Thermodynamic analysis of carbon dioxide reforming of methane to syngas with statistical methods

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Thermodynamic analysis of carbon dioxide reforming of methane to syngas with statistical methods Hossein Atashi a,*, Jaber Gholizadeh a, Farshad Farshchi Tabrizi b, Jaber Tayebi a, Seyed Amir Hossein Seyed Mousavi a a b

Department of Chemical Engineering, Faculty of Engineering, University of Sistan and Baluchestan, Zahedan, Iran Faculty of Chemical Engineering, Petroleum and Gas, University of Shiraz, Shiraz, Iran

article info

abstract

Article history:

The present theoretical work deals with thermodynamic analysis based on Gibbs energy

Received 28 November 2015

minimization method combined with a statistical approach: response surface methodol-

Received in revised form

ogy. By combining these two methodologies, the conditions of optimal operation were

23 June 2016

obtained. This study brings a novel methodology for thermodynamic analyses, which are

Accepted 25 July 2016

normally based only on the Gibbs energy minimization method. Thermodynamic analysis

Available online xxx

of carbon dioxide reforming of methane has been investigated by method of Gibbs free energy minimization for production of desirable products at a wide range of temperature

Keywords:

(600e1300 K), pressure (1e20 bar) and carbon dioxide to methane ratio (0.5e3). Moreover,

Carbon dioxide

the surface response methodology was used to determine the cubic polynomial models for

Reforming

mole fraction of hydrogen, carbon monoxide and ratio of H2/CO based on temperature,

Methane

pressure and carbon dioxide to methane ratio. Numerical optimization was employed for

Hydrogen

determining the maximum production of hydrogen while keeping the production of carbon

Syngas

dioxide, methane and carbon monoxide to a minimum; in addition, the optimum ratio of hydrogen to carbon monoxide (1e3) occurs at 1 bar, 1011.99 K and carbon dioxide to methane ratio of 0.5. © 2016 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.

Introduction Nowadays, utilization of alternative fuels such as natural gas and hydrogen is very important considering the decrease of fossil fuel reserves, production, environmental pollution and rising prices of petroleum products. Hence, the application of new technologies to reduce the use of fossil fuels is essential. The natural gas and hydrogen, with minimal environmental pollution, will have an important role in future energy

supplies. Natural gas is one of the most abundant sources of energy and its application in the chemical industry is very significant. The high cost of natural gas transportation is the major problem of its utilization, which can be solved by converting it into valuable chemicals such as ethylene, propylene and methanol. FischereTropsch synthesis is of known processes for indirect production of valuable fuels from natural gas [1e4]. Syngas (a mixture of hydrogen and carbon monoxide) is obtained from natural gas and are used as feedstock in the FischereTropsch process.

* Corresponding author. E-mail address: [email protected] (H. Atashi). http://dx.doi.org/10.1016/j.ijhydene.2016.07.184 0360-3199/© 2016 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article in press as: Atashi H, et al., Thermodynamic analysis of carbon dioxide reforming of methane to syngas with statistical methods, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.07.184

