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Extended adiabatic flame temperature method for lower flammability limits prediction of fuel-air-diluent mixture by nonstoichiometric equation and nitrogen equivalent coefficients Runzhao Li, Zhongchang Liu, Yongqiang Han, Manzhi Tan, Yun Xu, Jing Tian, Jiahong Chai, and Jiahui Liu Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.6b02459 • Publication Date (Web): 09 Dec 2016 Downloaded from http://pubs.acs.org on December 10, 2016

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Energy & Fuels

1

Extended adiabatic flame temperature method for lower flammability limits

2

prediction of fuel-air-diluent mixture by non-stoichiometric equation and nitrogen

3

equivalent coefficients

4 5

Runzhao Li, Zhongchang Liu, Yongqiang Han, Manzhi Tan*, Yun Xu, Jing Tian, Jiahong Chai, Jiahui

6

Liu

7

State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun 130025, China

8 9

ABSTRACT

10 11

The extended adiabatic flame temperature method aims at predicting the lower flammability limits of

12

fuel-air-diluent mixtures (including fuel mixtures and diluent mixtures) by nonstoichiometric equation

13

and nitrogen equivalent coefficients. A cubic function is introduced to describe the relation between the

14

critical adiabatic flame temperature and inert volume concentration. This method applies to ten

15

compounds including methane, propane, iso-octane, ethylene, acetylene, benzene, methanol, dimethyl

16

ether, methyl formate and acetone for validation. A well agreement is obtained between the predicted and

17

measured value that the average relative deviations are all below 3.6%. The sources of error mainly

18

attribute to three causes: First, the adiabatic flame temperature method does not regard for the heat losses

19

from flame front to surroundings. Second, the test method and determined criterion both have a

*

Corresponding author.

E-mail address: [email protected] (M. Tan). 1

ACS Paragon Plus Environment

Energy & Fuels

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20

significant impact on the experimental data. Third, the functional relationship between adiabatic flame

21

temperature and inert concentration also influences the exactness.

22 23 24

Highlights:

25



26

The extended adiabatic flame temperature method aims at predicting lower flammability limits of fuel-air-diluent mixture.

27



The proposed method can apply to substances which containing C-H-O-N atoms.

28



The proposed method is capable of processing diluent mixtures by nitrogen equivalent

29 30

coefficients. 

31 32

A cubic function is introduced to describe the relation between adiabatic flame temperature and inert concentration.



The average relative deviations for lower flammability limits estimation are all below 3.6%.

33 34 35

Keywords:

36

Lower flammability limits; Fuel-air-diluent mixture; Extended adiabatic flame temperature method;

37

Non-stoichiometric equation; Nitrogen equivalent coefficients.

2


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Energy & Fuels

Nomenclature

a0 , a1 , a2 , a3

empirical coefficients of heat capacity

Ai

mole fraction of the i th fuel in the mixture

Bj

mole fraction of the j th diluent in the mixture

cinert

inert gas concentration (vol%)

cp

heat capacity at constant pressure (J∙mol-1∙K-1)

c p ,l

heat capacity at constant pressure of products (J∙mol-1∙K-1)

C

mole fraction of the air in the mixture (vol%)

Fueli

the i th fuel in the mixture

H c , i

heat of combustion of the i th fuel (J/mol)

H i , reactants

enthalpy of the i th reactant (J)

H j , products

enthalpy of the j th product (J)

H 0f ,i , reactants

heat of formation of the i th reactants at standard condition (J/mol)

H 0f , j , products

heat of formation of the j th products at standard condition (J/mol)

Inert j

the j th diluent in the mixture

Kk

nitrogen equivalent coefficients

M

molecular weight (kg/kmol)

p,q,r,s

empirical coefficients of adiabatic flame temperature at lower flammability limit

P

gas pressure (Pa)

R

conventional gas constant (J∙mol-1∙K-1)

3


Energy & Fuels

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R2

correlation coefficient

SS E

sum of squares of residuals

SS T

sum of squares

Tad

adiabatic flame temperature of products (K)

Tad , LFL

adiabatic flame temperature at lower flammability limit (K)

Ti

initial temperature of reactants (K)

xf

mole fraction of combustible (vol%)

xC ,equiv

the number of carbon atoms in the equivalent fuel

xH ,equiv

the number of hydrogen atoms in the equivalent fuel

xO ,equiv

the number of oxygen atoms in the equivalent fuel

xN ,equiv

the number of nitrogen atoms in the equivalent fuel

xC ,i

the number of carbon atoms in the i th fuel

xH , i

the number of hydrogen atoms in the i th fuel

xO ,i

the number of oxygen atoms in the i th fuel

xN ,i

the number of nitrogen atoms in the i th fuel

xL

lower flammability limit (vol%)

xL ,exp

lower flammability limit derived from experimental data (vol%)

xL ,calc

lower flammability limit derived from calculated data (vol%)

x st

stoichiometric concentration (vol%)

yi

mole fraction of the i th fuel in the fuel mixture (vol%)

4


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Energy & Fuels

Greek letters λ

nitrogen/oxygen molar ratio



equivalence ratio

vair

stoichiometric concentration of air

 air

coefficient of air in non-stoichiometric equation

 CO

coefficient of carbon dioxide in non-stoichiometric equation

H O

coefficient of water in non-stoichiometric equation

N

coefficient of nitrogen in non-stoichiometric equation

2

2

O

2

2

coefficient of oxygen in non-stoichiometric equation

l

coefficient of products

vi , reactants

mole fraction of the i th reactant (vol%)

v j , products

mole fraction of the j th product (vol%)

δ

vapor specific gravity

Abbreviations AAD

average absolute difference (vol%)

AD

absolute difference (vol%)

ARD

average relative deviation (%)

LFL

lower flammability limit (vol%)

MAD

maximum absolute difference (vol%)

5


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MOC

minimum oxygen concentration (vol%)

MRD

maximum relative deviation (%)

RD

relative deviation (%)

UFL

upper flammability limit (vol%)

