Computational fluid dynamics comparison of prevalent liquid absorbents for the separation of SO2 acidic pollutant inside a membrane contactor

In recent years, the emission of detrimental acidic pollutants to the atmosphere has raised the concerns of scientists. Sulphur dioxide (SO2) is a harmful greenhouse gas, which its abnormal release to the atmosphere may cause far-ranging environmental and health effects like acid rain and respiratory problems. Therefore, finding promising techniques to alleviate the emission of this greenhouse gas may be of great urgency towards environmental protection. This paper aims to evaluate the potential of three novel absorbents (seawater (H2O), dimethyl aniline (DMA) and sodium hydroxide (NaOH) to separate SO2 acidic pollutant from SO2/air gaseous stream inside the hollow fiber membrane contactor (HFMC). To reach this goal, a CFD-based simulation was developed to predict the results. Also, a mathematical model was applied to theoretically evaluate the transport equations in different compartments of contactor. Comparison of the results has implied seawater is the most efficient liquid absorbent for separating SO2. After seawater, NaOH and DMA are placed at the second and third rank (99.36% separation using seawater > 62% separation using NaOH > 55% separation using DMA). Additionally, the influence of operational parameters (i.e., gas and liquid flow rates) and also membrane/module parameters (i.e., length of membrane module, hollow fibers’ number and porosity) on the SO2 separation percentage is investigated as another highlight of this paper.


Reaction mechanism of SO 2 in different absorbents
The ball-and-stick molecular structure of employed liquid absorbents (DMA, NaOH and H 2 O) is presented in Fig. 1.
The chemical absorption of SO 2 acidic contaminant in H 2 O absorbent takes place by a hydrolysis reaction, presented by the equilibriums 1 to 4 7 .
(1) www.nature.com/scientificreports/ Seawater can be considered as a complex system, which includes disparate dissolved chemical components like Na + , Mg 2+ , Ca 2+ , K + , SO 4 2− and HCO 3 − and Br − . These components contain more than 95% of dissolved salt in seawater. Additionally, NaCl has a significant value in seawater and occupies nearly 85% of the constant component 8 . The existed carbonate system in the seawater can be obviously described by the following equilibriums 18,43,44 : According to the abovementioned equilibriums, seawater possesses great potential for the absorption of SO 2 acidic pollutant. The presence of complex CO 2 -H 2 O-HCO 3 − -CO 3 2− equilibrium system eventuates in increasing the mass transfer performance of SO 2 acidic pollutant in the seawater, which positively encourages its removal.
In the case of SO 2 separation using DMA liquid absorbent, the following reactions take place 45 : Moreover, formation of an additional compound occurs during the SO 2 − DMA reaction as follows 46 : The separation process of SO 2 acidic pollutant in the NaOH occurs by the following equilibrium 47 :