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Hydrogen is a clean source of energy, which creates a very small environmental pollution and its production is of great importance. Hydrogen can be a viable alternative to the fossil fuels, which today is known as a clean fuel and without pollution. Reduction of greenhouse effects, reversibility of its production cycle, and its easy transportation by pipeline and high heating value compared to the other fuels, are important features of hydrogen fuel. Hydrogen can be produced by electrolysis [5e8], thermolysis [9,10], pyrolysis [11,12], photocatalytic water [13e16] and fuel processing of hydrocarbons [17]. Common processes in the production of hydrogen are steam-methane reforming, partial oxidation of methane and carbon dioxide reforming [18e27]. Carbon dioxide is a greenhouse gas that is causing global warming. Combustion of fossil fuels such as coal, petroleum and natural gas has caused the concentration of carbon dioxide increase in the atmosphere. In the chemical industry, carbon dioxide is mainly used in the production of urea, methanol and other products. Methane and carbon dioxide are greenhouse gases; thus, converting them into valuable products such as hydrogen is an interesting approach. Carbon dioxide reforming of methane, also known as methane dry reforming, is one method to reduce greenhouse gas emissions and to produce synthesis gas [28e33]. In recent years, many studies have been carried out in thermodynamics equilibrium field, the production of hydrogen and synthesis gas production by minimizing the Gibbs free energy [34e38]. Additionally, carbon dioxide reforming of methane has been theoretical and experimentally investigated in several previous publications [28,29,32,33,39e42]; however, very few studies have been investigating the effects of different parameters and their interactions based on statistical methodology. In this study, thermodynamic analysis combined with a statistical method was applied to carbon dioxide reforming of methane. Cubic polynomial equations for mole fraction of hydrogen and carbon monoxide based on temperature, pressure and inlet CO2/CH4 were determined. The effect of temperature, pressure, inlet CO2/CH4 and interactions between them on the mole fraction of products was investigated with statistical approaches. Using mathematical equations can be obtained optimal condition for reduces the operating costs.

Thermodynamic and mathematical modeling Obtain equilibrium composition of products in the chemical reactions without carrying out experiments can be very important. Simulation and optimization of chemical processes and operational variables impact on production of equilibrium composition are essential. Gibbs free energy minimization is a useful method to predict the mole fraction of products at equilibrium condition. Moreover, using polynomial equations for the mole fraction composition based on different variables can predict the effect of variables on responses.

Gibbs free energy minimization method The mole fraction of products can be determined by the Gibbs free energy minimization method without the need of knowing chemical reactions. The total Gibbs free energy of the whole system is given by Eq. (1). Gt ¼

X

ni mi

(1)

i¼1

Where mi corresponds to the chemical potential of species i. The minimization of total Gibbs free energy of the system is subject to mass balance constraints given by Eq. (2). X

ni aik  Ak ¼ 0ðk ¼ H; O; C; i ¼ CH4 ; H2 O; CO2 ; H2 ; COÞ

(2)

i

Where Ak is the total number of k atoms in the system, and aik is the number of k atoms for the chemical species of i. Considering the Lagrange multipliers lk for each element, Eq. (3) was obtained. X

X

lk

k

! ni aik  Ak

¼0

(3)

i

A new function F (Lagrange function) is composed of the total Gibbs energy of the system, objective function, plus the mass balance restrictions (Eq. (4)). F¼G þ t

X

lk

k

X

! ni aik  Ak

(4)

i

The minimum of Gt is found when the partial derivative of F with respect to ni and lk is made equal to zero (first order condition in optimization process). When the mass balance restrictions are satisfied, F≡Gt. ðvGt =vni ÞT;P;ni , is the definition of the chemical potential. In the gas phase reactions for ideal gas at standard conditions, the chemical potential is obtained by Eq. (5). 

mi ¼ DG

fi

 .  þ RT ln b f i fi

(5)



Where mi , DG fi and R are the chemical potential, the standard Gibbs free energy of formation and the universal gas constant,  respectively. b f i and fi are fugacity and the standard fugacity, which are derived from Eqs. (6) and (7). b b iP f i ¼ yi ∅

(6)

fi0 ¼ P0

(7)

b i is the fugacity coefficient of species i. In the present work, ∅ b i ) is ideal gas phase is assumed; thus, the fugacity coefficient ( ∅ equal to unity. Eq. (8) is the final form of main equation. 

DG

fi

   X þ RT ln yi P P þ lk aik ¼ 0

(8)

k

The nonlinear system of equations (Eqs. (8) and (2)) results from the application of first order condition to Lagrange function and is solved with Matlab software. Thermodynamic  data for DG fi were taken from Ref. [43].

