Abstract
A mathematical model is developed of an abrupt pressure impact applied to a compressible fluid with solute, flowing through saturated porous media. Nondimensional forms of the macroscopic balance equations of the solute mass and of the fluid mass and momentum lead to dominant forms of these equations. Following the onset of the pressure change, we focus on a sequence of the first two time intervals at which we obtain reduced forms of the balance equations. At the very first time period, pressure is proven to be distributed uniformly within the affected domain, while solute remains unaffected. During the second time period, the momentum balance equation for the fluid conforms to a wave form, while the solute mass balance equation conforms to an equation of advective transport. Fluid's nonlinear wave equation together with its mass balance equation, are separately solved for pressure and velocity. These are then used for the solution of solute's advective transport equation. The 1-D case, conforms to a pressure wave equation, for the solution of fluid's pressure and velocity. A 1-D analytical solution of the transport problem, associates these pressure and velocity with an exponential power which governs solute's motion along its path line.
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References
Bear, J. and Bachmat, Y.: 1986, Macroscopic modeling of transport phenomena in porous media 2: Applications to mass, momentum and energy transport, Transportin Porous Media 1, 241–270.
Bear, J. and Sorek, S.: 1990, Evolution of governing mass and momentum balances following an abrupt pressure impact in porous medium, Transport in Porous Media 5, 169–185.
Bear, J. Sorek, S., Ben-Dor, G. and Mazor, G.: 1992, Displacement waves in saturated thermoelastic porous media. I. Basic equations, Fluid Dynamic Res. 9, 155–164.
Landau, L. D. and Lifshitz, E. M.: 1987, Fluid Mechanics, 2nd edn, Pergamon Press, London, pp. 378–385.
Sorek, S Bear, J., Ben-Dor, G. and Mazor, G.: Shock waves in saturated thermoelastic porous media, Transportin Porous Media 9, 3–13.
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Sorek, S. A model for solute transport following an abrupt pressure impact in saturated porous media. Transp Porous Med 22, 271–285 (1996). https://doi.org/10.1007/BF00161627
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DOI: https://doi.org/10.1007/BF00161627