Abstract
Transient models are needed to analyze time-dependent problems like hyperfiltration associated with head differences across clay barriers. Hyperfiltration (solute-sieving) effects create an increased concentration of natural groundwater solutes outside the clay barrier due to the inward head gradient. The purpose of our model is to predict solute buildup and distribution during hyperfiltration providing a basis for time analysis of solute migration. Required input parameters for the model include membrane properties like reflection coefficient, hydraulic conductivity, and solute concentration on the high-pressure side of the membrane before the onset of steady state, solution flux, and the effluent concentration. Model verification is based on published experimental results. The transient hyperfiltration model presented herein may prove useful in elucidating clay membrane (hyperfiltration) effects in the subsurface, however the sole purpose of this paper is to develop a transient model of hyperfiltration effects and test it by using published experimental data.
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REFERENCES
Carslaw, H. S., and Jaeger, J. C., 1959, Conduction of heat in solids, 2nd edn.: Clarendon Press, Oxford, UK, 482 p.
Charbeneau, R. J., 2000, Groundwater hydraulics and pollutant transport: Prentice-Hall, Upper Saddle River, NJ, 370 p.
Dankwerts, P. V., 1953, Continuous flow system distribution of residence times: Che. Eng. Sci., v. 2, p. 1–13.
Day, P. R., 1956, Dispersion of a moving salt-water boundary advancing through saturated sand: Am. Geophys. Union Trans., v. 37, p. 595–601.
DeGroot, S. R., and Mazur, P., 1963, Non-equilibrium thermodynamics: Dover, North-Holland, Amsterdam, 105 p.
Fritz, S. J., 1986, Ideality of clay membranes in osmotic processes; a review: Clays Clay Miner., v. 34, no. 2, p. 214–232.
Fritz, S. J., and Marine, I. W., 1983, Experimental support for a predictive osmotic model of clay membranes: Geochimica et Cosmochimica Acta, v. 47, p. 1515–1522.
Fritz, S. J., and Whitworth, T. M., 1994, Hyperfiltration-induced fractionation of lithium isotopes: Ramifications relating to representativeness of aquifer sampling: Water Resour. Res., v. 30, p. 225–235.
Irving, J., and Mulinneux, N., 1959, Mathematics in physics and engineering: Academic Press, New York, 883 p.
Katchalsky, A., and Curran, P. F., 1965, Biophysics: Harvard University Press, Cambridge,MA, 248 p.
Kedem, O., and Katchalsky, A., 1962, Thermodynamics of flow processes in biological systems: Biophys. J., v. 2, p. 53–54.
Lakshminarayanaiah, N., 1984, Equations of membrane biophysics: Academic Press, Orlando, FL, 426 p.
Liangxiong, L., Whitworth, T. M., and Lee, R., 2003, Separation of inorganic solutes from oil-field produced water using a compacted bentonite membrane: J. Membr. Sci., v. 217, p. 215–225.
Marine, J. W., and Fritz, S. J., 1981, Osmotic model to explain anomalous hydraulic heads: Water Resources Research, v. 17, no. 1, p. 73–82.
Ogata, A., and Banks, R. B., 1961, A solution of the differential equation of longitudinal dispersion in porous media: U.S. Geol. Survey, Prof. Paper, no. 411-A, p. A1–A7.
Porter, M. C., 1979, Membrane filtration, inP. A. Schweitzer, ed., Handbook of separation techniques for chemical engineers: McGraw-Hill, New York, p. 225–235.
Sourirajan, S., 1970, Reverse osmosis: Academic Press, Orlando, FL, 547 p.
Srivastava, R. C., and Jain, A. K., 1975, Non-equilibrium thermodynamics of electro-osmosis of water through composite clay membranes, 1. The electro-kinetic energy conversion: J. Hydrol. v. 25, p. 307–324.
Staverman, A. J., 1952, Non-equilibrium thermodynamics of membrane processes: Trans. Faraday Soc., v. 48, p. 176–185.
Whitworth, T. M., 1998, Steady-state mathematical modeling of geologic membrane processes in aquifer systems, it in WERC/WRHSRC/NMHWMS Joint Conference on the Environment, Proceedings, Albuquerque, NM, p. 37–41.
Whitworth, T. M., and DeRosa, G., 1997, Geologic membrane controls on saturated zone heavy metal transport: Las Cruces, New Mexico WRRI: Technical Completion Report, no. 303, 51 p.
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Oduor, P., Whitworth, T.M. Transient Modeling of Hyperfiltration Effects. Mathematical Geology 36, 743–758 (2004). https://doi.org/10.1023/B:MATG.0000039544.83678.a6
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DOI: https://doi.org/10.1023/B:MATG.0000039544.83678.a6