ASTM D7213 Standard Test Method for Boiling Range Distribution of Petroleum Distillates in the Boiling Range from 100 to 615°C by Gas Chromatography
10. Calculations
10.1 Load the sample chromatogram slices into a table.
10.2 Perform a slice offset.
10.2.1 Calculate the average slice offset at start of chromatogram as follows:
10.2.1.1 Calculate the average and standard deviation of the average of the first five area slices of the chromatogram.
10.2.1.2 Throw out any of the first five slices that are not within one standard deviation of the average and recompute the average. This eliminates any area that is due to possible baseline upset from injection.
10.2.2 Subtract the average slice offset from all the slices of the sample chromatogram. This will zero the chromatogram.
10.3 Load the blank run chromatogram slices into a table.
NOTE 4 - For instruments that compensate the baseline directly at the detector producing an electronically corrected baseline, either process the sample chromatogram directly or do a baseline subtraction. If the compensation is made by the instrument 10.4, 10.5, 10.6, and 10.7 may be eliminated and proceed to 10.8.
10.4 Repeat 10.2 using the blank run table.
10.5 Verify that the slice width used to acquire the sample chromatogram is the same used to acquire the blank run chromatogram.
10.6 Subtract from each slice in the sample chromatogram table with its correspondent slice in the blank run chromatogram table.
10.7 Offset the corrected slices of the sample chromatogram by taking the smallest slice and subtracting it from all the slices. This will zero the chromatogram.
10.8 Verify the extent of baseline drift.
10.8.1 Calculate the average and standard deviation of the first five area slices of the chromatogram.
10.8.2 Eliminate any of the first five slices that are not within one standard deviation of the average and recompute the average. This eliminates any area that is due to possible baseline upset from injection.
10.8.3 Record the average area slice as Initial Baseline Signal.
10.8.4 Repeat 10.8.1 and 10.8.2 using the last five area slices of the chromatogram.
10.8.5 Record the average area slice as Final Baseline Signal.
10.8.6 Compare and report the Initial and Final Baseline Signals. These numbers should be similar.
10.9 Determine the Start of Sample Elution Time:
10.9.1 Calculate the Total Area - Add all the corrected slices in the table. If the sample to be analyzed has a solvent peak, start counting area from the point at which the solvent peak has eluted completely. Otherwise, start at the first corrected slice.
10.9.2 Calculate the Rate of Change between each Two Consecutive Area Slices - Begin at the slice set in 10.9.1 and work forward. The rate of change is obtained by subtraction the area of a slice from the area of the immediately preceding slice and dividing by the slice width. The time where the rate of change first exceed 0.0001 % per second of the total area (see 10.9.1) is defined as the start of the sample elution time.
10.9.3 To reduce the possibility of noise or an electronic spike falsely indicating the start of sample elution time, a 3 s slice average can be used instead of a single slice. For noisier baselines, a slice average larger than 3 s may be required.
10.10 Calculate the Sample Total Area - Add all the corrected slices in the table stating from the slice corresponding to the start of sample elution time.
10.10.1 Calculate the Rate of Change between each Two Consecutive Area Slices - Begin at the end of run and work backward. The rate of change is obtained by subtracting the area of a slice from the area of the immediately preceding slice and dividing by the slice width. The time where the rate of change first exceeds 0.0001 % per second of the total area (see 10.9.1) is defined as the end of sample elution time.
10.10.2 To reduce the possibility of noise or an electronic spike falsely indicating the end of sample elution a 3 s slice average can be used instead of a single slice. For noisier baselines a slice average larger than 3 s may be required.
10.11 Calculate the Sample Total Area - Add all the slices from the slice corresponding to the start of sample elution time to the slice corresponding to the end of sample elution time.
10.12 Normalize to Area Percent - Divide each slice in the sample chromatogram table by the total area (see 10.11) and multiply it by 100.
