A two-parameter cubic Soave-Redlich-Kwong (SRK) equation of state with modified binary interaction coefficients has been used for phase equilibrium calculations of multicomponent systems under supercritical and near-supercritical conditions. Example calculations of the phase behavior of multicomponent reaction mixtures are presented and used to illustrate the increased accuracy of the SRK equation of state with the new binary interaction coefficients. The homotopy continuation method was adapted for the solution of the model equations by using temperature and pressure as continuation parameters. The effective models and algorithms thus created are used for phase state calculations, localization of the critical point of multicomponent mixtures, studies of phase properties near the critical point, and determination of parameter regions that are of practical importance for process performance under supercritical conditions. The problems of existence and uniqueness of a solution are studied. A new method for solving equations for the critical phase is suggested. Many examples of the calculation of phase diagrams of mixtures with a supercritical solvent are resented and the results compared with the reference data. Thermodynamic and macrokinetic models of the Fischer-Tropsch (FT) reaction are developed and used for the calculation of reactor performance.