#
Droplet Characteristics of Rotating Packed Bed in H_{2}S Absorption: A Computational Fluid Dynamics Analysis

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## Abstract

**:**

_{2}S selective absorption with N-methyldiethanolamine (MDEA) solution have seldom been fully investigated by experimental method. Therefore, a 3D Eulerian–Lagrangian approach has been established to investigate the droplet characteristics. The discrete phase model (DPM) is implemented to track the behavior of droplets, meanwhile the collision model and breakup model are employed to describe the coalescence and breakup of droplets. The simulation results indicate that rotating speed and radial position have a dominant impact on droplet velocity, average residence time and average diameter rather than initial droplet velocity. A short residence time of 0.039–0.085 s is credited in this study for faster mass transfer and reaction rate in RPB. The average droplet diameter decreases when the initial droplet velocity and rotating speed enhances. Restriction of minimum droplet diameter for it to be broken and an appropriate rotating speed have also been elaborated. Additional correlations on droplet velocity and diameter have been obtained mainly considering the rotating speed and radial position in RPB. This proposed formula leads to a much better understanding of droplet characteristics in RPB.

## 1. Introduction

_{2}S removal in natural gas.

_{2}S selective absorption were also presented.

## 2. Simulation

#### 2.1. Physical Model and Grid Refinement of RPB

#### 2.2. Mathematical Modelling

#### 2.2.1. Governing Equations

**Mass conservation equation**

**Momentum conservation equation**

#### 2.2.2. Turbulence Model

#### 2.2.3. Droplet Force Balance

**Drag force**

**Virtual mass force**

**Forces in rotating reference frames**

#### 2.2.4. Droplet Coalescence and Breakup Model

**The coalescence model**

**Taylor Analogy Breakup (TAB) model**

#### 2.3. Fluid Properties

_{2}S selective absorption. In this study, the gas mixture consists mainly of methane and the mass fraction of the aqueous solution is 35%. The properties of the gas and liquid used for the CFD simulations are shown in Table 2. The MDEA aqueous solution is assumed to operate at a constant temperature of 30 °C and 2 MPa, which are close to the real operation conditions for H

_{2}S selective absorption in RPB. Under these temperature and pressure conditions, the density and viscosity of the gas mixture are 15.99 kg/m

^{3}and 1.203 × 10

^{−5}kg/(m·s), respectively; the density and viscosity of the aqueous solution are and 1027 kg/m

^{3}and 1.203 × 10

^{−5}kg/(m·s), respectively.

#### 2.4. Solution Procedure

^{−5}. In addition, the maximum number of iterations for steady calculation is 4000 to achieve the steady state in RPB.

#### 2.5. Grid Independence

## 3. Results and Discussions

_{2}S selective absorption into MDEA solution in RPB.

#### 3.1. Droplet Velocity in RPB

#### 3.1.1. Effect of Initial Droplet Velocity on Droplet Velocity

#### 3.1.2. Effect of Rotating Speed on Droplet Velocity

#### 3.2. Average Residence Time Distribution in RPB

_{2}S while thermodynamically selective towards CO

_{2}[15]. According to the theory of the diffusion–reaction process for H

_{2}S selective absorption, the reaction and mass transfer on H

_{2}S are both instantaneously fast, while those process are restrained in CO

_{2}mass transfer into the liquid film. Therefore, average residence time of droplet is considered as a key parameter in the H

_{2}S selective absorption into MDEA process in RPB. A method to obtain the residence time distribution is applied by tracking droplets, and residence time distributions in RPB under various initial droplet velocities and rotating speeds are shown in Figure 9.

#### 3.2.1. Effect of Initial Droplet Velocity on Average Residence Time

#### 3.2.2. Effect of Rotating Speed on Average Residence Time

_{2}S selective absorption, enhancing rotating speed seems to be an optimal way. Lower residence time in RPB compared with that in conventional column is ascribed to intensification process under centrifugal force. The higher the droplet velocity is, the lower the residence time obtained will be. Therefore, a commonsense calculation can be proposed to describe the residence time in RPB, and that is the ratio of radial distance to droplet velocity, calculated by Equation (35).

