Toward predicting SO2 solubility in ionic liquids utilizing soft computing approaches and equations of state

https://doi.org/10.1016/j.jtice.2022.104220Get rights and content

Highlights

  • Machine learning approaches are used to estimate SO2 solubility in ionic liquids.

  • Five EOS are also employed to predict SO2 solubility.

  • DBN exhibits excellent performance with an AAPRE of 3.56%.

  • The GMDH correlation provides good estimations with an AAPRE of 8.05%.

  • The PR EOS represents better estimations among other EOSs.

Abstract

Background

The use of novel and green solvents like ionic liquids (ILs) for the capture of air pollutant gases has gained extensive attention in recent years. However, getting reliable and fast predictions of gases solubility in ILs is complex.

Methods

Four soft computing methods including deep belief network (DBN), group method of data handling (GMDH), genetic programming (GP), and K-nearest neighbor (KNN) were utilized for estimating the solubility of sulfur dioxide (SO2) in ILs. A total of 374 experimental data points of SO2 solubility in 15 types of ILs were collected and used for model development. Moreover, Valderrama-Patel-Teja (VPT), Zudkevitch-Joffe (ZJ), Peng-Robinson (PR), Redlich-Kwong (RK), and Soave-Redlich-Kwong (SRK) equations of state (EOSs) were applied for the solubility predictions in the SO2 + ILs systems.

Significant findings

The results illustrated that DBN model is the most reliable predictive tool for the SO2 solubility in ILs by having an average absolute percent relative error (AAPRE) of 3.56%. Furthermore, the proposed simple to use GMDH mathematical correlation also provides good estimations with an AAPRE of 8.05%. Despite the weaker performance of the EOSs than the intelligent models, the PR EOS presented better estimations among other EOSs for the SO2 solubility in ILs.

Introduction

Sulfur dioxide (SO2) as an acidic gas has detrimental effects on humans and the environment and its removal from the combustion of fossil fuels, sulfide-based metal smelters, and petroleum refineries are crucial [1], [2], [3]. The combustion of fossil fuels, as one of the major sources of commercial energy supplies, creates gaseous pollutants and these are believed to have a detrimental impact on the atmosphere, the environment, and the ozone layer [4]. Furthermore, non-hydrocarbon gases including SO2, hydrogen sulfide (H2S), carbon dioxide (CO2), and other gaseous compounds as the impurity exist in natural gas [5]. The main disadvantages and harms of existing such impurities in natural gas include the lower calorific values of natural gas, reduction in capacity compressor stations, corrosion in pipelines, and decrease in the economic cost of natural gas. One of the most critical stages in designing the relative equipment and exploitation of fossil fuels is capturing harmful gases from natural gas and the atmosphere. Acidic gases must be removed from natural gas to avoid emissions into the atmosphere [6]. Hence, a series of pretreatment processes are essential to gain higher quality energy sources for optimal utilization of natural gas in domestic consumption or industrial plants [7], [8], [9]. On the other hand, flue gases that are emitted from combustion plants and composed of water vapor, particulates, heavy metals, nitrogen, CO2, and SO2 cause changes in the ecosystem and global warming. Hence, removing acidic gases like SO2 and CO2 from flue gas streams is an important step in many industrial processes [10,11]. Direct and indirect greenhouse gases emissions have maintained upward mobility in spite of over 1260 Climate Acts across the globe and commitment by at least 20 countries to achieve net-zero emission in the next few decades [12]. There are many suggestions to reduce direct and indirect greenhouse gases emissions to lower the risks and influences of climate change and to reach net-zero emissions. For example, the role of hydrogen in helping the environment and reducing carbon emissions is crucial. Hydrogenation processes are very crucial in coal processing plants and petroleum refineries to upgrade fuels quality and produce low-sulfur fuels [13]. Researchers showed that offshore geological storage of hydrogen holds great potential to advance the development of the hydrogen economy to the scale needed to achieve net-zero in the next few decades [12]. Furthermore, the injection of flue gases into gas hydrate reservoirs is deemed a promising prospect for the geological storage of CO2. Methane hydrate potentially provides a sustainable energy resource and powerful reservoirs to mitigate the increasing impact of CO2 on the climate, with respect to reduced geological hazards and adequate energy efficiency [14]. If we consider SO2 gas removal in particular, in the past years, organic solvents and limestone as conventional techniques have been suggested for the removal of SO2 [15], [16], [17]. A novel effective approach, chemical absorption of SO2 by ionic liquids (ILs), has been widely suggested in the last few years and it showed to be more cost-effective and environmentally friendly compared to conventional techniques [18], [19], [20], [21], [22], [23]. ILs are salts composed of organic or inorganic anions and organic cations that are liquids in temperatures below 212 °F [24], [25], [26]. ILs have many special and significant properties, including chemical stability, recyclability, negligible vapor pressure at room temperature, non-flammability, and non-volatility. They are proper candidates in catalytic reactions, gas handling, membrane separation, and waste recycling, which offers many advantages over traditional organic solvents [27], [28], [29], [30]. There is specific charge transfer interaction between SO2 and the anionic species of ILs. The higher the anion basicity, the greater the interaction with SO2 and the greater the ILs capacity for the gas absorption. Moreover, SO2 can drastically modify the structural and dynamic properties of ILs because of the shielding of Coulombic interactions and disruption of the ILs' long-range structure [31,32]. The tunable solvent power of ILs provides reversible absorption of high extents of SO2 in ambient circumstances. However, experimental solubility measurements of gases for extensive ranges of temperature and pressure are time-consuming, costly, and challenging [33,34]. Therefore, laboratory SO2 solubility measurements [[18], [19], [20],[35], [36], [37], [38], [39]] are limited and scattered, which demonstrates the need to use predictive tools for estimating the SO2 solubility in ILs.

