Analytical instrumentation
As biofuels are increasingly blended with conventional petroleum products, questions have emerged regarding the applicability of standard methods for converting density to a reference temperature. This report demonstrates that these methods remain reliable for a wide range of blends – particularly those containing biodiesel – when measured using Anton Paar’s modular benchtop density meters. It also outlines how simple, customized conversion approaches can be developed when standard methods fall short.
Accurate measurement of, and reporting on, petroleum products is essential for operational efficiency, regulatory compliance, and fair commercial transactions across the global energy sector. One of the most critical parameters in this process is density, which directly affects how petroleum volumes are calculated, classified, and traded. However, because density and volume vary with temperature, the industry relies on standardized correction methods based on fossil fuels to convert density values to a common reference temperature, typically 15 °C or 60 °F.
In recent years, the fuel industry has seen a notable shift toward blending traditional petroleum-based fossil fuels, such as gasoline and diesel, with alternative fuels, commonly known as biofuels, to boost the use of renewable energy sources. This development raises the important question of whether standardized correction methods for density-to-temperature conversion remain valid for these new fuel blends.
Biodiesels – e.g., fatty acid methyl esters (FAME) – can be blended according to any ratio with petroleum diesel fuel. In most European countries, biodiesel is mixed with conventional diesel fuel to a concentration up to 7 % v/v (B7). In the U.S., other common biodiesel concentrations include B5 (up to 5 % v/v biodiesel) and B20 (up to 20 % v/v biodiesel). Pure biodiesel (B100) or other high-level blends are rarely used as transportation fuel, as B100 typically requires special handling and equipment modification to avoid engine problems (1) (2).
The physical properties of biodiesel, such as density, depend on factors like the feedstock source, fatty acid composition, and processing conditions. Chemically, biodiesel differs significantly from fossil fuel components. Therefore, alternative fuels, such as biodiesel and bioethanol, along with their respective blends, may require specific correction factors, as established correction routines are based on petroleum-derived fuels only.
The density of petroleum products is often reported at a specific reference temperature (e.g., 15 °C or 60 °F), though the measurement may be performed at a higher temperature. The conversion of the density at the measured temperature to a defined reference temperature is described in various publications, such as the API MPMS (Chapter 11.1) (3).
Anton Paar’s DMA density meters support automatic conversion of measured density values to API standardized reference conditions across various base temperatures and product groups, including group B “Refined Products,” covering a wide range of conventional fuels.
Currently, no official standard reference methods are available for biofuel and biofuel blends. ISO/TR 19441:2018 (4) is a technical report that sums up a wide range of studies related to biofuels and the conversion of their measured density to reference temperatures.
This report evaluates the effectiveness of standard methods used to convert density to a reference temperature in the context of biodiesel blends. It explains how these methods function and how they should be applied. The findings confirm that these established procedures remain reliable for many petroleum products containing biodiesel, while also providing guidance on developing custom conversion approaches when standard methods are insufficient.
To test the suitability of conventional conversion methods with regard to biofuels, the following samples were analyzed:
Density measurements were performed at various temperatures between 40 °C and 15 °C using a five-digit modular benchtop DMA density meter. After the sample was filled, the instrument automatically performed measurements at each temperature step.
A standard conversion method was applied according to API MPMS Chapter 11.1 (3).
From each measuring result, the mean values were defined (n=3), and the respective API density at 15 °C was calculated using product group B “Refined Products.”
In addition, a standardized approach based on ISO/TR 19441:2018 (4) was performed, with the thermal expansion coefficient α15. While advanced PMT tables utilize a defined regression procedure to determine the coefficients needed for converting density values to a reference temperature, a thermal expansion coefficient α can be easily calculated and applied to a specific sample.
According to our approach, a simplified linear formula was used to determine α15 (referenced at 15 °C):
ρT … density at current temperature T
ρ15 … measured density at 15 °C
T … current temperature (°C)
α15 … thermal expansion coefficient (1/°C)
The value of α15 is only valid for the examined sample and is temperature-dependent. In general, using the thermal expansion coefficient provides the most accurate results over narrow temperature ranges, due to the assumption of linear behavior. Values of α15 for different fuel types can be found in the literature.
