Safe volume of storage tank

It is recommended to refer to the \"Regulations on Safety Supervision of Pressure Vessels\" as well as a paper titled \"Determination of the Loading Factor for Liquefied Gas Storage Vessels\" by Wang Bilin There is a passage in the paper that might be useful for reference: For example, in the case of a liquid ammonia storage tank, the design temperature is 50 °C, the design filling coefficient is 0.9, and the temperature during filling is 10 °C. If the impact of the charging temperature is not taken into account during use, and filling is still carried out using the designed charging coefficient of 0.9, then when the temperature rises to the design value, the container will be completely filled with liquid, leading to overpressure. According to reference [2], ρ=0.6247 kg/L and ρt=0.562 kg/L. When Φ=0.9, at a design temperature of 50 ℃, Φt=(ρ/ρt)Φ=1＞Φv=0.9, which clearly does not meet the requirements of the pressure vessel regulations. 　　If, according to equation (3), the actual filling coefficient is calculated based on the actual filling temperature, with a designed filling coefficient of Φv = 0.9, and ρt and ρ can be obtained from reference [2], then:
When filling at 10 °C, Φ = (0.526/0.6247) × 0.9 = 0.8097;
When filling at 0 °C, Φ = (0.562/0.6389) × 0.9 = 0.792;
When filling at –10 °C, Φ = (0.562/0.652) × 0.9 = 0.775. 　　That is, when filling with liquid ammonia at 10 ℃, only 80% of the container’s volume can be filled. When filling at 0 °C, the loading is allowed to be 79% of the container’s capacity. It is even less when filling at –10 ℃, and the loading must not exceed 77.5% of the container’s volume. Only in this way can it be ensured that there is still 10% gas space inside the container at the design temperature (50 ℃).