Modeling and simulation of membrane separation process using computational fluid dynamics

Kambiz Tahvildari; Seyed Mohammad Reza Razavi; Hamed Tavakoli; Ashkan Mashayekhi; Reza Golmohammadzadeh

doi:10.1016/j.arabjc.2015.02.022

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Original article

9 (

); 72-78

doi:

10.1016/j.arabjc.2015.02.022

Modeling and simulation of membrane separation process using computational fluid dynamics

Kambiz Tahvildari^{^a}, Seyed Mohammad Reza Razavi^{^b}, Hamed Tavakoli^{^c,⁎}, Ashkan Mashayekhi^{^d}, Reza Golmohammadzadeh^{^d}

a Department of Chemical Engineering, Faculty of Engineering, Robat Karim Branch, Islamic Azad University, Tehran, Iran

b Young Researchers and Elite Club, Shahreza Branch, Islamic Azad University, Shahreza, Iran

c The Young Research Club of the Islamic Azad University, Nour Branch, Nour, Iran

d Department of Chemical Engineering, Faculty of Engineering, South Tehran Branch, Islamic Azad University, P.O. Box 11365-4435, Tehran, Iran

⁎Corresponding author. ha.tavakoli159@gmail.com (Hamed Tavakoli)

Received: 2013-4-14, Accepted: 2015-2-19, Published: 2015-01-01

Disclaimer:
This article was originally published by Elsevier and was migrated to Scientific Scholar after the change of Publisher.

Peer review under responsibility of King Saud University.

Abstract

Separation of CO₂ from air was simulated in this work. The considered process for removal of CO₂ was a hollow-fiber membrane contactor and an aqueous solution of 2-amino-2-metyl-1-propanol (AMP) as absorbent. The model was developed based on mass transfer as well as chemical reaction for CO₂ and solvent in the contactor. The equations of model were solved using finite element method. Simulation results were compared with experimental data, and good agreement was observed. The results revealed that increasing solvent velocity enhances removal of CO₂ in the hollow-fiber membrane contactor. Moreover, it was found that counter-current process mode is more favorable to achieve the highest separation efficiency.

Keywords

Membrane

Separation

Numerical simulation

Computational fluid dynamics

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Nomenclature

a: inner radius of fiber (m)
b: outer radius of fiber (m)
c: radius of free surface (m)
C: concentration (mol/m³)
C_gas: CO₂ concentration in the gas phase (mol/m³)
C_m: CO₂ concentration inside the membrane (mol/m³)
C₀: inlet concentration of CO₂ in the gas phase (mol/m³)
D: diffusion coefficient (m²/s)
D_CO2: diffusion coefficient of CO₂ (m²/s)
L: length of fiber (m)
m: partition coefficient
p: pressure (Pa)
T: temperature (K)
r: radial distance (m)
z: axial distance (m)

1 Introduction

Design and development of novel separation processes for reduction of emissions of carbon dioxide as the major greenhouse gas is of great importance. It has been reported that emission of CO₂ in atmosphere has adverse environmental effects such as global warming. Therefore, there is a definite need for development of efficient and novel separation processes for removal of CO₂ from gas streams. The main criteria for development of efficient separation processes for capture of carbon dioxide include consumption of low energy and high removal rate (Le Moullec et al., 2014; Razavi et al., 2013; Shirazian et al., 2012a ). Currently, gas absorption is the most commonly used method for removal of CO₂ from gas streams which is used extensively at industrial scale. The process involves selective absorption of CO₂ into chemical solvents such as aqueous solutions of NaOH or amines.

Gas absorption is carried out using conventional contactors such as columns and towers in which some usual technical problems are encountered in these contactors. The most common encountered problems in conventional contactors include flooding, foaming, entraining, and channeling (Shirazian and Ashrafizadeh, 2010; Shirazian et al., 2011, 2012b; Sohrabi et al., 2011a,b ). These problems detract efficiency of CO₂ capture using conventional separation processes. Therefore, development of alternative separation processes for removal of CO₂ from gas mixtures is of great importance.

