The invention comprises a main and a subsequent stage. At the main stage, the medium is pumped into a first instrument line. This first instrument line is mounted in a main pipeline system and is equipped with an inlet mass meter with a first flow rate range. After reaching of a set value from the instruments, an automated control system (ACS) stops the first line pump, ensures operation of its driving isolation valves, thus, completing the main stage measurement cycle, and switches the system into the subsequent stage mode. At the subsequent stage, the medium flow is collected from the tank and cavities of the measuring system. It flows by gravity into the bottom of the system inner volume (9) and is then supplied by a to a second instrument line equipped by a mass meter with a second and lower flow rate range.