This paper presents a detailed numerical analysis of two methods for phase-behavior computations associated with thermal compositional reservoir simulation. Specifically, we analyze and compare the standard K-values approach with an Equation of State (EoS) model. We study steam and steam-solvent injection into a one-dimensional reservoir saturated with heavy oil in order to identify the impact of using different methods to describe the phase behavior. We then present results for complex displacement processes in multidimensional reservoir models. The investigation shows the differences in the predictions between K-values- and EoS-based simulations can vary from small to quite significant depending on the compositional interactions between the injected and resident fluids in the modeled displacement process.