Please cite this article in press as: Atashi H, et al., Thermodynamic analysis of carbon dioxide reforming of methane to syngas with statistical methods, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.07.184

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Response surface methodology (RSM) Since there are many theoretical and experimental studies in the field of carbon dioxide reforming of methane, the statistical study can be very useful. After obtaining the mole fraction of products by minimizing the Gibbs free energy method in the carbon dioxide reforming of methane, determining the appropriate mathematical model to investigate the role of each parameter is consequential. Response surface methodology is a collection of statistical and mathematical method for analysis and modeling of issues, which explain the conduct of a data collection. Select an experimental design is the first step in this methodology. RSM designs, such as BoxBehnken and central composite design (CCD), are used to fit quadratic equations. Generally, this degree of the polynomial is sufficient to estimate the correct response. But when the responses are wavy, should be used cubic models. The central composite design most applied to the quadratic equations. In this study, Box-Behnken design has been applied, which is more commonly used in published works. The next step is the selection of independent variables. Temperature, pressure and carbon dioxide to methane ratio are independent variables. Then, for statistical analysis of experimental data, the fit of a polynomial equation was investigated. Analysis of variance (ANOVA) is a suitable way to evaluate the model's fitness. In this way, F-value, P-value and sum of the square is very important. According to the amounts of F-value, P-value and sum of the square for quadratic and cubic models, the degree of polynomial equations were determined. Also, the amounts of these statistical indicators were used to identify the significant model terms.

Results and discussions In order to determine the mathematical model for the production of H2, CO and H2/CO ratio, thermodynamic analysis based on the Gibbs energy minimization approach was employed along with the response surface methodology. Polynomial equations are appropriate for investigating the impact of operating conditions such as temperature, pressure and carbon dioxide to methane ratio on responses. Finally, optimum operating conditions are determined through numerical optimization.

Mathematical model of hydrogen production Hydrogen creates a very small environmental pollution and large amount of H2 are required in the petroleum and chemical industries. Table 1 shows the range of temperature, pressure and CO2/ CH4.

Table 1 e The range of temperature, pressure and CO2/ CH4. Temperature (K) Pressure (bar) Inlet CO2/CH4

600e1300 1e20 0.5e3

Fig. 1 e Mole fraction of H2 based on pressure, temperature and inlet CO2/CH4. The surface behavior of the hydrogen mole fraction based on temperature, pressure and inlet CO2/CH4 is shown Fig. 1. It is so clear that the mole fraction of hydrogen increases with increasing temperature. The effect of inlet CO2/CH4 at high temperature is so weaker than low temperature. At low temperature, mole fraction of hydrogen decreases with increasing the inlet CO2/CH4. Mole fraction of hydrogen increases by reducing the pressure at different ratio of inlet CO2/CH4. Eq. (9) shows relationship among temperature, pressure, inlet CO2/CH4 and mole fraction of hydrogen. A summary of the statistical results of the model is shown in Table 2. “Adeq

Table 2 e Model summary statistics. Std. Dev. R-Squared Adj R-Squared Pred R-Squared Adeq Precision

0.021 0.9872 0.9809 0.9664 34.129

Please cite this article in press as: Atashi H, et al., Thermodynamic analysis of carbon dioxide reforming of methane to syngas with statistical methods, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.07.184

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Table 3 e Analysis of variance (ANOVA).

Model A-Temperature B-Pressure CeCO2/CH4 AB AC BC A2 B2 C2 A2B A 2C AC2 A3

Sum of squares

Mean square

F-value

P-value

Coefficient estimate

Standard error

0.90157 0.233828 0.057109 1.30E-07 0.000936 0.001814 0.000313 0.000149 0.004164 0.002143 0.018422 0.001223 0.001519 0.031707

0.069352 0.233828 0.057109 1.30E-07 0.000936 0.001814 0.000313 0.000149 0.004164 0.002143 0.018422 0.001223 0.001519 0.031707

154.8054 521.9473 127.4767 0.000289 2.090389 4.048208 0.698577 0.333559 9.295911 4.78254 41.12103 2.730462 3.390881 70.77678

