Gas Holdup in Turbulent Bed Contactor: Experiments and Prediction Model

Knowledge of gas holdup is important for the development of the three-phase fluidized bed reactors. This work concerns the study of the effect of different operating conditions on gas retention in a turbulent bed contactor type 2 (TBC), such as superfi cial gas and liquid velocities, liquid to gas mass flows ratio ( L / G ), particle diameter and density, static bed height and free-open area of the supporting grid. The influence of the free area of the packing support grid ( φ ) on gas holdup was demonstrated and proved. The gas holdup increased to 22.92 % when φ decreased from 0.82 to 0.32. The experimental data (1746) led to the development of two correlations to predict gas holdup, one of which incorporated the ratio ( L / G ) which is an important design factor for gas-liquid contactors. The predicted results of holdup gas were in good agreement with the experimental data.


Introduction
The turbulent bed contactor (TBC) is a gas-liquid contactor which offers new ways and solutions, particularly in the fields of reduction of air pollution, 1 humidification and dehumidification, biological processing, air-cooling, and particulate removal. 2 TBC are three-phase fluidized beds in which the liquid is sprayed downward over the bed and flows downward by gravity through an expanded bed of solid packing supported by the upflowing continuous gas phase. The highly turbulent motion of the particles creates fast interface renewal and a large interfacial area, which in turn enhances the mass and heat transfer rates. This contacting device has many advantages over a conventional contactor, namely, a higher capacity and a higher efficiency.
O'Neil et al. 3 demonstrated that the turbulent bed contactor can operate in one of the following two hydrodynamic regimes: i) fluidization without flooding, and ii) fluidization due to incipient flooding. These two operating modes, respectively: Type 1 TBC and Type 2 TBC, depend on the density of the packing.
The gas holdup is one of the most important hydrodynamic and design parameters for the TBC. 4,5 The information available in literature regarding gas holdup in TBC is relatively limited, and the most recent articles, [6][7][8][9][10][11] which use numerical simulation and CFD or even artificial intelligence, and which are devoted to the study of the hydrodynamics of the TBC, are only focused on pressure drops and bed expansion.
Gel'perin et al. 12 conducted the earliest studies of gas holdup using heavy particles and with grids of small open areas. A study carried by Balabekov et al. 13 showed that, at a constant gas velocity, the gas holdup was practically independent of liquid velocity, but when the gas velocity increased the gas holdup increased. The authors proposed an equation to determine the gas retention when liquid retention and expanded bed height are known. Kito et al. 14 showed that the gas holdup is practically independent of the viscosity of the liquid, the static bed height, and the packing density. For both operating regimes in TBC (types 1 and 2 TBC) and for partially and fully fluidized beds, empirical correlations for gas holdup were proposed by Vunjak-Novakovic et al. 15 The study conducted in a single TBC stage by Soundarajan and Krishnaiah 16 showed that the gas holdup is practically independent of the velocity of the liquid, free open area, particle density, and static bed height for the type 1 and type 2 operations.
For the gas-liquid-solid fluidized bed, various methods of measurement of the gas holdup were described by Fan. 17 Among the non-invasive techniques, the manometric method is one of the most used. It is more interesting to try to estimate the gas retention from experimental data that are easy to determine, such as pressure drop and bed expansion.
Generally, the data of pressure drop measured over the whole height of the column allows estimation of the gas holdup through the fluidized bed by manometric method, 18 i.e., those including pressure drops through the fluidized bed and those across the supporting grid, while assuming that the pressure drops across the supporting grid are negligible. 12 Nevertheless, this assumption is not always correct, especially for relatively high gas velocities. Bensebia et al. 18 reported that the pressure drops of the supporting grid can represent up to 30 % of the total pressure drops. It would thus be reasonable to assume that certain inconsistencies noted in the results of the determination of the gas holdup, estimated using the pressure loss profile, were caused mainly by the omission of the pressure losses caused by the pressure grid support.
The aim of this work was to (i) study the gas holdup characteristics of a turbulent bed contactor (Type 2-TBC) across large variation intervals for operating conditions, (ii) try to explain the discrepancies noted by some authors' work between the experimental and the estimated gas holdup, when the experimental method of their determination was based on the profiles of pressure drop. Furthermore, using the experimental data and statistical analysis, two correlations were developed to predict gas holdup in the type-2 TBC.

Experimental procedure and apparatus
The experimental setup ( Fig.1) consisted mainly of a Plexiglas column of 0.12 m inside diameter with a total height of 1.60 m. Water was admitted to the bed through a dis-tributor specially designed for this work, 18 which gave a uniform liquid distribution over the top of the bed. The air from a compressor passed through a pressure reducer before being injected into the gas distribution system at the bottom of the fluidization section. The liquid from the tray was pumped with a centrifugal pump to the liquid distributor, placed on top of the fluidizing section. The bed of particles consisted of polypropylene and hollow spheres that laid in the static state on a support grid, and placed at different openings to the inlet of the fluidizing section. The liquid and gas flow were measured by appropriated rotameters, and their rates were controlled by valves. The pressure drop through the column was measured using a U-tube water manometer.

