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Transport of kinetically sorbing solute by steady random velocity in heterogeneous porous formations

Published online by Cambridge University Press:  26 April 2006

Vladimir Cvetkovic  and
Gedeon Dagan
Vladimir Cvetkovic
Affiliation:
Department of Water Resources Engineering, Royal Institute of Technology, S-10044 Stockholm, Sweden
Gedeon Dagan
Affiliation:
Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel
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Abstract

A Lagrangian framework is used for analysing reactive solute transport by a steady random velocity field, which is associated with flow through a heterogeneous porous formation. The reaction considered is kinetically controlled sorption–desorption. Transport is quantified by the expected values of spatial and temporal moments that are derived as functions of the non-reactive moments and a distribution function which characterizes sorption kinetics. Thus the results of this study generalize the previously obtained results for transport of non-reactive solutes in heterogeneous formations (Dagan 1984; Dagan et al. 1992). The results are illustrated for first-order linear sorption reactions. The general effect of sorption is to retard the solute movement. For short time, the transport process coincides with a non-reactive case, whereas for large time sorption is in equilibrium and solute is simply retarded by a factor R = 1+Kd, where Kd is the partitioning coefficient. Within these limits, the interaction between the heterogeniety and kinetics yields characteristic nonlinearities in the first three spatial moments. Asymmetry in the spatial solute distribution is a typical kinetic effect. Critical parameters that control sorptive transport asymptotically are the ratio εr between a typical reaction length and the longitudinal effective (non-reactive) dispersivity, and Kd. The asymptotic effective dispersivity for equilibrium conditions is derived as a function of parameters εr and Kd. A qualitative agreement with field data is illustrated for the zero- and first-order spatial moments.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 265 , 25 April 1994 , pp. 189 - 215
Copyright
© 1994 Cambridge University Press

