Universal Devolatilization Process Model for Numerical Simulations of

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A Universal-Devolatilization-Process (UDP) Model for Numerical Simulations of Coal Combustion Kun Luo, Jiangkuan Xing, Yun Bai, and Jianren Fan Energy Fuels, Just Accepted Manuscript • Publication Date (Web): 18 May 2017 Downloaded from http://pubs.acs.org on May 23, 2017

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Energy & Fuels

A Universal-Devolatilization-Process (UDP) Model for Numerical Simulations of Coal Combustion

By

Kun Luo, Jiangkuan Xing, Yun Bai, Jianren Fan* State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou 310027, P.R. China

Submitted to

Energy & Fuels

*Corresponding author, E-mail: [email protected], Tel: 86-0571-87951764

ACS Paragon Plus Environment

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Abstract: A universal-devolatilization-process (UDP) model, considering the effect of particle instantaneous heating rates and coal types, is developed for an accurate prediction of devolatilization process in numerical simulations of coal combustion. This model is developed in the framework of a competing two-step model, based on the fitting and correlation works from the database which is constructed from the devolatilization process of 23 coal types under 40 heating rates predicted by the chemical percolation devolatilization (CPD) model. The kinetic parameters are determined in terms of coal types and instantaneous heating rates with the correlations obtained. The thorough validations of the UDP model, including the internal and external validations, are carried out through comparing the devolatilization process of the selected 23 coals and other 10 coals predicted by the UDP model and the CPD model, respectively. It is found that the UDP model can accurately predict the coal devolatilization process for a wide range of coal types and heating rates with a less computational cost, which will significantly improve the efficiency and accuracy of numerical simulations of coal combustion. The devolatilization components are not taken into account in the present study, and will be investigated in the future work. Keywords:

Coal

combustion;

Universal-devolatilization-process

(UDP)

Computational model;

devolatilization (CPD) model; Heating rates; Coal types.


fluid

dynamics;

Chemical

percolation

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1. Introduction As a major energy source, coal accounts for about 29.2% and 64.0% in the world and China’s energy structure respectively in 2016 [1, 2]. It has been widely utilized using the pulverize coal combustion (PCC) technology in majority of coal-fired thermal power plants [2]. With increasing environmental concerns, achieving clean and efficient utilization of coal in various combustion system is becoming a major and challenging problem that needs to be solved. Thus it is of great significant to get deep understanding of the coal combustion performance. However due to the difficulty and expensive cost to investigate the coal combustion field by measurement technique for industrial scale boilers, numerical simulation is becoming a powerful tool to understand coal combustion performance and optimize burner and furnace conditions [3]. Due to the complexity of coal combustion phenomena, numerical simulations of coal combustion require adequate sub-models to model chemical or physical processes [3-5], such as devolatilization, char combustion, particle movements and turbulent combustion. Coal devolatilization is always the key process and plays an essential role in coal combustion [6], such as the flame ignition and the formation of stabilization zone [7-9]. Thus the modeling of coal devolatilization is vital to obtain the correct coal combustion characteristic [10]. Coal devolatilization is a complex thermal decomposition process, and involves processes of cracking of labile bonds inside the coal structure, formation and reattachment of metaplast and vaporization of light gases and tars [11]. Models of coal devolatilization have progressed from


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simplified global models to network models with more complex description of chemical and physical processes involved. In simplified global models, such as one-step model [12-17], two-step model [14, 16] and distributed activation energy model [18-20], coal devolatilization is simplified as a global reaction with finite kinetic pathways without considering the physical structure of coal. In complicated network models, such as the chemical percolation devolatilization model (CPD) model [11, 21], the FLASHCHAIN model [22] and the FG-DVC model [23, 24], coal devolatilization is reasonable simplified considering the coal structure, chemistry and physical processes with the help of modern measurement techniques, such as Pyrolysis-Field Ionization Mass Spectrometry (Py-FIMS),

13

C-Nuclear Magnetic

Resonance (13C-NMR), and Thermogravimetry-Fourier Transform Infrared analysis (TG-FTIR). Comparatively simplified global kinetic models such as one-step model and two-step model have been widely employed for the coal devolatilization in most coal combustion simulations due to the simpler form in computation [25-30]. It is well-known that the devolatilization of coal particles is strongly affected by heating rates [11, 31, 32]. However, the kinetic parameters of those simplified global models are usually constant for different heating conditions instead of changing with heating rate and not universal for wide rank coals, causing large errors in predicting the coal particle behavior. Recently, those complex network models have been utilized in coal combustion simulations and more accurate predictions on the particle behavior compared with simple global models have been demonstrated [33, 34]. However, due


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to the computational complexity of those network models, the computational cost would observably increase compared with those with simplified global models. Rieth et al. [33] has directly coupled the CPD model into flamelet LES modeling of coal combustion, and compared with the single first order reaction model (SFOR). The computational cost of coal devolatilization with CPD is five times more than that with SFOR. Wang et al. [34] developed an online-CPD-coupled LES method. Compared to SFOR-LES, the online-CPD-LES costs 51.4% more computational time for one step, and the computational cost is increases by 124.4% for the particle equations. Thus it is an obvious contradiction between the prediction accuracy and the computation cost when employing the devolatilization models. Several groups have attempted to fit the kinetic parameters of a simplified global model from a more complex network model to resolve the contradiction. Ko et al. [35] developed a correlation for the heating rate dependent activation energy and pre-exponential factor of a one-step model from a distributed activation energy model (DAEM) for a Montana lignite. Liu et al. [36, 37] proposed a method to determine the kinetic parameters of a one-step model for a giving heating rate from PC Coal Lab using

the

FLASHCHAIN

model.

Hashimoto

et

al.

[38]

proposed

a

tabulated-devolatilization-process (TDP) model to determine the kinetic parameters of a one-step model for the next iteration based on the particle temperature history using the PC Coal Lab. Richards et al. [39] modified six different simplified global models to get better agreement with the CPD model predictions for a Utah bituminous Sufco coal through introducing parameters without physical meaning. These meaningful


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works are able to reduce computational cost, but the proposed models are not universal for different coals and heating rates. Thus it is necessary to develop a universal devolatilization model, considering the effect of coal type and heating rate, to get the similar prediction accuracy on the coal devolatilization as that of the complicated network models with acceptable computational cost. The

purpose

of

present

study

is,

therefore,

to

develop

a

universal-devolatilization-process (UDP) model to predict the devolatilization processes for numerical simulations of coal combustion, combing the advantages of the simplified global models and complicated network models. In the present study, only the devolatilization rate and total volatiles are considered, and the devolatilization components have not been taken into account. A devolatilization process database are constructed from devolatilization processes of 23 coals under 40 heating rates predicted by the CPD model. In the UDP model, all coal devolatilization processes are described with two competing reactions, of which kinetic parameters are determined by the correlations of heating rates and coal types, and the correlations are developed based on the fitting and analysis work from the database. Its validations, including internal and external validations, are carried out through comparing the devolatilization process of the selected 23 coals and other 10 coals predicted by the UDP model and the CPD model. The reminder of the paper is organized as follows. The two-step model, the CPD model and the brief methods of the UDP model are introduced in Section 2. The concrete procedure and methods used to propose the UDP model are presented in


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Section 2.3, including methods for fitting works, the UDP model for the specific coal and multi-coals. The proposed UDP model for the specific coal, UDP model for different coals and its validations, including final volatiles yield, total volatiles mass fraction and release rates, are presented and discussed in Section 3. Summary and conclusions are made in Section 4.

