture/matrix interactions and dispersion of nonreactive solutes in saturated volcanic tuff , 2000 .

[27]  R. Glass,et al.  Challenging models for flow in unsaturated, fractured rock through exploration of small scale processes , 1995 .

[28]  Ivars Neretnieks,et al.  Porosities and Diffusivities of Some Nonsorbing Species in Crystalline Rocks , 1986 .

[29]  J. Smellie,et al.  The use of natural analogues to assess radionuclide transport , 1999 .

[30]  Numerical study of geometrical dispersion in self-affine rough fractures , 1998 .

[31]  S. P. Neuman.  Comment on ``A critical review of data on field-scale dispersion in aquifers'' by L. W. Gelhar, C. Welty, and K. R. Rehfeldt , 1993 .

[32]  A. Zuber,et al.  On the calibration and validation of mathematical models for the interpretation of tracer experiments in groundwater , 1992 .

[33]  Arturo A. Keller,et al.  Effect of fracture aperture variations on the dispersion of contaminants , 1999 .

[34]  Robert Bibby,et al.  Mass transport of solutes in dual‐porosity media , 1981 .

[35]  Chin-Fu Tsang,et al.  Flow and Contaminant Transport in Fractured Rock , 1993 .

[36]  P. Grathwohl,et al.  Tracer diffusion coefficients in sedimentary rocks: correlation to porosity and hydraulic conductivity. , 2001, Journal of contaminant hydrology.

[37]  P. Hölttä,et al.  Na, Ca and Sr Retardation on Crushed Crystalline Rock , 1998 .

[38]  K. Novakowski,et al.  A semi-analytical model for the simulation of solute transport in a network of fractures having random orientations , 1999 .

[39]  Pierre M. Adler,et al.  Fractures and Fracture Networks , 1999 .

[40]  Sally M. Benson,et al.  Dynamics of fluids in fractured rock , 2000 .

[41]  M. Mazurek,et al.  Contaminant retardation in fractured shales: matrix diffusion and redox front entrapment , 1996 .

[42]  Stephen R. Brown,et al.  Fluid flow through rock joints: The effect of surface roughness , 1987 .

[43]  I. Neretnieks,et al.  Analysis of Some Laboratory Tracer Runs in Natural Fissures , 1985 .

[44]  E. Mouche,et al.  Influence of variable fracture aperture on transport of non-sorbing solutes in a fracture: a numerical investigation , 1998 .

[45]  Bruce A. Robinson,et al.  Dispersed fluid flow in fractured reservoirs: An analysis of tracer‐determined residence time distributions , 1984 .

[46]  Issues in Single‐Fracture Transport Modeling: Scales, Algorithms, and Grid Types , 1995 .

[47]  I. Neretnieks,et al.  Some evidence for surface ion mobility in rock , 1998 .

[48]  G. Dagan.  Flow and transport in porous formations , 1989 .

[49]  Foam flow through a transparent rough-walled rock fracture , 1995 .

[50]  John F. Pickens,et al.  Solute transport through fractured media: 1. The effect of matrix diffusion , 1980 .

[51]  M. Bradbury,et al.  Investigations into the factors influencing long range matrix diffusion rates and pore space accessibility at depth in granite , 1986 .

[52]  J. Timonen,et al.  The effects of matrix diffusion on radionuclide migration in rock column experiments , 1996 .

[53]  K. Novakowski,et al.  Preliminary interpretation of tracer experiments conducted in a discrete rock fracture under conditions of natural flow , 1995 .

[54]  Fritz Stauffer,et al.  Transport modeling in heterogeneous aquifers: 2. Three‐dimensional transport model and stochastic numerical tracer experiments , 1994 .

[55]  Chin-Fu Tsang,et al.  A variable aperture fracture network model for flow and transport in fractured rocks , 1992 .

[56]  L. Gelhar,et al.  Transport in three-dimensionally heterogeneous aquifers: 2. Predictions and observations of concentration fluctuations , 1994 .

[57]  Robert W. Zimmerman,et al.  Fluid flow in rock fractures: From the Navier-Stokes equations to the cubic law , 2013 .

