Mathematical Modeling and Numerical Simulation of CO2 Removal by Using Hollow Fiber Membrane Contactors

Document Type: Research Paper

Authors

1 M.S. Student, Young Researchers and Elites Club, Science and Research Branch, Islamic Azad University, Tehran, Iran

2 Ph.D. Candidate, Russ College of Engineering and Technology, Ohio University, Athens, OH

3 M.S. Student, Young Researchers and Elites Club, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran

4 M.S. Student, Department of Chemical Engineering, Sahand University of Technology, Tabriz, Iran

Abstract

Abstract
In this study, a mathematical model is proposed for CO2 separation from N2/CO2 mixtureusing a hollow fiber membrane contactor by various absorbents. The contactor assumed as non-wetted membrane; radial and axial diffusions were also considered in the model development. The governing equations of the model are solved via the finite element method (FEM). To ensure the accuracy of the developed model, the simulation results were validated using the reported experimental data for potassium glycinate (PG), monoethanol amine (MEA), and methyldiethanol amine (MDEA). The results of the proposed model indicated that PG absorbent has the highest removal efficiency of CO2, followed by potassium threonate (PT), MEA, amino-2-methyl-1-propanol (AMP), diethanol amine (DEA), and MDEA in sequence. In addition, the results revealed that the CO2 removal efficiency was favored by absorbent flow rate and liquid temperature, while the gas flow rate has a reverse effect. The simulation results proved that the hollow fiber membrane contactors have a good potential in the area of CO2 capture.

Keywords

Main Subjects


1. Introduction

It is well known that the emission of the greenhouse gases such as carbon dioxide (CO2), which is accounted for about 80% of greenhouse gas emission, is associated with global warming and climate change (Herzog et al., 2000). While there are veracious natural sources of CO2 emission, the emissions associated with human related activities are the main reason of carbon dioxide increase in the atmosphere in recent decades. The main human related CO2 emission is the combustion of fossil fuels (oil, natural gas, and coal). However, 80% of the world’s total energy sources is supplied by fossil fuels (Wang et al., 2004). On the other hand, concentrated CO2 is needed for some industrial applications such as enhanced oil recovery (Herzog, 2001). Therefore, the development of CO2 capture methods is so attractive (Esmaili and Ehsani, 2014, Rahmandoost et al., 2014).

Several CO2 capture techniques have been developed over the years, including adsorption, chemical and physical absorption, cryogenic distillation, molecular sieve adsorption, and gas-separation membrane. Among these techniques, the absorption of CO2 into alkanolamine solutions (such as monoethanol amine (MEA), diethanol amine (DEA), triethanol amine (TEA), and methyldiethanol amine (MDEA)) using towers and other traditional contactors is the most widely used method (Lyngfelt and Azar, 1999; Zhao et al., 2008; Oexmann and Kather, 2009; Tuinier et al., 2010). Nevertheless, some problems arise from using conventional absorption methods such as flooding, foaming, channeling, air entrainment, and high energy consuming (Al-Marzouqi et al., 2008; Lin et al., 2008). Membrane contactors are the answer to these problems (Gabelman and Hwang, 1999). The idea of combining absorption by chemical solvent and membrane separation technology was proposed by Qi and Cussler (Qi and Cussler, 1985). Hollow fiber membrane contactors (HFMC) are a group of such contactors, which have been the subject of many studies over the past years (Gabelman and Hwang, 1999; Li et al., 2000; Wang et al., 2004; Li and Chen, 2005; Yan et al., 2007; Lin et al., 2008; Park et al., 2008).

Recently many researchers have been studied CO2 capture from flue gas. Several factors such as different absorbents, gas and liquid flow rate, and membrane type have been investigated (Lee et al., 2001; Wang et al., 2004; Ren et al., 2006; Atchariyawut et al., 2007; Lu et al., 2007; Yan et al., 2007; Al-Marzouqi et al., 2009; Faiz and Al-Marzouqi, 2009; Rezakazemiet al., 2011). Wang et al. (2004) studied the effect of Amino-2-methyl-1-propanol (AMP), MDEA, and DEA absorbents on CO2 capture. Their simulations indicated that AMP and DEA have higher removal efficiency than MDEA. Ren et al. (2006) studied CO2 capture by poly(vinylidene fluoride) (PVDF) hollow fiber membranes. Lu et al. (2007) investigated the effect of AMP and piperazine (PZ) activators on CO2 removal. Their results showed that the mass-transfer fluxes of activated solutions were much higher than that of the non-activated solution. Yan et al. (2007) used MEA, MDEA, and potassium glycinate (PG) as absorbents for CO2 capture from flue gas. The experiments were conducted in polypropylene (PP) hollow fiber membrane contactors. They concluded that the PG absorbent is more suitable than MEA and MDEA because it has a lower potential of membrane wetting (which has a direct effect on removal efficiency) and higher reactivity toward CO2 compared to MEA and MDEA. Kazemi et al. (2011) studied experimentally and theoretically simultaneous removal of CO2 and H2S through a HFMC using MDEA as a chemical absorbent. Their results indicated that MDEA is very efficient for H2S removal.

