Mathematical Modeling for Coal Gasification Kinetics in Supercritical

Sep 30, 2016 - ABSTRACT: Supercritical water gasification of coal is a newly clean coal technology. In this study, we established a quantitative model...
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Mathematical Modeling for Coal Gasification Kinetics in Supercritical Water Xiaohui Su, Liejin Guo,* and Hui Jin State Key Laboratory of Multiphase Flow in Power Engineering (SKLMF), Xi’an Jiaotong University, 28 Xianning West Road, Xi’an, 710049 Shaanxi, China ABSTRACT: Supercritical water gasification of coal is a newly clean coal technology. In this study, we established a quantitative model for the reaction kinetics of coal gasification in supercritical water. The large number of real intermediates formed during gasification were lumped using volatile and fixed carbon, and mass balance was also ensured in kinetic equation which would facilitate access to a comprehensive model considering flow and heat transfer. The model focused on the formation of the individual gaseous species (H2, CO2, CH4, CO). Then the model was applied to fit the experimental data and kinetic parameters were estimated. It was found that predicted results of the model were in accordance with experiments. The model predicted that volatile completely converted into gas quickly when temperature reached above 650 °C, and the reforming reaction of fixed carbon became the control step of gasification. Hydrogen was mainly from volatile decomposition in the initial short stage and water gas shift reaction then contributed to the hydrogen production. Carbon reforming reaction dominated hydrogen generation after about 5 min. Methane generated from the direct decomposition of volatile and the effect of methanation reaction was negligible. Carbon monoxide was generated during the volatile decomposition and it was consumed simultaneously in water gas shift reaction with substantial carbon dioxide produced. As a result, carbon monoxide content accounted for a small percentage and hydrogen and carbon dioxide dominated the gas products of gasification.

1. INTRODUCTION Coal based energy will continue to dominate the energy supply of China in the coming decades.1 However, the carbon emission and environment pollution (NOx, SOx, and PM 2.5) caused by overuse of coal have become a threat to human survival and development. It is an urgent task to find an alternative coal utilization way. Supercritical water gasification (SCWG) presents a new way to utilize the chemical energy in coal.2,3 It holds great advantage over traditional coal gasification: (1) Supercritical water (SCW) has unique physical and chemical properties, such as low viscosity, high diffusivity, and good miscibility with various organic compounds, which makes it a perfect solvent for intermediates formed during reaction.4,5 As a result, chemical reactions can be promoted by conducting in an environment of homogeneous aqueous phase; (2) Wet feedstock can be processed without drying step, which is profitable for saving energy needed; (3) There is no sulfur and nitrogen oxides emitted directly into air and carbon dioxide produced can be easily captured by manipulating the temperature and pressure.2 The combined power generation and synthesis gas production based on coal gasification in SCW holds great promise to meet the huge energy demands of China in the future.2 Many research on SCWG were focused on gasification characteristics, experimental apparatus development, and catalysts screening in the past decades and plenty of useful information was obtained.6−12 Deshpande et al.13 investigated lignite and bituminous coal conversion in SCW in an autoclave and found that char formation was serious before the reactor was heated to supercritical condition. Townsend et al.14 studied the volatile extraction from coal in SCW and concluded that volatile was mainly produced through hydrolysis reaction. The role of water in supercritical condition was emphasized and it © XXXX American Chemical Society

was thought that water could participate in coal conversion and facilitate the formation of light products.15,16 However, studies on reaction mechanism and kinetics of coal SCWG are far from enough, which impedes the scale-up and industrialization of this technology. Comprehensive kinetics for this process are of great practical importance and in urgent demand. Some work has been conducted to quantify the reaction kinetics of biomass and model compound conversion in SCW,17−23 which may provide us useful information. Wang et al.24 investigated the conversion and kinetics of coal oxidation in SCW and found that the process can be viewed as a pseudo first order reaction. Vostrikov et al.25 considered homogeneous, random pore and unreacted core models for coal gasification in supercritical water. The kinetic model was established with assuming first-order reaction and Arrhenius law. Pre-exponential factor was estimated to be 1.3 × 103.1 s−1 and activation energy was 103 kJ/mol. Jin et al.26 developed a more detailed gasification kinetics model considering the formation of each gas species. Carbon reforming, water gas shift (WGS), and methanation reactions were all taken into account thus the gas generation and consumption details were predicted. Nevertheless, the kinetics model above failed to distinguish pyrolysis reaction and carbon gasification occurring in the process.25,26 The two key components, volatile and fixed carbon in coal, have different reacting behavior in SCW according to previous research.14,27 Coal conversion goes through fast gasification of volatile and slow gasification of fixed carbon in Received: June 27, 2016 Revised: August 12, 2016

