Using Artificial Neural Network and Ideal Adsorbed Solution Theory for

Article pubs.acs.org/IECR

Cite This: Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Using Artificial Neural Network and Ideal Adsorbed Solution Theory for Predicting the CO2/CH4 Selectivities of Metal−Organic Frameworks: A Comparative Study Kourosh Esfandiari, Ali Asghar Ghoreyshi,* and Mohsen Jahanshahi Chemical Engineering Department, Babol Noshirvani University of Technology, Shariati Street, Babol, Iran ABSTRACT: Predicting the adsorptive separations of gaseous mixtures by metal−organic frameworks (MOFs) is a difficult task, because it is a complex function of the textural properties of the MOF, its surface chemistry, and the operating conditions. In this research, the separation behavior of multicomponent mixtures of CO2/CH4 in MOFs was predicted by means of artificial neural networks (ANNs). To validate the as-designed ANN model, a well-known MOF, CuBTC or HKUST-1, was synthesized in our laboratory, and the selectivity of CO2/CH4 mixtures was determined using ideal adsorbed solution theory (IAST) and the extended Langmuir model (ELM). On the basis of the obtained results, it was demonstrated that ANN modeling could be a good candidate for predicting the separation behavior of CO2/CH4 mixtures in MOFs in the absence of data from laboratory experiments. Zr, Mg, Ni, and Fe 11 ) connected to organic linkers (ligands).12−14 High specific surface areas, high pore volumes, and design simplicity make MOFs promising alternatives as porous solids that are applicable to adsorptive separation processes.15 In addition, high selectivity16 and milder regeneration conditions17 are important advantages of MOFs over traditional adsorbents such as zeolites and ACs. MIL-53 (Al), MIL-100 (Cr), Mg-MOF-74, MOF-5, and CuBTC are among the most popular MOFs for adsorptive CO2/CH4 separations.1,15,18−23 Molecular sieving, gas−solid interactions, and the combined effects of the two are the main phenomena affecting the selective adsorption of CO2 over CH4 on pristine MOFs.24 Generally, there are two main experimental procedures for evaluating the selectivity of gaseous mixtures on porous media: calculating the ideal selectivity by means of single-gas adsorption isotherms [based on ideal adsorbed solution theory (IAST)25] and evaluating the separation factor using multicomponent breakthrough experiments. Although numerous studies have focused on the use of these techniques for CO2/ CH4 mixtures in MOFs,16,21,24,26−28 such investigations require a great deal of experimental data that must be obtained using specific and expensive equipment. On the other hand, simulation methods, such as molecular dynamics (MD) or grand canonical Monte Carlo (GCMC) simulations, are highly complex and require precise information about the nature of

1. INTRODUCTION Carbon dioxide and methane are two major components of natural gas, biogas (25−45% of CO2), and landfill gases (35− 50% of CO2).1 The presence of CO2 in natural gas could result in a loss of heating value and also pipeline corrosion, and therefore, removal of CO2 typically to levels of less than 2−3% is critical for CH4 applications.2 Moreover, significant amounts of CO2 released to the atmosphere as a result of the tremendous consumption of fossil fuels has created substantial environmental problems such as global warming and, hence, CO2 is known to be responsible for approximately 60% of the global warming in recent years.3 For about 60 years, the selective absorption/stripping of CO2 by means of different amines4,5 or glycol derivatives6 was the most commonly used method in natural gas industries. Despite their frequent application in high capacity, these methods suffer from numerous shortcomings such as high corrosive behavior; amine degradation in the presence of SO2, NO2, HCl, HF, and O2; and also high energy demands in the solvent recovery step.5,7,8 In contrast, the adsorptive separation of gaseous streams is known to be an economical alternative with relatively low energy consumption, especially for smaller-volume applications.9 Zeolites and activated carbons (ACs) are two well-established porous solids that are employed in cyclic processes with high efficiency. However, zeolites are difficult to regenerate, and ACs have low selectivities, which could result in high investment costs for relatively poor separations.10 A newly evolved class of crystalline hybrid materials is metal−organic frameworks (MOFs) or porous coordination polymers (PCPs), which are made of secondary building units (SBUs) consisting of metal ions/clusters (such as Zn, Cu, Cr, © XXXX American Chemical Society

Received: July 21, 2017 Revised: October 23, 2017 Accepted: November 16, 2017

A

DOI: 10.1021/acs.iecr.7b03008 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research

Figure 1. Typical feed-forward network architecture.

