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Investigating the optimum blending condition on DCN of gasolinealcohol mixtures using Gaussian model Fabiyan Angikath, Nimal Nasser, Mani Sarathy King Abdullah University of Science & Technology, Clean Combustion Research Centre (CCRC), Saudi Arabia
GAUSSIAN FIT MODEL
ABSTRACT
There is clear evidence that the non-linearity depends on the structural composition of base fuel considered and the type of alcohol chosen. Gasoline fuels containing hundreds of different compounds making it challenging to clearly understand the antagonistic effect observed in the blending studies. The present study utilizes molar based Gaussian fit to model the antagonistic effect and optimum blending condition.
−(𝑥−𝑏)2
In Mathematics, a Gaussian Equation is expressed as follows 𝑓 𝑥 = 𝑎. 𝑒
2𝑐2
The parameter “a‟ is the height of curve’s peak. 𝐴𝑡 𝑥 = 𝑏, 𝑓(𝑥) = 𝑓(𝑏) = 𝑎. 𝑒 −0 = 𝑎. The parameter “b‟ is the value of variable “x‟ at which the curve reaches the peak. The parameter “c‟ tells about the width of the curve or extend of deviation (standard deviation or Gaussian RMS width) from the mean point 𝑓(𝑏) = 𝑎.
Inflection Point (IP) In a Gaussian curve, 𝑥 ∗ is an inflection point where 𝑓 ′′ (𝑥 ∗ ) = 0 => 𝑥 ∗ = 𝑏 ± 𝑐. At Inflection point, curvature changes from steep to moderate and 𝒇 𝒙∗ depends only on “a”.
𝑓 𝑥∗ = 𝑓 𝑏 + 𝑐 =
𝒇 𝒙
= 𝟎. 𝟔𝟎𝟔𝟓
Compare the antagonistic effect of the alcohols studied. Find an optimum volume or mole fraction of alcohols that maximize the blending effect.
DCN* of PRF 84 vs POH & BOH
DCN* of FACE vs n-propanol
In this study, the DCN of Primary Reference Fuels PRF 60, 70 and 84 and three Fuels for Advance Combustion Engines (FACE) gasoline namely FACE I, A and J were blended with two alcohols - propan-1-ol and butan-1-ol, and measured using Ignition Quality Tester (IQT) following ASTM D6890 method.
90
PRF 84
80
PRF 70
70
Aromatic mol%
FACE A
40
.
FJ
35
FACEI
PRF
0.7
25
0.6
10 0
14
FJ
0.4
P 60
P 70
0.3
5 0
P 60 P 70 P 84 F A
FI
References
FA
FI
8 6
0.2
4
0.1
2
0
FACE I
10
P 84
15 10
Antagonistic distance comparison FACE A PRF 84
12
0.5
30 20
0.8
30
20
FACE J
Branching Index
AD* (at IP)
Iso-paraffinic mol%
50
1. Anderson JE, DiCicco DM, Ginder JM, Kramer U, Leone TG, Raney-Pablo HE,et al. High octane number ethanol–gasoline blends: Quantifying the potential benefits in the United States. Fuel 2012;97:585–94. 2. Da Silva R, Cataluna R, de Menezes EW, Samios D, Piatnicki CMS. Effect of additives on the antiknock properties and Reid vapor pressure of gasoline, Fuel 2005;84:951–9. 3. ASTM D6890 Standard Test Method for Determination of Ignition Delay and Derived Cetane Number (DCN) of Diesel Fuel Oils by Combustion in a Constant Volume Chamber;2013. 4. Naser,N.,Yang,S(2017).Relating the octane numbers of fuels to ignition delay times measured in an ignition quality tester (IQT).Fuel,187,117-127. 5. Standard test method for research octane number of spark-ignition engine fuel. ASTM D 2699 - 13b; 2013. 6. Anderson J, Kramer U, Mueller S, Wallington T. Octane numbers of ethanol and methanol gasoline blends estimated from molar concentrations. Energy Fuels 2010; 24:6576–85 7. J. Badra, A. S. AlRamadan, and S. M. Sarathy, “Optimization of the octane response of gasoline/ethanol blends,” Appl. Energy, 2017.
PRF 84 10.00
FACE A
FACE I
5.00
= −0.31 + 0.024 ∗ p + 0.086 ∗ I − 𝟎. 𝟐𝟒𝟓 ∗ 𝑨 + 0.97 ∗ N − 0.109 ∗ O + 𝟐𝟐. 𝟒𝟑 ∗ 𝐁. 𝐈 −𝟎. 𝟗𝟑 ∗ 𝑫𝑪𝑵𝒂
In all cases of blending curves, the DCNmix is lower than its corresponding linear trend . In other terms, there is antagonistic blending effects. The lower volume of alcohol at IP can be obtained for higher antagonistic blends and thereby more reduction in DCN. The curve changes the direction at inflection point from steep to moderate. So for fuel designers, it is profitable to blend until mole-fraction of alcohol =IP, thereby optimizing the alcohol blending effect. The antagonistic behaviour is observed higher for POH than BOH. This shows that POH is a better blending agent than BOH. Antagonistic trend of fuels as follows, FACE A>PRF 84>FACE I>PRF 70>PRF 60>FACE J. More the branching, more the A∗D . Contribution of aromatics and olefins to the antagonistic behavior is seen negative.
