(382x) Molecular Calculation of the Critical Parameters of Classical Helium

Many engineering approaches for calculating thermophysical properties of mixtures are based on corresponding states, where properties and parameters are scaled based on the critical parameters of the components. This approach is problematic for mixtures containing helium (such as some natural gases), because the location of the critical point is distorted by quantum effects. These quantum effects, while large near the critical temperature of 5.2 K, are nearly negligible at the higher temperatures associated with gas processing. For calculations at such conditions, it would be more appropriate to use the critical parameters of a hypothetical “classical” helium.

Previous estimates of effective classical critical parameters for quantum gases have been mostly empirical. However, for helium the existence of highly accurate ab initio pair and three-body potentials makes a more rigorous calculation possible. We perform this rigorous calculation in two ways. First, we calculate the virial coefficients up to the seventh virial (sufficient to be accurate at the critical density) and find the conditions where an isotherm satisfies the critical conditions. Second, we use Gibbs Ensemble Monte Carlo (GEMC) to calculate the vapor-liquid equilibrium, extrapolating the phase envelope to the critical point.

Both methods yield results that are consistent within their uncertainties. The critical temperature of classical helium is 13.0 K, the critical pressure is 0.93 MPa, and the critical density is 28-30 mol/L. The effect of three-body forces on the location of the critical point is small (lowering the critical temperature by roughly 0.1 K), suggesting that we are justified in ignoring four-body and higher interactions in our calculations.