Reconciliation of process flow rates by matrix projection. Part II: The nonlinear case

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Abstract

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.

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