Coal Char Gasification in the Mixture of H - American Chemical

Dec 26, 2013 - traditional L-H model to predicate the char-CO2−CO gasification reaction rates. But the parameters and function in their model are ne...
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Coal Char Gasification in the Mixture of H2O, CO2, H2, and CO under Pressured Conditions Rui Zhang, Qin H. Wang,* Zhong Y. Luo, Meng X. Fang, and Ke F. Cen State Key Laboratory of Clean Energy Utilization, Zhejiang University, 310027, Zheda Road 38, Hangzhou, Zhejiang, China ABSTRACT: The kinetic study of coal char gasification at elevated pressure is very limited and much less than that at atmospheric pressure, especially in the mixture of H2O, CO2, H2, and CO. The inhibition effect of H2 and CO and a suitable reaction model are both needed to be studied under pressured conditions. A Langmuir−Hinshelwood (L-H) type model has been widely adopted to describe coal char gasification at atmospheric pressure. But its applicability to pressured conditions is questionable. In this paper, the experiments of coal char gasification in the mixture of H2O, CO2, H2 and CO were carried out using a modified pressured thermogravimetric analyzer (PTGA) system at 0.5 MPa and within 1148−1198 K. Experimental results indicate that the gasification reaction rates of H2O and CO2 under pressured conditions are much higher than those at atmospheric pressure, and the inhibition effects of H2 and CO are also stronger. The kinetic parameters in L-H model were determined from pressured pure H2O and CO2 gasification (N2 as diluent). And the applicability of L-H model to pressured conditions was verified. It is shown that the L-H models based on common or separate active sites assumptions could not give satisfactory predictions to experimental data. Finally, we proposed a modified L-H model. This model only needs several extra experiments to calculate the modification factor, and can describe char gasification in the mixture of H2O, CO2, H2 and CO under pressured conditions very well.

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INTRODUCTION It is well-known that the fluidized bed gasification technology has good fuel flexibility.1,2 And the gasification of coal char using fluidized bed has been presented and researched by some scholars in recent years.3−6 However, the fluidized bed gasification is always operated at a temperature below 1273 K, and the coal char gasification is quite slow at this low temperature. Therefore, fluidized bed gasification at elevated pressure is a feasible choice to solve this problem.7 In order to design, optimize, and simulate the gasifier, we have to deeply study the reaction kinetics of coal char gasification at elevated pressure. Unfortunately, our understanding of char gasification at elevated pressure is generally limited, and some research areas are almost blank. The generally accepted reaction mechanisms for coal char gasification are proposed by Gadsby et al.:8,9 For char-H2O reaction:

Langmuir−Hinshelwood (L-H) type models based on these reaction steps to describe char gasification reactions: rchar − H2O =

k1PH2O 1 + k 2PH2O + k 3PH2

(7)

rchar − CO2 =

k4PCO2 1 + k5PCO2 + k6PCO

(8)

10,11

Blackwood et al. investigate the reaction mechanisms of char gasification at high pressure conditions (up to 50 bar) and find that some extra reaction steps should be added to the reaction scheme proposed by Gadsby et al.: The step added to char-H2O reaction: (CH 2) + H 2O → CH4 + (O)

(9)

The steps added to char-CO2 reaction:

Cf + H 2O ⇌ C(O) + H 2

(1)

CO2 + C(CO) ⇌ 2CO + C(O)

(10)

C(O) → CO

(2)

CO + C(CO) ⇌ CO2 + 2Cf

(11)

Cf + H 2 ⇌ C(H 2)

(3)

Cf +

1 H 2 ⇌ C(H) 2

And the models based on their reaction scheme are

(4)

rchar − H2O =

2 k1PH2O + k4PH2PH2O + k5PH2O 1 + k 2PH2 + k 3PH2O

(12)

rchar − CO2 =

2 k1PCO2 + k5PCO2 1 + k 2PCO + k 3PCO2

(13)

And for char-CO2 reaction: Cf + CO2 ⇌ C(O) + CO

(5)

C(O) → CO

(6)

Received: September 16, 2013 Revised: December 26, 2013 Published: December 26, 2013

Where Cf is free active sites, and C(O), C(H), C(H2) are absorbed surface complex. Gadsby et al. also give the © 2013 American Chemical Society

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Table 1. Characteristics of Char Samples and Parent Coal proximate analysis coal char

Mad% 5.83 Mad% 1.28

Aad% 16.89 Aad% 21.51

Vad% 26.18 Vad% 1.90

BET(m2/g)

ultimate analysis FCad% 51.10 FCad% 75.31

Cad% 62.24 Cad% 75.36

Had% 3.56 Had% 0.10

Nad% 0.85 Nad% 0.98

St,ad% 0.73 St,ad% 0.58

Oad% 9.90 Oad% 0.19

ND 8.12

Figure 1. Schematic of the modified PTGA system.

