Computational simulation of CO₂ removal from gas mixtures by chemical absorbents in porous membranes

Abstract

In this study chemical absorption of CO₂ from a N₂/CO₂ gas mixture in tetramethylammonium glycinate ([N₁₁₁₁][Gly]) solution using hollow-fiber membrane contactors by employing the CFD (computational fluid dynamics) method was investigated. A two dimensional mathematical model was developed to describe diffusion in axial and radial directions of the HFMC (hollow-fiber membrane contactor). Also, the model gives an account of convection in the tube and the shell sides with chemical reaction between CO₂ and the absorbent. Results of simulation showed good agreement with experimental data which reveals the validity of the model. CO₂ absorption from the gas mixture increases as the flow rate and the concentration of the absorbent goes up. On the other hand, increase of gas flow rate decreases removal of CO₂. The proposed model can predict CO₂ capture from gas mixtures in HFMCs.

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1. Introduction

Throughout the recent years, development of industrial processes has increased the content of acid gases such as CO₂, H₂S and other sulphuric compounds in the atmosphere. These compounds are released into the atmosphere from burning of fossil fuels, natural gas, and industrial activities. Since carbon dioxide constitutes about 80% of greenhouse gases in the atmosphere, CO₂ capture is of great importance in this regard.¹ Also, different chemical industries always take into account H₂S and CO₂ removal from gas mixtures like natural gas since CO₂ reduces efficiency of natural gas energy and H₂S is categorized as a toxic and corrosive gas.²

Due to necessity of CO₂ capture in industries, different devices for this purpose are applied. Packed towers, spray towers, and bubble columns are typical examples of convectional industrial equipment for absorption of carbon dioxide, yet it is difficult to estimate gas–liquid mass transfer surface exactly in them and there is limited range of gas and liquid flow rates due to operational problems.

Nowadays, CO₂ removal by using gas–liquid membrane contactors has aroused great interest. A number of researchers have investigated the efficiency of membrane systems for absorption of carbon dioxide as a suitable alternative to conventional methods.^3–12 In this kind of contactor, membrane plays the role of a physical barrier between gas and liquid phases without having any considerable effect on separation selectivity.¹³ Gas–liquid membrane contactors have a high surface area per unit of contactor and due to the absence of interpenetration of two phases, they don't suffer from operational problems occurring in conventional equipment such as flooding, weeping, loading, entrainment and foaming. Other advantages of membrane systems include: smaller size, easier scaling up and scaling down, and known surface of gas–liquid interface.¹⁴ Advantages and disadvantages of membranes have been studied by Gabelman and Hwang in more details.¹⁵

Hollow-fiber membrane contactors (HFMCs) are being studied more than other membrane geometries because of their higher surface/volume ratio.¹³ In gas–liquid absorption by HFMCs, the driving force is concentration gradient whereas the driving force is pressure gradient for systems which employ these contactors for filtration (like microfiltration). In recent years, a large number of researchers have tried to improve performance of membrane contactors for removal of CO₂ and H₂S from gas mixtures. Different parameters such as variation of liquid absorbents and their concentration, membrane materials, membrane modules, and gas and liquid flow rates were investigated in their studies.^{5–11,16–41}

Membranes could provide thermal and chemical stability, and fouling and plugging problems should be kept to minimum. Furthermore, on the basis of chosen liquid absorbent, wettability should be considered for better understanding the mechanism of separation. Porous membranes are of greater interest compared with nonporous membranes since the latter have a higher penetration resistance. Nevertheless, their selectivity for carbon dioxide can be more than porous membranes.^42,43 Polysulfone (PS), polyethersulfone (PES), polyethylene (PE), polytetrafluoroethylene (PTFE), polypropylene (PP) and poly(vinylidene fluoride) (PVDF) are examples of common hollow-fiber membranes in gas–liquid contactors, of which PP, PE and PTFE are the most conventional materials.¹⁴

As the first researchers utilizing porous membrane as the gas–liquid contactor, Esato and Eiseman used a polytetrafluoroethylene to oxygenize blood.⁴⁵ In the following cases, researchers have used this method for separation. Qi and Cussler evaluated non-wetted polypropylene hollow-fiber membranes for the first time to capture CO₂ while there was aqueous solution of sodium hydroxide as the liquid absorbent.^3,46

Various liquid absorbents have been taken into consideration for acid-gas removal from gas mixtures by membrane processes (e.g. aqueous solutions of NaOH, KOH, NH₃, Na₂SO₃, Na₂CO₃, K₂CO₃, amines and amino acid salts). MEA, DEA, MDEA, TEA, AMP, DGA and DIPA are instances of amine solutions. Selection of liquid absorbent is affected by high reactivity with CO₂, surface tension, good thermal stability, low vapor pressure and ease of regeneration.^44,68–70

Lu et al. added AMP and piperazine as activators to methyldiethanolamine (MDEA) solution and applied it to remove carbon dioxide from CO₂/N₂ gas mixture.⁴⁷ In the other study, Ren et al. used PVDF for absorption of CO₂.⁴⁸ Kreulen et al. put emphasis on physical and chemical removal of CO₂ by HFMCs. They studied carbon dioxide absorption in aqueous solution of glycerol by using PP membrane.⁴⁹ Dubois and Thomas evaluated performance of different absorbents including MEA, MDEA, AMP, PZ and PZEA in CO₂ capture. As they indicated, mixture of different amines improved carbon dioxide absorption efficiencies.⁵⁰

