Hydrogen Sulfide Solubility in Ionic Liquids (ILs ... - ACS Publications

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Hydrogen Sulfide Solubility in Ionic Liquids (ILs): An Extensive Database and a New ELM Model Mainly Established by ImidazoliumBased ILs Yongsheng Zhao,†,‡ Hongshuai Gao,† Xiangping Zhang,*,† Ying Huang,†,‡ Di Bao,†,‡ and Suojiang Zhang*,† †

Beijing Key Laboratory of Ionic Liquids Clean Process, State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China ‡ School of Chemistry and Chemical Engineering, University of Chinese Academy of Sciences, Beijing 100049, China S Supporting Information *

ABSTRACT: A database and forecasting models of the solubility of hydrogen sulfide (H2S) in ionic liquids (ILs) are important for the industrial processes of gas sweetening. However, the specialized H2S solubility database and accurate predictive models are scarce at present. Therefore, this study first established a comprehensive database on the solubility of H2S in ILs, which includes 1334 pieces of data covering the period from 2007 to 2016. On the basis of the database, a new model is proposed using an extreme learning machine (ELM) intelligence algorithm and the number of fragments, which are easy to obtain and thus eliminate the need to use experimental data as input parameters. A total of 1282 pieces of data for 27 ILs (including 23 imidazolium-based and four ammonium-based ILs) have been used to build and test the model. The coefficient of determination (R2) and root-mean-square error (RMSE) of the ELM model for the test set are 0.990 and 0.0301, respectively. The results show that the established ELM model is applicable for predicting the solubility of H2S in ILs, which is important for the design, simulation, and analysis of new gas sweetening processes.

1. INTRODUCTION Hydrogen sulfide (H2S) exists extensively within many gas fields, such as natural gas, refinery gas, synthesis gas, and so on, as well as within hydrodesulfurization processes of crude oils.1 Because of its high acidicity and toxicity, H2S must be removed from the industrial processes. At present, alkanolamine solutions such as monoethanolamine, diethanolamine, and methyldiethanolamine are often used as commercial absorbents. However, there are some deficiencies with the alkanolamine solutions during the absorbent process, including high energy consumption, high economic cost, and caustic byproducts.2 Therefore, environmentally friendly and highly efficient absorbents to effectively remove H2S are needed. As a new class of solvents for the past few years, ionic liquids (ILs) exhibit many remarkable features, such as negligible vapor pressure, stability at high temperatures, wide liquid range, noninflammability, and tunable properties.3−6 Therefore, ILs are promising candidates for replacing traditional organic solvents, © XXXX American Chemical Society

and they have been applied to absorb and separate acidic and alkaline gases including CO2,7−10 SO2,11 H2S,12 NH3,13 and so on. However, to the best of our knowledge, although the solubility of CO2 in ILs has been extensively studied, the solubility of H2S in ILs has been studied only in recent years.14,15 To date, most of the studies have mainly focused on physical absorption. The advantage of physical absorption is that the solvents can be easily regenerated by changing the temperature and pressure. However, the absorption capacity is relatively low, especially at low H2S partial pressures/ concentrations. Therefore, chemical absorption is starting to attract the attention of researchers.16 Although chemical absorption has the disadvantage of being highly energySpecial Issue: Proceedings of PPEPPD 2016 Received: June 2, 2016 Accepted: November 4, 2016

A

DOI: 10.1021/acs.jced.6b00449 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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The fragment or group contribution method is an effective method for estimating properties.31−34 In this method, the property is a function of structure-related parameters that are determined by the number of each fragment belonging to the molecule. Hence, the numbers of different fragments were used as the input parameters in this study. Extreme learning machine (ELM) is a relatively new intelligence algorithm that was proposed by Huang and co-workers.35−37 The ELM algorithm generally has a higher speed than the ANN and SVM algorithms, and it can tend to reach a global optimum. It has very recently been effectively used by our group to predict the heat capacities of ILs.38 Therefore, the new ELM intelligence algorithm was also employed to build the new predictive model in this study. In this work, first a comprehensive database on the solubility of H2S in ILs was established. The database includes 1334 pieces of data, which were collected from the literature under wide ranges of temperature and pressure. Then, in order to overcome the shortcomings of the current models, which employ experimental data as the input parameters, a new model based on the database was established that uses the ELM algorithm with the number of fragments as the input parameters. Finally, the performance of the obtained model was verified and compared with previous work.