Nozaki et al.12 point out that the reaction steps proposed by Gadsby et al. are not applicable to char-CO2 gasification when reaction pressure is above 1.0 MPa, and they give new models which have similar form with eq 13. Matsuoka et al.7 and Wang et al.13 demonstrate that eq 7 can still be used to describe charH2O gasification up to 0.6 MPa. Roberts et al.14,15 indicate that the models given by Gadsby et al. are suitable to describe the reaction kinetics when H2O or CO2 partial pressure is lower than 1.0 MPa, while not suitable when CO2 partial pressure is higher than 1.0 MPa. And they propose a new method based on traditional L-H model to predicate the char-CO2−CO gasification reaction rates. But the parameters and function in their model are needed to be determined in the future research.

r=

In practice, char is usually gasified in the mixture of H2O, CO2, H2, and CO. However, the research of char gasification in the mixture of H2O, CO2, H2 and CO is much less than that of gasification in pure H2O or CO2. Shaw16 summarizes the elementary reaction steps proposed by Ergun, Blackwood, and other investigators to derive a kinetic model (eq 14) which can describe the char gasification reactions in the mixture of H2O, CO2, H2 and CO. But this equation has not yet been verified by experiments, because there are too many parameters in this model. It is very hard to determine all these parameters accurately, so this model is inconvenient to use. The model proposed by Muhlen et al.17 (eq 15) have the same problem as that proposed by Shaw, therefore, it has not yet been used by other scholars.

2 2 k1PCO2 + r9 P H2O + r8PCO2 + r14PH2OPCO2 + r11PH2O + r13PCO2PH2 + r12PH2OPH2

1 + r2PCO2 + r10PH2O + r3PCO + r5PH2

r=

(14)

2 2 2 + r9 P H2O + r11PH2O + r12PCO2PH2 + r4PH2 k1PCO2 + r8PCO2

1 + r2PCO2 + r3PCO + r10PH2O + r5PH2

833

(15)

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The widely used model which can describe the char gasification reactions in the mixture of H2O, CO2, H2, and CO is the traditional L-H model. It has two forms based on common active sites assumption or separate active sites assumption, as eqs 16 and 17. These two L-H models have been verified by many scholars using different coal chars, and are accurate enough to predict the experimental results.18−21 However, previous experiments are all carried out at atmospheric pressure, so the applicability of L-H model to pressured conditions is still doubtful. Umemoto et al.22 propose a new assumption of partially sharing active sites and give a new model, but their model have only been verified in the mixture of H2O and CO2. r=

k1PH2O + k4PCO2 1 + k 2PH2O + k 3PH2 + k5PCO2 + k6PCO (common active sites)

Figure 2. Mass and temperature curves during entire pressured experimental procedure.

(16)

(separate active sites)

(17)

In this paper, we will investigate the kinetics of char gasification under pressured conditions. And the H2 and CO inhibition effects on char gasification are also analyzed. We will also verify the widely accepted L-H models under pressured conditions. Finally, we will propose a modified L-H model to predict the char gasification reaction rates in the mixture of H2O, CO2, H2 and CO under pressured conditions. The modified L-H model is more accurate than traditional L-H models and is very simple to use.

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W0 − W W0 − Wf

(18)

dX = kapp(1 − X ) dt

(19)

− ln(1 − X ) = kappt

(20)

X=

k4PCO2 k1PH2O r= + 1 + k 2PH2O + k 3PH2 1 + k5PCO2 + k6PCO

Where X is carbon conversion (%), W0 (mg) is the weight of char just after switching to reactant gas; Wf (mg) is the final weight of char, W (mg) is the weight of char at a given time, kapp is the apparent reaction rate constant (s−1), t is the reaction time (t). kapp is used to characterize the reaction rate.7,21 eq 19 is based on the homogeneous reaction model,18 and a linear plot of −ln(1 − X) versus t is a suitable test of the validity of the homogeneous reaction model.7,19 Figure.3 shows that −ln(1 − X) and t have good linear relationship under all conditions. Therefore, the homogeneous reaction model is suitable in our research.

