A new approach for correlating of H2S solubility in [emim][Lac],[bmim][ac] and [emim][pro] ionic liquids using two-parts combined models

Alireza Afsharpour

Faculty of Chemical and Materials Engineering,Shahrood University of Technology,Shahrood,Iran

Keywords:Solubility Thermodynamics Ionic liquids CPA RETM mSRK

ABSTRACT Two bi-part combined models containing reaction equilibrium thermodynamic model and an equation of state (EoS) including cubic plus association (CPA) or modified Soave-Redlich-Kwong (SRK),were employed to correlate H2S solubility in ionic liquids [emim][Lac],[bmim][Ac] and [emim][Pro].RETM and CPA/mSRK are responsible for chemical and phase equilibria calculations,respectively.The RETM defines a complex formation reaction between an H2S and two IL molecules into the liquid phase so that a complex in the form of H2S(IL)2 is probable to produce.On the other side,CPA/mSRK EoSs perform phase equilibria computations to find pressure and vapor phase concentrations.In the case of CPA,both of H2S and the ionic liquids were considered as self-associating components which pursue 4C and 2B schemes,respectively.This model computes the pure IL parameters using experimental density data.In this work,critical properties were estimated through the modified Lydersen-Joback-Reid method,Eotvos and Guggenheim relations.Afterward,the binary systems were investigated by applying RETM.CPA presents average absolute deviations (AADs) equal to 2.41%,13.42% and 3.52% for [emim][Lac],[bmim][Ac],and [emim][Pro],respectively.Moreover,the AADs obtained by mSRK are 3.75%,5.07%,and 6.06%,respectively.As it is evident from the results,the combination of RETM with both CPA and mSRK EoSs will result in good correlation accuracy.

1.Introduction

An almost new type of chemical solvents,known as RTILs(room temperature ionic liquids),is increasingly utilized for different uses because of their designable structure [1].This class of compounds consist of an organic cation and an inorganic/organic anion which could be specially selected for a specific purpose [2].Indeed,they could be reformed to employ in various applications and therefore they are called ‘‘designer solvents”.Alkanolamines,such as MDEA(methyldiethanolamine),are conventionally used as the acid gas removal agents.But,the existence of some deficiencies will limit their applications [1].One of the most significant features of ILs is their capability for acid gas absorption.In these components,the existence of long-range forces among the cations and anions leads to ignorable volatility (nonvolatility).Furthermore,they are known as high thermal and electrochemical stable components.

Up to now,limited trials performed to obtain the acid gases absorption into the various ionic liquids.Such experiments need to spend many times,costs,and energy.A good substitute may be the application of a precise thermodynamic model [3].

Because of the associating nature of the present components,the phase behavior of such systems is too far from ideality [4].As yet,some association EoSse.g.,SAFT(statistical associating fluid theory),CPA,and their different variations,have been employed these systems that few of them is mentioned below.

EPC (electrolyte perturbed chain)-SAFT EoS implemented by Jiet al.[5],to calculate the density and gas absorption in different ILs consisting of imidazolium cations and [BF4],[PF6],and [Tf2N]anions.They used the primitive Debye-Hückel model with no augmented parameters to bring long-range interactions into consideration.Similarly,in another work [6],they employed the same EoS to model the absorption of H2S in ILs with imidazolium cations.

Pure CO2and H2S removal utilizing fourteen ionic liquids([C2mim][eFAP],[C2mim][EtSO4],[C2mim][OTf],[C2mim][Tf2N],[C4mim][BF4],[C4mim][PF6],[C6mim][PF6],[C6mim][Tf2N],[C8mim][PF6],[C8mim][Tf2N],[HOemim][BF4],[HOemim][OTf],[HOemim][PF6] and [HOemim][Tf2N]) correlated using the CPA EoSviaa novel approach by Soltani Panah [7].They obtained AAD below 10% for all the investigated binaries.

