In all bubble-point calculations, we know the composition of the liquid (x/s are all given). In addition we must be given either the pressure or the temperature of the system. The problem is to calculate the unknown temperature or pressure and the composition of the vapor phase (j>y).
Bubble-Point Temperature Calculation. This is by far the most common type of calculation encountered in distillation work because column pressure is usually known. The calculation procedure is iterative:
1. Guess a temperature T.
2. Calculate vapor pressures of all components at T.
3. Calculate:
where
Nc = number of components
4. Check to see if Pctc is sufficientiy close to PT.
5. If not, reguess T and go back to step 2. If P^c is less than P, increase T. If Pctc is greater than PT, decrease T.
6. When convergence has been achieved, calculate vapor compositions.
Example. Given:
O-Xylene (X) x3 = 0.25 Guess T = 120°C Guess T = 125°C P; at P, at
B 0.40 2300 920 2600 1040 0.671
T 0.35 1000 350 1140 399 0.258
Notice the enriching of lighter component that occurs in the vapor in the above example. Benzene, the lightest component, has a higher concentration in the vapor than in the liquid. O-Xylene, on the other hand, the heaviest component, has a higher concentration in the liquid than in the vapor. This illustrates precisely why a distillation column can be used to separate chemical components. The vapor rising in the column gets richer and richer in light components at each stage. The liquid moving down the column gets richer and richer in heavy components.
Bubble-Point Pressure Calculation. In this case temperature T and liquidphase composition are known. Total system pressure is easily calculated (with no iteration involved) from:
Vapor pressures Pt are known since temperature is given.
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