Handbook of Solvents - George Wypych - ChemTech - Ventech!

21.1 Supercritical solvents 1429
K
i
( TPx)
( TPy)
= � , , ϕ
ϕ�
, ,
β
i i
α
i i
For the unsymmetrical approach:
β
γ ( TPx , , ) f( TP
i i i , )
Ki
α
ϕ�
TPy , ,
( )
i i
where:
Ki partition coefficient of component i in phases α and β
�ϕ β
i fugacity coefficient of component i in mixture for phase β
�ϕ α
i fugacity coefficient of component i in mixture for phase α
γ β
i activity coefficient of component i in mixture for phase β
fi fugacity of pure component i
If one assumes no solvent in the solid phase, the relation for solubility of the solid in
the supercritical solvent reduces to:
y
i
sub
PiT =
P
⎛
⎜
⎝
( )
s sub
() ⎞⎛
⎞ ⎛ViP
−P
() T
⎟⎜
1
⎟⎜
⎠⎝ϕ�
DG
i
⎟
exp⎜
⎠
⎜
⎝
RT
A B C
where:
yi mole fraction of component i in gas phase
sub
Pi sublimation pressure of component i
P total pressure
�ϕ
DG
i fugacity coefficient of component i in mixture for dense gas phase
s
Vi partial molar volume of component i in solid phase
R universal gas constant
T absolute temperature
The first term A is for ideal gas solubility, the second term B accounts for the
non-ideality, while the third term C (Poynting correction) accounts for the pressure effects.
The product of the second and third terms is often referred as the Enhancement Factor (over
the ideal). In the absence of data, the sublimation pressure may be approximated through extrapolation
of the vapor pressure information.
21.1.2.1.3 Modeling
The approaches to modeling the high pressure phase behavior follow either use of the equation
of state models for fugacity coefficient determination or the treatment of the dense gas
as an “expanded liquid” through an activity coefficient model, the former approach being
more popular.
The macroscopic dense gas modeling approaches include van der Waals family of
equation of states, virial family of equation of states, and non-classical approaches. The molecular/theoretical
approaches and considerations contribute not only to more comprehensive
models but also provide insight bringing forth sound parameters/terms to the
macroscopic models. Computer simulation (molecular) can also be used to directly compute
phase behavior with some success. 27,28 The virial family of equation of states finds limited
use in supercritical applications due to the necessity for a large number of terms and
⎞
⎟
⎟
⎠