Pressure-volume-temperature correlations for H2S absorption in 12 various imidazolium-based ionic liquids were performed by Shojaeian [8] applying PR-TS Eos.Their results present overall AAD equal to 3.40% for binary systems.

Afsharpour [9] implemented the RETM,and SRK-CPA EoS to model H2S solubility in [C2mim][Ace],and [C6mim][Ace] ILs.The results show AADs below 2% for pure ILs.Also,average deviations equal to 12.44% and 4.75% for the [hmim][Ace] and [emim][Ace]were obtained,respectively.Furthermore,Afsharpour and kheiri[10–13],modeled the CO2and H2S and their mixtures absorption in ILs [Omim][Tf2N],[C4mim][MeSO4],[C8mim][PF6] and [C2mim][PF6] employing SRK-CPA EoS with AADs below 20% for all the ILs.

In the present communication,H2S absorption into the three ILs of 1-ethyl-3-methylimidazolium lactate ([emim][Lac]),1-butyl-3-methylimidazolium acetate ([bmim][Ac]) and 1-ethyl-3-methylimidazolium propionate ([emim][Pro]) correlated implementing CPA and modified SRK EoSs together with RETM.

2.Thermodynamic Modeling

2.1.Reaction equilibrium thermodynamic model (RETM)

Huanget al.[14]developed the RETM based on the possibility of two following chemical reactions in the liquid phase:

where A,B,AB and AB2denote H2S,IL and two probable complexes,respectively.

The Henry’s law,equilibrium constants,and mass balance should be simultaneously solved to compute the concentration of the components in the liquid phase.All these equations thoroughly described at the work of Huanget al.[14].Simplification of the equations leads to the below relation:

wheremA0andmB0represent initial H2S and ILs molality,respectively.

The unknown parameters,K1(first reaction equilibrium constants),K2(second reaction equilibrium constants)andH(constant of Henry’s law),might be estimated through fitting the solubility data.They amazingly obtained the first reaction constants (K1)equal to zero for all the systems.TheK2andHvariables,reported in Ref.[14].Following relation is proposed to correlate theK2andHvariables as a temperature function:

As one can expect,this equation makes the parameter prediction capability for other various temperatures.The coefficients of Eq.(3),reported in Table 1.

Table 1 Adjustable parameters of RETM for the investigated ionic liquids

Now,the solution of the following equations calculates the liquid molalities [14]:

Determining the liquid phase mole fractions,VLE calculations through CPA/mSRK EoS will be accomplished to obtain pressure and vapor phase concentrations.

2.2.CPA equation of state

The well-known SRK-CPA EoS developed by Kontogeorgiset al.[15].This model divided into two main parts including SRK EoS in addition to Wertheim’s association term to consider hydrogen bonding effect.

On the basis of the compressibility factor,CPA EoS may be written as:

stands for unbounded type A sites of moleculei,which might be computed as

wherein the association strengthobtained as bellow:

As our previous works,H2S was supposed as an associating component following the 4C association scheme.Furthermore,for the sake of molecular structures (cation+anion),[emim][Lac],[bmim][Ac] and [emim][Pro] assumes to have two association sites.

According to the Eq.(13),for H2S(4 sites)+IL(2 sites)binaries,to find six unbounded site fractions,the following six equations should be solved simultaneously.

wherein,subscripts 1 and 2 stand for H2S and the IL,respectively.Moreover,A,B,C,and D denote the association sites.

Fig.1.Schematic of considered association sites on (a) H2S,(b) [emim][Lac],(c)[bmim][Ac] and (d) [emim][Pro] molecules.

Fig.1,illustrates a schematic of considered association sites on H2S and the IL molecules.

