Dynamic Thermodynamics with Internal Energy, Volume, and Amount of Moles as States: Application to Liquefied Gas Tank

Dynamic models for process design, optimization, and control usually solve a set of heat and/or mass balances as a function of time and/or position in the process. To obtain more robust dynamic models and to minimize the amount of assumptions, internal energy, volume, and amount of moles are chosen as states for the conservation laws of the dynamic model. Temperature, pressure, and the amount and composition of the phases are calculated on the basis of these states at every time step. The Redlich-Kwong and Peng-Robinson (RK-PR) cubic equation of state is used as the thermodynamic model. This study describes the aspects of this approach and additionally gives a wide view over the whole internal energy and volume surface in specific phase diagrams. A complete separation between the dynamic balance model and the thermodynamic model is achieved. Several examples show the application of this approach for a liquefied gas tank and demonstrate that the method is applicable to one and two phases in a wide temperature and pressure range, from liquid and/or gas phase to supercritical conditions.