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References

Andricevic, R. & Foufoula-Georgiou, E. 1992 Modeling kinetic non-equilibrium using the first two moments of the residence time distribution. Stochastic Hydrol. Hydraul. 5, 155–171.Google Scholar
Bellin, A., Salandin, P. & Rinaldo, A. 1992 Simulation of dispersion in heterogeneous porous formations: Statistics, first-order theories, convergence of computations. Water Resources Res. 28, 2211–2228.Google Scholar
Brusseau, M. L. & Rao, P. S. C. 1989 Sorption nonideality during organic contaminant trasport in porous media. CRC Crit. Rev. Environ. Control 19, 33–99.Google Scholar
Cameron, D. R. & Klute, A. 1977 Convective-dispersive solute transport with combined equilibrium and kinetic adsorption model. Water Resources Res. 13, 183–188.Google Scholar
Chin, D. A. & Wang, T. 1992 An investigation of the validity of first-order stochastic dispersion theories in isotropic porous media. Water Resources Res. 28, 1531–1542.Google Scholar
Chrysikopoulos, C. V., Kitanidis, P. K. & Roberts, P. V. 1992 Macrodispersion of sorbing solutes in heterogeneous porous formations with spatially periodic reatardation factor and velocity field. Water Resources Res. 28, 1517–1530.Google Scholar
Cvetkovic, V. & Shapiro, A. M. 1990 Mass arrival of sorptive solute in heterogeneous porous media. Water Resources Res. 26, 2057–2067.Google Scholar
Cvetkovic, V., Shapiro, A. & Dagan, G. 1992 A solute flux approach to transport in heterogeneous formations: 2. Uncertainty analysis. Water Resources Res. 28, 1377–1388.Google Scholar
Dagan, G. 1982 Stochastic modeling of groundwater flow by unconditional and conditional probabilities, 2, The solute transport. Water Resources Res. 18, 835–848.Google Scholar
Dagan, G. 1984 Solute transport in heterogeneous formations. J. Fluid Mech. 145, 151–177.Google Scholar
Dagan, G. 1987 Theory of solute transport by groundwater. Ann. Rev. Fluid Mech. 19, 183–215.Google Scholar
Dagan, G. 1989 Flow and Transport in Porous Formations. Springer.
Dagan, G. 1990 Transport in heterogeneous formations: Spatial moments, ergodicity and effective dispersion. Water Resources Res. 26, 1281–1290.Google Scholar
Dagan, G. 1991 Dispersion of a passive solute in non-ergodic transport by steady velocity fields in heterogeneous formations. J. Fluid Mech. 233, 197–210.Google Scholar
Dagan, G., Cvetkovic, V. & Shapiro, A. 1992 A solute flux approach to transport in heterogeneous formations: 1. The general framework. Water Resources Res. 28, 1369–1376.Google Scholar
Dagan, G. & Cvetkovic, V. 1993 Spatial moment of a kinetically sorbing plume in a heterogeneous aquifer. Water Resources Res. 29, 4053–4062.Google Scholar
Destouni, G. & Cvetkovic, V. 1991 Field Scale mass arrival of sorptive solute into the groundwater. Water Resources Res. 27, 1315–1325.Google Scholar
Freyberg, D. L. 1986 A natural gradient experiment on solute transport in a sand aquifer 2. Spatial moments and the advection and dispersion of nonreactive tracers. Water Resources Res. 22, 2031–2046.Google Scholar
Gelhar, L. J. & Axness, C. L. 1983 Three-dimensional stochastic analysis of macrodispersion in aquifers. Water Resources Res. 19, 161–180.Google Scholar
Genuchten, M. Th. van & Dalton, F. N. 1986 Models for simulating salt movement in aggregated field soils. Geoderma 38, 165–183.Google Scholar
Genuchten, M. Th. van & Wierenga, P. J. 1976 Mass transfer studies in sorbing porous media, 1. Analytical solutions. Soil Sci. Soc. Am. J. 40, 473–480.Google Scholar
Goltz, N. M. & Roberts, P. V. 1986 Interpreting organic transport data from a field experiment using physical nonequilibrium models. J. Contam. Hydrol. 1, 77–93.Google Scholar
Goltz, N. M. & Roberts, P. V. 1987 Using the method of moments to analyze three-dimensional diffusion-limited solute transport from temporal and spatial perspectives. Water Resources Res. 23, 1575–1585.Google Scholar
Hess, K. M., Wolf, S. H. & Celia, M. A. 1992 Large-scale natural gradient tracer test in sand and gravel, Cape Cod, Massachussets, 3, Hydraulic conductivity variability and calculated macrodispersivities. Water Resources Res. 28, 2011–2028.Google Scholar
Kabala, Z. J. & Sposito, G. 1991 A stochastic model of reactive solute transport with time-varying velocity in a heterogeneous aquifer. Water Resources Res. 27, 341–350.Google Scholar
Knapp, R. B. 1989 Spatial and temporal scales of local equilibrium in dynamic fluid-rock systems. Geochim. Cosmochim. Acta 53, 1955–1964.Google Scholar
Kreft, A. & Zuber, A. 1978 On the physical meaning of the dispersion equation and its solutions for different initial and boundary conditions. Chem. Engng Sci. 33, 1471–1480.Google Scholar
Lassey, K. R. 1988 Unidimensional solute transport incorporating equilibrium and rate-limited isotherms with first-order loss, 1, Model conceptualizations and analytic solutions. Water Resources Res. 24, 343–350.Google Scholar
Miller, C. T. & Weber, W. J. 1986 Sorption of hydrophobic organic pollutants in saturated soil systems. J. Contam. Hydrol. 1, 381–391.Google Scholar
Neretnieks, I. & Rasmuson, A. 1984 An approach to modelling radionuclide migration in a medium with strongly varying velocity and block sizes along the flow path. Water Resources Res. 20, 1823–1836.Google Scholar
Neuman, S. P. 1993 Eulerian–Lagrangian theory of transport in space-time nonstationary velocity fields: Exact nonlocal formalism by conditional moments and weak approximation. Water Resources Res. 29, 633–645.CrossRefGoogle Scholar
Neuman, S. P., Winter, C. L. & Newman, C. M. 1987 Stochastic theory of field-scale Fickian dispersion in anisotropic porous media. Water Resources Res. 23, 453–466.Google Scholar
Nkedi-Kizza, P., Biggar, J. W., Genuchten, M. Th., van, Wierenga, P. J., Selim, H. M., Davidson, J. M. & Nielsen, D. R. 1983 Modelling tritium and chloride 36 transport through an aggregated oxisol. Water Resources Res. 19, 691–700.Google Scholar
Ptacek, C. J. & Gillham, R. W. 1992 Laboratory and field measurements of non-equilibrium transport in the Borden aquifer, Ontario, Canada. J. Cont. Hydrol. 10, 119–158.Google Scholar
Roberts, P. V., Goltz, N. M. & Mackay, D. M. 1986 Natural-gradient experiment on solute transport in a sand aquifer, 3. Retardation estimates and mass balances of organic solutes. Water Resources Res. 22, 2047–2058.Google Scholar
Rosen, J. B. 1952 Kinetics of a fixed bed system for solid diffusion into spherical particles. J. Chem. Phys. 20, 387–394.Google Scholar
Rubin, Y. 1990 Stochastic modeling of macrodispersion in heterogeneous porous media. Water Resources Res. 26, 133–141.Google Scholar
Sardin, M., Schweich, D., Leij, F. J. & Genuchten, M. Th. van 1991 Modeling the nonequilibrium transport of linearly interacting solutes in porous media: A review. Water Resources Res. 27, 2287–2307.Google Scholar
Selroos, J. O. & Cvetkovic, V. 1992 Modeling solute advection coupled with sorption kinetics in heterogeneous formations. Water Resources Res. 28, 1271–1278.Google Scholar
Shapiro, A. M. & Cvetkovic, V. 1988 Stochastic analysis of solute arrival time in heterogeneous porous media. Water Resources Res. 24, 1711–1718.Google Scholar
Simmons, C. S. 1982 A stochastic-convective transport representation of dispersion in one-dimensional porous media systems. Water Resources Res. 18, 1193–1214.Google Scholar
Valocchi, A. J. 1985 Validity of the local equilibrium assumption for modeling sorbing solute transport through homogeneous soils. Water Resources Res. 21, 808–820.Google Scholar
Valocchi, A. J. 1989 Spatial moment analysis of the transport of kinetically adsorbing solutes through stratified aquifers. Water Resources Res. 25, 273–279.Google Scholar
Villermaux, J. 1974 Deformation of chromatographic peaks under the influence of mass transfer phenomena. J. Chromatographic Sci. 12, 822–831.Google Scholar
Weber, W. J., McGinley, P. M. & Katz, L. E. 1991 Sorption phenomena in subsurface systems: concepts, models and effects on contaminant fate and transport. Water Res. 25, 499–528.CrossRefGoogle Scholar