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ENGR 4457 Separation Process Principles

The Rayleigh Equation (see below) is used for calculations in simple batch distillation processes.
∫ ∫ −
= = 1
2
1
2 2
ln 1 L
L
x
x y x
dx
L
L
L
dL
(11.3-10)
In which L1 is the original moles of charge of composition x1, L2 is the moles of residue liquid of
composition x2.
a) For a simple distillation system, if the relative volatility is quite constant and the average
value is α av over the concentration range involved, prove that Rayleigh equation
becomes:
1
2
2 1
1 2
2
1
1
ln1
(1 )
ln (1 )
1
ln 1
x
x
x x
x x
L
L
av −

+



=
α [20 marks]
b) For the system of n-heptane/n-octane at 1 atm, α av = 2.16. Now a liquid with 50mol%
n-heptane and 50% mol% n-octane was charged for a batch distillation at 1 atm. Using
the above derived equation, compute the composition of the residue after 60 mol% of the
feed is batch distilled. [10 marks]
2
Problem 4. [30 marks]
An adiabatic distillation column operating at 0.5 atmospheres total pressure takes in a saturated
vapour feed containing 40% hexane and 60% toluene. A total condenser is used and the distillate and
bottoms are specified at 90% and 2% hexane, respectively. (All molar percentages). Equimolar
overflow may be assumed.
The equilibrium data for the hexane-toluene system at 0.5 atm. pressure can be reasonably well
represented by a constant relative volatility of “αHT = 4.02.
(a) On a basis of 100 kmol/hr of feed calculate the amount of distillate and residue produced.
(b) Get out the equilibrium line in the y-x plot.
(c) Assuming a reflux ratio of 3.88, and that the feed enters the column at the optimal location,
calculate the number of theoretical plates required to meet the column specifications.
(d) For Total Reflux, find the minimum number of theoretical plates (using which equation?) and
check calculation from the graphical construction.
(e) Calculate the minimum reflux ratio analytically and check this calculation from the graphical
construction.
(f) Assuming a reflux ratio of 3.88, and that the feed enters the column at the 6th ideal plate from
the top, calculate the number of theoretical plates required to meet the column specifications.
{same as part (c) but stay on the upper operating line until the 6th plate, then switch to the lower
operating line}
(g) For the condition in part (f), calculate the flow rates of liquid and vapour above and below the
feed inside the column.

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