Computational evaluation of micropores wetting effect on the removal process of CO₂ through the membrane contactor

Abstract

In the current years, gas–liquid membrane contactors (GLMCs) have been introduced as a promising, versatile and easy-to-operate technology for mitigating the emission of major greenhouse contaminants (i.e., CO₂ and H₂S) to the ecosystem. This paper tries to computationally study the role of membrane pores wettability on the removal performance of CO₂ inside the HFMC. To fulfill this purpose, a mathematical model based on finite element procedure (FEP) has been employed to solve the momentum and mass transport equations in the partial-wetting (50% wetting of micropores) and non-wetting (0% wetting of micropores) modes of membrane during operation. Additionally, a comprehensive simulation was ensembled to predict the results. In this research, 2-amino-2-methyl-l-propanol (AMP) has been employed as a relatively novel alkanolamine absorbent to separate CO₂ form CO₂/N₂ mixture. Analysis of the results implied that the wetting of membrane micropores significantly deteriorated the removal efficiency due to the enhancing mass transfer resistance towards transferring CO₂ (75% in the non-wetting mode > 8% considering 50% wetting of micropores).

Introduction

Despite gradual increment in the application of renewable energy sources, fossil fuels are still regarded as the prominent energy sources all over the world^1–3. However, the combustion of fossil fuels causes the release of different types of detrimental greenhouse gases (GHGs) (i.e., CO₂, H₂S and NO₂), which results in the occurrence of undesirable and irreversible environmental-related phenomena such as global climate change, air pollution, respiratory disease and the desertification of fertile areas. The emergence of these challenges has endangered the human well-beings^4,5. In doing so, developing trustworthy approaches for mitigating the release of GHGs to the ecosystem by increasing the absorption percentages is an indisputable duty of scientists in the separation science and technology.

Over the last twenty years, the removal process of CO₂ (as the major GHG) using gas–liquid membrane contactor (GLMC) has been of prime attention thank to its noteworthy advantages during industrial operation such as flexibility, compactness, high interfacial area and easy scale-up^6–8. Despite the abovementioned advantages, wettability of membrane micropores owing to the penetration of liquid absorbent into them is an important disadvantage of GLMC, which results in deteriorating the mass transfer of CO₂ molecules and hence, reduces its removal percentage^9,10.

Proper selection of chemical absorbents with high reaction rates is a vital step toward increasing the removal efficiency of CO₂ molecules through the GLMC. Alkanolamine solutions like MEA, MDEA, DEA and TEA have recently been employed as benchmark chemical absorbents for CO₂ separation^11–14. The existence of important positive points like ease of accessibility, excellent absorption yield, high water solubility and affordability compared to other chemical absorbents has motivated the researchers to discover novel types of amines in the gas separation industry. Despite noteworthy advantages, some cons such as thermal/oxidative degradation, environmental toxicity and the requirement of great amount of energy for regeneration have challenged their employment^15,16. Figure 1 presents the molecular structure of AMP amine absorbent.

Fig. 1.

Molecular structure of AMP amine absorbent¹⁷.

Currently, expensive and time-consuming nature of experimental/laboratorial researches have convinced the scientists to employ mathematical models based on finite element method (FEM) to assess the absorption efficiency of different GHGs from gaseous feed and also solution of governing transport equations inside the GLMC^18–20.

In this paper, the authors have made their endeavor to numerically analyze the removal of CO₂ GHG from CO₂/N₂ gaseous feed using novel amino-2-methyl-l-propanol (AMP) amine solution inside the GLMC under non-wetting and partial-wetting operational modes. To reach this aim, a 2D simulation and an FEM-associated mathematical modeling are developed to compare the effect of membrane pores wettability on the removal of CO₂. Additionally, the effectiveness of AMP absorbent on CO₂ separation of aims to be studied. Ultimately, the negative/positive effects of momentous module/membrane-based parameters on the absorption of CO₂ GHG are studied comprehensively.

