TECHNICAL PAPERS
Jul 1, 2006

Numerical Modeling and Analysis of Solute Velocity and Macrodispersion for Linearly and Nonlinearly Sorbing Solutes in a Single Fracture with Matrix Diffusion

Publication: Journal of Hydrologic Engineering
Volume 11, Issue 4

Abstract

The behavior of the solute velocity and effective macrodispersivity of solute front in the fracture for the transport in a single fracture in the presence of rock matrix diffusion is analyzed using numerical modeling. The study is limited to a constant continuous solute source boundary condition in a single fracture with constant aperture. Analysis is made for linear and nonlinear sorption cases. Expressions are provided for solute velocity and effective macrodispersivity of the solute fronts during asymptotic and preasymptotic stages using spatial moment analyses. The effective retardation factor and dispersivity of solutes in the fracture are found to follow an exponential function with an exponent related to fracture-matrix parameters.

Get full access to this article

View all available purchase options and get full access to this article.

References

Abelin, H., Birgersson, L., Moreno, L., Widen, H., Agren, T., and Neretnieks, I. (1991). “A large-scale flow and tracer experiment in granite. II: Results and interpretation.” Water Resour. Res., 27(12), 3119–3135.
Abelin, H., Birgersson, L., Widen, H., Agren, T., Moreno, L., and Neretnieks, I. (1994). “Channeling experiments in crystalline fractured rocks.” J. Contam. Hydrol., 15(3), 129–158.
Abulaban, A., Nieber, J. L., and Misra, D. (1998). “Modeling plume behavior for nonlinearly sorbing solutes in saturated homogeneous porous media.” Adv. Water Resour., 21, 487–498.
Amadei, B., and Illangasekare, T. (1994). “A mathematical model for flow and solute transport in non-homogeneous rock fractures.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 31, 719–731.
Arnold, B. W., Zhang, H., and Parsons, A. M. (2000). “Effective porosity and dual-porosity approaches to solute transport in the saturated zone at Yucca Mountain: Implications for repository performance assessment.” Geophys. Monogr., 122, 313–322.
Banton, O., and Bangoy, L. M. (1997). Hydrogeologie, multiscience ennvironnmentale des eaux souterraines (Hydrologeology, environmental multiscience of groundwater). Presses de l’Universite du Quebec/AUPELF, Sainte-Foy, Quebec.
Barenblatt, G. I., Zheltov, Iu. P., and Kochina, I. N. (1960). “Basics concepts in the theory of seepage of homogeneous liquids in fissured rocks.” J. Appl. Math. Mech., 24, 1286–1303.
Barker, J. (1982). “Laplace transform solutions for solute transport in fissured aquifers.” Adv. Water Resour., 5(2), 98–104.
Berkowitz, B., and Zhou, Z. (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.
Bodin, J., Delay, F., and de Marsily, G. (2003). “Solute transport in a single fracture with negligible matrix permeability: I. Fundamental mechanisms.” Hydrogeol. J., 11, 418–433.
Bosma, W. J. P., and van der Zee, S. E. A. T. M. (1995). “Dispersion of a continuously injected, nonlinearly adsorbing solute in chemically or physically heterogeneous porous formations.” J. Contam. Hydrol., 18(3), 181–198.
Boving, T. B., and Grathwohl, P. (2001). “Tracer diffusion coefficients in sedimentary rocks: Correlation to porosity and hydraulic conductivity.” J. Contam. Hydrol., 53, 85–100.
Brown, S. R., Caprihan, A., and Hardy, R. (1998). “Experimental observation of fluid flow channels in single fracture.” J. Geophys. Res., 100(B3), 5125–5132.
Cormenzana, J. (2000). “Transport of two-member decay chain in a single fracture: Simplified analytical solution for two radionuclides with the same transport properties.” Water Resour. Res., 36(5), 1339–1346.
Cvetkovic, V., Selroos, J. O., and Cheng, H. (1999). “Transport of reactive tracers in rock fractures.” J. Fluid Mech., 378, 335–356.
Delay, F., Porel, G., and Banton, O. (1998). “An approach to transport in heterogeneous porous media using the truncated temporal moment equations: Theory and numerical validation.” Transp. Porous Media, 32(2), 199–232.
Detwiler, R. L., Pringle, S. E., and Glass, R. J. (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), 2606–2617.
