Method and system for measuring RON and MON values for light distillates
View Patent ↗A method and a system is disclosed for determining RON and/or MON 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 RON and/or MON values for light distillate fluid samples using a series expansion equation.
1. A method for calculating derived RON and/or MON values comprising the steps of:
first autoigniting a calibration sample having a known RON and/or MON value in the constant volume combustion chamber apparatus to produce a calibration pressure versus time combustion profile,
selecting at least one calibration data point from the calibration profile,
computing a derived RON and/or MON values from a power series expansion equation expanded about the selected calibration data points and/or ratios of the selected calibration data points,
adjusting expansion coefficients in the equation to minimize a difference between the known RON and/or MON value and the derived RON and/or MON value to obtain a set of optimized expansion coefficients,
second autoigniting an unknown sample to obtain a pressure versus time combustion profile of said unknown sample using the constant volume combustion chamber apparatus capable of yielding a pressure versus time combustion profile of said unknown sample,
selecting at least one sample data point from the profile of said unknown sample, and
calculating a derived RON and/or MON values for said unknown sample from a power series expansion equation expanded about the selected sample data points of said unknown sample and/or ratios of the selected calibration data points using the optimized expansion coefficients;
wherein the power series expansion equation is selected from the group consisting of the form of equations (I), (II), and (III):
RON=C 1a *ID 1 +C 2a *ID 2 +C 1b *( ID 1 ) 2+ C 2b *( ID 2 ) 2 +I (I)
where ID 1 is a data point selected from the A region of the pressure/time profile representing an ignition delay of components in the A region, ID 2 is a data point selected from the B region of the pressure/time profile representing an ignition delay of components in the B region, C 1a , C 1b , C 2a , C 2b are coefficients and I is the intercept, where the coefficients obtained from solving equation (I) for a set of standard or reference samples with known RON value;
RON=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 ID 1 is a data point selected from the A region of the pressure/time profile representing an ignition delay of components in the A region, ID 2 is a data point selected from the B region of the pressure/time profile representing an ignition delay of components in the B region, C 1a , C 1b , C 2a , C 2b , C ra , and C rb are coefficients and I is the intercept, where the coefficients are obtained from solving equation (II) for a set of standard or reference samples with known RON values; or
RON=C ra ID 1 /ID 2 +C rb ( ID 1 /ID 2 ) 2 +I (III)
where ID 1 is a data point selected from the A region of the pressure/time profile representing an ignition delay of components in the A region, ID 2 is a data point selected from the B region of the pressure/time profile representing an ignition delay of components in the B region, C ra and C rb are coefficients and I is the intercept, where the coefficients are obtained from solving equations (III) for a set of standard or reference samples with known RON values.
2. The method of claim 1 , wherein the two selecting steps select a single data point from each profile.
3. The method of claim 1 , wherein the two selecting steps select at least two data points from each profile.
4. The method of claim 1 , wherein the two selecting step selects at least two data points and the two calculating step includes calculating an arithmetic ratio of the data points.
5. The method of claim 1 , wherein the two selecting steps select a plurality of data points from each profile.
6. The method of claim 1 , wherein each profile has a plurality of regions and the two selecting step selects a single data point from each region.
7. The method of claim 1 , wherein each profile has a plurality of regions and the two selecting steps select at a plurality of data points from each region.
8. The method of claim 1 , wherein the power series expansion equation terminates with second order terms.
9. A method for calculating derived RON and/or MON values comprising the steps of:
first autoigniting a calibration sample having a known RON and/or MON value in the constant volume combustion chamber apparatus to produce a calibration pressure versus time combustion profile,
selecting at least one calibration data point from the calibration profile,
computing a derived RON and/or MON values from a power series expansion equation expanded about the selected calibration data points and/or ratios of the selected calibration data points,
adjusting expansion coefficients in the equation to minimize a difference between the known RON and/or MON value and the derived RON and/or MON value to obtain a set of optimized expansion coefficients,
second autoigniting an unknown sample to obtain a pressure versus time combustion profile of said unknown sample using the constant volume combustion chamber apparatus capable of yielding a pressure versus time combustion profile of said unknown sample,
selecting at least one sample data point from the profile of said unknown sample, and
calculating a derived RON and/or MON values for said unknown sample from a power series expansion equation expanded about the selected sample data points of said unknown sample and/or ratios of the selected calibration data points using the optimized expansion coefficients:
wherein the power series expansion equation is selected from the group consisting of the form of equations (IV), (V), (VI), and (VII);
RON
=
∑
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 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, c ij and c′ kl 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, and l is an integer representing the number of terms in the expansion for the selected data points in the B region, and where the coefficients and intercept are obtained from solving equation (IV) for a set of standard or reference samples;
RON
=
∑
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
=
m
+
p
kk
=
1
ii
=
n
,
jj
=
o
,
c
iijjkk
(
ID
ii
/
ID
jj
)
kk
+
I
(
V
)
where 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 /ID jj ratios of 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;
RON
=
∑
i
=
1
n
∑
j
=
1
,
k
=
1
j
=
m
,
k
=
o
c
ijk
ID
j
k
+
I
(
VI
)
