Phase Equilibria calculations are fundamental for the majority of EoS based modelling either for processes or when studying phase-behaviour.

In yaeos most of phase-equilibria procedures return the EquilibriaState type EquilibriaState, which holds all the relevant information of an equilibria point.

The implemented methods, and their usage are:

Flash calculations

Flash calcuations are one of the most used phase-equilibria calculations during modelling of processes.

In yaeos it is possible to make Flash calculations either specifying:

• $zPT \rightarrow x, y, \beta (V)$
• $zVT \rightarrow x, y, \beta (P)$

type(EquilibriaState) :: result

! zPT flash
result = flash(model, z, p_spec=P, T=T)

! zVT flash
result = flash(model, z, v_spec=P, T=T)

! It is possible to provide initialization compositions in terms of the
! K-factors. Where k0=y/x
result = flash(model, z, v_spec=P, T=T, k0=k0)

Saturation points

Single saturation point calculations are included with the procedures saturation_pressure and saturation_temperature. Both procedures solve the equation

$$f(T \lor P) = \sum ln K_i - 1 = 0$$

With a newton procedure with respect to the desired variable (either $P$ or $T$.

type(EquilibriaState) :: sat_point

sat = saturation_pressure(model, z, T=T, kind="bubble")
sat = saturation_pressure(model, z, T=T, kind="dew")

sat = saturation_temperature(model, z, P=P, kind="bubble")
sat = saturation_temperature(model, z, P=P, kind="dew")

Phase envelopes

Phase envelopes are the conection of all the saturation points of a system. When the interest is in calculating a whole phase diagram instead of a single point, or the point is hard to converge. It is better to use a robust mathematical algorithm that eases the calcuation providing an easy-to-converge point and using its information to initialize a next one and continue along the whole phase-boundary. This can be done with the procedure pt_envelope_2ph

type(PTEnvel2) :: env

sat = saturation_pressure(model, z, T=150._pr, kind="bubble")
env = pt_envelope_2ph(model, z, sat)