An advanced general dominant eigenvalue method of accelerating successive substitution during flash calculation for compositional reservoir model
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Abstract
The efficiency and accuracy of phase equilibrium calculations are essential in compositional reservoir models. Usually, a significant part of the computational effort in compositional reservoir simulations is spent on phase equilibrium calculations. The nonlinear nature of phase equilibrium calculations requires an iterative solution procedure. Although the successive substitution method (SSM) is robust and simple to implement, it suffers from slow convergence, especially near the critical point of the mixture. The general dominant eigenvalue method (GDEM) has been widely used to accelerate SSM, but its stability and efficiency deteriorate as the temperature and pressure approach the critical point. This paper proposes a modified form of GDEM to improve its performance in the near-critical region. The modifications have two aspects. First, the liquid phase fraction in the mixture is added as a variable when performing GDEM acceleration, improving both stability and efficiency. The second modification is a post-calibration step imposed to replace the conventional criterion, which is applied before triggering GDEM. With the help of the post-calibration step, the stability of the modified GDEM is ensured, and more importantly, the calculation efficiency can be improved. Numerical tests of three hydrocarbon mixtures, including different numbers of components, show that the stability of the modified GDEM is almost the same as SSM and that its calculation efficiency is much higher than SSM and the conventional GDEM.
Cited as: Wang, X., Wei, D., Wang, X., Zhao, X., Li, J., Noetinger, B. An advanced general dominant eigenvalue method of accelerating successive substitution during flash calculation for compositional reservoir model. Advances in Geo-Energy Research, 2022, 6(3): 241-251. https://doi.org/10.46690/ager.2022.03.07
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Afanasyev, A., Andreeva, A., Chernova, A. Numerical optimisation of CO2 flooding using a hierarchy of reservoir models. Advances in Geosciences, 2021, 56: 19-31.
Belkadi, A., Yan, W., Moggia, E., et al. Speeding up compositional reservoir simulation through an efficient implementation of phase equilibrium calculation. Paper SPE 163598 Presented at SPE Reservoir Simulation Symposium, The Woodlands, Texas, 18-20 February, 2013.
Coats, K. H. An equation of state compositional model. Society of Petroleum Engineers Journal, 1980, 20(5): 363-376.
Coats, K. H. A note on IMPES and some IMPES-based simulation models. SPE Journal, 2000, 5(3): 245-251.
Gorucu, S. E., Johns, R. T. Comparison of reduced and conventional two-phase flash calculations. SPE Journal, 2015, 20(2): 294-305.
Crowe, C., Nishio, M. Convergence promotion in the simulation of chemical processes—the general dominant eigenvalue method. AIChE Journal, 1975, 21(3): 528-533.
Gupta, A. K., Bishnoi, P., Kalogerakis, N. An accelerated successive substitution method for single stage flash calculations. The Canadian Journal of Chemical Engineering, 1988, 66(2): 291-296.
Haugen, K. B., Beckner, B. L. Highly optimized phase equilibrium calculations. Paper SPE 163583 presented at the SPE Reservoir Simulation Symposium, The Woodlands, Texas, 18–20 February, 2013.
Hearn, C. L., Whitson, C. H. Evaluating miscible and immiscible gas injection in the safah field, Oman. Paper SPE 29115 presented at the SPE Reservoir Simulation Symposium, San Antonio, Texas, 12–15 February, 1995.
Hendriks, E. M., Van Bergen, A. Application of a reduction method to phase equilibria calculations. Fluid Phase Equilibria, 1992, 74: 17-34.
Hu, X., Wang, M., Shi, A., et al. A modified sequential method for solving the full composition model innumerical reservoir simulation. IOP Conference Series: Materials Science and Engineering, 2020, 782(4): 042054.
Kenyon, D. Third SPE comparative solution project: Gas cycling of retrograde condensate reservoirs. Journal of Petroleum Technology, 1987, 39(8): 981-997.
Li, H. Multiphase Equilibria of Complex Reservoir Fluids: An Equation of State Modeling Approach. Berlin, Germany, Springer Nature, 2021.
Li, Y., Johns, R. T. Rapid flash calculations for compositional simulation. SPE Reservoir Evaluation and Engineering, 2006, 9(5): 521-529.
Li, Z., Firoozabadi, A. General strategy for stability testing and phase-split calculation in two and three phases. SPE Journal, 2012, 17(4): 1096-1107.
Lian, P., Ji, B., Duan, T., et al. Parallel numerical simulation for a super large-scale compositional reservoir. Advances in Geo-Energy Research, 2019, 3(4): 381-386.
