One of the main applications of science of thermodynamics in the petroleum industry is for the prediction of phase behavior of petroleum fluids. In this chapter calculations related to vapor-liquid and solid-liquid equilibrium in petroleum fluids are presented. Their application to calculate gas-oil ratio, crude oil composition, and the amount of wax or asphaltene precipitation in oils under certain conditions of temperature, pressure, and composition is presented. Methods of calculation of wax formation temperature, cloud point temperature of crude oils, determination of onset of asphaltene, hydrate formation temperature, and methods of prevention of solid formation are also discussed. Finally application of characterization techniques, methods of prediction of transport properties, equations of state, and phase equilibrium calculations are demonstrated in modeling and evaluation of gas injection projects.