Semianalytical Solution for Nonequilibrium Sorption of Pollutant Transport in Streams
Publication: Journal of Environmental Engineering
Volume 137, Issue 11
Abstract
During pollutant transport in a stream, many pollutants get adsorbed in the streambed materials and are subsequently released. A conceptual hybrid-cells-in-series model for adsorption (HCIS-A), which consists of a plug flow zone and two thoroughly mixed zones of unequal residence times, has been developed to simulate adsorption-desorption in addition to advection and dispersion processes. Sorption processes governed by first-order mass exchange kinetics along with advection in the plug flow zone have been solved analytically using the Laplace transform technique. Analytical solutions have been derived for transport of pollutants through the first and second thoroughly mixed zones of the hybrid model considering sorption. Using the convolution technique and ramp kernel coefficients, the pollutants have been routed through all the zones to derive a semianalytical solution at the end of first hybrid unit. The advantages of this conceptual hybrid model are (1) the conversion of the second-order partial differential equation to a first-order ordinary differential equation; (2) the model’s capacity to incorporate variation of stream geometry and flow velocity in different stream reaches; and (3) the model’s capability to incorporate sorption kinetics. The responses of the hybrid model correspond to the finite-difference solutions of the partial differential equation (PDE) that accounts for advection, dispersion, and adsorption. The first arrival time of the pollutant downstream of a point disposal has been estimated. This is not clearly identified in other models. The effect of sorption on pollutant transport was studied and demonstrated in various profiles as the pollutant moved downstream of a disposal point. The characteristics of the profiles for a conservative pollutant in streams with adsorbing streambed were in the expected trend.
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References
Bajracharya, K., and Barry, D. A. (1993a). “Mixing cell models for nonlinear equilibrium single species adsorption and transport.” J. Contam. Hydrol., 12(3), 227–243.
Bajracharya, K., and Barry, D. A. (1993b). “Mixing cell models for nonlinear non-equilibrium single species adsorption and transport.” Water Resour. Res., 29(5), 1405–1413.
Bajracharya, K., and Barry, D. A. (1995). “Analysis of one dimensional multispecies transport experiments in laboratory soil columns.” Environ. Int., 21(5), 687–691.
Banks, R. B. (1974). “A mixing cell model for longitudinal dispersion in open channels.” Water Resour. Res., 10(2), 357–358.
Bansal, M. K. (1971). “Dispersion in natural streams.” J. Hydraul. Div., 97(11), 1867–1886.
Barry, D. A., and Bajracharya, K. (1995). “Optimised Muskingum-Cunge solution method for solute transport with equilibrium Freundlich reactions.” J. Contam. Hydrol., 18(3), 221–238.
Bear, J. (1972). Dynamics of fluids in porous media, American Elsevier, New York.
Bear, J., and Bachmat, Y. (1990). Theory and applications of transport in porous media, Kluwer Academic, Dordrecht, Nederlands.
Bencala, K. E., McKnight, D. M., and Zellweger, G. W. (1990). “Characterization of transport in an acidic and metal-rich mountain stream based on a lithium traces injection and simulations of transient storage.” Water Resour. Res., 26(5), 989–1000.
Bencala, K. E., and Walters, R. A. (1983). “Simulation of solute transport in a mountain pool-and riffle stream: A transient storage model.” Water Resour. Res., 19(3), 718–724.
Beven, K. J., and Young, P. C. (1988). “An aggregated mixing zone model of solute transport through porous media.” J. Contam. Hydrol., 3(2–4), 129–143.
Cameron, D. R., and Klute, A. (1977). “Convective dispersive solute transport with combined equilibrium and kinetic adsorption model.” Water Resour. Res., 13(1), 183–188.
Carnahan, C. L., and Remer, J. S. (1984). “Non-equilibrium and equilibrium sorption with a linear sorption isotherm during mass transport through an infinite porous medium: Some analytical solutions.” J. Hydrol. (Amsterdam), 73(3–4), 227–258.
Chatwin, P. C. (1980). “Presentation of longitudinal dispersion data.” J. Hydraul. Div., 106(1), 71–83.
Chatwin, P. C., and Allen, C. M. (1985). “Mathematical models of dispersion in rivers and estuaries.” Annu. Rev. Fluid Mech., 17(1), 119–149.
Czernuszenko, W., and Rowinski, P. M. (1997). “Properties of the dead zone model of longitudinal dispersion in rivers.” J. Hydraul. Res., 35(4), 491–504.
Day, T. J. (1975). “Longitudinal dispersion in natural channels.” Water Resour. Res., 11(6), 909–918.
Day, T. J., and Wood, I. R. (1976). “Similarity of the mean motion of fluid particles dispersing in natural channels.” Water Resour. Res., 12(4), 655–666.
De Smedt, F., Brevis, W., and Debels, P. (2005). “Analytical solution for solute transport resulting from instantaneous injection in streams with transient storage.” J. Hydrol. (Amsterdam), 315(1–4), 25–39.
Deacon, J. R., and Driver, N. E. (1999). “Distribution of trace elements in streambed sediment associated with mining activities in the upper Colorado River Basin, Colorado, USA.” Arch. Environ. Contam. Toxicol., 37(1), 7–118.
