This paper describes the development and implementation of a thermodynamic model for recharging high pressure gas storage tank systems from a high pressure source. The objective of this model is for use in a predictive control strategy that will fill a high pressure gas storage tank in minimum time with a specified amount of a two-component gas mixture subject to pressure and temperature constraints. The nonlinearity in this system arises from the non-ideal thermodynamic behavior of the individual gas components and the gas mixture at the high operating pressures under consideration.

Of particular concern in this process is the Joule--Thompson coefficient behavior of the gas components comprising the mixture. For systems with a positive Joule--Thompson coefficient, the gas mixture will cool as it expands from source pressure into the storage tank. In this case, the maximum pressure constraint must be lowered to account for the future increase in pressure as the system reaches ambient temperature. For systems with a negative Joule-Thompson coefficient, the gas mixture temperature will rise as the storage tank is filled. In this case, the rate of temperature rise must be controlled to reach the desired final pressure without exceeding the maximum temperature limit of the storage tank and delivery system. Over the supply pressure ranges in this work, however, some gas components can exhibit significant changes in the Joule—Thompson coefficient including sign changes.

Because there will typically not be temperature measurements within the storage tank and delivery system, the model will be used to estimate the tank temperature and pressure. Model corrections will be provided solely by source and delivery pressure measurements. The sensitivities to the initial conditions and process measurements are solved along with the model to account for the dynamic uncertainty in the state of the storage tank. Assuming the posterior distribution of the state of the storage tank can be adequately described by a linearized approximation, these sensitivities are used in the formulation of uncertainty in the terminal state of the tank. When the uncertainty in the storage tank state exceeds a maximum threshold, the filling algorithm automatically degrades into a fail-safe operation.

The thermodynamic model is illustrated using a nitrogen--helium gas mixture. We choose this system because the sign of the Joule-Thompson coefficient is different for each component; negative for helium and positive for nitrogen. There are also significant differences in the intermolecular potentials leading to deviations from ideal behavior at high pressure.