<0.0001 <0.0001 <0.0001 0.9866 0.1602 0.0547 0.4109 0.5685 0.0052 0.0379 <0.0001 0.1105 0.077 <0.0001

0.332635 0.08142 0.00019 0.01113 0.0501 0.010121 0.00655 0.026532 0.03474 0.084702 0.048434 0.049585 0.15767

0.01456 0.007212 0.011321 0.007695 0.024899 0.012109 0.011346 0.008702 0.015887 0.013209 0.029311 0.026927 0.018742

Precision” measures the ratio of signal to noise. Ratios greater than 4 are favorable. The “Pred R-Squared” of 0.9664 is in reasonable agreement with the “Adj R-Squared” of 0.9809. One

indicator of dispersion is the standard deviation that its value close to zero is better. Its value for model is 0.021. Analysis of variance (ANOVA) for cubic model is presented in Table 3. For statistical analysis, F-value and P-value factors is very important. Values of “P-value” less than 0.05 indicates model terms are significant. In this case, temperature, pressure, pressure2, (CO2/CH4)2, Temperature2  pressure and Temperature3 are significant model terms. Values greater than 0.1 indicate the model terms are not significant. yH2 ¼ þ0:76725  5:88801  103  T þ 0:05263  P þ 0:76445   CO2   1:41635  104  T  P  1:03283  103  T CH4     CO2 CO2 þ 8:5229  104  P  þ 9:10977  106  CH4 CH4  2 CO2  T2 þ 2:93986  104  P2  0:10837  þ 7:27835 CH4   CO2  108  T2  P þ 3:16303  T2  þ 9:06699  105 CH4  2 CO2 T  3:67755  109  T3 CH4 (9)

Mathematical model of carbon monoxide production Carbon monoxide is known as an industrial gas that has many applications in industry and in the different chemical processes such as FischereTropsch reaction as a feedstock is used. In the FischereTropsch process, liquid hydrocarbon fuels are produced by the hydrogenation of carbon monoxide. Carbon monoxide is an atmospheric pollutant from incomplete combustion of various fuels. Fig. 2 illustrates the mole fraction of carbon monoxide based on temperature, pressure and inlet CO2/CH4. According

Table 4 e Model summary statistics.

Fig. 2 e Mole fraction of CO based on pressure, temperature and inlet CO2/CH4.

Std. Dev. R-Squared Adj R-Squared Pred R-Squared Adeq Precision

0.018 0.9948 0.9919 0.9421 49.838

Please cite this article in press as: Atashi H, et al., Thermodynamic analysis of carbon dioxide reforming of methane to syngas with statistical methods, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.07.184

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Table 5 e Analysis of variance (ANOVA).

Model A-Temperature B-Pressure CeCO2/CH4 AB AC BC A2 B2 C2 A2B A2C AC2 BC2 A3

Sum of squares

Mean square

F-value

P-value

Coefficient estimate

Standard error

1.539299 0.34557 0.043307 5.09E-04 1.77E-05 0.00228 2.59E-05 0.01165 0.004769 0.001293 0.016098 0.002914 0.001804 0.004591 0.030744

0.10995 0.34557 0.043307 5.09E-04 1.77E-05 0.00228 2.59E-05 0.01165 0.004769 0.001293 0.016098 0.002914 0.001804 0.004591 0.030744

342.3055 1075.857 134.8256 1.586085 0.055194 7.097813 0.080493 36.26844 14.84609 4.026876 50.11662 9.071125 5.616052 14.29369 95.71452

<0.0001 <0.0001 <0.0001 0.2195 0.8162 0.0133 0.7790 <0.0001 0.0007 0.0557 <0.0001 0.0059 0.0258 0.0009 <0.0001

0.404535 0.07795 0.01212 0.00162 0.05909 0.00295 0.05801 0.028844 0.02722 0.080646 0.081597 0.055227 0.047207 0.1553