Detwiler, R. L., Rajaram, H., and Glass, R. J. (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, D. G., and Silliman, S. E. (1993). “Velocity dependence of dispersion for transport through a single fracture of variable roughness.” Water Resour. Res., 29(10), 3477–3483.
Ewing, R. P., and Jaynes, D. B. (1995). “Issues in single fracture transport modeling: Scales, algorithms and grid types.” Water Resour. Res., 31, 303–312.
Freeze, J. F., and Cherry, J. A. (1979). Groundwater, Prentice-Hall, Englewood Cliffs, N.J.
Fujikawa, Y., and Fukui, M. (1990). “Adsorptive solute transport in fractured rock: Analytical solutions for delta-type source conditions.” J. Contam. Hydrol., 6, 85–102.
Gelhar, L. W. (1993). Stochastic subsurface hydrology, Prentice-Hall, Englewood Cliffs, N.J.
Gerke, H. H., and van Genuchten, M. T. (1996). “Macroscopic representation of structural geometry for simulating water and solute movement in dual-porosity media.” Adv. Water Resour., 19(6), 343–357.
Goltz, M. N., and Roberts, P. V. (1987). “Using the method of moments to analyze three-dimensional diffusion-limited solute transport from temporal and spatial perspectives.” Water Resour. Res., 23(8), 1575–1585.
Grisak, G. E., and Pickens, J. F. (1980). “Solute transport through fractured media. I. The effect of matrix diffusion.” Water Resour. Res., 16(4), 719–730.
Hadermann, J., and Heer, W. (1996). “The Grimsel (Switzerland) migration experiment: Integrating field experiments, laboratory investigations and modeling.” J. Contam. Hydrol., 21, 87–100.
Haldeman, W. R., Chuang, Y., Rasmussen, T. C., and Evans, D. D. (1991). “Laboratory analysis of fluid flow and solute transport through a fracture embedded in porous tuff.” Water Resour. Res., 27(1), 53–65.
Hamaker, J. W., and Thompson, J. M. (1972). “Adsorption.” Organic chemicals in the soil environment, C. M. Goring and J. W. Hamaker, eds., Marcel Dekker, New York.
Harvey, C. F., and Gorelick, S. M. (1995). “Temporal moment-generating equations: Modeling transport and mass transfer in heterogenous aquifers.” Water Resour. Res., 31(8), 1895–1911.
Huyakorn, P. S., Lester, B. H., and Mercer, J. W. (1983). “An efficient finite element technique for modeling transport in fractured porous media. I. Single species transport.” Water Resour. Res., 19(3), 841–854.
Ippolito, I., Daccord, G., Hinch, E. J., and Hulin, J. P. (1994). “Echo tracer dispersion in model fractures with a rectangular geometry.” J. Contam. Hydrol., 16(1), 87–108.
Isakov, E., Ogilvie, S. R., Taylor, C. W., and Glover, P. W. J. (2001). “Fluid flow through rough fractures in rocks. I: High resolution aperture determinations.” Earth Planet. Sci. Lett., 191, 267–282.
Keller, A. A., Roberts, P. V., and Blunt, M. J. (1999). “Effect of fracture aperture variations on the dispersion of contaminants.” Water Resour. Res., 35(1), 55–63.
Keller, A. A., Roberts, P. V., and Kitanidis, P. K. (1995). “Prediction of single phase transport parameters in a variable aperture fracture.” Geophys. Res. Lett., 22(11), 1425–1428.
Kennedy, C. A., and Lennox, W. C. (1995). “Control volume model of solute transport in a single fracture.” Water Resour. Res., 31(2), 313–322.
Kessler, J. H., and Hunt, J. R. (1994). “Dissolved and colloidal contaminant transport in a partially clogged fracture.” Water Resour. Res., 30(4), 1195–1206.
Lapcevic, P. A., Novakowski, K. S., and Sudicky, E. A. (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.
Lee, C.-H., and Teng, S.-P. (1993). “An analytical model for radionuclide transport in a single fracture: Considering nonequilibrium matrix sorption.” Nucl. Technol., 101(1), 67–78.
Leo, C. J., and Booker, J. R. (1996). “A time stepping finite element method for analysis of contaminant transport in fractured porous media.” Int. J. Numer. Analyt. Meth. Geomech., 20(12), 847–864.
Lichtner, P. C. (2000). “Critique of dual continuum formulations of multicomponent reactive transport in fractured porous media.” Geophys. Monogr., 122, 281–298.
Lin, B.-S., and Lee, C.-H. (1998). “An explanation of distance-dependent dispersion of mass transport in fractured rock.” J. Chin. Inst. Eng., 21(3), 365–372.