Mehra, R., Heidemann, R., Aziz, K. An accelerated successive substitution algorithm. The Canadian Journal of Chemical Engineering, 1983, 61(4): 590-596.
Michelsen, M. Phase equilibrium calculations. What is easy and what is difficult? Computers and Chemical Engineering, 1993, 17(5-6): 431-439.
Michelsen, M. L. The isothermal flash problem. Part I. Stability. Fluid Phase Equilibria, 1982a, 9(1): 1-19.
Michelsen, M. L. The isothermal flash problem. Part II. Phase-split calculation. Fluid Phase Equilibria, 1982b, 9(1): 21-40.
Michelsen, M. L. Simplified flash calculations for cubic equations of state. Industrial and Engineering Chemistry Process Design and Development, 1986, 25(1): 184-188.
Michelsen, M. L., Yan, W., Stenby, E. H. A comparative study of reduced-variables-based flash and conventional flash. SPE Journal, 2013, 18(5): 952-959.
Moncorgé, A., Møyner, O., Tchelepi, H. A., et al. Consistent upwinding for sequential fully implicit multiscale compositional simulation. Computational Geosciences, 2020, 24(2): 533-550.
Moortgat, J. Adaptive implicit finite element methods for multicomponent compressible flow in heterogeneous and fractured porous media. Water Resources Research, 2017, 53(1): 73-92.
Mostafavi, S. E., Khodapanah, E., Tabatabaei-Nezhad, S. A. Development of a fast EoS based compositional model for three-phase core flooding. SN Applied Sciences, 2020, 2(1): 44.
Nichita, D. V., Graciaa, A. A new reduction method for phase equilibrium calculations. Fluid Phase Equilibria, 2011, 302(1-2): 226-233.
Nichita, D. V., Leibovici, C. F. A rapid and robust method for solving the Rachford–Rice equation using convex transformations. Fluid Phase Equilibria, 2013, 353: 38-49.
Orbach, O., Crowe, C. Convergence promotion in the simulation of chemical processes with recycle-the dominant eigenvalue method. The Canadian Journal of Chemical Engineering, 1971, 49(4): 509-513.
Pan, H., Firoozabadi, A. Fast and Robust Algorithm for Compositional Modeling: Part II–Two-Phase Flash Computations. SPE Journal, 2003, 8(4): 380-391 Peng, D. -Y., Robinson, D. B. A new two-constant equation of state. Industrial and Engineering Chemistry Fundamentals, 1976, 15(1): 59-64.
Petitfrere, M., Nichita, D. V. A comparison of conventional and reduction approaches for phase equilibrium calculations. Fluid Phase Equilibria, 2015, 386: 30-46.
Rachford, H. H., Rice, J. Procedure for use of electronic digital computers in calculating flash vaporization hydrocarbon equilibrium. Journal of Petroleum Technology, 1952, 4(10): 19-13.
Soave, G. Equilibrium constants from a modified Redlich-Kwong equation of state. Chemical Engineering Science, 1972, 27(6): 1197-1203.
Soeder, D. J. Greenhouse gas sources and mitigation strategies from a geosciences perspective. Advances in Geo-Energy Research, 2021, 5(3): 274-285.
Soliman, M. A modified general dominant eigenvalue method for convergence acceleration of cyclic systems. The Canadian Journal of Chemical Engineering, 1981, 59(3): 395-397.
Soliman, M. A. On the convergence acceleration of iterative processes. Computers and Chemical Engineering, 1985, 9(1): 97-98.
Wang, S., Yuan, D., Winterfeld, P. H., et al. Understanding the multiphysical processes in CO2-EOR operations: A numerical study using a general simulation framework. SPE Journal, 2021, 26(2): 918-939.
Wegstein, J. H. Accelerating convergence of iterative processes. Communications of the ACM, 1958, 1(6): 9-13.
Xu, T., Tian, H., Zhu, H., et al. China actively promotes CO2 capture, utilization and storage research to achieve carbon peak and carbon neutrality. Advances in Geo-Energy Research, 2022, 6(1): 1-3
Zhao, H., Jing, H., Fang, Z., et al. Flash calculation using successive substitution accelerated by the general dominant eigenvalue method in reduced-variable space: Comparison and new insights. SPE Journal, 2020, 25(6): 3332-3348.
Zhu, D., Eghbali, S., Shekhar, C., et al. A unified algorithm for phase-stability/split calculation for multiphase isobaric-isothermal flash. SPE Journal, 2018, 23(2): 498-521.
DOI: https://doi.org/10.46690/ager.2022.03.07
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