2.3.Modified SRK equation of states

In addition to CPA EoS,a modified form of the generalized Redlich-Kwong EoS for ILs presented by Yokozeki and Schiflett[16] was employed to correlate the solubility data.This model could be presented as below:

in which

wherein the coefficients βi,τij,lij,lji,andmijare the adjustable parameters of the model.βiare related to the pure components while others are utilized as binary interaction coefficients.βiparameters for H2S have been reported in Ref.[16].Moreover,for ILs,β0is considered equal to one and β1will be adjusted together with the other binary interaction coefficients.More details about the model can be found in Ref.[16].

2.4.Combiantion of the RETM with CPA/mSRK EoS

In the present work,the RETM employed as an auxiliary model which helps to take into account the possible chemical/physical reactions between gases and ILs and therefore leads to lower AADs.For more clarification about using RETM together with the CPA/mSRK EoSs,at first,the association (hydrogen bonding) and then the RETM will be discussed here.

The selected association scheme for IL+H2S binaries is 2B+4C.It means that an IL molecule has two associating sites,including an electron donor and an electron acceptor.In fact,ILs have one positive (electron acceptor) and one negative (electron donor) association sites that correspond to their charges of the cations and anions,respectively.On the other hand,H2S was assumed to have 4 association sites,including two electron donors(relate to its two couples of unbound electrons)and two electron acceptors(related to its two hydrogen atoms).Therefore,the ILs and H2S could establish cross associations (association with each other) through their electron donor/acceptor sites.In this way,the electron acceptor sites of a molecule could construct associations with the electron donor sites of the other molecule andvice versa.

Now we should see what The RETM says.As mentioned before,RETM introduces a reaction-based mechanism to obtain effective concentrations (the free molecular components that can transfer between the liquid and vapor phases) in the liquid phase.As discussed,RETM proposes that two IL molecules could form a complex with one H2S molecules (this is may not be the only form but is the most probable form).It should be emphasized that the concept of the reaction should not necessarily interpret as a chemical reaction.But the RETM just predicts the possibility of formation of a complex between IL and H2S.This complex (as shown in Eq.(1) and Fig.2) could present a molecular physical absorption(e.g.through cross-association).In simple words,the RETM covers hydrogen bonding effects in addition to another possible known/unknown mechanisms to form a complex.

Fig.2.Schematic of complex formation between H2S and ILs according to the RETM.

Briefly,the association term and the RETM are two parallel complementary concepts that could be used simultaneously or even separately.The simultaneous use of them leads to lower AADs.

From another aspect,A main crucial task to use of association models,is to find the most suitable association schemes for the present components.Although usually,the first choice is based on the molecular structures,it may present inappropriate results.Indeed,the best way to find the best association scheme is to investigate all the possible forms.In this way,for IL+H2S,many various manners including 1A+1D,1D+1A,1A+2B,2A+2B,2B+1A,2B+2A,2B+2B,2B+4C,4C+2B,4C+4C,2B+3B and etcetera could be supposed.Investigation of all the existing forms will be so challenging.RETM helps to cover some probable deviations related to the unsuitable selection of the association schemes.In a similar way,the RETM can covers some deviations corresponding to the leak of association term in the employed mSRK EoS.

3.Results and Discussion

3.1.The pure components parameters

3.1.1.Critical properties estimation

3.1.1.1.The modified Lydersen-Joback-Reid method.Before optimizing pure component parameters in each model,it is necessary to find critical temperatures of H2S and the ILs.As it is very difficult or even impossible to measure these parameters of ILs experimentally,some alternative methods have been developed.One of such methods is to use group contribution models.In this way,the modified Lydersen-Joback-Reid(mLJR)method[17]is employed in the present work.In the model,the physical properties may be calculated through the following relations:

where ΔTbM,ΔTMand ΔPMare the parameters of the method which are presented in[17].Moreover,nstands for the number of a specified functional group.The estimated values was verifiedviathe calculation of liquid densities.Indeed,the estimated critical properties were used to determine liquid density,so that low AAD values about two were obtained comparing the experimental data presented in [18,19].