38

6


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Energy & Fuels

1. INTRODUCTION

40

Many apparatuses used in the chemical and petrochemical processes contain hazardous materials that

41

are flammable in air. As a result, the flammability limit is one of the important physical properties of the

42

flammable substances and it is necessary to evaluate the fire potential by experimental measurement and

43

theoretical derivation. According to the definitions of standard ASTM E681-09 1, the lower/upper

44

flammability limits (LFL/UFL) denote the minimum/maximum concentration of a combustible substance

45

that is capable of self-sustaining a flame propagation in a homogeneous mixture which involves

46

combustible and air under specific condition. The flame propagation has different determined criterions

47

according to the requirement of specific standard test method. Both ASTM E681-09

48

10156:2010

49

criterions in industry. Meanwhile, Bureau of Mines in America has performed extensive research on the

50

subject of explosion limits and summarized the flammability characteristics of gases and vapors

51

including paraffins, olefins, cycloparaffins, acetylenes, aromatic compounds, alcohols, aldehydes, ethers,

52

ketones, organic acids, organic salts, sulfur compounds and fuel blends 3-5.

2

1

and ISO

standards are a set of widely-accepted flammability limits test methods and determined

53

There are four significant challenges concerning flammability limits estimation which lists as below:

54

1.

To estimate the flammability limits of fuel-air-diluent mixture at ambient temperature and pressure.

55

2.

To estimate the flammability limits of fuel-air-diluent mixtures which containing various types of

56

fuels and diluents.

57

3.

To estimate the flammability limits of fuel-air-diluent mixtures as a function of temperature.

58

4.

To estimate the flammability limits of fuel-air-diluent mixtures as a function of pressure.

59

From the first category, many published references concerned the flammability limits of fuel-air

60

mixture without taking inert gases into account

6-10

. However, these data are easily available among

7


Energy & Fuels

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thousands of combustible from reference books, articles, websites, manuals, bulletins etc. 3-5, 11-16. Indeed,

62

removing all flammable mixtures or ignition sources is an effective measure to avoid the explosion hazard.

63

Nevertheless, it is unrealistic, combustible mixtures and ignition sources regularly present in industrial

64

operation. In processing industry, inert gases usually add into flammable mixture to reduce the explosion

65

potential 4. From the second category, the fuel and diluent mentioned above can be fuel mixtures and

66

diluent mixtures respectively in the practice of chemical safety and loss prevention

67

of inert gases affects both the upper and lower flammability limits. The existence of inert gases affects

68

both the upper and lower flammability limits. Rare data about flammability limits for fuel-air-diluent

69

mixtures is available in literature 21. Therefore, to investigate the flammability limits of fuel-air mixture

70

diluted with inert gases is of tremendous interest. Likewise, research on flammability limits of fuel

71

mixtures is no less important. From the third and fourth category, many available flammability limits of

72

combustible gases and vapors are derived from ambient temperature and pressure conditions. However,

73

the hazardous materials are formed usually under high temperature (>200oC) and pressure (>10bar) in

74

the chemical processing industry. Hence, it is more reasonable to predict the flammability limits at

75

elevated temperature and pressure 9, 10, 22-24.

17-20

. The existence

76

Generally, the methods for flammability limits estimation can grossly divide into five groups including

77

empirical correlation, Le Chatelier’s rule, adiabatic flame temperature method, burning velocity method

78

and numerical method as shown in Table 1.

79

From the first category, the empirical correlation consists of empirical formula and group contribution

80

model. The empirical formula is under long-term research, Shimy 25 suggested the functional relationship

81

between flammability limit and the number of specific atoms in combustible. Ma summarized the

82

flammability correlations in reference

26

from the perspectives of oxygen-based and fuel-based. The 8


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Energy & Fuels

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former established on the stoichiometric oxygen number while the latter established on the heat of

84

combustion of fuel. The former established his method on the stoichiometric oxygen number while the

85

latter established it on the heat of combustion of fuel. Recently, the group contribution model has been

86

the subject of extensive studies which provides a new approach to deal with the flammability limits 6, 27.

87

It aims at developing a quantitative structure property relationship to predict the flammability limits of

88

combustibles

89

fuel-air-diluent mixture because the method itself does not take the dilution effect of inert gases into

90

consideration.

7, 28, 29

. However, so far none of them is capable of estimating the flammability limits of

91

From the second category, the extended Le Chatelier’s formula is proposed by Kondo et al. 20, 30, 31. It

92

expands the scope to fuel-air-diluent mixture while the original one is only applicable to fuel-air mixture.

93

According to the assumption and principle of extended Le Chatelier’s formula, it still belongs to semi-

94

empirical formula.

95

From the third category, adiabatic flame temperature method is derived from the thermal equilibrium

96

theory. That means the enthalpy of reactants is equal to that of products without energy dissipation.The

97

critical reaction temperature at the minimum concentration of a combustible that is capable of

98

propagating a flame is known as adiabatic flame temperature at lower flammability limits Tad , LFL

99

If the adiabatic flame temperature at lower flammability limits Tad , LFL is known through experimental

100

measurement, the lower flammability limits variation with diluent volume percent can be calculated.

101

Since it has difficulty to evaluate the heat capacity of unburned fuel accurately under fuel rich condition,

102

it is inappropriate to predict the upper flammability limits. Owing to adiabatic flame temperature method

103

taking all compositions into consideration, it has the potential to solve the first and second challenges

104

mentioned above. 9


32, 33

.

Energy & Fuels

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105

From the fourth category, Liao et al.

34-37

argued that the low burning velocity is the cause of flame

106

extinction because sufficient burning velocity is necessary to overcome the thermal dissipation process.

107

This method is based on the flame propagation theory that provided a new way to deal with the

108

flammability limits of fuel-air-diluent mixture. From the fifth category, the numerical method is also a

109

promising method to predict the fire potential and much commercial software are available such as

110

CHEMKIN, CHETAH, CHEM 1D and SuperChemsTM. They all base on a specific database concerned

111

with physical-chemical properties of gases and vapors. For more information, please refer to references

112

listed in Table 1.