where 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 raised the k th power and I is the intercept, i is an integer representing number of regions, j is an integer representing a number of data points selected from the i th region, k is an integer representing the number of terms in the expansion for the selected data points in expansion; or
RON
=
∑
i
=
1
n
∑
j
=
1
,
k
=
1
j
=
m
,
k
=
o
c
ijk
ID
j
k
+
∑
ii
=
1
,
jj
=
1
kk
=
o
kk
=
1
ii
=
m
,
jj
=
m
,
c
iijjkk
(
ID
ii
/
ID
jj
)
kk
+
I
(
VII
)
where 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 i th point of the i th region raised the k th power, ID ii /ID 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. A method for calculating derived RON and/or MON values comprising the steps of:
first autoigniting a calibration sample having a known RON and/or MON value in the constant volume combustion chamber apparatus to produce a calibration pressure versus time combustion profile,
selecting at least one calibration data point from the calibration profile,
computing a derived RON and/or MON values from a power series expansion equation expanded about the selected calibration data points and/or ratios of the selected calibration data points,
adjusting expansion coefficients in the equation to minimize a difference between the known RON and/or MON value and the derived RON and/or MON value to obtain a set of optimized expansion coefficients,
second autoigniting an unknown sample to obtain a pressure versus time combustion profile of said unknown sample using the constant volume combustion chamber apparatus capable of yielding a pressure versus time combustion profile of said unknown sample,
selecting at least one sample data point from the profile of said unknown sample, and
calculating a derived RON and/or MON values for said unknown sample from a power series expansion equation expanded about the selected sample data points of said unknown sample and/or ratios of the selected calibration data points using the optimized expansion coefficients;
wherein the power series expansion equation is selected from the group consisting of the form of equations (VIII), (IX), and (X);
MON=C 1a *ID 1 +C 2a *ID 2 +C 1b *( ID 1 ) 2 +C 2b *( ID 2 ) 2 +1 (VIII)
where ID 1 is a data point selected from the A region of the pressure/time profile representing an ignition delay of components in the A region, ID 2 is a data point selected from the B region of the pressure/time profile representing an ignition delay of components in the B region, C 1a , C 1b , C 2a , C 2b are coefficients and I is the intercept;
MON=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 (IX)
where ID 1 is a data point selected from the A region of the pressure/time profile representing an ignition delay of components in the A region, ID 2 is a data point selected from the B region of the pressure/time profile representing an ignition delay of components in the B region, C 1a , C 1b , C 2a , C 2b , C ra and C rb are coefficients and I is the intercept, where the coefficients are obtained from solving equation (IX) for a set of standard or reference samples with known MON values; or
MON=C ra ID 1 /ID 2 +C rb ( ID 1 /ID 2 ) 2 +I (X)
where ID 1 is a data point selected from the A region of the pressure/time profile representing an ignition delay of components in the A region, ID 2 is a data point selected from the B region of the pressure/time profile representing an ignition delay of components in the B region, C ra and C rb are coefficients and I is the intercept, where the coefficients are obtained from solving equation (X) for a set of standard or reference samples with known MON values.
11. A method for calculating derived RON and/or MON values comprising the steps of:
first autoigniting a calibration sample having a known RON and/or MON value in the constant volume combustion chamber apparatus to produce a calibration pressure versus time combustion profile,
selecting at least one calibration data point from the calibration profile,
computing a derived RON and/or MON values from a power series expansion equation expanded about the selected calibration data points and/or ratios of the selected calibration data points,
adjusting expansion coefficients in the equation to minimize a difference between the known RON and/or MON value and the derived RON and/or MON value to obtain a set of optimized expansion coefficients,
second autoigniting an unknown sample to obtain a pressure versus time combustion profile of said unknown sample using the constant volume combustion chamber apparatus capable of yielding a pressure versus time combustion profile of said unknown sample,
selecting at least one sample data point from the profile of said unknown sample, and
calculating a derived RON and/or MON values for said unknown sample from a power series expansion equation expanded about the selected sample data points of said unknown sample and/or ratios of the selected calibration data points using the optimized expansion coefficients;
wherein the power series expansion equation is selected from the group consisting of the form of equations (XI), (XII), (XIII), and (XIV);
MON
=
∑
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
(
XI
)
where 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, c ij and c′ kl 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, and l is an integer representing the number of terms in the expansion for the selected data points in the B region, and where the coefficients and intercept are obtained from solving equation (XI) for a set of standard or reference samples;
MON
=
∑
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
=
m
+
p
kk
=
1
ii
=
n
,
jj
=
o
,
c
iijjkk
(
ID
ii
/
ID
jj
)
kk
+
I
(
XII
)
where 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 /ID jj ratios of selected data points from the A region and ID jj are selected points from the B region, c ij , c kl , 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;
MON
=
∑
i
=
1
n
∑
j
=
1
,
k
=
1
j
=
m
,
k
=
o
c
ijk
ID
j
k
+
I
(
XIII
)
where 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 raised the k th power and I is the intercept, i is an integer representing a number of regions, j is an integer representing a number of data points selected from the i th region, k is an integer representing the number of terms in the expansion for the selected data points in expansion, and coefficients and intercept are obtained from solving equation (XIII) for a set of standard or reference samples; or
MON
=
∑
i
=
1
n
∑
j
=
1
,
k
=
1
j
=
m
,
k
=
o
c
ijk
ID
j
k
+
∑
ii
=
1
,
jj
=
1
,
kk
=
o
kk
=
1
ii
=
m
,
jj
=
m
,
c
iijjkk
(
ID
ii
/
ID
jj
)
kk
+
I
(
XIV
)
where 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 /ID 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.