Numerical simulation of CO2 separation from gas mixtures in membrane modules: Effect of chemical absorbent

Seyed Mohammad Reza Razavi; Saeed Shirazian; Mahboobeh Nazemian

doi:10.1016/j.arabjc.2015.06.006

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Original article

9 (

); 62-71

doi:

10.1016/j.arabjc.2015.06.006

Numerical simulation of CO₂ separation from gas mixtures in membrane modules: Effect of chemical absorbent

Seyed Mohammad Reza Razavi^{^a}, Saeed Shirazian^{^a,⁎}, Mahboobeh Nazemian^{^b}

a Young Researchers and Elite Club, South Tehran Branch, Islamic Azad University, Tehran, Iran

b Iran Polymer and Petrochemical Institute, Tehran, Iran

⁎Corresponding author. Tel.: +98 9378459498. saeed.shirazian@gmail.com (Saeed Shirazian)

Received: 2015-4-3, Accepted: 2015-6-3, 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

In this study, a mathematical model is proposed for prediction of CO₂ absorption from N₂/CO₂ mixture by potassium threonate in a hollow-fiber membrane contactor (HFMC). CFD technique using numerical method of finite element was applied to solve the governing equations of model. Effect of different factors on CO₂ absorption was analyzed and for investigation of absorbent type effect, functioning of potassium threonate was compared with diethanolamine (DEA). Axial and radial diffusion can be described with the two dimensional model established in this work. The obtained simulation results were compared with the reported experimental data to ensure accuracy of the model predictions. Comparison of model results with experimental data revealed that the developed model can well predict CO₂ capture by potassium threonate in HFMCs. Increment of absorbent flow rate and concentration eventuate in enhancement of CO₂ absorption. On the other hand, capture of CO₂ will be reduced with increment of gas flow rate. According to the model results, potassium threonate can be considered as a more efficient absorbent as compared with DEA.

Keywords

Separation

Membrane

Mathematical modeling

Numerical simulation

Mass transfer

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Nomenclature

C: concentration (mol/m³)
$C_{outlet}$: outlet concentration of solution the tube side (mol/m³)
$C_{inlet}$: inlet concentration of solution the tube side (mol/m³)
$C_{i - tube}$: concentration of solution the tube side (mol/m³)
$C_{i - shell}$: concentration of solution the shell side (mol/m³)
$C_{i - membrane}$: concentration of solution membrane (mol/m³)
D: diffusion coefficient (m²/s)
F: liquid feed flow (m³/s)
m: physical solubility
P: pressure (pa)
r: radial coordinate (m)
$r_{1}$: inner tube radius (m)
$r_{2}$: outer tube radius (m)
$r_{3}$: inner shell radius (m)
u: average velocity in tube side (m/s)
z: axial coordinate
$V_{z-shell}$: z – velocity in the shell (m/s)
$V_{z-tube}$: z – velocity in the tube (m/s)

1 Introduction

CO₂ that normally exists in natural gas streams, biogas produced from anaerobic absorption, flue gas generated by combustion of fossil fuels, and coal gasification is the most important greenhouse gas on the earth (Zhang et al., 2013). CO₂ capture will improve the calorific value of natural gas (NG), reduce the volume of gas that is transported through the pipeline, decrease equipment corrosion and inhibit atmospheric pollution and global warming (Zhang et al., 2013; Chew et al., 2010; Razavi et al., 2015 ). Consequently there is a need to design a novel method to eliminate CO₂ from gas streams.

CO₂ can be removed from gas streams by different methods that two most important of them are absorption and membrane separation (Razavi et al., 2013; Fasihi et al., 2012; Shirazian et al., 2012a,b; Rezakazemi et al., 2013a; Ghadiri et al., 2013a; Shirazian and Ashrafizadeh, 2013, 2011; Fadaei et al., 2011 ). From the mentioned methods, absorption has been established as a well-accepted method at industrial applications (Adewole et al., 2013). However this method has some drawbacks such as expensive chemical solvents, low efficiency of process, production of large amounts of wastewater and sludge in the process, costly equipment, consumption of energy for solvent regeneration, high complexity of the processes, and negative environmental impact due to consumption of solvents (Thiruvenkatachari et al., 2009). Accordingly, there is a need to find an alternative technology that would be cost effective and energy efficient such as membrane separation for CO₂ removal from gas streams.