113

The extended adiabatic flame temperature method aims at predicting the lower flammability limits of

114

fuel-air-diluent mixtures which including fuel mixtures or diluent mixtures. The atoms equivalence and

115

nitrogen equivalent coefficients are employed to convert fuel mixtures and diluent mixtures into

116

equivalent fuel and nitrogen. The lower flammability limits can be computed by combining the non-

117

stoichiometric equation and critical adiabatic flame temperature. A cubic function is introduced to

118

describe the relation between Tad , LFL and cinert . The proposed method applies to ten compounds

119

including methane, propane, iso-octane, ethylene, acetylene, benzene, methanol, dimethyl ether, methyl

120

formate and acetone for validation. Furthermore, the comparison between the calculated and measured

121

values is carried out and the source of error is analyzed in detail. The framework of this article is plotted

122

in Figure 1.

10


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123

Energy & Fuels

Table 1. A concise summary of the flammability limits predicted methods Methods for flammability limit prediction

Ref.

Characteristic

Principle/Fundamental

Specific approach

Empirical correlation

Empirical formula

25, 26

They both develop black box model by providing fits to experimental data. instead

Group contribution model

6, 7, 27-29

of basing on the theory of combustible ignition, flame propagation and flame extinction.

Le Chatelier’s rule

It expands the scope of original Le Chatelier’s rule from fuel-air mixture to fuel-

20, 30, 31

Extended Le Chatelier formula

air-diluent mixture. Thermal equilibrium theory

Adiabatic flame temperature method

8, 32, 38, 39

This method is inappropriate to estimate the upper flammability limits because the heat capacity of unburned fuel is difficult to evaluate accurately.

Theory of flame propagation

Burning velocity method

34-37

It bases on the hypothesis that flammable mixture fails to support self-sustained

and thermal dissipation

flame propagation if the burning velocity is too low to conquer the dissipation effect. 11


Energy & Fuels

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CHETAH software

40

They are based on the database about the physical and chemical properties of

CHEM 1D software

41, 42

flammable materials. It is an effective and promising tool to estimate the

SuperChemsTM software

32

flammability limits.

Numerical method-asymptotic

One dimensional adiabatic premixed

43, 44

It proposes one dimensional, planar, premixed, non-adiabatic flames model

theory

flame model considering detailed

considering detailed chemistry and variable properties. In addition, the effect of

chemistry

heat losses is systematically considered

Numerical method

124

12


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Energy & Fuels

Thermal equilibrium theory

Validation

Extended adiabatic flame temperature mothod

Non-stoichiometric equation

Nitrogen equivalent coefficients

Lower flammability limits estimation of fuel-air-diluent mixtures

Experimental measurement

To examine the calculated results with experimental data from literatures and identify the sources of error

125 126

Figure 1. The framework of this article.

127 128

2. THEORY AND METHODOLOGY

129

In this section, the calculated procedures of proposed method are presented. This method is also

130

applicable to fuel mixtures and diluent mixtures. Furthermore, seven evaluation indexes are provided to

131

assess the accuracy of the proposed method.

132

2.1. The computational procedures of extended adiabatic flame temperature method.

133

The first step is to identify the composition of fuel-air-diluent mixture. The composition of a mixture

134

containing n flammable gases, p inert gases and air can be described by eq (1):

135

A1 %Fuel1 

 Ai %Fueli 

An %Fueln  B1 %Inert1 

 B j %Inert j 

Bp %Inert p  C%Air

(1)

136

The symbol of Ai , B j , C , Fueli and Inert j denote mole fraction of the i th fuel in the mixture, mole

137

fraction of the j th diluent in the mixture, mole fraction of the air in the mixture , the i th fuel in the mixture and the

138

j th diluent in the mixture respectively.

139

The second step is to convert all the inert gases fractions into their nitrogen equivalent by nitrogen 13


Energy & Fuels

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140

equivalent coefficients K k which provided by standard ISO 10156:2010. The nitrogen equivalent

141

coefficients are summarized in Table 2. Then the composition of the mixture can be represented as eq

142

(2):

143

A1 % Fuel1 

144

If D%  K1 B1 % 

145

 Ai % Fueli 

An % Fueln   K1 B1 % 

 K j Bj % 

K p B p %  N 2  C % Air

 K jBj % 

K p Bp % , then the composition of the mixture can be presented by

eq (3):

146

A1 % Fuel1 

147

Table 2. Nitrogen equivalent coefficients K k α for inert gases relative to nitrogen 2

148 149

(2)

 Ai % Fueli 

An % Fueln  D % N 2  C % Air

(3)

Gas

N2

CO2

He

Ar

Ne

Kr

Xe

SF6

CF4

C3F8

𝐾𝑘

1

1.5

0.9

0.55

0.7

0.5

0.5

4

2

1.5

α

The nitrogen equivalent coefficient K k =1.5 should be used when the inert gases containing three or

more atoms in their molecular formula.

150

The third step is to approximate the fuel-air-diluent mixture to fuel-oxygen-nitrogen mixture. The mole

151

fraction of oxygen and nitrogen are E%  20.95%  C% and F %  D%  79.05%  C % respectively.

152

The composition of the mixture can be expressed by eq (4):

153

A1 % Fuel1 

154

The fourth step is to calculate the nitrogen/oxygen molar ratio λ 

155

The fifth step is to convert various types of fuels (Fuel1 

 Ai % Fueli 

An % Fueln  E %O2  F % N 2

(4) F . E

 Fueli 

Fueln ) into the equivalent

156

fuel ( C a H b Oc N d ) by their respective mole fractions as described in eq (5) ~ (8). xC ,equiv , xH , equiv ,

157

xO ,equiv and xN ,equiv represent the number of carbon, hydrogen, oxygen and nitrogen atoms in the

158

equivalent fuel respectively. xC ,i , xH ,i , xO ,i and xN ,i denote the number of carbon, hydrogen,

14


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Energy & Fuels

159

oxygen and nitrogen atoms in the i th fuel respectively. The symbol yi describes the mole fraction of

160

the i th fuel in the fuel mixture as expressed in eq (9). n

161

a  xC , equiv   yi  xc ,i

(5)

1 n

162

b  xH ,equiv   yi  xH ,i

(6)

1 n

163

c  xO , equiv   yi  xO ,i

(7)

1 n

164

d  xN , equav   yi  xN ,i

(8)

1

Ai

165

yi 

166

The sixth step is to establish the non-stoichiometric equation (fuel lean mixture, equivalence ratio

167

A1 

 Ai 

(9)

An

  1 ) as shown in eq (10).

