An Optimization Framework for Kinetic Model Building from Concentration and Spectroscopic Data

 This dissertation deals with the development of an optimization framework for kinetic model building from experimentally measured concentration and spectroscopic data. We develop mechanistic models based on first-principles and use a statistical criteria for model discrimination when more than one model is proposed. While many predictive model building methods exist using data-driven approaches, mechanistic models provide a physical understanding of resulting estimates and allow the investigator to elicit additional information about the underlying structure of the system. Tightly coupled with kinetic model building is parameter estimation, where degrees of freedom are related to unknown reaction rate parameters and other sources of measurement uncertainty such as unknown initial conditions and spectroscopic absorbance. Accurate estimation methods which maximize the information from experimentally collected data are imperative, but detailed physics-based models with multiple datasets present a computational challenges as the problem size and complexity increases. In this work, we present strategies to address these common obstacles. The model building framework is based on simultaneous full-discretization approaches and interior-point nonlinear programming (NLP) solvers which exploit problem structure and exact second derivatives resulting in favorable computational efficiency. 

First, we review relevant nonlinear optimization theory, which motivates the use of interior-point algorithms for kinetic model building. In addition, we discussion advantages and disadvantages of different approaches for parameter estimation from spectroscopic data, with special emphasis on the advantages of the simultaneous solution strategy. To present the flexibility and robustness of this framework, we investigate various reaction networks with real-world experimentally measured data. Chapter 3 describes an application of nonlinear mixed-effects models, an alternative modeling technique commonly used in pharmacometrics to capture batch-to-batch variation between experiments, to a single response hydrogenation reaction in a trickle-bed batch reactor system. Chapters 4, 5, and 6 examine different applications of our kinetic model building framework to obtain accurate predictions of rate constants, concentration profiles, and pure component absorbance profiles from in situ spectroscopic data. In Chapter 4 and Chapter 6, we develop population balance models for ring-opening polymerization reactions. Chapter 5 presents a challenging case study where temperature dependence and hydrogen-bonding effects play an important role. All modeling strategies use the state-of-the-art NLP solver IPOPT and the algebraic modeling language Pyomo.