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Dewpoint Calculation for a multicomponent mixture
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Dew Point calculations with an example
The dew point of the temperature at which a liquid begins to condense from a vapor. The calculation is
very simple for a pure component it is the boiling point of the pure component. A simple equation like
Antoine’s equation can be used to calculate this.
For multicomponent mixtures, the vapor-phase composition Yi is given. If along with the vapor
composition, the temperature is given, then we must increase the pressure till the first drop of liquid is
formed. This is called Dew point pressure calculation. If the pressure is given, then we must decrease
the temperature till the formation of liquid. This is called Dew point temperature calculation. In both the
cases the temperature or Pressure is adjusted till the liquid composition of the liquid is equal to 1.
∑Xi = 1.0
We shall calculate Dew point temperature calculations here. For an ideal mixture that follows Raoult’s
law this becomes
∑
Antoine’s equation can be used to calculate the vapor pressure of each component.
( )
Where,
P is the vapor pressure A, B and C are component specific constants T is the temperature
Let us calculate the Dew point temperature of a mixture of Benzene (0.3),
Toluene (0.4) and m-Xylene (0.3) at a pressure of 1 bar.
The Antoine’s coefficient are given in the table below
A B C
Benzene 9.2806 2788.51 -52.36
Toluene 9.3935 3096.52 -53.67
m-Xylene 9.5188 3366.99 -58.04
Note: It is very important to pay attention to the UNITS of the temperature and Pressure as the
parameters have been obtained by regression and the units are very important. Our coefficients are
with temperature in K and pressure in Bars.
To get a first estimate we can get the boiling point of each component by inverting the Antoine’s
equation:
( )
BP (K)
Benzene 352.8266
Toluene 383.315
m-Xylene 411.76
Mole fraction averaged the first estimate is
yi yiT
Benzene 0.3 105.848
Toluene 0.4 153.326
m-Xylene 0.3 123.528
SUM 382.702
Calculate the vapor pressures at this temperature and sum the Liquid mole fractions:
yi PVap yi/PVap xi=yiP/PVap
Benzene 0.3 2.314785 0.129602 0.129602
Toluene 0.4 0.982652 0.407062 0.407062
m-Xylene 0.3 0.42658 0.703268 0.703268
P 0.806496 1.239932
Now take Benzene as or “key” component and get a new estimate of the temperature. We use the
following equation:
∑
Using the inverted Antoine’s equation we can now get a “new” estimate of the temperature as
Tnew = 391.33 (K)
PVap yi/PVap xi=yiP/PVap
Benzene 2.870176 0.139364 0.139364
Toluene 1.25006 0.239989 0.239989
m-Xylene 0.558087 0.537551 0.537551
P 1.090628 0.916903
New vapor pressure of “key” (Benzene) component is recalculated
Using the inverted Antoine’s equation we can now get a “new” estimate of the temperature as
Tnew = 387.8 (K)
yi Pvap yi/Pvap xi=yiP/Pvap
Benzene 0.3 2.631674 0.151995 0.151995
Toluene 0.4 1.134399 0.264457 0.264457
m-Xylene 0.3 0.500769 0.599079 0.599079
P 0.984707 1.015531
We are getting close:
New vapor pressure of “key” (Benzene) component is recalculated
Using the inverted Antoine’s equation we can now get a “new” estimate of the temperature as
Tnew = 388.42 (K)
yi Pvap yi/Pvap xi=yiP/Pvap
Benzene 0.3 2.672546 0.14967 0.14967
Toluene 0.4 1.154134 0.259935 0.259935
m-Xylene 0.3 0.510504 0.587654 0.587654
P 1.002748 0.997259
New vapor pressure of “key” (Benzene) component is recalculated
Using the inverted Antoine’s equation we can now get a “new” estimate of the temperature as
Tnew = 388.312 (K)
Since the temperature does not change by more than 0.2 (K) we have reached our solution: For grins we
can calculate the sum of liquid mole fractions.
yi Pvap yi/Pvap xi=yiP/Pvap
Benzene 0.3 2.672546 0.14967 0.14967
Toluene 0.4 1.154134 0.259935 0.259935
m-Xylene 0.3 0.510504 0.587654 0.587654
P 1.002748 0.997259
Thus our Dew Point Temperature for a mixture of Benzene (0.3), Toluene
(0.4) and m-Xylene (0.3) at 1 Bar is 388.12K.