# The Effects of the Properties of Gases on the Design of Bubble Columns Equipped with a Fine Pore Sparger

^{1}

^{2}

^{*}

## Abstract

**:**

_{2}, He) that cover a wide range of physical property values. The purpose is to investigate the validity of the design equations, which were proposed in our previous work and can predict with reasonable accuracy the transition point from homogeneous to heterogeneous regime as well as the gas holdup and the mean Sauter diameter at the homogeneous regime. Although, the correlations were checked with data obtained using different geometrical configurations and several Newtonian and non-Newtonian liquids, as well as the addition of surfactants, the gas phase was always atmospheric air. The new experiments revealed that only the use of low-density gas (He) has a measurable effect on bubble column performance. More precisely, when the low-density gas (He) is employed, the transition point shifts to higher gas flow rates and the gas holdup decreases, a fact attributed to the lower momentum force exerted by the gas. In view of the new data, the proposed correlations have been slightly modified to include the effect of gas phase properties and it is found that they can predict the aforementioned quantities with an accuracy of ±15%. It has been also proved that computational fluid dynamics (CFD) simulations are an accurate means for assessing the flow characteristics inside a bubble column.

## 1. Introduction

_{2}) and in this case the different gas density affects the amplitude of the forces that act on an under-formation bubble.

## 2. Experimental Set-Up and Procedure

^{®}1000S, DEL Imaging, Cheshire, CT, USA) for bubble size and gas holdup measurements and a computer for acquiring and processing the data. A Plexiglas

^{®}rectangular box, filled with the same fluid as the one used at the corresponding experiment was placed around the bubble column to eliminate image distortion caused by light refraction.

^{®}, Farmington, CT, USA) with a nominal pore size of 40 μm or 100 μm, that covers the whole bottom plate. The effect of the sparger to column diameter ratio on the bubble column performance has been investigated and discussed in a previous paper [9]. To ensure that the gas phase is evenly distributed over the whole sparger area, the gas phase was injected through a 1 cm nozzle to a vessel of 35 cm height placed beneath the bubble column, following the design proposed in a previous paper [9]. A recording rate of 125 frames per second (fps) was used for the measurement of gas holdup, while a speed of 500 fps was selected for measuring the bubble size.

_{2}and He, covering a sufficiently wide range of density values (Table 4) were individually employed. All the experiments were performed with no liquid throughput, at atmospheric pressure and ambient temperature conditions (i.e., around 20 °C).

_{G}) is estimated by calculating the bed expansion as follows:

_{ο}and Η is the liquid level before and after gas injection respectively, ΔΗ is the liquid level difference and n is the number of recurrent measurements for each gas flow rate (in this case n = 50). In all our experiments the estimated maximum uncertainty of the measurements is less than 15%.

_{32}), was calculated:

_{bi}and n

_{i}are the diameter and the number of the bubbles of size class i respectively and N is the number of classes used for the distribution. The minimum number of classes required for the construction of the size distributions, $k$ was estimated by the Sturges’ rule:

_{32}for each experiment.

## 3. Results and Discussion

#### 3.1. Bubble Size Distribution

_{c}= 9 cm), for all gases studied and for a constant U

_{GS}value. As expected [4], the distributions are log-normal while regardless of the liquid phase only the low density He gas exhibits an observable effect on the bubble distribution curve. This can be attributed to the considerably lower momentum force exerted by the low density He gas (Table 1). However, the value of mean Sauter diameter is not considerably affected by the type of gas but is mainly affected by the type of liquid phase employed (Table 5).

_{32}) based on dimensionless numbers was proposed. The same correlation can be used for predicting the mean Sauter diameter when different gases are employed provided that the constants of the correlation are suitably adjusted (Equation (4)).

_{32}values with reasonable accuracy (i.e., ±15%) for all the gases employed.

#### 3.2. Regime Transition

_{G}is the gas holdup and U

_{GS}is the superficial gas velocity defined as:

_{G}is the gas flow rate and A the column cross section. When the drift flux is plotted versus the gas holdup, the change in the slope of the curve indicates the transition from homogeneous to heterogeneous regime [12].

_{GS}values.

_{trans}is the Froude number at the transition point and Eo the Eotvos number based on d

_{32}:

_{GS,trans}values are in very good agreement, i.e., better than 15%, with the corresponding experimental data. The proposed correlation is suitable for predicting the transition point from homogeneous to heterogeneous regime.