2. Approaches In the present study, the UDP model is developed based on the framework of the competing two-step model and database structured from the devolatilization processes predicted by the CPD model. Thus, the brief introduction of the two-step model, the CPD model and the methods and steps used to propose the UDP model are presented in this section. 2.1 Two-step Model In the two-step devolatilization model, the two competing reactions have widely varying activation energies so that one step dominates the devolatilization at low temperature, and the other one step dominates the devolatilization at high temperature [15]. The following simple scheme represents the devolatilization process of the two-step model:

(1) The volatile evolution is expressed as the following Eq. (2):


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-E1

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-E2

dV RT RT = C (α1 K1e p +α 2 K 2 e p ) dt Where

dV dt

(2)

donates the total volatiles release rate, C donates the raw coal fraction,

α1 and α2 are mass stoichiometric coefficients, K1 and K2 are pre-exponential factors, E1 and E2 are activation energies for two competing reactions. It is found that numerical results can be strongly affected by these six kinetic parameters [40], but it is difficult to obtain approximate values for those six kinetic parameters in advance of the simulation. A trial-and error method is usually used to obtain approximate values for those parameters and it may take a long time and effect. 2.2 Chemical Percolation devolatilization (CPD) model The CPD model describes the devolatilization behavior of rapidly heated coal based on the chemical structure of the parent coal [21, 41]. Thus it requires five chemical structural parameters: the average molecular weight per side chain ( Mδ ), the average molecular weight per aromatic cluster ( Mcl ), the coordination number ( σ +1 ), the initial fraction of intact bridges ( p ) and the initial fraction of char bridges 0

( c0 ). These parameters can be directly measured with the 13C-NMR. A correlation of the five input structure parameters ( Mδ , Mcl , σ +1 , p and c0 ) was also 0

developed so that the reasonable estimates of coal structure parameters could be obtained when

13

C-NMR data are not available if its elemental composition and

proximate analysis are in the fitting boundaries [42]. In the CPD model, coal is visualized as a macromolecular array composed of aromatic clusters that are interconnected by a variety of chemical bridges, and attachments to clusters may also include side chains. Upon heating, the CPD model


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describes the devolatilization process includes percolation statistics for a two-dimensional Bethe lattice to relate the number of broken bridges to the distribution of clusters that detached from the lattice, rates for bridge broken and side chain release, crosslinking of non-vaporized detached fragments that become part of the char, and vapor-liquid equilibrium to determine the size of detached clusters that vaporize to form tar. The CPD model has been proven to have great agreements with the experimental data over a wide range of heating rates, temperatures, coals, and pressures [11, 21, 43-46]. In this study, the CPD model is used as the accurate network model to generate devolatilization process database for the fitting of the competing two-step model and validations of the proposed UDP model. 2.3 Universal-devolatilization-process (UDP) model To develop the UDP model, several assumptions are first made: 1) Coal particle is homogeneous inside the particle and of uniform temperature; 2) Devolatilization product is a simple homogeneous mass and no specific components is considered; 3) Volatile release rate is given only by the particle temperature and the heating rate; 4) Devolatilization of different coals follows similar kinetic steps, and the kinetic parameters are determined upon the coal types and operating conditions. To get better accuracy, the framework of the competing two-step model is used to develop the present UDP model as expressed in Eq. (3), and the kinetic parameters are determined upon the coal types and heating rates as expressed in Eq. (4) based on the fitting and correlation works from the database constructed by the CPD model. − E1

− E2

dV RT RT = (V1∞ -V1t ) K1e p + (V2 ∞ -V2t ) K 2e p dt


(3)

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g = f ( C o a l ,T& ) , 　 g = K 1 , K 2 , E 1 , E 2 , V 1 ∞ ,V 2 ∞ 　　

(4)

Where V1 ∞ and V2 ∞ are the final volatiles yield of the two competing reactions,

V1t and V2t are the volatile yield at time t, K 1 , K 2 , E 1

an d E 2 are the kinetic

parameters same as the competing two-step model in Section 2.1, Coal donates the coal types, and T& donates the instantaneous heating rates. The detail expressions of

f (Coal,T& ) are investigated and presented in Section 3.The detailed procedure to propose the present UDP model is listed as below and shown in Fig. 1. Step 1: Obtain the devolatilization process for a specific coal at a constant heating rate with the CPD model. Step 2: Fit the kinetic parameters of the two-step model from the devolatilization processes obtained in Step 1. Step 3: Repeat Step 1 and Step 2 for 40 heating rates in a wide range for the specific coal. Step 4: Correlate the fit kinetic parameters with heating rates, and obtain the UDP model for the specific coal. Step 5: Validate the UDP model for the specific coal obtained in step 4 via predicting the devolatilization processes under heating conditions with varied heating rates, and compared with these predicted by the CPD model. Step 6: Repeat step 1, 2, 3 and 4 for another 22 selected coals with a wide range of volatiles matter (VM), and obtain the coefficients of the correlations with heating rates for each coal. Step 7: Correlate the coal structural parameters with the coefficients obtained in step 6


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to obtain the UDP model for different types of coals. Step 8: Validate the UDP model via predicting other 10 coals with a wide range of VM at four different heating conditions, and comparing with these predicted by the CPD model. Step 6 (Loop): Repeat step 1, 2 and 3 for another 22 coals The chemical percolation with a wide range of VM devolatilization (CPD) model Step 1: Obtain the devolatilization process with the CPD model

Step 3 (Loop): Repeat the fit work for 40 kinds of heating rates in a wide range

Devolatilization process of a specific coal at a constant heating (database) Step 2: Fit kinetic parameters of the two step model

Validate the applicability of the UDP model at heating condition with varied heating conditions

Kinetic parameters: V1∞ , V2 ∞ , K1, K2, E2, E1

Step 4: Correlate the kinetic parameters with heating rates The universal-devolatilizationprocess (UDP) model for the specific coal Step 7: Correlate with the coal structural parameters Obtain the expressions and coefficients of the correlations, and develop the universaldevolatilization-process (UDP) model for different-coals

Step 5: Validate the UDP model for the specific coal

Step 8: Validate the UDP model for different coals

Validate the applicability of the UDP model for wide ranges of coal and heating conditions

Fig. 1. Investigation flow charts of the proposition and validations of the UDP model.