MATERIALS AND METHODS

Char Preparation. The char samples used in this research are the same as those used in the previous research of char gasification in the mixture of H2O and CO2 at atmospheric pressure.21 The char samples were prepared from a bubbling fluidized bed in N2 atmospheric at 823 K and 1 atmospheric pressure for about 15 min. After screening, the particle size of char samples is smaller than 80 um. Characteristics of the char samples and parent coal were shown in Table 1. Experimental Method. A pressurized thermogravimetric analyzer system (PTGA, Thermax 500, ThermoFisher Scientific Inc., Waltham, MA) was used in this study. Since the original PTGA system is not suitable for the experiment, we have made some modifications to this system. The schematic of the modified system is shown in Figure.1. Isothermal experiments have been carried out in our research. The experimental steps include (1) Load the char samples into the furnace; (2) Increase operational pressure; (3) Adjust operational pressure; (4) Gasification reaction; (5) Stop reaction and release pressure. The mass and temperature curves during the entire experimental procedure are shown in Figure.2. In this research, the partial pressure of H2O and CO2 varied from 0.05 to 0.25 MPa and 0.2−0.5 MPa, respectively. The reaction temperature is between 1148 K and 1198 K, and the reaction pressure is 0.5 MPa. In order to minimize the effect of diffusion, a pretest was undertaken to choose proper sample mass and gas flow for the following experiments. The pretest indicated that the diffusion effect could be neglected when the sample mass was 10 ± 0.3 mg, and gas flow was 2 L/min (standard temperature and pressure, STP) for charH2O reaction and 1.5 L/min (STP) for char-CO2 reaction. Data Analysis. The method of data analysis used in this research is the same as that used by other scholars.7,23 The apparent reaction rate constant is derived from the following equations:

Figure 3. Validation of the homogeneous reaction model.

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RESULTS AND DISCUSSION Effects of Pressure on H2O and CO2 Gasification. Figure.4 shows the effect of pressure on gasification reaction rate at 1173 K. It is obviously that the gasification reaction rates of H2O and CO2 reactions both increase as the reaction pressure increases. For char-H2O gasification, the reaction rate 834

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Figure 4. Effect of pressure on H2O and CO2 gasification.

Figure 6. Inhibition effect of CO on CO2 gasification.

at 0.5 MPa is about 1.9 as high as that at 0.1 MPa. And for charCO2 gasification, the reaction rate at 0.5 MPa is about 2.1 as high as that at 0.1 MPa. The reaction rate of H2O gasification is 1.36 as high as that of CO2 gasification at 0.1 MPa, while the reaction rate of H2O gasification is 1.23 as high as that of CO2 gasification at 0.5 MPa. Inhibition Effects of H2 and CO on H2O and CO2 Gasification. Figure.5 shows the inhibition effect of H2 on

Determination of the Kinetic Parameters in L-H Model. Existed researches indicate that the L-H models of pure H2O or CO2 gasification, as shown by eqs 7 and 8, are applicable to pure H2O and CO2 gasification under 1.0 MPa. And we can derive the kinetic parameters of k1, k2, k4, k5 from the chart of 1/r versus 1/PH2O or 1/PCO2, if 1/r has good linear relationship with 1/PH2O or 1/PCO2. With the known k1, k2, k4, k5, we can calculate k3 and k6 at a given PH2/PH2O or PCO/ PCO2.19,21 Therefore, the linear relationship between 1/r and 1/ P is the prerequisite of deriving the kinetic parameters, and is also a sign of applicability of eqs 7 and 8. Figure.7 and Figure.8 indicate that 1/r has good linear relationship with 1/PH2O or 1/ PCO2 at different temperatures.