A

DOI: 10.1021/acs.energyfuels.6b01557 Energy Fuels XXXX, XXX, XXX−XXX

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SCW. In this study, a mathematical model of reaction kinetics will be established based on the reaction pathway summarized in previous study27 and it will be applied to fit the experimental data obtained with quartz reactor. Reaction rates were estimated by the least-square method. Then the model was used to predict the gasification behavior and gas formation rate was also analyzed.

C + 2H 2O → CO2 + 2H 2

(6)

Water gas shift reaction: k7

CO + H 2O ↔ CO2 + H 2

(7)

Mathanation reaction: k8

CO + 3H 2 ↔ CH4 + H 2O

2. MODEL DEVELOPMENT

The equations above are the overall reaction network of coal gasification in supercritical water. It considers the all potential gas formation pathway and avoids the fussy description of intermediates conversion. 2.2. Mathematical Modeling of Reaction Kinetic. The kinetics equation then was built after the reaction network was established. Each equation was assumed to be the first order of each reactant.24,25 Arrhenius equation was employed to evaluate rate constant. Reaction rate for every single reaction is shown in eq 9.

2.1. Reaction Mechanism and Pathway. Coal conversion process in SCW is very complicated with various intermediates formed. Competitive pyrolysis and hydrolysis reaction, we simply call this the pyrohydrolysis reaction, occurred simultaneously in supercritical water environment. Fragments released during pyrohydrolysis reaction can be dissolved in SCW. They decompose into gas eventually after a series of intermediate conversions. The methyl groups in the macromolecule, for example, can be directly converted into CH4 during the pyrohydrolysis.28,29 After that, the residual solid part, mainly composed of polycyclic aromatic hydrocarbon, will react with water to produce H2, CO, and CO2. Carbon reforming is a relatively slow process and it contributes to the most gas produced in the later stage of gasification. Methanation reaction is generally thought to take place in gasification. However, its effect is limited according to thermodynamics. We do not assume the molecular formula of coal and intermediates in the reaction equation proposed in our research, just the coal composition (content of volatile and fixed carbon) needs to be known. This could avoid the quantification of thermophysical properties of the assumed intermediates when considering flow and heat transfer in a CFD model. The assumed intermediates by previous research17,26 are unknown, thus their properties are not available. The mass balance in every single reaction is also ensured during the construction of kinetic difference equations in this model, which is more nearing to reality than research by others.17,19 Light hydrocarbons in coal matrix will first be released once the coal contacts with SCW because of the breakup of weak bonds in the big molecules and they will decomposed further into smaller hydrocarbon molecule (C1 and C2). This process goes through a series of intermediate conversion and the conversion occurred quickly. The final outcome is the formation of gases (H2, CO2, CH4, CO, and C2) despite the detailed intermediate process. C2 content accounts for a small percentage generally and its contribution to carbon gasification is negligible.30 It is ignored in this study. We just care about the gas formation and ignore the comprehensive middle process. Therefore, eqs 1 to 4 are summarized to describe the conversion of volatile to gas. The solid residuals will be converted into gas through the heterogeneous carbon reforming reaction, as shown in eqs 5 and 6. The homogeneous reactions, such as water gas shift reaction (eq 7) and methanation reaction (eq 8), occurring among the gas products determine the eventual distribution of gas products. The light hydrocarbons released at the beginning of gasification are presented by Vol and the solid residual by C. The large amount of inenarrable intermediates will be ignored because it is neither practical nor economic to consider all intermediates and reactions involved in gasification. Vol pyrohydrolysis reaction: k1