Step 2, 4 and 7 are significant to develop the UDP model, and the corresponding methods are introduced in Sections 2.3.1, 2.3.2 and 2.3.3, respectively. 2.3.1 Fitting the two-step model from the CPD model


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Tot Volatiles Release Rates (1/s)

Energy & Fuels

CPD model Reaction 1+2 Reaction 1 Reaction 2

0

Time (s)

Fig. 2. Brief description of the fitting of the two-step model from the CPD model

Compared to the study of Richards et al. [39], the present fitting parameters are K 1 , K 2 , E 1 , E 2 ,V1∞ a n d V 2 ∞ 　 , and each has its kinetic meaning. Fig.2 shows the

brief description of the fitting work. All the kinetic parameters are fitted with equations below for different coal types under a wide range of heating rates. − Ei

dVi = (Vi∞ -Vit ) Ri， Ri = K i e RT dt

p

(5)

  dVi 1 ln   = ln ( K i ) - Ei ( ) RT V -V dt p  i∞ it 

(6)

V∞ =V2∞ +V1∞, Vt =V2t +V1∞

(7)

V2∞ -V2t = (V2∞ +V1∞) - (V2t +V1∞) =V∞ -Vt

(8)

dV2 d (Vt − V1∞ ) dVt = = dt dt dt

(9)

Where Vi∞ and V it are the final and instantaneous volatiles yield for each reaction in the fitting work and unclear before fitting, V∞ and V t donates the final and instantaneous volatiles yield predicted by the CPD model. Ri donates the rate constant for reaction I, and its value follows the Arrhenius equations. Each reaction rate can be expressed as Eq. (5), and i donates the reaction number. Kinetic parameters of each


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reaction can be obtained with the least square method for Eq. (6). Since the value of

dV1 and V 1 ∞ - V 1 t for reaction 1 cannot be obtained before fitting, but the value of dt dV2 and V 2 ∞ - V 2 t for reaction 2 can be obtained through Eqs. (7), (8) and (9) based dt on the devolatilization process predicted by the CPD model in the high temperature region. Thus the fitting work starts from the reaction 2 (high temperature region), and the detailed procedure is listed below. 1. Fit the kinetic parameters of reaction 2 with least square method from devolatilization process in the high temperature region predicted by the CPD model. 2. Calculate the devolatilization process of reaction 2 in all temperature region, and that of reaction 1 equals to the difference between that of the CPD model and reaction 2. 3. Fit the kinetic parameters of reaction 1 with least square method from devolatilization process obtained above. Through procedure above, all these six kinetic parameters V1∞ , V2∞ , K1 , K2 ,

E1 and E2 can be derived from the CPD model for a specific coal devolatilization process under a constant heating rate. This fitting work is essential and important to obtain the kinetic parameters form the CPD model and provides the data used for correlations of heating rates and coal types.

2.3.2 Universal devolatilization process model for a specific coal To study the effect of coal particle heating rates on the coal devolatilization and develop a UDP model applicable to a wide range of heating rates for a specific coal,


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the similar fitting works in Section 2.3.1 are carried out for each heating rate. In real pulverized coal combustor, most of the coal particles are usually rapidly heated at typical average heating rate of 105 K/s to a temperature more than 1700 K, and the devolatilization process is almost completed at the temperature of 1600 K [10, 34, 47]. Thus the effect of the final temperature is negligible and the final temperature is set to be 1600 K in the present study, and the coal is heated from 300 K to 1600 K under 40 constant heating rates with hold time twice as the time used to heat from 300 K to 1600 K. The 40 constant heating rates are in a wide range from 1 0 3 to 1 .2 × 1 0 6 K/s with more focus on high heating rates as shown in Fig. 3. All these kinetic parameters are obtained via fitting work from the CPD model. Correlations between the fitted kinetic parameters and the heating rates are developed and used to determine the kinetic parameters in the UDP model for the specific coal. The validations of the UDP model for the specific coal are carried out by predicting the devolatilization under four heating conditions as described in equations below and shown in Fig. 4, and comparing with that of the CPD model. Eqs. (10), (11) and (12) describe heating conditions with increasing heating rates since the volatiles release and burn, resulting a higher gas temperature and heating rates [26]. Heating condition 1: T&

= 106

t + 103

2.5 ×10 T& = 103 +

11

Heating condition 2:

(10) − 10

2600

6

t

Heating condition 3: T& = 1 0 3 + 1 0 0 t (12)


(11)

Page 15 of 43

2.5 × 10 − 10 5 t Heating condition 4: T& = 5 ×10 − 11

6

(13)

2600

1.2x106

Heating Rate (K/s)

1.0x106 8.0x105 6.0x105 4.0x105 2.0x105 0.0 0

5

10

15

20

25

30

35

40

45

Heating Rate Numbers Fig. 3. The distribution of heating rates used in present study. 6.0x10+05 5.0x10

Heating Rates (K/s)

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Heating condition 1 Heating condition 2 Heating condition 3 Heating condition 4

+05

4.0x10+05 3.0x10+05 2.0x10+05 1.0x10+05

300

600

900 Temperature (K)

1200

1500

Fig. 4. Heating conditions with varied heating rates used for validation in present study.

2.3.3 General devolatilization process model for different types of coals To extend the UDP model to be applicable for a wide range of coal types, 23 coals with a wide range of VM are investigated to study the effect of coal types on the devolatilization process with the similar methods in Section 2.3.2. The coal type


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information is listed in Table 1, and the content of carbon and VM are plotted in Fig. 5. All six kinetic parameters are obtained via fitting from the results of CPD model for these 23 coals and correlated with the measured coal structural parameters ( Mδ , Mcl ,

σ +1 , p and c0 ). Then, these devolatilization kinetic parameters could be obtained 0

through the above correlations with coal structure parameters instead of doing the fitting works again when other types of coals are studied. Table 1. Elements composition and volatile matter content for coals investigated in this study [48-52]. No.

Coal Source

%C (daf)

%H (daf)

%O (daf)

%N (daf)

%S (daf)

ASTM VM(daf)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Tomita et al. PSOC-1507D (Sandia) PSOC-1520 (BYU) DECS-11 (BYU) Tomita et al. DECS-1 (BYU) Tomita et al. PSOC 1507 (AR) Tomita et al. PSOC-1493 (AR) Tomita et al. ANL (AR) PSOC-1451 (AR) Kurose et al. ANL (AR) Tomita et al. Tomita et al. Goudey B (AFR) PSOC-1508D (Sandia) Tomita et al. PSOC-1508 (AR) DECS-21 (BYU) PSOC-1468 (ACERC)

65.4 66.6 67.4 68.5 69.1 70.7 71.8 72.9 74 77.7 78.5 82.6 83.2 84.79 85.5 86.9 87.8 88.5 88.8 89.4 91.1 93.8 95.4

4.9 4.26 5.37 4.94 4.8 5.83 4.7 4.83 5 5 5.8 5.25 5.32 5.19 4.7 5.6 4.7 4.94 4.37 4.4 4.44 3 1.38

28.80 25.16 24.39 24.96 23.90 20.83 19.20 20.34 18.60 13.51 14.40 9.83 8.83 7.7 7.51 5.2 5 1.4 5.14 3.2 2.47 1.4 1.86

0.6 1.12 1 1 1.4 1.47 1.4 1.15 1.9 1.37 0.9 1.56 1.64 1.78 1.55 1.9 2.1 2.23 1.06 2.2 1.33 1.3 0.84

0.3 2.89 1.84 0.64 0.6 1.18 2.9 0.7 0.4 2.38 0.4 0.65 0.89 0.54 0.74 0.3 0.4 1.75 0.6 0.8 0.5 0.5 0.53

54.00 49.60 53.40 61.70 52.00 53.60 45.00 49.80 39.00 47.40 50.00 37.60 41.70 31.72 31.60 41.00 25.00 19.30 17.20 17.00 19.50 8.00 3.90

This is the UDP model, in the framework of the competing two-step model, and


Page 17 of 43

its kinetic parameters are determined with heating rates and coal types via the fitting and correlation works from the database, which is constructed from devolatilization processes predicted by the CPD model for a wide range of coals and heating conditions. 100

70 Carbon content Volatile content

60

90

50

85

40

80

30

75

20

70

10

65

0 0

4

8

12

16

20

Volatile content

95

Carbon content

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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24

Coal Numbers Fig. 5. Carbon and volatile content of 23 coals in present study showing the diversity of the rank of selected coals.