[58]  Charles F. Harvey,et al.  Temporal Moment‐Generating Equations: Modeling Transport and Mass Transfer in Heterogeneous Aquifers , 1995 .

[59]  Anders Rasmuson,et al.  Migration of radionuclides in fissured rock: The influence of micropore diffusion and longitudinal dispersion , 1981 .

[60]  TRACER TRANSPORT IN FRACTURES : ANALYSIS OF FIELD DATA BASED ON A VARIABLE-APERTURE CHANNEL MODEL , 1991 .

[61]  S. Foster.  The Chalk groundwater tritium anomaly — A possible explanation , 1975 .

[62]  Candace C. Cady,et al.  Variation in aperture estimate ratios from hydraulic and tracer tests in a single fracture , 1993 .

[63]  C. Fidelibus,et al.  Derivation of equivalent pipe network analogues for three‐dimensional discrete fracture networks by the boundary element method , 1999 .

[64]  Y. Tsang,et al.  Study of alternative tracer tests in characterizing transport in fractured rocks , 1995 .

[65]  R. Glass,et al.  Solute transport in variable‐aperture fractures: An investigation of the relative importance of Taylor dispersion and macrodispersion , 2000 .

[66]  M. Bradbury,et al.  Measurement of important parameters determining aqueous phase diffusion rates through crystalline rock matrices , 1985 .

[67]  E. Sudicky,et al.  The interpretation of a tracer experiment conducted in a single fracture under conditions of natural groundwater flow , 1999 .

[68]  A. Hansen,et al.  Study of tracer dispersion in self‐affine fractures using lattice–gas automata , 1995 .

[69]  Ivars Neretnieks,et al.  A note on fracture flow dispersion mechanisms in the ground , 1983 .

[70]  Anders Rasmuson,et al.  Radionuclide Transport in Fast Channels in Crystalline Rock , 1986 .

[71]  M. Siitari-Kauppi,et al.  Attempt to model laboratory-scale diffusion and retardation data. , 2001, Journal of contaminant hydrology.

[72]  Karsten Pruess,et al.  Two‐Phase Flow Visualization and Relative Permeability Measurement in Natural Rough‐Walled Rock Fractures , 1995 .

[73]  Paul V. Roberts,et al.  A Solute Transport Model for Channelized Flow in a Fracture , 1991 .

[74]  R. Glass,et al.  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 , 1999 .

[75]  Harald Kunstmann,et al.  Joint inversion of tracer tests using reversed flow fields , 1997 .

[76]  A. Lindberg,et al.  Radionuclide transport and retardation in rock fracture and crushed rock column experiments , 1997 .

[77]  J. Timonen,et al.  The effect of microscale pore structure on matrix diffusion—a site-specific study on tonalite , 1997 .

[78]  I. Neretnieks,et al.  Tracer movement in a single fissure in granitic rock: Some experimental results and their interpretation , 1982 .

[79]  R. Wooding.  Instability of a viscous liquid of variable density in a vertical Hele-Shaw cell , 1960, Journal of Fluid Mechanics.

[80]  A. Wörman,et al.  Implications of sorption kinetics to radionuclide migration in fractured rock , 1999 .

[81]  A. Shapiro,et al.  Assessing the validity of the channel model of fracture aperture under field conditions , 1989 .

[82]  Chin-Fu Tsang,et al.  Flow channeling in a single fracture as a two‐dimensional strongly heterogeneous permeable medium , 1989 .

[83]  M.M.R. Williams,et al.  Radionuclide transport in fractured rock , 1996 .

[84]  C. Broeck.  Taylor dispersion revisited , 1990 .

[85]  I. Neretnieks,et al.  Rock matrix diffusivity determinations by in-situ electrical conductivity measurements. , 2001, Journal of contaminant hydrology.

[86]  Roger Beckie,et al.  The influence of surface sorption on dispersion in parallel plate fractures , 1997 .

[87]  E. Teller,et al.  ADSORPTION OF GASES IN MULTIMOLECULAR LAYERS , 1938 .

[88]  Chin-Fu Tsang,et al.  Channel model of flow through fractured media , 1987 .

