Standard EOS-based phase equilibrium modeling in reservoir simulators involves computationally intensive and time-consuming iterative calculations for stability analysis and flash calculations. Therefore, speeding up stability analysis and flash calculations and improving robustness of the calculations are of utmost importance in compositional reservoir simulation. Prior knowledge of the tie lines traversed by the solution of a gas injection problem translates into valuable information with significant implications for speed and robustness of reservoir simulators. The solution of actual gas injection processes follows a very complex route due to dispersion, pressure variations, and multi-dimensional flow. The multiple mixing-cell (MMC) method originally developed to calculate minimum miscibility pressure of a gas injection process, accounts for various levels of mixing of the injected gas and initial oil. This observation suggests that the MMC tie lines developed upon repeated contacts may represent a significant fraction of the actual simulation tie lines encountered. We investigate this idea and use three tie-line-based K-value simulation methods for application of MMC tie lines in reservoir simulation. In two of the tie-line-based K-value simulation methods, we examine tabulation and interpolation of MMC tie lines in a framework similar to the compositional space adaptive tabulation (CSAT). In the third method, we perform K-value simulations based on inverse distance interpolation of K values from MMC tie lines. We demonstrate that for the displacements examined the MMC tie lines are sufficiently close to the actual simulation tie lines and provide excellent coverage of the simulation compositional route. The MMC-based methods are then compared to the computational time using other methods of phase equilibrium calculations including a modified application of CSAT (an adaptive tie-line-based K-value simulation), a method utilizing only heuristic techniques, and the standard method in an IMPEC-type (implicit pressure, explicit concentration) reservoir simulator. The results show that tabulation and interpolation of MMC tie lines significantly improves phase equilibrium and computational time compared to the standard approach with acceptable accuracy. The results also show that computational performance of the MMC-based methods with only prior tie-line tables are very close to that of CSAT, which requires flash calculations during simulation. The K-value simulations using MMC-based tie-line interpolation methods improve the total computational time up to 51% in the cases studied with acceptable accuracy. The results suggest that MMC tie lines represent a significant fraction of the actual tie lines during simulation and can be used to significantly improve speed and robustness of phase equilibrium calculations in reservoir simulators.