In a new paper, we present quantum corrections for cubic EoS that dramatically improve their performance for hydrogen, helium, deuterium, neon and mixtures that contain these components.

Our paper entitled Accurate quantum-corrected cubic equations of state for helium, neon, hydrogen, deuterium and their mixtures has been published in Fluid Phase Equilibria.

Cubic equations of state have thus far yielded poor predictions of the thermodynamic properties of quantum fluids such as hydrogen, helium and deuterium at low temperatures. In our paper, we derive temperature-dependent quantum corrections for the covolume parameter of cubic equations of state by mapping it onto the excluded volume of quantum-corrected Mie potentials.

The quantum corrections result in a significantly better accuracy, especially for caloric properties: while the average deviation of the isochoric heat capacity of liquid hydrogen at saturation exceeds 70% with the present state-of-the-art, the average deviation is 3% with quantum corrections. Average deviations in saturation pressure are well below 1% for all four fluids, and by using Peneloux volume shifts, we achieve average errors in saturation densities that are below 2% for helium and about 1% for hydrogen, deuterium and neon.

Parameters are presented both for Peng–Robinson and Soave–Redlich–Kwong. The quantum corrected cubic equations of state are also able to reproduce the vapor–liquid equilibrium of binary mixtures of quantum fluids, and it is the first cubic equations of state able to accurately model the helium–neon mixture, as shown in the figure below. Quantum-corrected cubic equations of state pave the way for technological applications of quantum fluids that require models with both high accuracy and computational speed, such as the identification of optimal multicomponent quantum refrigerants for improved hydrogen liquefaction processes.

We believe that the quantum corrections presented in the paper will become the new state-of-the-art for describing hydrogen, helium, neon, deuterium and their mixtures with cubic EoS. The work results from a collaboration between the team in Trondheim (A. Aasen, M. Hammer and myself), and a team in France consising of Silvia Lasala and Jean-Noël Jaubert.