Investigation on Kinetic Parameters of Combustion and Oxy

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Investigation on Kinetic Parameters of Combustion and OxyCombustion of Calcined Pet Coke (CPC) employing Thermo-Gravimetric Analysis (TGA) coupled to Artificial Neural Network (ANN) Modeling Bhuvaneswari Govindan, Sarat Chandra Babu Jakka, T.K. Radhakrishnan, Anil K Tiwari, T.M Sudhakar, P Shanmugavelu, A.K Kalburgi, A Sanyal, and S Sarkar Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.8b00223 • Publication Date (Web): 26 Feb 2018 Downloaded from http://pubs.acs.org on March 3, 2018

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Energy & Fuels

1

Investigation on Kinetic Parameters of Combustion and Oxy-Combustion of Calcined

2

Pet Coke (CPC) employing Thermo-Gravimetric Analysis (TGA) coupled to Artificial

3

Neural Network (ANN) Modeling

4 5

Bhuvaneswari Govindan1,*, Sarat Chandra Babu Jakka1, T. K. Radhakrishnan1, Anil K

6

Tiwari2, T.M.Sudhakar2, P.Shanmugavelu2, A.K. Kalburgi2, A.Sanyal2, S.Sarkar2

7 8 9 10

1 – Department of Chemical Engineering, National Institute of Technology Tiruchirappalli, Tiruchirappalli, Tamil Nadu, India. 2 – ChTG, Bhaba Atomic Research Centre, Mumbai, India.

11 12

Corresponding author: Email: *[email protected]

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Highlights

13

14

•

The isothermal data from Thermo-Gravimetric Analysis (TGA) has been employed to predict the kinetic parameters of combustion and oxy-combustion of Calcined Pet Coke (CPC).

15 16

•

The kinetic parameters are estimated using shrinking particle and weight fraction model.

17

•

The activation energy estimated for combustion of CPC with air is found to be higher than with pure oxygen.

18 19

•

ANN Model predicted the isothermal TG curve with high degree of accuracy.

20

•

The predicted kinetics of both the model fits experimental data with R2 value greater than

21

0.90.

22


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Energy & Fuels

23

Abstract

24

The objective of the present study is to understand the combustion behaviour and to estimate kinetic

25

parameters for combustion and oxy-combustion of calcined pet-coke (CPC) employing

26

thermogravimetric analysis (TGA), which is crucial for subsequent design and modelling of the

27

combustion systems. In order to estimate the kinetics, the onset reaction temperature (ORT) is

28

estimated using TGA for both the systems and, all subsequent experiments are conducted at

29

temperatures higher than the ORT. The kinetic parameters viz., activation energy ( ) and pre-

30

exponential factor () are estimated using shrinking particle model (SPM) and weight fraction model

31

(WFM). While SPM assumes uniform particle size and first-order intrinsic kinetics, WFM is used to

32

estimate even order of reaction besides and . Prediction from SPM fits better to the data obtained

33

from TGA albeit WFM estimating the order of the reaction as 0.6 in this case. The present study will

34

be useful in employing the predicted kinetic data to design an industrial scale pet coke combustor.

35

Artificial Neural Network (ANN) modelling is applied to isothermal TGA data to predict the TG

36

curves of combustion and oxy-combustion of CPC. The ANN model predicted the TG curve with

37

high degree of accuracy i.e., with a coefficient of determination in the order of 0.99999. The

38

agreement between the experimental and predicted data substantiate the accuracy of ANN model.

39 40

Keywords: Calcined Pet Coke; Combustion; Kinetics; Shrinking Particle Model; Weight Fraction

41

Model, ANN Modelling.

42


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1. Introduction

44

The depleting fossil fuels and their spiralling prices are pressing the world to go for an alternative

45

source of energy. Relatively cheaper, pet coke, a by-product of a refinery plant, is regarded as one

46

of the alternate sources of energy for industrial applications. Pet coke produced by delayed coking

47

process[1] in final stages of an oil refinery can be used as carbonaceous fuel in utility boilers,

48

electric power plants and cement kilns because of its low moisture and ash, and high calorific

49

value[2]. Comparatively lower price than fossil fuels and increase in production of pet coke gives a

50

powerful economic stimulus to utilize it for steam and power generation. For design of pet coke

51

fueled thermochemical equipments such as gasifiers, pyrolysis and combustion reactors, etc., in-

52

depth knowledge on thermal decomposition and kinetics of pet coke is crucial[3-8]. Further,

53

estimation of reaction kinetics would suggest an optimal operating condition for combustion/oxy-

54

combustion of pet coke.

55

Combustion and Oxy-combustion refers to an exothermic chemical process in which fuel reacts

56

with air and oxygen respectively. Burning of carbonaceous fuels usually takes place in the

57

temperature range of 230 to 800oC producing gaseous products mainly, CO2, CO, etc.[9],[

58

[11]

59

using thermogravimetric analysis (TGA) techniques is well reported in the literatures[12-22]. A

60

summary of work carried out by various researchers on the aforesaid systems is shown in Table 1.

10],

.Assessment of combustion of rice, wheat, straw, char, coal, biomass fuels and raw pet coke

Table 1: Published kinetic parameters

61 Researcher

Fuel

Atmosphere

Order

A, m/min

Ea, kJ/mol

Arthur J.R.., 1950[9]

Charcoal

-

-

-

120-205

Smith I.W., 1982[23]

Coal

Oxygen

0.17 – 1

9 - 6.337E03

67 – 142

Smith I.W., 1982[23]

Petroleum Coke

Oxygen

0.5

-

82.4248

Raw pet coke

Oxygen

0.6

3.55E06

151-167

Graphite

Oxygen

0.5 – 0.8

-

200-208

Ralph J.Tyler,1985[24] Ranish J.M&Walker.P.L.,


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Energy & Fuels

1992[25] Hurt R.H & Calo.

