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SiO2 catalyst at elevated pressure
Journal of the Taiwan Institute of Chemical Engineers 42 (2011) 751–759
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Optimization of OCM reaction conditions over Na–W–Mn/SiO2 catalyst at elevated pressure Jafar Sadeghzadeh Ahari a,b, Mohammad T. Sadeghi a,*, Saeed Zarrin Pashne b a b
Process Simulation and Control Laboratory, Chemical Engineering College, Iran University of Science and Technology (IUST), Narmak 16765-163, Tehran, Iran Gas Research Division - Research Institute of Petroleum Industry (RIPI), P.O. Box 14665-137, Tehran, Iran
A R T I C L E I N F O
A B S T R A C T
Article history: Received 9 October 2010 Received in revised form 11 February 2011 Accepted 28 February 2011 Available online 5 April 2011
Performance of the oxidative coupling of methane (OCM) at elevated pressures has been simulated by a set of supervised Artificial Neural Network (ANN) models using reaction data gathered in a microreactor device. Accuracy of the developed models were evaluated by comparing the predicted results with the test data set showing a good agreement. In order to enhance the performance of OCM process at 0.4 MPa as a desired operating pressure for commercial application of OCM, the Hybrid Genetic Algorithm (HGA) was used to obtain the optimal values of the operating conditions. Nondominated Pareto optimal solutions were obtained and additional experiments were carried out at two different optimum conditions in order to verify the optimums. The results show that combination of ANN models with HGA could be used in finding the suitable operating conditions for OCM process at elevated pressures. It was shown that the C2+ yield of above 23% can be achieved at 0.4 MPa by using Na–W–Mn/SiO2 as the OCM catalyst. ß 2011 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
Keywords: OCM Catalyst Elevated pressure Optimization Artificial Neural Network (ANN) Hybrid Genetic Algorithm (HGA)
1. Introduction Catalytic oxidative coupling of methane (OCM) converting it to higher hydrocarbons is one of the most attractive methods to utilize natural gas as chemical feedstock. It is commonly accepted that this reaction proceeds through a radical mechanism. Therefore, the initiating step is the generation of methyl radicals caused by hydrogen abstraction from methane at particular active sites on the catalyst surface. These radicals can be released into the gas phase where then undergo a variety of reactions producing desired C2+ hydrocarbons as well as undesired carbon oxides. Moreover, deep oxidation of the hydrocarbon products may occur at the catalyst surface (Dittmeyer and Hofman, 1994). After the pioneer work by Keller and Bhasin (1982), there have been extensive research and development efforts in the OCM process. A wide variety of catalysts have been used for OCM process. One of the most effective catalysts for the OCM is Na–W– Mn/SiO2 catalyst, which was firstly reported by Fang et al. (1992a,b). Due to its excellent performance, the catalyst has been extensively studied by several researchers (Chou et al., 2002a; Chua et al., 2007; Ji et al., 2002; Liu, 1997; Palermo et al., 1998; Sadeghzadeh Ahari et al., 2009; Wang et al., 1995; Wang et al., 2006).
* Corresponding author. Fax: +98 21 77240495. E-mail address: [email protected] (M.T. Sadeghi).
Considering commercial and technical limitation, it is necessary to make the OCM reactor size as small as possible. This can be achieved by operating the reactor at pressures higher than atmospheric. On the other hand, higher pressure will lead to a drop in C2+ selectivity and yield, i.e. higher pressures will facilitate undesired total oxidation reactions. Among the earliest economic studies on commercialization of OCM based processes by Union Carbide in 1992 (Martherne and Culp, 1992) it had been assumed that the reactor pressure could increase up to 0.44 MPa without a major impact on C2+ yield of the reaction per pass. In a more recent feasibility study by RIPI and JOGNEC (2004) it has been found that the plant cost index reaches its minimum value if the reactor operate at 0.4 MPa pressure, assuming the catalyst performance does not change by increasing the pressure to 0.4 MPa. In order to reach a more reliable result however, it is necessary to know the behavior of the OCM catalyst (or reaction) at higher pressures, a subject that has not been much investigated yet. In the case of Na–W–Mn/SiO2 catalyst most of the reported kinetic models in the literatures (Daneshpayeh et al., 2009; Kamali Shahri and Alavi, 2009), were based on reaction data gathered at atmospheric total pressure. Chou and coworkers (2002) have studied the OCM reactions on Na–Mn–W/SiO2 catalyst at pressure levels of 0.6–2 MPa using undiluted CH4/O2 feed (CH4/O2 range of 6–10 and very high GHSV values of 1–2 105 h1). They have succeeded to obtain the maximum C2+ yield of near 14% at 1.0 MPa and 750 8C. This performance figure is much lower than that of atmospheric pressure (yield of near 30% have been reported for the
1876-1070/$ – see front matter ß 2011 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.jtice.2011.02.005
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same type of catalyst at atmospheric pressure). Their finding may suggest that working at pressure near 1.0 MPa is not commercially attractive due to the low C2+ yield achieved. The lack of suitable kinetic models for the OCM reactions at elevated pressures makes the conventional modeling methods not suitable for this system. However, the problem can be overcome by using nonlinear calculation methods such as Artificial Neural Network (ANN). ANNs are useful modeling tools particularly if there exist pertinent wide range of data sets or data bank of some input variables and output performance characteristic figures. Moreover, the ANN models have been used increasingly in various aspects of science and engineering due to its ability in modeling both linear and nonlinear problems without any assumption. In chemical engineering, ANNs are used to predict the product yield in methanol to olefin process (Nabavi et al., 2009), octane number (Pasadakis et al., 2006), sulfur content of sour gases (Mehrpooya et al., 2010), kinetics of solid/liquid sorption system (Kumar et al., 2008) and interfacial tension at catalyst/liquid interface (Kumar, 2009). In the field of OCM process, Abdolahi et al. (2005) used a neural network for prediction of CH4 conversion, ethylene and C2+ selectivity on the periodic operation of OCM process over Ce/Li/ MgO catalyst. The combination of ANN and genetic algorithm (GA) has been used for integrated process modeling and optimization. A hybrid GA with ANN was also used by Huang et al. (2003) to design optimal catalyst and operating conditions in the OCM process. Recently, Istadi and Amin (2007) used this technique for modeling and optimization of catalytic dielectric barrier discharge plasma reactor for CO2-OCM process.
Nevertheless, there is no report addressing modeling and optimization of OCM reactions at elevated pressures. Thereupon, in the present work an ANN model is suggested for modeling the isothermal bed reactor at elevated pressures. In addition, in order to obtain pareto optimal solutions, the GA multi objective optimization algorithm is applied for maximization of CH4 conversion and C2+ selectivity simultaneously. Finally, additional experiments have been carried out in order to validate some optimization results. 2. The experimental work 2.1. Catalyst preparation The SiO2 ingredient was first prepared by the coprecipitation method. Calculated amounts of sodium silicate (Na2SiO4, supplied by MERCK with purity >98%) and sulfuric acid (H2SO4, supplied by MERCK with purity >95%) were added slowly to a well-stirred container which is containing 400 ml of distilled water at 80 8C. During the procedure, pH and temperature of the precipitating solution were kept around 8 and 80 8C respectively. The mixture was further aged at 80 8C for 1 h. After filtration and washing with distillated water, the obtained solid was dried in air at ambient temperature for 24 h and then heated up to 100 8C for 1 day. Next, it was calcined in air for 5 h at 450 8C. The Na–W–Mn/SiO2 catalyst was prepared via two-step incipient wetness impregnation method. The prepared SiO2 support was impregnated with aqueous solution in appropriate concentration of Mn(NO3)26H2O (MERCK, >98%), evaporated to dryness and dried in air at ambient temperature for 24 h and then
Fig. 1. Schematic diagram of the experimental setup.
J.S. Ahari et al. / Journal of the Taiwan Institute of Chemical Engineers 42 (2011) 751–759
100 8C for 1 day. An aqueous solution of Na2WO42H2O (MERCK, 98%) was added to the prepared material followed by drying similar to the previous step. The prepared catalyst was calcined in air at 850 8C for 15 h and the resulting powder was pelletized, crushed and sieved to 30–35 mesh. Results of Atomic Absorption Spectrophotometry (AAS) (AAnalyst 200) and Inductively Coupled Plasma (ICP) (Wear Metal Analyzer-Plasma 400) analysis, show that the wt% of components in prepared catalyst are 1.4 wt% Na–2.1 wt% W–1.5 wt% Mn/SiO2. 2.2. Experimental setup The experimental setup used in this work is depicted in Fig. 1. The catalyst performance was evaluated in a quartz fixed-bed micro reactor (ID = 10 mm). An amount of 0.4 g catalyst is placed at the hottest part of the reactor heated by an electrical furnace. The remaining space of the reactor was filled with quartz chips (20– 25 mesh) to minimize any gas phase reaction contribution. A Ktype thermocouple was positioned at the hottest part of the reactor to indicate the temperature of the catalyst bed. The reactant gases consisted of CH4 (99.99%), O2 (99.99%) and N2 (99.99%), were cofed into the reactor and their flow rates were controlled by mass flow controllers (BROOKS, 5850TR). The dried effluent gas flow rate was measured by a bubble flowmeter. The reactor effluent gases, after removing water by condensation at 5 8C were analyzed by an online gas chromatograph equipped with thermal conductivity detector detecting O2, N2, CH4, CO, CO2, C2H4 and C2H6. Furthermore, flame ionization detector was used for detecting the higher hydrocarbons. The carbon balance errors across the reactor and during the tests were between 2% and 5%. The pressure of the system was controlled using a pressure controller valve that contains a built in pressure sensor (BROOKS, 5866). Since the reactor is made from quartz, the operating pressure was not increased beyond 0.4 MPa due to safety concerns. The CH4 conversion, selectivity and yield of product hydrocarbons are calculated using the following equations: X CH4 % ¼
moles of CH4 converted 100 ðmoles of CH4 Þfeed
(1)
Y C2þ % ¼ X CH4 SC2þ 100
Variable
Range
T (8C)
720–775a 700–750b 675–750c 12,765, 14,285, 15,790 3.15, 4.0, 6.0 0.0, 10.0, 20.0
b c
P = 0.2 MPa. P = 0.3 MPa. P = 0.4 MPa.
(a) Determination of transfer function type (sigmoid, hyperbolical tangent or linear) in each layer. (b) Determination of the number of hidden layers and nodes.
