Prediction of critical points: A new methodology using global optimization

AIChE Journal

Volumn 50, Issue 6, 2004, Pages 1300-1314

  Henderson, Nélio ^a   Freitas, Léa ^a   Platt, Gustavo M ^a  

^a STATE UNIVERSITY OF RIO DE JANEIRO   (Brazil)

Author keywords

Critical point; Gibbs tangent plane criterion; Global optimization; Objective function; Thermodynamic system

Indexed keywords

GIBBS FREE ENERGY; ROBUSTNESS (CONTROL SYSTEMS); STOCHASTIC CONTROL SYSTEMS;

CRITICAL POINTS; GIBBS TANGENT PLANE;

PHASE TRANSITIONS;

HEPTANE; HYDROGEN SULFIDE; METHANE;

PREDICTION;

ARTICLE; MATHEMATICAL MODEL; MISCIBILITY; PHASE TRANSITION; PRESSURE; STOCHASTIC MODEL; SUPERCRITICAL FLUID EXTRACTION; TEMPERATURE; THERMODYNAMICS;

EID: 2542543481     PISSN: 00011541     EISSN: None     Source Type: Journal    
DOI: 10.1002/aic.10119     Document Type: Article

References (41)

1. Alvarado, G. E., M. Castier, and S. I. Sandler, "Predictions of Critical Behavior Using the Wong-Sandler Mixing Rule," J. Supercrit. Fluids, 13, 49 (1998).
2. Baker, L. E., A. C. Pierce, and K. D. Luks, "Gibbs Energy Analysis of Phase Equilibria," Soc. Pet. Eng. J., 22, 731 (1982).
3. Baker, L. E., and K. D. Luks, "Critical Point and Saturation Pressure Calculations for Multipoint Systems," Soc. Pet. Eng. J., 20, 15 (1980).
4. Billingsley, D. S., and S. Lam, "Critical Point Calculation With Non-zero Interaction Parameters," AIChE J., 32, 1393 (1986).
5. Callen, H. B., Thermodynamics and an Introduction to Thermostatistics, Wiley, New York (1985).
6. Cardoso, M. F., R. Salcedo, S. Feyo de Azevedo, and D. Barbosa, "A Simulated Annealing Approach to the Solution of MINLP Problems," Comput. Chem. Eng., 21, 1349 (1997).
7. Cardoso, M. F., R. Salcedo, S. Feyo de Azevedo, and D. Barbosa, "Optimization of Reactive Distillation Processes with Simulated Annealing," Chem. Eng. Sci., 55, 5059 (2000).
8. Corana, A., M. Marchesi, C. Martini, and S. Ridella, "Minimizing Multimodal Functions of Continuous Variables with the 'Simulated Annealing' Algorithm," ACM Trans. Math. Software, 13, 262 (1987).
9. Dolan, W. B., P. T. Cummings, and M. D. Le Van, "Process Optimization via Simulated Annealing: Application to Network Design," AIChE J., 35, 725 (1989).
10. Eaton, B. E. On the Calculation of Critical Points by the Method of Heidemann and Khalil, NBS Technical Note 1313, National Bureau of Standards, Boulder, CO (1988).
11. Eglese, R. W., "Simulated Annealing: A Tool for Operational Research," Eur. J. Oper. Res., 46, 271 (1990).
12. Ekiner, O., and G. Thodos, "Critical Temperatures and Pressures of the Ethane-n-Pentane-n-Heptane System," J. Chem. Eng. Data, 11, 457 (1966).
13. Gibbs, J. W., "On the Equilibrium of Heterogeneous Substances" (October 1876-May 1877), Collected Works, Vol. 1, Yale Univ. Press, New Haven, CT, p. 55 (1928).
14. Gomes, J., Henderson, N., and Rocha, M., "Modelling the Vapor-Liquid Equilibrium of Polymer Solutions Using a Cubic Equation of State," Macromol. Theory Simul., 10, 816 (2001).
15. Heidemann, R. A., and A. M. Khalil, "The Calculation of Critical Points," AIChE J., 26, 769 (1980).
16. Henderson, N., J. R. de Oliveira, Jr., H. P. Amaral Souto, and R. Pitanga Marques, "Modeling and Analysis of the Isothermal Flash Problem and Its Calculation with the Simulated Annealing Algorithm," Ind. Eng. Chem. Res., 40, 6028 (2001).
17. Hycks, C. P., and C. L. Young, "The Gas-Liquid Critical Properties of Binary Mixtures," Chem. Rev., 75, 119 (1975).
