Analytical Solution for Four Component Gas Displacements with Volume Change on Mixing

Analytical solutions obtained by the method of charac teristics are reported for the material balance equations that describe one-dimensional flow of four-component mixtnres in which components change voinme as they transfer between phases. Volume change induces variations in local flow ve locity, but we show that the variations can be decoupled from composition variations. We report example solutione for dis placements of a methane(CH4)/butane(C4)/decane(Cie) mix ture by carbon dioxide (C02) or nitrogen (N2). They show that flow behavior is controlled by three key tie lines: the in jection tie line, the initial tie line, and a crossover tie line. We calculate the eigenvalues and eigenvectors for the eigen value problem in terms of ruled surfaces of tie lines and the tie-line envelopes. That representation shows when continu ous composition variations connect pairs of key tie lines and when self-sharpening shocks are required. We also prove for ne-component systems with volume change that if there is a self-sharpening wave between two tie lines, the tie line exten sions must intersect. Finally, we show that development of miscibility can be controlied by any of the three key tie lines.