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International Journal of Chemical Engineering

Volume 2014 (2014), Article ID 256840, 7 pages

http://dx.doi.org/10.1155/2014/256840

## Numerical Simulation and Analysis of CO_{2} Removal in a Polypropylene Hollow Fiber Membrane Contactor

Key Laboratory of Low-Grade Energy Utilization Technologies and Systems, Chongqing University, Chongqing 400044, China

Received 19 July 2013; Revised 1 December 2013; Accepted 20 December 2013; Published 30 January 2014

Academic Editor: Mahesh T. Dhotre

Copyright © 2014 Zhien Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This present study shows a comprehensive 2D numerical model for removal of CO_{2}
in a polypropylene (PP) hollow fiber membrane contactor (HFMC) using the computational fluid dynamics (CFD) method. Monoethanolamine (MEA) solution was used as the liquid absorbent in a nonwetting mode. The simulation results represented that higher liquid velocity and concentration and lower gas velocity and concentration led to higher percent of CO_{2} removal. The most proper parameters for CO_{2} removal were less than 1 mol m^{−3} gas concentration and 0.2 m s^{−1} gas flow rate, and for MEA the values were above 8 mol m^{−3} concentration and approximately 1 m s^{−1} liquid velocity. Furthermore, the model was validated with the experiment results. Therefore, the modeling results provided references to the selection of absorbents and operation parameters in the experimental study and pilot-scale applications.

#### 1. Introduction

In recent years, human-induced CO_{2} severely results in global climate change [1]. Especially the combustion of fossil fuels produces a large number of gas emissions. So capturing CO_{2} from flue gas in the postcombustion process will be an effective way to reduce CO_{2} emissions. Nowadays several methods of CO_{2} removal have been used like adsorption, chemical and physical absorption, and membrane separation. But conventional absorption methods have plenty of shortcomings such as flooding, foaming, channeling, air entrainment, and high capital and operational costs [2, 3]. In order to solve those problems, the membrane gas absorption which combines the merits of membrane separation and chemical absorption is gradually introduced by some researchers. In a hollow fiber membrane contactor, the absorbent always flows on one side while gas mixture flows in the other side. Meanwhile, a gas-liquid interface is formed at membrane pores, which are filled with gases. In the membrane absorption process, gas mixture initially diffuses through the gas-liquid interface, and then CO_{2} reacts with the liquid. After that the rich liquid is sent into a gas-liquid separator or other membrane contactors. Ultimately the lean solution flows back to the membrane contactor for recycling. Compared with conventional absorption technologies, the gas membrane separation provides faster mass transfer rate, good operational flexibility, and bigger gas-liquid contacting area. Therefore, it runs well without entrainment, flooding, foaming, and so forth. And this technique is considered to be a promising large-scale application of CO_{2} capture [4, 5].

Since Qi and Cussler [6] first investigated the hollow membrane contactor, a large number of scholars studied gas absorption in these devices in succession. Al-Marzouqi et al. [7] performed chemical absorption of CO_{2} from CO_{2}/CH_{4} gas mixture in a membrane contactor module using MEA and NaOH solutions. They developed a PVDF membrane contactor model on the conditions of complete and partial wetting. Meanwhile, they also used distilled water and MEA for absorbing CO_{2} from gas mixture in nonwetting mode [8]. A similar system was performed by Ghadiri et al. [9]. Zhang et al. [10] investigated the CO_{2} absorption from a CO_{2}/N_{2} gaseous mixture in a hollow fiber membrane using alkanolamine solutions including DEA and water. The gas-liquid contacting process was assumed at different membrane wetting degrees. Additionally, a membrane model of CO_{2} removal using potassium glycinate (PG) solution was built up by Eslami et al. [11]. They investigated the effects of PG concentration, liquid velocity, and liquid temperature on CO_{2} absorption performance in this work.

Some scholars experimented and simulated on the absorption of pure CO_{2}. Rajabzadeh et al. [12, 13] performed the capture of pure CO_{2} using MEA solutions in polyvinylidene fluoride (PVDF) HFMCs and compared the difference between PVDF and polytetrafluoroethylene (PTFE). Rongwong et al. [14] studied the CO_{2} removal using MEA solutions in membrane modules and made a comparison of theoretical results with experimental data. In the process of CO_{2} membrane absorption, PG and 2-amino-2-methyl-1-propanol (AMP) were used as a blended solvent in nonwetting mode [15]. It is well known that MEA is a high-effective absorbent of absorbing CO_{2}, which attracts many scholars’ interests [16, 17].

The aim of the current study is to develop and solve a comprehensive 2D model for CO_{2}-MEA system, which is based on the nonwetting mode in a HFMC. Assuming the axial and radial diffusion inside the tube side, membrane and the shell side are investigated in this model. The paper focuses on the effects of the gas concentration, gas velocity, liquid concentration, and liquid velocity. Yet still, there is no literature discussing the influence on gas concentration using a PP HFMC and comprehensive consideration of liquid and gas properties. And this is the first time to compare the experimental data with simulation results in such a CO_{2}-MEA system.

