Derivation of the safe discharge capacity for gas storage tanks in pressure vessels

Thread Content

The derivation of the safe discharge volume for gas storage tanks in pressure vessels is based on principles such as energy conservation and mass conservation. The following is the general derivation process: Basic assumptions and principles – Ideal gas assumption: The gas inside the tank is considered an ideal gas, which obeys the ideal gas law pV = nRT. - Law of conservation of energy: The heat supplied to the storage tank per unit time is used in part to increase the internal energy of the gas, and in part to enable the gas to do work externally. - Law of conservation of mass: The mass of gas discharged through the safety valve per unit time is equal to the decrease in the mass of gas inside the tank. Derivation process – Calculation of heat input: According to the principles of heat transfer, the amount of heat Q that enters the tank per unit time is given by Q = αAΔT, where α is the heat transfer coefficient, A is the area of the tank’s surface exposed to heat, and ΔT is the temperature difference between the tank wall and the surrounding environment. - Energy balance equation: According to the law of conservation of energy, Q = ΔU + W. For an ideal gas, the internal energy U = \frac{i}{2}nRT, so \Delta U = \frac{i}{2}nR\Delta T. During a isobaric process, the work done by the gas is W = pΔV. Using the ideal gas law, ΔV = VΔT/T; substituting this into the equation gives Q = ∫(i/2)nRΔT dt + pVΔT/T. - Mass flow rate calculation: Based on the ideal gas law pV = nRT, we have n = \frac{pV}{RT}; since mass m = nM, it follows that m = \frac{pVM}{RT}. Taking the derivative with respect to time gives \(\frac{dm}{dt}=-\frac{pVM}{RT^{2}}\frac{dT}{dt}\). - Formula for safe discharge volume: By combining the previous formulas and making appropriate adjustments and transformations, the formula for the safe discharge volume G can be derived. Taking the fire condition as an example, G = \frac{2.55\times 10^{5}\alpha F A^{0.82}}{C_{p}(T - T_{0})}. For other operating conditions, such as input from a gas pressure source, factors such as the mass flow rate of the gas flowing in must be taken into account during derivation, and the formulas will differ.