Prediction and Experimental Verification of CO2 Adsorption on Ni

Article pubs.acs.org/IECR

Prediction and Experimental Verification of CO2 Adsorption on Ni/ DOBDC Using a Genetic Algorithm−Back-Propagation Neural Network Model Zhi Guo Qu,† Hui Wang,† Wen Zhang,*,‡ Liang Zhou,† and Ying Xin Chang‡ †

MOE Key Laboratory of Thermo-Fluid Science and Engineering, School of Energy and Power Engineering, and ‡School of Science, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China S Supporting Information *

ABSTRACT: A model combined a back-propagation neural network (BPNN) with a genetic algorithm (GA) based on experimental data as training samples was established to predict the CO2 adsorption capacity for metal organic frameworks (MOFs) of Ni/DOBDC. The random function of the conventional BPNN model was modified by the GA−BPNN model for optimizing the initial weights and bias nodes. The amounts of adsorbed CO2 and corresponding isosteric heat of adsorption on Ni/DOBDC were synchronously studied within a wide temperature range (25−145 °C) and pressure range (0−3.5 MPa). The predicted results of the proposed GA−BPNN model and those of theoretical models and a BPNN model were compared with the experimental data. The proposed model provided a more accurate prediction than those of the theoretical models and BPNN model. In particular, the theoretical models were invalid in the low-pressure range (0−0.1 MPa).

1. INTRODUCTION Carbon dioxide has increasingly become a most pressing environmental concern as the predominant greenhouse gas. Carbon capture and storage (CCS) is a promising option to address this problem. Porous materials, such as activated carbon,1 zeolites,2 metal−organic frameworks (MOFs),3 and modified porous media,4 have been used in CCS technology. Of these materials, MOFs such as MOF-5,5 CuBTC,6 ZIF-68,7 MIL-53,8 and soc-MOF9 are considered novel adsorbents because of their adjustable chemical functionality, large surface area, fine-tunable pore structure, high selectivity, and high controllability. MOFs have higher saturated CO2 capacities than conventional adsorbents. Ni/DOBDC has become a popular material among MOFs since it was first synthesized by Dietzel et al.10 Ni/DOBDC contains hexagonally packed helical O5Ni chains connected by 2,5-dihydroxyterephthalte linkers. The onedimensional pore size is approximately 1.1 nm. Ni/DOBDC has been widely investigated because of its high-temperature stability (up to 300 °C), reversible adsorption,11 and unsaturated metal centers.12 Dietzel et al.13,14 found that the high CO2 adsorption on Ni/DOBDC is due to short Ni2+··· OCO bonds. Caskey et al.15 determined that the isosteric heat of CO2 adsorption on Ni/DOBDC decreases with the CO2 uptake at 23 °C. Chavan et al.16 showed that N2 and C2H4 adsorption on Ni/DOBDC is a reversible process. Liu et al.17−19 used Ni/DOBDC in the separation and found that the CO2/N2 selectivity reaches 22 at 0.015 MPa, whereas the Xe/ Kr selectivity is 7.3 at 0.1 MPa. Kizzie et al.20 reported that Ni/ DOBDC is significantly affected by humidity compared with other microporous coordination polymers at different pressures. The aforementioned experimental studies all focused on the low-pressure range (0−0.1 MPa) and a fixed temperature and scarcely considered the isosteric heat of adsorption experimentally. © 2014 American Chemical Society

Different theoretical models and numerical methods have been used in predicting the adsorption performance of MOFs, and each of them is successful to some extent. The Langmuir model21 was the basic adsorption model based on monolayer adsorption theory. The Toth isotherm model15 was then developed by introducing the adsorption sites. Various models were later established. Among these models, the Toth equation developed by Wang et al.22 and the equilibrium model developed by Guerrero et al.23,24 were the most popular ones. The formulas for various models are summarized in Table S1 in the Supporting Information (SI). The multisite Langmuir model has a clear physical explanation; however, the prediction accuracy is not very satisfying in the low-pressure range. This is not a failure of the theoretical models but a failure of their application because the correlations from the model cannot cover a wide range of parameters. Numerical methods, mainly grand-canonical Monte Carlo simulations (GCMC) and molecular dynamics, have been introduced introduced to predict the adsorption behavior. Snurr et al.25 adopted GCMC to simulate CO2 uptake in 14 types of MOFs at low pressure and found that the results are considerably different from the experimental results, specifically for Ni/DOBDC. However, the researchers considered only the effect of low pressure and ignored that of temperature. The numerical methods involve a large number of time-consuming calculations. Moreover, the model also fits poorly in the low-pressure regime because it does not take into consideration the metal sites. Adsorption is a typical nonlinear process. The artificial neural network (ANN) model provides another approach to predict Received: Revised: Accepted: Published: 12044

