(664c) Multiple Hydrodynamic States in Trickle Flow: Correlating Pressure Drop and Liquid Holdup

Multiple hydrodynamic states are possible in trickle flow reactors (Kan & Greenfield, 1979). They have mostly been quantified through pressure drop and liquid holdup variation. It is well established that these two parameters are influenced by the flow history. In this study, we report the extent of possible variation of these hydrodynamic parameters for the 3 mm glass sphere?air?water system. The ranges of liquid and gas flow rates investigated were 1-9 kg/m2s and 0.013-0.117 kg/m2s respectively. Limiting cases are identified according to specifically defined prewetting procedures (following the approach of Van der Merwe & Nicol, 2005): (1) Non-prewetted, (2) Levec prewetted (the bed is flooded and drained before fluid introduction), (3) KanL prewetted (increased liquid flow until pulsing, then reduction), (4) KanG prewetted (increased gas flow until pulsing, then reduction) and (5) Super prewetted (flooding and gas and liquid flows are introduced once draining commences). Some selected results are shown in figures 1 and 2. The different prewetting procedures resulted in three distinct pressure drop regions. The upper and lower limiting cases are the KanL and Levec modes respectively, with a difference of 700 % between them. Liquid holdup is different in all five prewetting modes. The upper and lower limiting cases are the KanG and Non-prewetted modes respectively. Importantly, the lower limiting case for prewetted beds is the Levec mode. These results are in qualitative agreement with those reported in literature. Using the present classification, Kan & Greenfield (1979) studied only the Super and KanG modes, Levec et al. (1986, 1988) the Super and Levec modes for no gas flow and the KanL and Levec modes with gas flow. Christensen et al. (1986) studied the KanL and Levec modes. Lazzaroni et al. (1988) compared the Dry mode with the Super mode. Wang et al. (1995) investigated the KanL, KanG and Levec modes through pressure drop hysteresis only. Lutran et al. (1991), Ravindra et al. (1997) and Sederman & Gladden (2001) all report visualizations of the Levec and KanL modes. Van der Merwe & Nicol (2005) studied the Super, Levec and Dry modes for no gas flow. A host of correlations have been developed in the past 20 years based on data from the KanL mode of operation. Broadly speaking, three approaches have been used to model hydrodynamic multiplicity: The gas tortuosity effect (Kan & Greenfield, 1979), relative permeability (Levec et al., 1986) and the rivulet/film concept (Melli & Scriven, 1991 and Wang et al., 1995). In modelling two-phase flow, increased pressure drops are seen to be the result of the holdup reducing the cross-sectional flow area for gas flow. The difficulty in modelling hysteresis lies therein that non-uniform flows exist and interfacial areas and interstitial velocities in the momentum balance need to be corrected. Such corrective measures are mode specific: For liquid flow rate variation hysteresis, increased pressure drops are accompanied by increased holdups (compare Levec and KanL modes), while for gas flow rate induced hystersis lower pressure drops are associated with higher holdups (compare Super and KanG modes). Present models only consider one of these hysteresis loops. Kan & Greenfield (1979) suggested a gas tortuosity decrease associated with the maximum gas flow rate to which the bed had been subjected. Their model underpredicts our pressure drop data when the recommended parameters are used. However, the maximum gas Reynolds number dependency compensates for the increased gas velocity history and the predicted trends agree with our data qualitatively both in pressure drop and holdup for the Super and KanG modes. The model is highly unsatisfactory due to the large number of empirical parameters. It is, however, the only correlation available for the KanG mode. The relative permeability approach advocated by Levec et al. (1986) for the prediction of the liquid flow rate variation induced hysteresis, has since been validated for various choices of packing and pressures (Nemec et al. 2005) for the KanL mode. For liquid holdup in the Levec mode, Levec et al. (1986) suggested that the liquid phase relative permeability ? reduced saturation relationship be altered. The model is shown for selected data from Levec et al. (1986) and this study in figure 2. One adjusted parameter (the coefficient of the reduced saturation) seems capable of compensating for the alternate mode of operation. The model performs well at low Reynolds numbers but not at high Reynolds numbers. The reason is apparent from the liquid phase relative permeability - reduced saturation correlation. At high saturations (> 0.33 in this case) the holdups of the two modes are equal, but Levec's model predicts higher Levec mode permeabilities. Figure 2 also suggests that the gas phase permeability-saturation relationship will also need modification for the Levec mode since the model under-predicts the holdup but over-predicts the pressure drop for this mode. Wang et al. (1995) adopted Christensen et al.'s (1986) interpretation of dividing the bed into rivulet and film dominated flow cross-sections. The model is unable to model gas flow rate variation induced hysteresis (probably because they measured only pressure drop and not holdup as well). It is more suited to investigating the flow uniformity rather than being a predictive pressure drop model. Melli & Scriven (1991) introduced a 2-D network of pores model capable of predicting hysteresis, at least in qualitative terms. Van der Merwe & Nicol (2005) introduced a simple momentum balanced-based holdup model for stagnant gas conditions. It corrects the interstitial velocity and liquid-solid interfacial area with a single parameter (volumetric utilization) that is measured independently. In this study, we have evaluated existing hysteresis modelling approaches in light of new and more complete pressure drop and holdup data. Models perform reasonably well for the modes of operation employed by their authors, but no general hysteresis model exists for prediction of all multiple hydrodynamic states.

References Christensen, G., McGovern, S.J. and Sundaresan, S. (1986) A.I.Ch.E. J., 32, 1677. Kan, K.M. and Greenfield, P.F. (1979) Ind. Eng. Chem. Process Des. Dev., 18, 740. Lazzaroni, C.L., Keselman, H.R. and Figoli, N.S. (1988) Ind. Eng. Chem. Res., 27, 1132. Levec, J., Grosser, K. and Carbonell, R.G. (1988) A.I.Ch.E. J., 34, 1027. Levec, J., Saez, A.E. and Carbonell, R.G. (1986) A.I.Ch.E. J., 32, 369. Lutran, P.G., Ng, K.M. and Delikat, E.P. (1991) Ind. Eng. Chem. Res., 30, 1270. Melli, T.R. and Scriven, L.E. (1991) Ind. Eng. Chem. Res., 30, 951. Ravindra, P.V., Rao, D.P. and Rao, M.S. (1997) Ind. Eng. Chem. Res., 36, 5133. Sederman, A.J. and Gladden, L.F. (2001) Chem. Eng. Sci., 56, 2615. Van der Merwe, W. and Nicol, W. (2005) Ind. Eng. Chem. Res., 44, 9446. Wang, R., Mao, Z. and Chen, J. (1995) Chem. Eng. Sci., 50, 2321.