To estimate the solubility of gases in ILs, equations of state (EOSs) and predictive approaches such as Monte Carlo simulations, and artificial intelligence have been executed in recent years. Yokozeki and Shiflett [40] studied the solubilities of gases, including SO2, in ILs utilizing a generic van der Waals EOS [40]. Carvalho and Coutinho [41] studied the non-ideality of solutions of H2S, SO2, and NH3 in ILs and used the Flory-Huggins Model for predicting their solubilities [41]. Wick et al. [42] utilized a polarizable force field to investigate the binding of CO2 and SO2 at the air/liquid interface of 1-Butyl-3-methylimidazolium Tetrafluoroborate IL in a molecular dynamics study. Their results demonstrated the importance of IL interfacial ordering for understanding gas solvation in them [42]. Some researchers applied the group contribution EOS for the thermodynamic modeling of the phase behavior of gases + ILs mixtures [43], [44], [45], [46]. Ghobadi et al. [47] utilized Monte Carlo simulation for calculating the solubility of SO2 and CO2 in a series of imidazolium-based ILs [47]. Ramdin et al. [48] also employed Monte Carlo simulations to calculate the solubilities of SO2, CH4, C2H6, and CO2 in ILs and Selexol [48]. Although the obtained results were valuable, this method is extremely time-consuming, in most cases not accurate enough, and requires powerful hardware facilities. Llovell et al. [49] modeled the solubilities of SO2, H2S, and NH3 in ILs utilizing the soft statistical associating fluid theory (soft-SAFT) EOS [49]. Polishuk [50] implemented simple molecular-weight-based correlations for calculating the parameters of critical-point-based modified perturbed-chain statistical association fluid theory (CP-PC-SAFT) in order to predict thermodynamic properties and various gases (SO2, Kr, R1234ze(E), R134a, CO2, CO, N2O, CH4, H2S, and O2) solubilities in 1‑Alkyl-3-methylimidazolium Bis(trifluoromethylsulfonyl)imide ILs without fitting binary parameters [50]. Kapoor et al. [51] using molecular dynamics simulations indicated that SO2 is the most soluble gas because of the strongest interaction with ILs compared to CO2, CH4, and NH3 [51]. Gholizadeh et al. [52] utilized the COSMO-RS model and modified Sanchez-Lacombe EOS for the determination of SO2 solubility in ILs [52]. Chiko et al. [53] compared CP-PC-SAFT and SAFT of Variable Range and Mie Potential (SAFT-VR-Mie) in estimating phase equilibria of binary systems containing various gases (SO2, CH4, O2, CO, H2S, C3H8, and the refrigerants) and 1-Alkyl-3-methylimidazolium based ILs. Their results showed that despite some quantitative inaccuracies, both models were capable of accurate predictions of regularities characteristic for the considered systems [53]. Due to the difficulties of utilizing EOSs such as complex iterative calculations, the non-ideality of the studied system, requirement of proper mixing rules, and adjustable parameters along with the time-consuming and requirement of powerful hardware facilities in molecular dynamic simulation and other complex simulation methods, the development of an easier prediction method like artificial intelligence has been interested in recent years. Bahmani et al. [34] used a databank of 232 SO2 solubility data points and artificial neural networks (ANNs) for the estimation of SO2 solubility in eight ILs [34]. Ghazani et al. [54] performed a computational study for predicting the solubilities of CO2-rich gases in ILs in the absence or presence of impurities such as CH4, H2, H2S, N2O, and SO2 [54]. Baghban et al. [55] modeled the solubility of SO2 in eight ILs applying 232 data points and the least square support vector machine coupled with the group contribution methods [55]. Mokarizadeh et al. [33] collected 232 data points of SO2 solubility in eight ILs and developed intelligence models using the least square support vector machine and genetic algorithm. The average absolute error of their best-developed model was 4.6% [33]. Amirkhani et al. [56] utilized soft computing methods for estimating the solubilities of N2O, CH4, CO2, CO, H2S, and SO2 in ILs. In terms of SO2 solubility, their database contained 238 data points [56]. A literature survey shows that modeling of SO2 solubility in ILs has always been of interest to researchers, and several intelligent models have been developed in this regard. However, the databases used in these studies have been similar, and given the data-driven nature of predictive intelligent approaches, collecting more solubility SO2 data for more ILs and using other intelligent models may lead to the development of a general comprehensive model for estimating SO2 solubility in ILs. Beside, developing simple to use mathematical correlations by robust algorithms can facilitate and accelerate the estimation of SO2 solubility in ILs.