168

Ca H b OC N d   air  O2   N 2   CO2 CO2   H 2O H 2O   N 2 N 2  O2 O2

169

In the fuel lean mixture (   1 ), the quantity of heat release depends on the amount of consumed fuel.

170

Therefore, the residual oxygen in products is a function of initial fuel concentration, as shown in eq (11)

171

~ (16). b c  4 2 1 xf v  air   4.773 x f

(10)

172

vair  a 

(11)

173

 air

(12)

174

CO  a

(13)

175

H O 

b 2

(14)

176

 N     air 

177

 O   air   CO 

178

where x f is the combustible mole fraction in the mixture. From the perspective of energy balance,

179

the energy released by reactants heats the reaction products to adiabatic flame temperature in the absence

180

of heat losses which can be expressed by eq (17) 24, 32, 33.

2

2

2

2

d 2 2

(15) H O 2

2



c 2

(16)

15


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181

H

182

H i , reactants Ti , P  and H j , products Tad , P  are the enthalpy of the i th reactant at the initial temperature

183

and the enthalpy of the j th product at the adiabatic flame temperature respectively. The oxidation reaction

184

is regarded as constant pressure process. If the adiabatic flame temperature Tad

185

combustible concentration x f can be calculated by eq (18) because the coefficient of products 𝜇𝑙 is a

186

function of combustible mole fraction x f .

187

i , reactants

Tad  Ti 

Ti , P   H j , products Tad , P 

y  H   c i

l

(17)

is known, the

c ,i

(18)

p ,l

188

Tad , Ti , yi , H c ,i ,  l and c p,l are adiabatic flame temperature, initial temperature, mole fraction

189

of the i th fuel in the fuel mixtures, heat of combustion of the i th fuel in the fuel mixtures, the coefficient

190

of products and heat capacity at constant pressure of products respectively. The heat of combustion

191

depicts the total energy difference between reactants and products as expressed in eq (19) 11. In other

192

words, the heat of combustion is the total energy released in the reaction when the substances undergo

193

complete oxidation at standard conditions.

194

H c  vi , reactants  H 0f ,i , reactants  v j , products  H 0f , j , products

195

0 0 vi , reactants , H f ,i , reactants , v j , products and H f , j , products represent mole fraction of the i th reactant, heat

196

of formation of the i th reactant at standard condition, mole fraction of the j th product and heat of

197

formation of the j th product at standard condition. The heat capacity at constant pressure of products

198

c p,l is expressed as a function of temperature which is shown in eq (20) 13, 21. The empirical coefficients

199

and heat of formation are listed in Table 3 that can be retrieved from the relevant literatures 5, 11, 13 .

200 201

cp R

 a0  a1T  a2T 2  a3T 3  a4T 4

(19)

(20)

where c p and R denote heat capacity and conventional gas constant respectively. The conventional 16


Page 17 of 49

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

202

Energy & Fuels

gas constant equals to 8.31441 J/(mol∙K).

203

Generally, the eq (10) ~ (18) establishes the functional relation between the combustible mole fraction

204

in mixture x f and the adiabatic flame temperature Tad . Therefore, if the adiabatic flame temperature

205

at lower flammability limit Tad ,?LFL is known, its lower flammability limits xL can be calculated by the

206

adiabatic flame temperature expression (18) and non-stoichiometric equation (10) mentioned above.

207 208

In order to make the principle of extended flame temperature method more distinct, the general idea of the proposed method is shown in Figure 2. Fuel1

Fueli

Atoms equivalence

Fueln

Inert1

Inertj

Inertp

Air


CaHbOcNd

Air

N2 equivalent

N2 equivalent

+ 20.95%Air

79.05%Air

CaHbOcNd

N2



209 210

Lower flammability limits XL

Figure 2. The general idea of extended adiabatic flame temperature method.

17


O2

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

211

Page 18 of 49

Table 3. The standard heat of formation and empirical coefficients of heat capacity of the studied substances Name

Formula

H 0f ,i ,298 (kJ/mol)

c p / R  a0  a1T  a2T 2  a3T 3  a4T 4

CAS # a0

a1 103

a2 105

a3 108

a4  1011

Methane

CH4

74-82-8

4.568

-8.975

3.631

-3.407

1.091

-74.87

Ethane

C2H6

74-84-0

4.178

-4.427

5.660

-6.651

2.487

-84.55

Propane

C3H8

74-98-6

3.847

5.131

6.011

-7.893

3.079

-120.92

Octane

C8H18

111-65-9

10.824

4.983

17.751

-23.137

8.980

-250.10

Ethylene

C2H4

74-85-1

4.221

-8.782

5.795

-6.729

2.511

52.40

Acetylene

C2H2

74-86-2

2.410

10.926

-0.255

-0.790

0.524

227.06

Benzene

C6H6(g)

71-43-2

3.551

-6.184

14.365

-19.807

8.234

82.96

Methanol

CH4O

67-56-1

4.714

-6.986

4.211

-4.443

1.535

-239.20

Dimethyl ether

C2H6O

115-10-6

4.361

6.070

2.899

-3.581

1.282

-277.60

Methyl formate

C2H4O2

107-31-3

2.277

18.013

1.160

-2.921

1.342

-349.94

18


Page 19 of 49

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Energy & Fuels

Acetone

C3H6O

67-64-1

5.126

1.511

5.731

-7.177

2.728

-248.40

Argon

Ar

7440-37-1

2.500

0.000

0.000

0.000

0.000

0.00

Carbon monoxide

CO

630-08-0

3.912

-3.913

1.182

-1.302

0.515

-110.53

Carbon dioxide

CO2

124-38-9

3.259

1.356

1.502

-2.374

1.056

-393.52

Hydrogen

H2

1333-74-0

2.883

3.681

-0.772

0.692

-0.213

0.00

Helium

He

9440-59-7

2.500

0.000

0.000

0.000

0.000

0.00

Water

H2O(g)

