(342a) Kinetic Parameter Estimation from Multiple Spectroscopic Datasets with or without Unwanted Spectral Contributions Using Kipet

Authors: 
Short, M., Carnegie Mellon University
Biegler, L. T., Carnegie Mellon University
Accurately determining reaction kinetics is an important step in the development of any commercial process. In many industries, lab-scale experiments are conducted on systems where little is known in advance regarding the reaction mechanism. These experiments can be costly to run and therefore it is imperative to maximize the use of information gathered during the experiment. A common, non-intrusive method of gathering data during reaction experiments is through the use of spectroscopic instruments that collect data based on absorption of the mixture over time in the ultraviolet visible (UV-vis), Raman, near-infrared (NIR), and infrared wavelength regions. Analyzing data from spectroscopic measurements from such devices is extremely challenging for a number of reasons. Firstly, the data often contains considerable noise and it is common for there to be unwanted spectral contributions from a number of time-variant and time invariant sources. Examples of time invariant contributions can include such effects as baseline shift, distortion, or the presence of absorbing species that do not form a part of the model or that are inert, interfering species. Time variant contributions could be due to scattering based on solids in the mixture or spectral drift. Unwanted contributions are often treated by preprocessing the data using one of a number of different techniques. However, none of the preprocessing strategies guarantee removal of these phenomena, and the choice of preprocessing strategy is not obvious. Another challenge for analyzing spectroscopic data is that the datasets can be extremely large, especially when attempting to estimate parameters that are common across datasets. This is often needed in laboratory applications where chemists attempt to estimate reaction behavior at different conditions.

In a breakthrough approach, Chen et al. (2016) presented a unified framework based on maximum likelihood principles, nonlinear optimization techniques, and orthogonal collocation methods to solve the systems of differential equations. The approach first estimates the variances related to both system variable noise and measurement noise through an iterative optimization-based algorithm and then simultaneously determines the concentration profiles, kinetic parameters, and individual species’ absorbance profiles using the nonlinear programming solver, IPOPT. Using the sensitivity properties at the optimal solution, the technique is also able to obtain the covariance matrix and confidence intervals of the estimated parameters. This approach was recently developed into an open-source Python-based package called KIPET (Kinetic Parameter Estimation Toolkit) (Short et al., 2019). KIPET makes use of Pyomo (Hart et al., 2017) as the algebraic modeling language, however users need not be experts in Python nor Pyomo to make use of the many parameter estimation tools therein.

In this work we develop a novel extension to the framework presented by Chen, et al. (2016, 2019) where multiple experimental datasets are simultaneously used to determine the reaction kinetic parameters, concentration profiles in each experimental run, as well as individual species absorbances. In certain experimental setups, new reactants and reactions are introduced and in other examples, different process conditions with different feed times and temperatures are used. In this way, local parameters are introduced in certain datasets, with global parameters linking each experimental dataset. In addition to simultaneously estimating both local parameters and global parameters, we also introduce the ability to determine unwanted contributions that are either time-dependent or time independent. The new approach is demonstrated through a set of case studies that show the utility of performing parameter estimation across datasets as well as the effects of explicitly including unwanted contributions into the model.