This report outlines progress in the first quarter of the second year of the DOE project ''High Resolution Prediction of Gas Injection Process Performance for Heterogeneous Reservoirs''. The application of the analytical theory for gas injection processes, including the effects of volume change on mixing, has up to now been limited to fully self-sharpening systems, systems where all solution segments that connect the key tie lines present in the displacement are shock fronts. In the following report, we describe the extension of the analytical theory to include systems with rarefactions (continuous composition and saturation variations) between key tie lines. With the completion of this analysis, a completely general procedure has been developed for finding solutions for problems in which a multicomponent gas displaces a multicomponent oil.