Nowadays, capture of CO₂ from gas streams using membrane separation technology has become an attractive approach as compared to the aforementioned separation methods (Yeo et al., 2012; Fadaei et al., 2011; Ghadiri and Shirazian, 2013 ). This method is more capital efficient and could achieve higher efficiency of separation with this method. Additionally, simplicity of process in modern compact modules, high reliability, low capital and operating cost of process, the nature of environmentally friendly, high space efficiency, low energy consumption, clean and continuous process are some of the advantages of application of membrane for gas separation which makes it favorable for large scale applications (Adewole et al., 2013; Yeo et al., 2012; Rezakazemi et al., 2013b; Ghadiri et al., 2013b ).

As compared to different types of membranes, polymeric membranes that have low molecular weight, process ability into thin films, absorbent materials, composites and hollow fibers and large variety in structure and properties have the most usage in industrial applications (Zhang et al., 2013; Razavi et al., 2015; Yeo et al., 2012; Miramini et al., 2013 ). Numerous polymers that so far have been utilized for membranes fabrication used in gas separation, include cellulose acetate (CA), polyimide (PI), polysulfone (PSf), polyethersulfone (PES), and polycarbonates (PC) Zhang et al., 2013. Depending on different gas separation requirements, specific polymeric membrane is chosen and applied. Polysulfone and cellulose acetate are the earliest commercial membranes, while PI and CA have been mostly used for CO₂/CH₄ separation commercially (Han and Lee, 2011; Spillman, 1995).

Among the various kinds of membranes, hollow-fiber membrane contactors are the most desirable device since they present higher surface/volume ratio. In recent years, many researchers have focused on investigation of different factors affecting HFMCs performance such as different absorbents, various polymers as a membrane, and flow rate of gas and liquid (Fasihi et al., 2012; Ghadiri et al., 2013a,b,c, 2014a,b, 2015; Fadaei et al., 2011a,b, 2012; Miramini et al., 2013; Ghadiri and Ashrafizadeh, 2014; Marjani et al., 2012a,b, 2011a,b; Marjani and Shirazian, 2010, 2011a,b,c,d,e, 2012a ).

In membrane gas absorption, the absorbent plays a vital role for CO₂ capture. Among the various absorbents, alkanolamines such as AMP, DEA, TEA, DGA, MEA, MEDA and DIPA have the most appliances as absorbent for removal of CO₂ from gas streams. Choosing a liquid absorbent depends on the properties of absorbent such as rate of reaction with CO₂, thermal stability, vapor pressure and easily regeneration (Razavi et al., 2013; Li and Chen, 2005; Blauwhoff et al., 1984 ).

Lu et al. studied effect of AMP and Piperazine as activators for solution of MDEA on CO₂ capture from gas mixture (Lu et al., 2007). Ren et al. investigated CO₂ capture by PVDF membranes and also the effect of process parameters on separation efficiency (Ren et al., 2006). With the aim of simulation, use of membrane separation for elimination of CO₂ from gas mixtures in industrial scale would become more easily and more cost effective. Simulations of HFMCs have attracted many research attentions. Mathematical modeling and numerical simulation of membrane contactors considering chemical reaction have been studied in the literature (Fasihi et al., 2012; Shirazian et al., 2012a,b; Shirazian and Ashrafizadeh, 2013, 2011; Fadaei et al., 2011a,b, 2012; Ghadiri and Shirazian, 2013; Ghadiri et al., 2013b,c, 2014a,b; Marjani et al., 2012a,b, 2011a,b; Marjani and Shirazian, 2010, 2011a,b,c,d,e, 2012a; Fazaeli et al., 2015; Tahvildari et al., 2016 ). The main aim of the simulation works was to determine the concentration of CO₂ in the membrane contactor. However, some works accounted for chemical reaction.

Although amine solutions have more uses in membrane gas separation as compared with other absorbents, they have some disadvantages including easily degradation, particularly in oxygenated atmosphere, corrosion and high volatility (Mandal and Bandyopadhyay, 2005; Portugal et al., 2008). Because of these disadvantages, researchers try to develop more suitable absorbents such as amino acid salt solutions. Stability of amino acid salt solutions in the oxygenated atmosphere is higher than alkanolamines. Because amino acid salt solutions have ionic nature, not only they are less volatile but also they have high surface tensions. Potassium threonate is an amino acid salt that has a reasonable capacity in membrane separation of CO₂. Potassium threonate, in spite of good capability of regeneration, high surface tension and low volatility, is not deleterious for health (Portugal et al., 2008).

Portugal et al. (2008) investigated CO₂ capture in aqueous solution of Potassium threonate and determined densities and viscosities of aqueous solution at concentration range of 0.1–3 M and temperatures from 293 to 313 K. Their results showed that the pseudo-first-order reaction can be used to describe CO₂ absorption in the aqueous solution of Potassium threonate. Moreover, it was indicated that CO₂ absorption rate was enhanced by increasing CO₂ and potassium threonate concentrations (Portugal et al., 2008).

