Summary Analytical solutions for the initial stage of 1D countercurrent flow of water and oil in porous media are presented. Expressions are obtained for the time dependence of the water saturation profile and the oil recovered during spontaneous countercurrent imbibition in rod-like, cylindrical, and spherical cores, for which water is the wetting liquid. Some of the analytical solutions are found to be in good agreement with existing numerical solutions and available experimental data for oil recovery from cores with strong water wettability.
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Kashchiev et al. (2003) studied this question.
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