Prediction of gas holdup in the three-phase fluidized bed: air/Newtonian and non-Newtonian liquid systems

Prediction of gas holdup in the three-phase fluidized bed: air/Newtonian and non-Newtonian liquid systems The application of the three-phase fluidization technology in wastewater treatment and other biochemical processes has been regularly addressed in the past decades. For the design and development of the three-phase fluidized bed reactors, knowledge of the hydrodynamic parameter such as gas holdup is essential and hence in this paper an attempt has been made to study the effect of fundamental and operating variables on gas holdup. On the basis of the experimental results, a unified correlation has been developed to predict gas holdup in the fluidized bed using the Newtonian and the non-Newtonian liquids. The experimental results showed good agreement with those predicted according to the developed correlation.


INTRODUCTION
During the recent years the three-phase fluidized beds have emerged as one of the most promising devices for the applications in many industrial processes such as coal liquefaction, catalytic hydrogenation and desulphurization of petrochemicals, Fischer-Tropsch synthesis, biochemical fermentation and biological waste water treatment processes, polymerization processes, etc. The three-phase fluidized bed is preferred in many industries because of simple design and construction, high mass transfer rates as a result of good mixing 1 -5 . Now it has gained importance in biotechnology also, where bacteria or enzymes are entrapped within porous particles or immobilized on the surface of the inert solids 4 -7 . The successful scale up, design and operation of the fluidized beds mainly depend on the accurate prediction of the behavior and features of the system such as gas holdup. Over the years, many significant contributions have been made by investigators towards gas holdup in fluidized beds 8 -16 . Mostly Newtonian liquids were used to develop the correlations for the prediction of gas holdup 11 -13, 17 . The use of non-Newtonian liquids for the prediction of gas holdup has been done only on a limited scale 17 -20 . Since most of the industrial effluents behave as power law fluids, there is a vital need to obtain data with a wide range of variables using non-Newtonian liquids and to develop a generalized correlation to represent the data 4,5,15,18,19,21 . Since many biochemical reaction fluids behave as power law non-Newtonian liquids, an attempt has been made to study the effect of fundamental and operating variables on gas holdup, and also to develop a unified correlation for the estimation of gas holdup using the Newtonian and the non-Newtonian liquids.

EXPERIMENTAL SETUP AND PROCEDURE
All experiments were carried out in a Perspex column (0.15 m inner diameter and 1.8 m height) as shown in Fig.  1. The details of the experimental apparatus can be found elsewhere 3,22 . The details of the properties of the solids and fluids used in the present study are given in Table 1.
Water, different concentrations of glycerol (lab grade and commercial grade), butyric acid and Mono Ethanol Amine (MEA) were Newtonian liquid systems and different concentrations of Carboxy Methyl Cellulose (CMC), were the non-Newtonian liquids and 12 different particles were used. The experimental column had a provision to feed the gas and liquid at the bottom of the column. Compressed air was fed into the bottom of the column through a pressure regulating valve. A gas distributor was provided at the bottom of the fluidized column, whereas, a gasliquid separator was provided at the top of the fluidized column. The gas-liquid distributor is designed in such a way that uniformly distributed gas and liquid mixtures entered the fluidized column. The distributor section was made up of conical Plexiglas of 0.3 m in height, had a divergence angle of 4.5 o . The higher cross section end was fitted to a testing section, with a perforated plate made of perspex sheet of 0.001 m thick, 0.15 m diameter having the opening area of approximately 20% of the column area in between covered with 20 mesh stainless steel screen at the top. 0.0008 m diameter holes in triangular pitch were made in 15 circles of nearly 0.005 m gap from the centre. After attaining a steady state condition, air and liquid flow rates were suddenly stopped by closing both the valves simultaneously and gas holdup was measured 14, 19 . The experimental results were randomly checked and it was found that the reproducibility of the errors was within ± 2%. The equivalent volume diameter of non spherical particles has been calculated by using the following formula: = Volume of one non-spherical particle Where d p spherical volume equivalent diameter, which is the diameter of a sphere whose volume is the same as that of the solid volume of non spherical particle. Shear stress and shear rate were calculated using Brookfield Rheometer (model LVDV-II+). By plotting shear stress versus shear rate, the flow consistency index (k) and fluid behaviour index (n) were calculated.