Char

Air

0.6 – 1.0

-

105-180

Homogeneous

Air

0.6 - 1.1

8.22E06-

115-150

J.M.,2001[26] Kastanaki E & Vamvuka D., 2006[27] Kastanaki E &

Char Heterogeneous

Vamvuka D., 2006[27]

4.55E11 Air

0.5-1.45

Char

7.02E08-

132-226

7.26E10

62 63

However, the information on burning behaviour of calcined pet coke (CPC), which is a purer form

64

of carbon is scarce. In the reported work, after characterizing the CPC powder, TGA experiments

65

have been conducted to predict thermal behaviour under oxygen and air atmosphere and,

66

parameters of reactions kinetics have been deduced thereby. Thermogravimetric analysis (TGA) is

67

a simple, fast and high-precision method used for the thermal degradation study under well-

68

defined conditions[28],[29]. Determination of kinetics parameters such as activation energy ( ) and

69

pre-exponential factor () is carried out using two different models viz., shrinking particle model

70

(SPM) and weight fraction model (WFM). While SPM assumes particles of uniform size and

71

intrinsic chemical reaction of first order, the WFM is based on actual reduction in weight of CPC

72

during the course of reaction. Therefore, only Ea and A is determined using SPM whereas besides

73

Ea and A, order of reaction (n) is also predicted using WFM. The information thus obtained is

74

useful in designing an industrial scale pet coke combustor.

75

The artificial intelligence techniques, includes neural networks are widely accepted as a

76

technology that can be applied to complex problems in a non-linear fashion, which can be applied

77

for prediction and generalization at high speed, once trained. Artificial neural networks (ANN)

78

models use a non-physical modelling approach which correlates the input and output data to form a

79

process prediction model[30]. ANN models excel in fields of energy related processes for the

80

prediction of process parameters[31] but their potential to predict the parameters of isothermal

81

process is yet to be explored.


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82

In this study, the combustion and oxy-combustion characteristics of CPC are investigated by

83

TGA at a heating rate of 50oC/min. The knowledge of thermal behaviour, in particular, precise

84

estimation of kinetics, is essential to achieve effective design and operation of an industrial

85

combustor. Thus, this study is directed towards predicting kinetics with the help of TGA. An ANN

86

model is also developed to accurately predict the thermal behaviour of combustion and oxy-

87

combustion of CPC.

88

2. Characterization and TGA Experiments with Calcined Pet Coke

89

2.1 Petcoke Characterization

90

The CPC used in the present study is procured from M/s. Neo Carbons Pvt. Ltd. Haldia, West

91

Bengal, India. The properties analyzed are as follows:

92

•

The Particle Size Distribution (PSD) is analyzed with the help of Horiba LA-960 laser scattering particle size distribution analyzer.

93 94

•

The Particle density is estimated using a Pycnometer.

95

•

Determination of moisture content, ash and volatile content is performed respectively in a Perkin Elmer TGA- 4000 employing ASTM procedure D 5142 – 09.

96 97

•

The elemental analysis to find the elemental compositions such as C, H, O, N and S contents

98

of the sample is performed using Perkin Elmer 2400 Series II CHNS/O elemental analyzer.

99

The sample is weighted with a precision of 0.00001 mg (Perkin Elmer Auto Balance AD

100

6000) in a tin foil cup. Sample of around 1 mg is taken for analysis. In presence of excess

101

oxygen, samples are combusted to elemental gases.

102

•

Determination of micro chemical composition of CPC is carried out using Energy Dispersive

103

X-ray Spectroscopy (EDS). EDS Analysis detected the presence of only O, N, and S in

104

addition to C. The result is as shown in Figure 1. All experimentation are carried out thrice to avoid error due to sampling and the

105 106

average results are reported with the standard deviation from the average value in Table 2. Table 2: Calcined Pet Coke Characteristics and Properties

107

Characteristics

Values/Content


Standard Deviation

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Energy & Fuels

60.309

0.9521

Bulk density, kg/m3

1096.067

0.0198

True density, kg/m3

1735.186

0.0467

549.107

0.0023

Moisture Content, wt.%

0.185

0.0654

Volatile Matter, wt.%

0.316

0.0817

99.177

0.0958

0.322

0.0530

C, wt.%

99.197

0.0967

H, wt.%

0.173

0.0118

N, wt.%

0.051

0.0877

S, wt.%

0.177

0.0828

O, wt.%

0.080

0.0101

Particle Size

Mean size, µm

Density

Repose density, kg/m3 Proximate Analysis

Fixed Carbon Content, wt.% Ash, wt.% Ultimate Analysis

108 cps/eV 14

12

10

8

6

S C N O

S

4

2

0 0.5

1.0

1.5

109

2.0

2.5 keV

3.5

Figure 1: EDS analysis of chemical composition of CPC

110 111 112

3.0

2.2 Thermo- Gravimetric Analysis (TGA)


4.0

4.5

5.0

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113

The combustion and oxy combustion of CPC are observed using thermogravimetric analyser under

114

air and oxygen atmosphere respectively. CPC is subjected to thermal degradation study using a

115

Perkin Elmer TGA 4000 Series. The TGA has a sensitive microbalance of 0.1µg resolution and an

116

accuracy of +0.02%. The maximum temperature attained by its furnace is about 1000oC with

117

temperature precision of about + 0.8oC. The instrument is connected to a computer for data logging

118

and integrated with software module termed Pyris, which is used to analyse the data.

