1D Modeling of CO₂ Absorption Using K₂CO₃ in a Hollow Fibre Membrane Contactor

Abstract

Carbon dioxide (CO₂) is widely recognized as the main cause of climate change affecting our planet. In recent years, the concentration of CO₂ in the atmosphere has increased significantly due to the intensive combustion of fossil fuels. This study is devoted to the simulation of the 1D case of the CO₂ capture process by aqueous Potassium carbonate K₂CO₃ as a chemical solvent, using a membrane contactor in the counter current case. The system of partial differential equations resulting from the modeling was solved using MATLAB’s PDEPE function. We also carried out a parametric analysis to see the impact of various parameters on the CO₂ capture process. Among these parameters, we studied the influence of solvent concentration, gas velocity and liquid velocity. The results show that 13% increase (74–87%) in CO₂ capture while the increase of solvent concentration from 20 to 50 (mol/m³), also for gas and liquid velocity from 0.001 to 0.05 and 0.006 to 0.05 (m/s) we have 52% and 3% increase of CO₂ capture respectively.

1. Introduction

Carbon dioxide (CO₂) is widely recognized as a major contributor to global climate change. In recent years, the concentration of CO₂ in the atmosphere has increased significantly due to the intensive combustion of fossil fuels. Rising CO₂ emissions are a major cause of catastrophic environmental change that has led to growing interest in successful CO₂ capture [1]. Over the past decades, various technologies have been used for CO₂ capture. Chemical absorption by absorbents in trays and packed columns is the traditional method [2]. However, this method has economic and operational problems. Membrane contactor absorption is a new technology with many advantages, including: B. Prevention of interphase dispersion, high specific surface area, and compact size of the contactor [3]. In porous membrane contactors, absorption typically occurs when CO₂ diffuses from the shell side through the membrane pores and contacts the liquid phase within the fibers. Therefore, there are no flooding, bubbling, channeling or entrainment problems associated with traditional absorber towers. Although membranes have been used commercially for gas separation since his 1980s, researchers have studied membranes over his 150 years [4, 5, 6]. Much research has been done on the development of membrane contactor systems and the mass transfer rates of membranes [7, 8, 9, 10]. Membrane gas absorption has been introduced as one of the beneficial technologies to prevent CO₂ emissions due to its excellent mass transfer capabilities [11]. Many researchers compared his performance of CO₂ capture from flue gas using amine absorption (packed column or bubble column) as a conventional technique with membrane gas absorption technology [12, 13]. Their investigation showed that the membrane possesses a high surface-to-volume ratio, flexible operating characteristics, linear scaling, compact size, and modularity [3, 14, 15]. In addition, traditional absorber towers have many drawbacks such as channeling, foaming, flooding, aeration, and high operating and capital costs [16]. The use of membranes solves the above problem because CO₂ absorption occurs in the membrane contactor when the gas stream contacts the liquid phase on the other side of the membrane. In fact, the membrane acts as a barrier between the gas and liquid phases, preventing interpenetration of the gas and liquid phases. Additionally, increasing the membrane length may improve mass transfer between phases [16]. Furthermore, the membrane process has been introduced as an environmentally friendly alternative as a small amount of solvent, always lost to the atmosphere during the process [17]. Also, the liquid flow does not depend on the gas flow rate. However, the membrane process has some problems. The main problem is membrane wetting [18]. The most important criteria for choosing an absorbent in membrane gas absorption are the surface tension of the absorbent and its compatibility with the membrane material. Absorbents with low surface tension wet the pores of the membrane. Alkanolamine solvents such as MEA are the most commonly used absorbents for CO₂ capture due to their fast reaction rate with CO₂. However, amine solvents present challenges in terms of high regeneration energy and evaporative losses [19, 20]. Many researchers have spent a lot of time finding alternative absorbents to alkanolamines. A potential candidate is aqueous potassium carbonate (K₂CO₃). Potassium carbonate is an economical and environmentally friendly absorbent with low cost and low renewable energy for CO₂ absorption [21]. However, it slows down its reaction rate with CO₂, especially at low temperatures and low CO₂ partial pressures [22]. Adding an accelerator to potassium carbonate could be a viable approach to solve this problem [23].