intensive for the desorption process, it exhibits a high absorption capacity compared with physical absorption. However, as mentioned above, data on the solubility of H2S in ILs is scarce and mainly focused on physical absorption12 until now. Thus, it is necessary to establish a model for predicting the solubility of H2S in ILs, especially when the solubility data are scarce and the experimental measurements are often expensive and time-consuming. Recently, some works have been published on predicting the solubility of H2S in ILs using the conductor-like screening model for real solvents (COSMO-RS)17 and the machine learning approach.18−21 The COSMO-RS approach was first developed by Klamt and co-workers.22−25 It is a novel and priori prediction method that needs only the molecular structure as the input information and is independent of experimental data. Therefore, the COSMO-RS method has received growing attention for predicting the solubility of gases in ILs.26−30 Recently, a good review of the solubilities of a series of important gases in ILs has been made by Lei et al.17 In that work, the authors employed the COSMO-RS method (as implemented in the ADF combi2005 and ADF combi1998 versions) to predict a variety of gas solubilities in ILs, including that of H2S. However, as concluded in their work, from a quantitative point of view the COSMO-RS model is often not sufficient to accurately predict the solubilities of gases in ILs at present. For example, the average absolute relative deviation (AARD) values for the solubility of H2S for the established ADF combi2005 and ADF combi1998 COSMO-RS models are 38.64% and 38.14%, respectively.17 As described by Ahmadi and co-workers,18 all of the previously used methods, such as equations of state (EOSs), have the main shortcoming that they can be trusted exclusively for a special system, and thus, the artificial neural network (ANN) intelligence algorithm has been applied to build models using back-propagation (BP) and particle swarm optimization (PSO) to train the network. In their work, 465 experimental data points for 11 different ILs were used to establish the model, and the acentric factor (ω), critical temperature (Tc), and critical pressure (Pc) of the ILs accompanied by the pressure (P) and temperature (T) were employed as input variables. The results of the established BPANN and PSO-ANN models are good, with mean square errors (MSEs) of 0.00335 and 0.00025, respectively. Ahmadi and coworkers19,21 also employed other intelligence algorithms, namely, least-squares support vector machine (LSSVM) and gene-expression programming (GEP), to establish models based on the same data set and input parameters as used above. Because the SVM can overcome some obstacles of ANN, a better model was obtained, with an MSE of 6.6507 × 10−5. In addition, the LSSVM and GEP models are both more accurate than the widely used Soave−Redlich−Kwong (SRK) and Peng−Robinson (PR) approaches. Rahimpour and coworkers20 employed more data points (664) for 14 ILs to build models using the ANN algorithm and the Peng−Robinson EOS with the same input parameters as used above. The best results were obtained from the ANN model, with a coefficient of determination (R2) of 0.9987. However, the abovementioned studies18−20 first had to calculate or test the critical properties and acentric factor of the ILs before establishing the models (i.e., the models rely on experimental data). Furthermore, the ANN and SVM algorithms both have some disadvantages, for example, the calculations are slow. Therefore, new easy-to-use input parameters and intelligence algorithms are needed to establish better models.

2. METHODS 2.1. Database and Data Set. In this study, a comprehensive database on the solubility of H2S in ILs containing data collected from 16 references in the period from 2007 to 20161,2,12,14,15,39−49 was established. The collected data were carefully classified, grouped, named, assigned, and added to our previous database.5,50 The cations and anions are coded with six characters, with cation names containing the capital letter “C” and five digits and anion names containing the capital letter “A” and 5 digits. For example, C02011-A02001 denotes the IL 1-butyl-3-methylimidazolium tetrafluoroborate; C02011 denotes the cation, where “C” stands for “cation”, 02 denotes the presence of two alkyl side chains, and 011 indicates that this is the 11th cation of this type according to the sequence of molecular weight; A02001 denotes the anion, where “A” stands for “anion”, 02 denotes the second boric anion, and 001 indicates that this is the first anion in this type. However, the sequences of the ions are not strictly according to their molecular weights because of some of the high-molecularweight cations and anions were already present in our previous database (e.g., C02010 with a molecular weight of 141.19), and therefore, cations or anions that were added later with lower molecular weight have the larger numbers (such as C02011 with a molecular weight of 139.22). A total of 1298 pieces of data for 37 available ILs, including 15 cations and 13 anions, have been extracted. Detailed information for each IL (including the sequence number; code numbers of the cation, anion, and IL; abbreviation; full name; solubility value; method used to obtain the solubility; temperature; pressure; experimental method; and reference) is listed in the Supporting Information. Reliable experimental data points are vital for developing and checking prediction models.32 Therefore, data points tested by similar experimental methods and verified by previous work were employed in this study. Altogether, 1282 pieces of data (including 722 pieces of data used by Lei et al.17 and 465 pieces of data used by Ahmadi and co-workers18,19) were finally selected as the whole data set for establishing and verifying the B



