Spatial Moment Analysis for Transport of Nonreactive Solutes in Fracture-Matrix System
Publication: Journal of Hydrologic Engineering
Volume 10, Issue 3
Abstract
This paper presents an analysis using spatial moments for transport of nonreactive solutes in a single fracture-matrix system using a dual porosity framework. The velocity and dispersion obtained using the first and second spatial moments are found to have two regimes. The effect of fracture velocity, fracture dispersivity, fracture spacing, matrix diffusion coefficient, and matrix porosity on both regimes are analyzed. The first regime is characterized by a behavior wherein both velocity and dispersion are functions of time and all of the above parameters of the fracture-matrix system are found to have an influence. In the second regime, they are independent of time similar to the behavior of conservative solutes in an ideal porous media. This regime is characterized by the influence of a few parameters of the fracture-matrix system. The empirical relationships for solute velocity, macrodispersion coefficient, and dispersivity in the asymptotic stage are presented.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgment
The writers gratefully acknowledge the analytical code provided by Professor E. A. Sudicky, Waterloo Centre for Groundwater Research, University of Waterloo, Ontario, Canada.
References
Barenblatt, G. I., Zheltov, I. 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.
Bear, J. (1993). “Modeling flow and contaminant transport in fractured rocks.” Flow and contaminant transport in fractured rocks, J. Bear, C.-F. Tsang, and G. de Marsily, eds., Academic, San Diego, 1–37.
Grisak, G. E., and Pickens, J. F. (1980a). “Solute transport through fractured media. I: The effect of matrix diffusion.” Water Resour. Res., 16(4), 719–730.
Grisak, G. E., and Pickens, J. F. (1980b). “Solute transport through fractured media. II: Column study of Fractured Till.” Water Resour. Res., 16(4), 731–739.
Guven, O., Molz, F. J., and Melville, J. G. (1984). “An analysis of dispersion in a stratified aquifer.” Water Resour. Res., 10(10), 1337–1354.
Hadermann, J., and Heer, W. (1996). “The Grimsel (Switzerland) migration experiment: Integrating field experiments, laboratory investigations, and modeling.” J. Contam. Hydrol., 21, 87–100.
Haggerty, R., and Gorelick, S. M. (1995). “Multiple-rate mass transfer for modeling diffusion and surface reactions in media with pore-scale heterogeneity.” Water Resour. Res., 31(10), 2383–2400.
Haggerty, R., and Gorelick, S. M. (1998). “Modeling mass transfer processes in soil columns with pore-scale heterogeneity.” Soil Sci. Soc. Am. J., 62(1), 62–74.
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.
Kennedy, C. A. (1995). “A control volume model of solute transport in a single fracture.” Water Resour. Res., 31(2), 313–322.
Maloszewski, P., and Zuber, A. (1985). “On the theory of tracer experiments in fissured rocks with a porous matrix.” J. Hydrol., 79, 333–358.
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.
Moreno, L., Neretnieks, I., and Eriksen, T. (1985). “Analysis of some laboratory tracer runs in natural fissures.” Water Resour. Res., 21(7), 951–958.
Neretnieks, I., Eriksen, 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.
Noorishad, J., and Mehran, M. (1982). “An upstream finite element method for solution of transient transport equation in fractured porous media.” Water Resour. Res., 18(3), 588–596.
Novakowski, K. S., Evans, G. V., Lever, D. A., and Raven, K. G. (1985). “A field example of measuring hydrodynamic dispersion in a single fracture.” Water Resour. Res., 21(8), 1165–1174.
Novakowski, K. S., and Bogan, J. D. (1999). “A semianalytical 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.
Raven, K. G., Novakowski, K. S., and Lapcevic, P. A. (1988). “Interpretation of field tracer tests of a single fracture using a transient solute storage model.” Water Resour. Res., 24(12), 2019–2032.
Robinson, N. I., and Sharp, Jr., J. M. (1997). “Analytical solution for contaminant transport in a finite set of parallel fractures with matrix diffusion.” C.S.I.R.O. Mathematical and Information Sciences Report CMIS-C23.
Robinson, N. I., Sharp, Jr., J. M., and Kreisel, I. (1998a). “Contaminant transport in sets of parallel finite fractures with fracture skins.” J. Contam. Hydrol., 31, 83–109.
Stafford, P., Toran, L., and McKay, L. (1998b). “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, 1634–1642.
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, 555–564.
Warren, J., and Root, P. (1963). “The behavior of naturally fractured reservoirs.” Trans. Soc. Min. Eng. AIME, 228, 245–255.
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.
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
Journal of Hydrologic Engineering
Volume 10 • Issue 3 • May 2005
Pages: 192 - 199
Copyright
© 2005 ASCE.
History
Received: Dec 9, 2002
Accepted: Oct 26, 2003
Published online: May 1, 2005
Published in print: May 2005
Authors
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.