Development of a CFD simulation for the analysis of CO₂ separation percentage using novel [emim][C₂N₃] ionic liquid solution inside the gas–liquid contactor

Abstract

Growing emission of environmentally-hazardous greenhouse pollutants (especially CO₂) has motivated the researchers to apply gas–liquid membrane contactors as an easy-to-operate and cost-effective technique for increasing their separation efficiency from different sources. In the current decades, ionic liquids (ILs) have shown their potential in the gas separation industry owing to their noteworthy advantages such as great capacity, excellent adjustability and suitable thermal/chemical stability compared to commonly-employed amine absorbents. This investigation aims to analytically/numerically determine the separation yield of CO₂ from CO₂/N₂ gaseous flow using novel -Ethyl-3-methylimidazolium dicyanamide ([emim][C₂N₃]) IL inside the gas–liquid contactor. To fulfill the ultimate purpose, a CFD simulation has been proposed using COMSOL Multiphysics software to predict the results. Comparison of model outcome with experimental data has shown brilliant concurrence with the average relative deviation of almost 5%. Evaluation of the results has shown the excellent performance of [emim][C₂N₃] IL for the removal of CO₂ (Separation efficiency of around 100%). Finally, the effects of some module/membrane parameters on increasing or decreasing the separation efficiency has been studies in detail.

Introduction

The emergence of economic development and industrial revolution since the twentieth century has significantly deteriorated the quality of climate and environment^1–4. CO₂ has long been perceived as the leading greenhouse gas, which its increasing emission to the atmosphere in the current decades has exacerbated unfavorable environmental-based phenomena like wildfires, climate change and acid rain^5–7. Therefore, finding environmentally-benign, cost-effective and novel procedures for satisfying the market demand for efficient management of CO₂ emission. In the last decades, different gas separation approaches including low-temperature phase separation, cryogenic distillation and membrane-based absorption have been commonly employed. With the aim of using these techniques, disparate gas–liquid contact procedures (i.e., packed towers, spray towers and bubble towers) have been used^8–11. Figure 1 schematically presents different gas separation techniques in industries.

Fig. 1.

Different prevalent techniques for the separation of gas¹.

In the current two decades, industrial application of membrane contactor has attracted the attentions of scientists in the world. This technology has shown its great capability to incorporate the positive advantages of molecular absorption (excellent selectivity) and membrane separation (compactness)^2,12–14. The existence of noteworthy advantages like modularity, separated flowing of gas and liquid phases and high interfacial area in the gas–liquid contactors could significantly decline the size and facilitate operation^15–17.

Various endeavors have recently been conducted to apply more effective, green and operationally-safe absorbents for substituting with detrimental alkanolamine solutions in the process of CO₂ molecular separation. Ionic liquids (ILs) refer to a relatively novel class of chemical absorbent consisted of organic cations and inorganic anions^18,19. They have recently been considered as promising alternatives for amine solutions thanks to their outstanding physicochemical properties such as great capacity for the separation of CO₂, excellent adjustability and better thermal/chemical stability than commonly-employed amine absorbents^20–23.

The recovery of CO₂ may be regarded as an important energy-intensive level in CO₂ processes. Therefore, the analysis of regeneration energies is of prime necessity to evaluate the possibility of applying novel types of liquid absorbents like ILs in industrial applications^21,24. It has been understood from different scientific investigations that the simplicity of regeneration is a considerable advantage of ILs. The experimental results have illustrated the fact that the required regeneration energy for different prevalent types of ILs is significantly competitive with benchmark amine solutions (4.3 kJ g (CO₂)⁻¹ vs 2.3–4.5 kJ g (CO₂)⁻¹). Therefore, better efficiency and reasonable required energy for regeneration has made ILs promising for application in CO2-separation technologies²⁵.

This scientific research aims to analytically/numerically study the feasibility of using novel [emim][C₂N₃] IL inside the gas–liquid contactor for increasing CO₂ separation. To hit this point, a CFD-based simulation using COMSOL Multiphysics software is applied to solve partial differential equations (PDEs) in different geometries of contactor. Finally, the effects of some module/membrane parameters on increasing or decreasing the separation efficiency are analyzed and the results are discussed in detail.