Experimental conditions
The operating conditions are summarized in Table 1. Two packings (P I and P II ) were used. The operating conditions for each experimental system were described previously 18 for each experimental system. In this study, the gas flow rate (G) was varied (G) between 0 and 10 kg m − ² s −1 , and the liquid flow rates were: 4.57, 10.23, 15.84, 20.94, and 27.90 kg m −2 s −1 . The pressure drop was measured by U-manometer, and the dynamic bed height was measured visually. 18

Determination of gas holdup from column pressure drop measurement
For the fluidized bed section, the gas holdup in TBC can be expressed as: (1) Assuming that the fluidized bed volume is the sum of the volumes of the different phases: the following relationship among individual holdups can be written: This is the basic equation to determine the gas holdup (ε g ), if we can determine the solid holdup (ε p ) and the liquid holdup (ε l ). These two parameters can be linked to easily accessible experimental data: pressure drop through the column (−ΔP C ) and the bed expansion (H d /H st ). Writing the conservation of the mass of the solid at static and fluidized state, we obtain: which gives: To determine the gas retention with the manometric method using the experimental data on the pressure drop, it is suitable to write the general equation, which relates the liquid holdup (ε l ) to the pressure drop in the column. 18 The total pressure drop through the entire column (−ΔP c ), consists of the sum of two terms. 12,14,18,19 (7) where (−ΔP b ) represents the pressure drop in the fluidized bed due to the weight of the solid, liquid and gas phases, and (∑(−ΔP f )) is the sum of all the pressure drops other than those mentioned above, these are the pressure drops due to the flow of gas through the supporting grid, the spray section above the bed, the friction on the walls of the column, and the forces to overcome surface tension. 14,18,19,[22][23][24] According to Wozniak, 19 the pressure drop in a TBC can be determined by the following expression: When the density of the gas is negligible compared to that of the liquid and the packing, Eqs. (8) and (7) can be simplified to Eq. (9): When ε p is replaced by ε 0 (according to Eq. (6), which is more readily available, and considering Eqs. (4) and (5), we can write: The use of this equation requires knowledge of the fraction of the static bed voidage ε 0 , the dynamic bed height H d , and experimental data on total pressure drop (−ΔP c ). To use Eq. (10), it is necessary to know the pressure drops ((−ΔP f )), these are not always possible to neglect, especially for high superficial gas velocities; which is precisely the case for the TBC.

Determination of pressure drop ∑(−ΔP f )
Many authors 18,[20][21][22][23][24][25] have observed that these contributions could constitute an important part of the total pressure drop through the column. Based on their results, we can write: (11) where (−ΔP gr ), (−ΔP w ), and (−ΔP σ ), represent, respectively, the pressure drops due to the flow through the supporting grid, the gas friction against the walls of the column, and the gas-liquid surface tension.

Effect of gas and liquid velocities on gas holdup
As may be deduced from Fig. (4), the gas holdup was strongly linked to the gas velocity and practically independent of the velocity of the liquid. In addition, at low gas velocities, the gas holdup increased monotonically with higher values of the slope. These results were comparable to those mentioned by many authors. 12,25,37 As shown in Fig. (5), a slight variation of gas holdup with the superficial velocity of the liquid was observed at constant superficial gas velocity. This peculiarity was also noted by Mbua Egbe 39 , who explained it by the increase in drops of liquid and the turbulence that this generated, thus causing an additional retention of gas.
In general, the increase in the flow of liquid, in the presence of support grids with relatively small opening, causes an increase in the expansion of the bed, which generates an increase in gas holdup.

Effect of free open area of supporting grid on gas holdup
As shown in Fig. (6), the gas holdup decreased significantly when the free open area of the supporting grid increased, and this effect was accentuated when the superficial gas velocity increased.
The assertions of the authors, concerning the effect of the free opening of the support grid, present disparities; thus, some authors 13,26 asserted that the gas retention was independent from the opening of the free opening of the support grid, and others 13,15 reported dependence. This In Fig. (7), the effect of the free opening area of the supporting grid on the gas holdup was reported. This figure shows that when the liquid flow increased, the effect of supporting grid decreased. In conclusion, it may be suggested that, as the free area of the support grid decreased, the dynamic height of the fluidized bed increased, which increased the volume fraction of the gas and led to increased gas retention. This conclusion was confirmed by Eq. (10).

Effect of static bed height to column diameter ratio on gas holdup
As shown in Fig. (8), there was practically no effect of the static bed height to column diameter ratio (H st /D C ) on the gas holdup. These results were in accordance with those of other authors. 6,8

Effect of liquid to gas mass flux ratio (L/G) on the gas holdup
The L/G ratio was an important design parameter of liquid-gas contactors, used to estimate the efficiency of mass and heat transfer operations. 38,39 It was therefore essential to study its evolution. Fig. (9) shows that, when the gas velocity was maintained constant, the gas holdup increased with the L/G ratio and decreased very significantly when the gas velocity decreased.