0.012333 0.006714 0.00962 0.006915 0.02218 0.01041 0.009632 0.007486 0.013564 0.011392 0.027092 0.023304 0.012486 0.015874

to Fig. 2, at low temperature, the amount of carbon monoxide decreases with reducing the inlet CO2/CH4 and change of inlet CO2/CH4 has little effect on the carbon monoxide production at high temperature. With increasing the pressure, the amount of carbon monoxide increases in all ranges of inlet CO2/CH4. At low pressure, mole fraction of carbon monoxide increases initially and then decreases. Cubic equation for mole fraction of carbon monoxide based on temperature, pressure and inlet CO2/CH4 is shown in Eq. (10). A summary of the statistical results and analysis of variance (ANOVA) of the model is presented in Tables 4 and 5. The model F-value of 342.31 and the model P-value of <0.0001 imply the model is significant. In this case, (CO2/CH4), temperature  pressure and pressure  (CO2/CH4) are not significant model terms. The “Pred R-Squared” of 0.9421 is in reasonable agreement with the “Adj R-Squared” of 0.9919. yCO ¼ 0:17055  4:04628  103  T þ 0:058263  P þ 1:11578   CO2   1:32155  104  T  P  1:50098  103  T CH4     CO2 CO2   0:0113  P  þ 8:18934  106  T2 CH4 CH4  2 CO2 þ 3:19606  104  P2  0:14675  þ 6:9298 CH4   CO2  108  T2  P þ 5:32877  107  T2  þ 1:00986 CH4   2 2 CO2 CO2 þ 3:18025  103  P   104  T  CH4 CH4  3:62212  109  T3 (10)

Mathematical model of hydrogen per carbon monoxide ratio H2 to CO ratio is one of the important factors for the production of chemical products such as ethylene and propylene in the FischereTropsch reaction. For this reason, the thermodynamic and statistical analysis of the synthesis gas produced in the carbon dioxide reforming of methane can be very important. Fig. 3 show mole fraction of hydrogen per carbon monoxide as a function of temperature, pressure and inlet CO2/CH4. Fig. 3 indicates that at different pressures, ratio of H2/CO

Fig. 3 e Mole fraction of H2/CO based on pressure, temperature and inlet CO2/CH4.

Please cite this article in press as: Atashi H, et al., Thermodynamic analysis of carbon dioxide reforming of methane to syngas with statistical methods, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.07.184

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Table 6 e Model summary statistics.

Table 8 e 18 solutions of desirability.

Std. Dev. R-Squared Adj R-Squared Pred R-Squared Adeq Precision

Number

0.022 0.9934 0.99901 0.9764 52.907

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

decreases with reduction the temperature. Also at different inlet CO2/CH4, amount of H2/CO decreases with increasing the pressure. The cubic model for mole fraction of hydrogen per carbon monoxide based on temperature, pressure and inlet H2O/CH4 is shown in Eq. (11). Table 6 indicates a summary of the statistical results of the model. The “Pred R-Squared” of 0.9764 is in reasonable agreement with the “Adj R-Squared” of 0.9901. Analysis of variance (ANOVA) for model is presented in Table 7. The model F-value of 301.49 and the model P-value of <0.0001 imply the model is significant. yH2 =CO ¼ þ0:93763  4:34809  103  T  7:19764  103  P   CO2 þ 0:033763   1:35517  104  T  P CH4   CO2  2:62159  106  T  þ 1:22618  103  P CH4   CO2  þ 7:44594  106  T2 þ 3:97535  103  P2 CH4  2 CO2  0:010308  þ 9:41277  108  T2  P CH4

CO2/ CH4

Pressure (bar)