7732-18-5

4.395

-4.186

1.405

-1.564

0.632

-241.83

Oxygen

O2

7782-44-7

3.630

-1.794

0.658

-0.601

0.179

0.00

Nitrogen

N2

7727-37-9

3.539

-0.261

0.007

0.157

-0.099

0.00

212 213

19


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

214

Page 20 of 49

2.2. Evaluation indexes of computational accuracy.

215

In order to determine the accuracy of the extended adiabatic flame temperature method, seven

216

evaluation indexes including absolute difference ( AD ), average absolute difference ( AAD ), maximum

217

absolute difference ( MAD ), relative deviation ( RD ), average relative deviation ( ARD ), maximum

218

relative deviation ( MRD ) and correlation coefficient ( R 2 ) are offered in eq (21) ~ (27). The correlation

219

coefficient is computed by the sum of squares of residuals SS E and the total sum of squares SS T as

220

shown in eq (28) ~ (29) 45 :

221

AD  xL , exp  xL , calc  100%

222

AAD 

223

MAD  max xL , exp  xL ,calc  100%

224

RD 

225

ARD 

226

 xL , exp  xL , calc  MRD  max   100%  xL , exp  

227

R2  1 

228

SS E    xL , exp  xL ,calc 

(21)

1 n  xL,exp  xL,calc 100% n i 1



(22)



xL , exp  xL ,calc xL , exp

(23)

 100%

(24)

1 n xL , exp  xL , calc  100%  x n i 1 L , exp

(25)

(26)

SS E

(27)

SST

n

2

(28)

i 1

n

229

SST    xL , exp  i 1

2

 n    xL , exp  i 1   n

2

(29)

230 231

3. RESULTS AND DISCUSSION

232

In order to evaluate the feasibility and accuracy of this extended adiabatic flame temperature method,

233

ten compounds including methane, propane, iso-octane, ethylene, acetylene, benzene, methanol, 20


Page 21 of 49

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Energy & Fuels

234

dimethyl ether, methyl formate and acetone are under investigation. The lower flammability limits of

235

these ten compounds are computed by the extended adiabatic flame temperature method, then compared

236

with the observed values. Even though some latest literatures have reported the flammability limit of

237

methane, propane, propylene, methyl formate, dimethyl ether, their test method (ISO 10156, ASTM E681,

238

EN1839 etc.), apparatus (vessel size and shape) and determination criterion (visual criterion or pressure

239

criterion) are diverse 20, 30, 31, 33, 46, 47. Thence, the experimental data adopted in this article all derive from

240

bulletins of Bureau of Mines 3-5. The properties of the selected fuels are listed in Table 4.

241

The critical adiabatic flame temperature is the principle contributor of the estimated error. Many

242

literatures 8, 16, 21, 29, 32, 38-40, 48-50 have reported the adiabatic flame temperature at lower flammability limit

243

Tad ,?LFL of different kind of fuels. Vidal et al. 32 suggested specific threshold temperature to predict the

244

lower flammability limit for each combustible. However, the adiabatic flame temperature at lower

245

flammability limits hardly keep constant with increasing inert volume percent. For example, the lower

246

flammability limit of propane in air and at inertion point diluted with nitrogen are 2.2 vol% and 3 vol%

247

respectively. Quintiere

248

1380oC and the later one is 1200oC. Shebeko et al. 38 revealed that most of the flammable mixtures at the

249

inertion point are fuel-rich mixture besides methane, hydrogen and few other material. He found that the

250

intersection point of the upper and lower flammability limit curves usually meets the line of

251

stoichiometric combustion to CO and H2O as described in Figure 3. The adiabatic flame temperature

252

along the lower flammability limit curve varied with diluent volume percent. Thus, an empirical eq (30)

253

describing the relation between Tad , LFL and cinert is established by fitting calculation to the published

254

data 8, 16, 21, 29, 32, 38-40, 48-50. A cubic function is introduced to correlate the Tad , LFL and cinert which give

255

an alternative to linear function and has a potential to reduce the predicted error. The empirical

51

confirmed that the adiabatic flame temperature at the former condition is

21


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 22 of 49

256

coefficients p , q , r and s are listed in Table 5. The procedures of determining the constants p, q,

257

r and s are summarized as below:

258

1.

259 260

To identify several mixture compositions located at the lower flammability limits from the relevant literatures.

2.

To compute the adiabatic flame temperature by Chemkin Pro software using equilibrium model

261

which takes into account the flame temperature change causing by the reaction products

262

dissociation.

263

3.

To preliminarily determine p, q, r and s by correlating the Tad , LFL and cinert .

264

4.

To further reduce the predicted error by adjusting the empirical coefficients of p, q, r and s

265

especially for the region near inertion point. Because it is difficult to evaluate the heat capacity of

266

unburned fuel under fuel-rich condition.

267

3 2 Tad , LFL  pcinert  qcinert  rcinert  s

268

Since investigated additives have similar effects on explosion limits, so only methane, acetylene and

269

methanol are presented as examples. The measured and calculated lower flammability limits of methane,

270

acetylene and methanol are plotted in Figure 4~Figure 6. The results indicate that the predicted lower

271

flammability limits have an acceptable agreement with the observed values. The lower flammability

272

limits rise slightly with increasing inert volume percent. In addition, the relative deviation of the mixture

273

composition near the inertion point is relatively large comparing to those with lower diluent concentration.

274

Since it is difficult to accurately estimate the thermal capacity of unburned fuel under fuel-rich condition.

