### Abstract

Modeling rate-controlled chemically reactive systems in biocatalysis, fuel combustion, material science, and chemical process engineering involves the quantification and exploitation of interactions between many chemical species. These dynamic chemical systems, having relatively few limiting reactions, can be conceived as a series of snapshots where reactions have fixed extents but otherwise idle. Since the reactions affect the stoichiometric matrix of the internal constraints, such constrained equilibrium states cannot be defined in terms of conventional atomic mass balances.

A systematic method for obtaining generalized equilibrium constraints for reaction mechanisms of arbitrary complexity is presented. Reaction matrices are converted into entity conservation matrices using row operations. The simultaneously introduced virtual components enable Gibbs energy calculations for complex reaction schemes including organic systems and enzyme-catalyzed biochemical transformations having multiple limiting reactions. Classical Gibbs energy minimization, which would otherwise readily model phase transformations and solvent interactions, is thereby made accessible to these emerging application fields.

A systematic method for obtaining generalized equilibrium constraints for reaction mechanisms of arbitrary complexity is presented. Reaction matrices are converted into entity conservation matrices using row operations. The simultaneously introduced virtual components enable Gibbs energy calculations for complex reaction schemes including organic systems and enzyme-catalyzed biochemical transformations having multiple limiting reactions. Classical Gibbs energy minimization, which would otherwise readily model phase transformations and solvent interactions, is thereby made accessible to these emerging application fields.

Original language | English |
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Pages (from-to) | 1238-1250 |

Number of pages | 13 |

Journal | Computers and Chemical Engineering |

Volume | 35 |

Issue number | 7 |

DOIs | |

Publication status | Published - 2011 |

MoE publication type | A1 Journal article-refereed |

### Keywords

- Entity conservation matrix
- Gibbs energy minimization
- Rate-controlled constrained equilibrium
- Reaction constraint
- Virtual component