Table 1. Experimental Data Associated with 12 Selected MOFs set no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 a

MOF

SBET (m2/g)

pore volume (m3/g)

CO2 heat of adsorption (kJ/mol)

CH4 heat of adsorption (kJ/mol)

open metal sitesa

adsorption temperature (K)

adsorption pressure (bar)

50:50 CO2/CH4 separation factor

ref

MIL-53 (Cr) MIL-53 (Al) MIL-53 (Al) MIL-101 (Cr) MIL-101 (Cr) MIL-101 (Cr) CuBTC CuBTC CuBTC MOF-5 MOF-5 CPO-27-Mg CPO-27-Mg CPO-27-Mg CPO-27-Ni CPO-27-Ni CPO-27-Ni CPO-27-Co CPO-27-Co CPO-27-Co CPO-27-Zn CPO-27-Zn CPO-27-Zn CPO-27-Zn UiO-66 (Zr) Cu(BDC−OH) Cu(BDC−OH) Cu-MOF Cu-MOF Cu-MOF

1175 1235 1300 2471 2471 2471 1270 1270 1270 3800 3800 1174 1415 1415 1266 1266 1266 1093 1093 1093 885 806 806 806 1433 397 397 105 105 105

0.49 0.42 0.42 1.2 1.2 1.2 0.71 0.71 0.71 1.55 1.55 0.65 0.62 0.62 0.58 0.58 0.58 0.5 0.5 0.5 0.41 0.38 0.38 0.38 0.63 0.214 0.214 0.043 0.043 0.043

32 26.4 26.4 38.81 38.81 38.81 28.1 28.1 28.1 34 34 42.8 47 47 41 41 41 37 37 37 31 31 31 31 26.2 26.2 26.2 28.3 28.3 28.3

18 18.3 18.3 30.07 30.07 30.07 16.6 16.6 16.6 12.2 12.2 24.1 18.5 18.5 19.96 19.96 19.96 19.6 19.6 19.6 18.3 18.3 18.3 18.3 16.4 18.5 18.5 24.1 24.1 24.1

0 0 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 0

303 303 303 288 303 313 298 298 303 298 300 298 300 313 303 303 303 303 303 303 300 303 303 303 273 273 296 278 298 318

1 1 1 1 1 1 1 10 1 1 1 1 1 6 1 5 10 1 5 10 1 1 5 10 1 1 1 1 1 1

2.89 3.80 7 6.55 5.69 5.54 4 8.5 5 2 1.94 5 11.76 67.35 15 19 40 12 16 19 5.92 9 10 22 2.2 8.61 6.65 3.3 3.1 2.6

41 42 15 43 43 43 44 45 46 44 47 1 47 27 16 16 16 16 16 16 16 16 16 16 48 49 49 50 50 50

Yes = 1, no = 0.

porous solids, especially MOFs. Qu et al.35 examined a model that combined a back-propagation neural network (BPNN) with a genetic algorithm to investigate the CO2 adsorption capacity of Ni/DOBDC (DOBDC4− = 2,5-dioxido-1,4benzenedicarboxylate). They demonstrated that the proposed model results in more accurate predictions compared to

the porous medium as well as the gas−solid and gas−gas interactions. Although the effectiveness of computational intelligence such as neural networks in engineering science has been demonstrated,22,29−34 few studies have been reported about the use of ANNs to evaluate the gas−solid interactions in B


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Industrial & Engineering Chemistry Research theoretical techniques. Recently, Yıldız and Uzun36 demonstrated the potential of ANNs for predicting hydrogen adsorption capacities in different MOFs. In the present research, ANN modeling is used to predict the CO2/CH4 separation factors in different MOFs. For this purpose, the Brunauer−Emmett−Teller (BET) surface area, pore volume, adsorption thermodynamic factors such as the CO2 and CH4 heats of adsorption, the presence (or absence) of cationic unsaturated sites, and adsorption operating conditions such as the adsorption temperature and pressure were chosen as inputs, and the CO2/CH4 separation factors of different MOFs corresponding to the input data were considered as outputs. A multilayer perceptron (MLP) network consisting of three layers using back-propagation (BP) algorithm was suggested, and the optimum architecture was chosen by means of trial and error. In addition, a sensitivity analysis was carried out to evaluate the relative importance of different input variables while predicting the CO2/CH4 separation factor using ANN modeling. Finally, to validate the as-designed ANN model, a copperbased well-known MOF, CuBTC or HKUST-1, was synthesized, and single-component gas adsorption measurements were carried out to determine the CO2/CH4 selectivity of the as-designed MOF by means of ideal adsorbed solution theory (IAST) and the extended Langmuir model (ELM).

