We generalize the compositional space parameterization (CSP) approach, which was originally developed for immiscible two-phase multicomponent problems, to multicontact miscible dis-placements. The tie-line based parameterization method improves both the accuracy of the phase-behavior representation as well as the efficiency of equation of state (EOS) computations in compo-sitional flow simulation. For immiscible compositional simulation, compositional space adaptive tabulation (CSAT) can be used to avoid most of the redundant EOS calculations. Because the super-critical region cannot be parameterized using tie-lines, the original CSAT approach is not effective for modeling multicontact miscible gas injection processes. To deal with supercritical compositions, a supercritical state criteria (SSC) algorithm based on adaptive tabulation of the minimal critical pressure (MCP) tie-lines is pro-posed. For general-purpose simulation of miscible and immiscible compositional displacement processes, we combined the adaptive CSAT strategy in the region of tie-line extensions and the adaptive SSC scheme; we refer to the overall framework as CSAT Results of several challenging tests of practical interest indicate that the general CSAT strategy is quite robust and that it leads to an order of magnitude gain in computational efficiency. We also describe the extension of the CSP framework for mixtures that form more than two phases.