[89]  Y. Tsang.  Usage of “Equivalent apertures” for rock fractures as derived from hydraulic and tracer tests , 1992 .

[90]  N. Robinson,et al.  Contaminant transport in sets of parallel finite fractures with fracture skins , 1998 .

[91]  I. Neretnieks,et al.  Channeling experiments in crystalline fractured rocks , 1994 .

[92]  P. Zuidema,et al.  The development of a safety assessment model of the geosphere for a repository sited in the crystalline basement of northern Switzerland , 1997 .

[93]  J. Wan,et al.  Glass casts of rock fracture surfaces: A new tool for studying flow and transport , 2000 .

[94]  K. Novakowski,et al.  Field measurement of radial solute transport in fractured rock , 1994 .

[95]  K. V. Ticknor,et al.  Transport of radionuclides in natural fractures: some aspects of laboratory migration experiments , 1997 .

[96]  Stephen E. Silliman,et al.  An interpretation of the difference between aperture estimates derived from hydraulic and tracer tests in a single fracture , 1989 .

[97]  P. Jardine,et al.  Quantifying the diffusive mass transfer of nonreactive solutes in columns of fractured saprolite using flow interruption , 1996 .

[98]  Warren C. Day,et al.  222Rn transport in a fractured crystalline rock aquifer: Results from numerical simulations , 1997 .

[99]  L. Gelhar.  Stochastic Subsurface Hydrology , 1992 .

[100]  S. Ogilvie,et al.  Fluid flow through rough fractures in rocks I: high resolution aperture determinations , 2001 .

[101]  J. Motyka,et al.  Matrix porosity as the most important parameter of fissured rocks for solute transport at large scales , 1994 .

[102]  M. Deveughele,et al.  Molecular diffusion in water-saturated rocks: A new experimental method , 1997 .

[103]  D. Evans,et al.  Laboratory analysis of fluid flow and solute transport through a fracture embedded in porous tuff , 1991 .

[104]  Vivek Kapoor,et al.  Transport in three-dimensionally heterogeneous aquifers: 1. Dynamics of concentration fluctuations , 1994 .

[105]  F. Schwartz,et al.  An Analysis of the Influence of Fracture Geometry on Mass Transport in Fractured Media , 1984 .

[106]  E. Sudicky,et al.  Matrix Diffusion Effects on Contaminant Migration from an Injection Well in Fractured Sandstone , 1984 .

[107]  E. A. Sudicky,et al.  Contaminant transport in fractured porous media: Analytical solution for a single fracture , 1981 .

[108]  John F. Pickens,et al.  An analytical solution for solute transport through fractured media with matrix diffusion , 1981 .

[109]  Chin-Fu Tsang,et al.  Effects of high variance of fracture transmissivity on transport and sorption at different scales in a discrete model for fractured rocks , 1996 .

[110]  T. D. Streltsova.  Hydrodynamics of groundwater flow in a fractured formation , 1976 .

[111]  Björn Dverstorp,et al.  Discrete fracture network interpretation of field tracer migration in sparsely fractured rock , 1992 .

[112]  Vladimir Cvetkovic,et al.  Transport of reactive tracers in rock fractures , 1999, Journal of Fluid Mechanics.

[113]  Ivars Neretnieks,et al.  A Large-Scale Flow and Tracer Experiment in Granite: 2. Results and Interpretation , 1991 .

[114]  S. Silliman,et al.  VELOCITY DEPENDENCE OF DISPERSION FOR TRANSPORT THROUGH A SINGLE FRACTURE OF VARIABLE ROUGHNESS , 1993 .

[115]  Y. Tsang,et al.  The Effect of Tortuosity on Fluid Flow Through a Single Fracture , 1984 .

[116]  Stephen R. Brown,et al.  Experimental observation of fluid flow channels in a single fracture , 1998 .

[117]  G. Moridis.  Semianalytical solutions for parameter estimation in diffusion cell experiments , 1998 .

[118]  Jesús Carrera,et al.  A comparison of hydraulic and transport parameters measured in low-permeability fractured media , 2000 .

[119]  Chin-Fu Tsang,et al.  Flow and tracer transport in a single fracture: A stochastic model and its relation to some field observations , 1988 .

