Where Pa and Pb are the vapor pressures of components a and b at a given temperature.
The partial pressure p of component a above a binary ideal solution can be calculated by pa = Paxa
Where xa is the mole fraction of component a in the liquid. Similarly in a binary mixture, for component b. pb = Pb-xb
Notice that the sum of the partial pressures must equal the total system pressure: P=pb+pa. For non ideal mixtures (usually the case with steam stripping duties), the partial pressure is calculated from
Where y is the activity coefficient of the compound. The activity coefficient essentially quantifies the deviation from ideality.
For multicomponent mixtures, the mathematical representation of the VLE becomes more complex. It is necessary to use complex equations to predict the performance. The simplification commonly used as a substitute for the rigorous equations is K value. ya=Kxa. The ratio of the K value of different components reflects the relative volatilities between those components.
It is not the intention of this publication to discuss methods for calculating a distillation system. Classical graphical calculations have been the McCabe-Thiele method, using the data shown in Figure 2, and the Ponchon Savarit method, which is more accurate and uses an enthalpy diagram, as shown in Figure 3, as well as the VLE data.
All these graphical methods have been rendered obsolete by the various process simulation programs, such as SimSci. Even with these highly sophisticated programs, there is still a need for test work on many systems. For ideal mixtures, which are rare, the program will provide a theoretically correct solution. For non ideal mixtures, the program can only make estimates by using thermodynamic equations such as UNIFAC. Experimental data can be used for more precise solutions. A considerable amount of experimental data, however, is in the program database.
(1) ETHANOL
PRESSURE- 760.00 MM HG ( 1.013 BAR ) LT: DALAGER P . , J . CHEM . ENG . DATA 14,298 ( 1969 ) .
CONSTANTS:
MARGULES 1.7577
VAN LAAR 1.7850
WILSON 419.1380
NRTL -222.4277
UNIQUAC -94.6899
A21 0.7243 0.8978 911.1302 1557.2947 427.5173
Figure 2.
C2H6O H2O
CONSISTENCY METHOD 1 -METHOD 2 +
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Yr = 6.01 Yr= 2.62 | |||||||
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V |
ALPHA12 1200 1100 ^1000 CM CO ra 900 700 600 500 400 300 200 Si 100 -100 Figure 3. Calculations by enthalpy-composition diagram. 3 C7 LU 0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.1 Mass Fraction Ethanol Water Mixtures Figure 3. Calculations by enthalpy-composition diagram. |
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