Simulation of membrane process and application of results for industrial-unit design can have a considerable consequence on reduction of costs. Some researchers have simulated HFMCs.^{51–57,74–76} Faiz and Al-Marzouqi theoretically studied hollow-fiber membrane contactors for CO₂ and H₂S capture by using MEA liquid absorbent and developed a 2D mass transfer model.² Their model combined mass transfer along with chemical reaction. Kieffer et al. have simulated mass transfer phenomena in a liquid–liquid membrane system for laminar condition.⁵⁸ They used finite element methods for simulation of process and appropriate results were obtained. Sohrabi et al. used finite element method to develop a 2D mathematical model for CO₂ absorption in amine aqueous solutions (MEA, DEA, MDEA and AMP) and potassium carbonate.⁵⁹ As their findings revealed, amines have a better performance for carbon dioxide capture as compared with K₂CO₃, due to the fact that CO₂ have a higher reaction rate and solubility with amine absorbents.

Nevertheless, amine solutions have some drawbacks such as high regeneration energy, and solvent loss, due to volatility and corrosion. Researchers try to find better substitutes such as ionic liquids (ILs) for alkanolamines. Amino-functionalized ILs are considered as good alternatives for CO₂ removal because they have high thermal stability. Ease of regeneration, non-volatility and tunable physicochemical properties are some other advantages of these absorbents.^60–62 Tetramethylammonium glycinate ([N₁₁₁₁][Gly]) is an amino acid-based ionic liquid which shows a high capacity in removal of carbon dioxide in membrane processes.^63,64

Jing et al. examined the followings: density, viscosity and PH of [N₁₁₁₁][Gly], aqueous solution in concentration span of 5–30% of the absorbent and temperatures from 298 K to 323 K for CO₂ capture. Their findings demonstrated that removal of carbon dioxide in absorbent solution can be described by the fast pseudo-first order reaction regime. Increase in [N₁₁₁₁][Gly] concentration and CO₂ concentration would lead to increment of carbon dioxide absorption rate. On the contrary, CO₂ load shows a decrement.⁶⁴

Due to the advantages of membrane processes accompanied by the advantages of tetramethylammonium glycinate absorbent, the present study develops a 2D mathematical model for CO₂ separation from N₂/CO₂ gas mixture by [N₁₁₁₁][Gly] in HFMC. Also, it investigates the effects of different parameters on the performance of the HFMC.

2. Mass transfer model

Carbon dioxide capture from N₂/CO₂ gas mixture is simulated using a 2D mass transfer model considering a hollow-fiber membrane as contactor. Fig. 1 shows a HFMC schematically. There are 21 fibers in a module which is 16 mm in outer diameter. The fibers have an outer and inner diameter of 2.2 mm and 1.4 mm, respectively. All geometrical details of the simulated HFMC are listed in Table 1.⁶⁵ Gas mixture flows into the tube from top of the module with a flow rate of 200–1200 cm³ min⁻¹ and liquid absorbent enters into the shell from the bottom side with a concentration of 15% wt [N₁₁₁₁][Gly] and a flow rate of 50–120 cm³ min⁻¹.

Fig. 1 A schematic diagram for the hollow fiber membrane contactor.

Table 1 Characteristics of the membrane contactor used in the simulations

Characteristics of hollow fiber module^65
Module o.d. (mm)	16
Shell i.d. (mm)	14
Fiber o.d. (mm)	2.2
Fiber i.d. (mm)	1.4
Fiber length (cm)	31.4
Number of fibers	21
Fiber porosity, ε (%)	50

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2.1. Model equation

Velocity profile in the tube side can be obtained from the Navier–Stokes equation but velocity distribution in the tube side has been considered as follows by assuming a fully-developed Newtonian laminar flow:⁶⁶where r₁ is inner radius of fiber and u (m s⁻¹) is average velocity of stream in the tube.

It is worth noting that fiber cross-sectional area is supposed to be circle-shaped, on the basis of free surface model.⁶⁷ In all processes, and for component continuity, equation can be written as follows:⁶⁶

where C_i (mol m⁻³), t (s), V (m s⁻¹), J_i (mol m⁻² s⁻¹), and R_i (mol m⁻³ s⁻¹) indicate the concentration, time, velocity, diffusion flux and the reaction rate of component i respectively. Substitution of Fick's law for J_i and steady state assumption will simplify the above equation for tube side, shell side, membrane and absorbent.

2.1.1. Tube side equations. Since there occurs no chemical reaction in tube and the convection term of mass transfer in radial direction is negligible in comparison with z-direction, eqn (2) can be expanded as:where radial and axial coordinates are shown in the equation with r and z respectively. Boundary conditions related to the tube side equation are:

At r = r₁, C_CO2-tube = C_CO2-membrane (4)

At z = 0, convective flux (6)

At z = L, C_CO2-tube = C_CO2,0 (7)

It is worth noting that convective flux as boundary condition implies no diffusion mass transfer through the boundary.

2.1.2. Shell side equations. The equation in shell side of the HFMC is given below:

As mentioned before, for obtaining the velocity profile in the shell, Navier–Stokes equation has to be solved:⁶⁶

η, ρ, V, p are dynamic viscosity (kg m⁻¹ s⁻¹), density (kg m⁻³), velocity vector (m s⁻¹), pressure (Pa) and body force (N) respectively. Happel free surface model was employed to approximate shell radius (r₃):where r₂ is the tube outer radius. ϕ indicates volume fraction of void section which is defined as follows:where [scr R, script letter R]² and n are respectively the inner radius of the modules and the number of fibers. Boundary conditions for shell are as follows:

At r = r₂, C_CO2-shell = C_CO2-membrane × m (13)

At z = 0, C_CO2-shell = 0, V_z-shell = V₀ (14)

At z = L, convective flux, p = p_atm (15)

where m presents CO₂ solubility in absorbent.

