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Super-Ancillary Equations for Cubic Equations of State



Ian Bell, Ulrich K. Deiters


Calculation of thermodynamic phase equilibrium is error-prone and can fail both near the critical point and at very low temperatures because of the limited precision available in double precision arithmetic. Most importantly, these calculations frequently represent a computational bottleneck. In this work, we extend the "superancillary" equation approach developed for reference multiparameter equations of state to classical cubic equations of state (van der Waals, Redlich–Kwong–Soave, Peng–Robinson). Iterative calculations in double precision are replaced by noniterative evaluation of prebuilt Chebyshev expansions constructed with extended precision arithmetic. Exact solutions for the equation of state constants are given. The Chebyshev expansions are shown to reproduce the equation of state values to within nearly double precision (aside from in the very near vicinity of the critical point) and are more than 40 times faster to evaluate than the VLE calculations from the fastest computational library. In this way we further expand the domains in which iterative calculations for pure fluid phase equilibria may be rendered obsolete. A C++ header implementing these expansions (and with no external dependencies) is provided as deposited data.
Industrial and Engineering Chemistry Research


Chebyshev expansion, cubic equation of state, numerical approximation, extended precision


Bell, I. and Deiters, U. (2021), Super-Ancillary Equations for Cubic Equations of State, Industrial and Engineering Chemistry Research, [online],, (Accessed May 23, 2024)


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Created June 29, 2021, Updated November 29, 2022