Calculation of Critical Curves of Fluid Mixtures through Solution of Differential Equations

A novel, particularly robust method
for the calculation of critical
curves of fluid mixtures is proposed that makes use of differential
equations representing the critical conditions (isochoric thermodynamics
formalism). These differential equations are integrated with adaptive
numerical integration methods, thus avoiding the convergence problems
that so often afflict methods using algebraic equations. The novel
method can be used with all Helmholtz energy-explicit equations of
state, including models that can return unphysical results when applied
to thermodynamic states within a two-phase region, for example, the
GERG equations of state. In combination with the “parametric
marching” technique, the new approach is able to follow critical
curves of arbitrary shape. The Supporting Information provides an
implementation of this approach for the GERG-2008 and Peng–Robinson
models in the Python language.