Figure 5. Inhibition effect of H2 on H2O gasification.

char-H2O gasification reaction under different pressures. Introducing H2 into the reactant gas decreases the reaction rates substantially. The reaction rate of 50%H2O+10%H2 case is about 62% of the reaction rate of 50%H2O+50%N2 case at 0.1 MPa. While the reaction rate of 50%H2O+10%H2 case is about 29% of the reaction rate of 50%H2O+50%N2 case at 0.5 MPa. It seems that the inhibition effect of H2 becomes stronger as the reaction pressure increases. Figure.6 shows the inhibition effect of CO on char-CO2 gasification reaction under different pressures. Introducing CO into the reactant gas also decreases the reaction rates substantially. The reaction rate of 90%CO2+10%CO case is about 65% of the reaction rate of 100%CO2 case at 0.1 MPa. While the reaction rate of 90%CO2+10%CO case is about 40% of the reaction rate of 100%CO2 case at 0.5 MPa. Therefore, it seems that the inhibition effect of CO becomes stronger as the reaction pressure increases, either.

Figure 7. Linear relationship between 1/PH2O and 1/r at 0.5 MPa.

Therefore, the kinetic parameters ki at different temperatures can be calculated from the plots. We assume that the kinetic parameters ki is an exponential function of T (Arrhenius equation, as shown by eqs 21 and 22). If the experimental results are accurate enough, then ln(ki) and 1/T should have good linear relationship. Then we can calculate Ei and Ai of ki from the linear plots. Figure.9 indicates that the plots of ln(ki) and 1/T show good linearity. Therefore, Ei and Ai can be calculated and listed in Table 2. 835

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r=

k1PH2O + k4PCO2 1 + k 2PH2O + k 3PH2 + k5PCO2 + k6PCO (common active sites)

r=

(23)

k4PCO2 k1PH2O + 1 + k 2PH2O + k 3PH2 1 + k 5PCO2 + k6PCO (separate active sites)

Previous study has already demonstrated that the L-H model based on common active sites assumption can predict the experimental results at atmospheric pressure very well.21 Here we will verify the applicability of eqs 23 and 24 at 0.5 MPa. The reaction rates calculated by eqs 23 and 24 using the kinetic parameters derived above are compared with experimental results. We have verified two conditions: without H2 and CO, and with H2 and CO. The experimental conditions of reactant gas without H2 and CO are shown in Table 3. And the

Figure 8. Linear relationship between 1/PCO2 and 1/r at 0.5 MPa.

⎛ E ⎞ k i = A i exp⎜ − i ⎟ ⎝ RT ⎠ ln(k i) = −

Table 3. Experimental Conditions of Char Gasification in the Mixture of H2O and CO2

(21)

Ei + ln(A i ) RT

(24)

(22)

experiment number

total pressure (MPa)

T (K)

PH2O (MPa)

PCO2 (MPa)

1 2 3 4 5

0.5 0.5 0.5 0.5 0.5

1198 1198 1173 1148 1148

0.2 0.1 0.2 0.2 0.1

0.3 0.4 0.3 0.3 0.4

verification results are shown in Figure.10. It can be seen that the L-H models based on common or separate active sites assumptions cannot give satisfactory predictions to the experimental results.

Figure 9. Linear relationship between ln(ki) and 1/T.

Verification of the Applicability of L-H Model under Pressured Conditions. Some scholars have already verified that the L-H models of pure H2O or CO2 gasification are applicable to the experimental conditions below 1.0 MPa.7,13 In practical operation, char is always gasified in the mixture of H2O, CO2, H2, and CO. And the applicability of the L-H model for mixture to pressured conditions below 1.0 MPa is still questionable. The L-H model for the mixture of H2O, CO2, H2 and CO has two forms:

Figure 10. Verification of the L-H models in the mixture of H2O and CO2.

Table 2. Activation Energies and Frequency Factors of ki H2O gasification CO2 gasification

E1 (kJ/mol) 629 E4 (kJ/mol) 280

A1 (MPa−1s−1) 5.3776 × 1026 A4 (MPa−1s−1) 4.5455 × 1010

E2 (kJ/mol) 489 E5 (kJ/mol) 131 836

A2 (s−1) 1.1890 × 1023 A5 (s−1) 2.8711 × 106

E3 (kJ/mol) 412 E6 (kJ/mol) −72

A3 (s−1) 6.8832 × 1020 A6 (s−1) 5.2379 × 10−2

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Then, eqs 23 and 24 have also been verified in the reactant gas with H2 and CO. The experimental conditions are shown in Table 4, and the verification results are shown in Figure.11. It is

η = f (T , P , PH2O , PCO2 , PH2 , PCO)

At specified temperature and pressure, η is only a function of partial pressures of every gas component:

Table 4. Experimental Conditions of Char Gasification in the Mixture of H2O, CO2, H2, and CO experiment number

total pressure (MPa)

1 2 3 4 5

0.5 0.5 0.5 0.5 0.5

T (K)

PH2O (MPa)

PCO2 (MPa)

PH2 (MPa)

PCO (MPa)

1198 1198 1198 1198 1148

0.25 0.2 0.25 0.2 0.2

0.2 0.25 0.2 0.2 0.25

0.05 0.025 0.025 0.05 0

0 0.025 0.025 0.05 0.05

(26)

η = f (PH2O , PCO2 , PH2 , PCO)

(27)

Suppose the effect of every gas component on η is linear, then we can construct the function as: η = a·PH2O + b·PCO2 + c·PH2 + dPCO

(28)

If the coefficients of a ∼ d are obtained, then the modification factor can be calculated. At a given PH2O, PCO2, PH2 and PCO, the gasification reaction rate obtained from experiment is defined as rexp, and the gasification reaction rate obtained from eq 23 is defined as rmod. If η is completely correct, then

obviously that the L-H models based on common or separate active sites assumptions cannot give satisfactory predictions to the experimental results, either.

rexp =

k1PH2O + k4PCO2 ·η 1 + k 2PH2O + k 3PH2 + k5PCO2 + k6PCO

(29)

Therefore, η = rexp/rmod. With four different experiments (different partial pressures), we can obtain four different values of η. Then a ∼ d can be calculated from the following equations: ⎧ η = a·PH2O + b·PCO2 + c·PH2 + d·PCO ⎪ 1 ⎪ ′ + b·PCO2 ′ + c·PH2 ′ + d·PCO ′ ⎪ η2 = a·PH2O ⎨ ″ + b·PCO2 ″ + c·PH2 ″ + d·PCO ″ ⎪ η3 = a·PH2O ⎪ ⎪ η = a·PH2O ‴ + b·PCO2 ‴ + c·PH2 ‴ + d·PCO ‴ ⎩ 4

(30)

With the known a ∼ d, the modified L-H model is r= Figure 11. Verification of the L-H models in the mixture of H2O, CO2, H2, and CO.

(a·PH2O + b·PCO2 + c·PH2 + d·PCO)

k1PH2O + k4PCO2 ·η 1 + k 2PH2O + k 3PH2 + k5PCO2 + k6PCO

(31)

Then we can use eq 31 to predict the gasification reaction rate at a specified temperature and pressure. Compared with the model proposed by Shaw (eq 14) and Muhlen (eq 15), the modified L-H model is much simpler to use. There are too many parameters in eq 14 and eq 15. Deriving all parameters in these models is time-consuming and has severe requirements on experimental skills and apparatus. These have blocked the use of eq 14 and eq 15 for several decades. In contrast, the modified L-H model only needs four more experiments to calculate parameters a ∼ d for the mixture of H2O, CO2, H2, and CO, and only needs two more experiments to calculate parameters a and b for the mixture of H2O and CO2. In order to test the accuracy of modified L-H model, we have calculated a ∼ d using the experimental data in Figures 10 and 11. And we have also conducted several experiments at 0.8 MPa to validate the proposed model at other conditions. The experiments used for modification factor calculation are listed in Table 5. The experiments used for verification of the proposed model are listed in Table 6. The verification results are shown in Figure.12. The traditional L-H models based on common or separate active sites assumptions were also compared with the proposed model. Figure.12 shows that the values predicted from modified L-H model are closer to experimental results.

The Modified L-H Model. Figure.10 and Figure.11 indicate that the L-H model based on common or separate active sites assumptions cannot describe coal char gasification in the mixture of H2O, CO2, H2 and CO under pressured conditions. The gasification reaction rates from experiments are larger than the values predicted from the L-H model based on common active sites assumption. There are two possible explanations:12 (1) There are more chances for the surface oxide complexes to be collided by CO2 molecules, which will accelerate the desorption rate of surface oxide complexes. And the gasification rate is decided by the rate of desorption rate of surface oxide complexes.14 (2) The chemical bond strength of C−C(O) is weaken by the increase of surface oxide complexes. No matter which explanation is right, the gasification rate is larger than the value predicted by L-H model based on common active sites assumption. So we introduce a modification factor η into eq 23, and η is a function of temperature, pressure, and partial pressures of every gas component: r=

k1PH2O + k4PCO2 1 + k 2PH2O + k 3PH2 + k5PCO2 + k6PCO

(25) 837

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prerequisite can be fulfilled when reaction pressure is below 1.0 MPa. However, when reaction pressure is higher than 1.0 MPa, the linear relationship does not exist. At present, the modified L-H model can only be used when reaction pressure is lower than 1.0 MPa. We have to find other method to deal with the conditions with reaction pressures above 1.0 MPa.