#### 2. Model Development

In this work, a steady state 2D mathematical model was developed to describe the absorption process of pure CO_{2} using aqueous MEA solutions. Figure 1 shows a schematic diagram of a HFMC material module used in the model development. In this case, the liquid absorbent flows into the tube side (at ), while CO_{2} flows in the shell side (at ) in a counter-current arrangement. Firstly, CO_{2} diffuses from the gas phase to the liquid phase through the membrane pores. And then they react with the absorbents in the tube.

##### 2.1. Tube Side Equations

The steady state continuity equation for the transport and reaction of one species in the tube side due to diffusion, reaction, and convection may be written as
in which is CO_{2} or absorbent. Meanwhile, , , , and denote the diffusion coefficient, the concentration, the reaction rate of species , and the axial velocity inside the fiber tube, respectively. Especially when using a chemical sorbent like MEA, could be approximated by
where the reaction rate constant under the conditions of 298 K and 1 atm can be estimated as follows [18]:

The axial velocity distribution inside the tube is assumed to follow the Newtonian laminar flow [19]: where and are the average gas velocity in the tube side and the inner tube radius, respectively.

Boundary conditions are given as
where , , and denote the CO_{2} solubility in the aqueous solution, the CO_{2} concentration inside the membrane, and the absorbent concentration in the fiber tube, respectively.

##### 2.2. Membrane Equations (Nonwetting Mode)

In a nonwetting mode CO_{2} only diffuses in the membrane. So the steady state continuity equation for transport of CO_{2} inside the membrane could be written as
where is the diffusion coefficient in the membrane.

Considering the influences of the porosity and tortuosity of the membrane on the absorption performance, may be written as where , , and are the effective diffusion coefficient inside the shell, the membrane porosity, and the membrane tortuosity, respectively.

Boundary conditions are given as
where is the concentration of CO_{2} in the shell side.

##### 2.3. Shell Side Equations

The steady state continuity equation for CO_{2} transport inside the shell where only CO_{2} flows could be defined as

According to Happel’s free surface theory, the axial velocity in the shell may be estimated as follows [20]: in which and are the gas average velocity inside the shell and the outer fiber radius, respectively. At the same time, the inner shell radius may be written as where represents the volume fraction of the void in the shell side and could be estimated by where and denote the number of fibers and the inner module radius, respectively.

Boundary conditions are given as

#### 3. Numerical Solution

To solve the above equations, the module dimensions and physical and chemical properties are provided in Table 1. The above dimensionless model equations associated with the tube, membrane, and shell sides with the appropriate boundary conditions and properties were solved using a COMSOL Multiphysics software, which uses the computational fluid dynamics (CFD) method for numerical solutions of model equations. For the finite element analysis, the solver of UMFPACK is applied owing to memory efficiency. And this method is combined with adaptive meshing and error control. This solver, an implicit time-stepping scheme, is well suited for solving stiff and nonstiff nonlinear boundary value problems.

#### 4. Results and Discussion

##### 4.1. Model Validation

In order to validate the developed model, Figure 2 shows a comparison between experimental data and modeling predictions at different values of the absorbent concentration. The membrane parameters used in the simulations are the same as those in experiments. The hydrophobic PP hollow fiber membranes were purchased from Hangzhou Kaihong Membrane Technology Co., Ltd. The CO_{2} cylinder was purchased from Chongqing Ruike Gas Co., Ltd. and the aqueous MEA solution was purchased from Chongqing Dongfanghuaba Co., Ltd. 4 mol m^{−3} MEA was used as the absorbent in a PP HFMC. It is obvious that the CO_{2} removal rate goes up with an increase of liquid absorbent concentration. Additionally, the absorption rates calculated by this model are in well agreement with experiment results.

##### 4.2. Concentration Distribution and Flux Vectors

When using 12 mol m^{−3} MEA aqueous solution as the solvent, the concentration distribution and flux vectors of MEA inside the tube are described in Figure 3. It is obvious that the concentration of MEA gradually decreases from the inlet () to the outlet (). At the middle of the tube side, the concentration of MEA is higher than the other parts. But the minimum of the CO_{2} concentration distribution and flux vectors is below 2 mol m^{−3} at the tube-membrane interface because of the chemical reaction between CO_{2} and MEA.

Figure 4 depicts the concentration gradient and the total flux vectors of CO_{2} in the hollow fiber membrane model. The gas flows from the inlet of the shell side (), while the absorbent flows in a countercurrent from the inlet of the tube side (). Initially, the concentration of CO_{2 }inside the fiber is assumed to be zero. Then CO_{2} diffuses and flows into the shell side through the membrane pores owing to the variation of the gas concentration.

