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Reconciliation of process flow rates by matrix projection. Part II: The nonlinear case
Author(s) -
Crowe C. M.
Publication year - 1986
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690320410
Subject(s) - mathematics , projection (relational algebra) , flow (mathematics) , component (thermodynamics) , nonlinear system , matrix (chemical analysis) , least squares function approximation , sequence (biology) , volumetric flow rate , non linear least squares , process (computing) , statistics , algorithm , explained sum of squares , computer science , thermodynamics , geometry , chemistry , physics , biochemistry , quantum mechanics , chromatography , estimator , operating system
Flow rate and concentration measurements in a steady state process are reconciled by weighted least squares so that the conservation laws and other constraints are obeyed. Two projection matrices are constructed in turn, in order to decompose the problem into three subproblems to be solved in sequence. The first matrix eliminates all unmeasured component flow rates and concentrations from the equations; the second then removes the unmeasured total flow rates. The adjustments to component flow rates are iteratively determined, starting with guessed values of unmeasured total flow rates. Chi‐square and normal test statistics are derived by linearizing the equations, to allow detection of gross errors in imbalances and adjustments of measurements.