In this study, CO2 absorption with different absorbents, namely MEA, MDEA, DEA, AMP, PG, and potassium threonate (PT), is simulated in the case of non-wetted HFMC. The proposed model is validated using experimental data. The effects of different factors, including gas velocity, absorbent temperature, absorbent concentration, and hollow fiber membrane module specification for the preferred absorbent were investigated using the proposed model.

2. The Model development

A comprehensive 2D mathematical model has been developed for the separation of CO2 from CO2/N2 mixturethrough a hollow fiber membrane contactor including 7000 fibers. Three different kinds of aqueous solutions were studied as an absorbent to compare the capability of the solvent for CO2 removal. The model was proposed based on “non-wetted mode”. The schematic of the hollow fiber membrane used in the present work is shown in Figure 1.

 

gas

gas

absorbent

z

 

r

z = L

z = 0

r1

r2

r3

Absorbent

Flue Gas

Figure 1

A schematic of hollow fiber membrane contractor.

One of the fibers in the membrane module surrounded by a laminar gas flow has been simulated. The hollow fiber membrane consisted of three sections: (1) tube side, (2) membrane, and (3) shell side. The flue gas, including a mixture of nitrogen and carbon dioxide, is fed downward into the shell side at z=L. On the tube side, the fully developed laminar flow solvent is fed upward at z=0. Only the carbon dioxide portion of the gas flow is removed from the gas mixture by diffusing through the membrane and will then be absorbed by the solvent. Figure 2 represents the cross sectional area of the hollow fiber membrane contractor. Based on Happel’s free surface model (Happel, 1959), only a portion of fluid enveloping the fiber is considered and could be approximated as a circular cross section.

 

Hollow fiber

Circular approximation

Figure 2

The cross sectional area of the hollow fiber membrane contractor.

The assumptions for the simulation can be summarized as given below.

  1. The simulation conditions is steady-state and isothermal;
  2. Velocity profiles for the fluid through hollow fiber are fully developed;
  3. The gas mixture is considered as an ideal gas;
  4. A non-wetted mode in which the gas mixture fills the membrane pores is assumed;
  5. Henry’s law is applied to gas-liquid interface;
  6. No homogenous reaction takes place at the shell side.

2.1. Mass transfer equations

a) Tube side

The steady state continuity equation for the transport of CO2 in the tube side, consisting of Fick’s law to predict the diffusion flux, can be written by.

 

(1)

where, i refers to CO2 or absorbent, and Ri is the reaction rate of component i. It is assumed that the velocity distribution in the tube side follows the Newtonian laminar flow (Bird et al., 1960):

 

(2)

The boundary conditions on the tube side are considered as:

at z= 0,  and    

(3)

i stands for the solvents, namely MEA, DEA, AMP, MDEA, PG, and PT.

at ,

(4)

at ,  (symmetry)

(5)

where, m is the partition coefficient of CO2 in the solvent.

b) Membrane

As the membrane is assumed to be non-wetting and only CO2 could diffuse through it, the steady state continuity equation for the transport of CO2 in the membrane can be written as follows:

 

(6)

The effective diffusion coefficient of the porous membrane is calculated by Equation 7 (Faiz and Al-Marzouqi, 2009), where  and  are porosity and tortuosity respectively; they are defined by membrane manufacturers.

 

(7)

The boundary conditions on the shell side are considered as follows:

at ,  

(8)

at ,

(9)

c) Shell side

The steady state continuity equation for the transport of CO2 in the shell side can be expressed as given below:

 

(10)

The velocity distribution in the shell can be evaluated by considering Happel’s free surface model:

 

(11)

Also, Happel’s free surface model can be applied to estimating the radius of the shell:

 

(12)

where,  is the volume fraction of the void and can be defined as follows:

 

(13)

In which, n is the number of fibers, and R is the module inner radius.