[120]  E. Hinch,et al.  Echo tracer dispersion in model fractures with a rectangular geometry , 1994 .

[121]  J. Hadermann,et al.  The Grimsel (Switzerland) migration experiment : integrating field experiments, laboratory investigations and modelling , 1996 .

[122]  Ivars Neretnieks,et al.  Diffusion in the Matrix of Granitic Rock: Field Test in the Stripa Mine , 1990 .

[123]  Chin-Fu Tsang,et al.  Tracer transport in a stochastic continuum model of fractured media , 1996 .

[124]  I. Neretnieks,et al.  Diffusivity Measurements and Electrical Resistivity Measurements in Rock Samples Under Mechanical Stress , 1986 .

[125]  J. Guimerà,et al.  Tracer test at El Berrocal site , 1997 .

[126]  Tetsuji Yamaguchi,et al.  Consideration on Effective Diffusivity of Strontium in Granite , 1993 .

[127]  L. Toran,et al.  Influence of fracture truncation on dispersion: A dual permeability model , 1998 .

[128]  Vincent C. Tidwell,et al.  Effects of spatially heterogeneous porosity on matrix diffusion as investigated by X-ray absorption imaging , 1998 .

[129]  Gudmundur S. Bodvarsson,et al.  Improved Glass Micromodel Methods for Studies of Flow and Transport in Fractured Porous Media , 1996 .

[130]  L. Smith,et al.  Influence of Specific Surface Area on Transport of Sorbing Solutes in Fractures: An Experimental Analysis , 1996 .

[131]  Franklin W. Schwartz,et al.  A Stochastic Analysis of Macroscopic Dispersion in Fractured Media , 1983 .

[132]  Muhammad Sahimi,et al.  Flow and Transport in Porous Media and Fractured Rock: From Classical Methods to Modern Approaches , 1995 .

[133]  Tracer dispersion in 2‐D fractures with flat and rough walls in a radial flow geometry , 1993 .

[134]  C. Axness,et al.  Three‐dimensional stochastic analysis of macrodispersion in aquifers , 1983 .

[135]  Paul A. Witherspoon,et al.  The relationship of the degree of interconnection to permeability in fracture networks , 1985 .

[136]  J. Koplik,et al.  Tracer dispersion in rough channels: A two‐dimensional numerical study , 1993 .

[137]  J. Garnier,et al.  Traçage par 13C, 2H, I− et uranine dans la nappe de la craie sénonienne en écoulement radial convergent (Béthune, France) , 1985 .

[138]  A. Wörman,et al.  Heterogeneous matrix diffusion in crystalline rock--implications for geosphere retardation of migrating radionuclides. , 2001, Journal of contaminant hydrology.

[139]  M. Becker,et al.  Tracer transport in fractured crystalline rock: Evidence of nondiffusive breakthrough tailing , 2000 .

[140]  Chin-Fu Tsang,et al.  Multiple-Peak Response to Tracer Injection Tests in Single Fractures: A Numerical Study , 1991 .

[141]  B. Berkowitz,et al.  Reactive Solute Transport in a Single Fracture , 1996 .

[142]  Andrew V. Wolfsberg,et al.  Rock Fractures and Fluid Flow: Contemporary Understanding and Applications , 1997 .

[143]  Y. Rubin,et al.  The moments of the breakthrough curves of instantaneously and kinetically sorbing solutes in heterogeneous geologic media: Prediction and parameter inference from field measurements , 1997 .

[144]  R. Sidle,et al.  Spatially varying hydraulic and solute transport characteristics of a fractured till determined by field tracer tests, Funen, Denmark , 1998 .

[145]  S. P. Neuman.  Universal scaling of hydraulic conductivities and dispersivities in geologic media , 1990 .

[146]  R. Aris,et al.  On the dispersion of a solute by diffusion, convection and exchange between phases , 1959, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[147]  Ivars Neretnieks,et al.  Flow and nuclide transport in fractured media: the importance of the flow-wetted surface for radionuclide migration , 1993 .

[148]  E. Wendland,et al.  Transport simulation with stochastic aperture for a single fracture – comparison with a laboratory experiment , 2002 .

