Similarity solutions for immiscible phase migration in porous media: an analysis of free boundaries

1990 ◽  
Vol 5 (5) ◽  
pp. 491-515 ◽  
Author(s):  
Arieh Pistiner ◽  
Michael Shapiro ◽  
Hillel Rubin
Keyword(s):  
Porous Media ◽  
Similarity Solutions ◽  
Free Boundaries ◽  
Immiscible Phase

scholarly journals Stratified gravity currents in porous media

2016 ◽  
Vol 791 ◽  
pp. 329-357 ◽  
Author(s):  
Samuel S. Pegler ◽  
Herbert E. Huppert ◽  
Jerome A. Neufeld
Keyword(s):  
Porous Media ◽  
Density Distribution ◽  
Vertical Structure ◽  
Gravity Current ◽  
Gravity Currents ◽  
Similarity Solutions ◽  
Density Field ◽  
Vertical Position ◽  
Uniform Density ◽  
Convex Shape

We consider theoretically and experimentally the propagation in porous media of variable-density gravity currents containing a stably stratified density field, with most previous studies of gravity currents having focused on cases of uniform density. New thin-layer equations are developed to describe stably stratified fluid flows in which the density field is materially advected with the flow. Similarity solutions describing both the fixed-volume release of a distributed density stratification and the continuous input of fluid containing a distribution of densities are obtained. The results indicate that the density distribution of the stratification significantly influences the vertical structure of the gravity current. When more mass is distributed into lighter densities, it is found that the shape of the current changes from the convex shape familiar from studies of the uniform-density case to a concave shape in which lighter fluid accumulates primarily vertically above the origin of the current. For a constant-volume release, the density contours stratify horizontally, a simplification which is used to develop analytical solutions. For currents introduced continuously, the horizontal velocity varies with vertical position, a feature which does not apply to uniform-density gravity currents in porous media. Despite significant effects on vertical structure, the density distribution has almost no effect on overall horizontal propagation, for a given total mass. Good agreement with data from a laboratory study confirms the predictions of the model.

scholarly journals Similarity solutions for solute transport in fractal porous media using a time- and scale-dependent dispersivity

2005 ◽  
Vol 29 (9) ◽  
pp. 852-870 ◽  
Author(s):  
Ninghu Su ◽  
G.C. Sander ◽  
Fawang Liu ◽  
Vo Anh ◽  
D.A. Barry
Keyword(s):  
Porous Media ◽  
Solute Transport ◽  
Similarity Solutions
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