## 3 Mass Evaluation of Petroleum Products Using Weighing Methods
### Mass Measurement of LPP  
The mass of LPP and LPG is obtained by weighing them in the tank, whose mass is known. The mass of LPP is calculated as the difference between the filled tank and empty tank masses:  
Mass (Gross) = Empty (Tare) mass + Contents mass (Net),  
Contents mass (Net) = Mass (Gross) \(-\) Empty (Tare) mass or  
\[m=m_{\rm gross}-m_{\rm t}, \tag{1}\] \begin{table}
\begin{tabular}{l c c} \hline \hline
**Measuring Instrument for** & & \\
**Volume, Density and** & **Maximum** & **Significant Measurement** \\
**Temperature** & **Permissible Error** & **Range** \\
**Determination** & & \\ \hline \hline \multicolumn{3}{c}{The volumetric mass estimation method} \\ \hline Rotary chamber volume & & \\ meter (flow computer & \(\pm\)0.3\% & (25–125) m\({}^{3}\) \\ converts L/min to L) & & \\ \hline Temperature sensor & \(\pm\)0.1 \({}^{\circ}\)C & (\(-\)30–70) \({}^{\circ}\)C \\ \hline Density meter & \(\pm\)0.5 kg/m\({}^{3}\) & (750–850) kg/m\({}^{3}\) \\ \hline \hline \multicolumn{3}{c}{The geometric mass estimation method} \\ \hline Volume measuring tank & & \\ (the volume is evaluated & \(\pm\)0.2\% & (0–56,000) m\({}^{3}\) \\ using a graduated table) or & & \\ \hline Level meter & \(\pm\)0.5 mm & (0–20) m \\ \hline Temperature sensor & \(\pm\)0.5 \({}^{\circ}\)C & (\(-\)20–90) \({}^{\circ}\)C \\ \hline Density meter & 0.6 kg/m\({}^{3}\) & (0.75–0.95) kg/L \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Measuring instruments for the volumetric and geometric mass estimation method. where \(m\) is the mass of LPP (Net), kg, \(m_{\rm gross}\) is the gross mass (weight indicated by the weighing instrument: tare + product), kg, and \(m_{\rm t}\) is the empty (Tare) mass, kg. Because the weighing instrument indicates a value that is proportional to the gravitational force on the object reduced by the buoyancy in air, the instrument's indication in general has to be corrected for the buoyancy effect [41]. The value of this correction depends on the density of the object (petroleum product) and the density of air [42]. When evaluating a product's mass in vacuum value, there is a need to convert the mass of liquid petroleum indicated on a weighing instrument to mass in vacuum, in which case air buoyancy corrections shall be made according to the equation [41]:  
\[m_{\rm vac}=C\cdot m, \tag{2}\]  
where \(m_{\rm vac}\) is the mass in vacuum value of LPP, kg, and \(C\) is the buoyancy correction coefficient. Coefficient \(C\), is given by the equation:  
\[C=\frac{1-\rho_{a}/\rho_{r}}{1-\rho_{\rm v}/\rho}, \tag{3}\]  
where \(\rho_{a}\) is the reference density of air value--equal to 1.2 kg/m\({}^{3}\), \(\rho_{r}\) is the reference density of calibration weight--8000 kg/m\({}^{3}\) (according to [41]), \(\rho_{\rm v}\) is the density of gas or vapor that is displaced when the container/vessel/tank is filled, \(\rho\) is the density of the LPP. Since the density of air (which has a relatively large value of about 1.2 kg/m\({}^{3}\)) can change due to pressure, temperature, or humidity, it may be necessary to consider those factors. When a liquid product is weighed in an open container/vessel/tank, then the gas displaced can be air, and then \(\rho_{\rm v}\) will be equal to \(\rho_{a}\), thus Equation (3) can be expressed as:  
\[C=\frac{1-\rho_{a}/\rho_{r}}{1-\rho_{a}/\rho}. \tag{4}\]  
Buoyancy corrections are adjustments made to account for the effect of air buoyancy when measuring the mass of an object in air. These corrections convert the conventional mass indicated by a weighing instrument to the mass in vacuum, where no buoyant force from the air is present. This process compensates for the reduction in weight due to the displacement of air by the object and ensures that the measured mass accurately reflects the object's mass without external buoyant influences. As mentioned before, product density depends on the temperature.