119

Thermal conversion process, combustion (at air atmosphere) and oxy-combustion (at oxygen

120

atmosphere) of the sample is analysed by conducting the experiments under non isothermal

121

condition for temperature range of 30 to 650oC at heating rates of 50oC per minute. Then the

122

experimental run is followed with isothermal mode, where the sample is being held at 650oC to

123

confirm the further possibilities of thermal degradation. The purge gases used for this study is

124

99.99% ultra-high purity nitrogen and oxygen with a flow rate of 40 ml/min. The maximum

125

variation in mass taken for analysis is within +5%. In order to eliminate the effect of system error

126

on the experimental result, blank run is being performed under the same conditions using empty

127

alumina pan. In TGA experiments, samples are analysed in a batch mode, so the residence time is

128

increased to ensure the complete combustion of the samples.

129

2.3 Evaluation of Kinetic Parameters

130

In order to predict kinetics of combustion of CPC, it is important to determine the onset

131

temperature under different oxidizing atmosphere, namely air and oxygen. Thermogravimetric

132

study has been conducted to estimate the onset reaction temperature for both combustion (CPC-

133

Air) and oxy-combustion (CPC-O2) systems. After obtaining the onset reaction temperature,

134

several isothermal experiments are performed for both the systems. Thus a total of twelve (12)

135

experiments involving CPC are carried out. Two of them have been done to estimate onset of

136

reaction temperature (ORT) for CPC-air and CPC-O2 systems. Five each isothermal experiments

137

are subsequently carried out for the two systems where temperatures considered are more than the

138

respective ORT. This exercise is intended at getting sizeable data for estimation of reaction

139

kinetics. The models employed, results and discussions as obtained from these trials are presented


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Energy & Fuels

140

in later section. A summary of experimental parameters followed during trials is presented in Table

141

3. Table 3: Experimental conditions during test trials in TGA-4000

142 Material

Calcined Pet Coke (CPC)

Sample amount, mg

6+1

Heating rate, oC per min

50

Purge gas

Nitrogen

Reactive gas

Oxygen /Air

Purge gas flow rate, ml per min

40

Reactive gas flow rate, ml per min

40

Initial temperature of the sample, oC

30

Final temperature of the sample, oC

650 to 900

143 144

2.4 ANN Model development

145

Different ANN training algorithms namely Levenberg-Marquardt (LM), Adaptive Learning Rate

146

(GDX), Gradient Descent Momentum (GDM), Scaled Conjugate Gradient (SCG) and Broyden –

147

Fletcher-Goldfarb-Shano-quasi-Newton (BFGS) exists [30-34]. In this study, a feed backward neural

148

network model termed LM back propagation algorithm is chosen to predict the isothermal TGA

149

curves obtained from the combustion of CPC as it has higher order of convergence compared to

150

other algorithms. This model is largely employed by researchers for its simplicity, efficiency and

151

high accuracy[32]. The most commonly used transfer functions are namely linear (purelin),

152

hyperbolic tangent sigmoid (tansig) and log-sigmoid (logsig) functions. The selection of a suitable

153

function is based on the influential factors such as degree of complexity to attain rapid

154

convergence[35]. The neural network consists of input, hidden and output layers. All layers are

155

connected by weights and biases. By adjusting the weights and biases, the non-linear functions can

156

be modelled. The input layer in the present study includes two neurons namely time and

157

temperature. Hidden layers are used to carry out complex and non-linear functions on the 9|Page ACS Paragon Plus Environment

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158

network[36]. The number of hidden layers in the model has been adjusted to achieve the maximum

159

R2 value. The number of hidden layers, number of neurons in the hidden layers, training epochs,

160

and activation functions are mostly selected by trial and error analysis depending on the

161

performance criteria. However, researchers have carried out studies to optimize the number of

162

hidden layers and numbers of neuron employed in the hidden layer to optimize the performance

163

criteria. Conesa et al., 2004, Jinchuan Ke and Xinzhe Liu., 2008 and Gnana Sheela K and Deepa

164

S.N., 2013 reviewed on selection of number of hidden layers in the ANN model. Thus, a single

165

hidden layer is chosen and the optimal number of neurons in the hidden layer of the network, is

166

been selected as follows:[37],[38],[39] =

167

(2.4.1)

168

Where, is the number of hidden layer, is the number of input, is the number of input

169

samples. The training and testing performances of the network has been determined with the root

170

mean square (RMSE), mean absolute error (MAE) and mean bias error (MBE) analysis methods.

171

The higher value of R2 and lower values of both RMSE and MAE means a better performance of

172

the developed ANN and an optimal ANN architecture. The errors are evaluated by equations

173

(2.4.2)-(2.4.4).

174

= ∑

& − ,

175

= ∑

&' − ,

176

( = ∑

& − ,

!"# $

%

(2.4.2)

!"# '

(2.4.3)

!"# $

(2.4.4)

177

The ANN modeling is performed using the ANN toolbox in the MATLAB, a mathematical

178

software.

179

3. Results and Discussion

180

3.1 Onset Reaction Temperature (ORT) and isothermal experiments

181

The ORT for CPC-Air and CPC-O2 systems is derived from Figure 2 and 3 respectively. The two

182

tangents are found to intersect each other at around 660+2.72oC in both the cases. Therefore all

183

subsequent experiments are carried out at temperature > 650oC. Consequently, for estimation of

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Energy & Fuels

184

kinetics parameters, five temperature points namely, 650, 675, 700, 725 and 750oC are selected for

185

CPC-Air system while CPC-O2 experiments are performed at 650, 700, 800, 850 and 900oC

186

respectively. The change in weight of CPC with time during the aforesaid experiments for CPC-

187

Air and CPC- O2 systems are shown in Figure 4 and Figure 5 respectively.