_{2}S selective absorption and CO

_{2}partial removal must meet the requirements on commercial natural gas, and the energy consumption also needs to be reduced in MDEA solution regeneration process. Therefore, higher mass transfer efficiency and lower residence time in RPB raise various concerns in natural gas purification. In the quantitative description of Qian’s work [16], it only took about 2.0 × 10

^{−9}s for H

_{2}S to establish a steady concentration gradient while the process needed 1 s to complete for CO

_{2}. Thus, it can be highlighted from Figure 10, that the residence time can be only 0.039–0.085 s under a rotating speed of 900 rpm. Droplets go through the packing in a short residence time, especially with high initial droplet velocity and rotating speed.

#### 3.3. Droplet Diameter Distribution in RPB

#### 3.3.1. Effect of Initial Droplet Diameter on Droplet Diameter Distribution

#### 3.3.2. Effect of Initial Droplet Velocity and Rotating Speed on Droplet Diameter

#### 3.4. Principle of Processing Intensification in RPB

_{2}S selective absorption into MDEA solution.

## 4. Conclusions

_{2}S selective absorption into MDEA solution. Droplet characteristics such as droplet velocity, average residence time and average diameter in RPB have been analyzed by diagrams and correlations, which are compared with available experimental data in the literature [14,17]. The results show that the velocity increases with increasing rotating speed and radial position, but the opposite conclusion is made on the average residence time. Specially, in the end zone, a phenomenon called “end effect” in mass transfer intensification has been observed and can be illuminated by droplet back-mixing. A correlation on droplet velocity has been deduced in Equation (33) mainly associated with rotating speed and radial position rather than initial droplet velocity. Under the condition of 900 rpm, a short average residence time 0.039–0.085 s in RPB has been recommended for H

_{2}S selective absorption into MDEA solution. This is because the reaction and mass transfer rate of H

_{2}S are both instantaneously fast compared with CO

_{2}, thus a short average residence time allows for efficient selective absorption between H

_{2}S and CO

_{2}. When the initial droplet velocity and rotating speed increase, the average droplet diameter decreases inordinately. However, the initial droplet diameter has a restriction (1 mm) to be captured and broken by the packing size under the simulation conditions. Furthermore, conclusions are made that the rotating speed determines the minimum droplet diameter and that a packing length in the radial direction is needed to meet droplet breakup completely. In addition, a balance between shear force and surface tension on the droplet indicates an appropriate rotating speed. A correlation (Equation (36)) on droplet diameter is obtained considering the effect of rotating speed, radial position and fluid density.

_{2}S selective absorption into MDEA solution through increasing the relative velocity and collision between droplets and packing.

