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Modeling two-phase flow of immiscible fluids in porous media: Buckley-Leverett theory with explicit coupling terms

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FIG. 1. Construction of the saturation fronts. (a) and (d) Plots of the flux function F i , the concave hull ˆ F i , and its derivative ˆ F i′ (see the Appendix)
FIG. 2. Illustrations of the two configurations considered: (a) configuration 1, drainage, and (b) configura- configura-tion 2, imbibiconfigura-tion.
FIG. 3. Velocity field in a cross section of a capillary tube illustrating the annular two-phase viscous flow.
FIG. 5. Comparison of steady-state profiles with (solid lines) and without (dashed lines) cross terms to experimental data from [3,17] with (a) water saturation and (b) the dimensionless pressure gradient as a function of N1
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