188


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Figure 2: TGA study- Onset Reaction Temperature of CPC – Air system

189

190 Figure 3: TGA study- Onset Reaction Temperature of CPC - O2 system

191


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Page 13 of 35

a) Isothermal 650oC 800

5 Weight, mg

600 4 3

400

2 200

Temperature, oC

6

Weight vs time Temperature vs time

1 0

0 0

20 40 Time, min

60

192

b) Isothermal 675oC

c) Isothermal 700oC

600

4 3

400

2

200

1 0

600

4 3

400

2

200

1

0 0

800

5 Weight, mg

Weight, mg

5

6

0

10 20 Time, min

Temperature, oC

800 Temperature, oC

6

0 0

5 10 Time, min

15

193

5

600

4 3

400

2

200

1

0

0 0

5 Time, min

10

5 Weight, mg

800 Temperature, oC

6

e) Isothermal 750oC 800 700 600 500 400 300 200 100 0

4 3 2 1 0 0

5 Time, min

Temperature, oC

d) Isothermal 725oC

Weight, mg

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

10

194 Figure 4: Temporal variation of weight at different temperature for CPC-Air system

195


Energy & Fuels

a) Isothermal 650oC 800

Weight, mg

7 6

600

5 4

400

3 2

200

Temperature, oC

8

Weight vs Time Temperature vs Time

1 0

0 0

5

10

15

Time, min

196

b) Isothermal 700oC

c) Isothermal 800oC 800

7

600

5 4

400

3 2

200

1 0 2

4

6

5

600

4 400

3 2

200

1

0 0

800

6

Weight, mg

6

Temperature, oC

Weight, mg

7

Temperature, oC

8

0

8

0 0

Time, min

1

2

3

4

Time, min

197

e) Isothermal 900oC

5

800

4

600

3 400

2 1

200

0

0 0

1

2

7

1000

6

Weight , mg

1000

Temperature, oC

6

800

5 4

600

3

400

2 200

1 0

Temperature, oC

d) Isothermal 850oC

Weight, mg

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 14 of 35

0 0

3

Time, min

1

2

3

Time, min

198 Figure 5: Temporal variation of weight at different temperature for CPC-O2 system

199 200

3.2 Determination of kinetic parameters using Shrinking Particle Model

201

The temporal variation of reduction in weight obtained from TGA data is suitably converted to

202

temporal variation of particle size as described in Appendix A and the result is shown in Figure 6

203

for one of the cases for CPC-Air system at 650oC. 14 | P a g e ACS Paragon Plus Environment

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CPC-Air System at T=650oC 0.00007

Particle size, m

0.00006 0.00005 Particle Size vs Time

0.00004 0.00003 y = -1E-06x + 6E-05 R² = 0.9893

0.00002 0.00001 0 0

10

20

204 205

30

40

50

Time, min

Figure 6: Temporal variation of particle size for CPC-Air system at isothermal temp, T=650oC.

1.00E+00 0.00095

0.001

0.00105

0.0011

1.00E-01

0.00115

CPC-Air

ks, m/min

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

1.00E-02 ks = 3E+08e-21154/T R² = 0.9962 1.00E-03

1/T, 1/K

206 Figure 7: Determination of kinetic parameters using SPM for CPC-Air system

207 208

As it is seen in the Figure 6, there is a linear relationship between particle size and time with a

209

negative slope. Using this slope and equation A.15 described in Appendix A, )* is determined

210

subsequently. Similarly, )* is obtained at other temperatures and the resultant Arrhenius Plot for

211

CPC-Air system is shown in Figure 7. and for CPC-Air system are subsequently calculated

212

from slope and intercept of the figure.

213

A similar exercise is repeated for CPC-O2 system albeit at different isothermal temperatures and

214

the results are shown in Figure 8.


Energy & Fuels

1 0.0008 0.00085 0.0009 0.00095

0.001

0.00105 0.0011 0.00115 CPC-Oxygen

ks, m/min

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 16 of 35

0.1

ks = 476.88e-9031/T R² = 0.9325

0.01

215 216 217

1/T, 1/K

Figure 8: Determination of kinetic parameters using SPM for CPC-Oxygen system The kinetics parameters thus obtained for both the system are summarized in Table 4. Table 4: Estimation of kinetic parameters using Shrinking Particle Model

218

System

R2

Pre-exponential

Activation Energy

factor (m/min)

(kJ/mol)

Combustion (CPC-Air)

3.00E08

175.8743

0.9962

Oxy-Combustion (CPC-O2)

4.77E02

75.0837

0.9325

219 220

3.3 Determination of kinetic parameters using Weight Fraction Model

221

Data obtained from CPC-Air and CPC-Oxygen experiments discussed in the previous section are

222

also fitted using WFM using equation B.7 described in Appendix B. As discussed earlier, order of

223

the reaction + is obtained by getting the slope from regression of ln .0

224

shown in Figure 9 for a typical case of temperature at 675oC. Subsequently, value of + obtained at

225

various other temperatures is shown in Figure 10.

