Method and system of measuring cetane values for middle distillate fuels
View Patent ↗A method and a system is disclosed for determining cetane values from constant volume combustion chamber apparatuses capable of producing pressure versus time combustion profiles having a fast combustion region and a slow combustion region, where data from the two regions is used to compute cetane values for middle distillate fluid samples using a series expansion equation.
1. A method for calculating derived cetane number values using a constant volume combustion chamber apparatus capable of yielding a pressure versus time combustion profile, the method comprising the steps of:
injecting a high pressure sample into the constant volume combustion chamber apparatus at a predetermined pressure and temperature;
combusting the sample in the constant volume combustion chamber apparatus;
measuring the pressure in the constant volume combustion chamber apparatus as a function of time after injection of the sample until combustion is complete;
obtaining a pressure versus time combustion profile of the sample;
selecting a plurality of data points from the pressure versus time combustion profile; and
calculating a derived cetane number value from a power series expansion equation expanded about the selected plurality of data points and/or arithmetic combination of the selected plurality of data points using a set of expansion coefficients.
2. The method of claim 1 , wherein the calculating step includes calculating an arithmetic ratio of the data points.
3. The method of claim 1 , wherein the pressure versus time combustion profile has a plurality of combustion regions and the selecting step selects a single data point from each region.
4. The method of claim 1 , wherein the pressure versus time combustion profile has a plurality of combustion regions and the selecting step selects a plurality of data points from each region.
5. The method of claim 1 , wherein the power series expansion equation terminates with second order terms.
6. The method of claim 1 , further comprising the steps of:
prior to the injecting a high pressure sample step, injecting a high pressure calibration sample having a known cetane number value into the constant volume combustion chamber apparatus at a predetermined pressure and temperature;
combusting the calibration sample in the constant volume combustion chamber apparatus to produce a calibration pressure versus time combustion profile;
selecting a plurality of calibration data points from the calibration pressure versus time combustion profile; and
computing a derived cetane number value from the power series expansion equation expanded about the selected plurality of calibration data points and/or ratios of the selected plurality of calibration data points.
7. The method of claim 1 , wherein the power series expansion equation is selected from the group consisting of the form of equations (I, II and III):
DCN= C 1a *ID 1 +C 2a *ID 2 +C 1b *( ID 1 ) 2 +C 2b *( ID 2 ) 2 +I (I)
where DCN is the derived cetane number value, ID 1 is the data point selected from the first region, ID 2 is a data point selected from the second region, C 1a , C 1b , C 2a , and C 2b are expansion coefficients and I is an intercept,
DCN= C 1a ID 1 +C 2a ID 2 +C 1b ( ID 1 ) 2 +C 2b ( ID 2 ) 2 +C ra ID 1 /ID 2 +C rb ( ID 1 /ID 2 ) 2 +I (II)
where DCN is the derived cetane number value, ID 1 is a data point selected from the first region, ID 2 is a data point selected from the second region, C 1a , C 1b , C 2a , C 2b , C ra , and C rb are coefficients and I is the intercept, and
DCN= C ra ID 1 /ID 2 +C rb ( ID 1 /ID 2 ) 2 +I (III)
where DCN is the derived cetane number value, ID 1 is a data point selected from the first region, ID 2 is a data point selected from the second region, C ra and C rb are coefficients and I is the intercept.
8. The method of claim 1 , wherein the power series expansion equation is selected from the group consisting of the form of equations (IV and V):
DCN
=
∑
i
=
1
,
j
=
1
i
=
m
,
j
=
n
c
ij
ID
i
j
+
∑
k
=
1
,
l
=
1
k
=
m
,
l
=
n
c
kl
′
ID
k
′
l
+
I
(
IV
)
where DCN is the derived cetane number value, ID i are the data points selected from the first region, ID′ k are the data points selected from the second region, c ij and c′ kl are expansion coefficients and I is the intercept, i is an integer representing a number of data points selected from the first region, j is an integer representing the number of terms in the expansion for the selected data points in the first region, k is an integer representing the number of data points selected from the second region, and l is an integer representing the number of terms in the expansion for the selected data points in the second region, and
DCN
=
∑
i
=
1
,
j
=
1
i
=
m
,
j
=
n
c
ij
ID
i
j
+
∑
k
=
1
,
l
=
1
k
=
o
,
l
=
p
c
kl
ID
k
l
+
∑
ii
=
1
,
jj
=
1
,
kk
=
1
ii
=
n
,
jj
=
o
,
kk
=
m
+
p
c
iijjkk
(
ID
ii
ID
jj
)
kk
+
I
(
V
)
where DCN is the derived cetane number value, ID i are data points selected from the A region of the profile representing an ignition delay of components in the A region, ID k are data points selected from the B region of the profile representing an ignition delay of components in the B region, and ID ii /D jj are ratios where ID ii are selected data points from the A region and ID jj are selected points from the B region, c ij , c kl and c iijjkk are coefficients and I is the intercept, i is an integer representing a number of data points selected from the A region, j is an integer representing the number of terms in the expansion for the selected data points in the A region, k is an integer representing the number of data points selected from the B region, l is an integer representing the number of terms in the expansion for the selected data points in the B region, ii is an integer representing the number of data points selected from the A region, jj is an integer representing the number of data points selected from the B region, kk is an integer representing the number of terms in the expansion for the ratios of selected data points from region A to selected data points from the B region.
