Identifying Chemical Reaction Network Models
Advancing the chemical engineering fundamentals
Chemical Reaction Engineering (T2-2P)
Keywords: Reactor modelling, Differential equations, System identification
Identifying Chemical Reaction Network Models
S. C. Burnham, K. Novakovic, M. J. Willis and A. R. Wright
School of Chemical Engineering and Advanced Materials, Newcastle University, Newcastle-upon-Tyne, NE1 7RU, UK.
s.c.burnham@ncl.ac.uk; katarina.novakovic@ncl.ac.uk; mark.willis@ncl.ac.uk; a.r.wright@ncl.ac.uk
One of the key issues for fine chemical and pharmaceutical companies is to reach the market with many new products as quickly as possible. Within these industries multi-purpose plants which are suitable for a variety of customer specifications are often used. This leads to fast changing discontinuous processes incorporating batch or semi-batch reactors. A major problem facing these companies is the scale up of a process from laboratory to full-scale production in the shortest possible time, preferably avoiding pilot-plant testing.
Modelling and simulation studies are often used to assist scale-up. For conventional equation-based modelling software it is necessary to formulate mathematical equations in order to describe the process dynamics. In general, the behaviour of process design variables such as flow-rates, reactor volumes and inlet concentrations of species are well understood. However, obtaining knowledge of the chemistry, in particular the chemical reaction network remains a limiting step.
Traditional methods for determining reaction networks involve postulating a number of different structures which are then fit to experimental data. The reaction network whose ordinary differential equation (ODE) model provides the highest prediction accuracy with respect to the experimental data is taken to be the correct structure. This is a time consuming procedure requiring both chemistry and modelling expertise.
From a system identification perspective, the task of identifying a useful network is one of determining the structure as well as the parameters of a set of non-linear ODEs. This is a non-trivial system identification task; however, recent work (2) has demonstrated that it is possible to elucidate the network by partitioning the problem into simpler subtasks. These subtasks are a) determine the number of reactions i.e. the number of rate expressions, b) define the structure of the individual rate expressions, c) determine the structure of the individual species’ ODEs d) determine the kinetic rate constants and the individual heats of reactions.
The number of reactions is determined through assessment of the linear dependence of species derivatives. The method uses singular valued decomposition (SVD) to select the set of largest eigenvalues which represent a summed variance larger than a fixed threshold. The number of eigenvalues contained in this set represents the estimated rank of the matrix, which infers the number of independent reactions. To define the structure of the individual rate expressions it is assumed that the reaction has been performed in a reaction calorimeter and that reaction heat (Qr) data is available. Best subsets regression of the Qr-time profile data provides an estimate of the structure of all the individual rate expressions. The structure of the individual species’ ODEs is determined by an additional regression stage. Finally, the kinetic rate constants and the individual heats of reactions are determined using standard kinetic fitting software.
The aim of this work is to a) test the sensitivity of the threshold value in SVD for determining the number of chemical reactions b) determine the benefit of the use of confidence bounds on the value of the number of chemical reactions (and hence the number of rate expressions) estimated c) adapt the network elucidation method for cases where Qr data is unavailable.
The approach is demonstrated and critically assessed through simulated case studies of two reaction systems, a) a four species, three reaction, Van der Vusse scheme (2) , b) an abstract eight species, five reaction, scheme. The practicality of the method is then demonstrated using real data obtained from an L-proline catalysed aldol reaction.
(1) Burnham, S. C., Willis, M. J., and Wright, A. R. (2007). Identifying Chemical Reaction Network Models, Submitted to The 8th Symposium on Dynamics and Control of Process Systems, Cancun, June.
(2) Van, de Vusse J. G. (1964) Plug-flow Type Reactor Versus Tank Reactor. Chem. Eng. Sci., 19, 994-997.
Presented Tuesday 18, 13:30 to 15:00, in session Chemical Reaction Engineering (T2-2P).