Xn ¼
Table 1 Experimental data ranges used in this study for development of ANN models.
a
The function of a neural network is often compared with the human or animal brain that is made of a large number of neurons. Similarly, an Artificial Neural Network is made of a number of simple processors (nodes) linked by weighted connections. As with the brain neuron, each receptor receives input from various other nodes and generates a scalar output signal that is distributed as input to other processing nodes. Several neural network architectures have been developed over the past years. One of the most popular and powerful architectures is the multi layer perceptron (MLP). The MLP neural networks are feed forward networks consisting number of layers of nodes. There are an input layer, an output layer and one or more hidden layers between the input and output layers. The number of nodes in the input and output layers represent effectively the number of variables used in the prediction and the number of variables to be predicted. However, appropriate number of hidden layers and their nodes cannot be known in advance but are normally set through trial and error. Each node in a certain layer is connected to every single node in the next layer via links with an appropriate and adjustable connection weight. A node receives incoming signals from each node in the previous layer. The effective incoming signal to each node is the weighted sum of all the incoming signals and the node threshold or bias value. The effective incoming signal is passed through a nonlinear operation function to produce the outgoing signal of the node. The two main steps involved in the ANN model development are: Step 1: The network architecture selection including
(3)
Overall range of the operating condition used in this work for developing the ANN models are summarized in Table 1.
Feed’s GHSV (h1) Feed’s CH4/O2 molar ratio Feed’s N2 mol%
3.1. Artificial Neural Network
(2)
products
n2
3. Predictive modeling and optimization methods
Step 2: Validation of the model The network architecture is determined by trial and error during the training phase while validation of the model is performed via evaluation of the model performance by using the test data. In order to achieve a fast convergence, it is useful to normalize the input and target values before the training so that they stand within a specified range. Using the following formula the experimental data were normalized into the range of 1 to 1:
P nðmoles of Cn hydrocarbonsÞproducts SC2þ % ¼ moles of CO þ moles of CO2 P þ nðmoles of Cn hydrocarbonsÞ 100;
753
2ðX X min Þ 1 X max X min
(4)
in which, Xmin and Xmax are the minimum and maximum values of the raw data, respectively. Normalizing the data, they were randomly divided in two subsets: training set (70% of total data at each investigated pressure) and test set (30% of total data at each investigated pressure). The training set was used to estimate the neural network’s parameters and the test set to validate the networks. During the training or learning phase, the network parameters (weights and biases) are optimized in a way that the error between the measured and estimated output is minimized. The most popular training algorithm for minimizing the error function for a MLP neural network is the standard back propagation (BP) technique. This technique includes four stages: (1) randomly initialization of all weights and biases; (2) feed forward of the input training pattern; (3) calculation and BP of the associated error, and
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(4) weights and biases adjustment. This procedure is repeated until the error between the predictive and target values is minimized. There are several different BP training algorithms. In this work, the Levenberg-Marquardt algorithm was used for training of the network due to its rapid convergence (Cigizoglu and Alp, 2006; Cigizoglu and Kisi, 2005; Hagan and Menhaj, 1994; Istadi and Amin, 2007). 3.2. Genetic algorithm Several local and global optimization algorithms have been used for optimization problems. In general, local optimization algorithms (LOA) have the advantage of solving the problem quickly, though their results are very much dependent to the initial starting point. Therefore, they can be easily trapped in a local optimum. On the other hand, global optimization algorithms (GOA) such as genetic algorithm (GA) are necessary to find the global optimum in optimization problems containing many local optimums. The algorithm was suggested by Holland in 1975 based on Darwin’s theory of evolution. Essentially, the GA approach starts with a set of trial solution (called population) and then the final solution evolves iteratively by applying some genetic operators (e.g. selection, cross over and mutation). Based on the GA ability to reach global optimum, it has been extensively applied in many engineering fields. It can find the region of the optimal value quickly and this is a notable characteristic of the algorithm. However, the ability of accurate search in this region is not satisfactory for complex systems. Therefore, GA is often hybridized with LOA to improve its performance as a global optimization technique. Some possible hybridizations using LOA are pre-hybridization, organic-hybridization and post-hybridization (Gudla and Ganguli, 2005; Saha et al., 2008). In this work, the post-hybridization method is used for multi objective optimization. MATLAB GA optimization toolbox (Version 7.6.0324) was employed using the function ‘‘fgoalattain’’ as the hybrid local search method (The Math. Works Inc., 2008). It takes the final solution from GA as its initial point. 4. Results and discussion 4.1. Predictive modeling with ANN It is known from experience that the lower reactor pressures will lead to higher C2+ yields. On the other hand, an optimum operating pressure, requires incorporation of technical and economical variables into the problem that is beyond the scope of this study. Different ANN models were developed for each level of operating pressure (i.e. 0.2, 0.3 and 0.4 MPa). In order to reduce
the time consuming trial and error steps for suitable numbers of hidden layer and nodes and to increase the accuracy of the models, separate networks for prediction of methane conversion (X CH4 ) and C2+ selectivity (SC2þ ) are developed. The input variables for each network were include: the reaction temperature, feed’s methane to oxygen molar ratio, feed’s GHSV and feed’s N2 molar percent. Different feed forward MLP neural networks were constructed using BP algorithm and trained by the neural network toolbox of the MATLAB software package version 7.6.0324 (R2008). Performances of the networks were evaluated using statistical and graphical criteria. The statistical criteria include correlation coefficient (R2), mean square error (MSE) and average absolute relative error (AARE). The statistic R2, measures linear correlation between the actual and predicted values. The MSE and AARE were used to quantify the error between observed and predicted values. Pn ðX X cal Þ2 R2 ¼ 1 Pi¼1 obs n ¯ 2 i¼1 ðX obs Xcal Þ
MSE ¼
(5)
n 1X ðX X cal Þ2 n h¼1 obs
AARE ¼
(6)
1 XX obs X cal X 100 n obs
(7)
where n is the number of data points, X¯ is the average of X over the n samples. Xobs and Xcal are the actual and predicted values, respectively. The optimal value for R2 was equal to 1.0 whereas for MSE and AARE was equal to 0.0. In the graphical criterion, the data pairs of xi,obs and xi,cal are shown in the Xobs vs. Xcal plane. Judgment on the goodness of training and testing phases can be made based on the closeness of all data pairs to the line Xobs = Xcal (called the first bisectrix). The final networks were selected based on the lowest errors (MSE and AARE) and highest R2 value on training and test sets of data. The results are presented in Table 2. According to the results listed in Table 2, the final networks for prediction of CH4 conversion and C2+ selectivity at each investigated reacting pressure are as follows: For all investigated pressures, the C2+ selectivity network consists of one input layer with four nodes, one hidden layer with six nodes and one output layer with one node (Fig. 2). The activation function used for the hidden layer is sigmoid type (Eq. (8)) while it is of linear type (Eq. (9)) for the output layer.
Table 2 Statistical results and details of the neural network models used for prediction of X CH4 % and SC2þ % at investigated reaction pressures. P = 0.2 MPa
No. of hidden layer No. of nodes Type of transfer function R2 (Train) MSE (Train) AARE%(Train) R2 (Test) MSE (Test) AARE% (Test)
P = 0.3 MPa
P = 0.4 MPa
SC2þ %
X CH4 %
SC2þ %
X CH4 %
SC2þ %
X CH4 %
1 4-6-1 logsig-purelin 0.929 1.78 1.488 0.942 1.86 1.657
2 4-6-2-1 tansig-tansig-purelin 0.995 0.867 7.712 0.989 2.429 13.754
1 4-6-1 logsig-purelin 0.988 0.668 0.711 0.893 6.896 3.134
2 4-7-3-1 tansig-tansig-purelin 1 0.008 0.225 0.948 11.07 19.86
1 4-6-1 logsig-purelin 0.994 0.272 0.612 0.976 0.861 1.05
2 4-6-2-1 tansig-tansig-purelin 1 0.006 0.237 0.998 0.209 1.479
Total number of weights and bias adjusted during the training period is 37, 47 and 63 for the 4-6-1, 4-6-2-1 and 4-7-3-1 networks, respectively. tansig: f(x) = (1 ex)/(1 + ex); logsig: f(x) = 1/(1 + ex); purelin: f(x) = x.
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Table 4 Bias and weights of the C2+ selectivity network at 0.4 MPa.
Fig. 2. Architecture of the neural network model used for prediction of SC2þ % at all of the investigated pressures.
1 1 þ ex
k
bk
1 2 3 4 5 6
5.6548 8.7851 0.4085 5.3775 18.2831 0.2401
1
2.2249
wij
1
2
3
4
1 2 3 4 5 6
5.6623 13.0869 5.7371 5.0728 2.2146 0.9206
1.3756 0.3800 3.9534 4.7809 3.2239 0.0618
7.2411 0.9592 3.5057 0.3336 2.0586 0.1198
0.1046 9.6449 6.7477 0.1757 15.4472 0.0191
wij
1
2
3
4
5
6
1
0.2970
1.2498
0.0551
2.2587
7.0653
4.0093
(8)
f ðxÞ ¼ x
(9)
For reaction pressures of 0.2 and 0.4 MPa, the CH4 conversion network consists of one input layer with 4 nodes, two hidden layers with six and two nodes respectively, and one output layer with one node. The activation function used for the hidden layers and output layers are hyperbolic tangent (Eq. (10)) and linear function, respectively. In the network used for prediction of CH4 conversion at reaction pressure of 0.3 MPa, the hidden layers have seven and three nodes.
f ðxÞ ¼
bj
1 ex 1 þ ex
(10)
As mentioned above, during the training phase the network parameters (weight and biases) are determined for each model. In order to be concise, the parameters of all developed models are not presented here. The weight and bias values of each layer for methane conversion and C2+ selectivity networks at 0.4 MPa are shown in Tables 3 and 4. Figs. 3–5 show the testing results for the final ANN models to estimate the CH4 conversion and C2+ selectivity at each investigated pressure. The parity plots show that for both parameters, the
predictive capability is satisfactory and data points are well concentrated around the first bisectrix. Results of the statistical and graphical criteria, confirm that the developed ANN models are suitable for prediction of CH4 conversion and C2+ selectivity of OCM process at investigated pressures. 4.2. Effects of operating parameters Effects of process variables on the performance of OCM with Na–W–Mn/SiO2 catalyst at elevated pressures were investigated using the ANN models. Simulations were carried out by varying one parameter while the others were kept constant.
40
(1)
35 30
X CH4 % (Cal)
f ðxÞ ¼
j
25 20 15
10
Table 3 Bias and weights of the methane conversion network at 0.4 MPa.
