Identifiability Study of a Liquid-Liquid Phase-Transfer Catalyzed Reaction System

Consistent model parameterization is an important issue when developing mathematical models because it dictates whether parameter values can be estimated uniquely. The problems inherent in model parameterization are presented in an identifiability study of a nonlinear liquid–liquid phase-transfer reactor model. This reactor model was proposed by Chen et al., in a 1991 study, to describe the reaction between organic-phase benzyl chloride and aqueous-phase sodium bromide, using tetrabutylammonium as the phase-transfer catalyst. The model consists of coupled differential and algebraic equations. Existing methods using differential-algebra for testing identifiability of differential-algebraic equation (DAE) models are computationally intensive for models with a large number of states and parameters. A new method for testing DAE systems for identifiability was recently proposed by Ben-Zvi et al. Using this method, the model proposed by Chen et al. is shown to be locally unidentifiable, indicating that it is impossible to uniquely identify all of the model parameters. Two alternatives for simplifying the model to make it identifiable are discussed. © 2004 American Institute of Chemical Engineers AIChE J, 50:2493–2501, 2004