Recovery of hydrocarbons from porous media is an ongoing concern. Advanced techniques augment conventional recovery methods by injecting fluids that favorably interact with the oil. These fluids interact with the oil by energy transfer, in the case of steam injection, or by mass transfer, as in a miscible gas flood. Often both thermal and compositional considerations are important. An understanding of these injection methods requires knowledge of how temperature variations, phase equilibrium and multiphase flow in porous media interact The material balance for each component and energy balance are cast as a system of non-strictly hyperbolic partial differential equations. This system of equations is solved using the method of characteristics. The model takes into account the phase behavior by using the Peng-Robinson equation of state to partition the individual components into different phases. Temperature effects are accounted for by the energy balance. Flow effects are modeled by using fractional flow curves and a Stone's three phase relative permeability model. Three major problems are studied in this dissertation. Each new problem adds an level of interaction to the solution before. The first problem eliminates the phase behavior aspect of the problem by studying the flow of a single component as it undergoes an isothermal phase change. The second problem couples the effects of temperature and flow behavior by including a second component that is immiscible with the original component. Finally, phase behavior is added by using a set of three partially miscible components that partition into two or three separate phases. Solutions for these equations are formed by spreading waves that propagate in space and time with a constant velocity. The spreading wave regions are connected by jump discontinuities or zones of constant state. The solutions are presented for the three example systems in the form of saturation or composition profiles and solution paths in the composition space. An analysis of the effect of varying some of the important parameters are also presented for each displacement system.