Maloszewski, P., and Zuber, A. (1985). “On the theory of tracer experiments in fissured rocks with a porous matrix.” J. Hydrol., 79, 333–358.
Maloszewski, P., and Zuber, A. (1990). “Mathematical modeling of tracer behavior in short-term tracer experiments and fissured rocks.” Water Resour. Res., 26, 1517–1528.
Maloszewski, P., and Zuber, A. (1992). “On the calibration and validation of mathematical models for the interpretation of tracer experiments in groundwater.” Adv. Water Resour., 15, 47–62.
Maloszewski, P., and Zuber, A. (1993). “Tracer experiments in fissured rocks: Matrix diffusion and the validity of models.” Water Resour. Res., 29(8), 2723–2735.
McCarty, P. L., Reinhard, M., and Rittman, B. E. (1981). “Trace organics in ground water.” Environ. Sci. Technol., 15, 40–51.
McKay, L. D., Gillham, R. W., and Cherry, J. A. (1993). “Field experiments in a fractured clay till. II. Solute and colloid transport.” Water Resour. Res., 29(12), 3879–3890.
Moench, A. F. (1995). “Convergent radial dispersion in a double-porosity aquifer with fracture skin: Analytical solution and application to a field experiment in fractured chalk.” Water Resour. Res., 31(8), 1823–1835.
Moreno, L., and Neretnieks, I. (1993). “Flow and nuclide transport in fractured media: “The importance of the flow-wetted surface for radionuclide migration.” J. Contam. Hydrol., 13, 49–71.
Moreno, L., Tsang, Y. W., Tsang, C. F., Hale, F. V., and 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.
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.” Flow and contaminant transport in fractured rock, J. Bear, C. F. Tsang, and G. Marsily, eds., Academic, San Diego, 39–127.
Neretnieks, I., Erksen, T., and 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, S. P. (1990). “Universal scaling of hydraulic conductivities and dispersivities in geologic media.” Water Resour. Res., 26(8), 1749–1758.
Novakowski, K. S., and Bogan, J. D. (1999). “A semi-analytical model for the simulation of solute transport in a network of fractures having random orientations.” Int. J. Numer. Analyt. Meth. Geomech., 23(4), 317–333.
Pinder, G. F. (1984). “Groundwater contaminant transport modeling.” Environ. Sci. Technol., 18, 108A–114A.
Rasmuson, A. (1985). “Analysis of hydrodynamic dispersion in discrete fracture networks using the method of moments.” Water Resour. Res., 21(11), 1677–1683.
Robinson, N. I., Sharp, J. M., and Kreisel, I. (1998). “Contaminant transport in sets of parallel finite fractures with fracture skins.” J. Contam. Hydrol., 31(1–2), 83–109.
Roux, S., Plouraboue, F., and Hulin, J. P. (1998). “Tracer dispersion in rough open cracks.” Transp. Porous Media, 32(1), 97–116.
Rowe, R. K., Hammoud, A., and Booker, J. R. (1989). “The effect of multi-directional matrix diffusion on contaminant transport through fractured systems.” Contaminant transport in groundwater, H. E. Kobus and W. Kinzelbach, eds., Balkema, Rotterdam, The Netherlands, 259–266.
Rubin, Y., Cushey, M. A., and Wilson, A. (1997). “The moments of the breakthrough curves of instantaneously and kinetically sorbing solutes in heterogenous geologic media: Prediction and parameter inference from field measurements.” Water Resour. Res., 33(11), 2465–2481.
Sato, H. (1999). “Matrix diffusion of simple cations, anions, neutral species in fractured crystalline rocks.” Nucl. Technol., 127(2), 199–211.
Srivastava, R., and Brusseau, M. L. (1996). Nonideal transport of reactive solutes in heterogeneous porous media: I. Numerical model development and moment analysis, J. Contam. Hydrol., 24(2), 117–143.
Stafford, P., Toran, L., and McKay, L. (1998). “Hydrology influence of fracture truncation on dispersion: a dual permeability model.” J. Contam. Hydrol., 30(1–2), 79–100.
Sudicky, E. A., and Frind, E. O. (1982). “Contaminant transport in fractured porous media: Analytical solutions for a system of parallel fractures.” Water Resour. Res., 18(6), 1634–1642.
Sudicky, E. A., and Frind, E. O. (1984). “Contaminant transport in fractured porous media: Analytical solution for a two-member decay chain in a single fracture.” Water Resour. Res., 20(7), 1021–1029.
Sudicky, E. A., and McLaren, R. G. (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.