Vol → H 2

⎛ E ⎞ ⎟[reactant 1][reactant 2] r = A exp⎜ − ⎝ RT ⎠

k2

k3

Vol → CH4 k4

Vol → CO2

dmVol /dt = − k1mVol − k 2mVol − k 3mVol − k4mVol

(10)

dmC /dt = − 12k5mC /12C H2O − 12k6mC /12C H2O

(11)

dC H2O/dt = − k5mC /12C H2O − 2k6mC /12C H2O − k 7C H2OCCO + k 7/K 7C H2CCO2 + k 8CCOC H2 − k 8/K8C H2OCCH4 (12) dC H2/dt = k1mVol /2 + k5mC /12C H2O + 2k6mC /12C H2O + k 7CCOC H2O − k 7/K 7C H2CCO2 − 3k 8CCOC H2 + 3k 8/K8CCH4C H2O

k5

(13)

dCCO/dt = k 2mVol /28 + k5mC /12C H2O − k 7CCOC H2O + k 7/K 7C H2CCO2 − k 8CCOC H2 + k 8/K8CCH4C H2O (14) dCCH4 /dt = k 3mVol /16 + k 8CCOC H2 − k 8/K8CCH4C H2O

(15)

dCCO2/dt = k4mVol /44 + k6mC /12C H2O + k 7CCOC H2O − k 7/K 7C H2CCO2 K7 =

(2)

K8 =

(3)

(16)

C H2·CCO2 CCO·C H2O

(17)

CCH4·C H2O CCO· C H32

(18)

where, mVol is the mass of unconverted volatile; mC is the mass of unconverted fixed carbon; Ci represents the molar concentration of gas species, subscript i denotes H2, CO, CH4, and CO2; k1−k8 are rate constants; K7 and K8 represent the chemical equilibrium constant of water gas shift reaction and methanation reaction, respectively. The value of chemical equilibrium constants at different temperature are shown in Table 1.

(4)

Fixed carbon reforming reaction: C + H 2O → CO + H 2

(9)

where, [reactant1] and [reactant2] represent the concentration of reactant in chemical reaction formula. Eqs 10 to 16 are the mole balance differential equation for each component during gasification reaction. Vol and C are accounted in mass and other gas species are in molar concentration.

(1)

Vol → CO

(8)

(5) B

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min and still increased significantly after 5 min. CH4 formed at the beginning and almost no longer changed the next time. A good model should predict the experiments well conducted under different conditions from the data used for parameters estimation. Figure 2 shows the comparison between predicted results by model and other sets of experimental data. It can be seen that model prediction can describe the gas formation behavior well. Therefore, the present mathematical kinetic model can adequately describe Zhundong coal gasification behavior in SCW within the operating conditions investigated. The model was then used to predict cases with different coal concentration. It was found that gas yields per unit mass of coal loaded in reactor increased when coal concentration increased. It is because water loaded in reactor is always in excess of its demand for complete conversion of carbon. Consequently gas yields are dependent on coal mass loaded. However, it is not consistent with the experimental result in our previous study,27 in which gas yields per unit of coal mass decreased with the increase of coal loading. This occurs because heat and mass transfer between particles and water may deteriorate when coal concentration increases. What is more, the particles are not dispersed uniform in quartz tube reactor according to experiments so the situation may be worse than we thought. As a result, particles may convert without keeping at the target temperature and the actual conversion temperature may be below the target temperature to some degree, especially for the site in reactor that particles gather. Constructing a comprehensive model considering particle flow, heat transfer, and reaction is a very complicated task and it will be discussed in detail in the future study. Thus, even the overall gas yields increase significantly, they decrease when normalized to per unit mass of coal. However, the kinetic model was built with the assumption that reaction conducts at a constant temperature. Thus, the error becomes significant when coal loading increases. It may be close to the isothermal condition when coal concentration is low. According to experiments, sensitivity of gas yields with coal concentration greatly reduced when coal concentration is below 5 wt% when temperature is less than 650 °C. Consequently experimental data under this condition may be closest to the intrinsic result at the target operating condition. Therefore, experimental data obtained with 5 wt% were viewed as the representative gasification results at the target temperature. It is necessary to improve the experimental setup to gain more precise data in order to make a thorough inquiry into coal gasification in SCW in the future. Volatile and fixed carbon amounts with residence time, which were not available from experiments directly, were also quantified with the present model. Volatile and fixed carbon amounts at temperature 600, 650, and 700 °C with 5 wt% coal loading are shown in Figure 3. It is observed that volatile

Table 1. Chemical Equilibrium Constants of Water Gas Shift Reaction and Methanation Reaction equilibrium constant