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Figure 1. Chemical structures of the cations and anions used in this study.

Figure 2 for a representative IL, namely, 1-(2-hydroxyethyl)-3methylimidazolium bis(trifluoromethylsulfonyl)amide. The cation of this IL is divided into [Im]+ (cation core), H (ring), −CH3 (methyl), −CH2− (methylene), and −OH (hydroxyl), and the anion is divided into −CF3−, −SO2−, and [O]−. Therefore, the numbers of fragments are 1, 3, 1, 2, and 1 for the cation and 1, 1, and 1 for the anion, respectively. The detailed method for fragment division can be found in our previous work.31 2.3. Extreme Learning Machine (ELM) Algorithm. In order to establish the relationship between temperature, pressure, the number of fragments, and H2S solubility in ILs, a relatively new intelligence algorithm, namely, ELM, was employed to build the predictive model. Compared with the traditional single-hidden-layer ANN and SVM algorithms, the ELM algorithm has some advantages in the following aspects: (1) the learning speed is very high; (2) the generalization ability is very good; (3) learning occurs without iterative tuning; (4) the ELM looks much simpler than the ANN and SVM; and (5) unlike traditional gradient-based algorithms, which only work for differentiable activation functions, the ELM can work for all bounded nonconstant piecewisecontinuous activation functions. Here we give only a simple description; a detailed theory introduction and descriptions of the ELM are available in the literature.35−37,53,54 In the ELM, the output function f L(x) is given by

predictive model. As shown in Figure 1, a total of 27 ILs, based on the cations methyldiethanolammonium (MEDAH), 1-ethyl3-methylimidazolium ([EMIM]+), 1-octyl-3-methylimidazolium ([OMIM]+), 1-butyl-3-methylimidazolium ([BMIM]+), 1-(2-hydroxyethyl)-3-methylimidazolium ([HEMIM]+), dimethylethanolammonium (DMEAH), and 1-hexyl-3-methylimidazolium ([HMIM]+) and different anions including tetrafluoroborate ([BF4]−), bromide (Br), acetate (OAc), formate (For), propionate (Pro), lactate (Lac), methylsulfate ([MeSO4]−), hexafluorophosphate ([PF 6 ] − ), tris(pentafluoroethyl)trifluorophosphate (TPTP), ethylsulfate ([EtSO4]−), trifluoromethanesulfonate ([TfO]−), and bis(trifluoromethylsulfonyl)amide ([Tf2N]−), have been investigated. As usually done in the open literature18,19 and our previous work,4,5,51,52 the entire data set was categorized into two subsets, namely, the training set and the test set, in the proportion of 80% to 20%. The training set was used to build and optimize the predictive model, and the test set was employed to verify and evaluate the predictive performance of the established model. Detailed information on each IL employed in this study (including the abbreviation, temperature range, pressure range, H2S solubility range, number of data points, and reference) is listed in Table 1, and the detailed value of each piece of data can be found in the Supporting Information. 2.2. Fragment Division. As mentioned above, the property is a function of structure-related parameters that are determined by the number of each fragment belonging to the molecule. Therefore, the numbers of fragments would be used as the input parameters in this work. A typical example is shown in

L

f L (x) =

∑ βi hi(x) = h(x)β i=1

C

(1) DOI: 10.1021/acs.jced.6b00449 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


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Table 1. Temperature, Pressure, and H2S Solubility Ranges and AARD Values for the ILs Used in This Study IL no. 1

IL [BMIM][PF6]