5
j
bj
k
bk
l
bl
1 2 3 4 5 6
1.9581 0.5607 1.2972 0.2590 5.7948 3.0097
1 2
1.7045 0.7044
1
1.1107
0 0
5
10
15
20
25
30
35
40
X CH4 % (Obs) 80
(2)
1
2
3
4
1 2 3 4 5 6
2.2272 2.2244 3.8495 0.4493 0.7259 1.2996
2.1889 1.5241 1.7432 1.0740 0.6185 2.6913
0.1811 1.1355 0.5784 1.5847 0.5221 0.1885
0.0188 0.1244 0.0096 6.1249 5.0198 0.1610
wij
1
2
3
4
5
6
1 2
0.9905 0.0301
0.1447 0.1179
0.1438 2.8829
0.0037 0.4337
0.0322 4.3413
0.0970 1.1219
wij
1
2
1
1.6211
2.9295
SC2+% (Cal)
75
wij
70 65 60
55 55
60
65
70
75
80
SC2+% (Obs) Fig. 3. Comparison between the actual test data set and ANN predictions for (1) CH4 conversion, (2) C2+ selectivity at 0.2 MPa.
J.S. Ahari et al. / Journal of the Taiwan Institute of Chemical Engineers 42 (2011) 751–759
756
40
(1)
35
80
30
70
20
60
20 15 10
10
0
50
XCH4%
5
SC2+%
25
X CH4 %
X CH4 % (Cal)
30
40
SC2+%
0
5
10
15
20
25
30
35
0 660
40
X CH4 % (Obs) 75
68 0
70 0
72 0
40 76 0
74 0
T (o C) Fig. 6. Effect of temperature on selectivity of C2+ and CH4 conversion (N2 = 0%, GHSV = 15,750 h1, CH4/O2 = 6 and P = 0.4 MPa).
(2)
SC2+% (Cal)
70
65 60 55
50
50
55
60
65
70
75
SC2+% (Obs) Fig. 4. Comparison between the actual test data set and ANN predictions for (1) CH4 conversion, (2) C2+ selectivity at 0.3 MPa.
40
(1)
35
X CH4 % (Cal)
30 25 20 15 10 5 0
0
10
20
30
The influence of reaction temperature on the CH4 conversion and C2+ selectivity are presented in Fig. 6. It can be seen that at the temperature range from 675 to 750 8C, the CH4 conversion and C2+ selectivity are increased by temperature up to 720 8C. Since increase of temperature enhances the reaction completion, the process performance improves. The parameters remain almost constant by increasing the temperature beyond 720 8C. This behavior can be explained by the fact that at about 720 8C, oxygen conversion reaches its maximum value of 100%. Further increase in temperature does not affect the methane conversion and C2+ selectivity since undesired consecutive oxidation reactions of the produced reactants cannot occur in the oxygen depleted medium. This is an interesting result showing that the finest temperature of the OCM reactions decreases significantly by increasing the reaction pressure. The effect of feed’s methane to oxygen molar ratio on the OCM performance at elevated pressure was investigated under the operating conditions where oxygen is completely consumed. Fig. 7 shows that increasing the methane to oxygen ratio, decreases the methane conversion while the selectivity of C2+ products increases. The results demonstrate that under the oxygen-rich atmosphere, the produced C2+ hydrocarbons can be more easily converted to COx. According to Eq. (3) the C2+ yield is product of methane conversion multiplied by C2+ selectivity. Therefore, C2+ yield is decreased with increase of methane to oxygen molar ratio (22.4% at CH4/O2 = 3.2 and 16.4% at CH4/O2 = 6.0).
40
X CH4 % (Obs) 75
80
30
75
60
20
70
10
55
SC2+%
65
X CH4 %
SC2+% (Cal)
70
50
40
(2)
65
XCH4% SC2+%
50
55
60
65
70
75
SC2+% (Obs) Fig. 5. Comparison between the actual test data set and ANN predictions for (1) CH4 conversion, (2) C2+ selectivity at 0.4 MPa.
0
2
3
4
5
6
7
60
CH4 /O2 Fig. 7. Effect of molar ratio of methane to oxygen in feed, on selectivity of C2+ and CH4 conversion (N2 = 0%, GHSV = 15,750 h1, T = 750 8C and P = 0.4 MPa).
J.S. Ahari et al. / Journal of the Taiwan Institute of Chemical Engineers 42 (2011) 751–759
77
36
76
24
73
22
X CH4 %
74
SC2+%
23
72 21
XCH4%
1300 0
1350 0
1400 0
GHSV
1450 0
1500 0
1550 0
73 71 30
70 1600 0
75
32
69
71
SC2+% 20 12500
SC2+%
34
75
X CH4 %
77 XCH4%
SC2+%
25
757
28 0.1
0.15
0.2
(h-1 )
0.25
0.3
0.35
0.4
67 0.5
0.45
P (MPa)
Fig. 8. Effect of feed’s GHSV on selectivity of C2+ and CH4 conversion (N2 = 0%, CH4/O2 = 6, T = 750 8C and P = 0.4 MPa).
Fig. 10. Effect of pressure on selectivity of C2+ and CH4 conversion (GHSV = 15,750 h1, CH4/O2 = 4, T = 750 8C, N2 = 0% and XO2 = 100%).
Fig. 8 shows the variation of methane conversion and C2+ selectivity under 0.4 MPa, CH4/O2 = 6.0, T = 750 8C and N2 = 0.0 mol% as a function of feed’s GHSV. The investigated operating conditions correspond to the total oxygen consumption. It can be seen that methane conversion decreases slightly with increasing of GHSV while C2+ selectivity passes a maximum. The existence of a maximum point for SC2þ vs. GHSV can be attributed to the complex interaction between the surface catalytic reactions, the homogeneous gas phase reactions and their different time scales (Chou et al., 2002b). Moreover, presence of inert gas in the feed was simulated under operating conditions corresponding to the complete oxygen consumption. Simulation results presented in Fig. 9 show that at N2 concentration of 0.0–20.0 mol% in the feed, CH4 conversion slightly increases by diluents concentration. The C2+ selectivity increases more than methane conversion when the inert content of the feed is increased. It is generally known that, increasing the diluents encourages the methane coupling reaction while it suppresses deep oxidation reactions (Tye et al., 2002). Further dilution, restricts deep oxidation as well as coupling oxidation reactions confirming that there is an optimal ratio for the feed inert gas in OCM reaction. Operating pressure of the reactor decreases both CH4 conversion and C2+ selectivity as shown in Fig. 10. Simulation results for the selected operating conditions show that increase of total pressure from 0.2 to 0.4 MPa, decreases CH4 conversion from 33.4% to 29.7% and C2+ selectivity from 74.6% to 67.8%. The C2+ yield obtained here are much more than those reported by Chou et al. (2002a) at P = 1.0 MPa. It proves that the pressure has a negative effect on both C2+ selectivity and methane conversion. This
behavior may be attributed to the high contribution of undesired gas phase reactions at higher pressures.
33
76
32
74
31
72
30
70
4.3. Multi objective optimization Having a model to predict the methane conversion and C2+ selectivity as a function of reaction temperature, feed’s CH4/O2 molar ratio, feed’s GHSV and inert contents, it is interesting to implement an optimization method to find the optimum operating conditions. Here, the optimal operating conditions are determined at 0.4 MPa pressure. The optimization problem can be expressed as following: f ðxi Þ ¼ maxðX CH4 %Þ gðxi Þ ¼ maxðSC2þ %Þ
(11)
where xi = T, CH4/O2, GHSV and N2 mol%. For the multi objective optimization problem, the decision variables (operating parameters) are chosen from the corresponding bounds listed in Table 1. The solution and results of multi objective problems are conceptually different from those of single objective functions. In the case of multiple objectives, there will be more than one solution for the problem. The presences of multiple objectives in a problem usually give rise to a family of nondominated or noninferior optimal points, which are known as Pareto optimal solutions. None of the nondominated solutions is superior to the other points while every point can be selected for design or operation. 69.5 69 68.5
29 28
68
XCH4 % 0
5
10
15
20
SC2+%
SC2+%
X CH4 %
68 67.5 67 66.5 66 65.5 25
66
N2 (mole%) Fig. 9. Effect of feed’s N2 mol% on selectivity of C2+ and CH4 conversion (GHSV = 15,750 h1, CH4/O2 = 4, T = 750 8C and P = 0.4 MPa).
65 34.4
34.6
34.8
35.0
35.2
35.4
35.6
35.8
36.0
X CH4 % Fig. 11. Pareto optimal solutions obtained from simultaneous maximization of CH4 conversion and C2+ selectivity for OCM process at 0.4 MPa in which Y C2þ > 23%.
J.S. Ahari et al. / Journal of the Taiwan Institute of Chemical Engineers 42 (2011) 751–759
758 3. 55
(1)
3. 50 3. 45 3. 40
CH4 /O2
3. 35 3. 30 3. 25 3. 20 3. 15 3. 10 34.40
34.60
34.80
35.00
35.20
35.40
35.60
35.80
36.00
X CH4 % 15800
(2)
GHSV (h-1 )
15790 15780 15770 15760 15750 34.40
34.60
34.80
35.00
35.20
35.40
35.60
35.80
36.00
X CH4 % 750
(3)
740 730
T (o C)
720 710 700
Pareto optimal set corresponding to simultaneous maximization of the CH4 conversion and C2+ selectivity were obtained when the C2+ yield is greater than 23%. The optimal set is presented in Fig. 11. It shows that moving from one point to another, one objective function may improve while the other worsens. For example, CH4 conversion can achieve as high as 35.8% with the C2+ selectivity equal to 65.5%, while the C2+ selectivity can be obtained as high as 69.2% having the CH4 conversion of 34.5%. As it is shown in Fig. 12, each point on the pareto set is associated with a set of decision variables. This figure shows that optimal results can be achieved by changing the operating parameters of feed’s methane to oxygen molar ratio and reaction temperature from 3.15 and 675 8C to 3.52 and 716 8C, respectively. However, the feed’s N2 mol% and feed’s GHSV have constant values (20 mol% and 15,790 h1). Additional experiments were carried out in order to validate the optimization results. Comparison of the experimental and predicted values for methane conversion and C2+ selectivity at two different optimum conditions are shown in Table 5. Experimental values corresponding to the selected operating conditions are reported as 33.98% and 35.80% CH4 conversion. Nevertheless, C2+ selectivity of 67.13% and 65.90% were obtained at the same operating conditions. No residual oxygen was detected at the investigated operating conditions, indicating that O2 conversion was 100%. The average relative errors between the predicted and observed values were 1.32% for CH4 conversion and 1.64% for C2+ selectivity. The low deviations from the observed values show that the combination of ANN and HGA can be regarded as a reliable tool for finding the optimum operating conditions within the feasible region. 5. Conclusion
690 680 670 34.40
34.60
34.80
35.00
35.20
35.40
35.60
35.80
36.00
X CH4 % 25
(4)
N2 mole %
20 15 10 5 0 34.40
34.60
34.80
35.00
35.20
X CH4 %
35.40
35.60
35.80
36.00
Fig. 12. Decision variables corresponding to different points on the Pareto set of Fig. 11: (1) feed’s CH4/O2 molar ratio; (2) feed’s GHSV; (3) reaction temperature, (4) feed’s N2 mol%.