When determined, the thermal expansion coefficient α15 can be used to calculate ρ15 using the following equation:
In a first step, the density of diesel fuel, biodiesel, and biodiesel blends was determined in the temperature range of 15 °C to
40 °C. All fuel types were measured reliably, with good repeatability. Standard deviations remained low for pure diesel (~2 g/cm³ × 10⁻⁵ g/cm³), confirming method robustness. Biodiesel/diesel blends showed similar precision to the 5th decimal place. For B100, deviations ranged from 1 g/cm³ × 10⁻⁶ g/cm³ at 40 °C to 8 g/cm³ × 10⁻⁵ g/cm³ at 15 °C, with improved precision at higher temperatures (5).
In a second step, API density values were calculated based on standard conversion methods as per API MPMS Chapter 11.1 (3) using the measured density values. To test the validity of API conversions for biofuels and blends, the deviation of the measured density value at a certain temperature was compared to the calculations.
For each measurement (n = 3), the mean value was determined. Using these averages, the API density at 15 °C was calculated based on product group B, “Refined Products,” and compared to the corresponding measured density at 15 °C. Figure 1 illustrates the deviations between the calculated and measured mean densities at 15 °C for each sample.
It can be clearly demonstrated that the greater the difference between the measurement temperature and the reference temperature, the larger the deviation between the calculated and measured density at the reference temperature. This trend was observed consistently across all fuel types tested.
As expected, the largest deviations occurred for the pure biodiesel sample (B100), since conventional conversion tables are based exclusively on petroleum-derived fuels. At a measurement temperature of 40 °C, the deviation for B100 reached approximately 0.0006 g/cm³. At the same temperature, pure diesel fuel also exhibited a measurable deviation, though lower in magnitude at approximately 0.0003 g/cm³.
The conversion to API density at a reference temperature of 15 °C is particularly accurate for these biodiesel blends with a biodiesel content of 15 % to 40 %. In this case, the deviation from the reference value is consistently ≤ 0.0001 g/cm³.
In a third step, the usability of the thermal expansion coefficient α15 for density conversions was evaluated. The measured density values for diesel fuel, biodiesel, and blends at 15 °C were compared to calculated values using the thermal expansion coefficient α15.
Figure 2 illustrates the differences between calculated and measured density values at the reference temperature of 15 °C, using the simplified α15 method. This approach estimated the density at 15 °C based on measurements taken at higher temperatures.
The data clearly show that as the measurement temperature increases, the deviation between the calculated and actual density at 15 °C increases across all tested fuel types. This effect is also observed with the standard API-based method (Chapter 3.1), proving that temperature difference is a dominant factor in conversion accuracy.
Unlike using API product group B, the α15 approach performs very well for pure biodiesel (B100). For B100, the calculated values match the measured densities, while for pure diesel fuel (B0) and blends with low biodiesel content, the deviations are much higher, with differences reaching up to 0.001 g/cm³.
The authors of the technical report ISO/TR 19441:2018 (4) reference the European Measurement Instrument Directive, which requires a prediction error (R) of less than 0.2 % to quickly verify whether the applied conversion yields comparable results. Using the obtained data, the measured values of the fuel samples at 15 °C were compared to the corresponding calculated values at the reference temperature, employing a straightforward formula-based approach:
R … prediction error
ρ15 … density measured at 15 °C
ρ15, pred … predicted density for 15 °C
If the ratio falls within the range 0.998 < R < 1.002, the requirement is satisfied, indicating a strong likelihood that the applied conversion is appropriate (4).
Using both the API calculation and the α15 approach, this condition is fulfilled for all tested fuel types over the whole temperature range. This demonstrates that the methods investigated are effective not only for conventional fuels but also for biofuels (5).
This report examines the suitability of standard petroleum-based density correction methods, such as API conversion, outlined in API MPMS Chapter 11.1 (3), for biofuels and their blends.
Experimental findings indicate that API-based corrections provide high accuracy, particularly for blends containing up to 40 % biodiesel. For pure biodiesel (B100), however, improved accuracy can be achieved by using alternative approaches, such as applying the thermal expansion coefficient at 15 °C (α15). While API methods generally prove effective, selecting the most appropriate correction method should be validated for each specific biofuel. In cases where standard methods are insufficient, further alternatives are provided in the referenced ISO technical report published by the International Organization for Standardization (4).
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