Enhanced Oil Recovery (EOR) processes usually involve complex phase behavior between the injected fluid (e.g., steam, hydrocarbon, CO2, sour gas) and the in-situ rock-fluid system. Several fundamental questions remain regarding Equation-of-State (EOS) computations for mixtures that can form three, or more, phases at equilibrium. In addition, numerical and computational issues related to the proper coupling of the thermodynamic phase behavior with multi-component transport must be resolved to accurately and efficiently model the behavior of large-scale EOR processes. Previous work has shown that the adaptive tabulation of tiesimplexes in the course of a compositional simulation is a reliable alternative to the conventional EOS-based compositional simulation. In this paper, we present the numerical results of reservoir flow simulation with adaptive tie-simplex parameterization of the compositional space. We study the behavior of thermalcompositional reservoir displacement processes across a wide range of fluid mixtures, pressures, and temperatures. We show that our approach rigorously accounts for tie-simplex degeneration across phase boundaries. We also focus on the complex behavior of the tie-triangles and tie-lines associated with three-phase, steam injection problems in heterogeneous formations. Our studies indicate that the tie-simplex based simulation is a potential approach for fast EOS modeling of complex EOR processes.