9. The method of claim 1 , wherein the power series expansion equation is selected from the group consisting of the form of equations (VI and VII):
DCN
=
∑
i
=
1
n
∑
j
=
1
,
k
=
1
j
=
m
,
k
=
o
c
ijk
ID
j
k
+
I
(
VI
)
where DCN is the derived cetane number value, ID j are the data points selected from the i th region of the profile, where each region represents components having different ignition delay time and c ijk are expansion coefficients corresponding to the i th region, the j th point raised the k th power and I is the intercept, and
DCN
=
∑
i
=
1
n
∑
j
=
1
,
k
=
1
j
=
m
,
k
=
o
c
ijk
ID
j
k
+
∑
ii
=
1
,
jj
=
1
,
kk
=
1
ii
=
m
,
jj
=
m
,
kk
=
o
c
iijjkk
(
ID
ii
ID
jj
)
kk
+
I
(
VII
)
where DCN is the derived cetane number value, ID j are data points selected from the i th region of the profile, where each region represents components having different ignition delay time and c ijk are expansion coefficients corresponding to the i th region, the j th point of the i th region raised the k th power, ID ii /D jj are ratios of data points from different regions, c iijjkk are expansion coefficients corresponding to the ii th data point from one region and the jj th data point from a different region raised to the kk th power and I is the intercept.
10. The system of claim 1 wherein the calculating step is performed by a computer.
11. A method for calculating derived cetane number values using a constant volume combustion chamber apparatus capable of yielding a pressure versus time combustion profile, the method comprising the steps of:
injecting a high pressure calibration sample having a known cetane number value into the constant volume combustion chamber apparatus at a predetermined pressure and temperature;
combusting the calibration sample in the constant volume combustion chamber apparatus to produce a calibration pressure versus time combustion profile;
selecting a plurality of calibration data points from the calibration pressure versus time combustion profile;
calculating a derived cetane number value from a power series expansion equation expanded about the selected plurality of calibration data points and/or ratios of the selected plurality of calibration data points;
injecting a high pressure sample into the constant volume combustion chamber apparatus at a predetermined pressure and temperature;
combusting the sample in the constant volume combustion chamber apparatus;
measuring the pressure in the constant volume combustion chamber apparatus as a function of time after injection of the sample until combustion is complete;
obtaining a pressure versus time combustion profile of the sample;
selecting a plurality of sample data points from the sample pressure versus time combustion profile; and
calculating a derived cetane number value from a power series expansion equation expanded about the selected plurality of sample data points and/or ratios of the selected plurality of sample data points.
12. The method of claim 11 , wherein each profile has a plurality of combustion regions and the two selecting steps select a single data point from each region.
13. The method of claim 11 , wherein each profile has a plurality of combustion regions and the two selecting steps select a plurality of data points from each region.
14. The method of claim 11 , wherein the power series expansion equation terminates with second order terms.
15. The method of claim 11 , wherein the power series expansion equation is selected from the group consisting of the form of equations (I, II and III):
DCN= C 1a *ID 1 +C 2a *ID 2 +C 1b *( ID 1 ) 2 +C 2b *( ID 2 ) 2 +I (I)
where DCN is the derived cetane number value, ID 1 is the data point selected from the first region, ID 2 is a data point selected from the second region, C 1a , C 1b , C 2a , and C 2b are expansion coefficients and I is an intercept,
DCN= C 1a ID 1 +C 2a ID 2 +C 1b ( ID 1 ) 2 +C 2b ( ID 2 ) 2 +C ra ID 1 /ID 2 +C rb ( ID 1 /ID 2 ) 2 +I (II)
where DCN is the derived cetane number value, ID 1 is a data point selected from the first region, ID 2 is a data point selected from the second region, C 1a , C 1b , C 2a , C 2b , C ra and C rb are coefficients and I is the intercept, and
DCN= C ra ID 1 /ID 2 +C rb ( ID 1 /ID 2 ) 2 +I (III)
where DCN is the derived cetane number value, ID 1 is a data point selected from the first region, ID 2 is a data point selected from the second region, C ra and C rb are coefficients and I is the intercept.