Table 2. Elements composition and volatile matter content for coals used for validation [47, 51, 52]. No.

Coal Source

%C (daf)

%H (daf)

%O (daf)

%N (daf)

%S (daf)

ASTM VM(daf)

1 2 3 4 5 6 7 8 9

Tomita et al. Tomita et al. Tomita et al. 312 73-2 73-1 DECS-21 (BYU) 310 73-4

70.2 65.8 80.3 78.75 89.14 89.67 93.8 84.41 68.94

5.2 5.5 5 5.31 5.07 4.54 2.72 5.41 5.18

22.4 27.6 12.2 14.27 4.71 3.8 1.96 8.52 22.8

1.8 0.8 2 1.07 1.05 1.54 0.92 1.35 1.77

0.2 0.315 0.4 0.6 0.43 0.45 0.62 0.31 1.31

46 56 37 32.22 20.63 13.63 5.1 24.59 41.33


Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

10

339

81.17

4.16

12.51

Page 18 of 43

0.77

1.39

23.41

2.3.4 Model validations methods The proposed UDP model must have to be validated before using in the numerical simulations. In the present study, the validations of the UDP model are divided into internal and external validations. The internal validations are carried out through predicting the devolatilization processes and the total volatiles mass fraction of the selected 23 coals, and comparing with that of the CPD model. The external validations are investigated by predicting the devolatilization processes and the total volatiles mass fraction of the other 10 coals shown in Table 2, and comparing with that of the CPD model.

3. Results and Discussions 3.1 Universal-Devolatilization-Process model for a specific coal The UDP model for a specific coal named Beulah-Zap (No. 2 in Table 1) is developed through fitting work of kinetic parameters and correlations with heating rates, and validated via comparing with the CPD model under different heating conditions with varied heating rates. The results are presented and discussed in this section.

3.1.1 Fitting results from the CPD model under constant heating rates In the present study, all the six kinetic parameters ( K 1 , K 2 , E 1 , E 2 , V 1 ∞ a n d V 2 ∞ 　 ) for the specific coal are obtained through fitting work from the results of the CPD model under each heating rates, and shown in Table 3. It is necessary to introduce that the activation energies E1 for different heating rates fluctuate in a small range, thus


Page 19 of 43

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

an average value about 1.4 × 10 5 J/mol is used here for all heating rates. It is obvious that kinetic parameters except E1 are variable for different heating rates. The value of K 1 , K 2 , E 2 a n d V 1 ∞ increase with heating rate and the value of V 2 ∞ decreases with heating rates, which means that the dominance of the reaction 2 decreases when heating rates increases. Table 3. Kinetic parameters fitted from the CPD model under different heating rates 5

Data No.

Heating rates /10

V1 ∞

(K/s)

K1 /1010

E1 /105

(1/s)

(J/mol)

3

V2 ∞

4

K2 /10

E2 / 10

(1/s)

(J/mol)

1 2

0.010 0.030

0.172 0.181

0.665 0.995

1.400 1.400

0.405 0.399

2.723 8.414

5.343 5.579

3

0.050

0.187

1.186

1.400

0.394

14.131

5.692

1.531

1.400

0.391

28.664

5.850

1.963

1.400

0.386

57.909

6.011

2.273

1.400

0.385

87.485

6.108

2.537

1.400

0.383

117.287

6.177

2.737

1.400

0.381

146.414

6.232

2.918

1.400

0.380

175.937

6.277

3.084

1.400

0.380

206.971

6.315

3.247

1.400

0.380

238.322

6.348

3.355

1.400

0.378

266.254

6.378

3.457

1.400

0.375

292.564

6.404

3.906

1.400

0.373

410.260

6.489

4.272

1.400

0.371

527.606

6.554

4.614

1.400

0.369

643.554

6.606

4.894

1.400

0.369

762.879

6.649

5.128

1.400

0.367

876.906

6.687

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

0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000 1.400 1.800 2.200 2.600 3.000

0.191 0.197 0.199 0.201 0.203 0.205 0.205 0.205 0.208 0.210 0.213 0.215 0.217 0.217 0.219

19

3.400

0.224

5.304

1.400

0.363

965.552

6.720

20

3.800

0.228

5.474

1.400

0.359

1050.871

6.749

21

4.200

0.221

5.791

1.400

0.365

1230.252

6.776

22

4.600

0.221

6.015

1.400

0.365

1355.149

6.800

23

5.000

0.222

6.150

1.400

0.364

1461.051

6.823

24

5.400

0.220

6.472

1.400

0.366

1591.986

6.843

25

5.800

0.221

6.577

1.400

0.366

1709.182

6.863

26

6.200

0.228

6.665

1.400

0.358

1737.737

6.881


Energy & Fuels

27

6.600

0.221

6.961

1.400

0.365

1959.122

6.897

28

7.000

0.222

7.059

1.400

0.365

2069.286

6.913

29

7.400

0.223

7.088

1.400

0.363

2169.758

6.929

30

7.800

0.222

7.336

1.400

0.364

2306.231

6.943

31

8.200

0.221

7.476

1.400

0.366

2447.853

6.957

32

8.600

0.221

7.586

1.400

0.366

2572.324

6.970

33

9.000

0.223

7.754

1.400

0.364

2686.901

6.982

34

9.400

0.223

7.808

1.400

0.363

2787.428

6.994

35

9.800

0.224

7.914

1.400

0.362

2877.438

7.006

36

10.200

0.225

8.069

1.400

0.362

3005.836

7.017

37

10.600

0.224

8.191

1.400

0.362

3134.276

7.027

38

11.000

0.224

8.308

1.400

0.362

3250.201

7.037

39

11.400

0.225

8.398

1.400

0.361

3357.097

7.047

40

11.800

0.226

8.461

1.400

0.360

3461.231

7.057

Tot Volaties Mass Fraction

0.6 0.5 0.4 0.3

CPD

0.2 0.1 0 600

800

1000

Fitting Results Heating Rate 3 10 K/s 4 10 K/s 5 10 K/s 5 5x10 K/s 106 K/s

1200

1400

1600

Temperature (K) (a) 2000

Tot Volatiles Release Rate (1/s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 43

CPD Fitting Results Heating Rate 105 K/s 5 5x10 K/s 6 10 K/s

1500

1000

500

0 600

800

1000

1200

Temperature (K) (b)


1400

1600

Page 21 of 43

40

Tot Volaties Release Rate (1/s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

35

CPD

30

Fitting Results Heating Rate 3 10 K/s 4

10 K/s

25 20 15 10 5 0 600

800

1000

1200

1400

1600

Temperature (K) (c)

Fig. 6. Comparisons of the total volatiles mass fraction and release rate between CPD model and the fitting results: (a) total volatiles mass fraction, (b) total volatiles release rate at heating rate of 105 , 5 × 105 and 106 K/s , (c) total volatiles release rate at heating rate of 103 and 104 K/s.