/ !0 3 1 !2

226 227


0

versus ln 40 5 and is 1

Page 17 of 35

-2.7 -1.2

-1

-0.8

-0.6

-0.4

-0.2

0 -2.75

ln (-1/wo*dw/dt)

-2.8

ln (-1/wo.dw/dt) vs ln w/wo

-2.85

y = 0.6109x - 2.38 R² = 0.9754

-2.9 -2.95 -3 -3.05

ln w/wo

228 Figure 9: Plot of ln .

229

/ !0 3 01 !2

0

vs ln 4 5 at isothermal 675oC for CPC-Air system 0 1

0.7 0.6

Order of reaction, n

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

0.5 0.4 CPC-Air

0.3

CPC-Oxygen 0.2 0.1 600

700

800

900

1000

Temperature, oC

230 231

Figure 10: Order of reaction, + at different temperature for CPC-Air & CPC-Oxygen system

232

As seen from Figure 10, value of + is nearly constant irrespective of temperature. Therefore, for

233

subsequent calculations an average value of n equal to 0.6 has been considered. After obtaining +,

234

the intercept values (−6/8 − 9+) from the plot between 9+ .

235

temperatures are obtained.

236


/ !0 3 01 !2

0

and 9+ 4 5 for various 0 1

Energy & Fuels

Intercept (lnA-Ea/RT)

0 0.00095 -0.5

0.001

0.00105

0.0011

0.00115

-1 y = -18266x + 16.215 R² = 0.994

-1.5 -2

CPC-Air

-2.5 -3 -3.5 -4 -4.5

1/T, 1/K

237 Figure 11: Determination of kinetic parameters using WFM for CPC-Air system

238 239

0 0.0008 -0.2

Intercept (-lnA-Ea/RT)

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 18 of 35

0.0009

0.001

0.0011

0.0012

-0.4 -0.6 -0.8 CPC-Oxygen

-1 -1.2 -1.4

y = -4524.7x + 3.4077 R² = 0.9967

-1.6 -1.8 -2

1/T, 1/K

240 241

Figure12: Determination of kinetic parameters using WFM for CPC-Oxygen system

242

Another plot is drawn between 1/T and 4− − 9+5 to deduce Ea and A as shown in Figure 11 ; 99.1 % C)) employing Perkin Elmer TGA-4000 is presented. The predicted

307

onset reaction temperature of CPC is about 660+2.72oC and therefore CPC combustion should be

308

carried out at temperatures higher than that. The kinetics modelling has been carried out through

309

two different approaches namely, using 1) Shrinking Particle Model (SPM) and, 2) Weight

310

Fraction Model (SPM). While a reaction order of one is assumed during SPM, the reaction order

311

estimated as obtained from WFM for both CPC-air and CPC-O2 systems is ~ 0.6. Constants of

312

Arrhenius equation namely Ea and A have been deduced for the two systems to get an estimate of

313

rate constant, k. The value of % is found to be greater than 0.90 in both the cases, hence the

314

predicted kinetic parameters using selected kinetic models is more reliable. When compared to


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

315

predictions from SPM, which is based on certain assumptions, ratio of CPC-air to CPC-O2

316

reaction rates is found to be lower in the case of WFM. Therefore, the kinetic data predicted by

317

WFM should be used for future designs and simulations. The ANN model predicts the isothermal

318

TG data at high degree of accuracy.

319

Acknowledgment

320

The authors from National Institute of Technology Tiruchirappalli gratefully acknowledge

321

support from Bhabha Atomic Research Centre (BARC), Government of India and the Ministry of

322

Human Resource Development (MHRD), India for providing a platform to carry out the research

323

work.

324 325

Abbreviations

326

ANN

327

ASTM - American Society for Testing and Materials

328

CPC

- Calcined Pet Coke

329

ORT

- Onset Reaction Temperature

330

PSD

- Particle Size Distribution

331

SPM

- Shrinking Particle Model

332

TGA

- Thermogravimetric Analysis

333

WFM - Weight Fraction Model

- Artificial Neural Network

334 335

Symbols

336

)*

- Surface reaction rate constant, m/min

337

)=

- Gas film diffusion rate constant, m/min

338

- Pre-exponential factor, 1/min

339

- Activation Energy, kJ/mol

340

- Universal Gas Constant, kJ/ (kmol K)

341

8

- Temperature (oC)


Page 24 of 35

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Energy & Fuels

342

Sh

- Sherwood Number (Dimensionless)

343

Sc

- Schmidt Number (Dimensionless)

344

Re

- Reynolds Number (Dimensionless)

345

>?

- Initial Diameter of the particle, m

346

>

- Diameter of the particle at time @, m

347

?

- Initial Radius of the particle, m

348

- Radius of the particle at time @, m

349

>

- Mass diffusivity, m2/s

350

μ

- Viscosity, kg/m.s

351

B

- Density, kg/m3

352

BC

- Molar density of Material, mol/m3

353

DE *

- Concentration of O2 at the solid interface, (pO2/RT), mol/m3

354

DE =

- Concentration of O2 in the bulk gas phase, (pO2/RT), mol/m3

355

F

- Weight fraction (Dimensionless)

356

w

- Weight of CPC at any time t, g

357

wo

- Initial weight of CPC, g

358

wf

- Weight of ash, g

359

)

- Kinetic rate constant, 1/min


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

360

List of Figures

361

Figure 1: EDS analysis of chemical composition of CPC

362

Figure 2: TGA study- Onset Reaction Temperature of CPC– Air system

363

Figure 3: TGA study- Onset Reaction Temperature of CPC-Oxygen system

364

Figure 4: Temporal variation of weight at different temperature for CPC-Air system

365

Figure 5: Temporal variation of weight at different temperature for CPC-Oxygen system

366

Figure 6: Temporal variation of particle size for CPC-Air system at isothermal, T=650oC.

