Extended K-value Method for Multi-contact Miscible Displacements

Accurate predictions of gas-injection processes usually require a compositional formulation based on an Equation of State (EoS). Because the thermodynamic behavior of multi-component multiphase systems is highly nonlinear and coupling to the flow equations is quite complex, EoS-based simulations can become computationally prohibitive. For immiscible displacements an efficient approximation of the general compositional problem can be used if the phase-equilibrium ratios (K-values) are assumed to be weak functions of composition; however, this assumption is questionable for near-miscible displacements. The standard K-value approach suffers from significant difficulties, both in terms of robustness and accuracy, in the critical region. Here, we describe an extended K-values method that takes advantage of the solution-path invariance in the compositional space with respect to the hydrodynamic properties. Specifically, we propose an additional degree-of-freedom, which captures the composition dependence of the phase behavior, for use in the tabulation and interpolation of the K-values. An important aspect of the method is the use of the so-called Minimal Critical Pressure criteria (MCP), which indicates when a given composition becomes super-critical. We compare results obtained with EoS- and K-values based simulations for several (isothermal) compositional problems, and we demonstrate the efficiency and accuracy of the proposed method.