(427d) Characterisation of the Dynamic Behaviour of Briggs-Rauscher Reaction in A Fed-Batch Reactor

A numerical investigation of the dynamics of the oscillatory Briggs-Rauscher (BR) reaction is reported in this paper. We simulate the oscillations of the BR reaction in an isothermal fed-batch reactor (FBR), modelled using the simplified mechanism proposed by (Kim et al., 2002). The reaction is perturbed at specific time instants by withdrawing a fraction of reacting mixture from the FBR and simultaneously replacing an equal volume of fresh feed into the reactor. Phase transition curves (PTCs) showing the phase change in the oscillations as a function of the perturbed phase, are constructed for different values of replacement time (Tf) and replacement ratio (R). Positive and negative phase shifts of oscillations are observed for different values of Tf and R, which are classified as Type I, according to the shape of the PTC. Simulations of the periodically forced FBR show quasi-periodicity and periodic behaviour in different regions of R-Tf parameter plane. The periodically pulsed system is then characterised using the firing number which is defined as the average number of oscillations in the reacting medium within one pulse perturbation. This shows a devil's staircase (Dolnik et al., 1989) like dependence on the forcing period. The firing number is used to categorize resonant/quasi-periodic states of the system when the reaction is subject to periodic forcing.

References

1. Dolnik, M., Finkeova, J., Schreiber, I. and Marek, M., (1989) Dynamics of forced excitable and oscillatory chemical reaction systems, The Journal of Physical Chemistry, 93, 2764-2774.

2. Kim, K.-R., Lee, D. J. and Shin, K. J., (2002) A simplified model for the Briggs-Rauscher reaction mechanism, Journal of Chemical Physics, 117, 6, 2710-2717.