(165b) A Simultaneous Approach for Kinetic Parameter Estimation and Curve Resolution Based on Spectroscopic Measurements

Authors: 
Biegler, L., Carnegie Mellon University
Chen, W., Carnegie Mellon University
Identification of reaction kinetics plays an important role in the development of the commercial product and process development for chemical and bio-chemical systems. Precise knowledge of kinetic parameters is critical in the reactor scale-up from laboratory to industrial levels and the design of robust, controllable and safe processes. Spectroscopic techniques are commonly used for chemical reaction monitoring especially within ultraviolet-visible, infrared and near-infrared wavelength regions; these measurements provide vast amounts of data related to the concentration of the species in the reaction medium. Ample research has been conducted in developing techniques to resolve the information in the spectral data, and identify the kinetic parameters of the underlying chemical reaction (MCR-ALS).

This work describes an efficient, unified framework for kinetic parameter estimation and curve resolution that is based on maximum likelihood principles and a simultaneous collocation approach that leads to improved estimates of parameters.

This study considers the dynamic equation model for the reaction kinetics as a stochastic differential-algebraic equation system, dc = f(c, y, q) + k dW(t), g(c, y, t) = 0, where c(t) is the concentration vector at time t, y(t) are additional algebraic states, q is the kinetic parameter vector and W(t) is the reaction system noise described by standard Brownian motion or Wiener processes. The spectroscopic measurements d(t, l) are governed by Beer-Lambertâ??s law, d(t, l) = Sk ck (t) sk (l) + z(t, l), with absorbance sk (l) for component k and wavelength l, and measurement noise z(t, l).

  Determination of q by parameter estimation requires consideration of a dynamic optimization problem derived from maximum likelihood principles, and this leads to two important challenges. First, an efficient and reliable optimization strategy is required, even for kinetic systems that exhibit open loop instability and dependent kinetic equations. We successfully address this task by applying a direct transcription nonlinear programming (NLP) approach that determines the optimal kinetic parameters and the concentration profiles simultaneously. Second, since only spectroscopic measurements are available, covariances and other distributional information for W(t) and z(t, l) cannot be determined directly. Instead, we apply maximum likelihood principles in order to derive the covariances needed for parameter estimation. Coupled solution of these two tasks leads to an iterative optimization-based approach that provides covariance estimates and initializes the kinetic parameters. These results allow the subsequent solution of the parameter estimation problem with fixed covariance terms. Confidence regions for the kinetic parameter estimates are then obtained through the application of NLP sensitivity, a byproduct of the direct transcription approach.

We demonstrate our proposed approach on six case studies, including a comprehensive treatment of aspirin kinetics. These cases include simulated as well as actual experimental datasets. Detailed numerical results for these cases are presented and compared with the MCR-ALS GUI 2.0 toolbox. These show significant improvements in performance and computational cost over state-of-the-art approaches.