Figure 5 shows the average CO_{2} concentration inside the membrane contactor module in the radial direction. It can be seen from the diagram that the values in the membrane and shell side are roughly the same around 2.75 mol m^{−3}. However, as there are effects of the diffusion and chemical reaction in the tube, the value rapidly drops to zero in the center of the membrane contactor.

In order to find out the optimal conditions, the removal efficiency is the most significant measurable indicator concerning the whole absorption process. The equation for calculating the percentage of CO_{2} removal is
where is the volumetric flow rate and is the average concentration of CO_{2} inside the shell in the axial direction. Because the change of volumetric velocity in the shell side could be neglected and is the CO_{2} concentration at the inlet of the shell, (14) can be estimated by

##### 4.3. Effect of MEA Concentration

A set of MEA solutions with different concentrations including 4, 6, 8, 10, and 12 mol m^{−3} are studied in this part. It can be clearly seen from Figure 6 that the outlet CO_{2} concentration gradually declines with the gradual rise in MEA consistence. As using 4 mol m^{−3} MEA the CO_{2} concentration represents approximately 1.5 mol m^{−3} CO_{2}, while the value is about 0.05 mol m^{−3} using 12 mol m^{−3} MEA solution. Meanwhile, Figure 2 shows an upward trend in the CO_{2}-removal percentage. Under the same conditions, it can be noticed that the percentage remains over 95 percent as the MEA concentration is higher than 10 mol m^{−3}. Hence, higher initial MEA concentration has higher removal percentage, which is beneficial to carbon capture.

##### 4.4. Effect of CO_{2} Concentration

The effect of different gas concentration on the CO_{2}-removal percent is described in Figure 7. With the augment in CO_{2} concentration, the removal percentage of the absorption process slightly declines, but the minimum still remains around 87%. Particularly lower CO_{2} concentration shows better absorption efficiency. So it can be seen from the graph that higher CO_{2} percent has a negligible influence on the total percentage of CO_{2} capture using MEA solution.

##### 4.5. Effect of Gas Velocity

Figure 8 shows the percent CO_{2} removal decreases by increasing the gas flow rates. It is noticed that lower gas velocity beneath 0.1 m s^{−1} performs well whatever the MEA concentration is. However, higher gas flow rate has an adverse performance in removal of CO_{2}, because the residence time reduces in the membrane contactor. And the reaction and the dissolution between liquid and gas are insufficient inside this module, which cuts down the concentration gradient of CO_{2} in the axial direction.

##### 4.6. Effect of Absorbent Velocity

Figure 9 indicates the change of removal efficiency caused by a function of absorbent velocity. It is evident that the fraction of CO_{2} removal goes up when increasing the solvent velocity. Meanwhile, it can be seen from the line chart that the liquid flow rate is a significant factor of absorption when the liquid concentration is comparatively low. The figure also reveals that the MEA velocity increases to above 1 m s^{−1}; however, the percent CO_{2} removal shows no changes. That is, the absorption is less dependent on the absorbent velocity at higher flow rates.

#### 5. Conclusions

This paper sets up a comprehensive 2D mathematical model for chemical absorption of pure CO_{2} under nonwetting condition in a PP hollow membrane contactor. Meanwhile, the effect of the concentration and velocity of both liquid and gas and radial and axial diffusion in a HFMC model were considered in this work. In the case of using MEA aqueous solution, the modeling results and experimental data showed that the removal efficiency rose with an increase of the velocity and concentration of MEA, which was similar to others’ work [21, 22]. However, as the liquid flow rate rose to 1 m s^{−1}, the percent of CO_{2} removal was nearly constant. On the other hand, higher velocity and concentration of gas led to the opposite effect on absorption performance. Amongst them, the most proper parameters were less than 1 mol m^{−3} gas concentration and 0.2 m s^{−1} gas flow rate. Thus, these works are helpful for the selection of absorbents and gas compositions before experiments through comparing the removal rates. The following work will focus on the impacts of membrane properties and operating conditions on the absorption performance.

#### Nomenclature

: | CO_{2} total mass transfer coefficient (mol/(m^{2} s kPa)) |

: | Total mass transfer coefficient (mol/(m^{2} s kPa)) |

: | Membrane mass transfer coefficient (mol/(m^{2} s kPa)) |

: | N_{2} total mass transfer coefficient (mol/(m^{2} s kPa)) |

: | Gas phase mass transfer coefficient (mol/(m^{2} s kPa)) |

: | Liquid phase mass transfer coefficient (mol/(m^{2} s kPa)) |

, : | Gas phase volume flow rate (m^{3}/h). |

#### Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

#### Acknowledgments

This work was supported by the Fundamental Research Funds for the Central Universities (no. CDJZR12140034) and China National Tobacco Corp Chongqing Branch (no. NY20130501010010).

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