In this work, because of potassium threonate advantages along with advantages of membrane separation, capture of CO₂ by potassium threonate in HFMC is simulated. In addition to the investigation of influence of various parameters on CO₂ removal, performance of potassium threonate is compared with DEA for selecting the most effective one.

2 Mass transfer model

In the present work, a comprehensive 2D phenomenological model is developed for the capture of CO₂ from CO₂/N₂ gas stream in a hollow-fiber membrane contactor. Fig. 1 represents the schematic diagram of the HFMC simulated in this study. The membrane module consists of 21 fibers with an inner and outer diameter of 1.4 mm and 2.2 mm respectively within a module which has an outer diameter of 16 mm. Razavi et al. have provided a table containing geometrical characteristics of the simulated HFMC in their study (see Table 1) (Razavi et al., 2013). Gas mixture and liquid solution of chemical absorbent flow counter currently into the tube and shell of the HFMC respectively. Flow rate of gas mixture is kept between 100 and 400 cm³/min and flow rate of liquid solution of absorbent is in the range of 50–350 cm³/min. Absorbent concentration in liquid solution is 0.5 M.

A graphical diagram for the hollow-fiber membrane contactor.

Table 1 Characteristics of hollow fiber module.

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
Average pore size (mm)	0.2
Fiber porosity, ε (%)	50
Surface area (m²)	0.02

2.1

2.1 Model equation

By applying Navier–Stokes equation, velocity distribution in the tube side can be derived, but for developing velocity profile in the tube side, a fully developed Newtonian laminar flow is assumed (Bird et al., 1960):

(1)

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

where r₁ and u indicate inner radius of fiber and average velocity of stream in the tube, respectively.

It should be noted that according to the free surface model, cross sectional area of fiber is considered to be circle-shaped (Happel, 1959). The continuity equation for each component can be expressed as follows (Bird et al., 1960):

(2)

\frac{\partial C_{i}}{\partial t} = - (\nabla \cdot C_{i} V) - (\nabla \cdot J_{i}) + R_{i}

where C_i, t, V, J_i and R_i indicate concentration (mol cm⁻³), time (s), velocity (m/s), diffusion flux (mol m⁻² s⁻¹) and reaction rate of component i (mol m⁻³ s⁻¹), respectively.

For simplifying Eq. (2), the process assumed to be steady state and J_i was substituted with Fick’s law.

2.1.1

2.1.1 Tube side equations

In the tube side of HFMC there is no chemical reaction, addition to the fact that convective mass transfer in radial direction is not considerable in comparison with axial direction. Consequently Eq. (2) can be written as follows:

(3)

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

where r and z denote the radial and axial coordinates, respectively.

Boundary conditions considered for the tube side are as follows:

(4)

At r = r_{1}, C_{{CO}_{2} - tube} = C_{{CO}_{2} - membrane}

(5)

At r = 0, \frac{\partial C_{{CO}_{2} - tube}}{\partial r} = 0

(6)

At z = 0, convective flux

(7)

At z = L, C_{{CO}_{2} - tube} = C_{{CO}_{2}, 0}

It should be noted that convective flux in Eq. (6) indicates that the mass transfer through this boundary by diffusion mechanism is neglected.

2.1.2

2.1.2 Shell side equations

The steady-state continuity equation in the shell side is expressed as follows:

(8)

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

As stated before, by solving Navier–Stokes equation, velocity distribution in the shell side can be obtained (Bird et al., 1960) as follows:

(9)

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

V (m/s), P (Pa), ρ (kg m⁻³), η (kg m⁻¹ s⁻¹) and F (N) denote velocity, pressure, density, dynamic viscosity and body force, respectively. The shell radius can be estimated by applying Happel free surface model as follows:

(10)

r_{3} = {(\frac{1}{1 - ϕ})}^{1 / 2} r_{2}

where r₂ indicates the tube outer radius. Φ is the volume fraction of void section and can be defined by

(11)

1 - ϕ = \frac{{nr}_{2}^{2}}{R^{2}}

where n and R are the number of fibers and inner radius of modules, respectively.

Boundary conditions used for the shell are as follows:

(12)

At r = r_{3}, \frac{\partial C_{{CO}_{2} - shell}}{\partial r} = 0

(13)

At r = r_{2}, C_{{CO}_{2} - shell} = C_{{CO}_{2} - membrane} \times m

(14)

At z = 0, C_{{CO}_{2} - shell} = 0, V_{z- shell} = V_{0}

(15)

At z = L, Convective flux, p = p_{atm}

where m denotes solubility of CO₂ in absorber.