Fig. 6 shows comparisons of the fitting results of total volatiles mass fraction release rate with these of the CPD model under a wide range of heating rates. It is found that the temperature at which devolatilization happens increases as the heating rate increases in the CPD model, and the heating rate has a remarkable impact on the devolatilization processes. In general, the fitting results are in good agreement with that of the CPD model both on the total volatiles mass fraction and release rate under a wide range of heating rates. The total volatiles release rate predicted by the CPD model has a local short peak in the relatively low temperature range (approximately 800 K), as marked by the red circle in Fig. 6. It is caused by the tar release due to the evaporation of the metaplast, but cannot be seized by the present fitting work, and can be taken into account by adding an extra reaction. However, the increase of the total volatiles caused by the local short peak can be neglected due to its small values


Energy & Fuels

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Page 22 of 43

compared with these in the high temperature range, thus local short peak is not taken into account in the present study.

3.1.2 Effect of heating rates As shown in Table 3, the kinetic parameters vary with different heating rates, which is different from the simplified global models. To describe the effect of heating rate on the devolatilization process and develop a devolatilization process model for the specific coal, correlations between the kinetic parameters and heating rates are developed below. It is found that all these kinetic parameters expect E1 , as plotted in Fig. 7, share a similar power function of the heating rate. Thus correlations, expressed as Eq. (14) and (15), are developed to describe the effect of heating rates on the devolatilzation process, in which the kinetic parameters are described by using a basic parameter a ( C o a l ) with the modifications of heating rate (T&)

b(Coal )

.

g(T&, Coal) = a(Coal) ×(T&)b(Coal )

(14)

g(T&) = a×(T&)b

(15)

) in Here, g donates the five kinetic parameters ( K 1 , K 2 , E 2 , V 1 ∞ a n d V 2 ∞ 　 each correlation, T& donates the instantaneous coal particle heating rate, and coefficients a and b are functions of coal types, Coal . In this section, the correlations are carried out for a specific coal, thus the effect of coal types are not taken into accounted here, and the expression can be expressed as Eq. (15). The values of coefficients a and b are different for each kinetic parameter and listed in Table 4, and the coefficients of the determination R2 are 0.9997, 0.9967, 0.9961, 0.9698 and 0.9681 for the correlation of E 2 , K 2 , K 1 , V 2 ∞

and 　 V1 ∞ , respectively,


as shown in Fig. 7.

Page 23 of 43

It is obviously found that the power function type of correlation can predict the kinetic parameters well for each constant heating rate in a wide range. Thus a UDP model for the specific coal is developed, and its kinetic parameter are determined by the correlations obtained above. Table 4. The value of coefficients

a and b for different kinetic parameters

K1

V1∞

Coefficients

(1/s)

a b

0.1457 0.03132

5.020E+08 0.3672

E2

(1/s)

4.070E+07 0.03933

0.4600 -0.01758

2.5241 1.011

4.0x106 3.5x106

7.0x104

K2 fit from CPD K2 predicted by correlation：

3.0x106

K2=aK2×(dT/dt)^bK2

2.5x106

6.5x104

E2 fit from CPD E2 predicted by correlation: 4

E2=aE2×(dT/dt)^bE2

6.0x10

2

R =0.99968

K2 (1/s)

E2 (J/mol)

K2

V2∞

(J/mol)

7.5x104

2

R =0.99668

2.0x106 1.5x106 1.0x106

5.5x104 5.0x105 0.0

5.0x104 0.0

2.0x105 4.0x105 6.0x105 8.0x105 1.0x106 1.2x106

0.0

2.0x105 4.0x105 6.0x105 8.0x105 1.0x106 1.2x106

Heating Rate (K/s)

Heating Rate (K/s)

(a)

(b)

1.0x1011

0.42 0.41

8.0x1010

V2∞ fit from CPD 0.40

6.0x10

V2∞ predicted by the correlation: V2∞=aV2∞×(dT/dt)^bV2∞

10

0.39

2

R =0.96813

V2∞

K1 (1/s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

4.0x1010

K1 fit from CPD

0.38

K1 predicted by the correlation: K1=aK1×(dT/dt)^bK1

2.0x1010

0.37

2

R =0.99605 0.36 0.0 0.35 0.0

2.0x105 4.0x105 6.0x105 8.0x105 1.0x106 1.2x106

0.0

2.0x105 4.0x105 6.0x105 8.0x105 1.0x106 1.2x106

Heating Rate (K/s)

(c)


Heating Rate (K/s)

(d)

Energy & Fuels

0.25 0.24 0.23 0.22 0.21

V1∞

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

0.20

V1∞ fit from CPD

0.19

V1∞ predicted by the correlation: V1∞ =aV1∞ ×(dT/dt)^bV1∞

0.18

2

R =0.96813

0.17 0.16 0.15 0.0

2.0x105 4.0x105 6.0x105 8.0x105 1.0x106 1.2x106

Heating Rate (K/s)

(e)

Fig. 7. Plots of kinetic parameters fitted from the CPD model and predicted by correlations : activation evergy: (a) E2 , pre-exponential factors: (b) K2 , (c) K1 , and final volatile yield of the two reactions: (d) V2∞ and (e) V1∞ .

3.1.3 UDP Model validations for a specific coal To validate the proposed UDP model for the specific coal, the devolatilization processes for Beulah-Zap under different heating conditions with varied heating rates as Eq. (10), (11), (12) and (13) describe are predicted by the UDP model and compared with that of CPD model. Fig. 8 shows the comparisons between devolatilization processes predicted by the proposed UDP model and the CPD model under different heating conditions. It is obvious that the proposed UDP model for the specific coal can predict the devolatilization process as precise as the CPD model in both total volatiles mass fraction and release rates under four heating conditions. For heating condition 1, 2 and 3, the peak value of the total volatiles release rate increases as the maximum heating rate increases. For heating condition 4, the release rate decreases relatively fast due to low heating rate and finite volatiles residues in the high temperature range.


Page 24 of 43

Page 25 of 43

(a)

Tot Volatiles Mass Fraction

0.6 0.5 0.4

CPD model UDP model Heating condition 1 Heating condition 2 Heating condition 3 Heating condition 4

0.3 0.2 0.1 0 600

800

1000

1200

1400

1600

Temperature (K)

(b)


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

CPD model UDP model

600

Heating condition 1 Heating condition 2 Heating condition 3 Heating condition 4

500 400 300 200 100 0 600

800

1000

1200

1400

1600

Temperature (K)

Fig. 8. Comparison results of total volatile mass fraction and release rate between the UDP model and CPD model under four heating conditions. (a) total volatiles mass fraction, (b) total volatiles release rates.

In summary, it is demonstrated to be feasible to determine the kinetic parameters of the two reactions dependent on the instantaneous heating rate through correlations above for the specific coal, even at heating conditions with varied heating rates. This proposed UDP model for the coal called Beulah-Zap is not universal for other types of coals, however, it is well known that coal types also have a significant influence on the coal devolatilization characteristic. In next section, the UDP model proposed for


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Page 26 of 43

the specific coal is extended to be applicable for different coals.

3.2 UDP Model validations for different coal types 3.2.1 Effect of coal types To expand the UDP model to be applicable for different types of coals, the fitting and correlation works are carried out using the similar approaches in Section 3.1, and the results are presented and discussed here.

aΩ and bΩ

are coefficients in the

correlations of heating rates for each parameters, and the subscript Ω donates the symbols of each kinetic parameters. It is necessary to explain that each of the coefficient

bK1 , bK2 , bE2 , bV1∞ and bV2∞ has the same value for different coals. Thus

these coefficients are set as the same value of 0.03933, 1.0, 0.3672, 0.03133 and -0.01758 for all coals respectively.

aK1 , aK2 , aE2 , aV1∞ and aV2∞ have

significant

dependence on the coal types, thus are used as the basic data for further correlations of coal types and listed below in Table 5. In the UDP model, coal types are distinguished by five structural parameters as the study of Fletcher et al. [21]. These structural parameters can be obtained through 13C-NMR or correlations developed by Fletcher et al. [21]. The coefficients of the correlations with heating rates obtained above are correlated with these five structural parameters as follows. Table 5.The coefficients of the correlations of different kinetic parameters with heating rates for different coal types.