and pressure (Pads) were taken into account as input variables because of their influence on the extent of adsorption, particularly in gaseous mixtures. On the other hand, the separation factor of CO2/CH4 mixtures was chosen as the output data. Overall, 30 input−output data sets were collected (see Table 1), and an MLP neural network equipped with the Levenberg−Marquardt (LM) training technique was used as the modeling tool. The LM technique, which is a modified version of the classic Newton algorithm, is faster than other optimization methods and less easily trapped in local minima.39,40 To ensure good generalization and to avoid overtraining of the model, a cross-validation technique is typically performed during ANN modeling. The purpose of cross-validation is to divide the data set into two subsets, one for training and the other one for the evaluation of model performance. Conventionally, the two most commonly used types of cross-validation are (a) hold-out cross-validation, wherein the data set is separated into three subsets of training, validation, and testing data, and (b) k-fold cross-validation, wherein the data set is divided into k parts of the same size, with two subsets of training and validation in each part.51 In this research, the holdout technique was employed owing to its efficiency and ease of use, and hence, 70% of the main data set was chosen as training data, 15% was selected for cross-validation, and the rest was used for testing. It should be noted that splitting the data set was done randomly using the ANN toolbox of Matlab. During network design, two different architectures are mostly considered: single hidden layer and multiple hidden layers (i.e., two hidden layers). Generally, employing more than two hidden layers is somewhat unnecessary for most ordinary problems.52,53 In terms of transfer functions, “tansig” and “purelin” were chosen as the transfer functions of the hidden layer(s) and output layer, respectively. Moreover, network training parameters such as the goal value of the error function, the learning rate of the training algorithm, and the maximum allowed number of validation checks before the training stops (a validation check stops the training after reaching a predetermined number of consecutive increases in validation error) were also adjusted prior to the beginning of the training procedure. To determine the optimum architecture that results in the best prediction performance of the network, the number of neurons in each hidden layer was changed by means of trial and error. For all investigated architectures with a specific number of neurons in each hidden layer, errors in the training, validation, and testing steps (i.e., the difference between the target and output data) and also the overall error for all data sets were evaluated. Finally, the architecture with minimum errors was chosen as the optimum architecture. The procedure for selecting the best network performance is described in detail in section 4.1.

2. DESCRIPTION OF THE ANN MODEL An artificial neural network (ANN) consists of small intelligent computational units called “neurons” that are used to model highly nonlinear complex systems by means of available input− output data sets.37 One well-established class of ANNs is feedforward networks (FFNs) in which the input signal propagates through the network in the forward direction and does not form a cycle. To date, MLPs wherein neurons interconnect in a feed-forward manner are known to provide an appropriate alternative to conventional analytical approaches.30,37,38 MLPs typically include an input layer (consisting of input data), one or more hidden layers of neurons, and an output layer (consisting of output data). Figure 1 depicts a typical MLP neural network with one hidden layer, where x1−xn are the input parameters; y is the network output; and w and b represent the network weights and biases, respectively. In general, the number of neurons within the hidden layer(s) is adjusted by means of trial and error to achieve the best prediction performance of the network. Meanwhile, the number of output layer(s) is always equal to the number of output data. In this research, to predict the separation factors of CO2/ CH4 mixtures (50:50) in an unknown MOF, the Neural Network Toolbox of Matlab R2014a was employed along with experimental data associated with 12 different MOFs. Input parameters were chosen as a combination of textural properties of the adsorbent and adsorption operating conditions. Among the textural properties, BET surface area, pore volume, and adsorbent surface chemistry [i.e., the presence (or absence) of cationic unsaturated sites (CUSs)] were chosen because of their importance in determining the adsorptive behavior of MOFs. Moreover, the heats of adsorption of the gases (ΔHads,CO2 and ΔHads,CH4) were chosen because they represent quantitative thermodynamic criteria for demonstrating the tendency of each adsorbate to be adsorbed on the surface of an MOF in a competitive state. On the other hand, in terms of the adsorption operating conditions, adsorption temperature (Tads)

3. EXPERIMENTAL SECTION To validate the ANN model, CuBTC was synthesized in our laboratory using a solvothermal technique at autogenous pressure. Afterward, the as-synthesized CuBTC was characterized, and discrete single-component adsorption measurements (CO2 and CH4) were carried out by means of a deadend apparatus that was well-established in previous publications.54,55 Subsequently, to evaluate the CO2/CH4 selectivity on CuBTC, the IAST and ELM methods were employed, C


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in the literature.56,58 The presence of sharp peaks in the XRD pattern is an indication of the good degree of crystallization in the as-synthesized CuBTC. In addition, the crystal size of the CuBTC sample was determined from the XRD data by means of the well-known Debye−Scherrer equation59