Model development

The schematic illustration of the experimental set up employed by Ghasem for the separation of CO₂ from CO₂/N₂ flow is demonstrated in Fig. 2.

Fig. 2.

Schematic demonstration of the experimental set up and the geometry of gas–liquid contactor for the separation of CO₂²⁶.

In order to facilitate the simulation process of CO₂ separation using [emim][C₂N₂] in the membrane contactor, the following mathematical/theoretical assumptions were implemented.

1. The employed system is assumed isothermal and steady state

2. Filling of membrane micropores with only gas molecules (non-wetted mode)

3. Application of Henry’s law for the expression of equilibrium between gas and IL

4. No reaction occurs inside the gas phase

5. Counter-current flow of gaseous flow and IL

6. Laminar regime of fluids

7. Hydrophobicity nature of membrane

8. Application of Happel’s free surface model (HFSM) for the approximation of hypothetical effective radius around each hollow fiber (r₃)

Essential module/membrane-based parameters following with feed conditions for the development of theoretical simulation is listed in Table 1. COMSOL Multiphysics is known as a promising commercial-package finite element-based analyzer/solver utilized for disparate physics and engineering applications. This software has recently shown its noteworthy potential to facilitate common physics-based user interfaces and coupled systems of PDEs^27–29. In this paper, the authors have made their ultimate efforts to increase the precision of modeling using UMFPACK solver. Computational time for solving the existed PDEs using this solver was approximately 2 min.

Table 1.

The detailed specifications and feed conditions for model development³⁰.

Parameter	Unit	Value
Inner radius of membrane ()	m	1.1 × 10−4
Outer radius of membrane ()	m	1.5 × 10−4
Thickness of membrane ()	m	0.4 × 10−4
Contactor length (L)	m	0.115
Number of fibers (n)	–	2300
Module packing factor (	–	0.39
Porosity ()	–	0.4
Tortuosity ()	–	2.5
Inlet concentration of CO2	Vol%	15
Liquid flow rate (Ql)	ml/min	50–90
Gas flow rate (Qg)	ml/min	50–100

Table 2 presents the prominent transport equations along with their associated boundary conditions in the tube side of membrane contactor^5,31,32.

Table 2.

Governing equations and corresponded boundary conditions in the tube.

Mass transfer	Momentum transfer
(1)	(2)
Boundary conditions
(3)
(4)
(5)
(6)

All parameters have been defined in the nomenclature list. Non-wetted mode of operation is an employed assumptions in this manuscript, which means the filling of membrane pores with only gaseous molecules. Thus, diffusion is the only mass transport mechanism through the microporous fibers^33–35. Table 3 enlists transport equations and boundary conditions inside the membrane^12,36–41.

Table 3.

Principal equations and boundary conditions inside the membrane.

Mass transfer	Boundary conditions
(7) (9)	(8) (10) (11) (12)

Principal transport equations and boundary conditions in the shell side are enlisted in Table 4. Application of two aforementioned assumption (laminar flow pattern and the HFSM model eventuates in deriving the velocity profile in this compartment (Eq. 14)^32,42–44.

Table 4.

Principal transport equations and boundary conditions inside the shell.

Mass transfer	Momentum transfer
(13)	(14)
	(15)
Boundary conditions
(16)
(17)
(18)
(19)

Equation 15 is employed to prognosticate the hypothetical radius around each hollow fiber^33,45. Based on this equation r₃ is calculated 1.92 × 10⁻⁴ m. Table 5 presents essential physical, mechanical, transport and chemical parameters for model development.

Table 5.

The essential physical, mechanical, transport and chemical parameters for model development.

