### Abstract

A number of computational methods have been proposed for solving multicomponent vapor-liquid equilibrium and distillation problems. Many of these methods employing a gradient-type algorithm involve numerical differentiation for evaluation of the partial derivatives. This may require a large amount of computation time and often gives rise to numerical instability, especially in problems with microcomponent. This paper presents a new computation procedure for multicomponent nonideal vapor-liquid equilibrium problems. The liquid compositions are chosen as the independent variables and the temperature is considered as the dependent variable. The partial derivatives of vapor compositions with respect to the liquid compositions are derived analytically by making use of the implicit function theorem. The iterative solution procedure is based on the gradient method (Newton-Raphson or Gauss-Newton method), which uses analytical equations for the partial derivatives and approach to the solutions with the liquid and vapor composition constraints satisfied. The iteration procedure gives numerically stable and rigorous solutions to multicomponent dew point problems.

Original language | English |
---|---|

Pages (from-to) | 1095-1101 |

Number of pages | 7 |

Journal | Kagaku Kogaku Ronbunshu |

Volume | 15 |

Issue number | 6 |

DOIs | |

Publication status | Published - 1989 |

### Fingerprint

### Keywords

- Dew Point
- Gauss-Newton Method
- Gradient Method
- Implicit Function
- Vapor-Liquid Equilibria

### ASJC Scopus subject areas

- Chemistry(all)
- Chemical Engineering(all)

### Cite this

*Kagaku Kogaku Ronbunshu*,

*15*(6), 1095-1101. https://doi.org/10.1252/kakoronbunshu.15.1095

**Calculation of Vapor-Liquid Equilibria by Making Use of Implicit Function.** / Shimizu, Kengo; Sayama, Hayatoshi; Kameyama, Yoshimasa; Suzuki, Kazuhiko.

Research output: Contribution to journal › Article

*Kagaku Kogaku Ronbunshu*, vol. 15, no. 6, pp. 1095-1101. https://doi.org/10.1252/kakoronbunshu.15.1095

}

TY - JOUR

T1 - Calculation of Vapor-Liquid Equilibria by Making Use of Implicit Function

AU - Shimizu, Kengo

AU - Sayama, Hayatoshi

AU - Kameyama, Yoshimasa

AU - Suzuki, Kazuhiko

PY - 1989

Y1 - 1989

N2 - A number of computational methods have been proposed for solving multicomponent vapor-liquid equilibrium and distillation problems. Many of these methods employing a gradient-type algorithm involve numerical differentiation for evaluation of the partial derivatives. This may require a large amount of computation time and often gives rise to numerical instability, especially in problems with microcomponent. This paper presents a new computation procedure for multicomponent nonideal vapor-liquid equilibrium problems. The liquid compositions are chosen as the independent variables and the temperature is considered as the dependent variable. The partial derivatives of vapor compositions with respect to the liquid compositions are derived analytically by making use of the implicit function theorem. The iterative solution procedure is based on the gradient method (Newton-Raphson or Gauss-Newton method), which uses analytical equations for the partial derivatives and approach to the solutions with the liquid and vapor composition constraints satisfied. The iteration procedure gives numerically stable and rigorous solutions to multicomponent dew point problems.

AB - A number of computational methods have been proposed for solving multicomponent vapor-liquid equilibrium and distillation problems. Many of these methods employing a gradient-type algorithm involve numerical differentiation for evaluation of the partial derivatives. This may require a large amount of computation time and often gives rise to numerical instability, especially in problems with microcomponent. This paper presents a new computation procedure for multicomponent nonideal vapor-liquid equilibrium problems. The liquid compositions are chosen as the independent variables and the temperature is considered as the dependent variable. The partial derivatives of vapor compositions with respect to the liquid compositions are derived analytically by making use of the implicit function theorem. The iterative solution procedure is based on the gradient method (Newton-Raphson or Gauss-Newton method), which uses analytical equations for the partial derivatives and approach to the solutions with the liquid and vapor composition constraints satisfied. The iteration procedure gives numerically stable and rigorous solutions to multicomponent dew point problems.

KW - Dew Point

KW - Gauss-Newton Method

KW - Gradient Method

KW - Implicit Function

KW - Vapor-Liquid Equilibria

UR - http://www.scopus.com/inward/record.url?scp=85004570376&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85004570376&partnerID=8YFLogxK

U2 - 10.1252/kakoronbunshu.15.1095

DO - 10.1252/kakoronbunshu.15.1095

M3 - Article

AN - SCOPUS:85004570376

VL - 15

SP - 1095

EP - 1101

JO - Kagaku Kogaku Ronbunshu

JF - Kagaku Kogaku Ronbunshu

SN - 0386-216X

IS - 6

ER -