wherein single-component adsorption isotherms were used to determine the selectivities of gaseous mixtures in an ideal state.25 It is worth mentioning that experimental validation techniques such as breakthrough experiments could not be employed in this study because of semicontinues procedure of single-gas adsorption measurements taken into account in this research. 3.1. Chemicals. Copper(II) nitrate trihydrate [Cu(NO3)2· 3H2O], benzene-1,3,5-tricarboxylic acid (H3BTC), and ethanol were purchased from Merck (Darmstadt, Germany) and were used as received without further purification. The purities of carbon dioxide and methane were 99.99% and 99.95%, respectively. 3.2. Material Synthesis and Characterization. CuBTC was synthesized according to the procedure reported elsewhere.56 Copper(II) nitrate trihydrate (1.75 g, 7.24 mmol) and H3BTC (0.84 g, 4 mmol) were dissolved in pure ethanol (48 mL) and stirred for 30 min to form a homogeneous solution that was then transferred into a Teflon-lined autoclave. The autoclave was capped tightly and placed in a temperatureprogrammable oven, with which it was heated from room temperature to 120 °C (1.5 °C/min) under autogenous pressure and kept in this temperature for 14 h. After the reaction time was completed, the autoclave was allowed to cool to room temperature, and the precipitated crystals of CuBTC were separated by three cycles of centrifugation (6000 rpm for 10 min) followed by washing with ethanol each time. Finally, the crystals were dried at 100 °C overnight. Nitrogen adsorption−desorption isotherms at 77 K (Belsorp Mini II, BEL Japan, Inc., Toyonaka, Japan) are presented in Figure 2 and reveal the microporous structure of the

τ=

Kλ β cos θ

(1)

where τ is the mean crystal size (nm), K is a dimensionless shape factor that is typically considered equal to 0.89, λ is the X-ray wavelength (0.154 nm in the case of Cu Kα1 radiation), β is the full width at half-maximum (fwhm) intensity of the peak in radians, and θ is the Bragg angle of the diffraction peak. Table 2 summarizes the obtained data associated with the mean crystal size determined by eq 1. The thermogravimetric analysis (Rheometric Scientific STA 1500, Piscataway, NJ) results are shown in Figure 4. As can be seen, there are two steps of weight loss during the increase in temperature to 400 °C. The initial loss (from about 70 to 120 °C) could be due to the removal of solvent (ethanol) or gaseous guest molecules (such as moisture) physically adsorbed on the surface of CuBTC. After this step, the sample weight remains approximately constant to about 300 °C, which suggests acceptable thermal stability of the CuBTC crystals. Finally, the second weight loss occurs at about 300 °C and corresponds to the decomposition and collapse of the CuBTC structure. This finding is in agreement with the observations of Yang et al.,60 who used ethanol solvent in the synthesis of CuBTC. Furthermore, the octahedral structure of the prepared CuBTC can be clearly seen in the field-emission scanning electron microscopy (FESEM) image in Figure 5 (Tescan Mira3 FEG, Kohoutovice, Czech Republic).

4. RESULTS AND DISCUSSION 4.1. Optimum Network Architecture. As mentioned before, two types of architectures were investigated in this research. In the architecture with one hidden layer, the number of neurons varied in the range of 1−20, whereas for the architecture with two hidden layers, the number of neurons ranged from 1 to 10 for each hidden layer. The performance of each architecture was determined using the root-mean-square error (RMSE), mean absolute error (MAE), mean bias error (MBE), and regression coefficient (r) of the training, validation, and testing steps, as well as the regression coefficient associated with all steps. RMSE, MAE, and MBE were calculated according to the equations Figure 2. Nitrogen adsorption−desorption isotherm at 77 K. Inset: MP plot of synthesized CuBTC.

1 N

RMSE =

synthesized CuBTC in accordance with IUPAC type I behavior.57 In addition, the micropore (MP) plot of the CuBTC sample (Figure 2, inset) reveals that the pore sizes were distributed below 1 nm, which supports the microporous structure of the as-synthesized sample. The textural properties of CuBTC sample were determined by means of N2 adsorption at 77 K. The Brunauer−Emmett−Teller (BET) specific surface area (SSA), the pore volume, and the mean pore diameter of the sample were determined to be equal to 1306 m2/g, 0.6556 cm3/g, and 1.6805 nm, respectively. A powder X-ray diffraction pattern (PANalytical X’Pert Pro, Almelo, The Netherlands) of the as-synthesized CuBTC is shown in Figure 3 and is in good agreement with that reported

MAE =

MBE =

1 N 1 N

N

∑ (targetsi − outputsi)2 i=1

(2)

N

∑ |targetsi − outputsi| i=1

(3)

N

∑ (targetsi − outputsi) i=1

(4)

To determine the optimum architecture, a trial-and-error procedure was used, and the architecture with the lowest errors (RMSE, MAE, and MBE) along with the highest overall regression coefficient (for all data) was chosen as the optimum architecture (bold data in Table 3). As can be seen, this D


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Figure 3. Powder X-ray diffraction of synthesized CuBTC.

