Research Article
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Year 2023, , 77 - 83, 01.12.2023

Gleb Belov , N. M. Aristova

https://doi.org/10.5541/ijot.1317496

Abstract

Project Number

State Assignment No. 075-01056-22-00

References

  • D. S. Villars, “A method of successive approximations for computing combustion equilibria on a high speed digital computer,” J. Phys. Chem., vol. 63, pp. 521-525, Apr. 1959, doi: 10.1021/j150574a016.
  • W. R. Smith and R. W. Missen, Chemical Reaction Equilibrium Analysis: Theory and Algorithms, New York, NY, USA: Wiley, 1982.
  • W. D. White, S. M. Johnson and G. B. Dantzig, "Chemical equilibrium in complex mixtures," J. Chem. Phys., vol. 28, pp. 751-755, May 1958, doi: 10.1063/1.1744264.
  • R. J Duffin and C. Zener, "Geometric programming, chemical equilibrium, and the anti-entropy function," Proc. Natl. Acad. Sci. U.S.A., vol. 63, pp. 629-636, Apr. 1969, doi: 10.1073/pnas.63.3.629.
  • G. Eriksson, "Thermodynamic study of high temperature equilibria," Acta. Chem. Scand. vol. 25, pp. 2651-2658, Jul. 1971, doi: 10.3891/acta.chem.scand.25-2651.
  • B. A. Murtagh and M. A. Saunders, "Large-scale linearly constrained optimization," Math. Program., vol. 14, pp.41-72, Dec. 1978, doi: 10.1007/BF01588950.
  • H. Greiner, "Computing complex chemical equilibria by generalized linear programming," Math. Comput. Model., vol. 10, pp. 529-550, Jul. 1988, doi: 10.1016/0895-7177(88)90082-9.
  • M. H. A. Piro and S. Simunovic, "Global optimization algorithms to compute thermodynamic equilibria in large complex systems with performance considerations," Comput. Mater. Sci., vol. 118, pp. 87-96, Jun. 2016, doi: 10.1016/j.commatsci.2016.02.043.
  • C. Tsanas, E. H. Stenby and W. Yan, "Calculation of multiphase chemical equilibrium by the modified RAND method," Ind. Eng. Chem. Res., vol. 56, pp. 11983–11995, Oct. 2017, doi: 10.1021/acs.iecr.7b02714.
  • B. Sundman, N. Dupin and B. Hallstedt, "Algorithms useful for calculating multi-component equilibria, phase diagrams and other kinds of diagrams," Calphad, vol. 75, p. 102330, Dec. 2021, doi: 10.1016/j.calphad.2021.102330.
  • W. A. Roos and J. H. Zietsman, “Accelerating complex chemical equilibrium calculations - A review,” Calphad, vol. 77, p. 102380, Jun. 2022, doi: 10.1016/j.calphad.2021.102380.
  • Available: https://www.factsage.com/ (accessed Aug. 27, 2023).
  • “Thermo-Calc Software.” Available: https://thermocalc.com/ (accessed Aug. 27, 2023).
  • Y. Lwin, "Chemical equilibrium by Gibbs energy minimization on spreadsheets," Int. J. Eng. Educ. vol. 16, pp.335-339, Apr. 2000.
  • L. Eriksson, "CHEPP-a chemical equilibrium program package for Matlab," SAE trans. , vol. 113, pp. 730-741, 2004.
  • M. H. A. Piro, S. Simunovic, T. M. Besmann, B. J. Lewis and W. T. Thompson, "The thermochemistry library Thermochimica," Comput. Mater. Sci., vol. 67, pp.266-272, Feb. 2013, doi: 10.1016/j.commatsci.2012.09.011.
  • “ORNL-CEES / thermochimica.” Available: https://github.com/ORNL-CEES/thermochimica (accessed Aug. 27, 2023).
  • A. Wächter and L. T. Biegler, “On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming,” Math. Program., vol. 106, pp. 25–57, Mar. 2005. doi: 10.1007/s10107-004-0559-y.
  • I. Prigogine and R. Defay, Treatise on thermodynamics: Based on the methods of Gibbs and De Donder, London: Longmans, 1954.
  • J. Bezanson, A. Edelman, S. Karpinsky and V. B. Shah, “Julia: A fresh approach to numerical computing,” SIAM Rev., vol. 59, pp. 65-98, Jan. 2017, doi: 10.1137/141000671.
  • Available: https://coin-or.github.io/Ipopt/index.html (accessed Aug. 27, 2023).
  • I. Dunning, J. Huchette and M. Lubin, “JuMP: A modeling language for mathematical optimization,” SIAM Rev., vol. 59, pp. 295-320, Feb. 2017, doi: 10.1137/15M1020575.
  • B. Legat, O. Dowson, J. D. Garcia and M. Lubin, “MathOptInterface: a data structure for mathematical optimization problems,” INFORMS J. Comput., vol. 34, pp. 672-689, Feb. 2022, doi: 10.1287/ijoc.2021.1067.
  • J. Lofberg, "YALMIP : a toolbox for modeling and optimization in MATLAB," in Proc. 2004 IEEE Int. Con. on Robotics and Automation (IEEE Cat. No.04CH37508), Taipei, Taiwan, Sep. 2004, pp. 284-289, doi: 10.1109/CACSD.2004.1393890.
  • “CVX: Matlab Software for Disciplined Convex Programming.” Available: http://cvxr.com/cvx/ (accessed Aug. 27, 2023).
  • W. E. Hart, C. D. Laird, J.-P. Watson, D. L. Woodruff, G. A. Hackebeil, B. L. Nicholson and J. D. Siirola, Pyomo-optimization modeling in Python. Berlin: Springer, 2017.
  • “JuliaMath / Roots.jl .” Available: https://github.com/JuliaMath/Roots.jl (accessed Aug. 27, 2023).
  • L. V. Gurvich and I. V. Veyts, Thermodynamic Properties of Individual Substances, New York: Hemisphere Publishing Corp., 1989.
  • G. V. Belov, S. A. Dyachkov, P. R. Levashov, I. V. Lomonosov, D. V. Minakov, I. V. Morozov, M. A. Sineva and V. N. Smirnov, “The IVTANTHERMO — оnline database for thermodynamic properties of individual substances with web interface,” J. Phys.: Conf. Ser., vol. 946, p. 012120, 2018, doi: 10.1088/1742-6596/946/1/012120.
  • “NIST Chemistry WebBook, SRD 69.” Available: webbook.nist.gov (accessed Aug. 27, 2023).
  • B. J. McBride, “NASA Glenn coefficients for calculating thermodynamic properties of individual species,” NASA, Cleveland, Ohio, USA, Tech. Rep. NASA/TP-2002-211556, Sep. 2002. Available: https://ntrs.nasa.gov/api/citations/20020085330/downloads/20020085330.pdf (accessed Aug. 27, 2023).
  • G. Belov, “On linear programming approach for the calculation of chemical equilibrium in complex thermodynamic systems,” J. Math. Chem., vol. 47, pp. 446-456, Jan. 2010, doi: 10.1007/s10910-009-9580-y.
  • A. D. Pelton, "Thermodynamic modeling and phase equilibrium calculations in nuclear materials," Pure Appl. Chem., vol. 69, pp. 2245-2252, Nov. 1997, doi: 10.1351/pac199769112245.
  • “CEARUN.” Available: https://cearun.grc.nasa.gov/ (accessed Aug. 27, 2023).
  • G. P. Sutton and O. Biblartz, Rocket Propulsion Elements, New York, NY, USA: Wiley, 2017.
  • “gvbelov / Heterogeneous-Equilibrium .” Available: https://github.com/gvbelov/Heterogeneous-Equilibrium (accessed Aug. 27, 2023).

