### Abstract

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

Place of Publication | Espoo |

Publisher | VTT Technical Research Centre of Finland |

Number of pages | 118 |

ISBN (Electronic) | 978-951-38-8135-1 |

ISBN (Print) | 978-951-38-8134-4 |

Publication status | Published - 2014 |

MoE publication type | Not Eligible |

### Publication series

Series | VTT Technology |
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Number | 160 |

ISSN | 2242-1211 |

### Fingerprint

### Keywords

- Gibbs free energy
- constrained minimization
- immaterial constraint
- work-coefficient
- extent of reaction
- paraequilibrium

### Cite this

*Introduction to constrained Gibbs energy methods in process and materials research*. Espoo: VTT Technical Research Centre of Finland. VTT Technology, No. 160

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*Introduction to constrained Gibbs energy methods in process and materials research*. VTT Technology, no. 160, VTT Technical Research Centre of Finland, Espoo.

**Introduction to constrained Gibbs energy methods in process and materials research.** / Koukkari, Pertti.

Research output: Book/Report › Report

TY - BOOK

T1 - Introduction to constrained Gibbs energy methods in process and materials research

AU - Koukkari, Pertti

N1 - Project code: 77213

PY - 2014

Y1 - 2014

N2 - In process and materials chemistry, digitalization with computational methods has been a long-time continuing process. The methodology based on numerical methods in reaction kinetics as well as for fluid phase thermodynamics applying equations of state has been well established. During the last two decades, however, multiphase technology based on the minimization of Gibbs free energy has made progress in such fields of process and materials chemistry, where the conventional methods have not been applicable. Recent advancements also include introduction of such new Gibbs'ian algorithms, which, in addition to complex equilibrium problems, facilitate modelling of time-dependent dynamic changes in multi-phase systems. Within the said period, VTT has been an active performer in the development of multiphase Gibbs'ian techniques. The research work performed at VTT has led to several new algorithms with practical industrial applications. The particular focus has been the development of the Constrained Gibbs Free energy minimization technique, where instead of material balances and stoichiometric relations derived thereof, also immaterial physical conditions are applied as constraints in the free energy minimizing calculation. In this report, the method of constrained Gibbs energy minimization for calculating chemical equilibria in arbitrary multiphase systems is derived using basic thermodynamic concepts. The method of Lagrange undetermined multipliers is introduced for a simple system of an ideal gas phase and a number of condensed phases, constrained by the number of moles of the system components. The use of additional constraints in the Gibbs energy minimization procedure is facilitated by applying the concept of generalised work-coefficients as the Lagrange multipliers of immaterial components in the system. The thus introduced method of immaterial constraints in Gibbs energy minimization is illustrated with a number of simple practical examples such as electrochemical Donnan equilibria applied for pulp suspensions, surface equilibria and systems constrained by reaction kinetics via the extent of chemical reactions. A few examples of non-equilibrium and parametric phase diagrams calculated with the immaterial constraints are also given. Finally, the applicability of the method for biochemical systems is shortly discussed.

AB - In process and materials chemistry, digitalization with computational methods has been a long-time continuing process. The methodology based on numerical methods in reaction kinetics as well as for fluid phase thermodynamics applying equations of state has been well established. During the last two decades, however, multiphase technology based on the minimization of Gibbs free energy has made progress in such fields of process and materials chemistry, where the conventional methods have not been applicable. Recent advancements also include introduction of such new Gibbs'ian algorithms, which, in addition to complex equilibrium problems, facilitate modelling of time-dependent dynamic changes in multi-phase systems. Within the said period, VTT has been an active performer in the development of multiphase Gibbs'ian techniques. The research work performed at VTT has led to several new algorithms with practical industrial applications. The particular focus has been the development of the Constrained Gibbs Free energy minimization technique, where instead of material balances and stoichiometric relations derived thereof, also immaterial physical conditions are applied as constraints in the free energy minimizing calculation. In this report, the method of constrained Gibbs energy minimization for calculating chemical equilibria in arbitrary multiphase systems is derived using basic thermodynamic concepts. The method of Lagrange undetermined multipliers is introduced for a simple system of an ideal gas phase and a number of condensed phases, constrained by the number of moles of the system components. The use of additional constraints in the Gibbs energy minimization procedure is facilitated by applying the concept of generalised work-coefficients as the Lagrange multipliers of immaterial components in the system. The thus introduced method of immaterial constraints in Gibbs energy minimization is illustrated with a number of simple practical examples such as electrochemical Donnan equilibria applied for pulp suspensions, surface equilibria and systems constrained by reaction kinetics via the extent of chemical reactions. A few examples of non-equilibrium and parametric phase diagrams calculated with the immaterial constraints are also given. Finally, the applicability of the method for biochemical systems is shortly discussed.

KW - Gibbs free energy

KW - constrained minimization

KW - immaterial constraint

KW - work-coefficient

KW - extent of reaction

KW - paraequilibrium

M3 - Report

SN - 978-951-38-8134-4

T3 - VTT Technology

BT - Introduction to constrained Gibbs energy methods in process and materials research

PB - VTT Technical Research Centre of Finland

CY - Espoo

ER -