2.1.3. Membrane equations. CO₂ transfer into the pores of the membrane is done only by the diffusion. Assumption of steady state and no reaction conditions provides the below simplified continuity equation:

Boundary conditions are required for calculating eqn (16) can be written as follows:

At r = r₁, C_CO2-membrane = C_CO2-shell (17)

Since the membrane is porous and hydrophobic, the interface is formed at the liquid phase. Therefore, no concentration change is occurred at the interface between gas and membrane.

2.1.4. Absorbent equations. Eqn (19) shows the governed equation in the shell side for [N₁₁₁₁][Gly]:R_i describes the chemical reaction between absorbent and CO₂. According to the zwitterion mechanism, carbon dioxide reacts with the absorbent with the formation of a zwitterion, subsequently deprotonated by a base present in solution:^61–64

H₂N–CH₂–COO⁻R⁺ + CO₂ ⇌ ⁻OCC⁺H₂N–CH₂–COO⁻R⁺

⁻OOC⁺H₂N–CH₂–COO⁻R⁺ + B_i → ⁻OOCHN–CH₂–COO⁻R⁺ + B_iH⁺

where B_i is the bases present in the solution which can deprotonate the zwitterions, including H₂O, OH⁻ and [N₁₁₁₁][Gly].

Boundary conditions of eqn (19) are:

At z = 0, C_{absorbent-shell} = C_absorbent,0 (22)

At z = L, convective flux (23)

2.2. Numerical procedure

The commercial finite element package of COMSOL Multiphysics version 3.5 was used to solve tube, membrane and shell side equations, by applying Finite Element Method (FEM). In addition, UMFPACK was employed as a powerful solver for symmetric problems. Accuracy of UMFPACK for membrane processes has been proved by some researchers.^59,65,71,73 Fig. 2 presents triangular mesh elements relating to examining gas transfer in the HFMC. In Fig. 2, r₁, r₂, and r₃ stand for inner radius of fiber, outer radius of fiber, and radius of free surface respectively. It should be pointed out that there were 3300 elements for whole geometry.

Fig. 2 Model domain and meshes used for simulation.

3. Results and discussion

3.1. Model validation

Respecting to the author's knowledge, there is no experimental data on CO₂ capture by hollow-fiber membranes using tetramethylammonium glycinate absorbent. So, validity of the model has been assessed on the basis of experimental findings of Su-Hsia Lin et al. about CO₂ separation from N₂ in the HFMC.⁷² As Fig. 3 indicates, simulation is generally accurate as compared with experimental data.

Fig. 3 Relation between reaction rate and gas flow rates (for validation of model), liquid flow rate = 100 (cm³ min⁻¹); CO₂ inlet concentration = 15 vol%; AMP inlet concentration = 1 (mol L⁻¹); PZ inlet concentration = 0.2 (mol L⁻¹); temperature = 298 K.

3.2. Velocity distribution

Fig. 4 and 5 indicate the velocity profile in the shell of the HFMC where the liquid absorbent flows through. The velocity distribution in the shell side is approximately parabolic. Moreover, the maximum velocity occurs at the middle of the shell and the amount of velocity on two walls of the shell is zero due to no-slip condition. In Fig. 4, fully developed condition exists after short distance from entrance. Indeed, hydraulic entrance length of the HFMC is small.

Fig. 4 Velocity field in the shell side (absorbent channel) of the hollow fiber membrane contactor, gas flow rate = 200 (L h⁻¹); liquid flow rate = 100 (L h⁻¹); CO₂ inlet concentration = 15 vol%; [N₁₁₁₁][Gly] inlet concentration = 15 wt%; temperature = 298 K.

Fig. 5 Velocity profile in the shell side (absorbent channel) along the membrane length, gas flow rate = 200 (L h⁻¹); liquid flow rate = 100 (L h⁻¹); CO₂ inlet concentration = 15 vol%; [N₁₁₁₁][Gly] inlet concentration = 15 wt%; temperature = 298 K.

3.3. Concentration distribution of CO₂

Fig. 6 shows dimensionless concentration distribution for CO₂ in the tube, the membrane and the shell of the HFMC. As gas mixture flows through tube, carbon dioxide transfers to membrane because of difference of concentration.⁶⁴ Regarding to Fig. 6, at z = L where gas enters the HFMC, the concentration of CO₂ has maximum value while in the other side of the membrane and at z = 0 the concentration of CO₂ is equal to zero.

Fig. 6 Dimensionless concentration distribution for CO₂ in the tube, the membrane and the shell of the HFMC. Gas flow rate = 200 (L h⁻¹); liquid flow rate = 100 (L h⁻¹); CO₂ inlet concentration = 15 vol%; [N₁₁₁₁][Gly] inlet concentration = 15 wt%; temperature = 298 K.

Mechanism of mass transfer in the tube and the shell are diffusion and convection. Since flow is in z-direction, mass is transferred via convection. In radial direction, diffusion plays the most important role on mass transfer phenomena. Gas diffuses through the pores of the membrane to the other side. According to Fig. 6, the presence of carbon dioxide at z = L in the shell side can be seen close to the membrane wall it is due to the fact that the concentration of the absorbent decreases along the HFMC and has its minimum value in the mentioned area (see Fig. 8). Consequently, reaction of absorbent with CO₂ is lower than other zones.