respectively. Figure 6 shows a schematic diagram of the optimum architecture, where x1−x7 are the input parameters and w and b are the network weights and biases, respectively, for each layer. It is also clear that the transfer function of hidden layers is “tansig”, whereas the transfer function of the output layer is “purelin”. Furthermore, the weights and biases of the optimum architecture corresponding to each layer (first hidden layer, second hidden layer, and output layer) are presented in Table 4. Figure 7 presents the linear regression between the target and output data for the network training, validation, and testing steps (Figure 7a−c), as well as for all data (Figure 7d). The higher the regression coefficient in each step (rmax = 1), the more precise the network performance in that step and vice versa. As one can see, the regression coefficients of the training, validation, and testing steps are almost unity (0.99752, 0.98295, and 0.99586, respectively), which suggests good performance of the designed network. In other words, the network training

Table 2. Crystal Size of As-Synthesized CuBTC Sample on the Basis of XRD Data peak position (deg, 2θ) 6.859 9.641 11.773 13.567 14.789 16.609 17.623 19.703 26.125 29.505 35.407 39.307 mean crystal size

fwhm (deg)

crystal size (nm)

0.200 0.150 0.167 0.182 0.140 0.18 0.172 0.199 0.203 0.210 0.300 0.300

39.34 52.54 47.27 43.45 56.56 44.09 46.20 40.05 39.71 38.67 27.48 27.80 41.93

architecture comprises two hidden layers, where the first and second hidden layers consist of seven and four neurons,

Figure 4. Thermogravimetric analysis (TGA) of synthesized CuBTC. E


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is about 6.368, and approximately 10% of the results have errors higher than 4, which demonstrates the good performance of the as-designed network. 4.2. Sensitivity Analysis. A sensitivity analysis was carried out to assess the relative importance of different input variables (Table 1) in the prediction of the CO2/CH4 separation factor by means of ANN modeling. Gevrey et al.61 reviewed and compared seven different sensitivity analysis methods (namely, the PaD, weights, perturb, profile, classical stepwise, improved stepwise a, and improved stepwise b methods), to determine the relative contributions of the input factors to the variations in the ANN output. They demonstrated that the PaD method is the most successful procedure for giving reliable results, whereas the other methods suffer from a lack of stability, as well as poor and unclear contributions.61 Therefore, the PaD method, which is based on the calculation of the partial derivatives of the output with respect to the input variables, was used in this research. To clarify the calculation procedure of the PaD method, a comprehensive schematic diagram of the ANN architecture with two hidden layers is shown in Figure 11 with all input/ output variables of each layer. In this figure, x, w, S, and N are the input variables, weights, inputs to transfer functions, and outputs of transfer functions, respectively. It should be noted that the output of the last transfer function (Nl) is equal to the CO2/CH4 separation factor calculated by the ANN model. The partial derivatives of the ANN output with respect to the input can be written as follows

Figure 5. FESEM image of as-synthesized CuBTC.

procedure was appropriate, as the network can predict unknown data sets accurately. Figure 8 compares the values of the target and output data corresponding to each step of network design. It can be clearly seen that, for all three steps of network design, the value of the targets and outputs are almost the same. The errors between the target and output values for each step of network design are presented in Figure 9. In addition, Figure 10 shows a histogram of errors for designing steps that consists of a “zero error” line. As can be seen, the maximum error of the prediction procedure

⎛ ∂Nl ⎞ ⎜ ⎟= ⎝ ∂xi ⎠

γ

m

∑ ∑ [wk ,l(1 − Nk 2)wj ,k(1 − Nj 2)wi ,j] (5)

k=1 j=1

Table 3. Network Architectures and Errors Associated with Each Architecture error type

regression coefficient

model

network architecture

RMSE

MAE

MBE

training

validation

testing

all data

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

1−1 3−1 5−1 7−1 10−1 13−1 15−1 17−1 20−1 1−1−1 5−1−1 10−1−1 1−2−1 5−2−1 10−2−1 1−4−1 5−4−1 7−4−1 10−4−1 1−7−1 5−7−1 10−7−1 1−10−1 5−10−1 10−10−1

11.5392 9.5767 2.4774 7.0549 7.7773 12.3872 12.3925 5.1699 15.1866 2.5225 9.072 6.2398 7.6845 5.276 5.1757 2.5904 2.9327 1.2659 4.3826 6.0995 3.3745 4.9115 9.8372 6.1509 4.9973

5.7216 3.5835 1.7381 6.0619 3.7547 10.6104 8.8897 2.433 10.5396 1.7874 2.9338 3.8675 4.355 3.5279 2.0447 1.5762 1.4758 1.1016 3.1748 3.1164 1.7091 3.5941 4.1061 3.943 1.7344

3.9159 2.0984 0.4189 −1.7586 0.8725 2.2828 1.5221 −1.9286 8.8551 −0.3045 2.1719 1.2468 −2.834 −0.413 0.4404 −0.6258 0.214 -0.0312 0.9596 0.1805 0.3088 −1.4029 −2.3768 −0.4325 −0.8351