Calculation of Complex Chemical Equilibrium Using Optimization Package Ipopt

Year 2023, , 77 - 83, 01.12.2023

Gleb Belov , N. M. Aristova

https://doi.org/10.5541/ijot.1317496

Abstract

An approach to the calculation of complex chemical equilibrium using the open-source optimization package Ipopt and the open-source package JuMP is proposed. The code of two procedures written in the open-source Julia programming language for calculating the equilibrium composition and properties of multicomponent heterogeneous thermodynamic systems is presented. The results of the test calculations showed a good performance of the code and a relatively high speed of calculations. Due to the compactness and simplicity of the code, it can be easily integrated into other applications, or used in combination with more complex models.

Keywords

chemical equilibrium thermodynamics Julia JuMP

Supporting Institution

Ministry of Science and Higher Education of the Russian Federation

Project Number

State Assignment No. 075-01056-22-00

Thanks

The authors are grateful to Dr. Igor Morozov for his help in preparing the manuscript

References

  • D. S. Villars, “A method of successive approximations for computing combustion equilibria on a high speed digital computer,” J. Phys. Chem., vol. 63, pp. 521-525, Apr. 1959, doi: 10.1021/j150574a016.
  • W. R. Smith and R. W. Missen, Chemical Reaction Equilibrium Analysis: Theory and Algorithms, New York, NY, USA: Wiley, 1982.
  • W. D. White, S. M. Johnson and G. B. Dantzig, "Chemical equilibrium in complex mixtures," J. Chem. Phys., vol. 28, pp. 751-755, May 1958, doi: 10.1063/1.1744264.
  • R. J Duffin and C. Zener, "Geometric programming, chemical equilibrium, and the anti-entropy function," Proc. Natl. Acad. Sci. U.S.A., vol. 63, pp. 629-636, Apr. 1969, doi: 10.1073/pnas.63.3.629.
  • G. Eriksson, "Thermodynamic study of high temperature equilibria," Acta. Chem. Scand. vol. 25, pp. 2651-2658, Jul. 1971, doi: 10.3891/acta.chem.scand.25-2651.
  • B. A. Murtagh and M. A. Saunders, "Large-scale linearly constrained optimization," Math. Program., vol. 14, pp.41-72, Dec. 1978, doi: 10.1007/BF01588950.
  • H. Greiner, "Computing complex chemical equilibria by generalized linear programming," Math. Comput. Model., vol. 10, pp. 529-550, Jul. 1988, doi: 10.1016/0895-7177(88)90082-9.
  • M. H. A. Piro and S. Simunovic, "Global optimization algorithms to compute thermodynamic equilibria in large complex systems with performance considerations," Comput. Mater. Sci., vol. 118, pp. 87-96, Jun. 2016, doi: 10.1016/j.commatsci.2016.02.043.
  • C. Tsanas, E. H. Stenby and W. Yan, "Calculation of multiphase chemical equilibrium by the modified RAND method," Ind. Eng. Chem. Res., vol. 56, pp. 11983–11995, Oct. 2017, doi: 10.1021/acs.iecr.7b02714.
  • B. Sundman, N. Dupin and B. Hallstedt, "Algorithms useful for calculating multi-component equilibria, phase diagrams and other kinds of diagrams," Calphad, vol. 75, p. 102330, Dec. 2021, doi: 10.1016/j.calphad.2021.102330.
  • W. A. Roos and J. H. Zietsman, “Accelerating complex chemical equilibrium calculations - A review,” Calphad, vol. 77, p. 102380, Jun. 2022, doi: 10.1016/j.calphad.2021.102380.
  • Available: https://www.factsage.com/ (accessed Aug. 27, 2023).
  • “Thermo-Calc Software.” Available: https://thermocalc.com/ (accessed Aug. 27, 2023).
  • Y. Lwin, "Chemical equilibrium by Gibbs energy minimization on spreadsheets," Int. J. Eng. Educ. vol. 16, pp.335-339, Apr. 2000.
