### Abstract

The calculation of solid-fluid equilibrium at high pressure is important in the modeling and design of processes that use supercritical fluids to selectively extract solid solutes. We describe here a new method for reliably computing solid-fluid equilibrium at constant temperature and pressure or for verifying the nonexistence of a solid-fluid equilibrium state at the given conditions. Difficulties that must be considered include the possibility of multiple roots to the equifugacity conditions and multiple stationary points in the tangent plane distance analysis done for purposes of determining global phase stability. Somewhat surprisingly, these issues are often not dealt with by those who measure, model, and compute high-pressure solid-fluid equilibria, leading in some cases to incorrect or misinterpreted results. It is shown here how these difficulties can be addressed by using a methodology based on interval analysis, which can provide a mathematical and computational guarantee that the solid-fluid equilibrium problem is correctly solved. The technique is illustrated with several example problems in which the Peng- Robinson equation of state model is used. However, the methodology is of general purpose and can be applied in connection with any model of the fluid phase.

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

Pages (from-to) | 1624-1636 |

Number of pages | 13 |

Journal | Industrial and Engineering Chemistry Research |

Volume | 39 |

Issue number | 6 |

Publication status | Published - 2000 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Chemical Engineering (miscellaneous)
- Environmental Science(all)
- Polymers and Plastics

### Cite this

*Industrial and Engineering Chemistry Research*,

*39*(6), 1624-1636.

**Reliable computation of high-pressure solid-fluid equilibrium.** / Xu, Gang; Scurto, Aaron M.; Castier, Marcelo; Brennecke, Joan F.; Stadtherr, Mark A.

Research output: Contribution to journal › Article

*Industrial and Engineering Chemistry Research*, vol. 39, no. 6, pp. 1624-1636.

}

TY - JOUR

T1 - Reliable computation of high-pressure solid-fluid equilibrium

AU - Xu, Gang

AU - Scurto, Aaron M.

AU - Castier, Marcelo

AU - Brennecke, Joan F.

AU - Stadtherr, Mark A.

PY - 2000

Y1 - 2000

N2 - The calculation of solid-fluid equilibrium at high pressure is important in the modeling and design of processes that use supercritical fluids to selectively extract solid solutes. We describe here a new method for reliably computing solid-fluid equilibrium at constant temperature and pressure or for verifying the nonexistence of a solid-fluid equilibrium state at the given conditions. Difficulties that must be considered include the possibility of multiple roots to the equifugacity conditions and multiple stationary points in the tangent plane distance analysis done for purposes of determining global phase stability. Somewhat surprisingly, these issues are often not dealt with by those who measure, model, and compute high-pressure solid-fluid equilibria, leading in some cases to incorrect or misinterpreted results. It is shown here how these difficulties can be addressed by using a methodology based on interval analysis, which can provide a mathematical and computational guarantee that the solid-fluid equilibrium problem is correctly solved. The technique is illustrated with several example problems in which the Peng- Robinson equation of state model is used. However, the methodology is of general purpose and can be applied in connection with any model of the fluid phase.

AB - The calculation of solid-fluid equilibrium at high pressure is important in the modeling and design of processes that use supercritical fluids to selectively extract solid solutes. We describe here a new method for reliably computing solid-fluid equilibrium at constant temperature and pressure or for verifying the nonexistence of a solid-fluid equilibrium state at the given conditions. Difficulties that must be considered include the possibility of multiple roots to the equifugacity conditions and multiple stationary points in the tangent plane distance analysis done for purposes of determining global phase stability. Somewhat surprisingly, these issues are often not dealt with by those who measure, model, and compute high-pressure solid-fluid equilibria, leading in some cases to incorrect or misinterpreted results. It is shown here how these difficulties can be addressed by using a methodology based on interval analysis, which can provide a mathematical and computational guarantee that the solid-fluid equilibrium problem is correctly solved. The technique is illustrated with several example problems in which the Peng- Robinson equation of state model is used. However, the methodology is of general purpose and can be applied in connection with any model of the fluid phase.

UR - http://www.scopus.com/inward/record.url?scp=0034044785&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034044785&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0034044785

VL - 39

SP - 1624

EP - 1636

JO - Industrial and Engineering Chemistry Research

JF - Industrial and Engineering Chemistry Research

SN - 0888-5885

IS - 6

ER -