3.1.1.2.Empirical equations.Although the mLJR method presents an applicable approach to estimate critical properties of ILs,in some cases,meaningful disagreements are seen between its results and those of other reliable approaches.Two of these well-known relations,are equations of Eotvos [20] and Guggenheim [21].These empirical relations,are written as below,respectively.

Despite their almost close results,the Eotvos relation expects to show more reliable results because of using simultaneous density and surface tension experimental data.As in the case of [emim][Lac] and [bmim][Ac],the results of the three methods are almost close,therefore,an average value was used.Besides,as the mLJR technique presents far results from other relations,an average between Eotvos and Guggenheim results was utilized.

To implement each of the methods mentioned above,density and surface tension data should be utilized.Density data for both of [emim][Lac],[bmim][Ac] were achieved from literature[18,19].Moreover,their surface tension data were obtained from[19,22].Unfortunately,no experimental data for liquid density and surface tension of [emim][Pro] exist.Therefore,to obtain the required data,a correlation-prediction approach was followed.In this way,the existing experimental density and surface tension data [23] for [Cnmim][Pro] (n=3–6) were fitted to the following relations with the overall AADs equal to 0.59% and 0.02%,respectively.Afterward,liquid density (ρ,g?cm-3) and surface tensions(γ,N?m-1) for [emim][Pro] (n=2) were predicted through following relations:

whereinnis the carbon number in alkyl chain.The predicted[emim][Pro] density and surface tension values at 298.15 K,show AADs equal to 2.2% and 1.77% compared with the only two exist experimental data [24].As one can conclude from the result,the presented correlations are reliable.

The estimated and employed critical properties of the ILs,have been reported in Table 2.

Table 2 The critical properties of the ionic liquids

Table 3 Pure component parameters of the CPA EoS (1 bar=105 Pa)

3.1.2.CPA EoS

According to the Eqs.(11)–(13),there are five adjustable parameters (a0,b,c,and) for each self-associating compound[15].H2S parameters were obtained from Ref.[25].To achieve the parameters,vapor pressure and liquid density data should be used.However,because the ILs are almost non-volatile,there are not vapor pressure data for them in the literature.Therefore,theparameters described above,may be determined by minimizing the following function:

whereinNPdenotes the number of data points.

The pure parameter values of H2S and the used ILs in addition to the AADs for the liquid density correlations,are presented in Table 3.

3.1.3.Prediction of IL’s vapor pressure

As stated before,no experimental data of vapor pressurePVap.of the ILs can be found in the literatures.It sounds to be for the sake of negligible values that can make such experiments,difficult or even impossible.Therefore,to have a rough estimation,the CPA was employed to predict these quantities.In this way the obtained pure prameters were applied to predict vapor pressures in different temperatures.Table 4 presents the predicted vapor pressures of the investigated ILs.

Table 4 Predicted vapor pressures of the ILs using CPA EoS

Table 5 The temperature dependent and independent binary interaction parameters for solubility of H2S in [emim][Lac],[bmim][Ac] and [emim][Pro] using RETM+CPA EoS

3.1.4.Modified SRK EoS

As mentioned before,pure parameters (β0to β3) of H2S were extracted from the literature [16].Moreover,parameter β1of the ILs is obtained through fitting the solubility data to the model so that in the next section will be discussed.

3.2.Binary systems

The binary interaction parameters of both models,for H2S+[emim][Lac],H2S+[bmim][Ac] and H2S+[emim][Pro] binary systems,could be optimized utilizing the following function:

H2S solubility data in the investigated ILs were achieved from Ref.[14].

3.2.1.CPA EoS

Two approaches were followed to find the binary interaction parameters of the model.In the first one,kijwere supposed as a uniform function in terms of temperature as Eq.(29) while the other considers them as constant values.

Fig.3.The experimental and calculated pressures (by CPA EoS) versus H2S liquid molality in ionic liquid [emim][Lac] at different temperatures.

