Fuel Density's Dance With Temperature: Understanding The Science

Fuel density is dependent on temperature. As temperature increases, fuel density decreases. This is because the molecules in the fuel move faster and take up more space, causing the fuel to expand. This relationship between fuel density and temperature is important in various applications, such as automotive engines and aviation fuel systems, where fuel density can impact performance and efficiency.

Fuel density and temperature correlations

Fuel density and temperature are inversely correlated. As temperature increases, fuel density decreases, and vice versa. This correlation is not constant across all temperatures, and fuel density can vary between different types of fuel.

For example, jet fuel is a mixture of kerosene and naphtha, two hydrocarbon liquids distilled from crude oil. The specific density of jet fuel is not fixed but falls within an allowable range. In summer, jet fuel is a 50/50 mix of these two liquids, while in winter, the proportion of naphtha is increased by about 5% to allow for lower temperatures.

Correlations for jet fuel density and temperature can be calculated using tools based on ASTM D 1250-04 and IP 200/04 (API Manual of Petroleum Measurement Standards). Each coloured line in the provided diagram represents a jet fuel with a given density at a given temperature. If the temperature changes, the density of the jet fuel changes along the coloured line.

Volume correction factors can be used to calculate the volume of jet fuel at a base temperature (15°C/59°F) if the density and volume at another temperature are known. For instance, if you have 100 litres of jet fuel with a density of 757 kg/m3 at 100°C, the volume at 15°C can be calculated using the yellow line in the jet fuel volume correction figure, resulting in a volume of 92 litres.

Similarly, fuel oil density and temperature correlations can be calculated using the same tools. Volume correction factors can be used to determine the volume of fuel oil at a base temperature (15°C/59°F) or another temperature if the density and volume are known. For example, if you have 1000 m3 of fuel oil with a density of 960 kg/m3 at 15°C, the volume at 100°C can be calculated using the light green line in the fuel oils volume correction figure, resulting in a volume of 1065 m3.

It is important to note that the coefficient of thermal expansion of fuel is not a constant over the entire range of temperatures. At very cold temperatures, fuel may no longer be in a purely liquid state, and additives can also influence the coefficient of thermal expansion.

Volume correction factors

The Volume Correction Factor (VCF), also known as the Correction for the Effect of Temperature on Liquid (CTL), is a standardised computed factor used to correct for the thermal expansion of fluids, primarily liquid hydrocarbons, at various temperatures and densities. It is a number between 0 and 2, rounded to five decimal places, which, when multiplied by the observed volume of a liquid, will return a "corrected" value standardised to a base temperature (usually 15° Celsius or 60° Fahrenheit).

The VCF is calculated using the following formula:

{\displaystyle VCF=C_{TL}=\exp\{-\alpha _{T}\Delta T[1+0.8\alpha _{T}(\Delta T+\delta _{T})]\}}

Where:

• {\displaystyle exp } refers to the mathematical constant, {\displaystyle e}
• {\displaystyle \alpha _{T}\Delta T[1+0.8\alpha _{T}(\Delta T+\delta _{T})]\}} refers to the change in observed temperature (in degrees Fahrenheit) minus the base temperature
• {\displaystyle \delta _{T}} refers to a small base temperature correction value
• {\displaystyle \alpha _{T}} refers to the coefficient of thermal expansion at the base temperature
• {\displaystyle \rho ^{}} refers to the density at the base temperature and 0 psig pressure
• {\displaystyle K_{0}}, {\displaystyle K_{1}}, and {\displaystyle K_{2}} refer to a specific set of constants, dependent upon the liquid's classification and density at the base temperature

For example, if you have 100 litres of jet fuel with a density of 757 kg/m3 at 100°C, you can use the VCF to calculate the volume at 15°C. First, you would refer to the Density vs Temperature figure to identify the relevant jet fuel (in this case, represented by the yellow line). Then, using the yellow line in the Jet Fuel Volume Correction figure (Density@Observed T/Density@15°C), you can determine that the correction factor at 50°C is 0.923. Therefore, the volume of your jet fuel at 15°C is 100 litres x 0.923 = 92 litres.