#### 3.3. Gas Holdup

_{2}. This behavior is attributed to the fact that, the lower density gas exerts a lower momentum force to an under-formation bubble (Table 1). This observation agrees with other researchers [22,23] who also reported that gases of higher density produce higher gas holdup values, attributing this behavior on phenomena occurring during bubbles formation on the sparger. However, it is worth noticing that, even though the density of CO

_{2}is 50% higher than that of atmospheric air, for the lower gas superficial velocities both air and CO

_{2}exhibit almost the same behavior and only when the density decreases by more than 80% (i.e., for He)) a noticeable change is observed (Figure 7).

_{G}, was proposed based on dimensionless numbers. The equation has the general form:

_{c}, d

_{s}, are the column and the sparger diameter, while d

_{p}is the mean pore size of the sparger material. The values of constants c

_{1}to c

_{7}depend on the of liquid phase. It was also proved [8,9,10,13] that the proposed correlations can predict hold up with reasonable accuracy, i.e., better than 15%.

_{G}prediction, the type of gas is not taken into account although the gas momentum affects bubble evolution (Table 1). From Figure 7, where the effect of gas type is presented, it is apparent that only the very low density gas He has has a measurable effect on gas holdup value. In case that the gas phase is other than air, it is necessary to introduce a term that incorporates the properties of the gas phase.

_{G}defined as:

_{G}values predicted by Equation (19) are in very good agreement (±15%) with the corresponding experimental data.

## 4. Numerical Simulations

## 5. Concluding Remarks

_{2}exhibit almost the same behavior, while the low density He shows a measurable effect on bubble column design quantities. This can be attributed to the fact that the low density He gas exhibits a lower momentum force. Thus, the previously proposed correlations for predicting the transition point from the homogeneous to the heterogeneous regime, the gas holdup and the Sauter mean diameter are slightly modified to include the effect of the type of gas employed. The new correlations can predict the aforementioned quantities with reasonable accuracy (better than 15%). Relevant CFD simulations were also performed and validated with the available experiments results in terms of gas holdup. Thus, it has been demonstrated that CFD can be used for predicting the flow characteristics that are generally difficult to be experimentally measured, but are essential during bubble column design, as for example the shear stress or the velocity distribution.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclature

A | column cross section, m^{2} |

d_{b} | bubble diameter, m |

d_{32} | Sauter mean diameter, m |

d_{c} | column diameter, m |

d_{p} | pore diameter, m |

d_{S} | sparger diameter, m |

F_{b} | buoyancy force, N |

F_{d} | drag force, N |

F_{g} | gas momentum force, N |

F_{i} | inertial force, N |

F_{p} | pressure force, N |

F_{σ} | surface tension force, N |

g | acceleration of gravity, m/s^{2} |

H_{C} | column height, m |

j | drift flux, m/s |

Q_{G} | gas flow rate, m^{3}/s |

U_{GS} | superficial gas velocity, m/s |

W_{g} | bubble formation velocity, m/s |

Greek letters | |

ε_{G} | average gas holdup, dimensionless |

μ_{G} | gas phase viscosity Pa s |

μ_{L} | liquid phase viscosity, Pa s |

ρ_{G} | gas density, Kg/m^{3} |

ρ_{L} | liquid density, Kg/m^{3} |

σ_{L} | surface tension, mN/m |

Dimensionless quantities | |

Ar | Archimedes number |

Eo | Eotvos number |

Fr | Froude number |

Fr_{tans} | Froude number at transition point |

k | minimum number of classes |

N | number of classes used for the distributions |

n_{i} | number of bubbles of size class i |

Re_{L} | Reynolds number based on liquid properties |

Re_{G} | Reynolds number based on gas properties |

S | sample size |

We | Weber number |

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**Figure 1.**Forces acting on an under-formation bubble (Table 1).

**Figure 3.**Effect of type of gas on bubble size distribution (U

_{GS}= 0.01 m/s): (

**a**) water; (

**b**) glycerin sol.

**Figure 4.**Comparison of the Sauter mean diameter prediction with experimental data (Table 5) (U

_{GS}= 0.01 m/s, d

_{p}= 40 μm, d

_{c}= 9 cm).

**Figure 9.**Bed expansion (ΔΗ) for different time snapshots: t = 0, 0.8, 1.6, 2.4 and 3.2 s (air-water, U

_{GS}= 0.2 m/s, d

_{p}= 40 μm, d

_{c}= 9 cm).