Due to techno-economical consideration, it is necessary to perform the OCM reactions under pressures higher than atmospheric pressure in industrial scale reactors. At this early stage of the research on high pressure OCM, gathering reaction data at high pressure levels and development of black box ANN models can be a quick route to obtain the optimum operating conditions and optimum performance of the reaction. Reaction data at the investigated pressures of 0.2, 0.3 and 0.4 MPa over Na–W–Mn/SiO2 catalyst were collected and used to develop ANN models for prediction of C2+ selectivity and CH4 conversion from operating conditions including feed’s composition, GHSV, temperature and pressure. Genetic algorithm was implemented to find the optimum operating conditions and reaction performance. The Pareto optimal solutions show that the optimal results can be achieved by varying the operating parameters of feed’s methane to oxygen molar ratio and reaction temperature from 3.15 and 675 8C to 3.52 and 716 8C, respectively, while the feed’s N2 mol% and feed’s GHSV remain at constant values of 20 mol% and 15,790 h1. The predicted operating conditions were experimentally tested to get the actual CH4 conversion and C2+ selectivity. The good agreement between predicted and observed values demonstrates the power and reliability of the ANN model and Hybrid Genetic Algorithm for optimization of the OCM reaction conditions. It was found that the
Table 5 Comparison of some optimized values and experimental results. Case no.
1 2
Optimal operating conditions
Estimated (%)
results
Experimental results (%)
Relative (%)
error
N2 mol%
CH4/O2
GHSV (h1)
T (8C)
X CH4
SC2þ
X CH4
SC2þ
X CH4
SC2þ
20.00 20.00
3.50 3.25
15,790.00 15,790.00
714.00 675.00
34.64 35.54
69.02 66.29
33.98 35.80
67.13 65.90
1.91 0.73
2.74 0.54
J.S. Ahari et al. / Journal of the Taiwan Institute of Chemical Engineers 42 (2011) 751–759
C2+ yield of 23.6% can be obtained at 0.4 MPa that is the highest reported performance for an OCM catalyst at high pressures. References Abdolahi, F., Y. Mortazavi, A. Khodadadi, R. R. Hudgins, and P. L. Silveston, ‘‘Modeling of Methane Oxidative Coupling Under Periodic Operation by Neural Network,’’ Chem. Eng. Technol., 28, 581 (2005). Chou, L., Y. Cai, B. Zhang, J. Niu, S. Ji, and S. Li, ‘‘Oxidative Coupling of Methane Over Na–Mn–W/SiO2 Catalyst at Higher Pressure,’’ React. Kinet. Catal. Lett., 76, 311 (2002a). Chou, L., Y. Cai, B. Zhang, J. Niu, S. Ji, and S. Li, ‘‘Oxidative Coupling of Methane over Na–W–Mn/SiO2 Catalyst at Elevated Pressures,’’ J. Nat. Gas Chem., 11, 131 (2002b). Chua, Y. T., A. R. Mohamed, and S. Bhatia, ‘‘Process Optimization of Oxidative Coupling of Methane for Ethylene Production Using Response Surface Methodology,’’ J. Chem. Technol. Biotechnol., 82, 81 (2007). Cigizoglu, H. K. and M. Alp, ‘‘Generalized Regression Neural Network in the Modeling River Sediment Yield,’’ Adv. Eng. Soft., 37, 63 (2006). Cigizoglu, H. K. and O. Kisi, ‘‘Flow Prediction by Three Back Propagation Techniques Using K-fold Partitioning of Neural Network Training Data,’’ Nordic. Hydrol., 36, 1 (2005). Daneshpayeh, M., A. Khodadadi, N. Mostoufi, Y. Mortazavi, R. Sotudeh-Gharabagh, and A. Talebizadeh, ‘‘Kinetic Modeling of Oxidative Coupling of Methane over Mn/ Na2WO4/SiO2 Catalyst,’’ Fuel. Process. Technol., 90, 403 (2009). Dittmeyer, R. and H. Hofman, Oxidative Coupling of Methane over a Ce/Li/MgO-Catalyst: Kinetic Analysis and Reactor Simulation, Natural Gas Conversion II, Elsevier Science B.V. (1994). Fang, X., S. Li, J. Gu, and D. Yang, ‘‘Preparation and Characterization of W–Mn Catalyst for Oxidative Coupling of Methane,’’ J. Mol. Catal. (China), 6, 255 (1992a). Fang, X., S. Li, J. Lin, and Y. Chu, ‘‘Oxidative Coupling of Methane on W–Mn Catalysts,’’ J. Mol. Catal. (China), 6, 427 (1992b). Gudla, P. K. and R. Ganguli, ‘‘An Automated Hybrid Genetic-Conjugate Gradient Algorithm for Multimodal Optimization Problems,’’ Appl. Math. Comput., 167, 1457 (2005). Hagan, M. T. and M. B. Menhaj, ‘‘Training Feedforward Technique with the Marquardt Algorithm,’’ IEEE Trans. Neural Netw., 5, 989 (1994). Holland, J., Adaptation in Natural and Artificial Systems, University of Michigan Press (1975). Huang, K., X. L. Zhan, F. Q. Chen, and D. W. Lu, ‘‘Catalyst Design for Methane Oxidative Coupling by Using Artificial Neural Network and Hybrid Genetic Algorithm,’’ Chem. Eng. Sci., 58, 81 (2003). Istadi, I. and N. A. S. Amin, ‘‘Modelling and Optimization of Catalytic-Dielectric Barrier Discharge Plasma Reactor for Methane and Carbon Dioxide Conversion Using Hybrid Artificial Neural Network-Genetic Algorithm Technique,’’ Chem. Eng. Sci., 62, 6568 (2007). Ji, S., T. Xiao, S. Li, C. Xu, R. Hou, K. S. Coleman, and M. L. H. Green, ‘‘The Relationship between the Structure and the Performance of Na–W–Mn/Sio2 Catalysts for the Oxidative Coupling of Methane,’’ Appl. Catal. A, 225, 271 (2002).
759
Kamali Shahri, S. M. and S. M. Alavi, ‘‘Kinetic Studies of the Oxidative Coupling of Methane Over the Mn/Na2WO4/Sio2 Catalyst,’’ J. Nat. Gas Chem., 18, 25 (2009). Keller, G. E. and M. M. Bhasin, ‘‘Synthesis of Ethylene via Oxidative Coupling of Methane. I. Determination of Active Catalysts,’’ J. Catal., 73, 9 (1982). Kumar, K. V., ‘‘Neural Network Prediction of Interfacial Tension at Crystal/Solution Interface,’’ Ind. Eng. Chem. Res., 48, 4160 (2009). Kumar, K. V., K. Porkodi, R. L. A. Rondon, and F. Rocha, ‘‘Neural Network Modeling and Simulation of the Solid/Liquid Activated Carbon Adsorption Process,’’ Ind. Eng. Chem. Res., 47, 486 (2008). Liu, Y., PhD Dissertation, Lanzhou Institute of Chemical Physics, Chinese Academy of Science (1997). Martherne, J. L. and G. L. Culp, Direct Conversion of Methane to C2,s and Liquid Fuels: Process Economics, Methane Conversion by Oxidative Processes Fundamental and Engineering Aspect, Van Nostrand Reinhold (1992). MATLAB help, Version 7.6.0324 (R2008), The Math. Works Inc. (2008). Mehrpooya, M., A. H. Mohammadi, and D. Richon, ‘‘Extension of an Artificial Neural Network Algorithm for Estimating Sulfur Content of Sour Gases at Elevated Temperatures and Pressures,’’ Ind. Eng. Chem. Res., 49, 439 (2010). Nabavi, R., D. Salari, A. Niaei, and M. T. Vakil-Baghmisheh, ‘‘A Neural Network Approach for Prediction of Main Product Yields in Methanol to Olefin Process,’’ Int. J. Chem. React. Eng., 7, A26 (2009). Palermo, A., J. P. H. Vazquez, A. F. Lee, M. S. Tikhov, and R. M. Lambert, ‘‘Critical Influence f the Amorphous Silica-to-Cristobalite Phase Transition on the Performance of Mn/Na2WO4/SiO2 Catalysts for the Oxidative Coupling of Methane,’’ J. Catal., 177, 259 (1998). Pasadakis, N., V. Gaganis, and C. Foteinopoulos, ‘‘Octane Number Prediction for Gasoline Blends,’’ Fuel. Process. Technol., 87, 505 (2006). Research Institute of Petroleum Industry (RIPI) and Japan Oil, Gas and Metals National Corporation (JOGMEC), the final report of the Technical collaboration Project on the Process Development for the OCM Technology (2004). Sadeghzadeh Ahari, J., R. Ahmadi, H. Mikami, K. Inazu, S. Zarrinpashne, S. Suzuki, and K. Aika, ‘‘Application of a Simple Kinetic Model for the Oxidative Coupling of Methane to the Design of Effective Catalysts,’’ Catal. Today, 145, 45 (2009). Saha, B., P. Chowdhury, and A. K. Ghoshal, ‘‘Al-MCM-41 Catalyzed Decomposition of Polypropylene and Hybrid Genetic Algorithm for Kinetic Analysis,’’ Appl. Catal. B, 83, 265 (2008). Tye, C. T., A. R. Mohamed, and S. Bhatia, ‘‘Modeling of Catalytic Reactor for Oxidative Coupling of Methane Using La2O3/Cao Catalyst,’’ Chem. Eng. J., 87, 49 (2002). Wang, J., L. Chou, B. Zhang, H. Song, J. Zhao, J. Yang, and S. Li, ‘‘Comparative Study on Oxidation of Methane to Ethane and Ethylene over Na2WO4–Mn/SiO2 Catalysts Prepared by Different Methods,’’ J. Mol. Catal. A: Chem., 245, 272 (2006). Wang, D. J., M. P. Rosynek, and J. H. Lunsford, ‘‘Oxidative Coupling of Methane Over Oxide Supported Sodium-Manganese Catalysts,’’ J. Catal., 155, 390 (1995).
Further reading (with label) Tarca, L. A., B. P. A. Grandjean, and F. Larachi, ‘‘Integrated Genetic Algorithm-Artificial Neural Network Strategy For Modeling Important Multi Phase-Flow Characteristics,’’ Ind. Eng. Chem. Res., 41, 2543 (2002).