It is important to note that the VCF is typically used for liquid hydrocarbons, but the underlying theory and principles can be applied to most liquids, with some exceptions like water.

Fuel density at base temperature

The density of fuel is dependent on temperature. As temperature increases, fuel expands, and its density decreases. Similarly, when the temperature decreases, the density of the fuel increases.

Volume correction factors can be used to calculate the volume of a product at base temperature (15°C/59°F) if the density and volume at another temperature are known. For example, if you have 100 litres of a fuel oil with a density of 800 kg/m3 at 200°C, you can calculate the volume at 15°C using the light blue line in the Fuel Oils volume correction figure (Density@Observed T/Density@15°C). The correction factor at 200°C is 0.859, so the volume of the fuel oil at 15°C is 100 litres x 0.859 = 86 litres.

The base volume and density of a fuel can also be used to calculate the volume at another temperature. For instance, if you have 1000 m3 of a fuel oil with a density of 960 kg/m3 at 15°C, and you want to know the volume if it is heated to 100°C, you can use the light green line in the Fuel Oils volume correction figure (Density@15°C/Density@observed T). The correction factor at 100°C is 1.065, so the volume of the fuel oil at 100°C is 1000 m3 x 1.065 = 1065 m3.

It is important to note that the coefficient of thermal expansion is not a constant and varies with temperature. Additionally, the density of fuel can also be affected by other factors such as additives and the distillation process.

Fuel density and temperature variations

Fuel density and temperature are inversely proportional, meaning that as the temperature of a fuel increases, its density decreases, and vice versa. This relationship is not unique to fuels and is true for most substances.

The density of a substance is defined as its mass per unit volume. As temperature increases, molecules move faster and take up more space, causing the substance to expand. This expansion results in an increase in volume and a decrease in density, assuming the mass remains constant.

For example, let's consider a fuel oil with a density of 900 kg/m3 at 15°C. If we heat this fuel oil to 100°C, its density will decrease to approximately 840 kg/m3. This change in density can be estimated using diagrams or calculated using volume correction factors.

It is important to note that the relationship between fuel density and temperature is not linear and can vary with different types of fuels. For instance, the density of jet fuel can change with the distillation process and the crude oils used. Additionally, the presence of additives can also impact the density of a fuel.

In practical terms, understanding the relationship between fuel density and temperature is crucial for various applications, such as aviation and automotive engineering. For instance, the volume of fuel in a car's fuel tank can change with temperature, affecting the amount of fuel purchased or the vehicle's performance. Similarly, in aviation, the weight and balance of an aircraft are critical, and fuel density variations due to temperature changes can impact these factors.

Fuel density and temperature calculations

The density of fuel is defined as "the mass of fuel per unit volume". It is usually measured with a hydrometer, which is calibrated against a scale used to determine the density for a given temperature. The density of fuel is determined by the quality of the crude used to produce the fuel and the refining process.

Correlations for fuel oils' density and temperature are calculated using tools based on ASTM D 1250-04 and IP 200/04 (API Manual of Petroleum Measurement Standards). Volume correction factors can be used to calculate the volume of a product at a base temperature if the density and volume at another temperature are known.

For example, if the density of a fuel oil is specified to be 900 kg/m3 at 15°C, the density of the same oil heated to 100°C is approximately 840 kg/m3. Volume correction factors can also be used to calculate the volume at another temperature if the base volume and density are known.

In another example, if you have 100 liters of jet fuel with a density of 757 kg/m3 at 100°C, the volume at 15°C can be calculated as follows: First, find the correction factor at 50°C (0.923) using the density vs temperature figure. Then, multiply the volume by the correction factor (100 liters * 0.923) to get the volume at 15°C, which is approximately 92 liters.

The density of fuel can also be expressed as a specific gravity or relative density, in which case it is expressed as a multiple of the density of a standard material, usually water or air.

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