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Jakub Tkaczuk

Equations of state for the thermodynamic properties of cryogenic mixtures

Published on 13 December 2021
Thesis presented December 13, 2021

This work is motivated by the needs of large cryogenic facilities and aims to improve their thermal efficiency in the range of 40 – 80 K. It allows describing the thermodynamic properties of cryogenic mixtures accurately.
The empirical multiparameter equations of state explicit in the Helmholtz energy are developed for the binary mixtures of helium, neon, argon, and nitrogen. The development process is presented and consists of the experimental data review, data points weighting, and minimizing the objective function using supervised non-linear regression.
The equations are valid in the single-phase and at the phase envelopes for the entire composition span and pressures as high as 1000 MPa. The single-phase uncertainties at low pressure (0 – 10 MPa) reach 0.5 – 2.5% for 95% of data points used for the EOS development. At higher pressures, some of the equations deviate up to 5% in density from the experimental data. The deviations in the speed of sound vary from 4 to 10%.
In addition to the single-phase uncertainty discussion, a new metric is proposed to evaluate the uncertainties in phase equilibria calculations. Its advantages and shortcomings over the classical pressure-based metric are presented.
The equations of state are validated at cryogenic temperatures in the single-phase region with measurements of the Joule-Thomson coefficient. Indirect measurements are first acquired for pure fluids, allowing for the experiment validation and then for mixtures, providing new results to the study. The expanded relative standard uncertainty is presented and discussed along with the Monte Carlo analysis for the combined uncertainty. The impact of the composition uncertainty on the Joule-Thomson coefficient is quantified for mixtures using the Monte Carlo simulations.
The presented equations of state are in good agreement with the acquired Joule-Thomson coefficient values. A short discussion on perspectives and further steps concludes this work and aims at a more accurate mixture property description thanks to new, more accurate measurements and modern minimization algorithms used to develop the equations.

equations of state, fluid mixtures, thermodynamic properties

On-line thesis.