Numerical Simulation and Analysis of CO2 Removal in a Polypropylene Hollow Fiber Membrane Contactor

This present study shows a comprehensive 2D numerical model for removal of CO 2 in a polypropylene (PP) hollow fibermembrane 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 1molm gas concentration and 0.2m s gas flow rate, and for MEA the values were above 8molm concentration and approximately 1m s 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.


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 gasliquid 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 gasliquid contacting process was assumed at different membrane wetting degrees.Additionally, a membrane model of CO 2 removal using potassium glycinate (PG) solution was built 2 International Journal of Chemical Engineering 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 higheffective 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.

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  = 0), 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.

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,  -tube ,  -tube ,   , and  -tube 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,  CO 2 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  tube and  1 are the average gas velocity in the tube side and the inner tube radius, respectively.Boundary conditions are given as at  = 0,  -tube  = 0 (symmetry) , where ,  CO 2 -membrane , and  absorbent-tube, initial 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.

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  CO 2 -membrane is the diffusion coefficient in the membrane.
Considering the influences of the porosity and tortuosity of the membrane on the absorption performance,  CO 2 -membrane may be written as where  CO 2 -shell , , and  are the effective diffusion coefficient inside the shell, the membrane porosity, and the membrane tortuosity, respectively.Boundary conditions are given as where  CO 2 -shell is the concentration of CO 2 in the shell side.

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  -shell in the shell may be estimated as follows [20]: in which  shell and  2 are the gas average velocity inside the shell and the outer fiber radius, respectively.At the same time, the inner shell radius  3 may be written as where  represents the volume fraction of the void in the shell side and could be estimated by

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.

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.

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 ( = 0) 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 ( = 0).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  0 is the CO 2 concentration at the inlet of the shell, ( 14) can be estimated by  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.

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.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.

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.Liquid phase mass transfer coefficient (mol/(m 2 s kPa))  in ,  out : Gas phase volume flow rate (m 3 /h).

3 Figure 1 :
Figure 1: A schematic diagram of a hollow fiber membrane model.

Table 1 :
Dimensions and properties of the membrane contactor module.
where  and  denote the number of fibers and the inner module radius, respectively.Boundary conditions are given as at  =  2 ,  CO 2 -shell =  CO 2 -membrane , at  = ,  CO 2 -shell =  0 (inlet) .