Membrane technology can be used for CO₂ capture. CO₂ removal using membrane technology can be accomplished either by porous or by nonporous membranes. Nonporous membranes are usually polymeric which provide low permeation flux. Porous membranes can be used for removal of CO₂ from gas mixtures in which high permeation flux can be obtained that enhances the efficiency of process (Moghadassi et al., 2011; Sohrabi et al., 2011c,d ). One of important membrane processes which can be used for CO₂ capture is membrane contactor. Membrane contactors are porous membranes which are used to keep in contact two specific phases such as gas–liquid or liquid–liquid (Gabelman and Hwang, 1999; Mansourizadeh and Ismail, 2009).

Membrane contactors can be used for absorption of CO₂ in which the problems of conventional contactors are not observed in membrane contactors. The most common and useful classes of membrane contactors are hollow-fiber membrane contactors. These novel devices have attracted much attention recently in separation of gas and liquid mixtures (Fadaei et al., 2011a; Fasihi et al., 2012; Ghadiri et al., 2012, 2013a,b,c, 2014; Ghadiri and Shirazian, 2013; Marjani et al., 2012a,b; Marjani and Shirazian, 2010 ). The main characteristic of hollow-fiber membrane contactors is provision of high surface area per unit volume for separation and reaction. The latter can increase the efficiency of process drastically which in turn makes the process attractive for CO₂ capture. In gas–liquid hollow-fiber membrane contactors, a feed gas is passed through one side while the chemical solvent is passed either co-currently or counter-currently in other side of membrane module.

The main aim of the present work was to develop a mass transfer model for description of CO₂ removal from air in a hollow-fiber membrane contactor. Aqueous solution of 2-amino-2-metyl-1-propanol (AMP) is considered as chemical solvent in the simulations. Computational fluid dynamic technique is used for numerical simulation, and the results of simulations are then compared with the experimental data reported in the literature.

2 Theory

The separation process studied in this work involves a microporous hollow-fiber membrane contactor, a feed gas containing CO₂ and N₂, and an aqueous solution of 2-amino-2-metyl-1-propanol (AMP). The gas mixture flows through the shell side of membrane contactor while the AMP solution is passed through the tube side (see Fig. 1). A gas–liquid interface is formed at the inner side of fiber due to the hydrophobicity of membrane. The latter means that the aqueous solution cannot wet the membrane pores and the membrane pores are filled by the gas phase. The characteristics of the hollow-fiber contactor and operational conditions are the same as those reported in the literature (Kim and Yang, 2000).

Geometry of hollow-fiber considered in modeling and simulation.

A single hollow fiber is considered as model domain in the simulations. The geometry of model is illustrated in Fig. 1. It should be pointed out that the equations of model are derived in cylindrical coordinate while axial symmetry is assumed.

2.1

2.1 Equations of gas phase

In the gas phase, feed containing CO₂ and N₂ is contacted with the solvent. Concentration distribution of CO₂ in the gas phase is obtained by numerical solution of mass transfer equation:

(1)

D_{gas - Shell} [\frac{\partial^{2} C_{gas - Shell}}{\partial r^{2}} + \frac{1}{r} \frac{\partial C_{gas - Shell}}{\partial r} + \frac{\partial^{2} C_{gas - Shell}}{\partial z^{2}}] = V_{z - Shell} \frac{\partial C_{gas - Shell}}{\partial z}

where D, C, and V are diffusivity (m²/s), concentration (mol/m³), and velocity (m/s) respectively. Velocity distribution of gas phase is calculated by the Navier–Stokes equations:

(2)

\begin{matrix} - \nabla . η (\nabla V_{z - Shell} + {(\nabla V_{z - Shell})}^{T}) + ρ (V_{z - Shell} . \nabla) V_{z - Shell} + \nabla p = 0 \\ \nabla . V_{z - Shell} = 0 \end{matrix}

where

η

ρ

, and p denote viscosity (Pa s), density (kg/m³), and pressure (Pa) of gas mixture respectively.

Therefore, simultaneous solution of mass transfer and the Navier–Stokes equations should be carried out to obtain concentration distribution of CO₂ in the shell side of membrane contactor. Boundary conditions for the shell side are listed in Table 1.

Table 1 Boundary conditions for gas phase.