2 3 4 5 6 7 8 9 10

[BMIM][EtSO4] [BMIM][MeSO4] [BMIM][BF4] [BMIM][Tf2N] [EMIM][Tf2N] [EMIM][PF6] [OMIM][Tf2N] [OMIM][PF6] [HMIM][Tf2N]

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

[HMIM][BF4] [HMIM][PF6] [HEMIM][BF4] [HEMIM][PF6] [HEMIM][Tf2N] [HEMIM][TfO] [EMIM][OAc] [EMIM][Pro] [EMIM][Lac] [BMIM][OAc] [HMIM][OAc] [EMIM][TPTP] [BMIM][Br] [MEDAH][OAc] [MEDAH][For] [DMEAH][OAc] [DMEAH][For]

T range (K)

P range (bar)

H2S solubility range (mole fraction)

no. of data points

AARD (%)

ref

298.15−403.15 303.15−333.15 303.15−353.15 298.10 303.15−343.15 303.15−343.15 303.15−353.15 333.15−363.15 303.15−353.15 303.15−353.15 303.15−353.15 303.15−343.15 303.15−343.15 303.15−343.15 303.15−353.15 303.15−353.15 303.15−353.15 303.15−353.15 293.15−333.15 293.15−333.15 293.15−333.15 293.15−333.15 293.15−333.15 303.15−353.15 299.15 303.2−333.2 303.2−333.2 303.2−333.2 303.2−333.2

0.69−96.30 1.23−10.11 1.14−12.70 0.11−7.51 0.61−8.36 0.94−9.16 1.08−16.86 1.45−19.33 0.94−19.12 0.85−19.58 0.69−20.17 0.97−10.50 1.11−11.0 1.38−10.9 1.21−10.66 1.34−16.85 1.56−18.32 1.06−18.39 0.014−3.248 0.011−3.239 0.044−3.216 0.001−3.415 0.003−3.309 0.582−19.415 1 0.097−1.396 0.079−1.242 0.031−1.111 0.058−1.153

0.016−0.875 0.044−0.405 0.012−0.118 0.022−0.521 0.03−0.354 0.051−0.51 0.049−0.609 0.032−0.359 0.063−0.7355 0.0463−0.6972 0.0368−0.7012 0.029−0.533 0.06−0.499 0.05−0.441 0.02−0.247 0.0347−0.4627 0.0576−0.5724 0.0357−0.5483 0.0917−0.5103 0.1206−0.5897 0.0759−0.4898 0.0740−0.5790 0.0900−0.6094 0.0220−0.5926 0.03 0.0095−0.1618 0.0061−0.0807 0.0104−0.2085 0.0065−0.1189

39 42 36 8 42 44 42 40 47 48 57 30 33 34 51 47 41 41 64 62 57 69 66 79 1 35 33 53 41

3.42 3.30 5.41 1.27 2.21 1.34 1.31 3.31 1.18 1.15 6.20 17.50 1.37 1.74 3.05 1.01 2.57 2.01 5.95 7.11 2.39 11.24 7.00 2.51 0 2.89 5.50 3.24 3.24

14 2 39 42 2 2 40 40 44 47 44 1 1 1 43 41 41 41 45 45 45 45 45 46 48 12 12 12 12

based on the hidden-node parameters ai and bi, which are randomly generated, and (2) linear parameter solving by calculating the weights β. In the second step, the weights β are obtained by solving β = H′T

(3)

where ⎡ h(x ) ⎤ ⎡ h (x ) ⋯ h (x ) ⎤ L 1 1 ⎢ ⎥ ⎢ 1 1 ⎥ ⋮ ⋮ ⎥ H=⎢ ⋮ ⎥=⎢ ⋮ ⎢ ⎥ ⎢ ⎥ ⎣ h(xN )⎦ ⎣ h1(xN ) ⋯ hL(xN )⎦

and

Figure 2. An exemplary fragment assignment in this study.

