Data Reconciliation for Reaction Systems Using Extents and Shape Constraints

Concentrations measured during the course of reactions are typically corrupted by random noise. Data reconciliation techniques improve the accuracy of measurements by using redundancies in the material and energy balances expressed as relationships between measurements. Since in the absence of kinetic models these relationships cannot integrate information regarding past measurements, they are expressed in the form of algebraic constraints. This paper shows that, even in the absence of a kinetic model, one can use shape constraints to relate measurements at different time instants, thereby improving the accuracy of reconciled estimates. The construction of shape constraints depends on the operating mode of the chemical reactor. Moreover, it is shown that the representation of the reaction system in terms of extents helps identify additional shape constraints. A procedure for deriving shape constraints from measurements is also described. Data reconciliation using numbers of moles and extents is illustrated via a simulated case study.