The boundary conditions on the shell side may be defined by:

at ,

(14)

at ,

(15)

at , (insulation)

(16)

The reaction rates and transport properties for different absorbents are given in Table 1.

Table 1

Reaction rates and transport properties used in this study (Tg= 298 K, Tl= 298 K, CAbsorbent= 1 M).

Absorbent

Parameter

Value

Unit

Reference

MEA

 (1 M)

DCO2-Tube

1.51×10-09

m2/s

(Versteeg and Van Swaalj, 1988)

DAbsorbent-Tube

9.32×10-10

m2/s

(Versteeg and Van Swaalj, 1988)

m

0.8

-

(Versteeg and Van Swaalj, 1988)

CO2 Rate of Reaction

 

mol/(m3.s)

(Liao and Li, 2002)

DEA

(1 M)

DCO2-Tube

1.47×10-09

m2/s

(Versteeg and Van Swaalj, 1988)

DAbsorbent-Tube

6.32×10-10

m2/s

(Versteeg and Van Swaalj, 1988)

m

0.79

-

(Versteeg and Van Swaalj, 1988)

CO2 Rate of Reaction

 

mol/(m3.s)

(Xu et al., 1996)

AMP (1M)

DCO2-Tube

1.18×10-09

m2/s

(Saha et al., 1993)

DAbsorbent-Tube

5.67×10-10

m2/s

(Paul et al., 2007)

m

0.8

-

(Paul et al., 2007)

CO2 Rate of Reaction

 

mol/(m3.s)

(Xu et al., 1996)

MDEA (1M)

DCO2-Tube

1.18×10-09

m2/s

(Versteeg and Van Swaalj, 1988)

DAbsorbent-Tube

6.21×10-10

m2/s

(Versteeg and Van Swaalj, 1988)

m

0.82

-

(Versteeg and Van Swaalj, 1988)

CO2 Rate of Reaction

 

mol/(m3.s)

(Littel et al., 1992)

PG

(1M)

DCO2-Tube

1.42×10-09

m2/s

(Portugal et al., 2007)

DAbsorbent-Tube

1.19×10-09

m2/s

(Hamborg et al., 2008)

m

1.50

-

(Portugal et al., 2007)

CO2 Rate of Reaction

 

mol/(m3.s)

(Portugal et al., 2007)

PT (1M)

DCO2-Tube

1.38×10-09

m2/s

(Portugal et al., 2008)

DAbsorbent-Tube

8.45×10-10

m2/s

(Portugal et al., 2008)

m

1.50

-

(Portugal et al., 2008)

CO2 Rate of Reaction

 

mol/(m3.s)

(Portugalet al., 2008)

2.2. Numerical simulation

The governing equations for CO2 removal related to tube, membrane, and shell are solved numerically using COMSOL Multiphysics software, which uses the finite element method (FEM) for the numerical solution of the governing equations of the model. FEM analysis along with an error control and an adaptive meshing technique is applied using the solver of parallel direct linear solver (PARDISO). This solver is well suited for solving stiff and non-stiff nonlinear boundary value problems. In order to assure the mesh independence of the model, the CO2 removal efficiency of MEA absorbent (at Vl= 0.0503 m/s; Vg= 0.317 m/s; Tl= 308 K; Tg= 298 K; Volume fraction of CO2 in gas= 14 vol.%; MEA concentration= 1 M) was investigated at different mesh numbers. The result is shown in Figure 3. As it could be seen from this figure, the efficiency does not change for the number of elements more than 25000, so this value is chosen as the mesh number in this study. The characteristics of HFMC used in numerical simulation are summarized in Table 2.

 

Figure 3

Checking mesh independence (Vl= 0.0503 m/s; Vg= 0.317 m/s; Tl= 308 K; Tg= 298 K; Volume fraction of CO2 in gas= 14 vol.%; MEA concentration= 1 M).

Table 2

Characteristics of hollow fiber module (Yan et al., 2007).