2. Material and methods

In this work, the study was made by taking a volume element of the CO₂ absorption model using a membrane. We have a counter current flow from which the gas containing the CO₂ molecules enters the shell side (Z = 0); afterwards it crosses the membrane through the pores arriving in the tube side which contains the counter current solvent (Z = l). Also, an unsteady-state of a one-dimensional mathematical model has been considered and solved using pdepe MATLAB software. The model is developed for an element volume as shown in Figure 1 and Table 1.

Figure 1.

Diagram of volume element mass transfer resistances.

Membrane material (abbreviation)	Reference	Gases separated	Solvent(s) trialed
Polypropylene (PP)	[25]	N2/CO2	MEA, DEA, MDEA, MEA/MDEA, DEA/2-amino2-methyl-1-propanol (AMP), a
	[26]	CO2, CO, H2, N2, CH4	Monoethanolamine, potassium carbonate
	[27]	CO2	MEA
	[28]	N2/CO2	Monoethanolamine (MEA), [3 M]
	[29]	N2/CO2/O2	Methyldiethanolamine (MDEA) [0.5e3 M]
Polyvinylidene fluoride (PVDF)	[30]	N2/CO2	Water
	[31]	N2/CO2	Diethanolamine (DEA)
Polytetrafuloroethylene (PTFE)	[26]	CO2, CO, H2, N2, CH4	Monoethanolamine [30 wt%], potassium carbonate [30 wt%]
	[32]	25% CO2, 75% N2	Monoethanolamine, MEA, 5 wt%
	[32]	CO2, N2	2-Amino-2-methyl-1-propanol (AMP)

Table 1.

Gas absorption membranes [24].

2.1 Mass transfer resistance in series model

The resistances in series in the hollow fiber membrane module Figure 1, can be written as following Eq. (1):

$${\mathrm{R}}_{\mathrm{T}}={\mathrm{R}}_{\mathrm{g}}+{\mathrm{R}}_{\mathrm{m}}+{\mathrm{R}}_{\mathrm{l}}$$E1

Where R_T is the total mass resistance, R_l is the mass resistance of the liquid phase, R_m is the mass resistance of HFMC and Rg is the mass resistance in the gas phase, as the resistance on the liquid side has been neglected. Then, by mass transfer term, “for example, see [33]”:

$$\frac{1}{K_G}=\frac{d_{\mathit{ext}}}{d_{\mathit{int}}}\frac{1}{k_g}+\frac{d_{\mathit{ext}}}{d_{\mathit{ln}}}\frac{1}{k_m}+\frac{\mathcal{H}}{k_l\times \mathit{Ha}}$$E2

$$d_{\mathit{ln}}=\frac{d_{\mathit{ext}}-d_{\mathit{int}}}{\mathit{ln}\left(\frac{d_{\mathit{ext}}}{d_{\mathit{int}}}\right)}$$E3

$$\mathit{Ha}=\frac{\sqrt{\mathit{Koh}\times C_{k2\mathit{co}3}\times D_{\mathit{co}2,l}}}{k_l}$$E4

Where d_int, d_ext and Ha are the internal, external diameter and hatta number, respectively, k_g is the gas-phase mass transfer coefficient that is estimated using next following Eqs. (5)–(8), k_l is the liquid-phase mass transfer coefficient and k_m is membrane mass transfer coefficient [34].