Model development

With the aim of analyzing the separation process of CO₂ GHG using AMP alkanolamine solution in different wetting ratios (non-wetting, 50% partial wetting and complete-wetting) inside the GLMC, a comprehensive two-dimensional simulation and a mathematical model is developed for studying mass transfer performance in the main domains of GLMC and prognosticating the results. Figure 2 schematically depicts the geometry, mass transfer trend and cross section of GLMC.

Fig. 2.

Schematic demonstration of geometry, cross section and Happel’s free surface model (HFSM) inside the GLMC. Adopted from⁸.

In this paper, countercurrent flowing of CO₂/N₂ mixture flows in the shell and AMP absorbent results in the movement of CO₂ molecules from the shell to the micropores and then after, its absorption by AMP absorbent in the tube of GLMC. The main role of employed membrane is the separation of shell and tube and selective passing of CO₂ molecules. Figure 3 aims to schematically demonstrates the non-wetted, partial-wetted and complete-wetted modes of membrane during operation inside the GLMC.

Fig. 3.

Schematic demonstration of membrane during operation inside the GLMC.

To simplify the simulation process of CO₂ GHG using AMP solution inside the, some assumptions have been used, which can be interpreted as follows:

1. steady state mode of operation inside the GLMC to solve the continuity and Navier-stocks equations;

2. Isothermal state;

3. The use Henry’s law in the gas–liquid interface;

4. Laminar flow pattern inside the shell and tube of GLMC;

5. Application of HFSM for the estimation of effective radius around each individual hollow fiber (r₃);

In this research, the authors have employed commercial COMSOL Multiphysics software to prognosticate the separation performance of CO₂ GHG through the GLMC thank to its brilliant advantages such as wide range of abilities, user-friendly environment and great capability to analyze equations^9,18,21–24. The needed time for running the 2D simulation and solving PDEs was almost 2 min. Essential parameters of GLMC and feed conditions are presented in Table 1. Complete definition of all employed parameters in the manuscript is presented in the nomenclature list.

Table 1.

Specifications of GLMC and feed conditions for developing predictive simulation²⁵.

Parameter	Unit	Value
	m	4 × 10–4
	m	6.5 × 10–4
	m	5 × 10–3
L	m	0.295
n	–	35
	–	0.6
T	K	303
Inlet concentration of CO2/N2	Vol%	20/80
Ql	ml/min	400–760
Qg	ml/min	200

Governing equations in different domains

Table 2 comprehensively presents all derived mass transfer (based on Fick’s law) and momentum transfer equations in the shell of GLMC. Velocity profile in the shell of GLMC has been derived by the incorporation of two assumptions (laminar flow regime and the HFSM) (Eq. 4). Combination of Eqs. (5) and (6) results in the prediction of effective hypothetical radius around each hollow fiber (r₃). Based on these equations, r₃ is calculated 8.45 × 10^–4 m.

Table 2.

Governing equations in the shell of GLMC^26–30.

Mass transfer	Momentum transfer

Governing transport equations along with the CO₂-AMP reaction rate inside the tube of GLMC are presented in Table 3.

Table 3.

Governing equations and CO₂-AMP reaction rate inside the tube of GLMC^13,29,31,32.

Mass transfer	Momentum transfer

Figure 4 schematically demonstrates the gas/liquid filled compartments of employed microporous membrane through the GLMC.

Fig. 4.

Schematic demonstration of gas/liquid filled compartments of employed microporous membrane through the GLMC.

In the gas-filled compartment of membrane, molecular diffusion is the only governing mechanism of transport. However, in the liquid-filled portion of membrane, both reaction and diffusion are important. Table 4 presents the governing equations inside the membrane.

Table 4.

Principal equations inside the membrane^8,33,34.

Mass transfer equation (gas-filled portion)	Mass transfer equation (liquid-filled portion)

Tables 5 and 6 list the corresponding momentum/mass boundary conditions in three major domains of GLMC under non-wetted and partial-wetted mode of membrane.

