1. Section C.2 Activity Coefficient (Gamma-Phi) Method 5
C.2 ACTIVITY COEFFICIENT (GAMMA-PHI) METHOD
The equation that must be solved is: yi P xiii
sat
Pi
sat
exp(Vi
L
(P Pi
sat
)/RT )
Bubble P
ˆ
i
V
1. Know xi, T
Calc ,i, Pi
sat
. Assume modified Raoult’s law
for first P, yi calculation.
i
sat
5. yT changed? Yes for
first inner loop pass.
2. Calc ,Poynting correction.ˆ
i
V
9. Guess P
6. yi = yi/yT
Calc at new yiˆ
i
V
4. yT yi
i
=
8. if yT > 1, P
if yT < 1, P
10. Bubble P and
yi found
7. yT = 1?
Yes
No
No
Yes
3. yi= xii fi
L
= xiKi
Pˆ
i
V
Inner loop can
often be elimi-
nated, and step
6 moved here.
For ideal gas,
no iterations
needed.
For ideal vapor
mixture, inner
loop not
required
2. 6 Appendix C Supplement Advanced VLE Strategies
Bubble T
Dew P
1. Know xi, P
Assume Raoult’s law for first T, yi calculation.
5. yT changed? Yes for
first inner loop pass.
2. Calc ,i, Pi
sat
, ,
Poynting correction.
i
sat
ˆ
i
V
9. Guess T
6. yi = yi/yT
Calc at new yiˆ
i
V
4. yT yi
i
=
8. if yT > 1, T
if yT < 1, T
10. Bubble T and
yi found
7. yT = 1?
Yes
No
No
Yes
3. yi= xii fi
L
= xiKi
Pˆ
i
V
Inner loop can
often be elimi-
nated, and step
6 moved here.For ideal vapor
mixture, inner
loop not
required
Ideal liquid mix-
ture rarely can
be assumed.
Inner loop
required
1. Know yi, T
Calc , Pi
sat
. Assume Raoult’s law for first P, xi
calculation, then calc i at xi.
i
sat
5. xT changed? Yes for
first inner loop pass.
2. Calc , Poynting correc-ˆ
i
V
9. Guess P
6. xi = xi/xT
Calc i at new xi
4. xT xi
i
=
8. if xT > 1, P
if xT < 1, P
10. Dew P and
xi found
7. xT = 1?
Yes
No
No
Yes
3. xi= yi P = yi/Ki
i fi
L
ˆ
i
V
Inner loop can
often be elimi-
nated, and step
6 moved here.