  • L. Eriksson, "CHEPP-a chemical equilibrium program package for Matlab," SAE trans. , vol. 113, pp. 730-741, 2004.
  • M. H. A. Piro, S. Simunovic, T. M. Besmann, B. J. Lewis and W. T. Thompson, "The thermochemistry library Thermochimica," Comput. Mater. Sci., vol. 67, pp.266-272, Feb. 2013, doi: 10.1016/j.commatsci.2012.09.011.
  • “ORNL-CEES / thermochimica.” Available: https://github.com/ORNL-CEES/thermochimica (accessed Aug. 27, 2023).
  • A. Wächter and L. T. Biegler, “On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming,” Math. Program., vol. 106, pp. 25–57, Mar. 2005. doi: 10.1007/s10107-004-0559-y.
  • I. Prigogine and R. Defay, Treatise on thermodynamics: Based on the methods of Gibbs and De Donder, London: Longmans, 1954.
  • J. Bezanson, A. Edelman, S. Karpinsky and V. B. Shah, “Julia: A fresh approach to numerical computing,” SIAM Rev., vol. 59, pp. 65-98, Jan. 2017, doi: 10.1137/141000671.
  • Available: https://coin-or.github.io/Ipopt/index.html (accessed Aug. 27, 2023).
  • I. Dunning, J. Huchette and M. Lubin, “JuMP: A modeling language for mathematical optimization,” SIAM Rev., vol. 59, pp. 295-320, Feb. 2017, doi: 10.1137/15M1020575.
  • B. Legat, O. Dowson, J. D. Garcia and M. Lubin, “MathOptInterface: a data structure for mathematical optimization problems,” INFORMS J. Comput., vol. 34, pp. 672-689, Feb. 2022, doi: 10.1287/ijoc.2021.1067.
  • J. Lofberg, "YALMIP : a toolbox for modeling and optimization in MATLAB," in Proc. 2004 IEEE Int. Con. on Robotics and Automation (IEEE Cat. No.04CH37508), Taipei, Taiwan, Sep. 2004, pp. 284-289, doi: 10.1109/CACSD.2004.1393890.
  • “CVX: Matlab Software for Disciplined Convex Programming.” Available: http://cvxr.com/cvx/ (accessed Aug. 27, 2023).
  • W. E. Hart, C. D. Laird, J.-P. Watson, D. L. Woodruff, G. A. Hackebeil, B. L. Nicholson and J. D. Siirola, Pyomo-optimization modeling in Python. Berlin: Springer, 2017.
  • “JuliaMath / Roots.jl .” Available: https://github.com/JuliaMath/Roots.jl (accessed Aug. 27, 2023).
  • L. V. Gurvich and I. V. Veyts, Thermodynamic Properties of Individual Substances, New York: Hemisphere Publishing Corp., 1989.
  • G. V. Belov, S. A. Dyachkov, P. R. Levashov, I. V. Lomonosov, D. V. Minakov, I. V. Morozov, M. A. Sineva and V. N. Smirnov, “The IVTANTHERMO — оnline database for thermodynamic properties of individual substances with web interface,” J. Phys.: Conf. Ser., vol. 946, p. 012120, 2018, doi: 10.1088/1742-6596/946/1/012120.
  • “NIST Chemistry WebBook, SRD 69.” Available: webbook.nist.gov (accessed Aug. 27, 2023).
  • B. J. McBride, “NASA Glenn coefficients for calculating thermodynamic properties of individual species,” NASA, Cleveland, Ohio, USA, Tech. Rep. NASA/TP-2002-211556, Sep. 2002. Available: https://ntrs.nasa.gov/api/citations/20020085330/downloads/20020085330.pdf (accessed Aug. 27, 2023).
  • G. Belov, “On linear programming approach for the calculation of chemical equilibrium in complex thermodynamic systems,” J. Math. Chem., vol. 47, pp. 446-456, Jan. 2010, doi: 10.1007/s10910-009-9580-y.
  • A. D. Pelton, "Thermodynamic modeling and phase equilibrium calculations in nuclear materials," Pure Appl. Chem., vol. 69, pp. 2245-2252, Nov. 1997, doi: 10.1351/pac199769112245.
  • “CEARUN.” Available: https://cearun.grc.nasa.gov/ (accessed Aug. 27, 2023).
  • G. P. Sutton and O. Biblartz, Rocket Propulsion Elements, New York, NY, USA: Wiley, 2017.
  • “gvbelov / Heterogeneous-Equilibrium .” Available: https://github.com/gvbelov/Heterogeneous-Equilibrium (accessed Aug. 27, 2023).
There are 36 citations in total.

