First, a novel mathematical model is proposed, based on thermodynamics and transport phenomena fundamentals, that aims to capture the CNG mixture's pressure, temperature and molar volume evolution during a CNG vehicle’s fill-up process. The CNG mixture's thermodynamic properties are calculated through the use of the generic cubic equation of state and residual properties. The obtained model gives rise to a set of differential-algebraic equations (DAE), which are then simulated using a hybrid Newton/Runge-Kutta method. The cooling behavior during the beginning of the fill-up is studied, as well as the heating behavior once the heating by compression mechanism takes place.
Afterwards, the fill-up process is formulated as a minimum time optimal control problem. The process of filling-up high pressure gas storage vessels consists of a gas source tank, an isenthalpic (Joule-Thomson or J-T) valve, a cooling system, and a gas storage vessel. These units are assumed to be thermally insulated. Despite the nonlinear nature of the aforementioned optimal control problem, its global solution is obtained analytically. A novel transformation technique is employed, to decompose the problem into a process simulation problem independent of time, and a simpler minimum time control problem that only depends on the final molar density value and the maximum allowable feed mass flowrate. The feasibility of the fill-up is uniquely determined by the process simulation problem, and upon fill-up feasibility, the minimum time control problem is then globally solved. Two fill-up case studies, involving two different system configurations are analyzed. In Case 1, the fill-up process has a constant molar enthalpy feed, and no cooling system. Case 2 considers a fill-up process with a constant temperature feed, delivered by an efficient cooling system. The obtained results for both case studies are compared to pure methane compression results.