Parameter

Unit

Symbol

Value

Module inner radius

cm

R

4

Inner radius of fiber

μm

R1

172

Outer radius of fiber

μm

R2

221

Length

cm

L

80

Porosity (%)

-

ε

45

Tortuosity

-

τ

1/ ε ¥

The average size of pore

μm

d

0.02×2

Number of fiber

-

n

7000

¥ Estimated from Wakao–Smith equation, τ= 1/ ε (Zhang et al., 2014)

3. Results and discussion

3.1. Model validation

The model was validated using the experimental results from Yan et al. work (Zhang et al., 2014) for CO2 absorption in MEA, MDEA, and PG. In this section, the results of the model are compared with the experimental data. The removal efficiency of CO2 may be defined as below:

 

(17)

where,  is removal efficiency of CO2, and  and  are the gas flow rates at the inlet and outlet respectively;  and  are the concentration of CO2 at inlet and outlet respectively. The concentration of CO2 at shell side outlet is obtained using Equation 18.

 

(18)

The CO2 removal efficiency at different gas velocities for MEA and PG is presented in Figure 4. The effects of CO2 volume fraction in gas phase on CO2 removal efficiency of MEA, MDEA, and PG are presented in Figure 5. As it can be seen, the simulation results are in good agreement with the experimental data. The characteristics of the hollow fiber membrane module are given in Table 2.

 

Figure 4

Comparison of the experimental results with the model results for the effect of gas velocity on the CO2 removal efficiency; Vl= 0.0503 m/s; Tl= 308 K; Tg= 298 K; Volume fraction of CO2 in gas= 14 vol.%; Absorbent concentration= 1M.

 

Figure 5

Comparison of the experimental results with the model results for effect of CO2 in the gas phase on the CO2 removal efficiency; Vl= 0.0503 m/s; Tl= 308 K; Vg= 0.211 m/s; Tg= 298 K; Absorbent concentration= 0.5 M.

3.2. CO2 Concentration distribution 

Figure 6 indicates the dimensionless concentration distribution of CO2 when PG is used as the absorbent. The gas mixture containing N2 and CO2 enters at the shell side from the top (z=L), where the concentration of CO2 is maximized. The fresh chemical absorbent (PG) enters at the tube side from the bottom (z=0), where the concentration of CO2 is zero. As the gas flows through the shell side, CO2 transfer across the membrane because the concentration difference (or chemical potential difference) between the shell side and the tube side gradually decreases. It should be noted that the concentration difference is the driving force for the diffusion of CO2 through the membrane from the shell side to the tube side. CO2 is transferred to the shell side of the contactor by two mechanisms, diffusion in the radial direction due to the concentration difference and convection in the axial direction. The removal of CO2 increases by increasing the diffusion of CO2 through the membrane; therefore, the diffusion mechanism is favorable. Due to non-wetted mode assumption, the concentration of CO2 at the same z-coordinate in the membrane and the shell side is uniform.

 

Figure 6

Dimensionless concentration of CO2; Vl= 0.0503 m/s; Tl= 308 K; Vg= 0.211 m/s; Tg= 298K; PG concentration= 1M.

3.3. Effect of gas and liquid velocity on removal efficiency

In this section, the performance of different absorbents is compared. The effect of liquid (absorbent) velocity on CO2 capture is presented in Figure 7. As we can see from Figure 7, initially, the removal efficiency of CO2 is relatively strong and increases as a function of the absorbent velocity. At later stages the removal efficiency of CO2 weakens, but it still increases as a function of absorbent velocity for MEA, DEA, AMP, PG, and PT absorbents. Therefore, the optimum amount of absorbent could be attained, and costs, due to expensive absorbents and environmental problems assigned to them, will be decreased. It is obvious that as the absorbent velocity increases, the removal efficiency of CO2 increases because increasing absorbent velocity increases the concentration gradient at the tube-membrane interface; thus, the removal efficiency of CO2 is increasing. Figure 7 also clearly depicts the fact that PG absorbent has the highest removal efficiency of CO2, followed by PT, MEA, AMP, DEA, and MDEA in sequence, which is similar to the trend of reaction rate. Amino acids (PG and PT) also have higher partition coefficients which improves the physical absorption and CO2 capture. It can be seen from Figure 7 that the removal efficiency of MDEA is much lower than that of the other absorbent, which is ascribed to the reaction rate of MDEA with CO2.

 

Figure 7

Effect of liquid phase velocity on the removal efficiency of CO2 for various absorbents; Vg= 0.423 m/s; Tl= 298 K; Tg= 298 K.

Figure 8illustrates the variation of CO2 removal efficiency against gas velocity. As expected, increasing gas velocity decreases the residence time of gas phase in the membrane contactor, which leads to decreasing the removal efficiency of CO2. The trend of removal efficiency of CO2 for different absorbents is similar to what presented in the previous part.