Fig. 7 Vector of total flux for CO₂ in the membrane contactor, gas flow rate = 200 (L h⁻¹); liquid flow rate = 100 (L h⁻¹); CO₂ inlet concentration = 15 vol%; [N₁₁₁₁][Gly] inlet concentration = 15 wt%; temperature = 298 K.

Fig. 8 Dimensionless concentration of tetramethylammonium glycinate ([N₁₁₁₁][Gly]) in the shell of the HFMC. Gas flow rate = 200 (L h⁻¹); liquid flow rate = 100 (L h⁻¹); CO₂ inlet concentration = 15 vol%; [N₁₁₁₁][Gly] inlet concentration = 15 wt%; temperature = 298 K.

Fig. 7 exhibits the vector of carbon dioxide concentration in the membrane contactor. It is clearly seen that CO₂ mass transfer flux reduces along the membrane module because of carbon dioxide capture by absorbent. Moreover, variation rate of CO₂ concentration along the contactor is significant which confirms the capability of membrane contactor in successful removal of CO₂.

3.4. Concentration distribution of the absorbent

Contour of dimensionless concentration of tetramethylammonium glycinate ([N₁₁₁₁][Gly]) in the shell of the HFMC is illustrated in Fig. 8. The liquid absorbent flows into the shell side (enters at z = 0) and reacts to CO₂ which has diffused through the membrane due to difference in concentrations of two sides. Fig. 9 shows the axial variation of tetramethylammonium glycinate concentration along the HFMC. Reduction of the absorbent concentration occurs more rapidly in the middle of the contactor length. On the other hand, [N₁₁₁₁][Gly] concentration in a short distance of the entrance of the shell does not vary considerably. Because there is no CO₂ in the tube along the mentioned length, absorbent passes this length in the shell side without any reaction to carbon dioxide.

Fig. 9 Axial variation of tetramethylammonium glycinate concentration along the HFMC. Gas flow rate = 200 (L h⁻¹); liquid flow rate = 100 (L h⁻¹); CO₂ inlet concentration = 15 vol%; [N₁₁₁₁][Gly] inlet concentration = 15 wt%; temperature = 298 K.

3.5. Effects of gas and liquid flow rates on CO₂ capture

The value of absorbed CO₂ is calculated by using the below equation:where v (m³ s⁻¹) and C (mol m⁻³) are volumetric gas flow rate and concentration respectively.

The percentage of CO₂ removal versus the liquid flow rate is indicated in Fig. 10. Increment of the liquid flow rate leads to increase of the amount of carbon dioxide removal because Reynolds number and in the following mass transfer coefficient go up. When the liquid flow rate increases more, no considerable change occurs in the absorption percentage of CO₂ from the gas mixture. So, as absorbents are expensive, this can lead to reduction of unnecessary costs.

Fig. 10 Percentage of CO₂ removal versus the liquid flow rate, gas flow rate = 200 (L h⁻¹); CO₂ inlet concentration = 15 vol%; [N₁₁₁₁][Gly] inlet concentration = 15 wt%; temperature = 298 K.

Fig. 11 indicates impacts of gas flow rate on the amount of CO₂ capture. Increase of gas flow rate associates with decrease in absorption of carbon dioxide by [N₁₁₁₁][Gly]. Since the resident time of the gas mixture goes down by increment of its flow rate, less amount of CO₂ can diffuse into pores of the membrane.

Fig. 11 Percentage of CO₂ removal versus the gas flow rate, liquid flow rate = 100 (L h⁻¹); CO₂ inlet concentration = 15 vol%; [N₁₁₁₁][Gly] inlet concentration = 15 wt%; temperature = 298 K.

3.6. Effects of the absorbent concentration on CO₂ capture

Fig. 12 shows relationship between the concentration of [N₁₁₁₁][Gly] and CO₂ absorption in the shell side. Increase in the absorbent concentration results in greater removal of CO₂. Therefore, carbon dioxide in outlet gas mixture stream decreases. Indeed, increment of the absorbent would lead to increase of reaction rate between CO₂ and the absorbent that ultimately causes more captured CO₂. Then, the absorbent concentration plays key role in carbon dioxide separation.

Fig. 12 Relationship between the concentration of [N₁₁₁₁][Gly] and percentage of CO₂ removal, gas flow rate = 200 (L h⁻¹); liquid flow rate = 100 (L h⁻¹); CO₂ inlet concentration = 15 vol%; temperature = 298 K.

3.7. Comparing different absorbents according to the amount of removed CO₂

For examining the efficiency of [N₁₁₁₁][Gly] absorbent, the amount of captured CO₂ by above-mentioned absorbent and two other conventional absorbents are compared in Fig. 13. As graphs show, the percentage of CO₂ removal by the studied absorbent ([N₁₁₁₁][Gly]) is close to MEA as one of the most effective CO₂ absorbents. Besides, the efficiency of [N₁₁₁₁][Gly] is higher than DEA that demonstrates great effectiveness of tetramethylammonium glycinate in CO₂ separation.

Fig. 13 Comparing different absorbents according to the amount of removed CO₂. Gas flow rate = 200 (L h⁻¹); liquid flow rate = 100 (L h⁻¹); CO₂ inlet concentration = 15 vol%; [N₁₁₁₁][Gly] inlet concentration = 15 wt%; temperature = 298 K.