Modeling
HFMC is a novel apparatus, which is designed to carry out the separation process using a hydrophobic microporous membrane 48 . Employed membrane in a gas-liquid HFMC is usually applied as a gas-liquid interface and provide better chance for efficient contact between two phases without direct mixing 49,50 . Great selectivity of the HFMC is due to the existence of gradient between the components' solubility in the liquid phase. Thus, the majority of commercial HFMC apply microporous membranes due to having higher mass transfer properties 51 . Figure 2 schematically shows the gas-liquid interface inside a microporous HFMC. Through each HFMC, the gas-liquid mass transfer process takes place via the mechanism of solution diffusion inside the micropores of a hydrophobic membrane. Figure 3 schematically presents the two-dimensional (2D) illustration of SO 2 mass transfer inside different domains (shell, membrane and tube) of HFMC.
As can be seen in Fig. 3, gaseous mixture including SO 2 air flows in the shell side form up to down (from z = L to z = 0) and H 2 O, DMA and NaOH liquid absorbents move in the tube side from down to top (from z = 0 to    www.nature.com/scientificreports/ z = L), counter-currently. The employed assumptions to implement the mathematical modeling and 2D simulation is presented in Table 1. COMSOL Multiphysics is as an attractive CFD-based software with brilliant capability to solve partial differential equations with different stiff/non-stiff boundary and initial conditions. In this paper, PDEs of mass and momentum are solved using this robust software based on CFD approach. To solve PDEs of mass and momentum, COMSOL Multiphysics version 6 was installed on a 64-bit platform with an Intel(R) core (TM) i7-10510U CPU and a 16 Gigabyte RAM. The needed time for solving the PDEs and present the results was about 20 s. Moreover, with the aim of managing the material balance error during the solution of mass/momentum PDEs, PARDISO numerical solver was employed owing to its brilliant advantages like excellent memory performance and robustness 58,59 . The principal PDEs of mass and momentum in tube, membrane and shell sides are presented in Table 2.
In Table 2, D SO 2 ,s ,D SO 2 ,mem are defined as the diffusion coefficient of SO 2 greenhouse gas in the shell and membrane. Also, D i,t is the diffusion coefficient of i (SO 2 , H 2 O, NaOH and DMA) in the tube. Additionally, V z,s, V z,t , V s ,V t and C are described as the shell's velocity in axial direction, tube velocity in the axial direction, the average velocity in the shell, the average velocity inside the tube and concentration, respectively. Boundary conditions at each main domains of HFMC are presented in Table 3.
The required parameters of microporous membrane and module following with important physicochemical properties of SO 2 acidic pollutants and seawater, NaOH and DMA liquid absorbents are rendered in Table 4.

Results and discussion
Validation of developed modeling and 2D simulation. Up to our knowledge, very few papers experimentally evaluated the performance of NaOH, DMA and H 2 O to separate SO 2 acidic pollutant. Therefore, the validation of developed 2D simulation was performed via the comparison of simulation outcomes with experimental results obtained by Karoor and Sirkar about the separation of SO 2 using pure water 63 . As demonstrated in Fig. 4, there is a favorable agreement between the experimental data and predicted results achieved by 2D simulation, which corroborates the accuracy and validation of employed modeling and simulation in this work.
With the aim of ensuring the accuracy of developed model outcomes, the second validation was implemented via the comparison of simulation results with obtained experimental data from Xu et al. for the separation of SO 2 using NaOH solution 72 . As can be seen in Fig. 5, an excellent agreement is again demonstrated between the experimental data and predicted results with the absolute relative deviation (ARD) of about 4%, which certainly corroborates the validation of developed model. Figures 6a, 6b and 6c show the axial concentration profile of SO 2 greenhouse gas in the shell and membrane sides of the contactor, respectively. The SO 2 /air gaseous mixture

