1090
Ind. Eng. Chem. Res. 2001, 40, 1090-1096
Modeling of Gas-Liquid Mass-Transfer Limitations in Slurry Olefin Polymerization Pål Kittilsen,† Rune Tøgersen,† Erling Rytter,†,‡ and Hallvard Svendsen*,† Department of Chemical Engineering, Norwegian University of Science and Technology (NTNU), and Statoil Research Centre, 7005 Trondheim, Norway
A model of gas to liquid mass transfer in a stirred laboratory reactor was developed with the purpose of controlling mass-transfer limitations in kinetic studies of olefin polymerizations. Renewing the liquid surface is controlling the mass transfer. Generally, two different scales of eddies can be envisaged to be responsible for the renewal: at low stirring rates, the mean liquid flow is the controlling mechanism; at high stirring rates, small-scale turbulence provides the renewal. The change is at a specified turbulent Reynolds number. The model for the high Reynolds number region is based on an established mass-transfer relationship from the literature. For low Reynolds numbers, a new correlation is developed based on literature studies of the liquid circulation velocity at the gas-liquid interface. The model predictions are compared with experimental data for propene polymerization in decane. It was found that the small-scale turbulence model was most appropriate, and fitted the data within a factor 2. The models are theoretically founded and form a basis for the control of mass-transfer effects in the measurements of kinetic data. 1. Introduction Quantifying the effect of gas-liquid mass-transfer resistance is vital in kinetic studies in heterogeneous systems. This paper deals with the theoretical modeling of gas-liquid mass transfer and comparison between predicted and experimental data. The experiments were performed using a laboratory-scale reactor for kinetic studies of olefin polymerization as described in a previous paper.1 A common model for describing gas-liquid mass transfer at a moving surface is the penetration model concept.2 The contact time between gas and liquid is a key parameter. Theofanous et al.3 found that two distinct mass-transfer regimes, associated with smallscale and macroscale turbulent motions, respectively, are controlling the renewing of the liquid surface and thus the contact time between the gas and liquid. A criterion for which of the scales are dominating was derived based on the turbulent Reynolds number. We will show how to use this criterion in a practical case. A common way of studying gas-liquid mass-transfer effects is experimentation with pure absorption in a stirred reactor (no reaction), where the change in either the gas pressure or the gas component concentration in the liquid phase is measured. Bin4 has made a comprehensive study on reported absorptions to free interfaces in turbulent stirred vessels. On the basis of a theoretical relation between the turbulent intensity and the mass-transfer coefficient derived by Lamont and Scott,5 he was able to correlate a large number of data with the theory of small-scale turbulence. The turbulence intensity is related to the energy dissipation, which, in turn, can be calculated from the geometry of the agitator-reactor system and the agitation rate. * To whom correspondence should be addressed. E-mail:
[email protected]. Fax: +47 73594080. † NTNU. ‡ Statoil Research Centre.
None of the investigated systems could be described by a macroscale turbulence model. Based on this study and earlier work, he concluded that the value for the transition between the regime controlled by the smallscale turbulence and that controlled by large-scale eddies is at turbulent Reynolds number about 100. The low turbulent Reynolds number regime was investigated by Dong et al.,6 who measured corresponding surface flow rates and mass-transfer rates in a stirred vessel. They found good agreement between predicted and measured mass-transfer coefficients when using the mean flow as a basis for calculating the contact time and thus the mass-transfer coefficient. However, the method requires a measure of the velocity components near the liquid surface and is thus not appropriate for predicting or designing new reactor systems. As part of this work, we have derived a new theoretical-based correlation for the cases where the mean flow is controlling the mass transfer. There are few papers describing the mass transfer in direct connection with polymerization reactions. As pointed out by Floyd et al.,7 as long as the properties of the liquid phase are not changed dramatically from that of the pure liquid, that is, at moderate (