3.8. Effect of membrane structure on separation

Effect of membrane structure in terms of porosity to tortuosity ratio on the separation performance of membrane was also investigated. The results are shown in Fig. 14 in which the percentage removal of CO₂ versus porosity/tortuosity ratio is plotted. As it can be seen, the removal of CO₂ can increase up to 90% when the porosity to tortuosity ratio increases from 0.1 to 0.9. This behavior could be attributed to the mass transfer resistance in the membrane pores. Increasing porosity of membrane results in reduction of mass transfer resistance in the membrane phase which in turn reduces the total mass transfer resistance for transport of CO₂ from gas phase to the absorbent.

Fig. 14 Effect of porosity to tortuosity ratio on the removal of CO₂. Gas flow rate = 200 (L h⁻¹); liquid flow rate = 100 (L h⁻¹); CO₂ inlet concentration = 15 vol%; [N₁₁₁₁][Gly] inlet concentration = 15 wt%; temperature = 298 K.

3.9. Effect of membrane wetting

Effect of membrane wetting on mass transfer of CO₂ from gas phase to the liquid phase was also studied to determine the favorable operational mode. The results for two different operations i.e. wetted and non-wetted modes are indicated in Fig. 15. When the membrane is considered to be hydrophobic, the pores of membrane are wetted with the gas phase, and the liquid absorbent cannot wet the membrane pores. In this case, the diffusion coefficient of CO₂ through the membrane is higher than the case when the membrane is hydrophilic. Therefore, higher mass transfer rate and also CO₂ removal is obtained in non-wetted mode (hydrophobic membrane).

Fig. 15 Effect of membrane wetting on the removal of CO₂. Gas flow rate = 200 (L h⁻¹); CO₂ inlet concentration = 15 vol%; [N₁₁₁₁][Gly] inlet concentration = 15 wt%; temperature = 298 K.

4. Conclusions

A 2D mass transfer model has been developed for studying CO₂ removal in HFMCs in which tetramethylammonium glycinate ([N₁₁₁₁][Gly]) as the absorbent was used. The continuity equations of shell, membrane and tube were solved using Finite Element Method (FEM). As regards simulation findings, the model is appropriate for prediction of hollow-fiber membrane processes performance. Increase of flow rate and concentration of absorbent improve efficiency of membrane contactor. On the contrary, by increment of gas flow rate, the percentage absorption of CO₂ declines. The amount of removed CO₂ by [N₁₁₁₁][Gly] is between that of DEA and MEA. Furthermore, the concentration of tetramethylammonium glycinate decreases along the HFMC mainly in the middle as it flows through the shell side.

Nomenclature

C0	Inlet concentration (mol m^−3)
C	Concentration (mol m^−3)
CCO2-shell	CO2 concentration in the shell (mol m^−3)
CCO2-tube	CO2 concentration in the tube (mol m^−3)
Ci	Concentration of any species (mol m^−3)
Ci-tube	Concentration of any species in the tube (m^2 s^−1)
Cin	Absorbent concentration at the inlet (mol m^−3)
Cinlet	Inlet concentration of CO2 in the shell (mol m^−3)
Coutlet	Outlet concentration of CO2 in the shell (mol m^−3)
Cabs-shell	[N1111][Gly] concentration (mol m^−3)
CM0	Inlet [N1111][Gly] concentration (mol m^−3)
D	Diffusion coefficient (m^2 s^−1)
Di-membrane	Diffusion coefficient of any species in the membrane (m^2 s^−1)
Di-tube	Diffusion coefficient of any species in the tube (m^2 s^−1)
K	Reaction rate coefficient of CO2 with absorbent (m^3 mol^−1 s^−1)
L	Length of a fiber (m)
m	Physical solubility (—)
n	Number of fibers
P	Pressure (Pa)
Qg	Gas flow rate (L h^−1)
Ql	Liquid flow rate (L h^−1)
r1	Tube inner radius (m)
r2	Tube outer radius (m)
r3	Inner shell radius (m)
r	Radial coordinate (m)
[scr R, script letter R]	Module inner radius (m)
Ri	Overall reaction rate of any species (mol m^−3 s^−1)
t	Time (s)
T	Temperature (K)
u	Average velocity (m s^−1)
V	Velocity in the module (m s^−1)
Vz-shell	z-velocity in the shell (m s^−1)
Vz-tube	z-velocity in the tube (m s^−1)
z	Axial coordinate (m)

Acknowledgements

Research council at Islamic Azad University-South Tehran Branch is highly acknowledged for the financial support of this work.