In the current survey, a data bank comprising 374 experimental data points of SO2 solubility in 15 types of ILs is gathered from the literature. To model SO2 solubility in ILs, four mathematical modeling and soft computing methods namely K-nearest neighbor (KNN), genetic programming (GP), group method of data handling (GMDH), and deep belief network (DBN) are used. Furthermore, five EOSs involving Redlich-Kwong (RK), Peng-Robinson (PR), Valderrama-Patel-Teja (VPT), Zudkevitch-Joffe (ZJ), and Soave-Redlich-Kwong (SRK) are implemented for the predictions of SO2 solubility in the SO2 + ILs systems. To investigate the validity of the proposed mathematical correlations and intelligent models, several statistical criteria and graphical error analyses are executed. Eventually, the definition of relevancy factor is implemented for specifying the relative effects of seven input parameters on SO2 solubility in ILs. Finally, using the results of the best-developed mathematical equation and intelligent model, the reliability of the database of SO2 solubility in ILs and applicability scopes of these predictive tools are assessed by the Leverage method.

Section snippets

Databank gathering

To model the SO2 solubility in different ILs, a data bank containing 374 data points was accumulated from the literature. The data bank used in this survey has about 140 more data points than data banks of similar works, and SO2 solubility data in seven new ILs have been added. The total solubility data reached 374 data points for 15 ILs. The experimental solubility data for all SO2 + ILs systems utilized for modeling in this work, as well as pressure and temperature ranges, are tabulated in

Deep belief network (DBN)

ANNs were first proposed in the 1960s and have since acquired popularity in many machine learning techniques such as classifying, grouping, regression, and estimation [66]. ANNs are computational methodologies with a lot of flexibility that can establish complex correlations between actual datasets. The back-propagation (BP) system is one of the most frequent constructions among the several varieties of ANNs. However, it should be noted that one of the problems with BP is the utilization of

Assessment of models

Several well-known statistical criteria, as their formula presented below, were utilized to determine the precision and performance of the suggested correlations and models [95]:

1. Root mean square error (RMSE):RMSE=1Ni=1Z(Si,expSi,pred)2

2. Coefficient of determination (R2):R2=1i=1Z(Si,expSi,pred)2i=1Z(Si,expSexp¯)2

3. Average absolute percent relative error (AAPRE):AAPRE=100Ni=1Z|Si,expSi,predSi,exp|

4. Standard deviation (SD):SD=1N1i=1Z(Si,expSi,predSi,exp)2where Z denotes the

Development of mathematical correlations

As already mentioned, GP and GMDH are two robust techniques for simulating complex systems and developing simple to use mathematical correlations. In this study, several equations were developed using four, five, six, and seven input parameters for estimating SO2 solubility in ILs. It is noteworthy that some of the final correlations developed with the GMDH technique may contain fewer input parameters despite the mentioned number of input parameters used for model training. This is because some

Conclusions

In this work, four soft computing and mathematical modeling techniques, namely KNN, DBN, GMDH, and GP, were used to establish intelligent models and mathematical correlations for predicting the SO2 solubility in ILs. To this end, 374 data points of SO2 solubility in 15 different ILs were collected and utilized for modeling based on four, five, six, and seven input variables including T, P, Tb, Zc, ω, Pc, and Tc. Furthermore, five EOSs, namely VPT, SRK, ZJ, PR, and RK, were applied for the

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgment

Fahimeh Hadavimoghaddam would like to acknowledge the support of the Ministry of Science and Higher Education of the Russian Federation under agreement No. 075-15-2020-900 within the framework of the development program for a world-class Research Center.

References (104)

  • M.D. Bermejo et al.

    Application of a group contribution equation of state for the thermodynamic modeling of the binary systems CO2–1-butyl-3-methyl imidazolium nitrate and CO2–1-hydroxy-1-propyl-3-methyl imidazolium nitrate

    J Supercrit Fluids

    (2009)
  • M. Ramdin et al.

    Solubilities of CO2, CH4, C2H6, and SO2 in ionic liquids and Selexol from Monte Carlo simulations

    J Comput Sci

    (2016)
  • U. Kapoor et al.

    Evaluation of the predictive capability of ionic liquid force fields for CH4, CO2, NH3, and SO2 phase equilibria

    Fluid Phase Equilibria

    (2019)
  • F. Gholizadeh et al.

    Determination of SO2 solubility in ionic liquids: COSMO-RS and modified Sanchez-Lacombe EOS

    J Mol Liq

    (2018)
  • S.H.H.N. Ghazani et al.

    Absorption of CO2-rich gaseous mixtures in ionic liquids: a computational study

    J Supercrit Fluids

    (2018)
  • A. Baghban et al.

    Sulfur dioxide solubility prediction in ionic liquids by a group contribution—LSSVM model

    Chem Eng Res Des

    (2019)
  • F. Amirkhani et al.

    Towards estimating absorption of major air pollutant gases in ionic liquids using soft computing methods

    J Taiwan Inst Chem Eng

    (2021)
  • M. Sattari et al.

    On the prediction of critical temperatures of ionic liquids: model development and evaluation

    Fluid Phase Equilibria

    (2016)
  • F. Ahmadizar et al.

    Artificial neural network development by means of a novel combination of grammatical evolution and genetic algorithm

    Eng Appl Artif Intell

    (2015)
  • S.B. Ghugare et al.

    Genetic programming based high performing correlations for prediction of higher heating value of coals of different ranks and from diverse geographies

    J Energy Inst

    (2017)
  • D.A. Nembhard et al.

    A symbolic genetic programming approach for identifying models of learning-by-doing

    Comput Ind Eng

    (2019)
  • G. Pazuki et al.

    A hybrid GMDH neural network to investigate partition coefficients of Penicillin G Acylase in polymer–salt aqueous two-phase systems

    J Mol Liq

    (2013)
  • S. Atashrouz et al.

    Estimation of the viscosity of nine nanofluids using a hybrid GMDH-type neural network system

    Fluid Phase Equilibria

    (2014)
  • N. Amanifard et al.

    Modelling of multiple short-length-scale stall cells in an axial compressor using evolved GMDH neural networks

    Energy Convers Manag

    (2008)
  • H. Ghanadzadeh et al.