Fischer, H. B. (1967). “The mechanics of dispersion in natural streams.” J. Hydraul. Div., 93(6), 187–216.
Fischer, H. B. (1968). “Dispersion predictions in natural streams.” J. Sanit. Eng. Div., 94, 927–943.
Fischer, H. B., Imberger, J., List, E. J., Koh, R. C. Y., and Brooks, N. H. (1979). Mixing in inland and coastal waters, Academic, New York.
Ghosh, N. C. (2001). “Study of solute transport in a river.” Ph.D. thesis, IIT Roorkee, India.
Ghosh, N. C., Mishra, G. C., and Muthukrishnavellaisamy, K. (2008). “Hybrid-cells-in-series model for solute transport in streams and relation of its parameters with bulk flow characteristics.” J. Hydraul. Eng., 134(4), 497–502.
Ghosh, N. C., Mishra, G. C., and Ojha, C. S. P. (2004). “A hybrid-cells-in-series model for solute transport in a river.” J. Envir. Eng. Div., 130(10), 1198–1209.
Godfrey, R. G., and Frederick, B. J. (1970). “Dispersion in natural streams.” Professional paper No. 433-K, USGS, Reston, VA, 1–38.
Hays, J. R., Krenkel, P. A., and Schnelle, K. B. (1966). “Mass transport mechanisms in open channel flow.” Tech. Rep. No. 8, Vanderbilt Univ., Nashville, TN.
Jain, C. K., and Sharma, M. K. (2002). “Adsorption of cadmium on bed sediments of River Hindon: Adsorption models and kinetics.” Water Air Soil Pollut., 137(1–4), 1–19.
Leij, F. J., and Toride, N. (1998). Analytical solutions for non-equilibrium transport models, in physical non-equilibrium in soils modelling and application, H. M. Selim and L. Ma, eds., Ann Arbor Press, Chelsea, MI.
Nordin, C. F., Jr., and Sabol, G. V. (1974). “Empirical data on longitudinal dispersion in rivers.” Water Resources Investigations Rep. No. 20-74, USGS, Reston, VA.
Nordin, C. F., and Troutman, B. M. (1980). “Longitudinal dispersion in rivers: The persistence of skewness in observed data.” Water Resour. Res., 16(1), 123–128.
Ogata, A., and Banks, R. B. (1961). “A solution of the deferential equation of longitudinal dispersion in porous media.” Professional paper No. 411-A, USGS, Reston, VA.
Perk Marcel, V., Owens, P. N., Deeks, L. K., and Rawlins, B. G. (2006). “Streambed sediment geochemical controls in stream phosphorus concentration during base flow.” Water Air Soil Pollut., 6(5–6), 443–451.
Runkel, R. L. (1998). “One dimensional transport with inflow and storage (OTIS): A solute transport model for streams and rivers.” Water Resources Investigations Rep. No. 98-4018., USGS, Denver.
Runkel, R. L., and Broshears, R. E. (1991). “One dimensional transport with inflow and storage (OTIS): A solute transport model for small streams.” Technical Rep. 91-01, Center for Advanced Decision Support for Water and Environmental System, Univ. of Colorado, Boulder, CO.
Runkel, R. L., and Chapra, S. C. (1993). “An efficient numerical solution of the transient storage equations for solute transport in small streams.” Water Resour. Res., 29(1), 211–215.
Rutherford, J. C. (1994). River mixing, Wiley, Chichester, UK.
Sardin, M., Schweich, D., Leij, F. J., and Van Genuchten, M. T. (1991). “Modeling the non-equilibrium transport of linearly interacting solutes in porous media: A review.” Water Resour. Res., 27(9), 2287–2307.
Selim, H. M., and Ma, L. (1998). Physical non-equilibrium in soils modelling and application, Ann Arbor Press, Chelsea, MI.
Sooky, A. A. (1969). “Longitudinal dispersion in open channels.” J. Hydraul. Div., 95(4), 1327–1346.
Stefan, H. G., and Demetracopoulos, A. C. (1981). “Cells in series simulation of riverine transport.” J. Hydraul. Div., 107(6), 675–697.
Thackston, E. L., and Krenkel, P. A. (1967). “Longitudinal mixing in natural streams.” J. Sanit. Eng. Div., 93(5), 67–90.
Van Genuchten, M. T., and Jury, W. A. (1987). “Progress in unsaturated flow and transport modelling.” Rev. Geophys., 25(2), 135–140.
Van Kooten, J. J. A. (1996). “A method to solve the advection-dispersion equation with a kinetic adsorption isotherm.” Adv. Water Resour., 19(4), 193–206.
Worman, A. (1998). “Analytical solution and time scale for transport of reacting solutes in rivers and streams.” Water Resour. Res., 34(10), 2703–2716.
Worman, A., Packman, A. I., Johansson, H., and Jonsson, K. (2002). “Effect of flow-induced exchange in hyporheic zones on longitudinal transport of solutes in streams and rivers.” Water Resour. Res., 38(1), 1001.
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Published In
Journal of Environmental Engineering
Volume 137 • Issue 11 • November 2011
Pages: 1066 - 1074
Copyright
© 2011 American Society of Civil Engineers.
History
Received: Jul 16, 2008
Accepted: Apr 28, 2011
Published online: Apr 30, 2011
Published in print: Nov 1, 2011
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