275

The detailed accuracy indicators are listed in Table 6. The average relative deviations and maximum

276

relative deviation all remain under 3.6 vol% and 15 vol% as shown in Figure 7. The comparison between

277

predicted and measured lower flammability limits of ethylene-air-carbon dioxide and ethylene-air-

(30)

22


Page 23 of 49

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Energy & Fuels

278

nitrogen respectively is shown in Figure 8. And the experimental results are obtained by Kondo et al. 30,

279

31

280

this work are on the conservative side in most cases because standard ISO 10156 underestimates the

281

inertion effect of diluents for safety purpose

282

components based on the “the worst case” to ensure security in industry operation. The main error sources

283

of this extended adiabatic flame temperature method summarize as below:

284

, Coward et al. 3 and Zabetakis et al. 4 respectively. It turns out that the predicted limits proposed by

1.

52, 53

. It is reasonable to design and determine the mixture

The adiabatic flame temperature method is based upon the theory of thermal equilibrium and does

285

not take heat losses into consideration. However, heat losses occurred at test vessel is unavoidable

286

in practice.

287

2.

The flammability limits derived from experiment are dependent on test method (including test

288

procedure, vessel size and shape etc.) and determined criterion (either visual criterion or pressure

289

criterion).

290

3.

The functional relationship between adiabatic flame temperature and diluent volume percent also

291

plays an important role on the predicted precision. Generally, this functional relationship is

292

established by fitting experimental data to obtain analytical expression.

293

4.

The nitrogen equivalent coefficients K k derived from standard ISO 10156:2010 is one of the

294

causes of discrepancy because the ISO standard is more conservative that underestimates the

295

dilution effect of inert gases 52, 53.

296

5.

297 298 299

Many published data have minor difference on combustion heat and formation heat which definitely affects the accuracy even though the influence is not distinct.

6.

This method does not take structure contribution into account that may produce deviation when predicting the flammability limits of isomers. 23


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

300 301

7.

The temperature dependence of heat capacity also affects the predicted accuracy, even though the effect is not remarkable.

302

24


Page 24 of 49

Page 25 of 49

Adiabatic flame temperature=C

Fuel volume concentration

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

Curve 1: Lower flammability limit Curve 2: Upper flammability limit Line 3: Stoichiometric line CO2 and H2O Line 4: Stoichiometric line CO and H2O Point 5: Intersection point between curve 1 and line 3 Point 6: Intersection point between curve 2 and line 4

2

4 Adiabatic flame temperature=C

3

6 5 1 Adiabatic flame temperature=A

Adiabatic flame temperature=B

Added inert volume percent

303 304

Figure 3. The adiabatic flame temperature at lower flammability limits varied with diluent volume

305

percent.

306 307

25


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

Page 26 of 49

Table 4. Propertiesα of selected fuels

308

Lower limit in air

M Type

Combustible

δ

Formula

x st

Δ H c /(kJ/mol) xL /(Vol%)

/(kg/kmol)

xL

Ref.

xst

Alkane

Methane

CH4

16.04

0.55

9.48

802.8

5

0.53

4, 32

Alkane

Propane

C3H8

44.09

1.52

4.02

2044.8

2.1

0.52

4, 32

Alkane

Iso-octane

C8H18

114.23

3.94

1.65

5118.5

0.95

0.58

4, 11, 26, 32

Alkene

Ethylene

C2H4

28.05

0.97

6.53

1323.6

2.7

0.41

4, 32

Alkyne

Acetylene

C2H2

26.04

0.90

8.38

1255.6

2.5

0.30

11, 26, 49, 54

Aromatic hydrocarbon

Benzene

C6H6

78.11

2.69

2.72

3170.8

1.3

0.48

4, 49

Alcohol

Methanol

CH3OH

32.04

1.11

12.25

665.6

6.7

0.55

4, 49

Ether

Dimethyl ether

CH3OCH3

46.07

1.59

6.53

1322.7

3.4

0.52

4, 49

Ester

Methyl formate

CHOOCH3

60.05

2.07

9.48

916.7

5

0.53

4

Ketone

Acetone

CH3COCH3

58.08

2.01

4.97

1686.9

2.6

0.52

4, 49

M — Molecular weight, kg/kmol; δ — Vapor specific gravity, dimensionless; x st — Stoichiometric concentration xst 

309

α

310

combustion, at 25oC and constant pressure to form H2O (gas) and CO2 (gas), kJ/mol; xL —Lower flammability limit, vol%.

26


1  100% ; Δ H c — Heat of b c  1   a     4.773 4 2 

Page 27 of 49

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

311

Energy & Fuels

Table 5. Temperature correction coefficients of different combinations of fuels and diluents Fuel

312

CO2

N2

p

q

r

s

p

q

r

s

Methane

0.0514

-1.5284

0.9332

1497.6

0.0026

-0.0745

-10.415

1497.6

Propane

0.0284

-0.942

8.504

1495.9

0.0077

-0.2807

-6.788

1495.9

Iso-octane

0.0362

-0.9834

-3.7779

1998.1

0.0111

-0.5232

-5.4299

1998.1

Ethylene

0.0259

-1.0672

-0.9386

1265.3

0.0037

-0.2244

-4.4299

1265.3

Acetylene

0.0048

-0.2763

-6.9797

1190.7

0.0005

-0.0637

-6.0637

1190.7

Benzene

0.0492

-0.883

-6.7057

1552.5

0.0106

-0.5543

-4.7407

1552.5

Methanol

0.0123

-0.5308

-0.1004

1497.4

0.0009

-0.0692

-7.5265

1497.4

Dimethyl ether

0.0219

-0.9293

3.5498

1512

0.0032

-0.1556

-8.528

1512

Methyl formate

0.0247

-1.0856

1.2357

1746.4

0.0063

-0.3586

-8.1647

1746.4

Acetone

0.0344

-1.4983

20.182

1444.7

0.0037

-0.2882

1.5219

1444.7

27


Energy & Fuels

313 (a) 15

Measured CH4-Air-CO2 Measured CH4-Air-H2O(v) Measured CH4-Air-N2 Predicted CH4-Air-CO2 Predicted CH4-Air-H2O(v) Predicted CH4-Air-N2 Stoichiometric line CO2 Stoichiometric line CO

14

Methane (vol%)

13 12 11 10 9 8 7 6 5 0

5

10

314

15 20 25 Added inert (vol%)

30

35

40

315 316 (b)

15

Measured CH4-Air-He Measured CH4-Air-Ar Measured CH4-Air-20%CO2+80%N2 Predicted CH4-Air-He Predicted CH4-Air-Ar Predicted CH4-Air-20%CO2+80%N2 Stoichiometric line CO2 Stoichiometric line CO

14 13 12

Methane (vol%)

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 28 of 49

11 10 9 8 7 6 5 4 0

317 318

5

10

15

20 25 30 35 Added inert (vol%)

40

45

50

55

Figure 4. Comparison between the measured lower flammability limits of methane 3 and predicted values.