Parameter	Value	Unit	Reference
	1.8 × 10−5	m2 s−1	33
		m2 s−1	33
	2.66 × 10−3	cm2 s−1	46
	34	cm3−mol−1	47
	1273	kg−m−3	48
	177.21	g−mol−1	49
		MPa	50
		–	30
	80	mPa s	48
kr	2.7 × 10−3	1/s	51

Mesh study

The prominent purpose of meshing is the segmentation of all domains of membrane contactor to finer dimensions to facilitate the study of effective parameters at each domain point with greater accuracy⁵. As would be expected, as the number of meshes increases, the modeling accuracy (as a favorable parameter) and computational time (as an unfavorable parameter) increases. Therefore, an optimum number of mesh needs to be provided to reach the maximum accuracy in low computational time. Mapped meshing approach has been employed in this research to divide the whole geometry of contactor into smaller cells thank to its indisputable capability to cover all points of existed domain⁵². Figure 3 shows the employed mapped meshes in different sides of contactor. As shown, the meshes in the membrane domain in the area of CO₂-IL contact is finer to facilitate the study of operational parameters with superior accuracy and lower error. The mapped meshing outcome has shown that after the 255^th mesh, no significant alteration in the concentration of CO₂ in the outlet of the tube occurs, which shows the independency of simulation results after the mesh number of 255.

Fig. 3.

Mapped meshing for different domains of membrane contactor.

Results and discussion

Validation of model outcomes

Owing to the lack of steady-state experimental data for [emim][C₂N₃] IL, simulation results were compared with the obtained data from the experiment of Rostami et al. for [Bmim][BF₄] IL in different IL mass fraction⁵³. Evaluation of data shows a favorable concurrence with average relative error of almost 3.65%. Figure 4 and Table 6 compare experimental and simulation outcomes for the molar flux of CO₂ in different IL mass fraction.

Fig. 4.

Validation of model outcome with achieved experimental data. Q_l = 25 ml/min, Q_g = 70 ml/min, r₁ = 1.375 × 10⁻⁴ m, r₂ = 1.85 × 10⁻⁴ m, L = 65 mm Data was obtained by the research of Rostami et al.⁵³.

Table 6.

Validation of developed model. Q_l = 25 ml/min, Q_g = 70 ml/min, r₁ = 1.375 × 10⁻⁴ m, r₂ = 1.85 × 10⁻⁴ m, L = 65 mm. Data was obtained by the research of Rostami et al. ⁵³.

IL mass fraction (%)	CO2 molar flux (mol m−2 s−1) (experimental)	CO2 molar flux (mol m−2 s−1) (Modeling)	Average relative error (%)
0	5.46 × 10−4	5.6 × 10−4	2.5
5	5.52 × 10−4	5.71 × 10−4	3.32
10	5.65 × 10−4	5.90 × 10−4	4.2
15	5.83 × 10−4	6.02 × 10−4	2.57
20	6.07 × 10−4	6.27 × 10−4	4.3
25	6.19 × 10−4	6.4 × 10−4	3.28

CO₂ Concentration distribution

Dimensionless concentration gradient of CO₂ through the tube side of contactor utilizing [emim][C₂N₃] IL is demonstrated in Fig. 5. By the countercurrent flowing of gaseous mixture in the tube (from down to top) and [emim][C₂N₃] IL in the shell compartment (from top to down) of contactor, CO₂ molecules diffuse from the tube to the walls of porous membrane and from the porous walls to the shell. It is important to note that the governing mass transfer mechanisms in the axial and radial coordinates are convection (due to the motion of fluids) and diffusion (due to concentration gradient). As demonstrated, the dimensionless concentration amount of CO₂ molecules reduces as it moves forward in the contactor however.

Fig. 5.

Dimensionless CO₂ concentration profile through the (a) tube, (b) membrane and (c) shell of contactor using [emim][C₂N₃] IL.

Moreover, the CO₂ dimensionless concentration (C_CO2,tube/C_CO20) in the tube-membrane interfacial zone is depicted in Fig. 6. At z = 0, this amount is maximum (1) and declines to 0 at the tube outlet (z = L) using employed IL, which implies 100% removal of inlet CO₂ to the membrane module. The substantial decrement in the CO₂ dimensionless concentration is mainly owing to the great efficiency of [emim][C₂N₃] IL to instantly react with CO₂ molecules and absorb them.