December 27, 2013 June 3, 2014 July 10, 2014 July 10, 2014 dx.doi.org/10.1021/ie404396p | Ind. Eng. Chem. Res. 2014, 53, 12044−12053

Industrial & Engineering Chemistry Research

Article

Figure 1. Systems for CO2 adsorption equilibrium measurement.

data; the results showed it can be a new promising approach to optimize the process design of sheet metal. Yao et al.32 used an evolutionary system to evolve the ANN model, which coevolved connection weights and bias nodes. They found it has a better generalization ability compared with the ANN model. As previously stated, the temperature and pressure ranges of experimental investigations on CO2 adsorption on Ni/DOBDC were relatively narrow, and the isosteric heat was rarely experimentally studied. Studies on the ANN model and GA− BPNN model for fitting and predicting the adsorption capacity have been scarce. In the present study, Ni/DOBDC was chosen as a typical MOF material, and the amount of adsorbed CO2 and the corresponding isosteric heat of adsorption on Ni/ DOBDC were synchronously measured using a combined PCTProE&E and Calvet calorimeter over expanded pressure and temperature ranges. The series of experimental data were used as training samples to facilitate the establishment of a neural network model. A GA−BPNN model was proposed to predict the CO2 adsorption properties of Ni/DOBDC. Small prediction deviations from experimental data were also detected.

the adsorption values based on the experimental data samples for these types of nonlinear problems. Recently, the ANN model has been combined with an optimized method to predict the adsorption capacity. The radial basis function neural network (RBFNN) and back-propagation neural network (BPNN) models are classical ANN models. The ANN model can effectively predict new information for complicated nonlinear problems based on training samples. Since Hosking et al.26 applied ANN model to error diagnosis for a chemical process, it has been widely used in chemical engineering, for instance, predicting the performance of adsorption systems. Turan et al.27 found that the RBFNN model describes the removal of Cu(II) from industrial leachate more accurately compared with traditional models. However, compared with the RBFNN model, the BPNN model had advantages in ease of use and was more popular. Du et al.28 showed that the BPNN model depicts solanesol adsorption in packing columns more accurately than general rate models. Aghav et al.29 found that the BPNN model is highly suitable in predicting the competitive adsorption of phenol and resorcinol from aqueous solutions. However, the aforementioned studies focused only on the fitting functions of the BPNN model in comparison with experimental data and did not consider the prediction functions. In addition, the BPNN model exhibits the intrinsic weaknesses of sensitivity to the initial values of weights and bias nodes and overfitting. The genetic algorithm (GA) is a search technique that is based on the mechanics of natural selection. The GA involves population initialization, fitness functions, selection, crossover, and mutation. This algorithm can readily identify global optimization solutions by simulating natural genetic mechanisms and biological evolution.30 A combination of GA and BPNN is expected to improve the prediction accuracy of the ANN model. Fu et al.31 adopted GA to optimize the weights of the BPNN model for minimizing the error between the predictive punch radius and experimental

2. EXPERIMENTAL STUDY 2.1. Experiment. The preparation and characterization [sample and crystal structure, X-ray diffraction (XRD) patterns, and N2 adsorption isotherm] of Ni/DOBDC used in the present study can be found in the SI. Figure 1 shows a schematic diagram of the test apparatus, which consists of four parts, namely, adsorption, calorimetric, gas supply, and data acquisition systems. A PCTProE&E equipped with a Calvet calorimeter (PCT and C80, French) served as the adsorption and calorimetric systems. The sample was pretreated to obtain high-purity Ni/DOBDC powder. The Ni/DOBDC powder was heated at 200 °C for 24 h under vacuum using the Calvet calorimeter to remove water and CO2 12045

dx.doi.org/10.1021/ie404396p | Ind. Eng. Chem. Res. 2014, 53, 12044−12053


Article

adsorption mainly occurred at the pore surface because of the short distance between the adsorption site and the adsorbed molecule, which resulted in strong adsorption forces. Furthermore, Ni/DOBDC had the open metal site Ni2+, which accelerated the adsorption at low pressure. As the pressure gradually increased, the amount of adsorbed CO2 reached equilibrium, and sites with the highest affinity became completely filled. As a result, adsorption occurred only at the pore periphery, which led to multilayer adsorption. Figure 2b shows the changes in the isosteric heat of adsorption with different adsorbed amounts. The isosteric heat of adsorption decreased and then approached a constant value as the adsorbed amount increased. The isosteric heat of adsorption was mainly released by the adsorption bond energy in the adsorption sites. As the adsorbed amount increased, the sites with the highest affinity were gradually filled, which resulted in a decreased isosteric heat of adsorption. 2.3. Effect of Temperature on CO2 Adsorption. Figure 3shows the adsorbed amount and isosteric heat of adsorption at