References

1. H. Herzog, B. Eliasson and O. Kaarstad, Capturing greenhouse gases, Sci. Am., 2000, 182(2), 72–79.
2. R. Faiz and M. Al-Marzouqi, Mathematical modeling for the simultaneous absorption of CO₂ and H₂S using MEA in hollow fiber membrane contactors, J. Membr. Sci., 2009, 342, 269–278.
3. Z. Qi and E. L. Cussler, Micro porous hollow fibers for gas absorption. Part 1: mass transfer in the liquid, J. Membr. Sci., 1985, 23, 321–332.
4. A. B. Shelekhim and I. N. Beckman, Gas separation processes in membrane absorbent, J. Membr. Sci., 1992, 73(1–2), 73–85,  DOI:10.1016/0376-7388(92)80187-O , ISSN 0376-7388.
5. N. Nishikawa, M. Ishibashi, H. Ohata and N. Akutsu, CO₂ removal by hollow fibers gas–liquid contactor, Energy Convers. Manage., 1995, 36, 415–418.
6. P. H. M. Feron and A. E. Jansen, Capture of carbon dioxide using membrane gas absorption and reuse in the horticultural industry, Energy Convers. Manage., 1995, 36, 411–414.
7. H. A. Rangwala, Absorption of carbon dioxide into aqueous solutions using hollow fiber membrane contactors, J. Membr. Sci., 1996, 112, 229–240.
8. P. H. M. Feron and A. E. Jansen, The production of carbon dioxide from flue gas by membrane gas absorption, Energy Convers. Manage., 1997, 38, S93–S98.
9. Y. S. Kim and S. M. Yang, Absorption of carbon dioxide through hollow fiber membranes using various aqueous absorbents, Sep. Purif. Technol., 2000, 21, 101–109.
10. P. H. M. Feron and A. E. Jensen, CO₂ separation with polyolefin membrane contactors and dedicated absorption liquids: performance and prospects, Sep. Purif. Technol., 2002, 27, 231–242.
11. P. S. Kumar, J. A. Hagendoorn, P. H. M. Feron and G. F. Versteeg, New absorption liquids for the removal of CO₂ from dilute gas streams using membrane contactors, Chem. Eng. Sci., 2002, 57, 1639–1651.
12. P. S. Kumar, J. A. Hogendorn, P. H. M. Feron and G. F. Versteeg, J. Membr. Sci., 2003, 213, 231.
13. M. Rezakazemi, Z. Niazi, M. Mirfendereski, S. Shirazian, T. Mohammadi and A. Pak, CFD simulation of natural gas sweetening in a gas–liquid hollow-fiber membrane contactor, Chem. Eng. J., 2011, 168, 1217–1226.
14. A. Mansourizadeh and A. F. Ismail, Hollow fiber gas–liquid membrane contactors for acid gas capture: a review, J. Hazard. Mater., 2009, 171, 38–53.
15. A. Gabelman and S.-T. Hwang, Hollow fiber membrane contactors, J. Membr. Sci., 1999, 159, 61–106.
16. H. Kreulen, C. A. Smolders, G. F. Versteeg and W. P. M. van Swaaij, Micro porous hollow fiber membrane modules as gas–liquid contactors. Part 1. Physical mass transfer processes: a specific application: mass transfer in highly viscous liquids, J. Membr. Sci., 1993, 78, 197–216.
17. S. Nii and H. Takeuchi, Removal CO₂ and/or SO₂ from gas streams by a membrane absorption method, Gas Sep. Purif., 1994, 8, 107–114.
18. P. H. M. Feron, A. E. Jansen and R. Klaasen, Membrane technology in carbon dioxide removal, Energy Convers. Manage., 1992, 23, 421–428.
19. H. Kreulen, C. A. Smolders, G. F. Versteeg and W. P. M. van Swaaij, Micro porous hollow fiber membrane modules as gas–liquid contactors. Part. 2. Mass transfer with chemical reaction, J. Membr. Sci., 1993, 78, 217.
20. S. Karror and K. K. Sirkar, Gas absorption study in micro porous hollow fiber membrane modules, Ind. Eng. Chem. Res., 1993, 32, 674–684.
21. M. S. Chun and K. H. Lee, Analysis on a hydrophobic hollow fiber membrane absorbent and experimental observations of CO₂ removal by enhanced absorption, Sep. Sci. Technol., 1997, 32(15), 2445–2466.
22. O. Falk-Pederson and H. Dannstorm, Separation of carbon dioxide from offshore gas turbine exhaust, Energy Convers. Manage., 1997, 38, S81–S86.
23. Y. Lee, R. D. Noble, B. Y. Yeon, Y. I. Park and K. H. Lee, Analysis of CO₂ removal by hollow fiber membrane contactors, J. Membr. Sci., 2001, 194, 57–67.
24. D. Bhaumik, S. Majumdar and K. K. Sirkar, Absorption of CO₂ in a transverse flow hollow fiber module having a few wraps of the fiber mat, J. Membr. Sci., 1998, 138, 77–82.
25. K. Li and W. K. Teo, Use of permeation and absorption methods for CO₂ removal in hollow fiber membrane modules, Sep. Purif. Technol., 1998, 13, 79–88.
26. M. Mavroudi, S. P. Kaldis and G. P. Sakellaropoulos, Reduction of CO₂ emissions by a membrane contacting process, Fuel, 2003, 82, 2153–2159.
27. S. H. Yeon, B. Sea, Y. L. Park and K. H. Lee, Determination of mass transfer rates in PVDF and PTFE hollow fibers membranes for CO₂ absorption, Sep. Sci. Technol., 2003, 38, 271.