**Figure 10.**Typical CFD results at the middle plane of the bubble column: (

**a**) Shear stress distribution; (

**b**) Streamlines colored with the liquid phase velocity (t = 5.8 s, U

_{GS}= 0.2 m/s, air-water, d

_{p}= 40 μm, d

_{c}= 9 cm).

Upward Forces | Downward Forces |
---|---|

Buoyancy: ${F}_{b}=\left({\rho}_{L}-{\rho}_{G}\right)g{V}_{b}$ | Drag: ${F}_{d}=\frac{1}{2}{\rho}_{L}{W}^{2}\frac{\pi {d}_{b}^{2}}{4}{C}_{D}$ |

Gas momentum: ${F}_{G}=\frac{\pi}{4}{d}_{p}^{2}{\rho}_{G}{W}_{G}^{2}$ | Inertial: ${F}_{i}=\left({a}_{i}+\frac{{\rho}_{G}}{{\rho}_{L}}\right){\rho}_{L}{V}_{b}{\gamma}_{b}$ |

Pressure: ${F}_{p}=\frac{\pi}{4}{d}_{p}^{2}\left({P}_{G}-{P}_{L}\right)$ | Surface tension: ${F}_{\sigma}=\pi {d}_{p}\sigma $ |

d_{c} (cm) | d_{S} (cm) | d_{p} (μm) | d_{p} min (μm) | d_{p} max (μm) |
---|---|---|---|---|

5 | 5 | 100 | 5 | 500 |

9 | 9 | 40 | 3 | 70 |

Liquid | ρ_{L} (Kg/m^{3}) | μ_{L} (mPa·s) | σ_{L} (mN/m) |
---|---|---|---|

water | 1000 | 1.0 | 72 |

aqueous glycerin 40% v/v | 1117 | 5.8 | 64 |

Gas | ρ_{G} (Kg/m^{3}) | μ_{G} (10^{−5} Pa·s) |
---|---|---|

Air | 1.39 | 1.8 |

CO_{2} | 2.11 | 1.5 |

He | 0.19 | 2.0 |

Liquid | Gas | d_{32} (mm) |
---|---|---|

water | Air | 1.42 |

He | 1.50 | |

CO_{2} | 1.40 | |

aqueous glycerin solution 40% v/v | Air | 1.16 |

He | 1.24 | |

CO_{2} | 1.19 |

C_{1} | C_{2} | C_{3} | C_{4} | C_{5} | C_{6} | C_{7} | C_{8} |
---|---|---|---|---|---|---|---|

0.020 | 0.300 | 0.015 | 3.50 | 0.043 | 1.10 | 2.62 | 1.18 |

Liquid Phase | Gas Phase | U_{GS}, m/s | ε_{G exp}, % | ε_{G calc}, % | Deviation % |
---|---|---|---|---|---|

water | He | 0.02 | 5.9 | 5.6 | 5.0 |

0.03 | 6.6 | 6.4 | 2.6 | ||

water | air | 0.02 | 6.5 | 6.2 | 4.5 |

0.03 | 7.9 | 8.0 | 0.7 | ||

aqueous glycerin 40% v/v | He | 0.02 | 8.4 | 8.0 | 5.0 |

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**MDPI and ACS Style**

Kanaris, A.G.; Pavlidis, T.I.; Chatzidafni, A.P.; Mouza, A.A.
The Effects of the Properties of Gases on the Design of Bubble Columns Equipped with a Fine Pore Sparger. *ChemEngineering* **2018**, *2*, 11.
https://doi.org/10.3390/chemengineering2010011

**AMA Style**

Kanaris AG, Pavlidis TI, Chatzidafni AP, Mouza AA.
The Effects of the Properties of Gases on the Design of Bubble Columns Equipped with a Fine Pore Sparger. *ChemEngineering*. 2018; 2(1):11.
https://doi.org/10.3390/chemengineering2010011

**Chicago/Turabian Style**

Kanaris, Athanasios G., Theodosios I. Pavlidis, Ariadni P. Chatzidafni, and Aikaterini A. Mouza.
2018. "The Effects of the Properties of Gases on the Design of Bubble Columns Equipped with a Fine Pore Sparger" *ChemEngineering* 2, no. 1: 11.
https://doi.org/10.3390/chemengineering2010011