1887
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
The effects of capillary forces on the axisymmetric propagation of two-phase, constant-flux gravity currents in porous media
Rent:
Rent this article for
USD
10.1063/1.4793748
/content/aip/journal/pof2/25/3/10.1063/1.4793748
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/3/10.1063/1.4793748
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

(Left) A sketch of an axisymmetric gravity current propagating below an impermeable horizontal boundary in a porous medium saturated with an immiscible fluid of higher density and different viscosity. (Right) A representative vertical saturation profile through the current, as indicated by the gray shading on the left.

Image of FIG. 2.
FIG. 2.

Contour plots of (a) the saturation function, , and (b) the flux function, , against and Λ. The shaded regions indicate the physical limits of (1) weak, (2) strong, and (3) intermediate capillary effects discussed in Secs. IV A–IV C , respectively, as well as the regions for which approximate expressions for and can be found. The dashed contour lines are plotted using the approximate expressions for and , given by (33a), (33b), (45a), and (45b) in regions 2 and 3, respectively, and are almost indistinguishable from the actual values there.

Image of FIG. 3.
FIG. 3.

Graphs demonstrating how the self-similar height profile of a two-phase gravity current, (), varies with the strength of capillary forces. The gray shading indicates how the saturation distribution within the gravity current changes. Strengthening capillary forces, corresponding to decreasing and Λ, lead to a thicker current, with a more rounded front and lower saturations. The dashed curve when = 10 and Λ = 1 shows the approximate profile in the limit of strong capillary forces, given by the solution of (40) . The single-phase height profile predicted by Lyle is almost identical to the two-phase profile displayed for = 10 and Λ = 10. Note the difference in vertical scale for each graph.

Image of FIG. 4.
FIG. 4.

Contour plot of the dimensionless current height, , at = 0.5, normalised by the corresponding height of a single-phase gravity current, (0.5) = 0.348, as a function of Λ and . The solid curves indicate solutions of the full numerical equations. The circled numbers correspond to regions of (1) weak, (2) strong, and (3) intermediate capillary forces, discussed in Secs. IV A–IV C , respectively. The dashed curves depict the contours calculated using the approximations in regions of strong and intermediate capillary forces. These approximate contour lines have been calculated using constants of proportionality 1 in (38a) in region 2, and 0.5 in (47) in region 3.

Image of FIG. 5.
FIG. 5.

Contour plot showing the variation of with Λ and , where is the value in the single-phase limit. The circled numbers correspond to regions of (1) weak, (2) strong, and (3) intermediate capillary forces, discussed in Secs. IV A–IV C , respectively. In the limit of strong capillary forces, η = 0.8704(2 + Λ)(/Λ), as discussed in Sec. IV B . The contours using this approximation for , 0.6, and 0.8 are shown by the dashed curves.

Image of FIG. 6.
FIG. 6.

Graph of the scaled current height profiles in various limits. The dashed curve shows () in the single-phase limit. The solid curve shows (), in the limit of very strong capillary forces, where () = [Λ (2 + Λ)] ().

Loading

Article metrics loading...

/content/aip/journal/pof2/25/3/10.1063/1.4793748
2013-03-21
2014-04-16
Loading

Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: The effects of capillary forces on the axisymmetric propagation of two-phase, constant-flux gravity currents in porous media
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/3/10.1063/1.4793748
10.1063/1.4793748
SEARCH_EXPAND_ITEM