2.1.1 Gas-side mass transfer coefficient k_g

$${\mathit{Sh}}_{\mathit{g}}=\frac{{\mathit{k}}_{\mathit{g}}{\mathit{d}}_{\mathit{h}}}{{\mathit{D}}_{\mathit{CO}\mathrm{2},\mathit{g}}}=\mathrm{0.6655}{{\mathit{R}}_{\mathit{e}}}^{\mathrm{0.5}}{\mathit{SC}}^{\mathrm{0.33}}$$E5

$${\mathit{D}}_{\mathit{CO}\mathrm{2},\mathit{g}}=\frac{\mathrm{1.013}\times {\mathrm{10}}^{-\mathrm{2}}{{\mathit{T}}_{\mathit{g}}}^{\mathrm{1.5}}{\left(\frac{\mathrm{1}}{{\mathit{M}}_{\mathit{CO}\mathrm{2}}}+\frac{\mathrm{1}}{{\mathit{M}}_{\mathit{i}}}\right)}^{\mathrm{0.5}}}{{\mathit{P}}_{\mathit{g}}{\left[{\left({\sum }_{\mathit{CO}\mathrm{2}}\mathit{v}\right)}^{\frac{\mathrm{1}}{\mathrm{3}}}+{\left({\sum }_{\mathit{i}}\mathit{v}\right)}^{\frac{\mathrm{1}}{\mathrm{3}}}\right]}^{\mathrm{2}}}$$E6

$$R_e=\frac{\rho .d.v}{\mu }$$E7

$$\mathit{Sc}=\frac{\mu }{\rho .D_{\mathit{CO}2,g}}$$E8

2.1.2 Membrane-side mass transfer coefficient k_m

$${\mathit{k}}_{\mathit{m}}=\frac{\mathit{\epsilon }.{\mathit{D}}_{\mathit{CO}\mathbf{2},\mathit{m}}}{\mathit{\tau }.\mathit{\delta }}$$E9

Where $\epsilon$ and $\tau$ are the porosity and the tortuosity of the membrane, respectively. D_e represents the effective gas diffusivity, and $\delta$ represents thickness of the membrane [35].

$$\mathit{\tau }=\frac{{\left(\mathrm{2}-\mathit{\epsilon }\right)}^{\mathrm{2}}}{\mathit{\epsilon }}$$E10

$${\mathit{D}}_{\mathit{CO}\mathrm{2},\mathit{m}}=\frac{\mathit{\epsilon }.{\mathit{D}}_{\mathit{CO}\mathrm{2},\mathit{g}}}{\mathit{\tau }}$$E11

2.1.3 Liquid-side mass transfer coefficient k_l [35]

$$\mathit{Sh}=\frac{{\mathit{k}}_{\mathit{l}}{\mathit{d}}_{\mathit{h}}}{{\mathit{D}}_{\mathit{CO}\mathrm{2},\mathit{l}}}=\mathrm{0.552}{{\mathit{R}}_{\mathit{e}}}^{\mathrm{0.5}}{\mathit{SC}}^{\mathrm{0.5}}$$E12

$${\mathit{D}}_{\mathit{CO}\mathrm{2},\mathit{l}}=\mathrm{2.35}\times {\mathrm{10}}^{-\mathrm{6}}\times {\mathit{e}}^{\left(-\frac{\mathrm{2119}}{\mathit{T}}\right)}{\left(\frac{{\mathit{\mu }}_{\mathit{H}\mathrm{2}\mathit{O}}}{{\mathit{\mu }}_{\mathit{K}\mathrm{2}\mathit{CO}\mathrm{3}}}\right)}^{\mathrm{0.8}}$$E13

2.2 Mathematical model of a membrane contactor for a carbonated solvent

The reaction system of CO₂ with K₂CO₃ is given by [36, 37]:

$${\mathrm{CO}}_2+\text{2KOH}\rightleftarrows {\mathrm{K}}_2{\mathrm{CO}}_3+{\mathrm{H}}_2\mathrm{O}$$E14

$${\mathrm{K}}_2{\mathrm{CO}}_3+{\mathrm{H}}_2\mathrm{O}+{\mathrm{CO}}_2\rightleftarrows {\text{2KHCO}}_3$$E15

$${\text{KHCO}}_3\rightleftarrows {\mathrm{K}}^{+}+{{\mathrm{HCO}}_3}^{-}$$E16

The expression for the chemical kinetics of this reaction is given by the following equation [36]:

$$r_{\left({\mathit{CO}}_2-K_2{\mathit{CO}}_3\right)}=K_{\mathit{OH}}.\left[{\mathit{OH}}^{-}\right]\left[{\mathit{CO}}_2\right]$$E17

$$\mathit{ln}\left({\mathit{K}}_{\mathit{OH}}\right)=\mathrm{26.437}-\frac{\mathrm{5111.2}}{\mathit{T}}$$E18