367

Figure 7: Determination of kinetic parameters using SPM for CPC-Air system

368

Figure 8: Determination of kinetic parameters using SPM for CPC-Oxygen system

369

Figure 9: Plot of ln .

370

Figure 10: Order of reaction, + at different temperature for CPC-Air & CPC-Oxygen system

371

Figure 11: Determination of kinetic parameters using WFM for CPC-Air system

372

Figure 12: Determination of kinetic parameters using WFM for CPC-Oxygen system

373

Figure 13: Neural network diagram used for predicting combustion behavior of Calcined Pet-Coke

374

Figure 14: Regression coefficients of ANN-2-81-1 model

375

Figure 15: Comparison of experimental and ANN predicted values for TG data

/ !0 3 01 !2

0

vs ln 4 5 at isothermal 675oC for CPC-Air system 0 1

376 377

List of Tables

378

Table 1: Published kinetic parameters

379

Table 2: Calcined Pet Coke characteristics and properties

380

Table 3: Experimental conditions during test trials in TGA-4000

381

Table 4: Estimation of kinetic parameters using Shrinking Particle Model

382

Table 5: Estimation of kinetic parameters using Weight Fraction Model

383

Table 6: Ratio of reaction rates from the two models at different temperature

384

Table 7: The comparison of different ANN structure performances.

385


Page 26 of 35

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Energy & Fuels

386

References

387

1.

circulating fluidized bed. Fuel, 1995, 74, 1415–1423.

388 389

2.

Borrego, A. G.; Alvarez, D. Comparison of chars obtained under oxy-fuel and conventional pulverized coal combustion atmospheres. Energy & Fuels, 2007, 21, 3171–3179.

390 391

Brereton, C. M. H.; Lim, C.J.; Grace, J.R.; Luckos, A.; Zhu, J. Pitch and coke combustion in a

3.

Edreis, E.M.A.; Luo, G.; Li, A.; Chao, C.; Hu, H.; Zhang, S.; Gui, B.; Xiao, L.; Xu, K., Zhang,

392

P.; Yao, H. CO2 co-gasification of lower sulphur petroleum coke and sugar cane bagasse via

393

TG-FTIR analysis technique. Bioresour. Technol. 2013, 136, 595–603.

394

4.

Jia, L.; Tan., Y.;Anthony E. J. Emissions of SO2 and NOx during Oxy-Fuel CFB combustion

395

tests in a mini-circulating fluidized bed combustion reactor. Energy and Fuels, 2010, 24, 910–

396

915.

397

5.

Yu Xi.; Yassir Makkawi.; Raffaella Ocone.; Martin Huard.; Cedric Briens.; Franco Berruti. A CFD

398

study of biomass pyrolysis in a downer reactor equipped with a novel gas–solid separator — I:

399

Hydrodynamic performance. Fuel Process. Technol. 2014, 126, 366–382.

400

6.

coke for co-gasification. Korean J. Chem. Eng. 2007, 24, 512–517.

401 402

Yoon, S. J.; Choi, Y. C.; Lee, S. H.; Lee, J. G. Thermogravimetric study of coal and petroleum

7.

Yüzbaşi, N. S.; Selçuk, N. Pyrolysis and combustion behavior of ternary fuel blends in air and

403

oxy-fuel conditions by using TGA-FTIR. in Combustion Science and Technology, 2012, 184,

404

1152–1163.

405

8.

Raveendran, K.; Ganesh, A.; Khilar, K. C. Influence of mineral matter on biomass pyrolysis characteristics. Fuel, 1995, 74 (12), 1812–1822.

406 407

9.

Arthur, J. R. Reactions between carbon and oxygen. Trans. Faraday Soc. 1951, 47, 164.

408

10.

Hayhurst, A. N.; Parmar, M. S. Does solid carbon burn in oxygen to give the gaseous

409

intermediate CO or produce CO2 directly? Some experiments in a hot bed of sand fluidized by


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

air. Chem. Eng. Sci. 1998, 53, 427–438.

410 411

11.

experimental investigation. Fuel Process. Technol. 2014, 117, 23–29.

412 413

Roy, B.; Bhattacharya, S. Oxy-fuel fluidized bed combustion using Victorian brown coal: An

12.

Zhaosheng, Y.; Xiaoqian, M.; Ao, L. Kinetic studies on catalytic combustion of rice and wheat

414

straw under air- and oxygen-enriched atmospheres, by using thermogravimetric analysis.

415

Biomass and Bioenergy, 2008, 32, 1046–1055.

416

13.

biomass samples using thermo-gravimetric analysis. Biomass and Bioenergy, 2013, 58, 58–66.

417 418

14.

Qin, K.;Thunman, H. Diversity of chemical composition and combustion reactivity of various biomass fuels. Fuel, 2015, 147, 161–169.

419 420

Parthasarathy, P.; Narayanan, K. S.; Arockiam, L. Study on kinetic parameters of different

15.

Russell, N. V.; Beeley, T. J.; Man, C. K.; Gibbins, J. R.; Williamson, J. Development of TG

421

measurements of intrinsic char combustion reactivity for industrial and research purposes. Fuel

422

Process. Technol. 1998, 57, 113–130.

423

16.

Ciuryla, V. T.; Weimer, R. F.; Bivans, D. A.; Motika, S. A. Ambient-pressure

424

thermogravimetric characterization of four different coals and their chars. Fuel, 1979, 58, 748–

425

754.

426

17.

1999, 37, 1227–1238.

427 428

Blasi, C. Di; Buonanno, F.; Branca, C. Reactivities of some biomass chars in air. Carbon N. Y.

18.