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Journal of the Taiwan Institute of Chemical Engineers journal homepage: www.elsevier.com/locate/jtice
Optimization of OCM reaction conditions over Na–W–Mn/SiO2 catalyst at elevated pressure Jafar Sadeghzadeh Ahari a,b, Mohammad T. Sadeghi a,*, Saeed Zarrin Pashne b a b
Process Simulation and Control Laboratory, Chemical Engineering College, Iran University of Science and Technology (IUST), Narmak 16765-163, Tehran, Iran Gas Research Division - Research Institute of Petroleum Industry (RIPI), P.O. Box 14665-137, Tehran, Iran
A R T I C L E I N F O
A B S T R A C T
Article history: Received 9 October 2010 Received in revised form 11 February 2011 Accepted 28 February 2011 Available online 5 April 2011
Performance of the oxidative coupling of methane (OCM) at elevated pressures has been simulated by a set of supervised Artificial Neural Network (ANN) models using reaction data gathered in a microreactor device. Accuracy of the developed models were evaluated by comparing the predicted results with the test data set showing a good agreement. In order to enhance the performance of OCM process at 0.4 MPa as a desired operating pressure for commercial application of OCM, the Hybrid Genetic Algorithm (HGA) was used to obtain the optimal values of the operating conditions. Nondominated Pareto optimal solutions were obtained and additional experiments were carried out at two different optimum conditions in order to verify the optimums. The results show that combination of ANN models with HGA could be used in finding the suitable operating conditions for OCM process at elevated pressures. It was shown that the C2+ yield of above 23% can be achieved at 0.4 MPa by using Na–W–Mn/SiO2 as the OCM catalyst. ß 2011 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
Keywords: OCM Catalyst Elevated pressure Optimization Artificial Neural Network (ANN) Hybrid Genetic Algorithm (HGA)
1. Introduction Catalytic oxidative coupling of methane (OCM) converting it to higher hydrocarbons is one of the most attractive methods to utilize natural gas as chemical feedstock. It is commonly accepted that this reaction proceeds through a radical mechanism. Therefore, the initiating step is the generation of methyl radicals caused by hydrogen abstraction from methane at particular active sites on the catalyst surface. These radicals can be released into the gas phase where then undergo a variety of reactions producing desired C2+ hydrocarbons as well as undesired carbon oxides. Moreover, deep oxidation of the hydrocarbon products may occur at the catalyst surface (Dittmeyer and Hofman, 1994). After the pioneer work by Keller and Bhasin (1982), there have been extensive research and development efforts in the OCM process. A wide variety of catalysts have been used for OCM process. One of the most effective catalysts for the OCM is Na–W– Mn/SiO2 catalyst, which was firstly reported by Fang et al. (1992a,b). Due to its excellent performance, the catalyst has been extensively studied by several researchers (Chou et al., 2002a; Chua et al., 2007; Ji et al., 2002; Liu, 1997; Palermo et al., 1998; Sadeghzadeh Ahari et al., 2009; Wang et al., 1995; Wang et al., 2006).
* Corresponding author. Fax: +98 21 77240495. E-mail address: [email protected] (M.T. Sadeghi).
Considering commercial and technical limitation, it is necessary to make the OCM reactor size as small as possible. This can be achieved by operating the reactor at pressures higher than atmospheric. On the other hand, higher pressure will lead to a drop in C2+ selectivity and yield, i.e. higher pressures will facilitate undesired total oxidation reactions. Among the earliest economic studies on commercialization of OCM based processes by Union Carbide in 1992 (Martherne and Culp, 1992) it had been assumed that the reactor pressure could increase up to 0.44 MPa without a major impact on C2+ yield of the reaction per pass. In a more recent feasibility study by RIPI and JOGNEC (2004) it has been found that the plant cost index reaches its minimum value if the reactor operate at 0.4 MPa pressure, assuming the catalyst performance does not change by increasing the pressure to 0.4 MPa. In order to reach a more reliable result however, it is necessary to know the behavior of the OCM catalyst (or reaction) at higher pressures, a subject that has not been much investigated yet. In the case of Na–W–Mn/SiO2 catalyst most of the reported kinetic models in the literatures (Daneshpayeh et al., 2009; Kamali Shahri and Alavi, 2009), were based on reaction data gathered at atmospheric total pressure. Chou and coworkers (2002) have studied the OCM reactions on Na–Mn–W/SiO2 catalyst at pressure levels of 0.6–2 MPa using undiluted CH4/O2 feed (CH4/O2 range of 6–10 and very high GHSV values of 1–2 105 h1). They have succeeded to obtain the maximum C2+ yield of near 14% at 1.0 MPa and 750 8C. This performance figure is much lower than that of atmospheric pressure (yield of near 30% have been reported for the
1876-1070/$ – see front matter ß 2011 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.jtice.2011.02.005
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J.S. Ahari et al. / Journal of the Taiwan Institute of Chemical Engineers 42 (2011) 751–759
same type of catalyst at atmospheric pressure). Their finding may suggest that working at pressure near 1.0 MPa is not commercially attractive due to the low C2+ yield achieved. The lack of suitable kinetic models for the OCM reactions at elevated pressures makes the conventional modeling methods not suitable for this system. However, the problem can be overcome by using nonlinear calculation methods such as Artificial Neural Network (ANN). ANNs are useful modeling tools particularly if there exist pertinent wide range of data sets or data bank of some input variables and output performance characteristic figures. Moreover, the ANN models have been used increasingly in various aspects of science and engineering due to its ability in modeling both linear and nonlinear problems without any assumption. In chemical engineering, ANNs are used to predict the product yield in methanol to olefin process (Nabavi et al., 2009), octane number (Pasadakis et al., 2006), sulfur content of sour gases (Mehrpooya et al., 2010), kinetics of solid/liquid sorption system (Kumar et al., 2008) and interfacial tension at catalyst/liquid interface (Kumar, 2009). In the field of OCM process, Abdolahi et al. (2005) used a neural network for prediction of CH4 conversion, ethylene and C2+ selectivity on the periodic operation of OCM process over Ce/Li/ MgO catalyst. The combination of ANN and genetic algorithm (GA) has been used for integrated process modeling and optimization. A hybrid GA with ANN was also used by Huang et al. (2003) to design optimal catalyst and operating conditions in the OCM process. Recently, Istadi and Amin (2007) used this technique for modeling and optimization of catalytic dielectric barrier discharge plasma reactor for CO2-OCM process.
Nevertheless, there is no report addressing modeling and optimization of OCM reactions at elevated pressures. Thereupon, in the present work an ANN model is suggested for modeling the isothermal bed reactor at elevated pressures. In addition, in order to obtain pareto optimal solutions, the GA multi objective optimization algorithm is applied for maximization of CH4 conversion and C2+ selectivity simultaneously. Finally, additional experiments have been carried out in order to validate some optimization results. 2. The experimental work 2.1. Catalyst preparation The SiO2 ingredient was first prepared by the coprecipitation method. Calculated amounts of sodium silicate (Na2SiO4, supplied by MERCK with purity >98%) and sulfuric acid (H2SO4, supplied by MERCK with purity >95%) were added slowly to a well-stirred container which is containing 400 ml of distilled water at 80 8C. During the procedure, pH and temperature of the precipitating solution were kept around 8 and 80 8C respectively. The mixture was further aged at 80 8C for 1 h. After filtration and washing with distillated water, the obtained solid was dried in air at ambient temperature for 24 h and then heated up to 100 8C for 1 day. Next, it was calcined in air for 5 h at 450 8C. The Na–W–Mn/SiO2 catalyst was prepared via two-step incipient wetness impregnation method. The prepared SiO2 support was impregnated with aqueous solution in appropriate concentration of Mn(NO3)26H2O (MERCK, >98%), evaporated to dryness and dried in air at ambient temperature for 24 h and then
Fig. 1. Schematic diagram of the experimental setup.
J.S. Ahari et al. / Journal of the Taiwan Institute of Chemical Engineers 42 (2011) 751–759
100 8C for 1 day. An aqueous solution of Na2WO42H2O (MERCK, 98%) was added to the prepared material followed by drying similar to the previous step. The prepared catalyst was calcined in air at 850 8C for 15 h and the resulting powder was pelletized, crushed and sieved to 30–35 mesh. Results of Atomic Absorption Spectrophotometry (AAS) (AAnalyst 200) and Inductively Coupled Plasma (ICP) (Wear Metal Analyzer-Plasma 400) analysis, show that the wt% of components in prepared catalyst are 1.4 wt% Na–2.1 wt% W–1.5 wt% Mn/SiO2. 2.2. Experimental setup The experimental setup used in this work is depicted in Fig. 1. The catalyst performance was evaluated in a quartz fixed-bed micro reactor (ID = 10 mm). An amount of 0.4 g catalyst is placed at the hottest part of the reactor heated by an electrical furnace. The remaining space of the reactor was filled with quartz chips (20– 25 mesh) to minimize any gas phase reaction contribution. A Ktype thermocouple was positioned at the hottest part of the reactor to indicate the temperature of the catalyst bed. The reactant gases consisted of CH4 (99.99%), O2 (99.99%) and N2 (99.99%), were cofed into the reactor and their flow rates were controlled by mass flow controllers (BROOKS, 5850TR). The dried effluent gas flow rate was measured by a bubble flowmeter. The reactor effluent gases, after removing water by condensation at 5 8C were analyzed by an online gas chromatograph equipped with thermal conductivity detector detecting O2, N2, CH4, CO, CO2, C2H4 and C2H6. Furthermore, flame ionization detector was used for detecting the higher hydrocarbons. The carbon balance errors across the reactor and during the tests were between 2% and 5%. The pressure of the system was controlled using a pressure controller valve that contains a built in pressure sensor (BROOKS, 5866). Since the reactor is made from quartz, the operating pressure was not increased beyond 0.4 MPa due to safety concerns. The CH4 conversion, selectivity and yield of product hydrocarbons are calculated using the following equations: X CH4 % ¼
moles of CH4 converted 100 ðmoles of CH4 Þfeed
(1)
Y C2þ % ¼ X CH4 SC2þ 100
Variable
Range
T (8C)
720–775a 700–750b 675–750c 12,765, 14,285, 15,790 3.15, 4.0, 6.0 0.0, 10.0, 20.0
b c
P = 0.2 MPa. P = 0.3 MPa. P = 0.4 MPa.
(a) Determination of transfer function type (sigmoid, hyperbolical tangent or linear) in each layer. (b) Determination of the number of hidden layers and nodes.