28. V. Y. Dindore, D. W. F. Brilman, P. H. M. Feron and G. F. Versteeg, CO₂ absorption at elevated pressures using a hollow fiber membrane contactor, J. Membr. Sci., 2004, 235, 99–109.
29. V. Y. Dindore, D. W. F. Brilman, F. H. Geuzebroek and G. F. Versteeg, Membrane solvent selection for CO₂ removal using membrane gas–liquid contactors, Sep. Purif. Technol., 2004, 40, 133–145.
30. R. Wang, D. F. Li and D. T. Liang, Modeling of CO₂ capture by three typical amine solutions in hollow fiber membrane contactors, Chem. Eng. Process., 2004a, 43, 849–856.
31. R. Wang, D. F. Li, C. Zhou, M. Liu and D. T. Liang, Impact of DEA solutions with or without CO₂ loading on porous polypropylene membranes intended for use as contactors, J. Membr. Sci., 2004b, 229, 147–157.
32. S. H. Yeon, K. S. Lee, B. K. Sea, Y. I. Park and N. H. Lee, Application of pilot-scale membrane contactor hybrid system for removal of carbon dioxide from flue gas, J. Membr. Sci., 2005, 257, 156–160.
33. R. Wang, H. Y. Zhang, P. H. M. Feron and D. T. Liang, Influence of membrane wetting on CO₂ capture in micro-porous hollow fiber membrane contactors, Sep. Purif. Technol., 2005, 46, 33–40.
34. S. P. Yan, M. X. Fang, W. F. Zhang, S. Y. Wang, Z. K. Zu, Z. Y. Luo and K. F. Cen, Experimental study on the separation of CO₂ from flue gas using hollow fiber membrane contactors without wetting, Fuel Process. Technol., 2007, 88, 501–511.
35. H. Y. Zhang, R. Wang, D. T. Liang and J. H. Tay, Modeling and experimental study of CO₂ absorption in a hollow fiber membrane contactor, J. Membr. Sci., 2006, 279, 301–310.
36. H. Y. Zhang, R. Wang, D. T. Liang and J. H. Tay, Theoretical and experimental studies of membrane wetting in the membrane gas–liquid contacting process for CO₂ absorption, J. Membr. Sci., 2008, 308, 162–170.
37. A. Bottino, G. Capannelli, A. Comite, R. Firpo, R. D. Felice and P. Pinacci, Separation of carbon dioxide from flue gases using membrane contactors, Desalination, 2006, 200, 609–611.
38. A. Bottino, G. Capannelli, A. Comite, R. D. Felice and R. Firpo, CO₂ removal from a gas stream by membrane contactor, Sep. Purif. Technol., 2008, 59, 85–90.
39. J. M. Zheng, Y. Y. Xu and Z. K. Xu, Sep. Sci. Technol., 2003, 38, 1247.
40. D. C. Nymeijer, B. Folkers, I. Breebaart, M. H. V. Mulder and M. Wessling, J. Appl. Polym. Sci., 2004, 92, 323.
41. H. Matsumoto, H. Kitamura, T. Kamata, M. Ishibashi, H. Ota and N. Akutsu, J. Chem. Eng. Jpn., 1995, 28, 125.
42. S. Nii, H. Takeuchi and K. Takahashi, J. Chem. Eng. Jpn., 1992, 25, 67.
43. M. Teramoto, K. Nakai, N. Ohnishi, Q. F. Huang, T. Watari and H. Matsuyama, Ind. Eng. Chem. Res., 1996, 35, 538.
44. J. L. Li and B. H. Chen, Review of CO₂ absorption using chemical solvents in hollow fiber membrane contactors, Sep. Purif. Technol., 2005, 41, 109–122.
45. K. Esato and B. Eiseman, Experimental evaluation of Core-Tex membrane oxygenator, J. Thorac. Cardiovasc. Surg., 1975, 69, 690–697.
46. Z. Qi and E. L. Cussler, Micro porous hollow fibers for gas absorption. Part 2: mass transfer across the membrane, J. Membr. Sci., 1985, 23, 333–345.
47. J. G. Lu, Y. F. Zheng, M. D. Cheng and L. J. Wang, Effects of activators on mass-transfer enhancement in a hollow fiber contactor using activated alkanolamine solutions, J. Membr. Sci., 2007, 289, 138–149.
48. J. Ren, R. Wang, H. Y. Zhang, Z. Li, D. T. Liang and J. H. Tay, Effect of PVDF dope rheology on the structure of hollow fiber membranes used for CO₂ capture, J. Membr. Sci., 2006, 281, 334–344.
49. H. Kreulen, C. A. Smolders, G. F. Versteeg and W. P. M. Van Swaaij, Micro porous hollow fiber membrane modules, Ind. Eng. Chem. Res., 1993, 32, 674–684.
50. L. Dubois and D. Thomas, Carbon dioxide absorption into aqueous amine based solvents: modeling and absorption tests, Energy Procedia, 2011, 4, 1353–1360.
51. S. Abolfazl Miramini, S. M. R. Razavi, M. Ghadiri, S. Z. Mahdavi and S. Moradi, CFD simulation of acetone separation from an aqueous solution using supercritical fluid in a hollow-fiber membrane contactor, Chemical Engineering and Processing: Process Intensification, 2013, 72, 130–136,  DOI:10.1016/j.cep.2013.07.005 , ISSN 0255-2701.
52. K. A. Hoff, O. Juliussen, O. F. Pedersen and H. F. Svendsen, Modeling and experimental study of carbon dioxide absorption in aqueous alkanolamine solutions using a membrane contactor, Ind. Eng. Chem. Res., 2004, 43, 4908–4921.
53. P. Keshavarz, J. Fathikalajahi and S. Ayatollahi, Analysis of CO₂ separation and simulation of a partially wetted hollow fiber membrane contactor, J. Hazard. Mater., 2008, 152, 1237–1247.