Table 5.

Corresponding boundary conditions in major domains of GLMC considering non-wetted mode of membrane.

Position	Shell side		Membrane	Tube
	Mass	Momentum	Mass	Mass
z = 0	Convective flux	Outlet: Pressure, no viscous stress, p = 0	Insulated
z = L		Inlet velocity V = V0,shell	Insulated	Convective flux
r = 0	–	–	–	Axial symmetry
r = r1	–	–
r = r2		No slip, Wall		–
r = r3		No slip, Table Wall	–	–

Table 6.

Corresponding boundary conditions in major domains of GLMC considering partial-wetted mode of membrane.

Position	Shell side	Gas-filled compartment	Liquid-filled compartment	Tube
z = 0	Convective flux	Insulated	Insulated
z = L		Insulated	Insulated	Convective flux
r = 0	–	–	–	Axial symmetry
r = r1	–
r = rw	–			–
r = r2	–		–
r = r3		–	–	–

Table 7 provides important physico-chemical properties of CO₂ and AMP absorbent for using in 2D simulation.

Table 7.

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

Parameter	Value	Unit	References
	1.8 × 10–5	m2 s−1	35
		m2 s−1	35
	1.8 × 10–9	m2 s−1	36
	0.8	–	37
	CO2][AMP]	mol m-3 s−1	38
(at T = 303 K)	0.988	m3 mol−1 K−1	38

Mapped meshing investigation

In this investigation, mapped meshing approach has been used to discretize the domains of GLMC into smaller compartment to increase the computational precision and reduce the error¹³. The main reason of applying this technique is its ability to cover all the domains’ points^27,39. It is clear from the Fig. 5 that the designed meshes in the membrane and around it is much denser and smaller due to the occurrence of CO₂-AMP reaction. Based on the evaluated data after the 300th mesh, no considerable variation in the concentration of CO₂ molecules in the shell outlet takes place, which implied the independency of the results after this mesh number.

Fig. 5.

Mapped meshing of GLMC in the non-wetted mode.

Results and discussion

Validation of results

In this paper, validation of developed 2D simulation results is performed via their compasrison with obtained experimental data from the research of Rongwong et al.²⁵. By comparison of obtained CO₂ flux values in an extensive range of liquid velocity, it can be denoted that there is a favorable agreement between the simulation predicted results and experimental findings with average absolute error (ARE) of about 3.6%. Table 8 compares the achieved data.

Table 8.

Validation of developed 2D simulation.

Liquid velocity (m/s)	CO2 flux (Experimental findings) (molm-2s−1)	CO2 flux (Simulation result) (molm-2s−1)	ARE (%)
0.5	2.21 10–4	2.27 10–4	2.14
0.775	2.27 10–4	2.31 10–4	1.71
1.05	2.29 10–4	2.4 10–4	4.5
1.37	2.32 10–4	2.47 10–4	6

Dimensional concentration profile

Figure 6 schematically compares the dimensionless concentration gradient (DCG) of CO₂ GHG inside the shell of GLMC. As can be seen, the utilization of AMP liquid absorbent significantly reduces the DCG of CO₂ in the outlet of shell from 1 to 0.25, which implied 75% separation of inlet CO₂. However, 50% wetting of membrane micropores via liquid significantly deteriorates the DCG of CO₂ from 1 to y 0.92, which denotes only 8% CO₂ removal. Wetting of membrane pores results in increasing the resistance toward the mass transfer of CO₂ molecules from shell to membrane pores and then after, tube side of GLMC, which ultimately causes decrement in the removal of inlet CO₂ GHG.

Fig. 6.

Dimensionless concentration profile inside the shell of GLMC considering (a) non-wetting and (b) partial-wetting modes of membrane.