16. The method of claim 11 , wherein the power series expansion equation is selected from the group consisting of the form of equations (IV and V):
DCN
=
∑
i
=
1
,
j
=
1
i
=
m
,
j
=
n
c
ij
ID
i
j
+
∑
k
=
1
,
l
=
1
k
=
m
,
l
=
n
c
kl
′
ID
k
′
l
+
I
(
IV
)
where DCN is the derived cetane number value, ID i are the data points selected from the first region, ID′ k are the data points selected from the second region, c ij and ck l are expansion coefficients and I is the intercept, i is an integer representing a number of data points selected from the first region, j is an integer representing the number of terms in the expansion for the selected data points in the first region, k is an integer representing the number of data points selected from the second region, and l is an integer representing the number of terms in the expansion for the selected data points in the second region, and
DCN
=
∑
i
=
1
,
j
=
1
i
=
m
,
j
=
n
c
ij
ID
i
j
+
∑
k
=
1
,
l
=
1
k
=
o
,
l
=
p
c
kl
ID
k
l
+
∑
ii
=
1
,
jj
=
1
,
kk
=
1
ii
=
n
,
jj
=
o
,
kk
=
m
+
p
c
iijjkk
(
ID
ii
ID
jj
)
kk
+
I
(
V
)
where DCN is the derived cetane number value, ID i are data points selected from the A region of the profile representing an ignition delay of components in the A region, ID k are data points selected from the B region of the profile representing an ignition delay of components in the B region, and ID ii /D jj are ratios where ID ii are selected data points from the A region and ID jj are selected points from the B region, c ij , c kl and c iijjkk are coefficients and I is the intercept, i is an integer representing a number of data points selected from the A region, j is an integer representing the number of terms in the expansion for the selected data points in the A region, k is an integer representing the number of data points selected from the B region, l is an integer representing the number of terms in the expansion for the selected data points in the B region, ii is an integer representing the number of data points selected from the A region, jj is an integer representing the number of data points selected from the B region, kk is an integer representing the number of terms in the expansion for the ratios of selected data points from region A to selected data points from the B region.
17. The method of claim 11 , wherein the power series expansion equation is selected from the group consisting of the form of equations (VI and VII):
DCN
=
∑
i
=
1
n
∑
j
=
1
,
k
=
1
j
=
m
,
k
=
o
c
ijk
ID
j
k
+
I
(
VI
)
where DCN is the derived cetane number value, ID j are the data points selected from the i th region of the profile, where each region represents components having different ignition delay time and c ijk are expansion coefficients corresponding to the i th region, the j th point raised the k th power and I is the intercept, and
DCN
=
∑
i
=
1
n
∑
j
=
1
,
k
=
1
j
=
m
,
k
=
o
c
ijk
ID
j
k
+
∑
ii
=
1
,
jj
=
1
,
kk
=
1
ii
=
m
,
jj
=
m
,
kk
=
o
c
iijjkk
(
ID
ii
ID
jj
)
kk
+
I
(
VII
)
where DCN is the derived cetane number value, ID j are data points selected from the i th region of the profile, where each region represents components having different ignition delay time and c ijk are expansion coefficients corresponding to the i th region, the j th point of the i th region raised the k th power, ID ii /D jj are ratios of data points from different regions, c iijjkk are expansion coefficients corresponding to the ii th data point from one region and the jj th data point from a different region raised to the kk th power and I is the intercept.
18. The system of claim 11 wherein the two calculating steps are performed by a computer.
19. A method for calculating derived cetane number values using a constant volume combustion chamber apparatus capable of yielding a pressure versus time combustion profile, the method comprising the steps of:
combusting a calibration sample having a known cetane number value in the constant volume combustion chamber apparatus to produce a calibration pressure versus time combustion profile where the pressure versus time calibration profile has a first region corresponding to sample components having earlier ignition temperatures and a second region corresponding to sample components having later ignition temperatures;
selecting at least one data point from each region of the calibration pressure versus time combustion profile;
computing a derived cetane number value from a power series expansion equation expanded about the selected data points;
burning a middle distillate sample in a constant volume combustion chamber apparatus;
measuring and storing a pressure versus time combustion profile of the middle distillate sample, where the pressure versus time profile has a first region corresponding to sample components having earlier ignition temperatures and a second region corresponding to sample components having later ignition temperatures;
selecting at least one sample data point from each region of the sample pressure versus time combustion profile; and
calculating a derived cetane number value from a power series expansion equation expanded about the selected sample data points.