0.58837 0.98464 0.99136 0.92739 0.98438 0.79457 0.88477 1 0.57519 0.9948 0.99354 0.97271 0.89325 0.95943 1 0.99768 0.99967 0.99752 0.99104 0.96755 0.99547 0.95751 0.9904 0.92766 1

0.75842 0.96748 −0.03566 0.92132 0.91498 0.94404 0.4006 0.86487 0.73607 0.98028 0.87245 0.59673 0.82391 0.93421 0.99429 0.93526 0.92505 0.98295 0.93785 0.86151 0.987 0.97927 0.88164 0.96982 0.79311

0.98017 0.70406 0.93129 0.62414 90.325 0.70643 0.79605 0.52907 0.66097 0.97194 0.94116 0.86106 0.69517 0.91408 0.87885 0.86421 0.84758 0.99586 0.89617 0.87239 0.6812 0.58691 0.63888 0.54632 0.91418

0.59806 0.7452 0.98243 0.91278 0.816 0.8018 0.79165 0.93674 0.5669 0.98249 0.8389 0.92643 0.88887 0.92012 0.92551 0.98198 0.97524 0.99286 0.94887 0.89279 0.97037 0.93304 0.76812 0.89086 0.93915

F


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Figure 6. Schematic diagram of the optimum MLP network with two hidden layers consist of seven and four neurons in the two layers.

where m (the number of neurons in the first hidden layer) and γ (the number of neurons in the second hidden layer) are equal to 7 and 4, respectively, in accordance with the optimum architecture. The relative contribution of each input variable was calculated from the sum of the squared partial derivatives (SSDi) obtained per input variable ⎛ ∂Nl ⎞ 2 SSDi = ∑ ⎜ ⎟ ∂xi ⎠ η=1 ⎝ η

amounts of CO2 and CH4 adsorbed on CuBTC were measured. Furthermore, the Langmuir isotherm ⎛ bP ⎞ ⎟ q = qmax ⎜ ⎝ 1 + bP ⎠

was fitted to the experimental adsorption data sets using the curve-fitting tool of Matlab (cftool). Figure 13 presents the experimental (dots) and calculated (solid lines) CO2 and CH4 adsorption isotherms of CuBTC. Table 5 also reports the fitting parameters of the Langmuir isotherm (eq 8) associated with CO2 and CH4 adsorption. In addition, the isosteric heats of adsorption (Qst) of CO2 and CH4 were calculated to be 38.63 and 31.71 kJ/kg, respectively. 5.2. CO2/CH4 Selectivity (IAST Method). A well-known method for determining the selectivity of a gas mixture is ideal adsorbed solution theory (IAST), developed by Myers and Prausnitz.25 The theory is based on the adsorption isotherms of single-component gases to find the selectivity of their mixtures. For the CO2/CH4 mixture, IAST has been employed by several researchers to determine the selectivities of mixtures with different compositions.26,62−65 While exploring IAST, phase equilibrium similar to what is written as Raoult’s law (in vapor/ liquid equilibrium) can be used as follows

Z

(6)

where η is the index of the data sets and Z is the number of data sets (for our study, Z = 30). Finally, the percentage contribution of each input variable is given by contribution of i th variable (%) =

SSDi n ∑i = 1 SSDi

(8)

× 100 (7)

Figure 12 presents the percentage contribution of each variable to the obtained results of the CO2/CH4 separation factor. As can be seen, pore volume, a textural characteristic, has the most significant role in predicting the CO2/CH4 separation factor by means of ANN modeling, followed by CUS, an indicator of surface chemistry, and the CO2 heat of adsorption, a thermodynamic property. Operating conditions such as adsorption temperature and pressure have minimal effects on the model prediction performance. This fact can be attributed to the narrow range of these variables in the collected input data. Finally, it is worth mentioning that, although the obtained result of this analysis is somewhat exclusive to the data sets employed for ANN modeling in this research, this could be an initial estimation for future research into the ANN modeling of CO2/CH4 separations with MOFs.

Pyi = Pi = xiPi0(π ),

i = 1, 2, 3, ..., N

(9)

where yi and xi are the mole fractions of component i in the gas phase and adsorbed phase, respectively, and P0i (π) is the pressure of component i at the same spreading pressure as that of the mixture. The spreading pressure (π), which is the negative of the surface potential, is given by

5. VALIDATION OF THE AS-DESIGNED ANN MODEL 5.1. CO2 and CH4 Adsorption Measurements. In this research, an experimental apparatus that was previously welldocumented54,55 was employed for single-component gas adsorption measurements. Prior to each adsorption experiment, CuBTC was activated by being heated at 150 °C overnight. (According to TGA, this elevated temperature does not damage the structure of CuBTC.) In the experimental procedure, the