550 °C

600 °C

650 °C

K7 K8(L2·mol−2)

3.64 273.70

2.68 41.66

2.05 7.66

3. PARAMETERS ESTIMATION The model was applied to fit the experimental data with quartz reactor.27 Gas yields with residence time are used to value the parameters estimation. The experimental data with temperature from 550 to 650 °C, which is common in fluidized reactor according to our previous research,12,31 was selected as the typical operating condition for the parameters estimation. The gasification was thought to proceed in a kinetically controlled region because the entire reaction was far from equilibrium. The kinetic parameter ki at a given temperature in the model was estimated by tuning them until the smallest sum of squared errors between the gas yields calculated from model and experimental data was achieved. Four-order and five-order Runge−Kutta algorithm was employed to solve the differential equations and local optimization algorithm was used to search the optimal values of parameters. The initial values for rate constants were obtained by trial-and-error method. The rate constants for reverse reactions (k7r, k8r) were determined by the forward rate constants (k7, k8) and the equilibrium constant (K7 and K8). The equilibrium constants were calculated from the gas species molar concentration after the chemical equilibrium was achieved, as shown in eqs 17 and 18. Table 2 shows the rate constants at given temperatures and Arrhenius parameters for each reaction were obtained. Preexponential and activation energy were estimated by the linear regression method. 4. RESULTS AND DISCUSSION The model was used to predict gas formation with the obtained kinetic data and the validity was confirmed. Then gas species formation rate was calculated and analyzed in order to evaluate the contribution of each single reaction for gas species formation. The applicability of present model for various types of coal samples was also tested in the end. 4.1. Model Validation. The balance differential equations were used to predict gas formation after kinetic data were obtained and the prediction was compared with experimental data which were used to fit by the model, as shown in Figure 1. It can be seen that parameters estimation is at a satisfactory level. Gas products generated quickly in the initial stage of gasification and then the rate slowed down after 2 min. CO amount reached maximum at about 1 min and then decreased to a constant value. H2 and CO2 amounts rose up quickly in 5 Table 2. Rate Constants and Arrhenius Parameters 550 °C −1

k1(min ) k2(min−1) k3(min−1) k4(min−1) k5(L.g−1·min−1) k6(L.g−1·min−1) k7(L.mol−1·min−1) k8(L.mol−1·min−1)

1.08 2.29 1.56 8.65 2.89 7.62 5.13 0

× × × × × × ×

−02

10 10−01 10−01 10−01 10−04 10−05 10−02

600 °C 2.52 5.40 2.73 9.83 3.87 4.67 1.74 0

× × × × × × ×

650 °C

−02

10 10−01 10−01 10−01 10−04 10−04 10−01

4.08 2.25 8.21 1.22 4.47 1.23 2.34 0 C

× × × × × × ×

−02

10 1000 10−01 1000 10−04 10−03 10−01

ln A

Ea (kJ/mol)

3.7482 15.2855 9.1584 −1.0679 −8.1678 12.3465 7.2192 

84.34 143.44 104.07 21.82 27.76 176.64 96.83  DOI: 10.1021/acs.energyfuels.6b01557 Energy Fuels XXXX, XXX, XXX−XXX

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Figure 1. Gas yields prediction with the kinetic model. (a) 550 °C, (b) 600 °C, (c) 650 °C, (d) CE with temperature (5 wt% coal loading).

Figure 2. Gas yields comparison between model prediction and experiments. (a) 580 °C, (b) 630 °C, (c) 680 °C, (d) 700 °C (5 wt% coal loading).

gas completely in 2 min and fixed carbon amount also decreased obviously. When temperature further increased to 700 °C, volatile completely converted more quickly and more fixed carbon consumed in the same residence time. It can be concluded that volatile conversion mainly controls the

content decreased significantly in 30 min while the change of fixed carbon amount with residence time was almost not detected at 600 °C. Fixed carbon was not reactive and volatile conversion dominated the process below 600 °C. When temperature increased to 650 °C, volatile almost converted into D