The general term for mass conservation is given as follows:

$$\text{Accumulation}=\text{input}-\text{output}+\text{appearance}–\text{disappearance}.$$

The following assumptions are used for the process modeling:

• Unidirectional (1D)

• Unsteady

• No wetting for membrane’s pores

2.2.1 Gas phase

For the gas phase

$$\frac{{\partial C}_{\mathit{CO}2,g}}{\partial t}=D_{\mathit{CO}2,g}\frac{{\partial }^2{C}_{\mathit{CO}2,g}}{{\partial z}^2}-V_g\frac{{\partial C}_{\mathit{CO}2,g}}{\partial z}-K_{G}a\left(\mathcal{H}\times C_{\mathit{CO}2,g}-C_{\mathit{CO}2,l}\right)$$E19

Where C_CO2,_g is the concentration of carbon dioxide in the shell side (gas), C_CO2,_l is the concentration of carbon dioxide in the tube side (liquid), Vg is the velocity on the gas phase, D_CO2,_g is the gas-side CO₂ diffusion coefficient (m²/s), K_g is the overall transfer coefficient gas side (m/s), and $\mathcal{H}$ is henry constant.

2.2.2 Liquid phase

For CO₂

$$\begin{array}{ll}\frac{{\mathrm{\partial C}}_{\mathrm{CO}2,\mathrm{l}}}{\mathrm{\partial t}}=& {\mathrm{D}}_{\mathrm{CO}2,\mathrm{l}}\frac{{\partial }^2{\mathrm{C}}_{\mathrm{CO}2,\mathrm{l}}}{{\mathrm{\partial z}}^2}-{\mathrm{V}}_{\mathrm{l}}\frac{{\mathrm{\partial C}}_{\mathrm{CO}2,\mathrm{l}}}{\mathrm{\partial z}}+{\mathrm{K}}_{\mathrm{G}}\mathrm{a}\left(\mathcal{H}\times {\mathrm{C}}_{\mathrm{CO}2,\mathrm{g}}-{\mathrm{C}}_{\mathrm{CO}2,\mathrm{l}}\right)-{\mathrm{K}}_{\mathrm{K}2\mathrm{CO}3}\\ & \times {\mathrm{C}}_{\mathrm{CO}2,\mathrm{l}}\times {\mathrm{C}}_{\mathrm{K}2\mathrm{CO}3}\end{array}$$E20

For K₂CO₃

$$\frac{\partial C_{K2\mathit{CO}3}}{\partial t}=D_{K2\mathit{CO}3,l}\frac{{\partial }^2{C}_{K2\mathit{CO}3}}{\partial z^2}-V_l\frac{\partial C_{K2\mathit{CO}3}}{\partial z}-K_{\mathit{OH}}\times C_{\mathit{CO}2,l}\times C_{K2\mathit{CO}3}$$E21

See (Table 2).

t = 0 (s)	Position	Shell side	Tube side
$C_{{\mathit{CO}}_2,g}\left(z,0\right)=0$; $C_{{\mathrm{K}}_2{\mathrm{CO}}_3}\left(z,0\right)=40\mathrm{mol}/{\mathrm{m}}^3$	Z = 0	$C_{{\mathit{CO}}_2,g}\left(0,t\right)=15.3\mathit{mol}/m^3$	$\frac{{\partial C}_{K_2{\mathit{CO}}_3}}{\partial z}\left(0,\mathrm{t}\right)=0$
	Z = L	$\frac{{\partial C}_{{\mathit{CO}}_2,g}}{\partial z}\left(L,t\right)=0$	$C_{{\mathrm{K}}_2{\mathrm{CO}}_3}\left(\mathrm{L},\mathrm{t}\right)=40\mathrm{mol}/{\mathrm{m}}^3$

Table 2.