π=

R gT

∫0

A R gT ... = A

P10(π )

q1 P1

∫0

PN0 (π )

dP1 = qN PN

R gT

dPN

A

∫0

P20(π )

q2 P2

dP2 =

(10)

where A is the specific surface area of the adsorbent (m2/kg), Rg is the gas constant (J/mol·K), T is the temperature (K), and q is the amount adsorbed (mmol/g) at a total pressure of P G


0.6327 −1.0696 −1.3642 −0.7500 −0.1494 1.1719 0.0233

−0.3513 −0.0702 −0.6307 2.0760 −0.1285 0.6717 1.8844

0.2494 0.7051 −0.0024 −1.2490 0.4949 0.0092 −1.2480

−0.6210 −0.8277 −1.0014 −0.8220 −0.7753 −0.9245 −0.2194

−0.1961 0.6176 −0.6698 1.2409 −0.7541 1.7256 1.3839

0.8054 0.9373 0.3967 −1.5893 0.1747 −0.0651 −2.9301

0.0372 −0.0434 0.9832 −0.5752

wij

wjk

wkl

3

2

1

weight

0.8563 1.0447 0.6922 0.5153 0.3210 0.8269 −0.9959

−0.2558 −0.4144 2.3594 1.0270 0.0893 0.6576 −0.8139

4

neuron no.

0.3806 1.4395 −1.1559 1.3473 0.3762 −0.7404 −0.4367

5 −0.8344 0.4367 −0.8516 0.3001 0.5060 −0.1494 −1.1852

6

Table 4. Weights and Biases for Each Layer of the Optimum Architecture 7

bias

1

Output Layer bl 0.5518

First Hidden Layer −1.3224 bj 3.1332 −2.5380 0.9988 −0.2558 −0.2808 1.2437 0.9249 Second Hidden Layer bk −2.2311 0.9354

−1.0053

2

−1.5588

0.4690

3

1.7837

−0.3739

4

neuron no.

−1.7615

5 −3.0125

6

−2.1294

7

Industrial & Engineering Chemistry Research Article

H


Article


As revealed before, the adsorption behaviors of pure CO2 and CH4 on CuBTC can be fitted with the Langmuir isotherm (eq 8). Therefore, by combining the Langmuir model with IAST (eqs 8 and 11), z can be determined and solved analytically to give the equation zi = qmax, i ln[1 + biPi0(π )]

(12)

Because the reduced spreading pressure of each component should be equal at the equilibrium state, one can write z1 = z 2 (13) where subscripts 1 and 2 denote CO2 and CH4, respectively. By combining eqs 9, 12, and 13, we have ⎛ ⎛ bCH4PyCH ⎞ bCO2PyCO ⎞ 4 2 ⎟⎟ = 0 ⎟⎟ − q qmax,CO ln⎜⎜1 + ln⎜⎜1 + max,CH 2 4 x x ⎠ ⎝ CO2 CH4 ⎝ ⎠ (14)

where (qmax,CO2, bCO2) and (qmax,CH4, bCH4) are the Langmuir fitting parameters of the adsorption equilibria of pure CO2 and oure CH4, respectively. The unknown x in eq 14 can be determined by solving this equation for fixed known P and y. Finally, the selectivity of CO2 over CH4 (SCO2/CH4) can be calculated using the equation xCO2 yCH4 SCO2 /CH4 = xCH4 yCO (15)

Figure 7. Linear regression diagrams for all steps of the training procedure.

2

In this article, the IAST method was used to predict the selectivity of a 50:50 CO2/CH4 mixture at 25 °C. Figure 14 presents the CO2/CH4 selectivity as a function of adsorption pressure, as predicted by the IAST method. As can be seen, the selectivity of CO2/CH4 decreases with increasing adsorption pressure, which is in good agreement with previous studies using CuBTC.65,66 It should be noted that the higher affinity of CuBTC for CO2 adsorption (high CO2/CH4 selectivity) could be a result of the quadrupole moments of CO2, which makes CO2 a good candidate to be adsorbed on the open metal sites

(MPa). Therefore, the reduced spreading pressure of the adsorbed phase, z, is given by z=

Aπ = R gT

∫0

PN0 (π )

∫0

qN PN

P10(π )

dPN

q1 P1

dP1=

∫0

P20(π )

q2 P2

dP2 = ...=

(11)

Figure 8. Values of targets and outputs corresponding to each step of network design. I


Article


Figure 9. Errors between target and output values for different steps of network design.