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclatures

CFD | Computational fluid dynamics |

HTU | Height of mass transfer unit |

IS-RPB | Impinging stream RPB |

RPB | Rotating packed bed |

RSR | Rotor-stator reactor |

SP-RPB | Split packing RPB |

TAB | Taylor analogy breakup |

Latin symbols | |

${C}_{D}$ | Drag coefficient |

$F$ | Aerodynamic force of droplet (N) |

$\overrightarrow{F}$ | External body force (N) |

${F}_{D}$ | Drag force (N) |

${F}_{r,x}$ | Force in rotating reference frame in x direction (N) |

${F}_{r,y}$ | Force in rotating reference frame in y direction (N) |

${F}_{m}$ | Virtual mass force (N) |

${F}_{x}$ | Additional acceleration term |

${G}_{b}$ | Influence of the buoyancy force |

${G}_{k}$ | Influence of the mean velocity gradients |

$P{r}_{t}$ | Turbulent Prandtl number for energy |

R | Radial position (m) |

$b$ | Actual collision parameter |

${b}_{crit}$ | Critical offset of collision |

${d}_{0}$ | Initial droplet diameter (mm) |

$\overline{d}$ | Arithmetic mean diameter of two droplet (m) |

$\overrightarrow{g}$ | Gravitational vector (9.8 m/s^{2}) |

$k$ | Turbulence kinetic energy |

$m$ | Mass of droplet (kg) |

${m}_{l}$ | Mass of large droplet (kg) |

${m}_{s}$ | Mass of small droplet (kg) |

$p$ | Static pressure (Pa) |

${r}_{l}$ | Radius of large droplet (m) |

${r}_{s}$ | Radius of small droplet (m) |

$u$ | Fluid velocity (m/s) |

${u}_{0}$ | Initial droplet velocity (m/s) |

${\overrightarrow{u}}_{l}$ | Velocity of large droplet (m/s) |

${u}_{p}$ | Droplet velocity (m/s) |

${\overrightarrow{u}}_{r}$ | Whirl velocity (m/s) |

${\overrightarrow{u}}_{s}$ | Velocity of small droplet (m/s) |

${\overrightarrow{v}}_{r}$ | Relative velocity (m/s) |

$x$ | Displacement of droplet (m) |

Greek symbols | |

$\rho $ | Fluid density (kg/m^{3}) |

${\rho}_{g}$ | Gas density (kg/m^{3}) |

${\rho}_{l}$ | Liquid density (kg/m^{3}) |

${\rho}_{p}$ | Droplet density (kg/m^{3}) |

$\omega $ | Rotating speed (rpm) |

$\overrightarrow{\omega}$ | Centrifugal acceleration (rad/s) |

${\mu}_{g}$ | Gas viscosity (mPa·s) |

${\mu}_{l}$ | Liquid viscosity (mPa·s) |

${\mu}_{eff}$ | Molecular viscosity (mPa·s) |

${\mu}_{t}$ | Turbulent viscosity (mPa·s) |

$\sigma $ | Liquid surface tension (N/m) |

$\epsilon $ | Dissipation rate |

Dimensionless groups | |

$\mathrm{Re}=\frac{\rho {d}_{p}\left|{u}_{p}-u\right|}{\mu}$ | Reynolds number |

$\mathrm{We}=\frac{{\rho}_{p}{\left|{\overrightarrow{u}}_{l}-{\overrightarrow{u}}_{s}\right|}^{2}\overline{d}}{\sigma}$ | Weber number |

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**Figure 2.**Three types of liquid pattern in RPB with a video camera, reproduced with permission from [3]. Copyright Elsevier, 1996.

**Figure 3.**(

**a**) 3D physical model diagram (1, gas inlet; 2, liquid inlet; 3, gas outlet; 4, foursquare obstacles; 5, liquid outlet; 6, end zone; 7, packing zone; 8, cavity zone). (

