Advertisement

Reconciliation of process flow rates by matrix projection. Part I: Linear case

Authors

  • C. M. Crowe,

    Corresponding author
    1. Department of Chemical Engineering, McMaster University, Hamilton, Ontario, Canada L8S 4L7
    • Department of Chemical Engineering, McMaster University, Hamilton, Ontario, Canada L8S 4L7
    Search for more papers by this author
  • Y. A. Garcia Campos,

    1. Department of Chemical Engineering, McMaster University, Hamilton, Ontario, Canada L8S 4L7
    Current affiliation:
    1. INTEVEP S.A., Evaluacion de Proyectos Apartado 76343, Caracas 1070A, Venezuela
    Search for more papers by this author
  • A. Hrymak

    1. Department of Chemical Engineering, McMaster University, Hamilton, Ontario, Canada L8S 4L7
    Current affiliation:
    1. Department of Chemical Engineering, Carnegie-Mellon University, Pittsburgh, PA 15213
    Search for more papers by this author

Abstract

Flow rate measurements in a steady-state process are reconciled by weighted least squares so that the conservation laws are obeyed. A projection matrix is constructed which can be used to decompose the linear problem into the solution of two subproblems, by first removing each balance around process units with an unmeasured component flow rate. The remaining measured flow rates are reconciled, and the unmeasured flow rates can then be obtained from the solution of the conservation equations. The basic case contains constraints which are linear in the component and the total flow rates. The method is extended to cases with bilinear constraints, involving unknown parameters such as split fractions.

Chi-square and normal statistics are used to test for overall gross measurement errors, for gross error in each node imbalance which is fully measured, and for each measurement adjustment.

Ancillary