18. Hycks, C. P., and C. L. Young, "Theoretical Predictions of Phase Behaviour at High Temperatures and Pressures for Non-Polar Mixtures: 1. Computer Solution Techniques and Stability Tests," J. Chem. Soc. Faraday II, 73, 597 (1977).
19. Huron, M. J., and J. Vidal, "New Mixing Rules in Simple Equations of State for Representing Vapor-Liquid Equilibria of Strongly Non-ideal Mixtures," Fluid Phase Equilib., 3, 255 (1979).
20. Kohse, B. F., "The Calculation of Tricritical Points," MS Thesis, The University of Calgary, Canada (1989).
21. Kolář, P., and K. Kojima, "Prediction of Critical Points in Multicomponent Systems Using the PSRK Group Contribution Equation of State," Fluid Phase Equilib., 118, 175 (1996).
22. Luenberger D. G., Linear and Nonlinear Programming, Addison-Wesley, Reading, MA (1984).
23. Michelsen, M. L., "Calculation of Phase Envelopes and Critical Points for Multicomponent Mixtures," Fluid Phase Equilib., 4, 1 (1980).
24. Michelsen, M. L., "The Isothermal Flash Problem. Part I. Stability," Fluid Phase Equilib., 9, 1 (1982).
25. Michelsen, M. L., "Calculation of Critical Points and Phase Boundaries in the Critical Region," Fluid Phase Equilib., 16, 57 (1984).
26. Michelsen, M. L., "A Modified Huron-Vidal Mixing Rule for Cubic Equations of State," Fluid Phase Equilib., 60, 213 (1990).
27. Michelsen, M. L., and R. A. Heidemann, "Calculation of Critical Points from Cubic Two-Constant Equations of State," AIChE J., 27, 521 (1981).
28. Nagarajan, N. R., A. S. Cullik, and A. O. Griewank, "New Strategy for Phase Equilibrium and Critical Point Calculation by Thermodynamic Energy Analysis. Part I - Stability Analysis and Flash," Fluid Phase Equilib., 62, 191 (1991).
29. Pan, H., and A. Firoozabadi, "Complex Multiphase Equilibria Calculations by Direct Minimization of Gibbs Free Energy by Use of Simulated Annealing," SPE Reservoir Eval. Eng., Feb., 36 (1998).
30. Peng, D., and D. B. Robinson, "A New Two-Constant Equation of State," Ind. Eng. Chem. Fundam., 15, 59 (1976).
31. Peng, D., and D. B. Robinson, "A Rigorous Method for Predicting the Critical Properties of Multicomponent Systems from an Equation of State," AIChE J., 23, 137 (1977).
32. Reid, R. C., and B. L. Beegle, "Critical Point Criteria in Legendre Transform Notation," AIChE J., 23, 726 (1977).
33. Reid, R. C., J. M. Prausnitz, and B. E. Poling, The Properties of Gases and Liquids, McGraw-Hill, Singapore (1988).
34. Sadus, R. J., "Calculating Critical Transitions of Fluid Mixtures: Theory vs. Experiment," AIChE J., 40, 1376 (1994).
35. Sewell, G., Computational Methods of Linear Algebra, Ellis Horwood, London (1990).
36. Smith, J. M., H. C. Van Ness, and M. M. Abbott, Introduction to Chemical Engineering Thermodynamics, McGraw-Hill, New York (1996).
37. Spear, R. R., R. L. Robinson, Jr., and K.-C. Chao, "Critical States of Ternary Mixtures and Equations of State," Ind. Eng. Chem. Fundam., 10, 588 (1971).
38. Stradi, B. A., J. F. Brennecke, J. P. Kohn, and M. A Stadtherr, "Reliable Computation of Mixture Critical Points," AIChE J., 47, 212 (2001).
39. Tester, J. W., and M. Modell, Thermodynamics and Its Applications, 3rd ed., Prentice Hall, Englewood Cliffs, NJ (1997).
40. van Konynenburg, P. H., and R. L. Scott, "Critical Lines and Phase Equilibria in Binary van der Waals Mixtures," Philos. Trans. R. Soc. Lond. A Phys. Sci., 298, 495 (1980).
41. Zhu, Y., and Z. Xu, "A Reliable Prediction of the Global Phase Stability for Liquid-Liquid Equilibrium Through the Simulated Annealing Algorithm: Application to NRTL and UNIQUAC Equations," Fluid Phase Equilib., 154, 55 (1999).