(169a) Efficient and Robust Multiphase Equilibrium Calculations for Compositional Simulation of CO2 Injection in Low Temperature Reservoirs

CO₂ injection into an oil reservoir at low temperature (less than 120⁰F) can form three hydrocarbon phases: a vapor phase, an oil-rich liquid phase and a CO₂-rich liquid phase. CO₂ has been used for miscible enhanced oil recovery in low temperature reservoirs throughout Texas and New Mexico for many years. Simulation of the CO₂injection process with three hydrocarbon phases is particularly challenging, and no such simulator exists for practical field simulation.

Efficient and robust multiphase equilibrium calculations are essential to enable compositional simulation of CO₂ injection at field scale. Two challenges persist in the development of multiphase equilibrium algorithms: (i) Robust three-phase split calculations, particularly in the vicinity of the critical region; (ii) Estimation of equilibrium ratios to initiate phase stability tests. Significant improvement of multiphase equilibrium calculations is necessary to meet the requirements of compositional simulation.

Stanford ADGPRS (Automatic Differentiation based General Purpose Research Simulator) provides a flexible framework for the development of multiphase compositional simulation capability. In this research we have developed efficient and robust multiphase equilibrium calculations to enable simulation of three-hydrocarbon-phase flow in ADGPRS. We employ the globally convergent trust-region optimization method for phase stability testing, as well as two- and three-phase split calculations. This optimization algorithm guarantees convergence for stability tests and phase split calculations. For optimal efficiency, we have implemented the sequential SSI (successive substitution iteration), Newton and trust-region algorithms.

Detection of phase instability requires good initial estimates of phase equilibrium ratios. Standard approaches require up to N_C+4 sampling compositions (N_C: number of components) for both two- and three-phase stability tests. This is inefficient and at times erroneous. We have developed a strategy which requires only three estimates for two-phase stability testing and six estimates for three-phase stability testing.

We have intensively tested our algorithms with 10 characterized fluids, primarily from reservoirs in Texas and New Mexico. The entire phase envelope was constructed by performing equilibrium computations over a wide range of pressures and injected CO₂ mole fractions. The pressure interval is less than 0.02 bar and the CO₂ mole fraction is varied in increments of less than 1%. The results show that our protocol for equilibrium computations correctly locates all three-phase regions, and is more robust and efficient than existing approaches.