Effect of gas flow rate

Figure 7 compares the separation percentage of CO₂ GHG considering non-wetting and 50% partial wetting of membrane micropores inside the GLMC in different gas flow rates. Operationally, increase in the flow rate of gaseous flow in the shell reduces the residence time of gas and as the result, gas–liquid contact in the membrane-shell interface. This causes the reduction of CO₂ separation. Increment of gas flow rates from 100 to 600 ml min⁻¹ declined the separation yield from 89 to 39% in non-wetting and from 15 to about 3% in partial-wetting mode.

Fig. 7.

Impact of gas flow rate on the removal efficacy in non-wetting and 50% partial-wetting of membrane.

Effect of hollow fibers’ count and module length

Figures 8 and 9 schematically illustrate the separation performance of CO₂ in wide ranges of hollow fiber numbers and module length in non-wetting and partial-wetting modes of membrane during operation, respectively. As demonstrated in Fig. 8, increase in the length of module from 0.1 to 0.4 m enhanced the separation yield from 49.5 to 80% in non-wetting and from 3.5 to 10% on 50% wetting of membrane due to providing greater chance for the contact of CO₂ with AMP solution and its better absorption by the absorbent in both non-wetting and partial-wetting modes of membrane.

Fig. 8.

Impact of module length on the removal efficacy in non-wetting and 50% partial-wetting of membrane.

Fig. 9.

Effect of hollow fibers number on the removal efficacy in non-wetting and 50% partial-wetting of membrane.

By glancing at Fig. 9, it is perceived that increase in the hollow fibers’ counts through the GLMC from 10 to 50 considerably improves the separation process due to increasing the contact area and thus, mass transfer of CO₂ (from 4 to 97% in non-wetting and from 1 to 32% in partial-wetting modes).

Conclusion

Nowadays, application of GLMCs has been able to open new horizon toward mitigating the anthropogenic emission of environmentally-hazardous CO₂ GHG. The prominent purpose of this scientific research is to theoretically evaluate removal of CO₂ GHG using novel AMP amine solution in non-wetting and 50% partial-wetting of membrane micropores inside the GLMC. To reach the abovementioned aim, a CFD simulation was developed using COMSOL software. Moreover, momentum and mass transport equations in non-wetting and 50% wetting of membrane were solved via assembling a mathematical model. To ensure the validity of model results, they were compared with experimental data. Based on the achieved findings, AMP can be introduced as an effective amine-based absorbent to separate CO₂. Also, it is perceived from the result that 50% wetting of membrane micropores could significantly decreased the separation of CO₂ GHG due to enhancing the resistance toward CO₂ mass transfer (75% vs. only 8%). Increase in the length of module and hollow fibers’ count positively improved the CO₂ GHG capture but increase in the gas flow rate significantly deteriorated the efficacy of CO₂ GHG capture.

List of symbols

Internal radius of fiber (m)

Exterior radius of fiber (m)

Approximated hypothetical radius around each fiber (m)

Membrane module length (m)

Diffusion coefficient of CO₂ in the shell (m²s⁻¹)

Diffusion coefficient of CO₂ in the membrane (m²s⁻¹)

Diffusion coefficient of AMP in the shell (m²s⁻¹)

Dimensionless CO₂ solubility

Number of fibers

Pressure (Pa)

Initial CO₂ concentration in the gas phase (molm⁻³)

Liquid flow rate (ms⁻¹)

Gas flow rate (ms⁻¹)

Temperature (K)

Average axial velocity of the liquid through the shell (ms⁻¹)

Average axial velocity of gas through the tube (ms⁻¹)

Reaction rate constant (s⁻¹)

Porosity

Tortuosity

Packing factor

Author contributions

A.S: Writing draft, Methodology Z.A: Writing draft V.J: Writing draft, Software R.R: Methodology A.K: Methodology, Software A.K: Analysis, Software M.K: Data curation S.G: Supervision, Funding G.V. S.P: Supervision, Research, Project Administration M.K.A: Project Administration.

Data availability

All data are available within the manuscript.

Declarations

Competing interests

The authors declare no competing interests.