Highly accurate correlating method for phase equilibrium data, and phase equilibrium calculation method
View Patent ↗A method for precisely predicting phase equilibrium from existing phase equilibrium data on the basis of a wide range of phase equilibrium data including binary vapor-liquid equilibrium data; a method or apparatus for designing or controlling a component separator or a refiner using the prediction method; and a program for designing this design or control apparatus. Binary phase equilibrium measurement data is used to calculate an index of proximity ratio to critical points and infinite dilution pressure gradients. The obtained index is correlated with the infinite dilution pressure gradients to newly calculate infinite dilution activity coefficients from the respective index to infinite dilution pressure gradients correlations. The obtained infinite dilution activity coefficients values are used to predict phase equilibrium. Thus, the obtained values are used to design or control a component separator or a refiner, such as a distillation column.
1. A method for controlling a separator or a refiner, comprising:
recording existing binary phase equilibrium data;
implementing a computer-based method for predicting binary phase equilibrium data comprising:
by using binary phase equilibrium measurement data, calculating an index X of proximity ratio to critical points according to
X
=
p
1
s
+
p
2
s
P
c
1
+
p
2
s
,
and calculating infinite dilution pressure gradients Y 1 and Y 2 according to:
Y
1
=
γ
1
∞
p
1
s
-
p
2
s
P
c
1
-
p
2
s
and
Y
2
=
p
1
s
-
γ
2
∞
p
2
s
P
c
1
-
p
2
s
,
wherein P c1 represents a critical pressure of a lighter component in a binary system, p 1s and p 2s represent vapor pressures of components 1 and 2, respectively, at a temperature T, and γ i ∞ and γ 2 ∞ represent infinite dilution activity coefficients of components 1 and 2 in a liquid phase, respectively;
correlating the obtained index X of proximity ratio to critical points with the infinite dilution pressure gradients Y 1 and Y 2 and calculating infinite dilution activity coefficients γ 1 ∞ and γ 2 ∞ or binary parameters A and B from the X-Y 1 correlation and the X-Y 2 correlation, respectively, the binary parameters A and B being given by A=ln γ 1 ∞ and B=ln γ 2 ∞ ; and
evaluating thermodynamic consistency of the X-Y 1 and X-Y 2 correlation data according to
H
=
β
e
x
p
-
β
ca
l
β
ca
l
using values of β exp and β cal obtained by incorporating values of binary parameters A and B into the following equation
β
=
F
B
-
A
to determine the correlations by confirming that data that satisfy the thermodynamic consistency within a predetermined error range is highly reliable data, and correlating X with Y 1 and Y 2 using only thermodynamically consistent data, wherein
β exp represents a value of β that is calculated according to F/|B−A| using F, A, and B determined from actually measured values;
β cal represents a value of β that is calculated from
F
B
-
A
=
aP
b
using values of a and b obtained by correlation of actually measured values:
A and B represent binary parameters;
F represents deviation from A=B in a one-parameter Margules equation;
P represents a pressure or an average vapor pressure;
a and b represent constants specific for a binary system; and
predicting new binary phase equilibrium data using the calculated values of the infinite dilution activity coefficients γ 1 ∞ and γ 2 ∞ or binary parameters A and B; and
controlling the separator or the refiner according to the predicted new binary phase equilibrium data.
2. The method according to claim 1 , wherein
the new binary phase equilibrium data which is predicted using the calculated values of the infinite dilution activity coefficients γ 1 ∞ and γ 2 ∞ or the binary parameters A and B make data of a plurality of systems of a homologous series, and
based on the data of a plurality of systems of homologous series, new infinite dilution activity coefficients γ 1 ∞ and γ 2 ∞ or binary parameters A and B in other systems of the homologous series are predicted.
3. The method according to claim 1 , further comprising:
calculating infinite dilution activity coefficients or binary parameters for atomic groups from the calculated infinite dilution activity coefficients γ 1 ∞ and γ 2 ∞ or binary parameters A and B; and
predicting new binary phase equilibrium data based on the calculated infinite dilution activity coefficients or binary parameters for atomic groups.
4. The method according to claim 1 , wherein the separator or refiner is a distillation column, an extraction column, or a crystallizer.