Adánez, J.; Luis F. de Diego.; Francisco Garcı´a-Labiano.;Alberto Abad.; Juan C. Abanades

429

Determination of biomass char combustion reactivities for FBC applications by a combined

430

method. Ind. Eng. Chem. Res. 2001, 40, 4317–4323.

431

19.

of pyrolysis chars from waste and biomass. J. Anal. Appl. Pyrolysis, 1999, 49, 221–241.

432 433

Henrich, E.; Bürkle, S.; Meza-Renken, Z. I.; Rumpel, S. Combustion and gasification kinetics

20.

Zolin, A.; Jensen, A.; Jensen, P. A.; Frandsen, F.; Dam-Johansen, K. The influence of


Page 28 of 35

Page 29 of 35 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

434

inorganic materials on the thermal deactivation of fuel chars. Energy and Fuels, 2001, 15,

435

1110–1122.

436

21.

analysis in combustion research. J. Therm. Anal. Calorim. 2001, 64, 1325–1334.

437 438

22.

Nagpal, S.; Sarkar, T. K.; Sen, P. K. Simulation of petcoke gasification in slagging moving bed reactors. Fuel Process. Technol. 2005, 86, 617–640.

439 440

Stenseng, M.; Zolin, A.; Cenni, R; Frandsen, F.; Jensen A; Dam-Johansen. K. Thermal

23.

Smith, I. W. The combustion rates of coal chars: A review. Nineteenth Symposium (International) on Combustion, 1982, 1045–1065.

441 442

24.

Tyler, R. J.,. Intrinsic reactivity of petroleum coke to oxygen. Fuel, 1986, 65, 235–240.

443

25.

Ranish, J. M.; Walker, P. L. High pressure studies of the carbon-oxygen reaction. Carbon,. 1993, 31(1), 135–141.

444 445

26.

Combustion and Flame, 2001, 125, 1138–1149.

446 447

27.

28.

29.

30.

Yildiz, Z.; Uzun, H.; Ceylan, S.; Topcu, Y. Application of artificial neural networks to cocombustion of hazelnut husk-lignite coal blends. Bioresour. Technol.2016, 200, 42–47.

454 455

Sanchez, M. E.; Otero, M.; Gómez, X.; Morán, A. Thermogravimetric kinetic analysis of the combustion of biowastes. Renew. Energy, 2009, 34, 1622–1627.

452 453

Lv, S.; Li, G; Liu, X. Particle dispersion behaviors of dense gas-particle flows in bubble fluidized bed. Adv. Mech. Eng. 2013, 1-14.

450 451

Kastanaki, E.; Vamvuka, D. A comparative reactivity and kinetic study on the combustion of coal-biomass char blends. Fuel, 2006, 85, 1186–1193.

448 449

Hurt, R. H.; Calo, J. M. Semi-global intrinsic kinetics for char combustion modeling.

31.

Mikulandrić, R.; Lončar, D.; Böhning, D.; Böhme, R.; Beckmann, M. Artificial neural network

456

modelling approach for a biomass gasification process in fixed bed gasifiers. Energy Convers.

457

Manag. 2014, 87, 1210–1223.


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

458

32.

Vani, S.; Sukumaran, R. K.; Savithri, S. Prediction of sugar yields during hydrolysis of

459

lignocellulosic biomass using artificial neural network modeling. Bioresour. Technol. 2015,

460

188, 128–135.

461

33.

Buyukada, M. Co-combustion of peanut hull and coal blends: Artificial neural networks

462

modeling, particle swarm optimization and Monte Carlo simulation. Bioresour. Technol. 2016,

463

216, 280–286.

464

34.

Pandey, D. S.; Das, S.; Pan, I.; Leahy, J. J.; Kwapinski, W. Artificial neural network based

465

modelling approach for municipal solid waste gasification in a fluidized bed reactor. Waste

466

Manag. 2016, 58, 202–213.

467

35.

Caner, M.; Gedik, E.; Keĉebaŝ, A. Investigation on thermal performance calculation of two

468

type solar air collectors using artificial neural network. Expert Syst. Appl. 2011, 38, 1668–

469

1674.

470

36.

Technique. Aquat. Procedia, 2015, 4, 1070–1077.

471 472

37.

Conesa, J. A.; Caballero, J. A.; Reyes-Labarta, J. A. Artificial neural network for modelling thermal decompositions. J. Anal. Appl. Pyrolysis, 2004, 71, 343–352.

473 474

Sarkar, A.; Pandey, P. River Water Quality Modelling Using Artificial Neural Network

38.

Jinchuan, K.; Xinzhe, L. Empirical analysis of optimal hidden neurons in neural network

475

modeling for stock prediction. Proc.-2008 IEEE Pacific-Asia Work. Comput. Intell. Ind. Appl.

476

2008, 828–832.

477

39.

Gnanan Sheela, K.,; Deepa, S. N. Review on methods to fix number of hidden neurons in neural networks. Math. Probl. Eng. 2013, 1-11.

478 479

40.

Levenspiel, O. Chemical reaction engineering. Ind. Eng. Chem. Res 38, (1999).

480

41.

Duvvuri, M. D., Muhlenkamp, S. P., Iqbal, K. Z. & Welker, J. R. Pyrolysis of natural fuels. J

481

Fire Flammabl. 1975, 6, 468–477.

482 30 | P a g e ACS Paragon Plus Environment

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483

Energy & Fuels

Appendix: Models for Prediction of kinetics

484

A) Shrinking Particle Model (SPM)

485

As there is negligible ash content in the sample obtained from proximate analysis as illustrated in

486

Table 3, during burning, carbon particle shrinks and finally disappears. The reaction is considered

487

to obey SPM[40]. The resistances such as surface reaction and gas film diffusion may play a role in

488

SPM.

