Reduced variables method for four-phase equilibrium calculations of hydrocarbon-water-CO2 mixtures at a low temperature

Motonao Imai*, Huanquan Pan, Michael Connolly, Hamdi Tchelepi, Masanori Kurihara

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


Carbon dioxide (CO2) flooding has been widely applied to enhance oil recovery. In low temperature reservoirs, CO2 injection may result in the formation of three hydrocarbon phases at thermodynamic equilibrium. In addition, an aqueous phase is always present in the reservoir. The aqueous phase can coexist with three hydrocarbon phases to form a four-phase equilibrium system. To evaluate CO2 utilization and storage in these low temperature petroleum reservoirs, a robust and efficient four-phase equilibrium calculation framework involving water is necessary for a compositional reservoir simulator. This is challenging not only because the number of variables increases but also because stability analysis becomes much complicated as the number of phases increases. In this research a novel four-phase equilibrium calculation framework is proposed for compositional reservoir simulation. A reduced variables method is used to solve four-phase flash problems efficiently and robustly. Multiphase flash calculations using reduced variables (RV) can converge to the equilibrium solution faster than formulations using conventional variables (Petitfrere and Nichita, 2015). Secondly, RV does not suffer from numerical problems in the Newton iterations when trace components are present in the aqueous phase. In addition to the implementation of the RV formulation, a systematic procedure consisting of stability analysis and flash calculations is proposed without any prior knowledge of initial K-values. Sets of different initial K-values are appropriately tested in each stability analysis. We performed comprehensive testing using characterized fluids found in the literature in order to validate the robustness of the proposed procedure. The four-phase regions in pressure-composition (Px) space could be accurately identified using our procedure. On the other hand, in some instances mixtures were incorrectly evaluated as three-phase when using existing approaches such as Li and Firoozabadi (2012). Our approach proposed in this paper is a promising four-phase equilibrium calculation framework for compositional reservoir simulation. The procedure achieved excellent robustness and efficiency with minimal modification to the conventional two or three-phase equilibrium calculation framework.

Original languageEnglish
Pages (from-to)151-163
Number of pages13
JournalFluid Phase Equilibria
Publication statusPublished - 2019 Oct 1


  • Compositional simulation
  • Multiphase flash
  • Phase behavior
  • Reduced variables method
  • Stability analysis
  • Trust region method

ASJC Scopus subject areas

  • Chemical Engineering(all)
  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry


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