**b**) Grid refinement.

**Figure 6.**The velocity values and vectors under various initial droplet velocities and rotating speeds. (

**a**) ${u}_{0}$ = 0.5 m/s, $\omega $ = 300 rpm; (

**b**) ${u}_{0}$ = 0.5 m/s, $\omega $ = 600 rpm; (

**c**) ${u}_{0}$ = 0.5 m/s, $\omega $ = 900 rpm; (

**d**) ${u}_{0}$ = 1.5 m/s, $\omega $ = 600 rpm; (

**e**) ${u}_{0}$ = 2.5 m/s, $\omega $ = 600 rpm.

**Figure 9.**Residence time distribution in RPB under various initial droplet velocities and rotating speeds. (

**a**) ${u}_{0}$ = 0.5 m/s, $\omega $ = 300 rpm; (

**b**) ${u}_{0}$ = 0.5 m/s, $\omega $ = 600 rpm; (

**c**) ${u}_{0}$ = 0.5 m/s, $\omega $ = 900 rpm; (

**d**) ${u}_{0}$ = 1.5 m/s, $\omega $ = 600 rpm; (

**e**) ${u}_{0}$ = 2.5 m/s, $\omega $ = 600 rpm.

**Figure 13.**The droplet diameter distribution under different initial droplet diameters. (

**a**) ${d}_{0}$ = 1 mm; (

**b**) ${d}_{0}$ = 3 mm; (

**c**) ${d}_{0}$ = 5 mm.

**Figure 15.**Droplet diameter under various initial droplet velocities and rotating speeds. (

**a**) ${u}_{0}$ = 0.5 m/s, $\omega $ = 600 rpm; (

**b**) ${u}_{0}$ = 2.5 m/s, $\omega $ = 600 rpm; (

**c**) ${u}_{0}$ = 1.5 m/s, $\omega $ = 300 rpm; (

**d**) ${u}_{0}$ = 1.5 m/s, $\omega $ = 900 rpm.

**Figure 16.**Effect of initial droplet velocity and rotating speed on average droplet diameter. (

**a**) ${d}_{0}$ = 3 mm, $\omega $ = 600 rpm; (

**b**) ${d}_{0}$ = 3 mm, ${u}_{0}$ = 1.5 m/s.

Inner Diameter (mm) | Outer Diameter (mm) | Height (mm) | |
---|---|---|---|

RPB | 45 | 160 | 24 |

Packing | 48 | 92 | 20 |

CH_{4} | C_{2}H_{6} | C_{3}H_{8} | C_{4}H_{10} | C_{5}H_{12} | CO_{2} | H_{2}S | N_{2} | |
---|---|---|---|---|---|---|---|---|

Gas (mol %) | 85.71 | 2.30 | 0.73 | 0.47 | 0.24 | 4.25 | 5.04 | 1.27 |

Liquid (m %) | An MDEA aqueous solution with a mass fraction of 35% |

Rotating Speed (rpm) | 300 | 600 | 900 | 900 | 900 |
---|---|---|---|---|---|

Initial droplet velocity (m/s) | 0.5 | 0.5 | 0.5 | 1.5 | 2.5 |

Number of droplets | 58 | 111 | 183 | 360 | 391 |

Total residence time (s) | 7.7 | 12.7 | 15.5 | 17.2 | 15.0 |

Average residence time (s) | 0.132 | 0.114 | 0.085 | 0.048 | 0.039 |

Force Field | Droplet Diameter |
---|---|

Rotating packed bed | ${\mathrm{d}}_{p}=\frac{3{C}_{D}\rho {\left(u-{u}_{p}\right)}^{2}}{4\left({\rho}_{p}-\rho \right){\omega}^{2}R}$ |

deposition process under gravity | ${\mathrm{d}}_{p}=\frac{3{C}_{D}\rho {(u-{u}_{p})}^{2}}{4\left({\rho}_{P}-\rho \right)g}$ |

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**MDPI and ACS Style**

Wang, Z.; Wu, X.; Yang, T.; Wang, S.; Liu, Z.; Dan, X.
Droplet Characteristics of Rotating Packed Bed in H_{2}S Absorption: A Computational Fluid Dynamics Analysis. *Processes* **2019**, *7*, 724.
https://doi.org/10.3390/pr7100724

**AMA Style**

Wang Z, Wu X, Yang T, Wang S, Liu Z, Dan X.
Droplet Characteristics of Rotating Packed Bed in H_{2}S Absorption: A Computational Fluid Dynamics Analysis. *Processes*. 2019; 7(10):724.
https://doi.org/10.3390/pr7100724

**Chicago/Turabian Style**

Wang, Zhihong, Xuxiang Wu, Tao Yang, Shicheng Wang, Zhixi Liu, and Xiaodong Dan.
2019. "Droplet Characteristics of Rotating Packed Bed in H_{2}S Absorption: A Computational Fluid Dynamics Analysis" *Processes* 7, no. 10: 724.
https://doi.org/10.3390/pr7100724