Stability of miscible displacements in porous media: rectilinear flow. (English) Zbl 0608.76087

Tan, C. T.; Homsy, G. M.

Phys. Fluids 29, 3549-3556 (1986).

A theoretical treatment of the stability of miscible displacement in a porous medium is presented. For a rectilinear displacement process, since the base state of uniform velocity and a dispersive concentration profile is time dependent, we make the quasi-steady-state approximation that the base state evolves slowly with respect to the growth of disturbances, leading to predictions of the growth rate.
Comparison of results with initial value solutions of the partial differential equations shows that, excluding short times, there is good agreement between the two theories. Comparison of the theory with several experiments in the literature indicates that the theory gives a good prediction of the most dangerous wavelength of unstable fingers. An approximate analysis for transversely anisotropic media has elucidated the role of transverse dispersion in controlling the length scale of fingers.

MSC:

76S05	Flows in porous media; filtration; seepage
76E99	Hydrodynamic stability
76T99	Multiphase and multicomponent flows
76M99	Basic methods in fluid mechanics

Keywords:

stability; miscible displacement; porous medium; rectilinear displacement process; dispersive concentration profile; quasi-steady-state approximation; initial value solutions; approximate analysis; transversely anisotropic media; length scale of fingers

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