Modelling of gas–liquid reactors — stability and dynamic behaviour of a hydroformylation reactor, influence of mass transfer in the kinetics controlled regime
Introduction
With respect to the development of a new hydroformylation reactor, a research project was initiated to examine the dynamics of hydroformylation processes. The dynamic behaviour of a reactor in general and especially of a hydroformylation reactor is a very important part of the reactor design. A literature survey indicated that undesired sustained temperature oscillations may exist in hydroformylation reactors under certain circumstances (Vleeschhouwer, Garton, & Fortuin, 1992). In plant operation, these conditions have to be avoided because they may adversely affect product quality, catalyst degradation and downstream operations and can lead to serious difficulty in process control and unsafe reactor operations. Two models to be used as design tools have been developed and validated: (1) A rigorous reactor model (van Elk, Borman, Kuipers, & Versteeg 1999, van Elk, Borman, Kuipers, & Versteeg 2000) and (2) an approximate reactor model for stability analysis (van Elk et al., 1999). The models are used to investigate the influence of the cooler design and the mass transfer coefficient and/or contact area on the stability and dynamic behaviour of the reactor.
The rigorous model (van Elk, Borman, Kuipers, & Versteeg 1999, van Elk, Borman, Kuipers, & Versteeg 2000) requires a minimum amount of model assumptions and simplifications; moreover, it takes all relevant phenomena into account. The rigorous model is based on the following major assumptions:
- 1.
The mass transfer in the gas phase is described with the stagnant film model.
- 2.
The mass transfer in the liquid phase is described with the Higbie (1935) penetration model.
- 3.
The contact time according to the penetration model is small compared to the liquid-phase residence time.
- 4.
Both the gas and the liquid phase are assumed to be perfectly mixed (i.e. CISTRs).
The approximate model (van Elk et al., 1999) is a much simpler one based on some additional assumptions. This model takes only the key phenomena into account. The model consists of liquid-phase material balances (ordinary differential equations) and an approximate algebraic expression for the enhancement factor. The approximate model is based on the following additional assumptions:
- 1.
The influence of mass transfer is sufficiently accurate described by an approximate and explicit analytical expression for the enhancement factor (Ea).
- 2.
The influence of temperature profiles on micro scale can be neglected.
- 3.
The resistance to mass transfer in the gas-phase can be neglected.
- 4.
The influence of the gas-phase heat balance can be neglected or alternatively the gas- and liquid-phase heat balances can be combined into one overall heat balance.
- 5.
The gas-phase concentration is constant or alternatively the gas-phase partial pressure is constant. This assumption is fulfilled when a sufficiently fast partial pressure regulation is present.
The approximate model is very useful to create stability maps from which design rules for stable operation can be obtained. Using the more accurate rigorous model as a final check-up for the chosen set of operating conditions is however recommended.
Illustrative examples (van Elk et al., 1999) showed that for fictitious gas–liquid reactors, with simple first- or second-order kinetics, operating conditions can be created where oscillations (limit cycles) are found. It was also shown that the approximate model is a very useful tool for predicting the regions where instabilities take place and more important to find design rules which ensure stable operations.
The current study presents the results of applying both the rigorous and the approximate reactor model on a hydroformylation process with more complex kinetics. It is shown that this reactor will show oscillatory behaviour under certain realistic operating conditions. The current study thus shows that limit cycles can be expected to exist for real industrial designs and not only for fictitious non-existing reactors and/or processes.
Section snippets
Conclusions
A rigorous and an approximate model are presented that can describe the dynamic behaviour of an ideally stirred hydroformylation reactor (two-phase CISTR). The rigorous model is valid over the entire range of conditions ranging from kinetics controlled pre-mixed feed to mass transfer controlled infinitesimal fast reaction (see Westerterp, van Swaaij, & Beenackers, 1990). The approximate model is, due to Eq. (23), only valid in the kinetics controlled regime (Ea=1). The approximate model is
Notation
specific contact area, heat transfer area, heat capacity, diffusivity, activation energy, enhancement factor, l heat transfer coefficient, overall heat transfer coefficient (defined by heat of reaction based on R, molar flux, mass transfer coefficient, reaction rate constant gas–liquid partition coefficient, l reaction rate, ideal gas constant,
Acknowledgements
The investigations were supported by DSM Research Geleen.
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