Mathematical Modelling of a Propellent Gauging System: A Case Study on PRISMA

Propellant gauging is crucial for a spacecraft approaching the end of its lifespan. Current gauging systems for satellites typically have an accuracy rate of a few months to a year at the end of their operational life. Therefore, it is essential to determine the appropriate gauging system for mission operations. This research focuses on modeling the propellant gauging system for PRISMA, an Earth Observation (EO) satellite of the Italian Space Agency. The analysis centers on implementing algorithms that calibrate the remaining propellant mass in the satellite tank using traditional methods such as bookkeeping (BKP) and pressure-volume-temperature (PVT). To enhance accuracy in quantification, an unconventional approach called thermal propellant gauging (TPG) has been considered. Preliminary computations were conducted using data obtained from the PRISMA thermal model to understand the calibration accuracy of the three methods. At the end of its operational life, the BKP and PVT methods exhibited error rates of 4.6% and 4.8%, respectively, in calculating the mass. In contrast, the TPG method demonstrated a significantly higher precision with an error rate of 1.86%. However, at the beginning of the satellite's operational life, the PVT and TPG methods showed error rates of 1.0% and 1.3%, respectively, while the BKP technique reported an error rate of 0.1%. Based on these findings, it has been concluded that combining the BKP and TPG approaches yields superior results throughout the satellite's lifespan. Furthermore, the researchers have determined the specific time duration for which each of these distinct approaches can be effectively utilized.