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

K. Shimizu, H. Sayama, Y. Kameyama, Kazuhiko Suzuki

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)103-112
Number of pages10
JournalInternational chemical engineering
Volume33
Issue number1
Publication statusPublished - Jan 1993

Fingerprint

Newton-Raphson method
Distillation
Chemical analysis
Derivatives
Liquids
Vapors
Distillation columns
Iterative methods
Temperature

ASJC Scopus subject areas

  • Engineering(all)

Cite this

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

In: International chemical engineering, Vol. 33, No. 1, 01.1993, p. 103-112.

Research output: Contribution to journalArticle

@article{47fff217c28f401fb2a5070d7953968e,
title = "Computation of multicomponent distillation processes by the Newton-Raphson method using an implicit function",
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.",
author = "K. Shimizu and H. Sayama and Y. Kameyama and Kazuhiko Suzuki",
year = "1993",
month = "1",
language = "English",
volume = "33",
pages = "103--112",
journal = "International chemical engineering",
issn = "0020-6318",
number = "1",

}

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 -