Bayesian Calibration of HEOS Mixing Models and Impact on Thermodynamic Cycles

The political, social and economic consequences of climate change drastically influence the requirements of modern energy systems and its components. This includes not only energy production but also concepts and innovations for its storage, especially in magnitudes of gigawatt hours. Carnot batteries, which convert electrical energy to thermal energy using a heat pump cycle, offer a potential solution. If required, the stored energy is converted back in a power cycle. Thereby, the efficiency of each conversion cycle is highly relevant for the final round trip efficiency of the Carnot battery. For the design, simulation, and optimisation of thermodynamic cycles, sufficient knowledge of the properties of the working fluid is required. These properties are commonly described using highly accurate multiparameter equations of state (EOS) in the form of the Helmholtz energy. When mixtures are used as working fluid, additional adjustable parameters in the mixing rules of the reducing values of the residual fluid contribution are required. These parameters need to be fitted to experimental data of the mixture that is subject to measurement uncertainties. When there is only very little data available, the impact of measurement uncertainty is particularly large. This leads to uncertainties in the derived parameters, which must be taken into account when using the EOS for further calculations. The process of determining model parameters and its uncertainties given noisy measurements can be referred to as model calibration. Uncertainties in the vapor-liquid-equilibrium (VLE) data lead to a calibration setting, where both inputs and outputs are random, hence, an Error-in-Variables approach is chosen. Here, this approach is exemplarily applied to the Recuperative Two-Phase Cycle (RTPC) using non-conventional asymmetric working fluid mixtures, where it offers a particularly high added value due to the small amount of measurement data. The RTPC is a novel cycle concept (Bederna et al., 2023), which is currently under investigation to increase the efficiency of the thermodynamic cycles in Carnot batteries. The specific characteristic is the use of asymmetric refrigerant mixtures. In this work, parameters are derived for the zeotropic mixture propane-dodecane, whose experimental VLE data is provided by Gardeler et al., 2002. Therefore, we embed the problem in a Bayesian probabilistic setting and sample from the posterior distribution using the affine invariant Markov Chain Monte Carlo ensemble sampler (Goodman and Weare, 2010). We compare the posterior mean with the results of other automatic fitting methods. Finally, the impact of the variance on the second law efficiency and the optimal process parameters for a basic heat pump version of the RTPC are shown.