The thermodynamic behavior of multicomponent multiphase systems is highly nonlinear, and the coupling to the flow equations is quite complex; as a result, equation-of-state (EOS) -based simulations can be computationally prohibitive. We describe a new Kvalue method that captures the compositional dependence of the phase behavior. Specifically, we propose a method for selecting compositions used in the tabulation of K-values and define an operator that interpolates the K-values as a function of pressure and composition. The method employs the minimal critical pressure (MCP) to detect supercritical compositions, which allows for effective modeling of multicontact miscible displacements. We compare our K-value approach with standard EOS compositional simulation for several isothermal problems, and we demonstrate the efficiency and accuracy of the proposed method.