Figure 10. Histogram of errors for the training, validation, and testing steps. Figure 12. Sensitivity analysis for the CO2/CH4 separation factor.

of CuBTC. On the other hand, at increasing adsorption pressures, higher interactions between the CH4 molecules and the pore walls of CuBTC could result in higher adsorption of CH4 molecules65 and, therefore, lower CO2/CH4 selectivities. 5.3. CO2/CH4 Selectivity (ELM Method). The extended Langmuir model (ELM), which is a less rigorous model than

IAST, constitutes a simple approach for describing sorption from multicomponent mixtures. This model is based on the single-gas Langmuir adsorption isotherm to predict the amount of adsorbed gas in multicomponent systems. For adsorption

Figure 11. Comprehensive schematic diagram of the optimum ANN architecture. J


Article


By combining eqs 17 and 18, we have the following equation for CO2/CH4 selectivity using ELM qCO yCH 4 2 SCO2 /CH4 = qCH yCO (19) 4

2

5.4. CO2/CH4 Selectivity (ANN Model). Finally, the ANN modeling performed in section 4.1 was used to measure the CO2/CH4 selectivity of CuBTC synthesized in our laboratory. For this purpose, the data associated with the as-synthesized CuBTC (Table 6) were used after normalization between −1 Table 6. Operating Parameters for Measuring CO2/CH4 Selectivity by Means of ANN Modeling Figure 13. Experimental (dots) and fitted (lines) data associated with CO2 and CH4 adsorption on as-synthesized CuBTC.

Table 5. Langmuir Fitting Parameters for CO2 and CH4 Adsorption on CuBTC parameter

CO2

CH4

qmax (mmol/g) b R2

9.363 0.547 0.9995

11.4 0.07394 0.9993

6. CONCLUSIONS In this study, the performance of MLP networks in the prediction of the separation behavior of CO2/CH4 mixtures by MOFs was investigated. The input parameters were chosen as a combination of practical contributing factors, namely, textural properties, adsorption thermodynamic factors, adsorbent surface chemistry parameters, and adsorption operating conditions, and the separation factor of CO2/CH4 mixtures was chosen as the output parameter for which input−output data sets was collected from the literature. By means of trial and error, the best architecture of the as-designed network was chosen as a two-hidden-layer network with seven and four neurons in the first and second hidden layers, respectively. The high value of the regression coefficient associated with all data (r = 0.99286) revealed the reliability of the ANN as an alternative candidate for the prediction of the separation behavior of MOFs in CO2/CH4 gaseous mixtures. Moreover, sensitivity analysis demonstrated that, in the prediction of the CO2/CH4 separation factor using ANN modeling, the pore volume of the MOF is the most significant variable, with a percentage contribution of about 28%. In conclusion, it was demonstrated that the as-designed ANN model with the obtained weights and biases is capable of predicting the CO2/ CH4 selectivity of the as-synthesized CuBTC in comparison to other methods such as IAST and ELM in the absence of experimental single-component adsorption data sets. It is worth mentioning that, although numerous existing studies (as well as this research) have permanently shown the capability of ANN modeling as a prediction tool, because the effectiveness of this method is inherently based on the number of inputs and the accuracy of data sets, the greater the number of precise data

measurements of a binary mixture of components i and j, the ELM is expressed as qmax, ibipi (1 + bipi + bjpj )

value 1306 0.6556 38.63 31.71 298.15 1.0 1

and +1, together with the optimum weights and biases determined by ANN modeling (Table 4). Consequently, the selectivity determined by the ANN model was calculated to be 5.5974, which is in good agreement with the values calculated by the IAST and ELM methods. Table 7 compares the results obtained by IAST, ELM, and ANN modeling for the prediction of the CO2/CH4 selectivity in CuBTC.

Figure 14. Selectivity of a 50:50 CO2/CH4 mixture at 25 °C versus adsorption pressure determined by means of IAST.

qi =

parameter BET surface area (m2/g) pore volume (m3/g) CO2 heat of adsorption (kJ/mol) CH4 heat of adsorption (kJ/mol) adsorption temperature (K) adsorption pressure (bar) open metal sites

(16)

where qmax,i and bi are the constants of the pure-gas Langmuir isotherms of each component. Furthermore, the mole fraction of component i, xi, can be determined ideally by the equation qi q xi = = i qi + qj qtotal (17) Finally, the adsorption selectivity of the binary mixture can be determined as follows x yj Si , j = i xj yi (18) K


Article

Industrial & Engineering Chemistry Research Table 7. Comparison among CO2/CH4 Selectivities Determined by Means of ELM, IAST, and ANN Modeling MOF

mixture

adsorption temperature (K)

adsorption pressure (bar)

prediction method

SCO2/CH4

CuBTC

CO2/CH4 (50:50)

298.15

1

ELM IAST ANN

6.0760 5.7073 5.5974

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values used as ANN inputs, the more reliable the predictions of the model.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +98 111 3234204. Fax: +98 111 3234204. ORCID

Ali Asghar Ghoreyshi: 0000-0002-2206-8802 Notes

The authors declare no competing financial interest.

■

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M


Using Artificial Neural Network and Ideal Adsorbed Solution Theory for

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