Position	Navier–Stokes	Mass transfer
z = L	V_z-shell = V₀	C_gas-shell = C_gas_,0
z = 0	p = p_atm	Convective flux
r = c	V_z-shell = 0	∂C_gas-shell/∂r = 0
r = b	V_z-shell = 0	C_gas-shell = C_gas-membrane

2.2

2.2 Equations of solvent phase

Concentration distribution of either CO₂ or absorbent (AMP) in the tube side of membrane contactor is obtained by solution of mass transfer equation as follows:

(3)

D_{i - tube} [\frac{\partial^{2} C_{i - tube}}{\partial r^{2}} + \frac{1}{r} \frac{\partial C_{i - tube}}{\partial r} + \frac{\partial^{2} C_{i - tube}}{\partial z^{2}}] = V_{z - tube} \frac{\partial C_{i - tube}}{\partial z} - R_{i}

where R refers to chemical reaction rate between CO₂ and AMP (mol/m³ s), and i refers to either AMP or CO₂. The velocity of solvent phase is estimated using parabolic laminar flow:

(4)

V_{z - tube} = 2 u [1 - {(\frac{r}{a})}^{2}]

where u is average velocity of solvent phase (m/s), and a is the inner radius of fiber (m).

Boundary conditions for mass transfer of CO₂ and AMP in the tube side are listed in Table 2. Moreover, the reaction mechanism and kinetics between CO₂ and AMP are taken from the literature (Kim and Yang, 2000).

Table 2 Boundary conditions for solvent phase.

Position	CO₂	AMP
z = 0	C_gas = 0	C_AMP-tube = C_M0
z = L	Convective flux	Convective flux
r = 0	$\frac{\partial C_{gas - Tube}}{\partial r} = 0$	$\frac{\partial C_{AMP - tube}}{\partial r} = 0$
r = a	C_gas-tube = C_gas-membrane × m	$\frac{\partial C_{AMP - tube}}{\partial r} = 0$

2.3

2.3 Equations of membrane

The mass transfer equation for CO₂ inside the membrane may be written as:

(5)

D_{gas - membrane} [\frac{\partial^{2} C_{gas - membrane}}{\partial r^{2}} + \frac{1}{r} \frac{\partial C_{gas - membrane}}{\partial r} + \frac{\partial^{2} C_{gas - membrane}}{\partial z^{2}}] = 0

The transport of CO₂ through the membrane pores is postulated to be due to diffusion. Boundary conditions for membrane are given as:

(6)

At r = a, C_{gas - membrane} = C_{gas - tube} / m

(7)

At r = b, C_{gas - membrane} = C_{gas - shell}

where m refers to partition coefficient for CO₂ between gas and liquid which the value is taken from the literature (Kim and Yang, 2000).

The derived equations as well as boundary conditions for all sections of membrane contactor were solved using COMSOL Multiphysics 3.5 package. Finite element is the basic solution procedure which COMSOL utilizes for numerical solution of the model equations. The accuracy of this numerical procedure for simulation of membrane separation processes has been proved in the literature (Razavi et al., 2013; Fadaei et al., 2011a; Fasihi et al., 2012; Ghadiri et al., 2012, 2013a,b,c, 2014; Ghadiri and Shirazian, 2013; Marjani et al., 2012b; Marjani and Shirazian, 2010; Fadaei et al., 2012; Fadaei et al., 2011b; Kohnehshahri et al., 2011; Marjani and Shirazian, 2011a,b,c,d,e, 2012a,b,c,d,e; Marjani et al., 2012c; Moradi et al., 2013; Pishnamazi et al., 2012; Ranjbar et al., 2013; Razavi et al., 2014; Rezakazemi et al., 2013a,b ).

3 Results and discussion

3.1

3.1 Validation of simulation results

The model findings for removal of CO₂ from N₂ using AMP as solvent in a hollow-fiber membrane contactor were compared with the experimental data reported in the literature to validate the model (Kim and Yang, 2000). The comparisons were conducted between simulated and experimental CO₂ removal at different values of solvent flow rates as indicated in Fig. 2. As it is seen from Fig. 2, enhancement of solvent flow rate (velocity) in membrane contactor results in increasing the removal rate of CO₂. The latter could be due to increasing driving force between gas and liquid phases with increasing solvent velocity. Moreover, Fig. 2 reveals that the model predictions are in good agreement with the experimental data at different values of solvent velocities in the module, and an average deviation of less than 10% was calculated between experimental and simulation results.

Comparisons between simulation results and experimental data.