Xn ¼
Table 1 Experimental data ranges used in this study for development of ANN models.
a
The function of a neural network is often compared with the human or animal brain that is made of a large number of neurons. Similarly, an Artificial Neural Network is made of a number of simple processors (nodes) linked by weighted connections. As with the brain neuron, each receptor receives input from various other nodes and generates a scalar output signal that is distributed as input to other processing nodes. Several neural network architectures have been developed over the past years. One of the most popular and powerful architectures is the multi layer perceptron (MLP). The MLP neural networks are feed forward networks consisting number of layers of nodes. There are an input layer, an output layer and one or more hidden layers between the input and output layers. The number of nodes in the input and output layers represent effectively the number of variables used in the prediction and the number of variables to be predicted. However, appropriate number of hidden layers and their nodes cannot be known in advance but are normally set through trial and error. Each node in a certain layer is connected to every single node in the next layer via links with an appropriate and adjustable connection weight. A node receives incoming signals from each node in the previous layer. The effective incoming signal to each node is the weighted sum of all the incoming signals and the node threshold or bias value. The effective incoming signal is passed through a nonlinear operation function to produce the outgoing signal of the node. The two main steps involved in the ANN model development are: Step 1: The network architecture selection including
(3)
Overall range of the operating condition used in this work for developing the ANN models are summarized in Table 1.
Feed’s GHSV (h1) Feed’s CH4/O2 molar ratio Feed’s N2 mol%
3.1. Artificial Neural Network
(2)
products
n2
3. Predictive modeling and optimization methods
Step 2: Validation of the model The network architecture is determined by trial and error during the training phase while validation of the model is performed via evaluation of the model performance by using the test data. In order to achieve a fast convergence, it is useful to normalize the input and target values before the training so that they stand within a specified range. Using the following formula the experimental data were normalized into the range of 1 to 1:
P nðmoles of Cn hydrocarbonsÞproducts SC2þ % ¼ moles of CO þ moles of CO2 P þ nðmoles of Cn hydrocarbonsÞ 100;
753
2ðX X min Þ 1 X max X min
(4)
in which, Xmin and Xmax are the minimum and maximum values of the raw data, respectively. Normalizing the data, they were randomly divided in two subsets: training set (70% of total data at each investigated pressure) and test set (30% of total data at each investigated pressure). The training set was used to estimate the neural network’s parameters and the test set to validate the networks. During the training or learning phase, the network parameters (weights and biases) are optimized in a way that the error between the measured and estimated output is minimized. The most popular training algorithm for minimizing the error function for a MLP neural network is the standard back propagation (BP) technique. This technique includes four stages: (1) randomly initialization of all weights and biases; (2) feed forward of the input training pattern; (3) calculation and BP of the associated error, and
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(4) weights and biases adjustment. This procedure is repeated until the error between the predictive and target values is minimized. There are several different BP training algorithms. In this work, the Levenberg-Marquardt algorithm was used for training of the network due to its rapid convergence (Cigizoglu and Alp, 2006; Cigizoglu and Kisi, 2005; Hagan and Menhaj, 1994; Istadi and Amin, 2007). 3.2. Genetic algorithm Several local and global optimization algorithms have been used for optimization problems. In general, local optimization algorithms (LOA) have the advantage of solving the problem quickly, though their results are very much dependent to the initial starting point. Therefore, they can be easily trapped in a local optimum. On the other hand, global optimization algorithms (GOA) such as genetic algorithm (GA) are necessary to find the global optimum in optimization problems containing many local optimums. The algorithm was suggested by Holland in 1975 based on Darwin’s theory of evolution. Essentially, the GA approach starts with a set of trial solution (called population) and then the final solution evolves iteratively by applying some genetic operators (e.g. selection, cross over and mutation). Based on the GA ability to reach global optimum, it has been extensively applied in many engineering fields. It can find the region of the optimal value quickly and this is a notable characteristic of the algorithm. However, the ability of accurate search in this region is not satisfactory for complex systems. Therefore, GA is often hybridized with LOA to improve its performance as a global optimization technique. Some possible hybridizations using LOA are pre-hybridization, organic-hybridization and post-hybridization (Gudla and Ganguli, 2005; Saha et al., 2008). In this work, the post-hybridization method is used for multi objective optimization. MATLAB GA optimization toolbox (Version 7.6.0324) was employed using the function ‘‘fgoalattain’’ as the hybrid local search method (The Math. Works Inc., 2008). It takes the final solution from GA as its initial point. 4. Results and discussion 4.1. Predictive modeling with ANN It is known from experience that the lower reactor pressures will lead to higher C2+ yields. On the other hand, an optimum operating pressure, requires incorporation of technical and economical variables into the problem that is beyond the scope of this study. Different ANN models were developed for each level of operating pressure (i.e. 0.2, 0.3 and 0.4 MPa). In order to reduce
the time consuming trial and error steps for suitable numbers of hidden layer and nodes and to increase the accuracy of the models, separate networks for prediction of methane conversion (X CH4 ) and C2+ selectivity (SC2þ ) are developed. The input variables for each network were include: the reaction temperature, feed’s methane to oxygen molar ratio, feed’s GHSV and feed’s N2 molar percent. Different feed forward MLP neural networks were constructed using BP algorithm and trained by the neural network toolbox of the MATLAB software package version 7.6.0324 (R2008). Performances of the networks were evaluated using statistical and graphical criteria. The statistical criteria include correlation coefficient (R2), mean square error (MSE) and average absolute relative error (AARE). The statistic R2, measures linear correlation between the actual and predicted values. The MSE and AARE were used to quantify the error between observed and predicted values. Pn ðX X cal Þ2 R2 ¼ 1 Pi¼1 obs n ¯ 2 i¼1 ðX obs Xcal Þ
MSE ¼
(5)
n 1X ðX X cal Þ2 n h¼1 obs
AARE ¼
(6)
1 XX obs X cal X 100 n obs
(7)
where n is the number of data points, X¯ is the average of X over the n samples. Xobs and Xcal are the actual and predicted values, respectively. The optimal value for R2 was equal to 1.0 whereas for MSE and AARE was equal to 0.0. In the graphical criterion, the data pairs of xi,obs and xi,cal are shown in the Xobs vs. Xcal plane. Judgment on the goodness of training and testing phases can be made based on the closeness of all data pairs to the line Xobs = Xcal (called the first bisectrix). The final networks were selected based on the lowest errors (MSE and AARE) and highest R2 value on training and test sets of data. The results are presented in Table 2. According to the results listed in Table 2, the final networks for prediction of CH4 conversion and C2+ selectivity at each investigated reacting pressure are as follows: For all investigated pressures, the C2+ selectivity network consists of one input layer with four nodes, one hidden layer with six nodes and one output layer with one node (Fig. 2). The activation function used for the hidden layer is sigmoid type (Eq. (8)) while it is of linear type (Eq. (9)) for the output layer.
Table 2 Statistical results and details of the neural network models used for prediction of X CH4 % and SC2þ % at investigated reaction pressures. P = 0.2 MPa
No. of hidden layer No. of nodes Type of transfer function R2 (Train) MSE (Train) AARE%(Train) R2 (Test) MSE (Test) AARE% (Test)
P = 0.3 MPa
P = 0.4 MPa
SC2þ %
X CH4 %
SC2þ %
X CH4 %
SC2þ %
X CH4 %
1 4-6-1 logsig-purelin 0.929 1.78 1.488 0.942 1.86 1.657
2 4-6-2-1 tansig-tansig-purelin 0.995 0.867 7.712 0.989 2.429 13.754
1 4-6-1 logsig-purelin 0.988 0.668 0.711 0.893 6.896 3.134
2 4-7-3-1 tansig-tansig-purelin 1 0.008 0.225 0.948 11.07 19.86
1 4-6-1 logsig-purelin 0.994 0.272 0.612 0.976 0.861 1.05
2 4-6-2-1 tansig-tansig-purelin 1 0.006 0.237 0.998 0.209 1.479
Total number of weights and bias adjusted during the training period is 37, 47 and 63 for the 4-6-1, 4-6-2-1 and 4-7-3-1 networks, respectively. tansig: f(x) = (1 ex)/(1 + ex); logsig: f(x) = 1/(1 + ex); purelin: f(x) = x.
J.S. Ahari et al. / Journal of the Taiwan Institute of Chemical Engineers 42 (2011) 751–759
755
Table 4 Bias and weights of the C2+ selectivity network at 0.4 MPa.
Fig. 2. Architecture of the neural network model used for prediction of SC2þ % at all of the investigated pressures.
1 1 þ ex
k
bk
1 2 3 4 5 6
5.6548 8.7851 0.4085 5.3775 18.2831 0.2401
1
2.2249
wij
1
2
3
4
1 2 3 4 5 6
5.6623 13.0869 5.7371 5.0728 2.2146 0.9206
1.3756 0.3800 3.9534 4.7809 3.2239 0.0618
7.2411 0.9592 3.5057 0.3336 2.0586 0.1198
0.1046 9.6449 6.7477 0.1757 15.4472 0.0191
wij
1
2
3
4
5
6
1
0.2970
1.2498
0.0551
2.2587
7.0653
4.0093
(8)
f ðxÞ ¼ x
(9)
For reaction pressures of 0.2 and 0.4 MPa, the CH4 conversion network consists of one input layer with 4 nodes, two hidden layers with six and two nodes respectively, and one output layer with one node. The activation function used for the hidden layers and output layers are hyperbolic tangent (Eq. (10)) and linear function, respectively. In the network used for prediction of CH4 conversion at reaction pressure of 0.3 MPa, the hidden layers have seven and three nodes.
f ðxÞ ¼
bj
1 ex 1 þ ex
(10)
As mentioned above, during the training phase the network parameters (weight and biases) are determined for each model. In order to be concise, the parameters of all developed models are not presented here. The weight and bias values of each layer for methane conversion and C2+ selectivity networks at 0.4 MPa are shown in Tables 3 and 4. Figs. 3–5 show the testing results for the final ANN models to estimate the CH4 conversion and C2+ selectivity at each investigated pressure. The parity plots show that for both parameters, the
predictive capability is satisfactory and data points are well concentrated around the first bisectrix. Results of the statistical and graphical criteria, confirm that the developed ANN models are suitable for prediction of CH4 conversion and C2+ selectivity of OCM process at investigated pressures. 4.2. Effects of operating parameters Effects of process variables on the performance of OCM with Na–W–Mn/SiO2 catalyst at elevated pressures were investigated using the ANN models. Simulations were carried out by varying one parameter while the others were kept constant.
40
(1)
35 30
X CH4 % (Cal)
f ðxÞ ¼
j
25 20 15
10
Table 3 Bias and weights of the methane conversion network at 0.4 MPa.