absorbed by Ni/DOBDC from the air. The gas supply system, which contained three high-purity gas supply lines, namely, CO2, N2, and He, was connected to the adsorption system. Nitrogen was used to drive pneumatic valves in the PCTProE&E. Helium was flowed through the Calvet calorimeter sample cell to calibrate the volume. CO2 (as the adsorbate gas) was fed to the sample cell to achieve the setting pressure. The target temperature was controlled using the Calvet calorimeter. During the adsorption, the amount and heat of adsorption were synchronously determined using the PCTProE&E−Calvet calorimeter system. The test signals were recorded using data acquisition systems. 2.2. Effect of Pressure on CO2 Adsorption. Figure 2a shows the amount of adsorbed CO2 on Ni/DOBDC at

Figure 2. (a) CO2 adsorption isotherms of Ni/DOBDC at different pressures and (b) isosteric heat of adsorption for different amounts of adsorbed CO2.

different pressures (0−3.5 MPa) and temperatures (25−115 °C). The adsorption curve fitted a type I isotherm.33 At 25 °C and 2.0 MPa, the amount of adsorbed CO2 on Ni/DOBDC typically reached 11.11 mol/kg, which was higher than the 8.75 mol/kg reported by Liu et al.;18 this result was due to the larger surface area of the present material compared with that of the material used by Liu et al.18 as shown in Table S2 in the SI. The applied Ni/DOBDC also had a smaller pore size, as shown in Figure S4 in the SI, which was associated with an increased pore volume. This result implied that the surface area and pore volume were key factors that determined the adsorption capacity. The adsorption significantly increased with the increase in pressure within the low-pressure range (0−0.1 MPa). The increase became milder within the high-pressure range (1.0−3.5 MPa). Within the low-pressure range, the

Figure 3. (a, top) Amount of adsorbed CO2 and (b) isosteric heat of adsorption on Ni/DOBDC at two typical pressures and at different temperatures.

different temperatures and under two typical pressures (0.1 and 1.0 MPa). The two selected pressures are commonly used in industrial applications. The amount of adsorbed CO2 decreased as the temperature increased (Figure 3a). This phenomenon was accompanied by exothermic adsorption. The forces between adsorbent and adsorbate mainly consist of van der Waals and Coulomb forces, which are weak physical bonds. As the temperature increased, the adsorbate molecules moved 12046



Article

more rapidly. This phenomenon increased the difficulty in fixing the adsorbates to the adsorption sites. Variations in temperature did not affect the isosteric heat of adsorption (Figure 3b). The absolute heat of adsorption decreased with increasing temperature because of the reduced amount of adsorbed CO2. The isosteric heat of adsorption is the ratio of the decreasing heat of adsorption and the amount of adsorbed molecules. In this parameter, the decreasing trends for the heat of adsorption and for the amount of adsorbed molecules were almost equivalent. Therefore, the isosteric heat of adsorption was not affected by temperature variations.

3. IMPROVED ANN MODEL 3.1. Brief Review of a Conventional BPNN Model. The BPNN model is an effective tool in predicting the amount of

Figure 4. Structure of the back-propagation neural network.

Figure 6. Flowchart for prediction procedure of the GA−BPNN model.

Table 1. Optimized Weights and Bias Nodes Figure 5. Standard deviations for different quantities of hidden layers.

ωkj bj ωjq bq ωqr br

adsorbed molecules because it voluntarily learns from the training samples and produces precise responses to new information. The present model consists of three layers, namely, the input, hidden, and output layers, and it is operated by sending signals to another layer with weighted connections through neuronal interactions. Every neuron is connected to all neurons in the preceding and subsequent layers. Input value is represented by a neuron in the input layer. Input values are normalized and then weighted before entering the hidden layer. The weighted values are transferred to the hidden layer. In the hidden layer, each neuron produces output values based on the sum of the weighted values from the input layer. The implementation details of the BPNN model were reported by Kumar and Spellman et al.34,35 Figure 4 shows the structure of the BPNN model. The temperatures and pressures were used as the input values. The selected temperatures ranged from 25 to 105 °C at intervals of 10, 50, 115, and 145 °C, whereas the selected pressures ranged from 0 to 3.5 MPa. The input and output values had different responses to the neural network. The input variables of temperature and pressure were weighted prior to the hidden layer. The output values of amount of adsorption were also

−1.2445 −2.9244 2.3561 −0.5273 −1.7834 −0.8987

1.2034 −2.1378 2.7007 0.3894 2.9283

−1.7198

1.6001

−1.0446

0.2539

normalized for consistency. Thus, the phenomenon of the saturation state of input and output could be avoided. In the present weighted process, the input and output parameters were scaled from 0.2 to 0.8.29 The pressure pi(net), temperature Ti(net), and amount of adsorption ni(net) were normalized using the following algorithm in the preprocessing of input values and output values: pi (net) = 0.2 + 0.6

Ti(net) = 0.2 + 0.6 12047

[pi − min(pi )] max(pi ) − min(pi )

(1a)

[Ti − min(Ti )] max(Ti ) − min(Ti )

(1b)



Article

Figure 8. Comparisons of adsorption amounts with experimental data with predication samples at 50 °C [when P = 0 (MPa), nC02 = 0 (kmol/kg)].

