Compositional simulation is necessary for modeling complex enhanced oil recovery (EOR) processes. For accurate simulation of compositional processes, we need to resolve the coupling of the nonlinear conservation laws, which describe multiphase How and transport, with the equilibrium phase behavior constraints. The complexity of the problem requires extensive computations and consumes significant time. This paper presents a new framework for the general compositional problem associated with mul-ticomponent multiphase flow in porous media. Here, adaptive construction and interpolation using the supporting tie lines are used to obtain the phase state and the phase compositions. For the parameterization of the full solution of a complex compositional problem, we need only a limited number of supporting tie lines in the compositional space. The parameterized tie lines are triangu-lated using Delaunay tessellation, and natural-neighbor interpola-tion is used inside the simplexes. Then, the computation of the phase behavior in the course of a simulation becomes an iteration- free, table look-up procedure. The treatment of nonlinearities associated with complex thermodynamic behavior of the fluid is based on the new set of unknowns-tie-line parameters that allow for efficient representation of the subcritical region. For the super-critical region, we use the standard compositional variable set based on the overall composition. The efficiency and accuracy of the method are demonstrated for several multidimensional compositional problems of practical interest. In terms of the computational cost of the thermodynamic calculations, the proposed method shows results comparable to those of state-of-the-art techniques. Moreover, the method shows better nonlinear convergence in the case of near-miscible gas- injection simulation.