5
j
bj
k
bk
l
bl
1 2 3 4 5 6
1.9581 0.5607 1.2972 0.2590 5.7948 3.0097
1 2
1.7045 0.7044
1
1.1107
0 0
5
10
15
20
25
30
35
40
X CH4 % (Obs) 80
(2)
1
2
3
4
1 2 3 4 5 6
2.2272 2.2244 3.8495 0.4493 0.7259 1.2996
2.1889 1.5241 1.7432 1.0740 0.6185 2.6913
0.1811 1.1355 0.5784 1.5847 0.5221 0.1885
0.0188 0.1244 0.0096 6.1249 5.0198 0.1610
wij
1
2
3
4
5
6
1 2
0.9905 0.0301
0.1447 0.1179
0.1438 2.8829
0.0037 0.4337
0.0322 4.3413
0.0970 1.1219
wij
1
2
1
1.6211
2.9295
SC2+% (Cal)
75
wij
70 65 60
55 55
60
65
70
75
80
SC2+% (Obs) Fig. 3. Comparison between the actual test data set and ANN predictions for (1) CH4 conversion, (2) C2+ selectivity at 0.2 MPa.
J.S. Ahari et al. / Journal of the Taiwan Institute of Chemical Engineers 42 (2011) 751–759
756
40
(1)
35
80
30
70
20
60
20 15 10
10
0
50
XCH4%
5
SC2+%
25
X CH4 %
X CH4 % (Cal)
30
40
SC2+%
0
5
10
15
20
25
30
35
0 660
40
X CH4 % (Obs) 75
68 0
70 0
72 0
40 76 0
74 0
T (o C) Fig. 6. Effect of temperature on selectivity of C2+ and CH4 conversion (N2 = 0%, GHSV = 15,750 h1, CH4/O2 = 6 and P = 0.4 MPa).
(2)
SC2+% (Cal)
70
65 60 55
50
50
55
60
65
70
75
SC2+% (Obs) Fig. 4. Comparison between the actual test data set and ANN predictions for (1) CH4 conversion, (2) C2+ selectivity at 0.3 MPa.
40
(1)
35
X CH4 % (Cal)
30 25 20 15 10 5 0
0
10
20
30
The influence of reaction temperature on the CH4 conversion and C2+ selectivity are presented in Fig. 6. It can be seen that at the temperature range from 675 to 750 8C, the CH4 conversion and C2+ selectivity are increased by temperature up to 720 8C. Since increase of temperature enhances the reaction completion, the process performance improves. The parameters remain almost constant by increasing the temperature beyond 720 8C. This behavior can be explained by the fact that at about 720 8C, oxygen conversion reaches its maximum value of 100%. Further increase in temperature does not affect the methane conversion and C2+ selectivity since undesired consecutive oxidation reactions of the produced reactants cannot occur in the oxygen depleted medium. This is an interesting result showing that the finest temperature of the OCM reactions decreases significantly by increasing the reaction pressure. The effect of feed’s methane to oxygen molar ratio on the OCM performance at elevated pressure was investigated under the operating conditions where oxygen is completely consumed. Fig. 7 shows that increasing the methane to oxygen ratio, decreases the methane conversion while the selectivity of C2+ products increases. The results demonstrate that under the oxygen-rich atmosphere, the produced C2+ hydrocarbons can be more easily converted to COx. According to Eq. (3) the C2+ yield is product of methane conversion multiplied by C2+ selectivity. Therefore, C2+ yield is decreased with increase of methane to oxygen molar ratio (22.4% at CH4/O2 = 3.2 and 16.4% at CH4/O2 = 6.0).
40
X CH4 % (Obs) 75
80
30
75
60
20
70
10
55
SC2+%
65
X CH4 %
SC2+% (Cal)
70
50
40
(2)
65
XCH4% SC2+%
50
55
60
65
70
75
SC2+% (Obs) Fig. 5. Comparison between the actual test data set and ANN predictions for (1) CH4 conversion, (2) C2+ selectivity at 0.4 MPa.
0
2
3
4
5
6
7
60
CH4 /O2 Fig. 7. Effect of molar ratio of methane to oxygen in feed, on selectivity of C2+ and CH4 conversion (N2 = 0%, GHSV = 15,750 h1, T = 750 8C and P = 0.4 MPa).
J.S. Ahari et al. / Journal of the Taiwan Institute of Chemical Engineers 42 (2011) 751–759
77
36
76
24
73
22
X CH4 %
74
SC2+%
23
72 21
XCH4%
1300 0
1350 0
1400 0
GHSV
1450 0
1500 0
1550 0
73 71 30
70 1600 0
75
32
69
71
SC2+% 20 12500
SC2+%
34
75
X CH4 %
77 XCH4%
SC2+%
25
757
28 0.1
0.15
0.2
(h-1 )
0.25
0.3
0.35
0.4
67 0.5
0.45
P (MPa)
Fig. 8. Effect of feed’s GHSV on selectivity of C2+ and CH4 conversion (N2 = 0%, CH4/O2 = 6, T = 750 8C and P = 0.4 MPa).
Fig. 10. Effect of pressure on selectivity of C2+ and CH4 conversion (GHSV = 15,750 h1, CH4/O2 = 4, T = 750 8C, N2 = 0% and XO2 = 100%).
Fig. 8 shows the variation of methane conversion and C2+ selectivity under 0.4 MPa, CH4/O2 = 6.0, T = 750 8C and N2 = 0.0 mol% as a function of feed’s GHSV. The investigated operating conditions correspond to the total oxygen consumption. It can be seen that methane conversion decreases slightly with increasing of GHSV while C2+ selectivity passes a maximum. The existence of a maximum point for SC2þ vs. GHSV can be attributed to the complex interaction between the surface catalytic reactions, the homogeneous gas phase reactions and their different time scales (Chou et al., 2002b). Moreover, presence of inert gas in the feed was simulated under operating conditions corresponding to the complete oxygen consumption. Simulation results presented in Fig. 9 show that at N2 concentration of 0.0–20.0 mol% in the feed, CH4 conversion slightly increases by diluents concentration. The C2+ selectivity increases more than methane conversion when the inert content of the feed is increased. It is generally known that, increasing the diluents encourages the methane coupling reaction while it suppresses deep oxidation reactions (Tye et al., 2002). Further dilution, restricts deep oxidation as well as coupling oxidation reactions confirming that there is an optimal ratio for the feed inert gas in OCM reaction. Operating pressure of the reactor decreases both CH4 conversion and C2+ selectivity as shown in Fig. 10. Simulation results for the selected operating conditions show that increase of total pressure from 0.2 to 0.4 MPa, decreases CH4 conversion from 33.4% to 29.7% and C2+ selectivity from 74.6% to 67.8%. The C2+ yield obtained here are much more than those reported by Chou et al. (2002a) at P = 1.0 MPa. It proves that the pressure has a negative effect on both C2+ selectivity and methane conversion. This
behavior may be attributed to the high contribution of undesired gas phase reactions at higher pressures.
33
76
32
74
31
72
30
70
4.3. Multi objective optimization Having a model to predict the methane conversion and C2+ selectivity as a function of reaction temperature, feed’s CH4/O2 molar ratio, feed’s GHSV and inert contents, it is interesting to implement an optimization method to find the optimum operating conditions. Here, the optimal operating conditions are determined at 0.4 MPa pressure. The optimization problem can be expressed as following: f ðxi Þ ¼ maxðX CH4 %Þ gðxi Þ ¼ maxðSC2þ %Þ
(11)
where xi = T, CH4/O2, GHSV and N2 mol%. For the multi objective optimization problem, the decision variables (operating parameters) are chosen from the corresponding bounds listed in Table 1. The solution and results of multi objective problems are conceptually different from those of single objective functions. In the case of multiple objectives, there will be more than one solution for the problem. The presences of multiple objectives in a problem usually give rise to a family of nondominated or noninferior optimal points, which are known as Pareto optimal solutions. None of the nondominated solutions is superior to the other points while every point can be selected for design or operation. 69.5 69 68.5
29 28
68
XCH4 % 0
5
10
15
20
SC2+%
SC2+%
X CH4 %
68 67.5 67 66.5 66 65.5 25
66
N2 (mole%) Fig. 9. Effect of feed’s N2 mol% on selectivity of C2+ and CH4 conversion (GHSV = 15,750 h1, CH4/O2 = 4, T = 750 8C and P = 0.4 MPa).
65 34.4
34.6
34.8
35.0
35.2
35.4
35.6
35.8
36.0
X CH4 % Fig. 11. Pareto optimal solutions obtained from simultaneous maximization of CH4 conversion and C2+ selectivity for OCM process at 0.4 MPa in which Y C2þ > 23%.
J.S. Ahari et al. / Journal of the Taiwan Institute of Chemical Engineers 42 (2011) 751–759
758 3. 55
(1)
3. 50 3. 45 3. 40
CH4 /O2
3. 35 3. 30 3. 25 3. 20 3. 15 3. 10 34.40
34.60
34.80
35.00
35.20
35.40
35.60
35.80
36.00
X CH4 % 15800
(2)
GHSV (h-1 )
15790 15780 15770 15760 15750 34.40
34.60
34.80
35.00
35.20
35.40
35.60
35.80
36.00
X CH4 % 750
(3)
740 730
T (o C)
720 710 700
Pareto optimal set corresponding to simultaneous maximization of the CH4 conversion and C2+ selectivity were obtained when the C2+ yield is greater than 23%. The optimal set is presented in Fig. 11. It shows that moving from one point to another, one objective function may improve while the other worsens. For example, CH4 conversion can achieve as high as 35.8% with the C2+ selectivity equal to 65.5%, while the C2+ selectivity can be obtained as high as 69.2% having the CH4 conversion of 34.5%. As it is shown in Fig. 12, each point on the pareto set is associated with a set of decision variables. This figure shows that optimal results can be achieved by changing the operating parameters of feed’s methane to oxygen molar ratio and reaction temperature from 3.15 and 675 8C to 3.52 and 716 8C, respectively. However, the feed’s N2 mol% and feed’s GHSV have constant values (20 mol% and 15,790 h1). Additional experiments were carried out in order to validate the optimization results. Comparison of the experimental and predicted values for methane conversion and C2+ selectivity at two different optimum conditions are shown in Table 5. Experimental values corresponding to the selected operating conditions are reported as 33.98% and 35.80% CH4 conversion. Nevertheless, C2+ selectivity of 67.13% and 65.90% were obtained at the same operating conditions. No residual oxygen was detected at the investigated operating conditions, indicating that O2 conversion was 100%. The average relative errors between the predicted and observed values were 1.32% for CH4 conversion and 1.64% for C2+ selectivity. The low deviations from the observed values show that the combination of ANN and HGA can be regarded as a reliable tool for finding the optimum operating conditions within the feasible region. 5. Conclusion
690 680 670 34.40
34.60
34.80
35.00
35.20
35.40
35.60
35.80
36.00
X CH4 % 25
(4)
N2 mole %
20 15 10 5 0 34.40
34.60
34.80
35.00
35.20
X CH4 %
35.40
35.60
35.80
36.00
Fig. 12. Decision variables corresponding to different points on the Pareto set of Fig. 11: (1) feed’s CH4/O2 molar ratio; (2) feed’s GHSV; (3) reaction temperature, (4) feed’s N2 mol%.
