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where P is pressure, φ is calculated from an equation of state, γ is an activity
coefficient calculated from an activity coefficient equation, and f i
is the standard
state fugacity, which is given by
exp P
P sat
RT dP
v L
f i
sat
i P sat
= φ
(6.3)
i
The exponential term above, known as the Poynting correction , is used for very
light components and is usually negligible. In most cases the vapor pressure,
P sat , is used as the componential liquid-phase fugacity.
The fundamental equation for liquid - liquid equilibrium equates two instances
of the right-hand side of equation (6.2) written once for each liquid phase.
Aspen Plus supplies property methods identified by a specific vapor-phase fugacity
equation and a specific activity coefficient equation which defines the use of equation
(6.1) or (6.2). For example, the method NRTL-2, which represents the nonrandom
two-liquid activity coefficient equation, also known as the Renon equation, is used in
conjunction with the ideal gas equation and employs equation (6.2) in calculations.
The “2” identifies the data set from which the NRTL parameters were derived. Aspen
Plus has the possibility of two sets of activity coefficient parameters for most activity
coefficient equations with an indicated range of applicability (i.e., temperature and
pressure). Henry's law is used in some property methods for light components with
Henry's law parameters provided in the Aspen Plus database. Aspen Plus supplies
more than 50 property methods.
6.1 PARAMETERS OF EQUATIONS OF STATE
The most commonly used nonideal equations of state available in Aspen Plus all have
the same basic structure: third order. The general formulation from which all modern
forms can be derived is the five-parameter form
RT
θ (V
− η )
P
=
b
(6.4)
b)(V 2
+ δ V
+ ε )
V
(V
The parameters a and b are functions of the critical properties and the acentric factor
ω
θ , η ,
δ
ε
have values that depend on the equation of state (chosen
details may be found in Poling, 2000). For example, the values for pure components
of the Peng - Robinson equation are
. The symbols
,and
θ = a α (T r )
(6.5)
δ = 2 b
(6.6)
ε =− b 2
(6.7)
α (T r ) =
2 )( 1
T 0 . 5
r
) ] 2
[1
+ ( 0 . 37464
+
1 . 5422
ω −
0 . 2699
ω
(6.8)
For mixtures, the most commonly used equations of state are ideal, Redlich - Kwong,
Soave - Redlich - Kwong with variants, and Peng - Robinson with variants. Most use
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