3.2

3.2 Concentration of CO₂

Concentration distribution of CO₂ in the gas phase is the most important parameter for optimization of process. Decreasing CO₂ concentration in the gas phase determines the removal rate of CO₂ using the hollow-fiber membrane contactor. Streamline of CO₂ concentration in the gas phase is shown in Fig. 3. Streamlines show the path of CO₂ transport in the shell side. As it is seen, CO₂ is transferred toward the membrane due to concentration gradient in radial direction. However, a portion of CO₂ is also transferred to the outlet of shell side (axial direction). Fig. 4 also shows total mass transfer flux of CO₂ in all subdomains of membrane contactor. The mass transfer flux in the shell and tube sides is composed of diffusion and convection. The convection mechanism tends to transfer CO₂ to the outlet of contactor due to high contribution of velocity in z-direction. CO₂ is transferred toward the membrane by diffusional mass transfer which is responsible for removal of CO₂.

Streamline of CO2 concentration in the gas phase.

Distribution of total mass transfer flux of CO2 in the membrane contactor.

3.3

3.3 Effect of flow pattern on CO₂ absorption

In the previous section the direction of both streams in simulation was considered to be counter-current, and it was evaluated according to different parameters. In this section the influence of co-current mode on the percent of CO₂ removal rate has been studied (see Table 3) to explore the possibility of co-current operation and compare it with counter-current mode. Comparing these results reveals that the percentage of CO₂ removal from N₂ in membrane module when the direction of streams is counter-current is more than the co-current mode. The latter could be attributed to the higher concentration gradient between two phases in the case of counter-current mode.

Table 3 Comparison of CO₂ removal results between co-current flow and counter-current flow modes.

Removal of CO₂ (%)		Inlet conditions
With co-current flow	With counter-current flow	CO₂ concentration (vol.%)	Liquid flow rate (ml/min)	Gas flow rate (ml/min)
38	73.2	40	25.8	170
43.3	78.1	40	50	170
46.5	81	40	75	170
49.9	83.4	40	92.8	170

3.4

3.4 Influence of AMP concentration on CO₂ removal

Fig. 5 illustrates the influence of AMP concentration on CO₂ removal. As it can be seen from Fig. 5, enhancement of absorbent content in the solvent phase increases CO₂ removal in membrane module which is favorable in gas absorption. It should be noted that because the reaction of absorbent and carbon dioxide is assumed to be elementary, it is proportional to concentration of both absorbent and CO₂ in the membrane contactor. Increasing absorbent concentration in the liquid phase enhances reaction rate between CO₂ and absorbent. The latter would result in reduction of CO₂ outlet concentration in the gas phase. The results also reveal that AMP concentration has considerable effect on CO₂ removal from gas mixtures.

Removal of CO2 as a function of amine concentration.

3.5

3.5 Mass transfer flux of AMP

Absorbent concentration in the tube side of membrane contactor is illustrated as contours in Fig. 6. It is seen that the concentration of AMP decreases drastically along the tube side of membrane contactor. The latter could be due to high reaction rate between CO₂ and AMP which results in high consumption of AMP in the process. This can increase the efficiency of process, but increases the cost of separation by consumption of absorbent. Total mass transfer flux of AMP in the tube side is also shown in Fig. 7. The highest mass transfer flux of AMP can be seen at the region near the inlet of tube. As AMP flows in the tube side, its mass transfer flux decreases due to chemical reaction with CO₂.

Distribution of total mass transfer flux of absorbent in the liquid phase.

4 Conclusions

Separation of CO₂ from N₂ as model of air in a hollow-fiber membrane module was studied theoretically in this work. The simulations were based on numerical solution of mass transfer as well as the Navier–Stokes equations for species in the membrane module. FEM analysis was used to solve the governing equations. Amine (AMP) aqueous solution was considered as chemical solvent in the simulations. The simulation results were validated thorough comparing with the experimental data for absorption of CO₂ in AMP aqueous solution. The simulation results were in good agreement with the experimental data for different liquid flow rates. The simulation results for absorption of CO₂ in AMP aqueous solution revealed that CO₂ removal rate increases with enhancement of solvent velocity and AMP concentration in the module. Moreover, the simulation results indicated that the CO₂ absorption in the membrane contactor with counter-current flow mode is higher than co-current mode.

Acknowledgment

The authors are grateful to the research council of Islamic Azad University, Robat Karim Branch for the financial support of this work.

