## 3 Mass Evaluation of Petroleum Products Using Weighing Methods
### Mass Measurement of LPG  
In the case of LPG, a closed hermetic tank (pressure vessel) is weighed. Measured mass comprises the mass of both liquid product and vapours inside. The resultant mass of LPG is calculated as difference between filled tank and empty tank masses as shown in Equation (1). A closed tank that is filled with LPG has a stable mass despite temperature or liquid and saturated gaseous phase changes [46]. With a temperature change, the liquid gas will expand or contract, and thus the amount of saturated gas in the tank will change; however, the total amount of energy will remain the same. This means that the measured mass will not change. Considering OIML R 125 [47], in a closed tank (e.g., LPG weighing case) \(\rho_{v}=0\) as no vapor is displaced. Then, the above-mentioned Equation (2) can be expressed as:  
\[m_{vac}=\frac{1-\left(\frac{1.2}{8000}\right)}{1-\left(\frac{0}{\rho}\right)}= m\frac{0.99985}{1}=0.99985\cdot m. \tag{7}\]  
A correction factor of 0.99985 is used to estimate the mass of LPG under vacuum in a closed container. The indication of the weighing instrument without correction in this case is the conventional mass [47], which is determined by the characteristics of the weighing instrument and the ambient conditions. Correction coefficient 0.99985 is universal and it does not depend on the type of used weighing instrument, cargo mass, product composition or measurement units. When LPG is weighed, then its amount has to be converted into liters using density \(\rho_{15^{\circ}\text{C}}\), LPG actual temperature \(T\)\({}^{\circ}\)C and coefficient \(VCF_{\text{T}}\):  
\[V_{\text{T}^{\circ}\text{C}}=\frac{m}{\rho_{15^{\circ}\text{C}}\cdot VCF_{ \text{T}}}, \tag{8}\]  
where \(V_{\text{T}^{\circ}\text{C}}\)--LPG volume at factual temperature, \(m\)--LPG mass, _VCF_--LPG volume recalculation, from factual temperature to the +15 \({}^{\circ}\)C, coefficient, \(\rho_{15^{\circ}\text{C}}\)--LPG density at +15 \({}^{\circ}\)C (from LPG quality certificate or measured in laboratory). A diagram of the volumetric correction factor (_VCF_) dependency on change of density and temperature is presented in Figure 4.  
_VCF_ coefficient is equal to the ratio of density at factual temperature and density at reference (+15 \({}^{\circ}\)C) temperature \(VCF=\frac{\rho_{1}}{\rho_{15}}\). Its variation is calculated according to  
Figure 4: VCF coefficient variation dependency on change of density and temperature.  
ASTM 54B tables (for petroleum products) [16] and the following conditions: density range 653-1075 kg/m\({}^{3}\); temperature range \(-\)15-50 \({}^{\circ}\)C.  
According to the Figure 4_VCF_ varies with the density of the petroleum product. As density changes (due to product type or composition), the _VCF_ adjusts to account for how much the volume shifts under temperature changes. Temperature fluctuations directly impact the _VCF_. As temperature increases or decreases, the VCF changes to reflect the corresponding expansion or contraction of the petroleum product volume. This adjustment is critical for accurate volume measurement, as temperature-induced expansion or contraction can lead to significant variations in perceived volume. Figure 4 thus provides insight into the sensitivity of the VCF to different densities and temperatures, emphasizing the importance of applying accurate VCF adjustments in petroleum measurement to ensure reliable data across varying operational conditions.