Figure 7. Comparisons of adsorption amounts with experimental data with training samples at 35 °C [when P = 0 (MPa), nC02 = 0 (kmol/ kg)].

ni(net) = 0.2 + 0.6

[ni , exp − min(ni , exp)] max(ni , exp) − min(ni , exp)

training sample groups with number NTS (NTS = 174) were used in the input layer. The hidden layer could be chosen as single hidden layer or multiple hidden layers. Multiple hidden layer networks could perform better on any linear or nonlinear problems than the single hidden layer networks, because multiple hidden layer networks allowed for higher degrees of nonlinearity than singlelayer networks. Hence, the multiple hidden layer networks were used in the present work in which all of the training samples were learned, and every neuron produced an output value based on the sum of the weighted values from the input layer of the algorithm. The intermediate output value Oij of the first hidden layer was shown as a second-order tensor, as follows:

(1c)

min (pi), min (Ti), and min (ni, exp) are the minimum pressure, temperature, and amount of adsorption, respectively. The min (ni, exp), min (Ti), and min (ni, exp) are the maximum pressure, temperature, and amount of adsorption, respectively. A few sample groups with number N (N = 231) were obtained from the operating temperature and pressure as input values. Each group consisted of two values of temperature and pressure. Hence, the input value coud be expressed as a second-order tensor in eq 2 as follows:

Xi1 = pi , i = 1−N

(2a)

Xi2 = Ti , i = 1−N

(2b)

H

Oij = f [∑ Xikωkj + bj], j = 1−L1 , i = 1−N

(3)

k=1

f(x) is the sigmoid transfer function shown in eq 4. 1 f (x ) = 1 + exp( −x)

Among all of the input samples, those of the 25−105 °C temperature range (10 °C interval) under a pressure range of 0−3.5 MPa were used as training samples. Hence, a few

(4)

Table 2. Fitting Standard Deviation Analysis [ERTS (%)] at 35 °C

all test pressures (0−3.5 MPa) low pressure (0−0.10 MPa)

NTS

Toth isotherm (%)

Toth equation (%)

equilibrium model (%)

BPNN (%)

GA−BPNN (%)

20 8

23.33 37.76

13.98 22.87

13.98 22.87

8.76 14.28

4.37 6.60

12048



Article



H is the number of input nodes, where H = 2 for the temperature and pressure. ωkj is the weight between the kth node of the input layer and the jth node of the hidden layer. bj is the bias node of the jth node. The intermediate output of the second hidden layer is also shown as a second-order tensor, as follows:

optimized on the basis of the single hidden layer, and then the multiple hidden layers were used to optimize it continually. The selection for the number of single hidden layers could be based on statistical method36 or empirical correlation.37 In the present study, the empirical correlation in eq 6 was applied to determine L.

L1

(M + H ) ≤ L ≤

Oiq = f [∑ Oijωjq + bq], q = 1−L 2 , i = 1−N j=1

(5)

(M + H ) + C

(6)

M is the number of output nodes, which is equal to 1 for the output variable (i.e., amount of adsorbed molecules). C is a number from 0 to 10. Therefore, L can be any integer from 1.732 to 11.732 and is finally denoted as 4 on the basis of the smallest standard deviation to avoid long training time and overfitting at large neurons number as explained. The concrete optimization process was formulated through the procedure described below. The output values were obtained by the above transfer function between the intermediate value Oiq in the second hidden layer and output layer. In the output layer, the amount of adsorbed molecules was obtained as the output value based on the intermediate output value Oiq in the second hidden layer via eq 7a

f [] is the sigmoid transfer function shown in eq 4. L1 is the number of the first hidden nodes. ωjq is the weight between the jth node of the first hidden layer and the qth node of the second hidden layer. bq is the bias node of the qth node. The initial values of weights and bias nodes were set as a number between −1.0 and 1.0 with a random function as recommended in Zhuo et al.36 The values of weights and bias nodes were further updated and optimized during the training process. The Levenberg−Marquart algorithm was used in the BPNN model training process to find a minimum. The learning rate was denoted by 0.1. The final optimal weights and bias nodes were obtained by iteration, and the convergence criterion was that the relative deviation for ωkj, ωjq, bj, and bq between two successive iterations was

Prediction and Experimental Verification of CO2 Adsorption on Ni

Recommend Documents