Coal Source Tomita et al. PSOC-1507D (Sandia) PSOC-1520 (BYU)

aE / 104 2

aK 2

aK / 108 1

aV

aV

0.1482 0.1457 0.1527

0.4407 0.4600 0.4377

1∞

(J/mol)

(1/s)

(1/s)

3.859 4.072 3.878

2.156 2.524 2.483

4.932 5.020 5.084


2∞

Page 27 of 43

DECS-11 (BYU) Tomita et al. DECS-1 (BYU) Tomita et al. PSOC 1507 (AR) Tomita et al. PSOC-1493 (AR) Tomita et al. ANL (AR) PSOC-1451 (AR) Kurose et al. ANL (AR) Tomita et al. Tomita et al. Goudey B (AFR) PSOC-1508D (Sandia) Tomita et al. PSOC-1508 (AR) DECS-21 (BYU) PSOC-1468 (ACERC)

3.943 3.907 3.871 3.911 3.899 3.924 3.246 3.202 3.004 3.000 3.355 3.216 3.209 3.959 3.889 4.462 4.542 4.168 5.047 5.495

2.453 2.319 2.896 2.376 2.295 2.427 0.891 0.931 0.654 0.678 0.967 0.840 0.963 2.483 2.258 5.280 5.990 3.399 11.079 23.578

4.975 5.035 4.413 4.794 4.825 4.641 4.384 4.187 4.111 4.151 4.080 3.780 4.480 4.296 4.459 4.590 4.372 3.665 3.665 3.668

0.1469 0.1395 0.1492 0.1505 0.1435 0.1474 0.1577 0.1587 0.1532 0.1589 0.1457 0.1527 0.1586 0.1540 0.1291 0.0726 0.0381 0.0434 0.0396 0.0509

0.4623 0.4706 0.4333 0.4689 0.4649 0.4352 0.4632 0.4388 0.4072 0.4075 0.3824 0.3230 0.3025 0.1889 0.1113 0.1220 0.1009 0.0985 0.0250 0.0250

0.18 0.16

0.18

0.14

0.16

0.12

0.14

0.10

0.12

0.08

aV1∞

aV1∝

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

0.06

2

0.10 0.08

R =0.9708

0.04

0.06

0.02

0.04

0.00 0

10

20

30

Mδ

40

50

60

0.02 0.00 200

250

300

350

400

450

Mcl

(a)

(b)


500

550

600

650

0.18

0.16

0.16

0.14

0.14

0.12

0.12

0.10

0.10

aV1∝

0.18

0.08

0.06

0.04

0.04

0.02

0.02

0.00

Page 28 of 43

0.08

0.06

0.00 3.8

4.0

4.2

4.4

4.6

4.8

5.0

0.4

5.2

0.5

0.6

0.7

0.8

0.9

1.0

p0

σ+1

(c)

(d) 0.18 0.16 2

R =0.9733

0.14 0.12

aV1∞

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

aV1∞

Energy & Fuels

0.10 0.08 0.06 0.04 0.02 0.00 0.0

0.1

0.2

0.3

0.4

c0

(e)

Fig. 9. Plots of

aV

1∞

versus each coal structural parameter: (a) the average molecular weight per

side chain ( M δ ), (b) the average molecular weight per aromatic cluster ( M cl ), (c) the coordination number ( σ +1 ), (d) the initial fraction of intact bridges (

p

0

) and (e) the initial

fraction of char bridges ( c0 ).

Take the coefficient

aV

1∞

as an example to show the correlations with the coal

structural parameters. From the plots of the

aV

1∞

versus each independent variable, as

shown in Fig. 9, the relation between the value of are studied.

It is found that the value of

aV

1∞

aV

1∞

and each structural parameter

depends significantly on the average

molecular weight per side chain ( M δ ) and the initial fraction of the char bridges ( c0 ) through a trial-and-error method, but slightly on the rest three coal structural parameters ( M cl , σ +1 and p0 ). The detailed expression of the dependence for each


Page 29 of 43

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Energy & Fuels

coal structural parameters ( M δ and c0 ), as expressed in Eq. (16)

a = η1 +η2 (η3 +η4 (φ )η5 )η6

(16)

V1 ∞

Where φ donates the independent coal structural parameters M δ and c0 for each expression, and

aV

are described using a basic parameter η 1

1∞

with the

modification of each coal structural parameter ( M δ , c0 ). The coefficients of the determination, R2, are 0.9708 and 0.9733 respectively. To obtain more precise correlations for wider range of coal types, all structural parameters are taken into account, and the final correlation of coal structural parameters are expressed in Eq. (17).

a V = η 1 + η 2 (η 3 + η 4 ( M δ )η 5 + η 6 ( c 0 )η 7 ) (

η 8 +η 9 M

cl

+ η 1 0 p 0 + η 1 1 (σ + 1 )

1∞

Where the value of

aV

1∞

)

(17)

is correlated with all the five coal structural parameters ( M δ ,

M cl , σ +1 , p and c0 ), using a basic parameter η 1 with the modifications of the 0

coal structural parameters. η i are coefficients of the correlation and different from these in Eq. (16) and (18).

aV

2∞

shares a similar expressions with

aV

1∞

, thus it is not

discussed here. For the rest kinetic parameter, it is necessary to introduce that the value of aK 2 and a E2 need to be synchronized to get a reasonable devolatilization rate through our correlations. Thus the rest kinetic parameters need to be correlated with coal types are a E2 and a K 1 , and it is found that all the five coal structural parameters have an equivalent impact on them. Consequently, a quadratic correlation of the coal structural parameters are developed to describe the dependences, as shown in Eq. (18). a K1

= η1 + η 2 M δ + η 3 M d 2 + η 4 M cl + η 5 M cl 2 + η6 p0 + η7 p0 2 + η 8 (σ + 1) +η 9 (σ + 1) + η10 c0 + η11c0 2

2


(18)

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Page 30 of 43

The value of a E2 shares the similar expression as the value of a K 1 , thus it is not discussed here, and all coefficients in Eq. (17) and (18) are listed in Table. 6. For the value of aK 2 , a correlation between aK 2 and is developed to determine a reasonable

aK2 synchronized with a E2 , as expressed in Eq. (19) and shown in Fig. 10. Table 6 The coefficients of the correlations of kinetic parameters with coal structural parameters Coefficients

aK

aE

1

aV

2∞

2

aV

1∞

η1

-1.569E+09

-1.693E+04

-1.584E-01

9.180E-03

η2

1.768E+07

-4.311E+02

1.619E-01

5.071E-01

η3

-2.194E+05

9.756E+00

2.038E-01

1.031E+00

η4

2.743E+06

-9.678E+01

8.594E-01

4.894E+00

η5

-3.251E+03

1.146E-01

-4.465E-02

-1.889E+00

η6

1.231E+09

-9.087E+04

5.444E-02

3.301E-01

η7

-7.812E+08

9.182E+04

1.317E+00

1.968E+00

η8

3.046E+08

3.541E+04

-3.303E+01

1.924E+01

η9

-3.468E+07

-3.318E+03

3.099E-02

-4.550E-02

η10

1.978E+08

2.845E+04

1.046E+01

-1.632E+01

η11

4.612E+08

-2.540E+04

-6.304E-01

-5.676E+00

aK = e1 × aE e2 2

Where the coefficients

e

1

and

2

e

2

(19)

are 7.334 × 10 −32 and 6.855 respectively.