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predict the gas yields and CE value under conditions investigated. The contribution of individual reaction to the conversion rate for each single species is also in interest during gasification and it can be calculated with rate constant and species mole concentration. For example, H2 generation rate in forward water gas shift reaction is k7CCOCH2O and consumption rate in reverse reaction is k7/K7CCO2CH2. Rate for each gas species formation and consumption in every single reaction in which it participated is presented and compared in this section. The operating condition is 650 °C with 5 wt% coal loading. In Figures 5, 6, 7, and 8, it is observed that gasification process shows two distinct regions. Almost all reactions

Figure 3. Volatile and fixed carbon unconverted with residence time.

gasification reaction rate below 600 °C and fixed carbon gasification completely controls reaction rate above 650 °C when catalysts are absent. Generally we make many efforts to raise the operating temperature until to 650 °C for fluidized bed reactor ensuring that volatile can convert into gas completely. At this time, carbon reforming reaction is always the limiting step of carbon conversion efficiency. Equilibrium composition for gas species based on minimizing Gibbs’ free energy of the system was also calculated and compared with model prediction, as shown in Figure 4. It can Figure 5. H2 generation and consumption rate with residence time.

Figure 4. Comparison of gas mole fraction between model prediction and equilibrium at 650 °C.

Figure 6. CO2 generation and consumption rate with residence time.

be seen that model predictions got closer to thermodynamic chemical equilibrium calculations when residence time is long enough at 650 °C. There was a tiny difference between model prediction and equilibrium data for gas mole fraction after 120 min. The model shows a good performance in predicting the equilibrium composition. Hydrogen production might be further improved by extending residence time. However, long residence time is not economic for a continuous tube or fluidized bed reactor. Thus, it brings catalysts to front and many efforts have been devoted to it and great progress has been achieved.6,10,11,29,32−34 4.2. Reaction Rate Analysis. Gas and intermediates amounts with residence time were calculated directly according to the model and it was found that the model could reasonably

conducted quickly in the initial 5 min and reaction rate slowed down significantly beyond 5 min. H2 generation and consumption rate are shown in Figure 5. Hydrogen was originally produced from volatile decomposition, carbon reforming, and water gas shift reaction and it mainly generated from volatile decomposition and forward WGS reaction. Conversion of volatile to H2 occurred in the initial 1 min rapidly and then WGS turned into the main reaction to produce H2 in the next time. Carbon reforming reaction SRI and SRII also contributed to hydrogen production although the hydrogen formation rates from them were much smaller than volatile decomposition and WGS in initial 5 min. However, SRII played an important role in hydrogen content increase after 5 min. Therefore, carbon reforming reaction is a relatively E

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confirm the point that CH4 is produced from methyl groups conversion in pyrohydrolysis.28,29 Thus, CH4 amount almost became a constant value when the volatile converted completely in the initial stage of reaction. This is different from the results obtained by other research19,26 that methanation reaction made a significant contribution to methane production according to their study. The results in the current study are supported by some viewpoints from previous studies.28,29,35,36 Resende calculated methanation reaction rate for cellulose and lignin28 and the results obtained are that the rate constant of methanation reaction is zero for cellulose and 7.71 × 10−2 L·mol−1·min−1 for lignin. Matsumura et al.35,36 concluded that methane would probably form through the pyrolysis of reactants rather than through carbon steam reforming reaction. Therefore, rate constant for each reaction in supercritical water gasification is influenced by the type of feedstock. Figure 8 is CO formation and consumption rate. It can be seen that it formed mainly through volatile decomposition, carbon reforming, and reverse reaction of WGS. SRI rate was so small thus its contribution was negligible. CO was released out quickly in volatile decomposition in initial stage of reaction and then consumed in WGS immediately. Therefore, CO was in smallest amount through entire reaction. The yellow curve below x axis represents the CO consumption rate in water gas shift reaction. It is a negative value because CO was consumed in this reaction. SCW environment makes WGS reaction shifting in the direction of CO consumption and H2 formation. Forward WGS are enhanced significantly in SCWG compared with conventional gasification conditions.19 As a result, hydrogen-rich gases with low CO amount are obtained directly from this process. 4.3. Coal Type Dependence. Various type of coal could be processed in SCW according to previous research.30,31,37−39 Kinetic data were evaluated with Zhundong coal as feedstock in the present study. The applicability of current kinetic model to other type of coal also needs to be explored. Carbon gasification efficiency of additional five coal samples were also predicted with the model and were compared with experimental data. Elemental and proximate analysis of these coal samples are shown in Table 3. Degree of coalification from Yimin lignite to Semicoke is from low to high rank. Figure 9 shows the carbon gasification efficiency at 600 °C with 5 wt% coal loading predicted by kinetic model. It can be seen that CE decreased with the increase of coalification degree. CE for lignite was much higher than bituminous coal and Semicoke CE is the smallest. Therefore, it can be concluded that coal becomes stubborn when coalification degree increases. Lignite has higher volatile content and volatile is tractable in converting into gas, thus leading to higher CE and more gas

Figure 7. CH4 generation and consumption rate with residence time.

