## 3 Mass Evaluation of Petroleum Products Using Weighing Methods
### Mass Measurement of LPP
For buoyancy correction, the density of the product at the observed temperature should be used, but usually the density from the product quality certificate, where it is given at +15 \({}^{\circ}\)C temperature, is used. To determine the influence of the density dependence on temperature on the result (i.e., mass in vacuum), we assume that the density of petrol ranges from 740 kg/m\({}^{3}\) (at 15 \({}^{\circ}\)C) up to 745 kg/m\({}^{3}\) (at 10 \({}^{\circ}\)C) [43]. This density change, due to the temperature change of 5 \({}^{\circ}\)C, influences the result by only 0.001%. This can be considered an extremely small value. If the density is measured at a factual temperature, it can be corrected to the density at 15 \({}^{\circ}\)C using ASTM Tables 53 [44]. According to the OIML G19 [45], the density is defined as the ratio of product mass (mass in vacuum) and its volume. Thus, we consider that the density specified in the certificates (determined by any method) is the density in vacuum. The diagram for direct product mass evaluation by weighing is given in Figure 3.  
Considering that mass evaluation is performed using wide-range weighing instruments, let's discuss a scenario where the scale error is \(\mathrm{e}=\pm 10\) kg at approximately 10 tonnes (corresponding to the tare mass of a rail tank car) and \(\mathrm{e}=\pm 50\) kg at 100 tonnes (corresponding to the gross mass of a full fuel rail tank car). Other data used: petroleum product density 740 kg/m\({}^{3}\), air density 1.2 kg/m\({}^{3}\), reference weight density 8000 kg/m. The scenario is chosen according to the significant measurement range presented in Table 2. Using the root sum squared (RSS) method, we can calculate the combined standard uncertainty for the net mass estimation from formula (1). \[\delta_{m}=\sqrt{\left(m_{\textit{\scriptsize{\it gross}}}\right)^{2}+\left(m_{ \textit{\scriptsize{\it t}}}\right)^{2}}\approx 54\ \mathrm{kg}. \tag{5}\]  
The standard uncertainty for the net mass is approximately 0.1%. The corrected mass in vacuum, where C is 1.00147, is equal to \(m_{\textit{\scriptsize{\it vac}}}=90,132\ \mathrm{kg}\). The expanded uncertainty is calculated by multiplying the combined standard uncertainty by the coverage factor k, which corresponds to a rectangular distribution with a 95% coverage probability:  
\[\frac{\delta_{m_{\textit{\scriptsize{\it vac}}}}}{m_{\textit{\scriptsize{ \it vac}}}}=1.73\cdot\sqrt{\left(\frac{\delta_{m}}{m_{\textit{\scriptsize{\it vac }}}}\right)^{2}}\approx 0.1\ \%. \tag{6}\]  
This indicates that the scale error is dominant for the weighing method. The correction does not increase the error; it simply increases the calculated mass in vacuum. As the net mass decreases to 20 t, the standard uncertainty for the net mass increases, and when considering the mass in vacuum, it rises by approximately 4%. Although the scale error is larger than this specific impact of air density change, the buoyancy correction algorithm removes a fundamental physical influence that consistently  
Figure 3: Diagram of LPP mass evaluation (volume recalculation) using weighing method, where \(m_{\textit{\scriptsize{\it air}}}\)—product mass (net) in air at observed temperature; _WCF_—weight correction factor; \(V_{15}\)—calculated volume (at 15 \({}^{\circ}\)C), \(m_{15}\)—product mass at 15 \({}^{\circ}\)C; \(\rho_{15}\)—product density at 15 \({}^{\circ}\)C; \(V_{\textit{\scriptsize{\it t}}}\)’c—recalculated volume at observed temperature; _VCF_—volumetric correction factor; ASTM D1250-19e1.2019—[16]. affects mass measurements in air. The algorithm allows for the conversion of'mass in the air' to'mass in vacuum', regardless of the initial weighing instrument's precision. This process is critical for obtaining an accurate and standardized mass evaluation, which is subsequently used for volume recalculation.