54. V. Evren, A numerical approach to determination of mass transfer performances through partially wetted micro-porous membranes: transfer of oxygen to water, J. Membr. Sci., 2000, 175, 97–110.
55. Y. Gong, Z. Wang and S. Wang, Experimental and simulation of CO₂ removal by mixed amines in a hollow fiber membrane module, Chem. Eng. Process., 2006, 45, 652–660.
56. B. P. Mandal and S. S. Bandyopadhyay, Simultaneous absorption of carbon dioxide and hydrogen sulfide into aqueous blends of 2-amino-2-methyl-1-propanol and diethanolamine, Chem. Eng. Sci., 2005, 60, 6438–6451.
57. M. Al-Marzouqi, M. El-Naas, S. Marzouk and N. Abdullatif, Modeling of chemical absorption of CO₂ in membrane contactors, Sep. Purif. Technol., 2008, 62, 499–506.
58. R. Kieffer, C. Charcosset, F. Puel and D. Mangin, Numerical simulation of mass transfer in a liquid–liquid membrane contactor for laminar flow conditions, Comput. Chem. Eng., 2008, 32, 1325–1333.
59. M. R. Sohrabi, A. Marjani, S. Moradi, M. Davallo and S. Shirazian, Mathematical modeling and numerical simulation of CO₂ transport through hollow-fiber membranes, Appl. Math. Model., 2011, 35, 174–188.
60. D. Wappel, G. Gronald, R. Kalb and J. Draxler, Ionic liquids for post-combustion CO₂ absorption, Int. J. Greenhouse Gas Control, 2010, 4, 486–494.
61. L. M. Galan Sanchez, G. W. Meindersma and A. B. de Haan, Kinetics of absorption of CO₂ in amino-functionalized ionic liquids, Chem. Eng. J., 2011, 166, 1104–1115.
62. Y. S. Zhao, X. P. Zhang, Y. P. Zhen, H. F. Dong, G. Y. Zhao, S. J. Zeng, X. Tian and S. J. Zhang, Novel alcamines ionic liquids based solvents: preparation, characterization and applications in carbon dioxide capture, Int. J. Greenhouse Gas Control, 2011, 5, 367–373.
63. F. Zhang, C. G. Fang, Y. T. Wu, Y. T. Wang, A. M. Li and Z. B. Zhang, Absorption of CO₂ in the aqueous solutions of functionalized ionic liquids and MDEA, Chem. Eng. J., 2010, 160, 691–697.
64. G. Jing, L. Zhou and Z. Zhou, Characterization and kinetics of carbon dioxide absorption into aqueous tetramethylammonium glycinate solution, Chem. Eng. J., 2012, 181–182(1), 85–92,  DOI:10.1016/j.cej.2011.11.007 , ISSN 1385-8947.
65. S. M. R. Razavi, S. M. J. Razavi, T. Miri and S. Shirazian, CFD simulation of CO₂ capture from gas mixtures in nanoporous membranes by solution of 2-amino-2-methyl-1-propanol and piperazine, Int. J. Greenhouse Gas Control, 2013, 15, 142–149.
66. R. B. Bird, W. E. Stewart and E. N. Lightfoot, Transport Phenomena, John Wiley & Sons, New York, 2nd edn, 1960.
67. J. Happel, Viscous flow relative to arrays of cylinders, AIChE J., 1959, 5, 174–177.
68. G. W. Xu, C. F. Zhang, S. J. Qin and Y. H. Wang, Kinetics study on absorption of carbon dioxide into solutions of activated methyldiethanolamine, Ind. Eng. Chem. Res., 1992, 31, 921.
69. G. W. Xu, C. F. Zhang, S. J. Qin, W. H. Gao and H. B. Liu, Gas–liquid equilibrium in CO₂–MDEA–H₂O system and the effect of piperazine on it, Ind. Eng. Chem. Res., 1998, 37, 1473.
70. D. J. Seo and W. H. Hong, Solubilities of carbon dioxide in aqueous mixtures of diethanolamine and 2-amino-2-methyl-1-propanol, J. Chem. Eng. Data, 1996, 41, 258.
71. S. Bishnoi and G. T. Rochelle, Absorption of carbon dioxide into aqueous piperazine: reaction kinetics, mass transfer and solubility, Chem. Eng. Sci., 2000, 55, 5531.
72. S.-H. Lin, et al., Absorption of carbon dioxide by the absorbent composed of piperazine and 2-amino-2-methyl-1-propanol in PVDF membrane contactor, JCICE, 2008, 39, 13–21.
73. S. Shirazian, A. Moghadassi and S. Moradi, Numerical simulation of mass transfer in gas–liquid hollow fiber membrane contactors for laminar flow conditions, Simulat. Model. Pract. Theor., 2009, 17, 708–718.
74. K. Tahvildari, S. M. R. Razavi, H. Tavakoli, A. Mashayekhi, R. Golmohammadzadeh and M. G. Samani, Modeling and simulation of membrane separation process using computational fluid dynamics, Arabian J. Chem., 2015 DOI:10.1016/j.arabjc.2015.02.022 , ISSN 1878–5352.
75. S. M. R. Razavi, S. Shirazian and M. S. Najafabadi, Investigations on the ability of di-isopropanol amine solution for removal of CO₂ from natural gas in porous polymeric membranes, Polym. Eng. Sci., 2015, 55, 598–603,  DOI:10.1002/pen.23924.
76. S. M. R. Razavi, A. Marjani and S. Shirazian, CO₂ Capture from Gas Mixtures by Alkanol Amine Solutions in Porous Membranes, Transp. Porous Media, 2015, 106(2), 323.

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