### Abstract

Two new approaches to the determination of constrained lumping schemes are presented. They are based on the property that the lumping schemes validated in the whole composition Y_{n}-space of y are only determined by the invariance of the subspace spanned by the row vectors of lumping matrix M with respect to the transpose of the Jacobian matrix J^{T}(y) for the kinetic equations. It is proved that, when a part of a lumping matrix M_{G} is given, each row of the part of the lumping matrix to be determined, M_{D}, is certain linear combinations of a set of eigenvectors of a special symmetric matrix. This symmetric matrix is related to M^{T}_{G} and A_{k}M^{T}_{G}, where A_{k} are the basis matrices of J^{T} (y). It is shown that the approximate lumping matrices containing M_{G} with different row number n̂(n̂ < n) and global minimum errors can be determined by an optimization method. Using the concept of the minimal invariant subspace of a constant matrix over a given subspace one can directly obtain the lumping matrices containing M_{G} with different n̂. The accuracy of these lumping matrices are shown to be satisfactory in sample calculations.

Original language | English (US) |
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Pages (from-to) | 95-111 |

Number of pages | 17 |

Journal | Chemical Engineering Science |

Volume | 46 |

Issue number | 1 |

DOIs | |

State | Published - 1991 |

### All Science Journal Classification (ASJC) codes

- Chemistry(all)
- Chemical Engineering(all)
- Industrial and Manufacturing Engineering