### Abstract

A new iterative method is presented for the rigorous simulation of multicomponent distillation processes using the Newton-Raphson method to solve the simultaneous equations, which is characterized by the use of the liquid compositions as the independent variables and analytical equations for evaluating the partial derivatives, with the vapor compositions and temperatures as the dependent variables. The analytical equations for the partial derivatives of the vapor compositions with respect to the liquid compositions are derived, using the implicit-function theorem. The advantages of the method are that a numerical differentiation of the partial derivatives is unnecessary, as is normalization of the liquid compositions. The method has excellent convergence characteristics when applied to 10 typical distillation columns of complicated structure.

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

Pages (from-to) | 103-112 |

Number of pages | 10 |

Journal | International chemical engineering |

Volume | 33 |

Issue number | 1 |

Publication status | Published - Jan 1993 |

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### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*International chemical engineering*,

*33*(1), 103-112.

**Computation of multicomponent distillation processes by the Newton-Raphson method using an implicit function.** / Shimizu, K.; Sayama, H.; Kameyama, Y.; Suzuki, Kazuhiko.

Research output: Contribution to journal › Article

*International chemical engineering*, vol. 33, no. 1, pp. 103-112.

}

TY - JOUR

T1 - Computation of multicomponent distillation processes by the Newton-Raphson method using an implicit function

AU - Shimizu, K.

AU - Sayama, H.

AU - Kameyama, Y.

AU - Suzuki, Kazuhiko

PY - 1993/1

Y1 - 1993/1

N2 - A new iterative method is presented for the rigorous simulation of multicomponent distillation processes using the Newton-Raphson method to solve the simultaneous equations, which is characterized by the use of the liquid compositions as the independent variables and analytical equations for evaluating the partial derivatives, with the vapor compositions and temperatures as the dependent variables. The analytical equations for the partial derivatives of the vapor compositions with respect to the liquid compositions are derived, using the implicit-function theorem. The advantages of the method are that a numerical differentiation of the partial derivatives is unnecessary, as is normalization of the liquid compositions. The method has excellent convergence characteristics when applied to 10 typical distillation columns of complicated structure.

AB - A new iterative method is presented for the rigorous simulation of multicomponent distillation processes using the Newton-Raphson method to solve the simultaneous equations, which is characterized by the use of the liquid compositions as the independent variables and analytical equations for evaluating the partial derivatives, with the vapor compositions and temperatures as the dependent variables. The analytical equations for the partial derivatives of the vapor compositions with respect to the liquid compositions are derived, using the implicit-function theorem. The advantages of the method are that a numerical differentiation of the partial derivatives is unnecessary, as is normalization of the liquid compositions. The method has excellent convergence characteristics when applied to 10 typical distillation columns of complicated structure.

UR - http://www.scopus.com/inward/record.url?scp=0027334184&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027334184&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0027334184

VL - 33

SP - 103

EP - 112

JO - International chemical engineering

JF - International chemical engineering

SN - 0020-6318

IS - 1

ER -