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The dispersion zone between fluids with different density and viscosity in a heterogeneous porous medium

Published online by Cambridge University Press:  26 April 2006

L. J. T. M. Kempers  and
H. Haas
L. J. T. M. Kempers
Affiliation:
Koninklijke/Shell Exploratie en Produktie Laboratorium, Volmerlaan 6, 2288 GD Rijswijk, The Netherlands
H. Haas
Affiliation:
Koninklijke/Shell Exploratie en Produktie Laboratorium, Volmerlaan 6, 2288 GD Rijswijk, The Netherlands
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Abstract

A shock front in the concentration between two miscible fluids flowing through a porous medium becomes dispersed owing to the heterogeneous structure of the porous medium. If the fluids have equal viscosity and density and the heterogeneity of the porous medium is statistically homogeneous, the length of the dispersion zone between the fluids is known to increase as (βX)½, where β is the dispersivity and X is the average displacement distance. At present the dispersivity is considered to be a property of only the porous medium. For the case where the fluids differ in density and/or in viscosity we have investigated the effect of the dynamics of the fluid flow on the magnitude of the dispersivity β and on the validity of the X½ dependence of the dispersion zone's length. First, we measured the dispersivity in a 1.8 m long sandstone core with brine displacing water and with gas displacing oil. The measurements demonstrate that the dispersivity does indeed depend on the displacement velocity. Second, we monitored the expansion of the dispersion zone using detailed numerical simulations of the flow in a porous medium with statistically homogeneous heterogeneity. We found that the dispersion zone does grow as X½ in the presence of a density contrast and a viscosity contrast, in spite of the nonlinearity of the governing equations. Third, we quantified the magnitude of the dispersivity by means of a random-walk model and tested the model against the experiments and the numerical simulations. Experiments, simulations and the model show that the dispersivity is strongly dependent on the displacement velocity in the conditionally stable flow regime. They also show that a nearly non-dispersive development of the shock front between the fluids occurs when gravity segregation dominates the dispersive effect of the porous medium. Even a very small difference in density, such as that between water and brine, can suppress the dispersivity significantly.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 267 , 25 May 1994 , pp. 299 - 324
Copyright
© 1994 Cambridge University Press

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