2.1.3

2.1.3 Membrane equations

Transport of CO₂ into the membrane pores is accomplished just via diffusion mechanism. Steady state and no reaction assumptions will simplify the continuity equation as follows:

(16)

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

In which boundary conditions can be written as follows:

(17)

At r = r_{1}, C_{{CO}_{2} - membrane} = C_{{CO}_{2} - shell}

(18)

At r = r_{2}, C_{CO 2 - membrane} = \frac{C_{{CO}_{2} - shell}}{m}

2.1.4

2.1.4 Absorbent equations

The steady state continuity equation for potassium threonate absorber is written as follows:

(19)

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

R_i denotes the chemical reaction between CO₂ and potassium threonate absorbent (Portugal et al., 2008). Boundary conditions required for solving Eq. (19) are given as follows:

(20)

At r = r_{3}, \frac{\partial C_{absorbent - shell}}{\partial r} = 0

(21)

At r = r_{2}, \frac{\partial C_{absorbent - shell}}{\partial r} = 0

(22)

At z = 0, C_{absorbent-shell} = C_{absorbent, 0}

(23)

At z = L, Convective flux

2.2

2.2 Numerical procedure

The governing equations in membrane, tube and shell side were solved by the commercial finite element package of COMSOL Multiphysics version 3.5., according to the finite element method (FEM). Moreover solver of UMFPACK was used for solving symmetric problems. Some researchers have asserted the applicability and accuracy of UMFPACK for solving membrane equations (Razavi et al., 2013, 2014; Fasihi et al., 2012; Shirazian et al., 2012a,b,c,d,e; Rezakazemi et al., 2013a,b,c, 2011a,b, 2012; Shirazian and Ashrafizadeh, 2013, 2011, 2010a,b, 2014, 2015a,b,c; Fadaei et al., 2011a,b, 2012; Ghadiri et al., 2013b; Marjani et al., 2012a,b,c, 2011a,b; Marjani and Shirazian, 2010, 2011a,b,c,d,e, 2012a,b,c,d,e; Hemmati et al., 2015; Hoshyargar et al., 2012; Khansary et al., 2015; Kohnehshahri et al., 2011; Moghadassi et al., 2011; Mohammadi et al., 2015; Moradi et al., 2013; Nosratinia et al., 2015; Pishnamazi et al., 2012; Ranjbar et al., 2013; Shirazian et al., 2011a,b, 2009, 2014; Sohrabi et al., 2011a,b,c,d,e; Valavi et al., 2013 ). Triangular mesh elements used for the evaluation of gas behavior in the HFMC are illustrated in Fig. 2 in which r₁ and r₂ represent the radius of shell side and free surface respectively.

Model domain and FE model used for simulation.

3 Results and discussion

3.1

3.1 Model validation

According to author’s investigations, absorption of CO₂ by potassium threonate using hollow-fiber membrane contactors has not been studied experimentally. Therefore, developed model in this study was validated through comparison of simulation results with experimental results of CO₂ removal from N₂ in the HFMC reported in the literature (Lin et al., 2008). As it can be seen in Fig. 3, there is a reasonable agreement between simulation results and experimental data. However, some deviations can be observed between experimental and modeling data which could be attributed to the estimation of reaction kinetics and constants.

Relation between reaction rate and gas flow rates (for validation of model).

3.2

3.2 Velocity distribution

Figs. 4 and 5 illustrate velocity distribution of absorbent inside the shell side of HFMC. It is clearly seen that the velocity profile is almost parabolic and reveals the maximum velocity of absorbent phase at the center of shell side. The latter could be due to the boundary conditions imposed on two sides of shell side and also the effects of viscous forces on the fluid which makes a symmetry velocity profile. Additionally, velocity amount on the two shell walls is zero because of no-slip conditions. Figs. 4 and 5 also represent that after a short distance from entrance of shell side, velocity profile becomes fully developed. The velocity profile in Fig. 5 is depicted against dimensionless radial distance (r/r₃).

Velocity field in the shell side (absorbent channel) of the hollow-fiber membrane contactor.

Figure 5

Velocity profile in the shell side (absorbent channel) along the membrane length.