 

Figure 8

Effect of gas phase velocity on the removal efficiency of CO2 for various absorbents; Vl= 0.0503 m/s; Tl= 298 K; Tg= 298 K.

Therefore, from the above discussion, it can be concluded that the CO2 removal efficiency using different absorbents follows the following sequence: PG> PT> MEA> AMP> DEA> MDEA. Therefore, PG is the preferred absorbent.

3.4. Effect of PG concentration on removal efficiency

Figure 9 illustrates the removal efficiency of CO2 at various PG inlet temperatures. It is evident that increasing absorbent temperature increases the removal efficiency of CO2. As the temperature rises, the reaction rate (Kumar et al., 2002; Dindore et al., 2005) and diffusivity (Snijder et al., 1993) of CO2 in absorbent increase, which results in an increase in the removal efficiency of CO2. Moreover, increasing absorbent temperature raises the absorbent evaporation (Tan and Chen, 2006), which leads to a reduction in the removal efficiency of CO2. In this temperature interval (293-313 K), the effect of temperature on the reaction rate and diffusivity is higher than the effect of temperature on evaporating the solvent. At other temperatures, different results may be attained. 

 

Figure 9

Effect of absorbent temperature on the removal efficiency of CO2; Vl= 0.0503 m/s; Vg= 0.528 m/s; Tg= 298 K; PG concentration= 1 M.

3.5. Effect of packing density on removal efficiency

The effect of packing density on the removal efficiency of CO2 is presented in Figure 10. Increasing the number of fibers resulted in an increase in the packing density. In other words, as the packing density increases, the effective area for mass transfer rises, which causes the removal efficiency of CO2 to improve, even to a hundred percent. 

 

Figure 10

Effect of packing density on the removal efficiency of CO2; Vl= 0.0503 m/s; Tl= 298 K; Vg= 0.8 m/s; Tg= 298 K; PG concentration= 1M.

3.6. Effect of fiber diameter on removal efficiency

The effect of fiber diameter on the removal efficiency of CO2 is illustrated in Figure 11. If the inner (R1) and outer (R2) radii of fiber are multiplied by enlargement factor (σ), the shell diameter (R3) is calculated by Equation 12. Therefore, increasing the enlargement factor resulted in an increase in the contact area, which in turn reduces the CO2 outlet concentration. In agreement with prior expectations, as the enlargement factor increases, the removal efficiency of CO2 is improved.

 

Figure 11

Effect of fiber diameter on the removal efficiency of CO2; Vl= 0.0503 m/s; Tl= 298 K; Vg= 0.528 m/s; Tg= 298 K; PG concentration= 1 M.

4. Conclusions

A comprehensive two-dimensional mathematical model was developed to describe CO2 capture by absorption in HFMC using various absorbents. In this study, the performance of six absorbents, namely PG, PT, MEA, AMP, DEA, and MDEA, in removing CO2 was compared. The model was established for a non-wetted mode and a parallel countercurrent gas-liquid flow arrangement. The radial and axial diffusions in the transport equations were assumed. The equations were solved by FEM, and the model was validated using the results reported by Yan et al. (2007); the simulation results were in good agreement with the experimental data. PG absorbent has the highest removal efficiency of CO2 followed by PT, MEA, AMP, DEA, and MDEA in sequence. The results of the proposed model indicated that the removal efficiency of CO2 increased with increasing absorbent velocity, absorbent temperature, packing density, and enlargement factor. Increasing gas velocity in the shell side has a reverse effect on CO2 removal efficiency. It is worth mentioning that the assumptions of ideal gas may introduce some limitations to the model, and it may not be applicable to high pressures. It is suggested that the effect of using equations of state be investigated in the future works.      

Nomenclature

C

: Concentration (M or mol/m3)

D

: Diffusion coefficient (m2/s)

L

: Hollow fiber membrane length (cm)

m

: Partition coefficient

n

: Number of hollow fiber

Q

: Volumetric flow rate (m3/s)

R

: Hollow fiber membrane module radius (cm)

r

: Radial coordinate (m)

R

: Reaction rate (mol/m3.s)

R1

: Inner radius of fiber (μm)

R2

: Outer radius of fiber (μm)

Tg

: Inlet gas phase temperature (K)

Tl

: Inlet liquid phase temperature (K)

Vg

: Gas phase velocity (m/s)

Vl

: Liquid phase velocity (m/s)

z

: Axial coordinate (m)

ε

: Membrane porosity

η

: CO2 removal efficiency

σ

: Enlargement factor

τ

: Membrane tortuosity

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