Mathematical model of the petroleum products mass balancing in their supply network through the detection of excessive losses by the least squares method

A method for balancing the mass of petroleum products in their entire supply network, from the manufacturer to the car fuel tank, was proposed. The method is based on the analysis of differences that occur during double measurements of the same mass using different instruments during each delivery-acceptance operation. The analysis of these differences was performed using the least squares method (LSM) by composition and solving equations. As a result, LSM-balanced mass values were obtained for each petroleum delivery-acceptance operation and for the supply network as a whole. Balancing is performed by detecting losses that occur before the mass measurements or during the mass measurements of each measuring instrument. Additive and/or multiplicative losses can be detected. The additives have the same losses for each delivery-acceptance operation, regardless of the measured mass. The multiplicative losses increased in proportion to the measured mass. The measurement uncertainty was strictly developed according to the LSM. The simulated test example shows that the losses were determined with a sufficiently high accuracy. A key condition for this is to ensure the traceability of the mass measurements by calibrating all measuring devices involved in the network. The application of this method will allow petroleum products suppliers to find and eliminate sources of excessive natural and technological losses in a timely manner. It is of equal importance to identify weaknesses in the supply network where thefts can occur.