Domain
Tube Membrane D SO2,mem   www.nature.com/scientificreports/ The role of gas and liquid flow rates on the SO 2 separation performance. Figure 7 illustrate the impact of gas flow rate on the separation yield of SO 2 . As presented, increase in the flow rate of gaseous mixture considerably declines the residence time in the module. As the result, decrement of residence time destroys the suitable contact of SO 2 with liquid absorbents, which results in decreasing the separation efficacy. By looking at the figure, it is perceived that increase in the gas flow rate from 0.25 to 0.3 L/min decreases the SO 2 separation percentage from 100 to 77% using seawater, from 91 to 33% using NaOH and from 72 to 29% using DMA. Table 5 enlists the separation percentage of SO 2 from the gaseous mixture using seawater, NaOH and DMA liquid absorbents in different gas flow rates. Additionally, the influence of liquid absorbents' flow rate on the percentage of SO 2 separation is shown in Fig. 8. By faster flowing of absorbents through the tube segment, the concentration of gas at the external surface of the hollow fiber along the length of the HFMC decreases significantly, which eventuates in greater mass transfer coefficient, superior concentration gradient at the shell-membrane interface and therefore, better SO 2 separation performance. Based on the figure, increase in the flow rate of liquid absorbents from 0.25 to 0.3 L/ min improves the SO 2 separation percentage from 95 to 100% using seawater, from 53.5 to about 67.5% using NaOH and from 50 to 60% using DMA.
The separation performance of SO 2 greenhouse pollutant from SO 2 /air gaseous stream applying seawater, NaOH and DMA absorbents in different gas flow rates is presented in Table 6.
Effect of membrane/module specifications on the separation performance. Figure 9 presents a schematic demonstration for evaluating the role of module length on the separation yield of SO 2 greenhouse gas. As illustrated, increase in the length of module possesses positive impact on improving the gas-absorbent residence time and contact area between two phases, which results in enhancing the separation yield of SO 2 greenhouse gas. It is observed that increase in the length of module from 0.05 to 0.3 m improves the SO 2 separation percentage from 83 to 100% using seawater, from 32.5 to about 72% using NaOH and from 25 to 66% using DMA.
The separation percentage of SO 2 from gaseous flow in different length of module is presented in Table 7.
Membrane porosity is a membrane-related parameter, which its increment may have an encouraging influence on the separation performance of various greenhouse gases. As shown in Fig. 10, increase in the porosity of polypropylene membrane from 0.1 to 0.5 cause a substantial enhancement in the removal efficacy of SO 2 greenhouse gas from 97 to 100% using seawater, from 35 to about 66% using NaOH and from 23 to 60% using DMA. This substantial increment can be justified due to this reality that increase in the porosity of membrane results in the enhancement of SO 2 diffusivity in the fiber micropores and also the deterioration of the mass transfer resistance inside the HFMC. Table 8 aims to present a data analysis about the role of porosity on increasing the separation percentage of SO 2 using employed chemical absorbents in the HFMC. Figure 11 schematically presents the effect of hollow fibers' number on the separation of SO 2 greenhouse pollutant. As would be expected, increase in the number of microporous fibers substantially improves the gasabsorbent mass transfer interface and also their related contact area. Increase in the gas-liquid mass transfer interface and their contact area significantly increases the mass transfer coefficient of SO 2 and therefore, its www.nature.com/scientificreports/ separation percentage. It is demonstrated that increase in the number of fibers from 20 to 160 improves the SO 2 separation percentage from 13 to 100% using seawater, from 4 to about 96% using NaOH and from 2 to 92% using DMA. Table 9 comprehensively presents the separation efficiency of SO 2 greenhouse contaminant in different number of hollow fibers. www.nature.com/scientificreports/

Conclusion
Over the last decades, industrial application of HFMCs to alleviate the extraordinary release of various greenhouse gases like SO 2 to the atmosphere has been of great attention. In this paper, the removal performance of SO 2 greenhouse contaminant form SO 2 /air mixture using three novel liquid absorbents (seawater (H 2 O), DMA and NaOH) was evaluated inside the HFMC. To reach this aim, a CFD-based comprehensive simulation was developed to predict the results. An FE-based mathematical model was also applied to solve the PDEs of transport in the main subdomains of contactor. The results corroborated that seawater can be recommended as the most efficacious liquid absorbent for removing SO 2 with the removal efficiency of around 99.36%. After seawater, NaOH and DMA were placed at the second and third rank with the SO 2 separation percentage of 62 and 55%, respectively (seawater (H 2 O) > NaOH > DMA). Evaluation of simulation outcomes proved the deteriorative impact of gas flow rate on the SO 2 separation yield (due to decreasing the residence time of gaseous mixture in the HFMC). But, increment of other parameters like absorbent's flow rate, length of membrane module, hollow fibers' number and porosity possesses encouraging influence on the separation performance of SO 2 acidic pollutant due to declining the concentration of gaseous mixture at the external surface of hollow fibers, increasing the gas-absorbent contact area, increasing the diffusivity of SO 2 and improving the gas-liquid residence time inside the contactor, respectively.  www.nature.com/scientificreports/  www.nature.com/scientificreports/ Figure 9. Effect of module length on the separation yield of SO 2 greenhouse gas. www.nature.com/scientificreports/ Figure 10. Effect of membrane porosity on the separation yield of SO 2 greenhouse gas. www.nature.com/scientificreports/

Data availability
All data generated or analyzed during this study are included in this published article.
Received: 27 August 2022; Accepted: 20 January 2023 Figure 11. Effect of the number of hollow fibers on the separation yield of SO 2 greenhouse gas. Table 9. Impact of the number of fibers on the SO 2 separation performance using seawater, NaOH and DMA liquid absorbents.