20. The method of claim 19 , wherein the power series expansion equation terminates with second order terms.
21. The method of claim 19 , wherein the equation is of the form of equation (I):
DCN= C 1a *ID 1 +C 2a *ID 2 +C 1b *( ID 1 ) 2 +C 2b *( ID 2 ) 2 +I (I)
where DCN is the derived cetane number value, ID 1 is the data point selected from the first region, ID 2 is a data point selected from the second region, C 1a , C 1b , C 2a , and C 2b are expansion coefficients and I is an intercept.
22. The method of claim 19 , wherein the equation is selected from the group consisting of the form of equations (I, II and III):
DCN= C 1a *ID 1 +C 2a *ID 2 +C 1b *( ID 1 ) 2 +C 2b *( ID 2 ) 2 +I (I)
where DCN is the derived cetane number value, ID 1 is the data point selected from the first region, ID 2 is a data point selected from the second region, C 1a , C 1b , C 2a , and C 2b are expansion coefficients and I is an intercept,
DCN= C 1a ID 1 +C 2a ID 2 +C 1b ( ID 1 ) 2 +C 2b ( ID 2 ) 2 +C ra ID 1 /ID 2 +C rb ( ID 1 /ID 2 ) 2 +I (II)
where DCN is the derived cetane number value, ID 1 is a data point selected from the first region, ID 2 is a data point selected from the second region, C 1a , C 1b , C 2a , C 2b , C ra , and C rb are coefficients and I is the intercept, and
DCN= C ra ID 1 /ID 2 +C rb ( ID 1 /ID 2 ) 2 +I (III)
where DCN is the derived cetane number value, ID 1 is a data point selected from the first region, ID 2 is a data point selected from the second region, C ra and C rb are coefficients and I is the intercept.
23. The method of claim 19 , wherein the equation is selected from the group consisting of the form of equations (IV and V):
DCN
=
∑
i
=
1
,
j
=
1
i
=
m
,
j
=
n
c
ij
ID
i
j
+
∑
k
=
1
,
l
=
1
k
=
m
,
l
=
n
c
kl
′
ID
k
′
l
+
I
(
IV
)
where DCN is the derived cetane number value, ID i are the data points selected from the first region, ID′ k are the data points selected from the second region, c ij and c′ kl are expansion coefficients and I is the intercept, i is an integer representing a number of data points selected from the first region, j is an integer representing the number of terms in the expansion for the selected data points in the first region, k is an integer representing the number of data points selected from the second region, and l is an integer representing the number of terms in the expansion for the selected data points in the second region, and
DCN
=
∑
i
=
1
,
j
=
1
i
=
m
,
j
=
n
c
ij
ID
i
j
+
∑
k
=
1
,
l
=
1
k
=
o
,
l
=
p
c
kl
ID
k
l
+
∑
ii
=
1
,
jj
=
1
,
kk
=
1
ii
=
n
,
jj
=
o
,
kk
=
m
+
p
c
iijjkk
(
ID
ii
ID
jj
)
kk
+
I
(
V
)
where DCN is the derived cetane number value, ID i are data points selected from the A region of the profile representing an ignition delay of components in the A region, ID k are data points selected from the B region of the profile representing an ignition delay of components in the B region, and ID ii /D jj are ratios where ID ii are selected data points from the A region and ID jj are selected points from the B region, c ij , c kl and c iijjkk are coefficients and I is the intercept, i is an integer representing a number of data points selected from the A region, j is an integer representing the number of terms in the expansion for the selected data points in the A region, k is an integer representing the number of data points selected from the B region, l is an integer representing the number of terms in the expansion for the selected data points in the B region, ii is an integer representing the number of data points selected from the A region, jj is an integer representing the number of data points selected from the B region, kk is an integer representing the number of terms in the expansion for the ratios of selected data points from region A to selected data points from the B region.