319 320

28


Page 29 of 49

321

90

Measured Acetylene-Air-CO2 Measured Acetylene-Air-N2 Predicted Acetylene-Air-CO2 Predicted Acetylene-Air-N2 Stoichiometric line CO2 Stoichiometric line CO

80

Acetylene (vol%)

70 60 50 40 30 20 10 0 0

5

10

15

20

322

25 30 35 40 45 Added inert (vol%)

50

55

60

65

323

Figure 5. Comparison between the measured lower flammability limits of acetylene

324

values.

4

70

and predicted

325 326

40 Measured Methanol-Air-CO2 Measured Methanol-Air-N2 Predicteded Methanol-Air-CO2 Predicteded Methanol-Air-N2 Stoichiometric line CO2 Stoichiometric line CO

35

Methanol (vol%)

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

30 25 20 15 10 5 0

327

5

10

15


35

40

45

328

Figure 6. Comparison between the measured lower flammability limits of methanol

329

values. 29


50 4

and predicted

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

330

Page 30 of 49

Table 6. The predictive precision of methane, propane, iso-octane, ethylene, acetylene, benzene, methanol, dimethyl ether, methyl formate and acetone Compounds

Number of data points

AAD (vol%)

MAD (vol%)

ARD (%)

MRD (%)

R2

Ref.

3

Fuel

Inert

Methane

CO2

8

0.0695

0.1141

1.1340

1.7672

0.9833

H2O

9

0.0265

0.0693

0.4330

1.0694

0.9962

N2

10

0.0331

0.1113

0.5832

1.8516

0.9659

He

10

0.07082

0.2260

1.2776

3.7590

0.8915

Ar

13

0.0428

0.0959

0.9155

2.1549

0.9604

20%CO2+80%N2

12

0.0645

0.1865

1.1095

2.9478

0.9471

CO2

11

0.0253

0.0919

0.7605

2.4389

0.9954

N2

14

0.0380

0.1212

1.4686

3.9902

0.9774

CO2

11

0.0330

0.1173

1.7776

5.2704

0.9720

N2

14

0.0251

0.1109

1.4938

5.6996

0.9546

15%CO2+85%N2

13

0.0452

0.1695

2.2587

6.7505

0.9742

CO2

14

0.0596

0.1352

1.9194

4.2181

0.9880

N2

15

0.1094

0.4366

3.5340

11.7500

0.7767

CO2

18

0.0767

0.2921

2.7095

8.5685

0.8224

Propane

Iso-octane

Ethylene

Acetylene

30


4

3

4

4

Page 31 of 49

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

Energy & Fuels

Benzene

Methanol

Dimethyl ether

Methyl formate

Acetone

N2

15

0.0674

0.5135

2.3635

15.6646

0.7023

CO2

13

0.0327

0.1207

1.5978

4.3808

0.9887

N2

12

0.0263

0.0943

1.7619

5.5781

0.8491

CO2

11

0.1173

0.3786

1.2724

3.6117

0.9832

N2

12

0.0399

0.1886

0.5162

2.2833

0.9815

CO2

10

0.0930

0.2929

2.0506

5.4214

0.9584

N2

14

0.1079

0.4309

2.7966

9.6092

0.7656

CO2

14

0.1066

0.3189

1.4390

3.8454

0.9674

N2

16

130.110307558

0.36890721

1.7683

5.3240

0.8287

CO2

13

0.059619732

0.160510937

1.5141

3.5686

0.9857

N2

15

0.032302954

0.0958091

0.9760

2.6442

0.9857

331 332

31


4

4

4

4

4

Energy & Fuels

333 (a) 9

Relative deviation (%)

8

Fuel-Air-CO2

P25 P0 P50 P100 P75

Fuel-Air-N2

P25 P0 P50 P100 P75

7

6 5 4 3 2 1 0

334 335 336 (b) 12 10


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 49

8

6 4 2 0

337 338

Figure 7. Relative deviation between experimental and predicted lower flammability limits of ten

339

compounds.

340 32


Page 33 of 49

341 (a)

4.8 Kondo, CO2 diluent Coward, CO2 diluent Zabetakis, CO2 diluent This work, CO2 diluent

Ethylene (vol%)

4.4 4.0 3.6 3.2 2.8 2.4

0

5

10

15

342


35

40

45

343 344 (b) 3.4 Kondo, N2 diluent Coward, N2 diluent Zabetakis, N2 diluent This work, N2 diluent

3.2

Ethylene (vol%)

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

3.0

2.8

2.6

2.4 0 345

10

20

30 40 Added inert (vol%)

50

60

346

Figure 8. Comparison between predicted and measured lower flammability limits of ethylene-air-

347

diluent.

348

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

349

4. CONCLUSIONS

350

This paper proposes an extended adiabatic flame temperature method for lower flammability limits

351

prediction of fuel-air-diluent mixture by non-stoichiometric equation and nitrogen equivalent coefficients.

352

The extended adiabatic flame temperature method is applied to ten compounds for validation and the

353

sources of error are analyzed carefully. The main conclusion can summarize as follow:

354

1.

355 356

ten compounds all remain under 3.6 volume percent. 2.