⎡ tT ⎤ ⎡ t ⋯ t ⎤ 1m ⎢ 1 ⎥ ⎢ 11 ⎥ ⎢ ⎥ T= ⋮ =⎢⋮ ⋮ ⋮ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢⎣ tTN ⎥⎦ ⎣ tN1 ⋯ tNm ⎦

where βi is the output weight vector connecting the ith hidden node and the output nodes and h(x) is the nonlinear feature mapping with respect to the input x. In real applications, h(x) can be expressed in the following form: h(x) = G(a i , bi , x)

(4)

(5)

where H′ is the Moore−Penrose generalized inverse of matrix H and T is the target matrix. As shown in Figure 3, the ELM structure is composed of three layers, namely, the input layer, hidden layer, and output layer. Each layer is connected by a specific number of neurons or nodes. Information is passed through the weight of the link. In this work, the temperature (T), pressure (P), and numbers of fragments are the input parameters and the H2S solubility in ILs is the output parameter. f1 and f 2 are the functions of the hidden and output layers. There is no bias between the hidden layer and the output layer, and the weights as well as the biases

(2)

where G(ai, bi, x) is a nonlinear piecewise-continuous function, ai ∈ Rd is the weight vector connecting the ith hidden node and the input nodes, and bi ∈ R is the threshold of the ith hidden node. It should be noted that the hidden-node parameters ai and bi should be adjusted in conventional neural networks. However, in the ELM algorithm, Huang et al.53 rigorously proved that the ai and bi can be randomly generated according to any continuous probability distribution. Therefore, the ELM can be trained in two main steps: (1) random feature mapping D



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Figure 3. Network structure of the ELM model used in this study.

between the input layer and the hidden layer are randomly assigned. 2.4. Model Validation and Evaluation. To evaluate the performance of the ELM model, a series of statistical parameters were employed, including the coefficient of determination (R2), relative deviation (RD), average absolute relative deviation (AARD %), mean square error (MSE), and root-mean-square error (RMSE). The detailed mathematical definitions of the statistical parameters are listed as follows: N

2

R =

Figure 4. Solubilities of H2S in ILs with different cations at 313.15 K.

N

∑i =p1 (yi exp − ym̅ )2 − ∑i =p1 (yi cal − yi exp )2 N

∑i =p1 (yi exp − ym̅ )2

(6)

⎛ y cal ⎞ RD = 100% × ⎜⎜ iexp − 1.0⎟⎟ ⎝ yi ⎠

(7)

Np yi cal − yi exp 1 AARD = 100% × ∑ Np i = 1 yi exp

(8)

Np

MSE =

∑ (yi cal

− yi exp )2 /Np

i=1

Figure 5. Solubilities of H2S in ILs with different anions at 313.15 K.

(9)

Np

RMSE =

∑ (yi cal i=1

− yi exp )2 /Np

However, the results mentioned above are not always correct, as some authors1,2 reported that when the cation is [BMM]+, the anion has the reverse trend ([BF4]− > [PF6]−). Overall, the H2S solubility in ILs is complicated and does not only follow a simple linear rule. Therefore, a nonlinear model is needed to obtain quantitative results. 3.2. Results of the ELM Model. As mentioned above, a whole data set including 1282 data points was divided into two subsets, namely, a training set (including 1026 data points) and a test set (including 256 data points), which were used to build the model and verify the model, respectively. In order to build the model, the functions f1 and f 2 (as shown in Figure 3) must be confirmed. Here, the sigmoid activation function35 was employed as f1, and a linear function without bias of the output neuron was used as f 2. After the functions f1 and f 2 were confirmed, we only needed to optimize the neurons between the input layer and hidden layer as well as the weights between the hidden layer and output layer in a linear way because the weights and bias between the input and hidden layers had been randomly assigned. Therefore, 400 was determined as the best number of neurons of the hidden layer, and thus the best model was obtained. As shown in Figure 6, it is obvious that the results (predicted value vs experimental value) are close to each other, which

(10)

where Np is the number of data points in the entire data set, y is the H2S solubility in ILs, the superscripts “exp” and “cal” denote the experimental and calculated values, respectively, and ym̅ is the average of the experimental H2S solubility values.