Fig. 6.

Axial dimensionless concentration of the CO₂ in tube-membrane interfacial zone.

Effect of module length

Another module-based parameter, which can influence the mass transfer and thus, the removal percentage of CO₂ within the membrane contactor is module length. Enhancement of the operational length of module can increase the gas–liquid residence time, which results in improving their contact inside and therefore, mass transfer rate. Ultimately, increase in the mass transfer rate can substantially intensifies the separation of CO₂ employing [emim][C₂N₃] IL. Figure 7 shows the influence of module length on the absorption yield of CO₂. When the length increases from 0.01 to 0.2 m, the removal yield of CO₂ improves from 95.8 to 100%.

Fig. 7.

Effect of module length on the CO₂ removal utilizing emim[C₂N₃] IL.

Effect of hollow fibers’ count

Figure 8 tries to analytically investigates the role of the fibers’ counts on the separation of CO₂ inside the contactor. As shown, increment in the number of fibers from 20 to 2500 positively enhances the absorption rate from 82 to 100% owing to providing better opportunity for the contact between CO₂ and [emim][C₂N₃] IL and as the result, improving the mass transfer. Increase in the fibers’ counts inside the contactor considerably improves the mass transfer area between the gas and IL significantly, which has positive influence on the separation efficiency.

Fig. 8.

The operational effect of hollow fibers number on the CO₂ separation efficiency.

Effect of gas flow rate

Figure 9 numerically compares the absorption yield of CO₂ through the gas–liquid contactor using [emim][C₂N₃] IL in different gas flow rates. As demonstrated, enhancement in the flow rate of gas intensifies the resistance toward the mass transfer of CO₂ molecules, reduces the residence time of gas and as the result, decreases the mass transfer of CO₂. It is concluded from the figure that by increasing the flow rate of gas in the shell of contactor from 20 to 150 ml min⁻¹, the removal of CO₂ decreases from 100 to about 91.4% using [emim][C₂N₃] IL.

Fig. 9.

Influence of gas flow rate on the CO₂ sequestration performance utilizing emim[C₂N₃] IL.

Conclusion

This research aimed to numerically assess the operational efficiency of [emim][C₂N₃] IL for separating CO₂ greenhouse pollutant from CO₂/N₂ mixture. For this purpose, a 2D CFD-based simulation was developed using COMSOL Multiphysics software to prognosticate the outcomes. Moreover, UMFPACK numerical solver was applied to analyze to governing mass transfer equations in disparate geometries of gas–liquid contactor. To ensure the validity of model results, they were compared with experimental data. There was a brilliant concurrence between the obtained results of simulation and literature data with the average relative deviation of almost 3.6%. With the removal efficiency of around 100%, [emim][C₂N₃] IL is introduced as a reliable and operationally-effective liquid absorbent for removing CO₂. Analysis of the results showed that increase in the amount of some module/membrane-based factors like porosity, number of fibers and module length enhance the sequestration yield due to improving mass transfer rate, residence time and gas–liquid contact. But increment in the flow rate of gas deteriorate the absorption efficacy due to increasing the resistance toward mass transfer and decreasing the residence time of gas in the membrane module.

List of symbols

Internal radius of each hollow fiber ()

Exterior radius of each hollow fiber ()

Approximated hypothetical effective radius around each fiber ()

Length of membrane module ()

CO₂ diffusivity in the shell ()

CO₂ diffusivity in the membrane ()

CO₂ diffusivity of the [emim][C₂N₃] IL in the shell ()

Dimensionless CO₂ solubility

Number of fibers

Pressure ()

Initial CO₂ concentration in the gas phase ()

Liquid flow rate ()

Gas flow rate ()

Temperature ()

Average axial velocity of the liquid through the shell ()

Average axial velocity of gas through the tube ()

Transformed constant ()

Porosity

Tortuosity

Packing factor

Author contributions

A.A: Writing draft, Investigation W.M: Methodology, Software, Analysis A.O: Funding, Project administration.

Data availability

All data are available within the manuscript.

Competing interests

The authors declare no competing interests.