.
60
REFERENCES
15.00
CONCLUSIONS
METHODOLOGY
For a constructive fitting of data, seven volumes of propan1-ol and butan-1-ol such as 5,10,15,20,30,50,70% on a gravimetric basis were considered for the experiment which then translated later into mole-fractions.
PRF 70
Linear Regression of AD* with respect to structural composition of base fuels, At global minima of rms = 2.468, the dependence on structural parameters is described ∗ AD
DCN* of PRF vs Mole-fraction of n-butanol
PRF 60
Linear Regression
Results 𝐷𝐶𝑁 − 𝐷𝐶𝑁 𝑏𝑙𝑒𝑛𝑑(𝑚𝑖𝑥) 𝐴𝑙𝑐𝑜ℎ𝑜𝑙(𝑎) ∗ 𝐷𝐶𝑁 = 𝐷𝐶𝑁𝑏𝑎𝑠𝑒(𝑏) − 𝐷𝐶𝑁𝐴𝑙𝑐𝑜ℎ𝑜𝑙(𝑎)
Under Normalized conditions, a~1
20.00
Fig 4: Blending volumes of POH with different fuels at same antagonistic distance as FACE J
𝑎 . 1.6487
In order to fit Gaussian model to blending studies, normalized (DCN*) vs molefraction (x) is plotted.
∗
FACE J
0.00
Normalized DCN (DCN*)
OBJECTIVES Quantify the antagonistic effect of blending and finds its dependence on structural composition of base fuel.
25.00
Volume of POH (ml)
Studying the ignition response alcohol blending with petroleum fuels is a subject of practical and research interest. Analogous to the octane number, Derived Cetane Number (DCN) of gasoline fuels non-linearly decreases with the addition of lower carbon number alcohols or can say there is antagonistic effect in blending.
Antagonistic effect comparison
0
PRF 70 PRF 60 FACE J
Future Work:- More fuels has to be considered for the blending study for an effective comparison of antagonistic performance. Typically fuels with more aromatic content such as TRF,TPRF fuels will be given priority. Comparison with synergism in RON blending with alcohols is helpful to summarize the ignition response to the structure of fuel.
GAUSSIAN FIT MODEL
ABSTRACT
There is clear evidence that the non-linearity depends on the structural composition of base fuel considered and the type of alcohol chosen. Gasoline fuels containing hundreds of different compounds making it challenging to clearly understand the antagonistic effect observed in the blending studies. The present study utilizes molar based Gaussian fit to model the antagonistic effect and optimum blending condition.
−(𝑥−𝑏)2
In Mathematics, a Gaussian Equation is expressed as follows 𝑓 𝑥 = 𝑎. 𝑒
2𝑐2
The parameter “a‟ is the height of curve’s peak. 𝐴𝑡 𝑥 = 𝑏, 𝑓(𝑥) = 𝑓(𝑏) = 𝑎. 𝑒 −0 = 𝑎. The parameter “b‟ is the value of variable “x‟ at which the curve reaches the peak. The parameter “c‟ tells about the width of the curve or extend of deviation (standard deviation or Gaussian RMS width) from the mean point 𝑓(𝑏) = 𝑎.
Inflection Point (IP) In a Gaussian curve, 𝑥 ∗ is an inflection point where 𝑓 ′′ (𝑥 ∗ ) = 0 => 𝑥 ∗ = 𝑏 ± 𝑐. At Inflection point, curvature changes from steep to moderate and 𝒇 𝒙∗ depends only on “a”.
𝑓 𝑥∗ = 𝑓 𝑏 + 𝑐 =
𝒇 𝒙
= 𝟎. 𝟔𝟎𝟔𝟓
Compare the antagonistic effect of the alcohols studied. Find an optimum volume or mole fraction of alcohols that maximize the blending effect.
DCN* of PRF 84 vs POH & BOH
DCN* of FACE vs n-propanol
In this study, the DCN of Primary Reference Fuels PRF 60, 70 and 84 and three Fuels for Advance Combustion Engines (FACE) gasoline namely FACE I, A and J were blended with two alcohols - propan-1-ol and butan-1-ol, and measured using Ignition Quality Tester (IQT) following ASTM D6890 method.
90
PRF 84
80
PRF 70
70
Aromatic mol%
FACE A
40
.