Details

Primary Language English
Subjects Thermodynamics and Statistical Physics
Journal Section Research Articles
Authors

Gleb Belov 0000-0001-7949-9403

N. M. Aristova This is me 0000-0001-8588-9280

Project Number State Assignment No. 075-01056-22-00
Early Pub Date October 23, 2023
Publication Date December 1, 2023
Published in Issue Year 2023

Cite

APA Belov, G., & Aristova, N. M. (2023). Calculation of Complex Chemical Equilibrium Using Optimization Package Ipopt. International Journal of Thermodynamics, 26(4), 77-83. https://doi.org/10.5541/ijot.1317496
AMA Belov G, Aristova NM. Calculation of Complex Chemical Equilibrium Using Optimization Package Ipopt. International Journal of Thermodynamics. December 2023;26(4):77-83. doi:10.5541/ijot.1317496
Chicago Belov, Gleb, and N. M. Aristova. “Calculation of Complex Chemical Equilibrium Using Optimization Package Ipopt”. International Journal of Thermodynamics 26, no. 4 (December 2023): 77-83. https://doi.org/10.5541/ijot.1317496.
EndNote Belov G, Aristova NM (December 1, 2023) Calculation of Complex Chemical Equilibrium Using Optimization Package Ipopt. International Journal of Thermodynamics 26 4 77–83.
IEEE G. Belov and N. M. Aristova, “Calculation of Complex Chemical Equilibrium Using Optimization Package Ipopt”, International Journal of Thermodynamics, vol. 26, no. 4, pp. 77–83, 2023, doi: 10.5541/ijot.1317496.
ISNAD Belov, Gleb - Aristova, N. M. “Calculation of Complex Chemical Equilibrium Using Optimization Package Ipopt”. International Journal of Thermodynamics 26/4 (December 2023), 77-83. https://doi.org/10.5541/ijot.1317496.
JAMA Belov G, Aristova NM. Calculation of Complex Chemical Equilibrium Using Optimization Package Ipopt. International Journal of Thermodynamics. 2023;26:77–83.
MLA Belov, Gleb and N. M. Aristova. “Calculation of Complex Chemical Equilibrium Using Optimization Package Ipopt”. International Journal of Thermodynamics, vol. 26, no. 4, 2023, pp. 77-83, doi:10.5541/ijot.1317496.
Vancouver Belov G, Aristova NM. Calculation of Complex Chemical Equilibrium Using Optimization Package Ipopt. International Journal of Thermodynamics. 2023;26(4):77-83.