Figure 8. CO generation and consumption rate with residence time.

slow process in SCW and longer time is needed in order to improve carbon conversion. Residence time (30 min) here used is much longer than that (15 s) by Jin et al.26 Longer time could provide more information about the change of gas yield and reaction rate with residence time and eliminating the accidental error in the experiments. Similar with H2, volatile decomposition, carbon reforming, and WGS reaction were main reactions for CO2 production. Carbon reforming reaction rate was much less than the two former reactions in 5 min and became important beyond 5 min for CO2 content increase. Methanation reaction is negligible for CH4 formation according to parameter estimation. It was produced from only one way from Figure 7, volatile decomposition. It might Table 3. Elemental and Proximate Analysis of Coal Samples elemental analysis (wt%)

a

proximate analysis (wt%)

coal samples

C

H

N

S

Oa

M

A

V

FC

Yimin lignite Hami lignite Zhundong bituminous coal Shenmu bituminous coal Hongliulin bituminous coal Semicoke

40.5 47.17 56.99 71.26 74.29 68.58

3.25 3.05 2.4 4.12 4.69 2.27

0.57 0.6 0.47 0.99 1.00 0.86

0.19 0.51 0.46 0.64 1.12 0.86

21.43 14.82 12.62 9.54 9.26 11.39

18.42 8.8 17.1 10.97 2.79 2.5

15.64 25.05 9.96 2.48 6.84 13.55

32.21 29.21 23.91 31.38 33.19 21.24

33.73 36.94 49.03 55.17 57.18 62.71

By difference. F

DOI: 10.1021/acs.energyfuels.6b01557 Energy Fuels XXXX, XXX, XXX−XXX

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ACKNOWLEDGMENTS This work was financially supported by the State Key Program of National Natural Science Foundation of China (Grant No. 51236007, 51306145, 51527808) and supported by the China National Key Research and Development Plan Project (No. 2016YFB0600100).

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Figure 9. CE prediction by kinetic model with different coal sampls at 600 °C with 5 wt% coal loading.

products. For Semicoke which has the highest fixed carbon content, more severe operating condition is necessary in order to achieve high carbon gasification efficiency. In addition to that, experimental values of CE for Yimin lignite, Hami lignite, Shenmu bituminous coal, and Semicoke were compared with the model prediction. It can be seen from Figure 9 that kinetic model can predict CE value with residence time with acceptable errors. As a result, the mathematical model developed in current research can adequately describe gasification behavior in SCW for different type of coal under the conditions investigated.

5. CONCLUSIONS A new quantitative model for the coal gasification kinetics in SCW was developed and validated in this study. The large amount of real intermediates generated during reaction were lumped by coal ingredient, volatile, and fixed carbon, and mass balance was also ensured which could facilitate access to a CFD model with flow and heat transfer taken into account. The model considered the potential sources of each gas species and ensured mass balance in conversion of every species. Kinetic parameters obtained from model were discussed and gas species formation or consumption rate was analyzed. It was found that carbon reforming was the control step above 650 °C while volatile pyrohydrolysis would limit reaction significantly below 600 °C. The maximum rate occurred within the initial 2 min and gas yields increased gently beyond 5 min thus excessive residence time is meaningless considering economic efficiency. The applicability of the present kinetic model for different type of coal was also validated. Kinetic model developed in our research can describe gasification behavior in SCW adequately for different types of coal within operating conditions investigated.

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REFERENCES

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*Telephone: +86 29 82663895; Fax: +86 29 82669033. E-mail: [email protected]. Notes

The authors declare no competing financial interest. G

DOI: 10.1021/acs.energyfuels.6b01557 Energy Fuels XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.energyfuels.6b01557 Energy Fuels XXXX, XXX, XXX−XXX