24. The method of claim 19 , wherein the equation is selected from the group consisting of the form of equations (VI and VII):
DCN
=
∑
i
=
1
n
∑
j
=
1
,
k
=
1
j
=
m
,
k
=
o
c
ijk
ID
j
k
+
I
(
VI
)
where DCN is the derived cetane number value, ID j are the data points selected from the i th region of the profile, where each region represents components having different ignition delay time and c ijk are expansion coefficients corresponding to the i th region, the j th point raised the k th power and I is the intercept, and
DCN
=
∑
i
=
1
n
∑
j
=
1
,
k
=
1
j
=
m
,
k
=
o
c
ijk
ID
j
k
+
∑
ii
=
1
,
jj
=
1
,
kk
=
1
ii
=
m
,
jj
=
m
,
kk
=
o
c
iijjkk
(
ID
ii
ID
jj
)
kk
+
I
(
VII
)
where DCN is the derived cetane number value, ID j are data points selected from the i th region of the profile, where each region represents components having different ignition delay time and c ijk are expansion coefficients corresponding to the i th region, the j th point of the i th region raised the k th power, ID ii /D jj are ratios of data points from different regions, c iijjkk are expansion coefficients corresponding to the ii th data point from one region and the jj th data point from a different region raised to the kk th power and I is the intercept.
25. The method of claim 19 , wherein the two selecting steps select a plurality of data points from the first region of each profile.
26. The method of claim 19 , wherein the two selecting steps select a plurality of data points from the second region of each profile.
27. The method of claim 19 , wherein the two selecting steps select a plurality of data points from each region of each profile.
28. The system of claim 19 wherein the two calculating steps are performed by a computer.
29. A method for determining coefficients of a series expansion equation for calculating derived cetane number values using a constant volume combustion chamber apparatus capable of yielding a pressure versus time combustion profile, the method comprising the steps of:
adjusting the chamber temperature and/or injection time by injecting a specified calibration fluid into the constant volume combustion chamber at a specified injection pressure, the calibration fluid having known ignition delay values;
injecting a set of samples having a known cetane number values into the constant volume combustion chamber apparatus at the specified injection pressure;
combusting the samples in the constant volume combustion chamber apparatus under controlled conditions to obtain pressure versus time combustion data to produce the pressure versus time combustion profile;
selecting a plurality of data points from the pressure versus time combustion profile, such plurality of data points corresponding to ignition delays of the set of samples;
computing the coefficients of the series expansion equation about the selected plurality of data points using regression.
30. A system for calculating derived cetane number values comprising:
a constant volume combustion chamber subsystem adapted to combust a high pressure sample of a middle distillate fluid/fuel in a controlled manner to produce pressure versus time data of the combustion; and
an analyzing subsystem in communication with the constant volume combustion chamber subsystem, wherein the analyzing subsystem is adapted to accumulate data during combustion of the sample to produce a pressure versus time combustion profile, to select at least one point from the pressure versus time data combustion profile and to calculate a derived cetane number based on a power series expansion equation expanded about the selected at least one point, where the coefficients of the series expansion equation are determined by minimizing a difference between the derived cetane number value and a cetane number value of a calibration sample having a known cetane number value.
31. The system of claim 30 wherein the constant volume combustion chamber subsystem comprises:
a combustion chamber having a fixed volume;
a heater adapted to heat the combustion chamber to a predetermined temperature;
a source of compressed air adapted to adjust the pressure of the combustion chamber to a predetermined pressure; and
a high pressure injection system for injecting a fuel sample into the combustion chamber.
32. The system of claim 31 wherein the constant volume combustion chamber subsystem further comprises a coolant pump adapted to cool the combustion chamber.
33. The system of claim 32 wherein the high pressure injector system further comprises an injector and a sample container wherein a sample from the sample container is delivered to the injector at an elevated predetermined pressure for injection into the combustion chamber.
34. The system of claim 33 wherein the constant volume combustion chamber subsystem further comprises a controller operably connected to the injector, the source of compressed air, and the coolant pump to maintain controlled combustion conditions.
35. The system of claim 34 wherein the constant volume combustion chamber subsystem further comprises a power supply.
36. The system of claim 35 wherein the constant volume combustion chamber subsystem further comprises an exhaust port.
37. The system of claim 30 wherein the analyzing subsystem comprises:
a plurality of sensors adapted to receive data from the combustion chamber; and
a computer for computing a derived cetane number value from a power series expansion equation.
38. The system of claim 37 wherein the analyzing subsystem further comprises an output device connected to the computer for outputting data.
39. The system of claim 38 wherein the output device is a display.
40. The system of claim 38 wherein the output device is a graphing device.
41. The system of claim 38 wherein the output device is a printer.