Critical point calculations for semi-continuous mixtures

Geraldo L. Rochocz, Marcelo Castier, Stanley I. Sandler

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

A typical problem in the oil and gas industry is the calculation of high pressure phase equilibria in systems containing a very large number of similar components. Treating the composition of these mixtures as a continuous distribution, instead of trying to characterize each individual component, has proven to be an elegant and efficient approach to solve this type of problem. In this paper, we rigorously formulate the critical point conditions for continuous and semi-continuous mixtures, but as is often the case with such formulations, the complexity of the expressions prevents an analytical solution of the equilibrium problem, and discretization is required in order to use realistic thermodynamic models. Once in discrete form, the critical point equations were solved using a modified form of the Hicks and Young algorithm and the thermodynamic stability of the solutions was guaranteed by the calculation of higher terms in the Helmholtz free energy expansion and by global phase stability analyses. The resulting procedure was employed to perform an investigation of the influence of the distribution parameters on the types of critical phase diagrams that can be obtained from the Peng-Robinson equation of state.

Original languageEnglish
Pages (from-to)137-153
Number of pages17
JournalFluid Phase Equilibria
Volume139
Issue number1-2
Publication statusPublished - Dec 1997
Externally publishedYes

Fingerprint

critical point
thermodynamics
Phase stability
Gas industry
Equations of state
Phase equilibria
Free energy
Phase diagrams
Oils
Thermodynamic stability
equations of state
oils
industries
free energy
phase diagrams
Thermodynamics
formulations
expansion
Chemical analysis
gases

Keywords

  • Continuous thermodynamics
  • Critical state
  • Equation of state
  • Method of calculation
  • Mixture
  • Vapor-liquid equilibria

ASJC Scopus subject areas

  • Fluid Flow and Transfer Processes
  • Physical and Theoretical Chemistry

Cite this

Rochocz, G. L., Castier, M., & Sandler, S. I. (1997). Critical point calculations for semi-continuous mixtures. Fluid Phase Equilibria, 139(1-2), 137-153.

Critical point calculations for semi-continuous mixtures. / Rochocz, Geraldo L.; Castier, Marcelo; Sandler, Stanley I.

In: Fluid Phase Equilibria, Vol. 139, No. 1-2, 12.1997, p. 137-153.

Research output: Contribution to journalArticle

Rochocz, GL, Castier, M & Sandler, SI 1997, 'Critical point calculations for semi-continuous mixtures', Fluid Phase Equilibria, vol. 139, no. 1-2, pp. 137-153.
Rochocz, Geraldo L. ; Castier, Marcelo ; Sandler, Stanley I. / Critical point calculations for semi-continuous mixtures. In: Fluid Phase Equilibria. 1997 ; Vol. 139, No. 1-2. pp. 137-153.
@article{a78c724a3f01438787321b6d11aff831,
title = "Critical point calculations for semi-continuous mixtures",
abstract = "A typical problem in the oil and gas industry is the calculation of high pressure phase equilibria in systems containing a very large number of similar components. Treating the composition of these mixtures as a continuous distribution, instead of trying to characterize each individual component, has proven to be an elegant and efficient approach to solve this type of problem. In this paper, we rigorously formulate the critical point conditions for continuous and semi-continuous mixtures, but as is often the case with such formulations, the complexity of the expressions prevents an analytical solution of the equilibrium problem, and discretization is required in order to use realistic thermodynamic models. Once in discrete form, the critical point equations were solved using a modified form of the Hicks and Young algorithm and the thermodynamic stability of the solutions was guaranteed by the calculation of higher terms in the Helmholtz free energy expansion and by global phase stability analyses. The resulting procedure was employed to perform an investigation of the influence of the distribution parameters on the types of critical phase diagrams that can be obtained from the Peng-Robinson equation of state.",
keywords = "Continuous thermodynamics, Critical state, Equation of state, Method of calculation, Mixture, Vapor-liquid equilibria",
author = "Rochocz, {Geraldo L.} and Marcelo Castier and Sandler, {Stanley I.}",
year = "1997",
month = "12",
language = "English",
volume = "139",
pages = "137--153",
journal = "Fluid Phase Equilibria",
issn = "0378-3812",
publisher = "Elsevier",
number = "1-2",

}

TY - JOUR

T1 - Critical point calculations for semi-continuous mixtures

AU - Rochocz, Geraldo L.

AU - Castier, Marcelo

AU - Sandler, Stanley I.

PY - 1997/12

Y1 - 1997/12

N2 - A typical problem in the oil and gas industry is the calculation of high pressure phase equilibria in systems containing a very large number of similar components. Treating the composition of these mixtures as a continuous distribution, instead of trying to characterize each individual component, has proven to be an elegant and efficient approach to solve this type of problem. In this paper, we rigorously formulate the critical point conditions for continuous and semi-continuous mixtures, but as is often the case with such formulations, the complexity of the expressions prevents an analytical solution of the equilibrium problem, and discretization is required in order to use realistic thermodynamic models. Once in discrete form, the critical point equations were solved using a modified form of the Hicks and Young algorithm and the thermodynamic stability of the solutions was guaranteed by the calculation of higher terms in the Helmholtz free energy expansion and by global phase stability analyses. The resulting procedure was employed to perform an investigation of the influence of the distribution parameters on the types of critical phase diagrams that can be obtained from the Peng-Robinson equation of state.

AB - A typical problem in the oil and gas industry is the calculation of high pressure phase equilibria in systems containing a very large number of similar components. Treating the composition of these mixtures as a continuous distribution, instead of trying to characterize each individual component, has proven to be an elegant and efficient approach to solve this type of problem. In this paper, we rigorously formulate the critical point conditions for continuous and semi-continuous mixtures, but as is often the case with such formulations, the complexity of the expressions prevents an analytical solution of the equilibrium problem, and discretization is required in order to use realistic thermodynamic models. Once in discrete form, the critical point equations were solved using a modified form of the Hicks and Young algorithm and the thermodynamic stability of the solutions was guaranteed by the calculation of higher terms in the Helmholtz free energy expansion and by global phase stability analyses. The resulting procedure was employed to perform an investigation of the influence of the distribution parameters on the types of critical phase diagrams that can be obtained from the Peng-Robinson equation of state.

KW - Continuous thermodynamics

KW - Critical state

KW - Equation of state

KW - Method of calculation

KW - Mixture

KW - Vapor-liquid equilibria

UR - http://www.scopus.com/inward/record.url?scp=0031412229&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031412229&partnerID=8YFLogxK

M3 - Article

VL - 139

SP - 137

EP - 153

JO - Fluid Phase Equilibria

JF - Fluid Phase Equilibria

SN - 0378-3812

IS - 1-2

ER -