Fig. 11 plots the kinetic parameters predicted by the correlations versus the kinetic parameters fitted from the CPD model for the selected 23 coals. The coefficients of determination R2 of the correlations above are 0.9627, 0.9914, 0.9497, 0.9953and 0.9953 for a E2 , aK 2 , a K 1 , aV2∞ and aV1∞ respectively. It is found that all the kinetic


Page 31 of 43

parameters coefficients predicted by the correlations have a good agreement with that fitted from the CPD model, which indicates that the correlations of coal structural parameters can describe the effect of coal types well on the coal devolatilization characteristics.

35

aK2 fit from CPD 30 25

aK2 (1/s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

aK2 predicted by the correlation: aK = e1 × aE e2 2

20

2

2

R =0.9914

15 10 5 0 30000

35000

40000

45000

50000

55000

60000

aE2 (J/mol) Fig. 10. Plots of aK versus a E 2 and their correlation results. 2

In summary, the UDP model, in the framework of the competing two-step model, are developed through procedures above, and its kinetic parameters are determined by Eq. (3), (4), (14), (17), (18) and (19). The coal structural parameters and the instantaneous heating rates are the input information. The coefficient a in Eq. (14) can be obtained through Eq. (17), (18) and (19) depending on the coal structural parameters, and b are set as constant values. The kinetic parameters can be obtained through Eq. (14) depending on the instantaneous heating rate. Finally, the


Energy & Fuels

5.5x104

25

5.0x104

20

predicted aK2 (1/s)

Predicted aE2 (J/mol)

devolatilization process is predicted via Eq. (3).

4.5x104

4.0x104

R2=0.96273

3.5x104

15 2

R =0.9914 10

5 3.0x10

4

3.0x104

3.5x104

4.0x104

4.5x104

5.0x104

0

5.5x104

0

5

10

CPD aE2 (J/mol)

15

20

25

CPD aK2 (1/s)

(a)

(b)

5.5x108

0.5

0.4

Predicted aV2∝

5.0x108

Predicted aK1 (1/s)

4.5x108

0.3

0.2

2

2

R =0.94972

4.0x108

R =0.99528 0.1

3.5x108 3.5x108

0.0 4.0x108

4.5x108

5.0x108

5.5x108

0.0

0.1

0.2

0.3

0.4

0.5

CPD aV2∝

CPD aK1 (1/s)

(c)

(d) 0.16 0.14 0.12

Predicted aV1∝

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 43

0.10 0.08 0.06

R2=0.99526

0.04 0.02 0.00 0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

CPD aV1∝

(e)

Fig. 11. Plots of the coefficients of the kinetic parameters predicted correlation expressions versus fitted from the CPD model: activation evergy: (a) a E 2 , pre-exponential factors: (b) a K 2 , (c) a K , 1

and final volatile yield of the two reactions: (d) aV and (e) aV . 2∞

1∞

3.2 Validations of the UDP model To prove the applicability of the UDP model for multi-coals and wide range of


Page 33 of 43

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

heating conditions, the validations of the UDP model are carried out in this section. The validations of the UDP model, include internal and external validations, and the results and discussions are presented below.

3.2.1 Internal validations The internal validations of the UDP model are carried out through predicting the devolatilization processes of the selected 23 coals, and comparing that of the CPD model. The comparisons of the final volatiles yields and the devolatilization processes are presented and discussed here.

(1) Final volatiles yield Fig. 12 shows the comparisons between the final volatiles yield predicted by the UDP model and the CPD model under different heating rates for the selected 23 coals. It is found that the UDP model can predict the final volatiles yield accurately compared with that of CPD model for all the 23 coals under a wide range of heating rates. The relative errors are generally less than 8 % for all those 23 coals, 5 % for high VM coals and slightly larger about 6 % for low VM coals due to its relative small value predicted by the CPD model. Besides, the relative error generally decreases with the heating rate increases and are less than about 5 % for all coals at a typical heating rates T& ~1 0 5 K/s.


Energy & Fuels

0.7

0.20

0.7

0.20

0.6

0.3

0.10

0.2

Final Volatles Yield

Heating rate =103 K/s UDP model CPD model Relative error

0.4

0.05

0.15

0.5 4

Heating rate = 10 K/s

0.4

0.10 0.3 0.2

0.1

Relative Error

0.15

0.5

Relative Error

0.05

0.1

0.0

0.00 0

4

8

12

16

20

0.0

24

0.00 0

4

8

12

16

20

24

Coal Number

Coal Number

(a)

(b)

0.7

0.7

0.20

0.20

0.6

0.6

0.15

0.4

Heating rate = 105 K/s 0.10

0.3 0.2

Relative Error

0.5

Final Volatiles Yield

0.15

0.05

0.5 0.4

Heating rate= 5x105 K/s

0.10

0.3 0.2

Relative Error


0.6


0.05

0.1

0.1 0.0 4

8

12

16

20

0.00

0.0

0.00 0

0

24

4

8

Coal Number

12

16

20

24

Coal Number

(c)

(d) 0.7

0.20

0.6 0.15 0.5 0.4


0.10

0.3 0.2

Relative Error


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 34 of 43

0.05

0.1 0.00

0.0 0

2

4

6

8

10

12

14

16

18

20

22

24

Coal Number

(e)

Fig. 12. Comparisons between the final volatiles yield of the selected 23 coals predicted by the UDP model and the CPD model at different heating rates: (a) 1 0 3 K/s, (b) 1 0 4 K/s, (c) 1 0 5 K/s, (d) 5 × 1 0 5 K/s and (e) 1 0 6 K/s.

(2) Devolatilization process Fig. 13 shows the comparisons between the devolatilization processes (total volatiles mass fraction and release rates) of three different rank coals (coal No. 5, 7 and 21 in Table 1) predicted by the CPD model and the UDP model under different


Page 35 of 43

heating rates. The devolatilization processes predicted by the UDP model are in good agreement with that of the CPD model in a wide range of heating rates for different rank coals both on total volatiles fraction and release rates, which means the correlations proposed above can describe the effect of the heating rates and coal types on the devolatilization processes well. However, all those validations focus on our selected 23 coals, which is not adequate to prove the universal applicability of the proposed UDP model, and the external validations would be discussed in Section

0.4 0.3 UDP model CPD model Heating rates 3 10 K/s 104 K/s 5 10 K/s 3 5x10 K/s 6 10 K/s

0.1 0 600

800

1000

1200

1400

1200 900

10

5 300 0 600

1600

800

1000



0.2

0.1

1000

1200

1400

900

10

600

6

300

4 2

0 600

1600

8

800

1000


0.12

0.06

1000

1400

0

1600

(2)

0.18

800

1200

Temperature (K)

(1)

0 600

0 1600

12

Temperature (K)

(c)

1400

(2)

0.3

800

1200

Temperature (K)

(1)

0 600

15

600

Temperature (K)

(b)

20


0.2

CPD m odel UDP model Heating rate 3 (right) 10 K/s (right) 4 (right) (right) 10 K/s (left) (left) 10 5 K/s (left) (left) 5x10 5 K/s (left) (left) 10 6 K/s

1500

1200

1400

1600

600

8

500 6 400 300

4

200 2 100 0 600

800

Temperature (K)

(1)

1000

1200

1400

0 1600



(a)

0.5

Tot Volatilea Release Rate (1/s)

1800

0.6

Tot Volatilea Release Rate (1/s)

3.3.2.


