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Chasing the bias – gasoline matrix matching to improve ASTM D2622 sulphur

With the implementation of the US EPA Tier III, Euro 5, and upcoming Euro 6 gasoline sulphur regulations (Table 1), there is an increasing concern with low-level sulphur data quality.

Leslie Johnson
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Article Summary
This not only includes analyser and test method precision, but also bias. ASTM terminology standard D4175 defines bias as “the difference between the expectation of the test results and an accepted reference value”. Throughout this paper, we will discuss the bias that is introduced by variations in elemental composition between gasoline, diesel, and mineral oil matrices when measuring sulphur by X-ray Fluorescence (XRF) Spectrometry, specifically ASTM D2622 (Standard Test Method for Sulphur in Petroleum Products by Wavelength Dispersive X-ray Fluorescence Spectrometry). For these sample types, oxygen, carbon, and hydrogen are the elements that contribute to this type of bias. In addition, we will review good calibration techniques and why a weighted least squared calibration is recommended for XOS’ Sindie analyser, and why tightly bracketing the calibration range is not. Lastly, a series of unknown gasoline samples will be measured multiple times with Sindie using a D2622 gasoline calibration to demonstrate typical repeatability for this analyser.

Fuels that contain large amounts of fatty acid methyl esters (FAME) or ethanol, such as biodiesel or gasoline-ethanol blends, have a high oxygen content that leads to significant absorption of sulphur Kα radiation leading to falsely low measurement results when measured on a standard mineral oil or non-oxygenated calibration. So, how much is too much? According to D2622, samples containing more than 25 mass % FAME and 8.6 mass % ethanol will require action to mitigate this interference. Additionally, differences in the carbon-hydrogen (C/H) ratio between the calibration standards (e.g. mineral oil) and samples (e.g. gasoline) may introduce errors in the sample measurement. While D2622 states that it is important to know the C/H ratio, it also states that  it is up to the user to decide when this error is large enough to be corrected for.

D2622 describes three methods to handle elemental interference, including differences in the carbon- hydrogen ratios and that from oxygen:

1. Dilution is not a practical option for gasoline and diesel considering the already low sulphur concentrations of these samples. This is because a sample that is diluted with blank sulphur solvent to mitigate the effect of the interference may also dilute the sulphur concentration below the method detection limit.

2. Correction factors can be used to mitigate the effect of elemental sample interferences, however, D2622 does not list specific correction factors within the method because correction factors are apparatus-specific, and there are multiple apparatus types that comply with D2622. A D2622 user will need to contact their instrument manufacturer to determine if there are correction factors that they may use. For example, a Sindie 2622 or Sindie +Cl user may use the correction factors in ASTM D7039, because the apparatus is identical whether in 7039 or 2622 mode.

3. Matrix matching the calibration standards to the sample type will be our focus throughout this paper. Section 5.3 of D2622 states that “a gasoline may be simulated by mixing isooctane and toluene in a ratio that approximates the expected aromatic content of the samples to be analysed. Standards made from this simulated gasoline can produce results that are more accurate than results obtained using white oil standards.”

We will explore the effects of matrix matching in more detail by looking at the following test scenarios:
A. Set up a D2622 mineral oil calibration curve and run diesel and gasoline checks to observe the magnitude of the sample-standard bias.
B. Set up a D2622 gasoline calibration curve to see if sample-standard bias is mitigated for gasoline samples.

Note: Although we will not discuss oxygen in this paper, D2622 users can use these three mitigation methods to correct for the low measurement bias found in samples containing oxygen.

Test Scenario A: Mineral Oil Calibration
A 0-500 ppm sulphur in mineral oil calibration curve was set up on a Sindie analyser according to D2622 using commercially available gravimetrically prepared standards. Each calibration standard was measured for 600s (300s background and 300s sulphur), and standards 100 ppm and less were measured in duplicate using a separate sample aliquot as required in Section 9.2.1 of D2622. These duplicate measurements were averaged before input into the weighted linear squares calibration model. The analyser demonstrated excellent calibration linearity with a correlation coefficient of determination (R2) of 0.99999. See Figure 1 for calibration results.

A good calibration is essential to minimise systematic error, so be sure to follow these steps to obtain a good Sindie D2622 calibration:
• Use Best Practices to obtain good measurements (visit
• Have a good calibration blank, as a bad blank will lead to a high calibration intercept and poor accuracy at the lower end of the calibration range
• Use a new sample aliquot for duplicate measurements (per D2622 methodology)
• Do not tightly bracket the calibration range
• Auto calibration is recommended to obtain a weighted least squares calibration
• Consider matrix matching when necessary to reduce sample-standard bias

Sindie users commonly follow good calibration practices, but many do not understand how weighted least squares work and why it is recommended, as well as why tightly bracketing the calibration range is discouraged.

Sindie uses Monochromatic Wavelength Dispersive X-ray Fluorescence (MWDXRF) spectrometry for analysis whether in D7039 or D2622 measurement mode, and the MWDXRF X-ray counting statistics are governed by the Poisson distribution. As a result, the standard deviation on any totalnumber of counts, X, is the square root of the counts, X0.5. This is confirmed by the precision of this methodology wherein the precision statement of ASTM D7039 (Standard Test Method for Sulphur in Gasoline, Diesel Fuel, Jet Fuel, Kerosene, Biodiesel, Biodiesel Blends, and Gasoline- Ethanol Blends by Monochromatic Wavelength Dispersive X-ray Fluorescence Spectrometry) is essentially represented by a square root function, r = 0.4998*X0.54 where X in this case refers to sulphur concentration in ppm. D7039 is used in this example because it exclusively uses MWDXRF technology, whereas D2622 is WDXRF but does not specify excitation type (monochromatic or polychromatic). Additionally, the D2622 method precision is not a square root function (r = 0.1462*X0.8015).

The square root function is also used for the Sindie auto calibration model (known as linear weighted least squares). This model assumes a square root relationship between the data value and its error. This means that the model takes into account that  the error is not the same on every calibration point, whereas the normal least squares (non-weighted) linear function assumes the same error for every data point regardless of concentration. The non-weighted calibration function does not consider the better absolute precision of the low concentration data and is therefore over-influenced by high concentration data. To combat this, the calibration range of a non- weighted calibration is traditionally tightly bracketed around the range of interest. This also means that multiple non-weighted calibration curves are needed to cover a larger range of interest.
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