Table 5. Experiments Used for Modification Factor Calculation experiment number 1 2 3 4 5 6 7 8 9 10

T (K)

total pressure (MPa)

PH2O (MPa)

PCO2 (MPa)

PH2 (MPa)

PCO (MPa)

1198 1198 1148 1148 1198 1198 1198 1198 1173 1173

0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.8 0.8

0.1 0.2 0.1 0.2 0.25 0.2 0.25 0.2 0.16 0.4

0.4 0.3 0.4 0.3 0.2 0.25 0.2 0.2 0.64 0.4

0 0 0 0 0.05 0.025 0.025 0.05 0 0

0 0 0 0 0 0.025 0.025 0.05 0 0

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CONCLUSIONS Coal char gasification in the mixture of H2O, CO2, H2, and CO was investigated on a modified PTGA system at 1148 to 1198 K and 0.5 MPa. The effect of pressure and the inhibition effect of H2 and CO on char gasification have been studied. Results show that the reaction rate of char-H2O gasification at 0.5 MPa is about 1.9 as high as that at 0.1 MPa, and the reaction rate of char-CO2 gasification at 0.5 MPa is about 2.1 as high as that at 0.1 MPa. The gasification reaction rates of char-H2O and charCO2 gasification are obviously inhibited by H2 and CO. And the inhibition effects seem stronger as the reaction pressure increases. The reciprocal of gasification reaction rate and the reciprocal of PH2O or PCO2 have good linear relationship at 0.5 MPa. Therefore, the kinetic parameters of k1 ∼ k6 in L-H model were derived from these linear plots. The L-H models based on common or separate active sites assumptions were verified for char gasification in the mixture of H2O, CO2, H2, and CO at 0.5 MPa. The results indicate that the L-H models based on common or separate active sites assumptions cannot predict experimental data and the gasification reaction rates from experiments are higher than those from L-H model based on common active sites assumption. Finally, a modified L-H model was proposed to describe char gasification in the mixture of H2O, CO2, H2, and CO at elevated pressure. The proposed model is very easy to use because the modification factor can be calculated simply. And the verification results show that the proposed model has better accuracy than the L-H models based on common or separate active sites assumptions.

Table 6. Experimental Conditions of Verification of the Proposed Model experiment number 1 2 3 4 5 6 7 8

T (K)

total pressure (MPa)

PH2O (MPa)

PCO2 (MPa)

PH2 (MPa)

PCO (MPa)

1198 1198 1148 1198 1198 1198 1173 1173

0.5 0.5 0.5 0.5 0.5 0.5 0.8 0.8

0.15 0.25 0.25 0.225 0.175 0.15 0.24 0.32

0.35 0.25 0.25 0.225 0.25 0.25 0.56 0.48

0 0 0 0.025 0.025 0.05 0 0

0 0 0 0.025 0.05 0.05 0 0

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AUTHOR INFORMATION

Corresponding Author

*Phone: +86-571-87952802. Fax: +86-571-87951616. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by National High Technology Research & Development Program of China (No. 20136AA051203), Program for New Century Excellent Talents in University (NCET-09-0696), and Collaboration Project of CERC-ACTC (2010DFA72730-201).

Figure 12. Verification of the proposed model.

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FUTURE WORK The modified L-H model can easily be used to describe char gasification in the mixture of H2O, CO2, H2 and CO under pressured conditions. Although it is more accurate than the L-H models based common or separate active sites assumptions, there is still room for improvement. Future research should be focus on the function of modification factor. The effect of partial pressures of every gas component may be not linear, so we could find some other functions to describe the modification factor. Another problem about the proposed model lies in the fact that the kinetic parameters of k1 ∼ k6 should be obtained at first. Deriving k1 ∼ k6 has a prerequisite of linear relationship between 1/r and 1/PH2O or 1/PCO2. This

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REFERENCES

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dx.doi.org/10.1021/ef4018527 | Energy Fuels 2014, 28, 832−839