10.13 Calculate the Boiling Point Distribution Table:
10.13.1 Initial Boiling Point - Add slices in the sample chromatogram until the sum is equal to or greater than 0.5 %. If the sum is greater than 0.5 %, interpolate (refer to the algorithm in 10.15.1) to determine the time that will generate the exact 0.5 % of the area. Calculate the boiling point temperature corresponding to this slice time using the calibration table. Use interpolation when required (refer to the algorithm in 10.15.2).
10.13.2 Final Boiling Point - Add slices in the sample chromatogram until the sum is equal to or greater than 99.5 %. If the sum is greater than 99.5 %, interpolate (refer to the algorithm in 10.15.1) to determine the time that will generate the exact 99.5 % of the area. Calculate the boiling point temperature corresponding to this slice time using the calibration table. Use interpolation when required (refer to the algorithm in 10.15.2).
10.13.3 Intermediate Boiling Point - For each point between 1 % and 99 %, find the time where the accumulative sum is equal to or greater than the area percent being analyzed. As in 10.13.1 and 10.13.2, use interpolation when the accumulated sum exceeds the area percent to be estimated (refer to the algorithm in 10.15.1). Use the calibration table to assign the boiling point.
10.14 Report Results - Print the boiling point distribution table.
10.15 Calculation Algorithms:
10.15.1 Calculations to determine the exact point in time that will generate the X percent of total area, where X = 0.5, 1, 2, ..., 99.5 %.
10.15.1.1 Record the time of the slice just prior to the slice that will generate an accumulative slice area larger than the X percent of the total area. Let us call this time, Ts, and the accumulative area at this point, Ac.
10.15.1.2 Calculate the fraction of the slice required to produce the exact X percent of the total area:
10.15.1.3 Calculate the time required to generate the fraction of area Ax:
Tf = Ax • W
where:
W = the slice width.
10.15.1.4 Record the exact time where the accumulative area is equal to the X percent of the total area:
Tt = Ts + Tf
10.15.2 Interpolate to determine the exact boiling point given the retention time corresponding to the cumulative slice area.
10.15.2.1 Compare the given time against each retention time in the calibration table. Select the nearest standard having a retention time equal to or larger than the interpolation time. (Warning - The retention time table shall be sorted in ascending order.)
10.15.2.2 If the interpolation time is equal to the retention time of the standard, record the corresponding boiling point.
10.15.2.3 If the retention time is not equal to a retention time of the standards (see 9.3), interpolate the boiling point temperature as follows:
10.15.2.4 If the interpolation time is less than the first retention time in the calibration table, then extrapolate using the first two components in the table:
BPx = m1 • (RTx - RT1) + BP1
where:
m1 = (BP2 - BP1) / (RT2 - RT1),
BPx = boiling point extrapolated,
RTx = retention time to be extrapolated,
RT1 = retention time of the first component in the calibration table,
BP1 = boiling point of the first component in the calibration table,
RT2 = retention time of the second component in the calibration table, and
BP2 = boiling point of the second component in the calibration table.
10.15.2.5 If the interpolation time is between two retention times in the calibration table, then interpolate using the upper and lower standard components:
BPx = mu • (RTx - RT1) + BP1
where:
mu = (BPu - BP1)/(RTu - RT1),
BPx = boiling point extrapolated,
RTx = retention time to be extrapolated,
RT1 = retention time of the lower bound component in the calibration table,
BP1 = boiling point of the lower bound component in the calibration table,
RTu = retention time of the upper bound component in the calibration table, and
BPu = boiling point of the upper bound component in the calibration table.
10.15.2.6 If the interpolation time is larger than the last retention time in the calibration table, then extrapolate using the last two standard components in the table:
BPx = mn • (RTx - RT(n-1)) + BP(n-1)
where:
mn = (BPn - BP(n-1))/(RTn - RT(n-1))
BPx = boiling point extrapolated,
RTx = retention time to be extrapolated,
RT(n-1) = retention time of the standard component eluting prior to the last component in the calibration table,
BP(n-1) = = boiling point of the standard component eluting prior to the last component in the calibration table,
RTn = retention time of the last component in the calibration table, and
BPn = boiling point of the standard component in the calibration table.