    Mathematical model of liquid–liquid equilibrium for a ternary system using the GMDH-type neural network and genetic algorithm

    Appl Math Model

    (2012)
  • D. Ronze et al.

    Hydrogen solubility in straight run gasoil

    Chem Eng Sci

    (2002)
  • D. Avlonitis et al.

    Prediction of VL and VLL equilibria of mixtures containing petroleum reservoir fluids and methanol with a cubic EoS

    Fluid Phase Equilibria

    (1994)
  • M.R. Mohammadi et al.

    Application of cascade forward neural network and group method of data handling to modeling crude oil pyrolysis during thermal enhanced oil recovery

    J Pet Sci Eng

    (2021)
  • A. Hemmati-Sarapardeh et al.

    A soft computing approach for the determination of crude oil viscosity: light and intermediate crude oil systems

    J Taiwan Inst Chem Eng

    (2016)
  • Z. Lei et al.

    Gas solubility in ionic liquids

    Chem Rev

    (2014)
  • A.G. Chmielewski

    Environmental effects of fossil fuel combustion

    (2009)
  • S. Mokhatab et al.

    Handbook of natural gas transmission and processing

    (2012)
  • J. Sánchez-Badillo et al.

    Solvation thermodynamic properties of hydrogen sulfide in [C4mim][PF6],[C4mim][BF4], and [C4mim][Cl] ionic liquids, determined by molecular simulations

    J Phys Chem B

    (2015)
  • D.B. Alvarado et al.

    Nitrogen removal from low quality natural gas

    (1997)
  • B. Shimekit et al.

    Natural gas purification technologies-major advances for CO2 separation and future directions

    (2012)
  • H. Lin et al.

    Natural gas purification

    Encyclopedia of membrane science and technology

    (2013)
  • S. Pacala et al.

    Stabilization wedges: solving the climate problem for the next 50 years with current technologies

    Science

    (2004)
  • F. Rezaei et al.

    SO x/NO x removal from flue gas streams by solid adsorbents: a review of current challenges and future directions

    Energy Fuels

    (2015)
  • A. Hassanpouryouzband et al.

    Offshore geological storage of hydrogen: is this our best option to achieve net-zero?

    ACS Energy Lett

    (2021)
  • M.R. Mohammadi et al.

    Application of robust machine learning methods to modeling hydrogen solubility in hydrocarbon fuels

    Int J Hydrog Energy

    (2021)
  • A. Hassanpouryouzband et al.

    CO2 capture by injection of flue gas or CO2–N2 mixtures into hydrate reservoirs: dependence of CO2 capture efficiency on gas hydrate reservoir conditions

    Environ Sci Technol

    (2018)
  • H.J. Ryu et al.

    Simultaneous CO2/SO2 capture characteristics of three limestones in a fluidized-bed reactor

    Energy Fuels

    (2006)
  • S. Wu et al.

    Effect of the pore-size distribution of lime on the reactivity for the removal of SO2 in the presence of high-concentration CO2 at high temperature

    Ind Eng Chem Res

    (2002)
  • M. Van Dam et al.

    Selective sulfur dioxide removal using organic solvents

    Ind Eng Chem Res

    (1997)
  • J.L. Anderson et al.

    Measurement of SO2 solubility in ionic liquids

    J Phys Chem B

    (2006)
  • A. Yokozeki et al.

    Separation of carbon dioxide and sulfur dioxide gases using room-temperature ionic liquid [hmim][Tf2N]

    Energy Fuels

    (2009)
  • M.B. Shiflett et al.

    Chemical absorption of sulfur dioxide in room-temperature ionic liquids

    Ind Eng Chem Res

    (2010)
  • M. Jin et al.

    Solubilities and thermodynamic properties of SO2 in ionic liquids

    J Phys Chem B

    (2011)
  • G. Cui et al.

    Acylamido-based anion-functionalized ionic liquids for efficient SO2 capture through multiple-site interactions

    ACS Sustain Chem Eng

    (2015)
  • T. Zhao et al.

    Efficient SO2 capture and fixation to cyclic sulfites by dual ether-functionalized protic ionic liquids without any additives

    ACS Sustain Chem Eng

    (2018)
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