(46u) Kinetic Identification and Risk Assessment Based on Non-Linear Fitting of Calorimetric Data

Chemical incidents are typically caused by loss of control, resulting in runaway reactions or process deviations in different units of production. These incidents could be foreseen and avoided or at least decreased with an appropriate process development and risk assessment methodology [1]. In case of fed-batch reactors, the main problem generally encountered is the accumulation of heat. In fact, understanding and controlling this aspect is one of the most important and challenging process safety tasks. One solution, for fed batch reactors, would be to adapt the feed rate to avoid rapid heat accumulation. Nevertheless, this approach is disadvantageous in terms of reaction time and costs involved. Indeed, to quantify and manage this problem in an optimal way, the reaction kinetics needs to be known.

Kinetic identification is aimed at providing a better understanding of the reaction pathways and thermal behavior [2]. The dynamics of the reaction system are represented by two mathematical models based on differential equations and whose parameters are estimated using measured data:

1. The reaction kinetic model which is based on a scheme of the different reactions taking place in the considered mixture.
2. The system dynamic model based on the measurement tools dynamics (Differential Scanning Calorimetry, Calvet and Reaction Calorimeter) and their respective conditions.

In order to acquire information about the reaction behavior, several calorimetric experiments at different scales (mg, g, kg) are necessary. Indeed, each scale, since the conditions in terms of temperature and heat transfer are different, introduces new perturbations to the system allowing for a stronger identification of the model parameters [3]. Nevertheless, this investigation can be very long with increasingly complex models involving a large number of parameters. Therefore, a new approach to solve these problems has been developed.

The proposed approach can be summarized in two points: 1) planning the measurements in a statistically optimal way to cover the experimental space efficiently with a minimum number of experiments [4-6]; 2) developing a robust numerical method able to extract the reaction kinetic parameters from the measurements obtained [7].

Using the reaction model, it is possible to predict the reaction behavior under very different conditions. Nevertheless, from a scale-up point of view, the behavior of an industrial system is completely different from one at the laboratory scale. Consequently, some measurements should be performed at industrial scale in order to fill this lack of information. This task is often long and arduous. Fortunately, Zufferey proposed a method allowing to simulate conditions approaching industrial one at laboratory scale [8] and avoiding large scale experiments.

Once all these steps are performed, a large scale dynamic model can be postulated and used to simulate the industrial process. These simulations will allow to define the safety constraints in order to maintain the process safe and productive. This last point was discussed by Ubrich for different reaction types [9].

The risk assessment can be then performed using the reaction model in different cases, such as cooling failure, poorly adapted feed profile or otherwise inadequate temperature control.

The proposed method was studied on a well-known reaction : the exothermic esterification reaction of acetic anhydride and methanol [10].

                                                        AcOAc     +     MeOH   à  AcOMe    +      AcOH

Where AcOAc is the acetic anhydride, MeOH is the methanol, AcOMe is the methyl acetate and AcOH is the acetic acid.

Several measurements were done initially on the milligram (DSC) and the gram (Calvet) scales, in non-isothermal conditions, in order to explore the working temperature range and the eventuality of secondary reactions. A series of experiments, selected using the space filling design method [11], was then carried out for kilogram scale in a Reaction Calorimeter (RC) for isothermal conditions.

r = k₀ * exp( -E_a/RT ) * ( C_AcOAc )^m * ( C_MeOH )ⁿ

Where k₀is the pre-exponential factor, E_a is the activation energy, R is the gas constant, T is the temperature, C is the concentration, m and nare the reactant orders.

Based on the power rate law, the reaction kinetic model parameters were evaluated using numerical optimization (Levenberg-Marquardt) to fit the proposed model to the calorimetric measurements. In order to validate the model, two different measurements (1 DSC and 1 RC) not included in the optimization database were compared with their respective simulations.

A risk assessment was performed around different safety criteria, such as the criticality of the chemical process, a cooling failure scenario and a Semenov diagram, in order to evaluate the process risk potential and determine the optimal process conditions. Finally, for a hypothetic industrial scale-up, some measurements were done in a Reaction Calorimeter following the Zufferey’s method and compared to their respective simulations.

In short, the aim of this presentation is to provide a first insight into a way of investigating reaction kinetics using non-linear model fitting. The obtained model can be used to improve the safety and optimize the process.

References

1. F. Stoessel, Thermal Safety of Chemical Processes: Risk Assessment and Process Design. 2008, Wiley.
2. D.G. Blackmond, Reaction Progress Kinetic Analysis: A Powerful Methodology for Mechanistic Studies of Complex Catalytic Reactions. Angewandte Chemie International Edition (28) 2005, 4302-4320.
3. J. Stegmaier, D. Skanda, and D. Lebiedz, Robust Optimal Design of Experiments for Model Discrimination Using an Interactive Software Tool. PLoS ONE (2) 2013, e55723.
4. S. Zaglauer, Bayesian design of experiments for nonlinear dynamic system identification. in Proceedings of the 5th International ICST Conference on Simulation Tools and Techniques. 2012. Desenzano del Garda, Italy: Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering.
5. Z.R. Lazic, Design of Experiments in Chemical Engineering. 2004, Wiley.
6. W. Tinsson, Plans d'expérience: constructions et analyses statistiques. 2010, Springer.
7. K. Madsen, N.B. Nielsen, and O. Tingleff, Methods for non-linear least squares problems (2nd ed.). 2004.
8. B. Zufferey, Scale-down approach: chemical process optimisation using reaction calorimetry for the experimental simulation of industrial reactors dynamics. Ph. D., Swiss Federal Institute of Technology, Lausanne, 2006.
9. O. Ubrich, Improving safety and productivity of isothermal semi-batch reactors by modulating the feed rate. Ph. D, Swiss Federal Institute of Technology, Lausanne, 2000.
10. S. Bohm, et al., Auto-catalytic effect of acetic acid on the kinetics of the methanol/acetic anhydride esterification. Institute of Safety Research 2005, 53-58.
11. J. Santiago, M. Claeys-Bruno, and M. Sergent, Construction of space-filling designs using WSP algorithm for high dimensional spaces. Chemometrics and Intelligent Laboratory Systems 2012, 26-31.