0.5 0.5 0.5 3 3 3 2.98 3 3 3 3 2.52 1.5 1.58 1.89 0.5 0.5 2.64

1 1.08 1.18 1 1 1 1 1.14 1.26 1 1 1 1 1 1 1.12 2.36 20

Temperature Desirability (k) 1011.99 1002.74 1001.28 1035.52 1032.26 1038.3 1036.46 1034.68 1036.64 1018.44 1071.71 988.31 957.83 958.33 963.46 1299.32 1297.23 664.12

0.635958 0.635261 0.634243 0.617915 0.617858 0.617856 0.617264 0.617011 0.616289 0.616183 0.609193 0.607497 0.607412 0.606436 0.603848 0.587227 0.580765 0.107523

monoxide (1e3). Table 8 shows the solutions for desirability. Desirability indicates the desired condition for reaching the optimized conditions. The desirability value is between 0 and 1, and if the value is closer to unit, it is better. Fig. 4 shows the desirability contour diagram based on the pressure and temperature in the ratio of CO2/CH4 ¼ 0.5.

 1:61023  106  T  P2  3:25502  109  T3

Conclusions

 6:0121  105  P3 (11)

Numerical optimization The main purpose of applying a statistical method (RSM) is the accurate determination of optimized operating condition for methane dry reforming. First, the goals should be identified for optimization process, which are included: (1) maximum production of hydrogen, (2) minimum production of methane, carbon dioxide and (3) optimum ratio of hydrogen to carbon

In this study, thermodynamic analysis combined with a statistical method was applied to carbon dioxide reforming of methane. Cubic polynomial equations for mole fraction of hydrogen and carbon monoxide based on temperature, pressure and inlet CO2/CH4 were determined. The effect of temperature, pressure and inlet CO2/CH4 on the mole fraction of products was investigated with statistical approaches. The results show that the temperature is one of the main factors affecting on the mole fraction of products. At temperatures higher than 1100 K, the production of hydrogen and

Table 7 e Analysis of variance (ANOVA).

Model A-Temperature B-Pressure CeCO2/CH4 AB AC BC A2 B2 C2 A2B AB2 A3 B3

Sum of squares

Mean square

F-value

P-value

Coefficient estimate

Standard error

1.959165 0.357682 0.018059 0.00045 0.007715 3.42  106 0.000654 0.052779 0.014506 0.001432 0.031519 0.006725 0.029152 0.003814

0.150705 0.357682 0.018059 0.00045 0.007715 3.42  106 0.000654 0.052779 0.014506 0.001432 0.031519 0.006725 0.029152 0.003814

301.4895 715.5517 36.12756 0.899305 15.43466 0.006834 1.309191 105.5867 29.01911 2.865345 63.05388 13.45363 58.31951 7.630018

<0.0001 <0.0001 <0.0001 0.3517 0.0006 0.9348 0.2630 <0.0001 <0.0001 0.1025 <0.0001 0.0011 <0.0001 0.0104

0.440663 0.10347 0.010085 0.031624 0.00115 0.014561 0.10321 0.049802 0.01611 0.109541 0.05086 0.13956 0.05155

0.016474 0.017214 0.010635 0.008049 0.013874 0.012726 0.010044 0.009245 0.009515 0.013795 0.013867 0.018275 0.018661

Please cite this article in press as: Atashi H, et al., Thermodynamic analysis of carbon dioxide reforming of methane to syngas with statistical methods, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.07.184

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Fig. 4 e Desirability contour diagram. carbon monoxide reaches to a constant value. At different ratios of CO2/CH4, increasing pressure has a positive effect on the appropriate ratio of H2/CO. However, mole fraction of hydrogen decreases with increasing pressure at temperatures higher than 800 K. The ratio of H2/CO reaches the lowest amount at low temperature (600 K) and high pressure (20 bar). The optimum ratio of hydrogen to carbon monoxide (1e3) occurs at 1 bar, 1011.99 K and carbon dioxide to methane ratio of 0.5, as determined by the optimization process.

[7]

[8]

[9]

Acknowledgement The authors would like to acknowledge the full financial support from the University of Sistan and Baluchestan, Iran.

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