Due to techno-economical consideration, it is necessary to perform the OCM reactions under pressures higher than atmospheric pressure in industrial scale reactors. At this early stage of the research on high pressure OCM, gathering reaction data at high pressure levels and development of black box ANN models can be a quick route to obtain the optimum operating conditions and optimum performance of the reaction. Reaction data at the investigated pressures of 0.2, 0.3 and 0.4 MPa over Na–W–Mn/SiO2 catalyst were collected and used to develop ANN models for prediction of C2+ selectivity and CH4 conversion from operating conditions including feed’s composition, GHSV, temperature and pressure. Genetic algorithm was implemented to find the optimum operating conditions and reaction performance. The Pareto optimal solutions show that the optimal results can be achieved by varying the operating parameters of feed’s methane to oxygen molar ratio and reaction temperature from 3.15 and 675 8C to 3.52 and 716 8C, respectively, while the feed’s N2 mol% and feed’s GHSV remain at constant values of 20 mol% and 15,790 h1. The predicted operating conditions were experimentally tested to get the actual CH4 conversion and C2+ selectivity. The good agreement between predicted and observed values demonstrates the power and reliability of the ANN model and Hybrid Genetic Algorithm for optimization of the OCM reaction conditions. It was found that the
Table 5 Comparison of some optimized values and experimental results. Case no.
1 2
Optimal operating conditions
Estimated (%)
results
Experimental results (%)
Relative (%)
error
N2 mol%
CH4/O2
GHSV (h1)
T (8C)
X CH4
SC2þ
X CH4
SC2þ
X CH4
SC2þ
20.00 20.00
3.50 3.25
15,790.00 15,790.00
714.00 675.00
34.64 35.54
69.02 66.29
33.98 35.80
67.13 65.90
1.91 0.73
2.74 0.54
J.S. Ahari et al. / Journal of the Taiwan Institute of Chemical Engineers 42 (2011) 751–759
C2+ yield of 23.6% can be obtained at 0.4 MPa that is the highest reported performance for an OCM catalyst at high pressures. References Abdolahi, F., Y. Mortazavi, A. Khodadadi, R. R. Hudgins, and P. L. Silveston, ‘‘Modeling of Methane Oxidative Coupling Under Periodic Operation by Neural Network,’’ Chem. Eng. Technol., 28, 581 (2005). Chou, L., Y. Cai, B. Zhang, J. Niu, S. Ji, and S. Li, ‘‘Oxidative Coupling of Methane Over Na–Mn–W/SiO2 Catalyst at Higher Pressure,’’ React. Kinet. Catal. Lett., 76, 311 (2002a). Chou, L., Y. Cai, B. Zhang, J. Niu, S. Ji, and S. Li, ‘‘Oxidative Coupling of Methane over Na–W–Mn/SiO2 Catalyst at Elevated Pressures,’’ J. Nat. Gas Chem., 11, 131 (2002b). Chua, Y. T., A. R. Mohamed, and S. Bhatia, ‘‘Process Optimization of Oxidative Coupling of Methane for Ethylene Production Using Response Surface Methodology,’’ J. Chem. Technol. Biotechnol., 82, 81 (2007). Cigizoglu, H. K. and M. Alp, ‘‘Generalized Regression Neural Network in the Modeling River Sediment Yield,’’ Adv. Eng. Soft., 37, 63 (2006). Cigizoglu, H. K. and O. Kisi, ‘‘Flow Prediction by Three Back Propagation Techniques Using K-fold Partitioning of Neural Network Training Data,’’ Nordic. Hydrol., 36, 1 (2005). Daneshpayeh, M., A. Khodadadi, N. Mostoufi, Y. Mortazavi, R. Sotudeh-Gharabagh, and A. Talebizadeh, ‘‘Kinetic Modeling of Oxidative Coupling of Methane over Mn/ Na2WO4/SiO2 Catalyst,’’ Fuel. Process. Technol., 90, 403 (2009). Dittmeyer, R. and H. Hofman, Oxidative Coupling of Methane over a Ce/Li/MgO-Catalyst: Kinetic Analysis and Reactor Simulation, Natural Gas Conversion II, Elsevier Science B.V. (1994). Fang, X., S. Li, J. Gu, and D. Yang, ‘‘Preparation and Characterization of W–Mn Catalyst for Oxidative Coupling of Methane,’’ J. Mol. Catal. (China), 6, 255 (1992a). Fang, X., S. Li, J. Lin, and Y. Chu, ‘‘Oxidative Coupling of Methane on W–Mn Catalysts,’’ J. Mol. Catal. (China), 6, 427 (1992b). Gudla, P. K. and R. Ganguli, ‘‘An Automated Hybrid Genetic-Conjugate Gradient Algorithm for Multimodal Optimization Problems,’’ Appl. Math. Comput., 167, 1457 (2005). Hagan, M. T. and M. B. Menhaj, ‘‘Training Feedforward Technique with the Marquardt Algorithm,’’ IEEE Trans. Neural Netw., 5, 989 (1994). Holland, J., Adaptation in Natural and Artificial Systems, University of Michigan Press (1975). Huang, K., X. L. Zhan, F. Q. Chen, and D. W. Lu, ‘‘Catalyst Design for Methane Oxidative Coupling by Using Artificial Neural Network and Hybrid Genetic Algorithm,’’ Chem. Eng. Sci., 58, 81 (2003). Istadi, I. and N. A. S. Amin, ‘‘Modelling and Optimization of Catalytic-Dielectric Barrier Discharge Plasma Reactor for Methane and Carbon Dioxide Conversion Using Hybrid Artificial Neural Network-Genetic Algorithm Technique,’’ Chem. Eng. Sci., 62, 6568 (2007). Ji, S., T. Xiao, S. Li, C. Xu, R. Hou, K. S. Coleman, and M. L. H. Green, ‘‘The Relationship between the Structure and the Performance of Na–W–Mn/Sio2 Catalysts for the Oxidative Coupling of Methane,’’ Appl. Catal. A, 225, 271 (2002).
759
Kamali Shahri, S. M. and S. M. Alavi, ‘‘Kinetic Studies of the Oxidative Coupling of Methane Over the Mn/Na2WO4/Sio2 Catalyst,’’ J. Nat. Gas Chem., 18, 25 (2009). Keller, G. E. and M. M. Bhasin, ‘‘Synthesis of Ethylene via Oxidative Coupling of Methane. I. Determination of Active Catalysts,’’ J. Catal., 73, 9 (1982). Kumar, K. V., ‘‘Neural Network Prediction of Interfacial Tension at Crystal/Solution Interface,’’ Ind. Eng. Chem. Res., 48, 4160 (2009). Kumar, K. V., K. Porkodi, R. L. A. Rondon, and F. Rocha, ‘‘Neural Network Modeling and Simulation of the Solid/Liquid Activated Carbon Adsorption Process,’’ Ind. Eng. Chem. Res., 47, 486 (2008). Liu, Y., PhD Dissertation, Lanzhou Institute of Chemical Physics, Chinese Academy of Science (1997). Martherne, J. L. and G. L. Culp, Direct Conversion of Methane to C2,s and Liquid Fuels: Process Economics, Methane Conversion by Oxidative Processes Fundamental and Engineering Aspect, Van Nostrand Reinhold (1992). MATLAB help, Version 7.6.0324 (R2008), The Math. Works Inc. (2008). Mehrpooya, M., A. H. Mohammadi, and D. Richon, ‘‘Extension of an Artificial Neural Network Algorithm for Estimating Sulfur Content of Sour Gases at Elevated Temperatures and Pressures,’’ Ind. Eng. Chem. Res., 49, 439 (2010). Nabavi, R., D. Salari, A. Niaei, and M. T. Vakil-Baghmisheh, ‘‘A Neural Network Approach for Prediction of Main Product Yields in Methanol to Olefin Process,’’ Int. J. Chem. React. Eng., 7, A26 (2009). Palermo, A., J. P. H. Vazquez, A. F. Lee, M. S. Tikhov, and R. M. Lambert, ‘‘Critical Influence f the Amorphous Silica-to-Cristobalite Phase Transition on the Performance of Mn/Na2WO4/SiO2 Catalysts for the Oxidative Coupling of Methane,’’ J. Catal., 177, 259 (1998). Pasadakis, N., V. Gaganis, and C. Foteinopoulos, ‘‘Octane Number Prediction for Gasoline Blends,’’ Fuel. Process. Technol., 87, 505 (2006). Research Institute of Petroleum Industry (RIPI) and Japan Oil, Gas and Metals National Corporation (JOGMEC), the final report of the Technical collaboration Project on the Process Development for the OCM Technology (2004). Sadeghzadeh Ahari, J., R. Ahmadi, H. Mikami, K. Inazu, S. Zarrinpashne, S. Suzuki, and K. Aika, ‘‘Application of a Simple Kinetic Model for the Oxidative Coupling of Methane to the Design of Effective Catalysts,’’ Catal. Today, 145, 45 (2009). Saha, B., P. Chowdhury, and A. K. Ghoshal, ‘‘Al-MCM-41 Catalyzed Decomposition of Polypropylene and Hybrid Genetic Algorithm for Kinetic Analysis,’’ Appl. Catal. B, 83, 265 (2008). Tye, C. T., A. R. Mohamed, and S. Bhatia, ‘‘Modeling of Catalytic Reactor for Oxidative Coupling of Methane Using La2O3/Cao Catalyst,’’ Chem. Eng. J., 87, 49 (2002). Wang, J., L. Chou, B. Zhang, H. Song, J. Zhao, J. Yang, and S. Li, ‘‘Comparative Study on Oxidation of Methane to Ethane and Ethylene over Na2WO4–Mn/SiO2 Catalysts Prepared by Different Methods,’’ J. Mol. Catal. A: Chem., 245, 272 (2006). Wang, D. J., M. P. Rosynek, and J. H. Lunsford, ‘‘Oxidative Coupling of Methane Over Oxide Supported Sodium-Manganese Catalysts,’’ J. Catal., 155, 390 (1995).
Further reading (with label) Tarca, L. A., B. P. A. Grandjean, and F. Larachi, ‘‘Integrated Genetic Algorithm-Artificial Neural Network Strategy For Modeling Important Multi Phase-Flow Characteristics,’’ Ind. Eng. Chem. Res., 41, 2543 (2002).