3.3

3.3 Concentration distribution of CO₂

Distribution of dimensionless concentration (C/C_o) for CO₂ in the membrane, tube and shell side of the HFMC is illustrated in Fig. 6. While gas mixture flows from one side of the HFMC, in which CO₂ concentration is maximum, the potassium threonate solution flows from the other side in which gas concentration of CO₂ is considered to be zero. As the gas mixture flows through the tube, concentration difference caused CO₂ transferred to the membrane (Shirazian et al., 2012a; Ghadiri et al., 2013c; Shirazian and Ashrafizadeh, 2010a; Sohrabi et al., 2011c ). Generally, the gas in the membrane contactor is transferred by two mechanisms, i.e. diffusion and convection. Diffusion is observed in radial direction due to concentration gradient, while convection is observed in axial direction due to velocity of fluid. However, in the tube side the diffusional mass transfer is favorable because it can increase the amount of CO₂ capture. Gas mixture is transferred through the membrane pores to the other side and the moving solvent in the shell side could absorb the CO₂.

Dimensionless concentration distribution for CO2 in the tube, the membrane and the shell of the HFMC.

Fig. 7 illustrates the distribution of CO₂ concentration in the tube in the axial direction. CO₂ concentration reduces with increasing the length of membrane due to CO₂ removal by absorbent solution. Additionally, variation rate of CO₂ along the HFMC has not been altered significantly.

Figure 7

The profile of carbon dioxide concentration in the tube (gas channel) in axial direction (z-direction).

3.4

3.4 Concentration distribution of the absorbent

Fig. 8 shows a representation of the distribution of dimensionless concentration of potassium threonate in the shell side of HFMC. When CO₂ diffuses through the membrane pores, it reacts with potassium threonate solution flowing in the shell side. Consequently, absorbent concentration reduces along the HFMC considerably due to consumption of solvent. Axial concentration distribution of potassium threonate along the contactor can be observed in Fig. 9. The absorbent concentration decays in the middle of HFMC length faster than entrance region of HFMC. It is due to the fact that CO₂ concentration in the entrance of shell side is negligible. Therefore, concentration of absorbent solution in the mentioned region has not changed significantly. Fig. 10 indicates total flux of CO₂ and absorbent simultaneously that helps to perceive the mechanism of system functioning.

Dimensionless concentration of potassium threonate in the shell of the HFMC.

Axial variation of potassium threonate concentration along the HFMC.

Total flux of CO2 and absorbent in the membrane module.

3.5

3.5 Effects of gas and liquid flow rates on CO₂ capture

In this section, simultaneous performance of potassium threonate and DEA absorbents is compared to evaluate the efficiency of separation process using each absorbent. Figs. 11 and 12 show relationship between reaction rate of CO₂ and the two mentioned absorbents versus liquid and gas flow rate, respectively. As it can be seen in Fig. 11, for both absorbents, the reaction rate increases by increase of liquid flow rate. This is because of the fact that the enhancement of liquid flow rate results in increase of Reynolds number and consequently mass transfer coefficient. Additionally, with further increment of liquid flow rate, reaction rate of CO₂ removal does not alter significantly. Therefore, optimum amount of absorbent could be achieved and costs due to expensive absorbents and environmental problems attributed to it, will be decreased. It is obvious from this figure that efficiency of potassium threonate is higher than DEA considerably and for all of the liquid flow rates, reaction rate of potassium threonate is much more than DEA. Therefore it seems that potassium threonate is better absorbent for CO₂ capture than DEA. Fig. 12 shows variation of reaction rate of CO₂ with absorber as a function of gas flow rate. According to this figure, enhancement of gas flow rate results in decrease of reaction rate. This could be due to the fact that as gas flow rate increases, resistance time in the contactor declines. Consequently absorption of CO₂ to liquid phase decreases.

Correlation between reaction rate and gas flow rate.

Correlation between reaction rate and liquid flow rate.

4 Conclusions

In this study, simulation of CO₂ capture by potassium threonate through HFMCs was conducted using CFD technique. Numerical method of finite element was applied to solve equations of mass transfer and a two dimensional mathematical model for prediction of the CO₂ absorption through the HFMC was developed. Because of importance of absorbent types in gas separation, function of two absorbents of potassium threonate and DEA was compared. Comparison of model predictions with experimental results reveals that reasonable agreement exists between them. Simulation results reveal that potassium threonate can be considered as a more efficient absorber as compared with DEA. According to the model results, that increment of absorbent concentration and flow rate eventuate in increment of CO₂ absorption. On the contrary, enhancement of gas flow rate reduces CO₂ capture. It can be concluded from the obtained results that the proposed model in this work can well predict CO₂ removal through the HFMCs.

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Introduction

Mass transfer model

Model equation
Numerical procedure

Results and discussion

Model validation
Velocity distribution
Concentration distribution of CO2
Concentration distribution of the absorbent
Effects of gas and liquid flow rates on CO2 capture

Conclusions

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