[149]  A. Woodbury.  A probabilistic fracture transport model: Application to contaminant transport in a fractured clay deposit , 1997 .

[150]  G. Bodvarsson,et al.  Alternative concepts and approaches for modeling flow and transport in thick unsaturated zones of fractured rocks , 1999 .

[151]  N. H. Spliid,et al.  Evaluation of chloride and pesticide transport in a fractured clayey till using large undisturbed columns and numerical modeling , 1998 .

[152]  R. Gillham,et al.  Field Experiments in a Fractured Clay Till 2. Solute and Colloid Transport , 1993 .

[153]  P. Kitanidis,et al.  Prediction of single phase transport parameters in a variable aperture fracture , 1995 .

[154]  G. Marsily,et al.  Solute transport in a single fracture with negligible matrix permeability: 2. mathematical formalism , 2003 .

[155]  Piotr Maloszewski,et al.  Tracer experiments in fractured rocks: Matrix diffusion and the validity of models , 1993 .

[156]  L. Katz,et al.  Sorption phenomena in subsurface systems: Concepts, models and effects on contaminant fate and transport , 1991 .

[157]  D. J. Drew,et al.  Analysis of the migration of nonsorbing tracers in a natural fracture in granite using a variable aperture channel model , 1997 .

[158]  H. Brenner,et al.  A general theory of Taylor dispersion phenomena , 1982 .

[159]  Stephen R. Brown,et al.  The effect of anisotropic surface roughness on flow and transport in fractures , 1991 .

[160]  T. Vandergraaf,et al.  Radionuclide migration experiments in a natural fracture in a quarried block of granite , 1996 .

[161]  M. Ibaraki.  A simplified technique for measuring diffusion coefficients in rock blocks , 2001 .

[162]  T. Illangasekare,et al.  A mathematical model for flow and solute transport in non-homogeneous rock fractures , 1994 .

[163]  Ivars Neretnieks,et al.  Fluid flow and solute transport in a network of channels , 1993 .

[164]  E. Sudicky,et al.  Numerical analysis of solute migration through fractured clayey deposits into underlying aquifers , 1992 .

[165]  P. Hölttä,et al.  Transport and Retardation of Non-Sorbing Radionuclides in Crystalline Rock Fractures , 1992 .

[166]  Emmanuel Ledoux,et al.  Modeling fracture flow with a stochastic discrete fracture network: Calibration and validation: 2. The transport model , 1990 .

[167]  K. Raven,et al.  A Field Example of Measuring Hydrodynamic Dispersion in a Single Fracture , 1985 .

[168]  L. Konikow,et al.  Ambiguity in Measuring Matrix Diffusion with Single‐Well Injection/Recovery Tracer Tests , 1997 .

[169]  C. Tsang,et al.  Flow channeling in heterogeneous fractured rocks , 1998 .

[170]  Emil O. Frind,et al.  Contaminant transport in fractured porous media: Analytical solutions for a system of parallel fractures , 1982 .

[171]  C. Welty,et al.  A Critical Review of Data on Field-Scale Dispersion in Aquifers , 1992 .

[172]  M. Sahimi.  Flow phenomena in rocks : from continuum models to fractals, percolation, cellular automata, and simulated annealing , 1993 .

[173]  Laura Toran,et al.  Sensitivity analysis of solute transport in fractured porous media , 1995 .

[174]  H. Sato.  Matrix Diffusion of Simple Cations, Anions, and Neutral Species in Fractured Crystalline Rocks , 1999 .

[175]  K. Raven,et al.  Interpretation of field tracer tests of a single fracture using a transient solute storage model , 1988 .

[176]  Piotr Maloszewski,et al.  On the theory of tracer experiments in fissured rocks with a porous matrix , 1985 .

[177]  Piotr Maloszewski,et al.  Mathematical modeling of tracer behavior in short‐term experiments in fissured rocks , 1990 .

[178]  Luis Moreno,et al.  Analysis of a long-term pumping and tracer test using the channel network model , 1998 .

[179]  Ivars Neretnieks,et al.  The Channel Network Model—A Tool for Transport Simulations in Fractured Media , 1999 .