489

To deduce the kinetics of the CPC, the following conditions are considered.

490

•

CPC is of pure carbon.

491

•

No unwanted Side reaction takes place as excess of oxygen provided.

492

•

Uniform Size of CPC of about 60µm.

493

•

Obeys Shrinking Particle Model (SPM) as negligible ash content in it.

494

•

The intrinsic chemical kinetics obeys first order reaction.

495

•

Gas film resistance is neglected.

496

The reaction of CPC taking place as follows,

497

C + O2 --- CO2 [B (s) + A (g) --- Gaseous products]

498 499

(A.1)

The mole balance for the above reaction is given as, −

500

! G !2

= −

! H !2

= )= 4J % 4DE = − DE * 5 = )* 4J % DEK ,

(A.2)

501

where, )* is surface reaction rate constant (m/min) and )= is gas film mass transfer constant

502

(m/min).

503

But, L

C = M J M BC

504

505

(A.3)

i.e. −

506

! H !2

!;

= 4J % BC !2


(A.4)

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

507

From equation (A.2),

508

)* 4J % DEK = )= 4J % 4DE = − DE * 5

509

DEK = DE = ∗ O

510

Now from (A.2) and (A.4),

PQ

PK PQ

R

!;

−4J % BC !2 = )* 4J % DEK

512

i.e.

/!; !2

/!; !2

(A.8)

TH

=

P PK D O Q R TH E = PK PQ

(A.9)

=

SG Q UT H

(A.10)

V V

R WQ WK

O

Considering in terms of diameter of particle, >

/!X

518

519

PK SGK

Dividing by )* )= throughout one gets,

516

517

=

!2

=

%∗SG Q UT H

(A.11)

V V

R WQ WK

O

For spherical particles falling in quiescent fluid, mass transfer takes place as, V

V

520

ℎ = 2 + 0.6 (_)` (a)b

521

or

522

(A.7)

Substituting for DEK , (A.8) becomes,

514

515

/!; !2

(A.5)

(A.6)

511

513

Page 32 of 35

PQ X X

c

(A.12) V `

V

X dT b 5 c

= 2 + 0.6 4TX5 4

For small particles falling under Stoke's regime, Equation A.13 reduces to,


(A.13)

Page 33 of 35 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

X ̴ %X PQ

523

(A.14)

524

As seen from the above equation, the mass transfer resistance is maximum at initial particle size,

525

Ro. This resistance reduces with decrease in particle size during the course of reaction. Value of

526

particle diameter being almost an order lower than the diffusivity term in equation (A.14), range of

527

1/kg would be less than 0.1 which is fairly a low value for mass transfer resistance. On neglecting

528

this term therefore, equation (A.11), can be rewritten as /!X

529

!2

=

%∗PK ∗ SG Q

(A.15)

TH

530

Now, what is observed during TGA experiments is the reduction in mass of particle which needs to

531

be converted in terms of diameter. The mass of spherically assumed CPC particle is given by, g

f = h > M ∗ BC ∗ i9a_j96k lamnℎ@ (o)

532 533

Subsequently, b V

534 535

(A.16)

p

= pq

Xb ` ∗T∗rs

X q V

`

∗T∗rs

(A.17)

and therefore,

/M

>b = 4b 5

536

V

∗ >V

(A.18)

537

Thus reduction in mass % is expressed in terms of reduction in diameter with respect to time and

538

the kinetics is determined following equation (A.15). ks (m/min) thus obtained can be converted

539

into k (1/min) by multiplying ks with ratio of surface area to mass of particle multiplied with mass

540

to volume of particle. In case of a solid sphere, this ratio is equal to 6/Dp.

541

In a separate exercise, while conducting TGA experiments, the flow rate of reactive gas is varied

542

between 40 and 100 ml per minute and no observable change in the slope of decomposition curve

543

is observed. This observation vindicates the hypothesis that the gas side mass transfer does not

544

limit the g-s reaction under study and, it is therefore, only surface reaction controlled.

545

Thus from modelling study, the gas film transfer resistance is found to be less compared to surface

546

reaction kinetics and hence the former is neglected in evaluation of kinetics parameters. Assuming

547

uniform particle size of 60 µm diameter at a given temperature, change in weight with time is 33 | P a g e ACS Paragon Plus Environment

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

Page 34 of 35

548

converted into change in particle diameter and the time gradient of diameter is equated to intrinsic

549

reaction kinetics, ()* ) as shown in equation A.15. Several such isothermal experiments are

550

performed to get an Arrhenius plot between )* and temperature, 8. Subsequently and are

551

evaluated from the intercept and slope of the plot respectively to predict a generic )* .

552

B) Weight Fraction Model (WFM)

553

Determination of kinetic parameters from TGA data using WFM is based on modified form of

554

Arrhenius equation[41].

555

In this study, determination of the kinetic parameters from TGA technique is based on the

556

modified form of Arrhenius equation proposed by Duvvuri et al., 1975[41].

557

Global kinetics of devolatilization reaction is written as, /!t !2

558 559

= )F

(B.1)

F , the weight fraction with respect to initial quantity of CPC can be written as, 0/0u

F=0

560

(B.2)

1 /0u

561

where, w is weight of CPC at any time t, wo is the initial CPC weight and wf is the weight of ash (if

562

any).

563

Applying Arrhenius Equation on rate constant k (1/min), :

) = exp 4− ;

Investigation on Kinetic Parameters of Combustion and Oxy

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