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Introduction

Theory

Equations of gas phase
Equations of solvent phase
Equations of membrane

Results and discussion

Validation of simulation results
Concentration of CO2
Effect of flow pattern on CO2 absorption
Influence of AMP concentration on CO2 removal
Mass transfer flux of AMP

Conclusions

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[1] Fadaei F., Shirazian S., Ashrafizadeh S.N., . Mass transfer simulation of solvent extraction in hollow-fiber membrane contactors. Desalination. 2011;275:126-132.
[Google Scholar]

[2] Fadaei F., Shirazian S., Ashrafizadeh S.N., . Mass transfer modeling of ion transport through nanoporous media. Desalination. 2011;281:325-333.
[Google Scholar]

[3] Fadaei F., Hoshyargar V., Shirazian S., Ashrafizadeh S.N., . Mass transfer simulation of ion separation by nanofiltration considering electrical and dielectrical effects. Desalination. 2012;284:316-323.
[Google Scholar]

[4] Fasihi M., Shirazian S., Marjani A., Rezakazemi M., . Computational fluid dynamics simulation of transport phenomena in ceramic membranes for SO₂ separation. Math. Comput. Model.. 2012;56:278-286.
[Google Scholar]

[5] Gabelman A., Hwang S.-T., . Hollow fiber membrane contactors. J. Membr. Sci.. 1999;159:61-106.
[Google Scholar]

[6] Ghadiri M., Shirazian S., . Computational simulation of mass transfer in extraction of alkali metals by means of nanoporous membrane extractors. Chem. Eng. Process.. 2013;69:57-62.
[Google Scholar]

[7] Ghadiri M., Shirazian S., Ashrafizadeh S.N., . Mass transfer simulation of gold extraction in membrane extractors. Chem. Eng. Technol.. 2012;35:2177-2182.
[Google Scholar]

[8] Ghadiri M., Fakhri S., Shirazian S., . Modeling and CFD simulation of water desalination using nanoporous membrane contactors. Ind. Eng. Chem. Res.. 2013;52:3490-3498.
[Google Scholar]

[9] Ghadiri M., Ghasemi Darehnaei M., Sabbaghian S., Shirazian S., . Computational simulation for transport of priority organic pollutants through nanoporous membranes. Chem. Eng. Technol.. 2013;36:507-512.
[Google Scholar]

[10] Ghadiri M., Marjani A., Shirazian S., . Mathematical modeling and simulation of CO₂ stripping from monoethanolamine solution using nano porous membrane contactors. Int. J. Greenhouse Gas Control. 2013;13:1-8.
[Google Scholar]

[11] Ghadiri M., Fakhri S., Shirazian S., . Modeling of water transport through nanopores of membranes in direct–contact membrane distillation process. Polym. Eng. Sci.. 2014;54:660-666.
[Google Scholar]

[12] Kim Y.-S., Yang S.-M., . Absorption of carbon dioxide through hollow fiber membranes using various aqueous absorbents. Sep. Purif. Technol.. 2000;21:101-109.
[Google Scholar]

[13] Kohnehshahri R.K., Salimi M., Mohaddecy S.R.S., Shirazian S., . Modeling and numerical simulation of catalytic reforming reactors. Orient. J. Chem.. 2011;27:1351-1355.
[Google Scholar]

[14] Le Moullec Y., Neveux T., Al Azki A., Chikukwa A., Hoff K.A., . Process modifications for solvent-based post-combustion CO2 capture. Int. J. Greenhouse Gas Control. 2014;31:96-112.
[Google Scholar]

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Modeling and simulation of membrane separation process using computational fluid dynamics

Abstract

Keywords

Membrane

Separation

Numerical simulation

Computational fluid dynamics

Nomenclature

1 Introduction

2 Theory

2.1 Equations of gas phase

2.2 Equations of solvent phase

2.3 Equations of membrane

3 Results and discussion

3.1 Validation of simulation results

3.2 Concentration of CO2

3.3 Effect of flow pattern on CO2 absorption

3.4 Influence of AMP concentration on CO2 removal

3.5 Mass transfer flux of AMP

4 Conclusions

Acknowledgment

References

Suggested read for related articles:

3.2 Concentration of CO₂

3.3 Effect of flow pattern on CO₂ absorption

3.4 Influence of AMP concentration on CO₂ removal