Prediction of gas holdup for the turbulent contact absorber (Type II TBC)
The variables on which the gas holdup may depend were: gas velocity (u g ), liquid velocity (u l ), density of gas (ρ g ), density of liquid (ρ l ), density of solid (ρ p ), particle size (d p ), static bed height (H st ), expanded bed height (H d ), free open area of supporting grid (φ), viscosity of gas (μ g ), viscosity of the liquid (μ l ), gas-liquid surface tension (σ), and gravitational constant (g). Therefore, if a theoretical relation exists between the gas holdup (ε g ), and the physical characteristic, and flow variables of the system, then ε g may be written in the following form: (19) By considering the results of the analysis of the dependence of the gas holdup on the operating variables, and with the results of the dimensional analysis carried out, the adequate expression to estimate the gas holdup can be simplified to: (20) The functional relationship between gas holdup and the dimensionless groups identified in Eq. (20), leads to Eq. (21), which gives a mean absolute percentage error value (MAPE) of 6.10 %.
We have also developed a correlation that incorporates the ratio (L/G), which was an important design factor for gas-liquid contactors: (22) In Figs. (11) and (12) we have reported the experimental data of gas retention for all experimental points (1746 points) with the proposed correlations (Eqs. (21) and (22)).

Comparison of gas holdup results with correlations
There are many empirical and semi-empirical correlations to predict gas retention. For the type II TBC, the equations used are summarized in Table (2). The results of this comparison (for the system II 2 , as well as for all the other systems) for five different correlations (Eqs. (15)- (18)) are presented in Fig. 13, and show that there are three groups of correlations: i. correlations which overestimate the gas holdup compared to the experimental data (Eqs (16) and (17)), ii. correlations which moderately overestimate the predictions from a certain range of superficial gas velocity (Eq. (14) and (18)); iii. Eqs. (21) and (22) proposed in this work give the best results for predicting gas holdup. Eq. (15) of Koundarajan & Krishnaiah 16 also gives very satisfactory results for the prediction of our experimental data.

Models evaluation
An essential step in developing a predictive model was to evaluate the precision, accuracy, and reliability of the correlation deduced from this model. The precision of the predictive correlation was evaluated using the mean absolute percentage error (MAPE), the root mean square error (RMSE), the correlation coefficient (ρ XY ), and the explained variance (VEcv). The statistical indicators used were defined as follows: where ( ) This evaluation was carried out to determine the predictive performances of the correlations developed in this study and those developed by other authors. The main results are presented in Table 3. The correlations proposed in this work gave the best results. In addition, the equations (Eq. (15)) proposed by Soundarajan & Krishnaiah 16 and to a lesser extent, (Eq. (18)), proposed by Kito et al., 28 gave acceptable predictions.
To evaluate the reliability of the correlations considered in this work, we estimated the relative distribution of prediction results with errors (MAPE) less than 5, 10, 15, and 20 %. The results are shown in Table 4. For Eqs. (20) and (21) developed in this work, about 50 % of the results had an error of less than 5 %, and more than 98 % of predicted values had an error of less than 20 %. For the Eq. (15), proposed by Soundarajan and Krishnaiah, 16 85.17 % of the predictions had a MAPE of less than 20 %. However, the other tested correlations were inadequate for predicting the gas holdup.
The applicability of the correlations developed in this work model was tested by using it with experimental data other than what was used in its development. The use of the correlations proposed in this work (Eqs. (21) and (22)) to correlate the data of Balabekov et al. 13 , gave very satisfactory results (8.60 % for Eq. (21) and 13.34 % for Eq. (22)), as shown in Fig. 14. However, as a very limited amount of experimental data on gas holdup was available under the operating conditions of TBC-Type II, we were only able to correlate the results of Balabekov et al. 13 and those of Abukhalifeh et al., 40 which also gave acceptable results (12.80 % for Eq. (21) and 13.21 % Eq. (22)). However, for the latter   12 Eq. (16) Kito et al. 14 Eq. (17) Vunjak-Novakovic et al. 15 Eq. (18) Kito et al. 27 Eq. (15) Soundarajan and Krishnaiah 16 Eq  author, the density of the packing was 315 kg m −3 , which places the operating regime in Type 1-TBC.
The results obtained for the prediction of gas holdup using the proposed correlations from the different experimental systems of this study were very satisfying.

Conclusion
The experimental results determining the gas holdup in the fluidization regime of TBC-Type 2 showed that: i. The gas holdup strongly depended on gas velocity; ii. The gas holdup was practically independent of the liquid velocity. However, further analysis showed a slight variation; iii. The gas holdup was not practically affected by the static bed height ; iv. The gas holdup increased, obviously, with the reduction of the free area of the support grid, and this effect was more pronounced when the superficial gas velocity increased. Furthermore, the dependence of the gas holdup on the free area of the packing support grid (φ) was demonstrated and proved. v. The prediction of gas holdup using the proposed correlations from the different experimental systems of this study and the data of Balabekov et al. 7 were very satisfying. The correlation proposed by Soundarajan & Krishnaiah 10 gave the best prediction of gas holdup for our experimental results. This was the only correlation that took into account the free opening area of the packing grid, and this result once again confirmed the relationship between the gas holdup and the free area of the support grid.