Estimation of the quantity of product within cryogenic storage vessels

Abstract Cryogenic products, such as oxygen, nitrogen and argon, can be delivered to customers either within vessels (cryogenic liquids) or cylinders (gaseous state), depending on the requested quantity. Cryogenic applications are numerous, from hospitals to glass furnaces and electronics manufacturers. Accurate estimation of the quantity of product stored at any time in cryogenic vessels is critical to avoid run-outs for the customer and to optimize the product deliveries, which means saving money and reducing pollution due to trucks fuel consumption. Our paper first details a method to estimate the vessel parameters and the mass stored within using measurement of the pressure at the top of the vessel and the differential pressure between the top and the bottom of the vessel. It is based upon a physical model of the vessel and estimates the liquid mass inside the vessel and the deliverable mass at each time-step. The added-value of the proposed algorithm has been assessed comparing to simple algorithm currently used in operations. The weaknesses of this simple algorithm are analyzed at the beginning of this paper. The method described is applicable for vertical, horizontal and spherical vessels. It has been validated on 40 vessels storing nitrogen, argon and oxygen (around 6 months of data involving 1000 fillings for all tanks) in reference to delivery bills (for deliverable mass estimation). Instantaneous mass estimation has been validated on vessels specially equipped with load cells measuring the weight of the vessel every hour. Validation showed this method to be at least twice as accurate as the simple algorithm previously used to estimate the mass. For high pressure vessels (above 15 barg), it reaches three times as accurate as the simple algorithm. Such results led to the industrialization of the algorithm, including simplifications to fit with operational constraints (especially calculation time).