Suresh Kumar, G., and Sekhar, M. (2005). “Spatial moment analysis for transport of nonreactive solutes in a fracture-matrix system.” J. Hydrologic Eng., 10(3), 192–199.
Tang, D. H., Frind, E. O., and Sudicky, E. A. (1981). “Contaminant transport in fractured porous media: Analytical solution for a single fracture.” Water Resour. Res., 17(3), 467–480.
Thompson, M. E., and Brown, S. R. (1991). “The effect of anisotropic surface roughness on flow and transport in fractures.” J. Geophys. Res., 96(B13), 21923–21932.
Tompson, A. F. B. (1993). “Numerical simulation of chemical migration in physically and chemically heterogeneous porous media.” Water Resour. Res., 29(11), 3709–3726.
Tsang, C. F., Tsang, Y. W., and Hale, F. V. (1991). “Tracer transport in fractures: Analysis of field data based on variable-aperture channel model.” Water Resour. Res., 27(12), 3095–3106.
Valliappan, S., Wang, W., and Khalili, N. (1998). “Contaminant transport under variable density flow in fractured porous media.” Int. J. Numer. Analyt. Meth. Geomech., 22(7), 575–595.
Valocchi, A. J. (1989). “Spatial moment analysis of transport of kinetically adsorbing solutes.” Water Resour. Res., 25, 273–280.
van Genuchten, M. Th., and Wierenga, P. J. (1974). “Simulation of one-dimensional solute transfer in porous media.” Bull. 628, NMSU Agricultural Experimental Station, New Mexico State Univ., Las Cruces, N.M., 40.
Wan, J., Tokunaga, T. K., Orr, T. R., O’Neill, J., and Connors, R. W. (2000). “Glass casts of rock fracture surfaces: A new tool for studying flow and transport.” Water Resour. Res., 36(1), 355–360.
Warren, J. E., and Root, P. J. (1963). “The behavior of naturally fractured reservoirs.” Soc. Pet. Eng. J., 3, 245–255.
Weber, W. J. J., McGinley, P. M., and Katz, L. E. (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., and Beckie, R. (1997). “The influence of surface sorption on dispersion in parallel plate fractures.” J. Contam. Hydrol., 28(1–2), 95–114.
Wels, C., Smith, L., and 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.
Wendland, E., and Himmelsbach, T. (2002). “Transport simulation with stochastic aperture for a single fracture, comparison with a laboratory experiment.” Adv. Water Resour., 25(1), 19–32.
Wood, E. F., Ferrara, R. A., Gray, W. G., and Pinder, G. F. (1984). Groundwater contamination from hazardous wastes, Prentice-Hall, Englewood Cliffs, N.J.
Wood, W. W., Shapiro, A. M., Hsieh, P. A., and Councell, T. B. (1993). “Observational, experimental and inferred evidence for solute diffusion in fractured granite aquifers—Examples from the Mirror Lake Watershed, Grafton County, New Hampshire.” Morganwalp, U.S. Geological Survey Toxic Substances Hydrology Program—Proc. Technical Meeting, Colorado Springs, Colo., D. W. Morganwalp and D. A. Aronson, eds., U.S. Geological Survey Water Resources Investigations Rep. No. 94-4015, Vol. 1, 167–170.
Wooding, R. A. (1960). “Instability of a viscous fluid of variable density in a vertical Hele-Shaw cell.” J. Fluid Mech., 7, 501–515.
Zimmerman, R. W., and Bodvarsson, G. S. (1996). “Hydraulic conductivity of rock fractures.” Transp. Porous Media, 23(1), 1–30.
Zuber, A., and Motyka, J. (1994). “Matrix porosity as the important parameter of fissured rocks for solute transport at large scales.” J. Hydrol., 158, 19–46.

Information & Authors

Information

Published In

Go to Journal of Hydrologic Engineering
Journal of Hydrologic Engineering
Volume 11Issue 4July 2006
Pages: 319 - 328

History

Received: Nov 12, 2004
Accepted: May 2, 2005
Published online: Jul 1, 2006
Published in print: Jul 2006

Permissions

Request permissions for this article.

Authors

Affiliations

M. Sekhar
Assistant Professor, Dept. of Civil Engineering, Indian Institute of Science, Bangalore 560 012, India. E-mail: [email protected]
G. Suresh Kumar
Postdoctoral Fellow, Dept. of Civil Engineering, Queens Univ., Kingston ON, Canada K7L 3N6. E-mail: [email protected]
D. Misra
Assistant Professor, Dept. of Mining and Geological Engineering, Univ. of Alaska, Fairbanks, P.O. Box 755800, Fairbanks, AK 99775-5800 (Corresponding author). E-mail: [email protected].

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share