3. RESULTS AND DISCUSSION 3.1. Qualitative Analysis of the Solubility of H2S in ILs. Like the solubility trend of the acidic gas CO2 in ILs, the solubility of H2S in ILs increases with decreasing temperature and increasing pressure. Compared with the anion, the cation has a relatively little effect on the solubility. If the anion is kept as [Tf2N]−, as shown in Figure 4, the ILs with longer alkyl chains can have higher solubility of H2S ([OMIM]+ > [HMIM]+ > [EMIM]+) compared with the ILs with shorter chains.40,43 This phenomenon can be explained by the fact that the ILs with longer alkyl chains will have larger free volumes and thus can not only strengthen the van der Waals interactions but also can accommodate more H2S molecules. As shown in Figure 5, when the ILs have the same cation ([HEMIM]+), greater fluorine content in the anion leads to higher H2S solubility in ILs ([BF4]− < [PF6]− < [TfO]− < [Tf2N]−).44,47 E



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Figure 8. Solubilities of H2S in [HMIM][Tf2N] from different references.

Figure 6. ELM-calculated vs experimental solubilities of H2S in ILs.

means that the performance of the ELM model is good. Relative deviations of the whole data set are depicted in Figure 7, and 81.3% of the relative deviations for the whole data set are

and [BMIM][OAc] should be treated carefully when using the ELM model established in this study. As for the remaining 25 ILs, the maximum deviation is only 7.11% for [EMIM][Pro], which indicates that the ELM model is suitable for these ILs. Figure 9 gives the sensitivities of the relative deviations of the investigated systems (1282 data points) by the ELM model versus (a) the H2S mole fraction, (b) the system pressure, and (c) the system temperature. As can be seen in Figure 9, large relative deviations of the 1282 data points belonging to the 27 ILs occurred at low pressure and low H2S solubility, while the role of the temperature is not as obvious as that of the abovementioned two factors. The statistical parameters for the training set, test set, and entire set are summarized in Table 2. As can be seen, the statistical parameters for the training set are R2 = 0.999, AARD = 3.71%, and RMSE = 0.0112, which means that the established model is reliable. The statistical parameters for the test set are R2 = 0.990, AARD = 5.78%, and RMSE = 0.0301, respectively, which indicates that the predictive performance is reasonable for the temperature rang (298.10 to 403.15 K) and pressure range (0.001 to 96.30 bar) used in this study. In addition, the required time to train and test a single ELM model having 400 neurons in this study was only 1.3865 s on an Intel 2.93 GHz desktop computer with 2 GB of RAM. 3.3. Comparison of the ELM Model and Other Models. A comparison of different models, including the ELM algorithm, COSMO-RS (ADF combi2005 and ADF combi1998 versions), EOS-based models (PR and SRK), and other intelligence algorithms (ANN, GEP, and LSSVM), is summarized in Table 3. It is obvious that because the intelligence algorithms (ELM, ANN, and LSSVM) have very low AARDs compared with the EOS-based and COSMO-RS methods, the results of intelligence algorithms are more accurate than the EOS and COSMO-RS results. Although the ELM algorithm did not use the same input parameters as the ANN, GEP, and LSSVM algorithms and hence may not be directly comparable, one can still note that the ELM algorithm has a relatively low AARD. The AARD is only 1.26% with the same data set (including 465 data points) as used by Ahmadi et al.18,19,21 Therefore, the ELM model is suitable for predicting the solubility of H2S in ILs. However, each method has its own advantages and drawbacks. Although the ELM model has high accuracy for predicting the solubility of H2S in ILs, its

Figure 7. Percentages of H2S solubility values in different deviation ranges for the ELM model: 39.9% of the H2S solubilities in ILs are estimated within 0−1% (relative deviation range in %), 41.4% within 1−5%, 9.2% within 5−10%, 4.2% within 10−15%, 2.0% within 15− 20%, and 3.3% over 20%.

within ±5%. The maximum deviation is 158.5%, which belongs to [BMIM][OAc]. As shown in Table 1, the AARD for [BMIM][OAc] is 11.24% for 69 data points, which has the second largest deviation. The reason maybe that the absorption mechanism of [BMIM][OAc] is chemical absorption. However, for most of the other kinds of ILs, the absorption mechanism is physical absorption. The AARD of [HMIM][Tf2N], which is the IL with the maximum deviation among all of the ILs, is 17.50% for ref 1 and 6.20% for ref 44. The reason may be that experimental errors exist between the two different references published by the same group.1,44 For example, as shown in Figure 8, the experimental data for [HMIM][Tf2N] from ref 1 (large predictive deviations) obviously show lower H2S solubility at pressures below 8 bar and higher H2S solubility at pressures above 8 bar compared with the data from ref 44. Therefore, we can reasonably assume that the experimental data for [HMIM][Tf2N] in ref 1 are perhaps not so accurate and thus should be treated carefully. If [HMIM][Tf2N] is not considered in this study, the AARD of the rest of the data set is only 1.26% (when using the same data set of refs 18, 19, and 21), which is extraordinarily good. Therefore, [HMIM][Tf2N] F