357 358

The extended adiabatic flame temperature method can predict the lower flammability limits of organic substances containing C-H-O-N atoms by atoms equivalence.

3.

359 360

The predicted values agree well with the reported data that the average relative deviations of these

The extended adiabatic flame temperature method is applicable to diluent mixture by adopting nitrogen equivalent coefficients which derived from standard ISO 10156.

4.

The predictive errors mainly cause by the following reasons: First, the extended flame temperature

361

method does not regard for the heat losses from flame front area to atmosphere. Second, the test

362

method and determined criterion both have a significant influence on the measured flammability

363

limits. Third, the functional relationship between adiabatic flame temperature and inert gases

364

volume percent also plays an important role on the exactness of the proposed method.

365

The lower flammability limit is one of the important properties of combustible mixture for fire and

366

explosion prevention in industry operation. It is widely applied in the fields of fire safety, combustion

367

process optimization, chemical engineering, process industries, suppression engineering and refrigerant

368

safety.

369 370 34


Page 34 of 49

Page 35 of 49

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

371

Energy & Fuels

AUTHOR INFORMATION

372

Corresponding Author

373

*E-mail: [email protected]

374

Notes

375

The authors declare no competing financial interest.

376 377

378

ACKNOWLEDGEMENT

379

This work is supported by the National Natural Science Foundation of China (No.51576089) and

380

Graduate Innovation Fund of Jilin University (No.2016026). Moreover, the field work is conducted in

381

State Key Laboratory of Automotive Simulation and Control, Jilin University. The authors thank the

382

laboratory managers and staff workers for their hospitability, time and opinions. The authors are indebted

383

to the reviewers of this article for their invaluable suggestions.

384

35


Energy & Fuels

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385

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41


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Page 42 of 49

Thermal equilibrium theory

Extended adiabatic flame temperature mothod


Validation


Lower flammability limits estimation of fuel-air-diluent mixtures

Experimental measurement

To examine the calculated results with experimental data from literatures and identify the sources of error

Figure 1. The framework of this article.


Page 43 of 49

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

Fuel1

Fueli

Atoms equivalence

CaHbOcNd

Fueln

Inert1

Inertj

Inertp

Air


Air

N2 equivalent

N2 equivalent

+ 20.95%Air

79.05%Air

CaHbOcNd

N2



Lower flammability limits XL

Figure 2. The general idea of extended adiabatic flame temperature method.


O2

Energy & Fuels

Adiabatic flame temperature=C

Fuel volume concentration

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 44 of 49

Curve 1: Lower flammability limit Curve 2: Upper flammability limit Line 3: Stoichiometric line CO2 and H2O Line 4: Stoichiometric line CO and H2O Point 5: Intersection point between curve 1 and line 3 Point 6: Intersection point between curve 2 and line 4

2

4 Adiabatic flame temperature=C

3

6 5 1 Adiabatic flame temperature=A

Adiabatic flame temperature=B

Added inert volume percent Figure 3. The adiabatic flame temperature at lower flammability limits varied with diluent volume percent.


Page 45 of 49

(a)

15

Measured CH4-Air-CO2 Measured CH4-Air-H2O(v) Measured CH4-Air-N2 Predicted CH4-Air-CO2 Predicted CH4-Air-H2O(v) Predicted CH4-Air-N2 Stoichiometric line CO2 Stoichiometric line CO

14

Methane (vol%)

13 12 11 10 9 8 7 6 5

0

(b)

5

10

15


30

35

40

Measured CH4-Air-He Measured CH4-Air-Ar Measured CH4-Air-20%CO2+80%N2 Predicted CH4-Air-He Predicted CH4-Air-Ar Predicted CH4-Air-20%CO2+80%N2 Stoichiometric line CO2 Stoichiometric line CO

14 13 12

Methane (vol%)

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

11 10 9 8 7

6 5 4

0

5

10

15

20 25 30 35 Added inert (vol%)

40

45

50

55

Figure 4. Comparison between the measured lower flammability limits of methane 3 and predicted values.


Energy & Fuels

1 90

Measured Acetylene-Air-CO2 Measured Acetylene-Air-N2 Predicted Acetylene-Air-CO2 Predicted Acetylene-Air-N2 Stoichiometric line CO2 Stoichiometric line CO

80 70

Acetylene (vol%)

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 46 of 49

60 50 40 30 20 10 0 0

2

5

10

15

20

25 30 35 40 45 Added inert (vol%)

50

55

60

65

3

Figure 5. Comparison between the measured lower flammability limits of acetylene

4

values.

5


4

70

and predicted

Page 47 of 49

6 40 Measured Methanol-Air-CO2 Measured Methanol-Air-N2 Predicteded Methanol-Air-CO2 Predicteded Methanol-Air-N2 Stoichiometric line CO2 Stoichiometric line CO

35

Methanol (vol%)

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

30 25 20 15 10 5 0

7

5

10

15


35

40

45

8

Figure 6. Comparison between the measured lower flammability limits of methanol

9

values.

10


50 4

and predicted

Energy & Fuels

(a) 9


8

Fuel-Air-CO2

P25 P0 P50 P100 P75

Fuel-Air-N2

P25 P0 P50 P100 P75

7

6 5 4 3 2 1 0

(b) 12 10


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 48 of 49

8

6 4 2 0

Figure 7. Relative deviation between experimental and predicted lower flammability limits of ten compounds.


Page 49 of 49

(a)

4.8 Kondo, CO2 diluent Coward, CO2 diluent Zabetakis, CO2 diluent This work, CO2 diluent

Ethylene (vol%)

4.4 4.0 3.6 3.2 2.8 2.4

0

5

10

15


35

40

45

(b) 3.4

Kondo, N2 diluent Coward, N2 diluent Zabetakis, N2 diluent This work, N2 diluent

3.2

Ethylene (vol%)

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

3.0

2.8

2.6

2.4 0

10

20

30 40 Added inert (vol%)

50

60

Figure 8. Comparison between predicted and measured lower flammability limits of ethylene-airdiluent.


Extended Adiabatic Flame Temperature Method for ... - ACS Publications

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