RESULTS AND DISCUSSION
The experimentally measured gas holdup values obtained in the present study have been analyzed for their dependency on the fundamental and operating variables such as superficial gas and liquid velocities, size and shape of the solid particles, physical and rheological properties of the fluids. From the experimental results, it was observed that both the superficial gas and liquid velocities  had a significant effect on gas holdup. Fig. 2 shows the variation in the gas holdup with respect to superficial liquid and gas velocities for the particle size (d p ) of 4.8 mm for air-0.1% CMC system. The gas holdup increased with an increase in gas velocity for a constant liquid flow rate. The same trend was observed in previous studies 4, 6, 23 . However, the increase of gas holdup with an increase of liquid velocity is not significant at low superficial gas velocities where as at higher superficial gas velocities gas holdup was increased slightly. This trend coincides with the results published by the previous authors 18, 19 . The effect of particle size on gas holdup is shown in Fig. 3 for air-water system. It was observed that there is a decrease in gas holdup with an increase in particle diameter, which is mainly due to increasing the bubble breakage. The same trend is in agreement with the published literature results 20 . The influence of the sphericity of particle on gas holdup is shown in Fig. 4, from which it is observed that an increase of the sphericity of particle decreases the gas holdup and it is mainly due to decreasing the surface area per unit volume of particle which leads to less bubble   breakage. The dependency of the gas holdup on liquid properties was analyzed using 11 different liquid systems. At constant liquid flow rate, gas holdup increases with increasing liquid viscosity, as shown in Figure 5. The same trend is also observed with an increasing flow consistency index (k) for non-Newtonian fluids (Fig. 6). Increasing the liquid viscosity/consistency index enhances the bubble breakages and hence the gas holdup increases 18 . The present experimental data and literature data 6,10,14,18,19,24,25 were analyzed using the available literature correlations (Table 2). Begovich and Watson correlation 4 predicted good results with the data of Bloxom et al., 10 , Miura and Kawase 18 and Miura et al. 19 with the minimum AARD limits (less than 13% AARD) but failed to comply with the rest of the data sets 6, 14, 24, 25 (more than 25% AARD). The reason could be that the effective physical properties of liquids and particle dimensions were not properly accounted for in the development of the correlation. The present experimental and literature data, when tested with the Parulekar and Shah 11  19 and this was mainly due to the fact that the appropriate effects of physical properties of liquids, were not properly taken into account for the development of the correlation. Though Ramesh and Murugesan 26 had studied the effect of particle diameter, phase velocities and physical properties of the fluids on gas holdup, their correlation was restricted to Newtonian systems. Graphical analysis of the present data ( Fig. 2 -Fig. 6) shows that the variation of gas holdup can be attributed to the effect of all the above said variables. From the literature it is observed that most of the literature correlations were restricted to Newtonian liquid systems 4, 11 -13, 16, 26 and hence those could not be used non-Newtonian fluids and hence in this study, the approach of dimensionless method was adopted for the establishment of the unified gas holdup  correlation for the prediction of gas holdup showed relatively high deviation (>70 % AARD). This deviation may be attributed to the fact that even though the author had used hydrogen-oil systems, the individual physical properties of liquids and the solids were not properly taken Table 3. The details of the literature particles used for the gas holdup analysis correlation for both Newtonian and non-Newtonian liquids with a wide range of operating conditions (Tables 3 -5).
The combined effects of the liquid properties of the Newtonian and the non-Newtonian fluids were accommodated using Modified Morton's number 27 , the effects of viscous force and gravity force were combined in terms of Froude number's of fluids, the ratio of the downward to upward force, the column geometry effects and particle sphericity were considered to develop the unified present correlation. Regression analysis of the available gas holdup data yielded the following constants and indices for the equation, (1) Statistical error analysis of the proposed correlation (Eqs. (1)) showed an AARD of 10.5% for gas holdup indicating a satisfactory representation of the available data for the air-Newtonian and the air-non Newtonian systems. The stastical analysis of the proposed and available literature correlations for the present and literature Table 4. The details of the literature liquid systems used for the gas holdup analysis Table 5. A range of variables used for the development of the proposed correlation Table 6. Statistical comparison of gas holdup with the present and literature data   Table 6. The validity of the present correlation has been tested with the available experimental literature gas holdup data and AARD found to be with in 15%, which shows a satisfactory agreement (Figs. 7 -9).

CONCLUSION
In the present work, a careful analysis of the effect of the fundamental and operating variables on gas holdup has been studied in a three-phase fluidized bed using various Newtonian and non-Newtonian liquids. The experimental results indicate that the gas holdup increases with increased gas flow rate; viscosity of the liquid and flow consistency index whereas gas holdup decreases with increased particle diameter. The unified correlation for the estimation of gas holdup in a three-phase fluidized bed was developed using literature and the present data covering a wide range of variables. The statistical error analysis of the proposed correlation showed an AARD of 10.5 % for gas holdup indicating a satisfactory represen-tation of the available data for the air-Newtonian and the air-non Newtonian systems. The validity of the present correlation has been tested with the available experimental literature gas holdup data and AARD found to be with in 15%, which shows a satisfactory agreement and also the graphical analysis showed that the predictive ability of the present proposed correlation is good. Therefore, the proposed correlation can be confidently used for the estimation of the gas holdup, with the knowledge of the fundamental and operating variables.