Dispersion in groundwater flow systems

Reddell, Donald Lee, author
Sunada, D. K., advisor
Breitenbach, E. A., committee member
Waltz, James P., committee member
Evans, Normal A., committee member
Morel-Seytoux, H. J., committee member
Corey, A. T., committee member
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A fundamental flow equation for a mixture of miscible fluids was derived by combining the law of conservation of mass, Darcy's law, and an equation of state describing the pressure-volume-temperature- concentration relationship. The result is an equation involving two dependent variables, pressure and concentration. A relationship for determining concentration was derived by expressing a continuity equation for the dispersed tracer. The problem was formulated on a microscopic basis and averaged over a cross-sectional area of the porous medium to give a macroscopic convective-dispersion equation. The resulting coefficient of dispersion was a second rank tensor. The two resulting differential equations are solved numerically on the digital computer. An implicit numerical technique was used to solve the flow equation for pressure and the method of characteristics with a tensor transformation was used to solve the convective-dispersion equation. The results from the flow equation were used in solving the convective-dispersion equation and the results from the convective-dispersion equation were then used to resolve the flow equation. The proposed computer simulator successfully solved the longitudinal dispersion problem and the longitudinal and lateral dispersion problem. Using the tensor transformation, problems of longitudinal and lateral dispersion were successfully solved in a rotated coordinate system. The computer simulator was used to solve the salt-water intrusion problem. The numerical results for the fresh water head in the aquifer closely matched those obtained analytically. Also, the numerical results for the location of the fresh-salt interface were good except in the region of the wedge toe.
December 1969.
Includes bibliographic references (pages 109-117).
Also has numbering: AED69-70DLR9.
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