FJ
35
FACEI
PRF
0.7
25
0.6
10 0
14
FJ
0.4
P 60
P 70
0.3
5 0
P 60 P 70 P 84 F A
FI
References
FA
FI
8 6
0.2
4
0.1
2
0
FACE I
10
P 84
15 10
Antagonistic distance comparison FACE A PRF 84
12
0.5
30 20
0.8
30
20
FACE J
Branching Index
AD* (at IP)
Iso-paraffinic mol%
50
1. Anderson JE, DiCicco DM, Ginder JM, Kramer U, Leone TG, Raney-Pablo HE,et al. High octane number ethanol–gasoline blends: Quantifying the potential benefits in the United States. Fuel 2012;97:585–94. 2. Da Silva R, Cataluna R, de Menezes EW, Samios D, Piatnicki CMS. Effect of additives on the antiknock properties and Reid vapor pressure of gasoline, Fuel 2005;84:951–9. 3. ASTM D6890 Standard Test Method for Determination of Ignition Delay and Derived Cetane Number (DCN) of Diesel Fuel Oils by Combustion in a Constant Volume Chamber;2013. 4. Naser,N.,Yang,S(2017).Relating the octane numbers of fuels to ignition delay times measured in an ignition quality tester (IQT).Fuel,187,117-127. 5. Standard test method for research octane number of spark-ignition engine fuel. ASTM D 2699 - 13b; 2013. 6. Anderson J, Kramer U, Mueller S, Wallington T. Octane numbers of ethanol and methanol gasoline blends estimated from molar concentrations. Energy Fuels 2010; 24:6576–85 7. J. Badra, A. S. AlRamadan, and S. M. Sarathy, “Optimization of the octane response of gasoline/ethanol blends,” Appl. Energy, 2017.
PRF 84 10.00
FACE A
FACE I
5.00
= −0.31 + 0.024 ∗ p + 0.086 ∗ I − 𝟎. 𝟐𝟒𝟓 ∗ 𝑨 + 0.97 ∗ N − 0.109 ∗ O + 𝟐𝟐. 𝟒𝟑 ∗ 𝐁. 𝐈 −𝟎. 𝟗𝟑 ∗ 𝑫𝑪𝑵𝒂
In all cases of blending curves, the DCNmix is lower than its corresponding linear trend . In other terms, there is antagonistic blending effects. The lower volume of alcohol at IP can be obtained for higher antagonistic blends and thereby more reduction in DCN. The curve changes the direction at inflection point from steep to moderate. So for fuel designers, it is profitable to blend until mole-fraction of alcohol =IP, thereby optimizing the alcohol blending effect. The antagonistic behaviour is observed higher for POH than BOH. This shows that POH is a better blending agent than BOH. Antagonistic trend of fuels as follows, FACE A>PRF 84>FACE I>PRF 70>PRF 60>FACE J. More the branching, more the A∗D . Contribution of aromatics and olefins to the antagonistic behavior is seen negative.
.
60
REFERENCES
15.00
CONCLUSIONS
METHODOLOGY
For a constructive fitting of data, seven volumes of propan1-ol and butan-1-ol such as 5,10,15,20,30,50,70% on a gravimetric basis were considered for the experiment which then translated later into mole-fractions.
PRF 70
Linear Regression of AD* with respect to structural composition of base fuels, At global minima of rms = 2.468, the dependence on structural parameters is described ∗ AD
DCN* of PRF vs Mole-fraction of n-butanol
PRF 60
Linear Regression
Results 𝐷𝐶𝑁 − 𝐷𝐶𝑁 𝑏𝑙𝑒𝑛𝑑(𝑚𝑖𝑥) 𝐴𝑙𝑐𝑜ℎ𝑜𝑙(𝑎) ∗ 𝐷𝐶𝑁 = 𝐷𝐶𝑁𝑏𝑎𝑠𝑒(𝑏) − 𝐷𝐶𝑁𝐴𝑙𝑐𝑜ℎ𝑜𝑙(𝑎)
Under Normalized conditions, a~1
20.00
Fig 4: Blending volumes of POH with different fuels at same antagonistic distance as FACE J
𝑎 . 1.6487
In order to fit Gaussian model to blending studies, normalized (DCN*) vs molefraction (x) is plotted.
∗
FACE J
0.00
Normalized DCN (DCN*)
OBJECTIVES Quantify the antagonistic effect of blending and finds its dependence on structural composition of base fuel.
25.00
Volume of POH (ml)
Studying the ignition response alcohol blending with petroleum fuels is a subject of practical and research interest. Analogous to the octane number, Derived Cetane Number (DCN) of gasoline fuels non-linearly decreases with the addition of lower carbon number alcohols or can say there is antagonistic effect in blending.
Antagonistic effect comparison
0
PRF 70 PRF 60 FACE J
Future Work:- More fuels has to be considered for the blending study for an effective comparison of antagonistic performance. Typically fuels with more aromatic content such as TRF,TPRF fuels will be given priority. Comparison with synergism in RON blending with alcohols is helpful to summarize the ignition response to the structure of fuel.