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Table 3. Comparison of Different Models for the Solubility of H2S in ILs method ANN PR EOSb SRK EOSb PR EOSc SRK EOSc LSSVM GEP PR EOSb PR EOSc empirical model ANN FC-ELMd COSMO-RS ADF 2005 ADF 1998 FC-ELM FC-ELM

Npa

NILa

AARD (%)

ref(s)

465 465 465 465 465 465 465 664 664 664 664 465

11 11 11 11 11 11 11 14 14 14 14 11

4.58 38.95 36.43 4.90 4.87 2.28 4.38 196.76 8.35 5.03 2.07 1.26

18 19, 21 19, 21 19, 21 19, 21 19 21 20 20 20 20 this work

722 722 722 1282

15e 15e 16 27

38.64 38.14 2.33 4.12

17 17 this work this work

a Np is the number of parameters, and NIL is the number of ILs. bThe interaction parameters (ki,j) were not considered. cThe ki,j were considered. dResults calculated by the ELM model established on the basis of 465 data points. eThe number should be 16.

fundamental physical basis is not as rigorous as those of the EOS and COSMO-RS models. However, for some more strongly nonlinear and complex systems, the ELM method has some excellent advantages, such as high speed, simplicity of use, and good generalization performance, and thus is a suitable choice.

4. CONCLUSIONS In this present work, a comprehensive database on the solubility of H2S in ILs that includes 1334 pieces of data covering the period from 2007 to 2016 was established. On the basis of the database, a new model was developed using the ELM intelligence algorithm. The established model needs only the numbers of fragments as the input parameters, which are easy to obtain compared with those in previous work (using the critical properties and acentric factor as the input parameters). The R2, AARD, and RMSE values for the whole data set are 0.997, 4.12%, and 0.0168, respectively. This indicates that the established ELM model can be satisfactorily used to predict the solubility of H2S in ILs over wide ranges of temperature (298.10 to 403.15 K) and pressure (0.001 to 96.30 bar). Finally, the ELM model has been compared with other previous models, and the ELM model has a lower AARD than the previous work. Meanwhile, the time required for this study was only 1.3865 s on an Intel 2.93 GHz desktop computer with 2 GB of RAM. Therefore, considering the series of advantages of the ELM algorithm (high speed, good generalization ability, and so on), further research could employ it to establish new models for predicting solubilities of other gases in ILs and other pure or mixture properties of IL-containing systems.

Figure 9. Relative deviations (RDs) of the ELM-calculated values for the investigated systems from the experimental values versus (a) H2S mole fraction, (b) the system pressure, and (c) the system temperature (including 1282 data pints).

Table 2. Statistical Parameters for the ELM Model data set

no. of data points

R2

AARD (%)

MSE

RMSE

training set test set total set

1026 256 1282

0.999 0.990 0.997

3.71 5.78 4.12

1.25 × 10−4 9.08 × 10−4 2.81 × 10−4

0.0112 0.0301 0.0168

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.6b00449. The mat file (MATLAB R2009 software file) for the ELM G



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model and the procedure to apply the program are available free of charge from the authors upon request. The database, a list of references, and results of the ELM model (XLSX)

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AUTHOR INFORMATION

Corresponding Authors

*Tel./Fax: +86 01062558174. E-mail: [email protected]. *E-mail: [email protected]. Funding

This work was financially supported by the National Basic Research Program of China (2013CB733506), the National Natural Science Fund for Distinguished Young Scholars (21425625), the Key Program of Beijing Municipal Natural Science Foundation (2141003), and the National Natural Science Foundation of China (21376242, 21436010, 51574215). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The ELM program is supported by the Binguang Huang team (Nanyang Technological University, Singapore).

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REFERENCES

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Hydrogen Sulfide Solubility in Ionic Liquids (ILs ... - ACS Publications

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