Boundary and initial conditions of governing equations.

3. Results and discussions

In this part the results show the simulation of the CO₂ capture process in a membrane contactor for the counter-current cases using the pdepe function of MATLAB, with this in mind, we will look at the effect of different parameters like solvent concentration, gas velocity and liquid velocity on CO₂ removal efficiency. The domain used in this study is shown in Figure 1. The parameters of the membrane used for the simulation are summarized in Table 3.

Parameters	Value	Unit
Material	PVDF	—
Membrane length	0.21	[m]
Membrane thickness (δ)	0.00034	[m]
Porosity (ε)	0.4585
Nanoparticle morphology	—	Tubular
DCO2,g	1.39 × 10^−5 m^2 s^−1	[m^2/s]
DCO2,m	1.58 × 10^−5	[m^2/s]
DCO2,l	1.45 × 10^−9	[m^2/s]

Table 3.

Membrane’s parameters [38].

3.1 The effect of gas velocity

Figure 2 shows that as gas velocity increases, elimination efficiency decreases. This is because the contact time between the gas phase and the liquid phase decreases.

Figure 2.

Effect of gas velocity on CO₂ removal.

3.2 The effect of liquid velocity

Figure 3 shows that as the velocity of the liquid increases, the efficiency of CO₂ elimination increases. This is due to the increase in the speed of elimination of the CO₂ molecules that enter the liquid, which leads to an increase in the flow of CO₂ transferred.

Figure 3.

Effect of liquid velocity on CO₂ removal.

3.3 The effect of inlet solvent concentration

It can be seen in Figure 4, that the efficiency of CO₂ elimination increases with increasing solvent concentration of the solvent. This is due to the increase in CO₂ reaction kinetics.

Figure 4.

Effect of loading concentration of K2CO3 on CO₂ removal.

4. Conclusion

In a nutshell, robust and reliable mechanistic model and simulation methodology was validated and implemented to study the effects of concentration, gas velocity and liquid velocity on CO₂ capture by K₂CO₃ using membrane process to study the performance of the hollow fiber membrane contactor in terms of CO₂ removal. The CO₂ removal was increased by 52% in the range of 20–50 (mol/m³) of Concentration of flow rate, also the results show that 13% increase (74–87%) on CO₂ capture while the increase of solvent concentration from 20 to 50 (mol/m³), also for gas and liquid velocity from 0.001 to 0.05 and 0.006 to 0.05 (m/s) we have 52% and 3% increase of CO₂ capture respectively.

Nomenclature

$a$	effective interface area [m^2/m^3]
$C_0$	inlet concentration of CO2 in shell side [mol/m^3]
${\mathrm{C}}_{{\mathrm{CO}}_2}$	concentration of CO2 [mol/m^3]
${\mathrm{C}}_{K2\mathit{CO}3}$	concentration of K2CO3 [mol/m^3]
$C_{\mathit{\text{in}}}$	concentration of K2CO3 in tube side [mol/m^3]
$D_h$	hydraulic diameter [m]
DCO2,g	diffusion coefficient of CO2 in the shell side [m^2/s]
DCO2,m	diffusion coefficient of CO2 in membrane [m^2/s]
DCO2,l	diffusion coefficient of CO2 in the tube side [m^2/s]
$K_m$	membrane mass transfer coefficient [m/s]
$\mathit{kg}$	gas-phase mass transfer coefficient [m/s]
$\mathit{kl}$	liquid-phase mass transfer coefficient [m/s]
$K_G$	gas-phase global mass transfer coefficient [m/s]
$\mathit{Re}$	Reynolds number
$\mathit{Sc}$	Schmidt number
$\mathit{Sh}$	Sherwood number
$t$	time [s]
$T$	temperature [k]
$V_g$	gas velocity [m/s]
$V_l$	liquid velocity [m/s]
$\mu$	dynamics viscosity [kg/m.s]
$\rho$	density [kg/m^3]
$\mathit{\mu H}2O$	water viscosity [kg/m^3]