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

Temperature (K)

(2)

Fig. 13. Comparisons between the devolatilization processes (total volatiles (1) mass fraction and (2) release rate) of three different rank coals (coal (a) No. 5, (b) No. 17 and (c) No. 17 in Table 1;


Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(3) predicted by the CPD model and the UDP model in a wide range of heating rates ( 1 0 3 K/s, 1 0 4 K/s, 105 K/s, 5 × 10 5 K/s and 1 0 6 K/s.).

3.2.2 External validations The external validations of the UDP model are carried out through predicting the devolatilization processes of the other 10 coals in Table 2, and comparing with that of the CPD model. The comparisons of the final volatiles yields and the devolatilization processes are presented and discussed here.

(1) Final volatiles yield Fig. 14 shows the comparisons of final volatiles yield of those 10 coals predicted by the CPD model and the UDP model at a wide range of heating rates ( 1 0 3 K/s, 1 0 4 K/s, 1 0 5 K/s, 5 × 10 5 K/s and 1 0 6 K/s). It is found that the relative errors of results

predicted by the UDP model compared with the CPD model are generally less than 8 %, and decrease with the increasing heating rates for each coal. The relative errors are less than 5% for high volatiles content coals but slightly larger for low content coals. It is generally thought that the typical heating rate of coal particle is about 105 K/s in coal combustions, thus the relative errors are less than 5 % from (c), (d) and (e)

in Fig.12, which can give us precise predictions on the final volatiles yield in a wide range in coal combustion simulations.


Page 36 of 43

Page 37 of 43

0.7

0.20

0.7

0.20

3

0.6

0.10 0.3

0.05

0.15 0.5 0.4 0.10 0.3 0.2

0.1

Relative Error

0.4

0.2


0.15


0.05

0.1

0.00

0.0 0

2

4

6

8

0.00

0.0

10

0

2

4

Coal Number

6

Coal Number

(a)

10

(b)

0.7

0.20

0.7

Heating rate = 105K/s

0.6

8

0.20

Heating rate =5x105 K/s

0.6

0.15

0.15 0.5

0.10 0.3 0.2

Relative Error

0.4


0.5 0.4 0.10

0.3 0.2

0.05

0.1

Relative Error


0.5

Relative Error

Heating rate = 10 K/s UDP model CPD model Relative error

0.6


0.05

0.1 0.00

0.00

0.0 0

2

4

6

8

0.0

10

0

2

4

6

8

10

Coal Number

Coal Number

(c)

(d) 0.7

0.20


0.6

0.15

0.4 0.10 0.3 0.2

Relative Error

0.5


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

0.05

0.1 0.00

0.0 0

2

4

6

8

10

Coal Number

(e)

Fig. 14. Comparisons between the final volatiles yield of the other 10 coals predicted by the UDP model and the CPD model at different heating rates: (a) 1 0 3 K/s, (b) 1 0 4 K/s, (c) 1 0 5 K/s, (d)

5 × 1 0 5 K/s and (e) 1 0 6 K/s.

(2) Devolatilization process


(a)


0.6 0.5 0.4 0.3


0.2 0.1 0 600

800

1000

1200

1400

Page 38 of 43

700


600 500 400 300 200 100 0 600

1600

800

Temperature (K)

(1) 0.5 0.4 0.3 CPD model UDP model Heating condition 1 Heating condition 2 Heating condition 3 Heating condition 4

0.2 0.1 0 600

800

1000

1200

1400

600

200

800

1400

1600

(2)


0.05

800

1000

1200

1400



1200

300

0.1

200 150 100 50 0 600

1600

C PD m ode l U D P m odel H e a ting condition 1 H e a ting condition 2 H e a ting condition 3 H e a ting condition 4

250

800

Temperature (K)

0.1


800

1000

1200

1400

1 600

(2)

1200

1400

1600

Tot Volatiles Release rate (1/s)

(1)

0.05

1 000

T em pe rature (K )

0.15

0 600

1000

Temperature (K)

(1)

(d)

1600

400

0 600

1600

0.15

0 600

1400


Temperature (K)

(c)

1200

(2) 800 Tot Volatiles Mass Fraction


(b)

1000

Temperature (K)

0.6


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Energy & Fuels

200 CPD model UDP model Heating condition 1 Heating condition 2 Heating condition 3 Heating condition 4

150

100

50

0 600

800

Temperature (K)

(1)

1000

1200

1400

1600

Temperature (K)

(2)

Fig. 15. Comparisons between the devolatilization processes of four different rank coals predicted by the CPD model and the UDP model at different heating conditions: coal (a) No. 2, (b) No. 3, (c) No. 5 and (d) No. 6 in Table 2.

Fig. 15 shows the comparisons between the devolatilization processes of four different rank coals (coal No. 2, 3, 5 and 6 in Table 2) predicted by the CPD model and the UDP model under different heating conditions with varied heating rates. It is found that the devolatilization processes predicted by the UDP model have a good agreement with that of the CPD model on both the total volatiles mass fraction and


Page 39 of 43

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

release rates for those four rank coals. The total volatiles mass fraction predicted by the UDP model is slightly smaller compared with that of the CPD model at the temperature region of 1100~1400K due to the neglect of the evaporation of the metaplast that causes the small peak in the low temperature region. Besides, the UDP model predicts the value and the temperature of the peak release rate accurately, but has some errors at the high temperature region (1200~1400K) may attributed to the correlations errors above. In summary, the UDP model can obtain the similar prediction accuracy on the devolatilization processes as that of the CPD model under different heating conditions.

4. Conclusions A universal-devolatilization-process (UDP) model, considering the effects of heating rates and coal types, is developed for an accurate prediction of devolatilization

process

in

numerical simulations

of

coal combustion.

A

devolatilization process database are constructed from devolatilization processes of 23 coals under 40 heating rates predicted by the CPD model. In the UDP model, the coal devolatilization is simplified to have two competing reactions, whose kinetic parameters are determined dependent on coal types and heating rates through fitting and correlations works from the database. The thorough validations, including the internal and external validations, of the UDP model are carried out through comparing the devolatilization process of the selected 23 coals and other 10 coals predicted by the UDP model and the CPD model respectively. The validation results show that the UDP model can accurately predict the coal devolatilzation process as the CPD model


Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

for a wide range of coals and heating rates with a less computational cost, and further improve the accuracy on coal combustion simulations. In addition, the light gas compositions are determined by a look up table based on coal rank and the extent of light gas release in the CPD model, which lacks of the significant physical and chemical explanations [53], thus the devolatilization components are not taken into accounted in present study and will be investigated based on the evolution of functional group composition in the future work.

Acknowledgements This work is supported by the National Natural Science Foundation (Grant Nos.: 51390493) of China. We are grateful to that.

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Universal Devolatilization Process Model for Numerical Simulations of

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