Rapid, Automated Determination of Reaction Models and Kinetic Parameters

We herein report a novel kinetic modelling methodology whereby identification of the correct reaction model and kinetic parameters is conducted by an autonomous framework combined with transient flow measurements to enable comprehensive process understanding with minimal user input. An automated flow chemistry platform was employed to initially conduct linear flow-ramp experiments to rapidly map the reaction profile of three processes using transient flow data. Following experimental data acquisition, a computational approach was utilised to discriminate between all possible reaction models as well as identify the correct kinetic parameters for each process. Species that are known to participate in the process (starting materials, intermediates, products) are initially inputted by the user prior to flow ramp experiments, then all possible model candidates are compiled into a model library based on their potential to occur after mass balance assessment. Parallel computational optimisation then evaluates each model by algorithmically altering the kinetic parameters of the model to allow convergence of a simulated kinetic curve to the experimental data provided. Statistical analysis then determines the most likely reaction model based on model simplicity and agreement with experimental data. This automated approach to gaining full process understanding, whereby a small number of data-rich experiments are conducted, and the kinetics are evaluated autonomously, shows significant improvements on current industrial optimisation techniques in terms of labour, time and overall cost. The computational approach herein described can be employed using data from any set of experiments and the code is open-source

Automated, computational approaches to kinetic model and parameter determination

A major bottleneck in the transition from chemistry research at lab scale to process development is a lack of quantitative chemical synthesis information. Critical aspects of this information include knowing the correct reaction model and precise kinetic parameters. If this information is available, classical reaction engineering principles may be utilised to shorten process development times and lower costs. Identifying the correct reaction model for a particular process, however, can be challenging and time-consuming, particularly for physical-organic chemists and kinetics experts that may be busy with other aspects of process development. The work presented herein describes computational approaches that automatically determine the most likely kinetic model and associated parameters based on the experimental data supplied, without expert chemical intuition. The concept for these methodologies involves a comprehensive model evaluation tool. The experimental data and the species involved in the process are inputted. Based on mass balance, all mass-balance-allowed transformations between these species are identified. All possible models are then compiled from this list of transformations, featuring unique combinations of these model terms. Every model is then evaluated using ordinary differential equation (ODE) solvers and optimisation algorithms to maximise the convergence of simulated reaction progression with the experimental data, thereby identifying the kinetic parameters. Each model is then statistically evaluated to determine which model is the most likely to be correct. Using these methodologies allows any chemist to automatically determine a reaction model and kinetic constants for a particular system, by performing all kinetic analysis autonomously. Their most expensive resource, time, can then be focussed on other tasks that cannot be automated

Concept of Variants and Invariants for Reaction Systems, with Application to Estimation, Control and Optimization

The concept of reaction variants and invariants for lumped reaction systems has been known for several decades. Its applications encompass model identification, data reconciliation, state estimation and control using kinetic models. In this thesis, the concept of variants and invariants is extended to distributed reaction systems and used to develop new applications to estimation, control and optimization. The thesis starts by reviewing the material and heat balances and the concept of variants and invariants for several lumped reaction systems. Different definitions of variants and invariants, in particular the vessel extents, are presented for the case of homogeneous reaction systems, and transformations to variants and invariants are obtained. The extension to systems with heat balance and mass transfer is also reviewed. The concept of extents is generalized to distributed reaction systems, which include many processes involving reactions and described by partial differential equations. The concept of extents and the transformation to extents are detailed for various configurations of tubular reactors and reactive separation columns, as well as for a more generic framework that is independent of the configuration. New developments of the extent-based incremental approach for model identification are presented. The approach, which compares experimental and modeled extents, results in maximum-likelihood parameter estimation if the experimental extents are uncorrelated and the modeled extents are unbiased. Furthermore, the identification problem can be reformulated as a convex optimization problem that is solved efficiently to global optimality. The estimation of unknown rates without the knowledge or the identification of the rate models is described. This method exploits the fact that the variants computed from the available measurements allow isolating the different rates. Upon using a Savitzky-Golay filter for differentiation of variants, one can show that the resulting rate estimator is optimal and obtain the error and variance of the rate estimates. The use of variants and invariants for reactor control is also considered. Firstly, offset-free control via feedback linearization is implemented using kinetic models. Then, it is shown how rate estimation can be used for control via feedback linearization without kinetic models. By designing an outer-loop feedback controller, the expected values of the controlled variables converge exponentially to their setpoints. This thesis presents an approach to speed up steady-state optimization, which takes advantage of rate estimation without rate models to speed up the estimation of steady state for imperfectly known dynamic systems with fast and slow states. Since one can use feedback control to speed up convergence of the fast part, rate estimation allows estimating the steady state of the slow part during transient operation. The application to dynamic optimization is also shown. Adjoint-free optimal control laws are computed for all the types of arcs in the solution. In the case of reactors, the concept of extents allows the symbolic computation of optimal control laws in a systematic way. A parsimonious input parameterization is presented, which approximates the optimal inputs well with few parameters. For each arc sequence, the optimal parameter values are computed via numerical optimization. The theoretical results are illustrated by simulated examples of reaction systems