Fig.4.The experimental and calculated pressures (by CPA EoS) versus H2S liquid molality in ionic liquid [bmim][Ac] at different temperatures.

Fig.5.The experimental and calculated pressures (by CPA EoS) versus H2S liquid molality in ionic liquid [emim][Pro] at different temperatures.

The coefficients together with the AAD for the H2S+IL systems,reported in Table 5.As it is observed in the table,the AADs for H2S+[emim][Lac],H2S+[bmim][Ac] and H2S+[emim][Pro] systems are 2.41%,13.42% and 3.52%,respectively.

Figs.3–5 illustrate the experimentalversuscalculated results for all binaries at various temperatures.As it is seen,suitable conformity between the experimental data and computed values can be observed.

3.2.2.Modified SRK EoS

The interaction parameters of the mSRK(τij,lij,lji,andmij),were considered as temperature independent values.These parameters in addition to β1parameters of the investigated ILs,were calculated through fitting solubility data to the model.All the obtained values with the corresponding AADs have been reported in Table 6.In brief,3.75%,5.07%,and 6.06%m.,were achieved as the AADs for H2S+[emim][Lac],H2S+[bmim][Ac] and H2S+[emim][Pro] systems,respectively.

Fig.6.The experimental and calculated pressures (by mSRK EoS) versus H2S liquid molality in ionic liquid [emim][Lac] at different temperatures.

Fig.7.The experimental and calculated pressures (by mSRK EoS) versus H2S liquid molality in ionic liquid [bmim][Ac] at different temperatures.

Fig.8.The experimental and calculated pressures (by mSRK EoS) versus H2S liquid molality in ionic liquid [emim][Pro] at different temperatures.

Table 6 The binary interaction parameters and AAD for solubility of H2S in [emim][Lac],[bmim][Ac] and [emim][Pro] using mSEK EoS with and without RETM

Figs.6–8 illustrate the experimentalversuscalculated results(by the mSRK EoS) for all binaries at various temperatures.As it is seen,suitable conformity between the experimental data and computed values can be observed.

It should be emphasized that the mSRK,adjust the β1parameter of the ILs together with the other binary interaction parameters,while CPA calculates pure parameters separately.In addition to this difference in approach,mSRK has five binary adjustable parameters while CPA has one for IL+H2S systems and two for CO2+IL binaries.In fact,three of the adjustable parameters in CPA are related to thekijas a function of temperature.Therefore,it is not far from the expectation that mSRK presents better results.Because of the different approaches used in the two EoSs,they cannot be compared precisely.But a rough comparison shows the strength of the CPA in spite of its lower number of fitting parameters.

4.Conclusions

H2S absorption in ionic liquids [emim][Lac],[bmim][Ac] and[emim][Pro] was thermodynamically modeled utilizing the CPA and mSRK EoSs.The RETM was employed to determine the mole fractions of the components in the liquid phase.Indeed,a twoparts nested loops was employed wherein the inner loop computes the liquid mole fractions through RETM while the outer one is responsible for VLE calculations using CPA or mSRK EoSs.Choose of these models is because of their capability to make a tradeoff between simplicity and accuracy compared to the more accurate models such as SAFT variants EoSs.In the case of CPA EoS,H2S was supposed to follow the 4C association scheme while the 2B was chosen for the ILs.The overall AADs in bi-component systems,including H2S+[emim][Lac],H2S+[bmim][Ac] and H2S+[emim][Pro] systems,achieved equal to 2.41% &3.75%,13.42% &5.07%,and 3.52%&6.29%,by CPA and mSRK EoSs,respectively.As the outputs show,the combination of CPA/mSRK with the RETM may result in very good accuracy to correlate H2S solubility in [emim][Lac],[bmim][Ac] and [emim][Pro] ionic liquids.While,without the use of RETM,AAD will obtain in many hundreds order of magnitude.

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.