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Solving a Binary Batch Distillation – Problem Description

Reference:

This is from E.M. Rosen and R. N. Adams, “A Review of Spreadsheet Usage in Chemical Engineering Calculations”, Computers and Chemical

www.wikipedia.org - Batch Distillation

www.wikipedia.org - Batch Distillation

Engineering, Vol. 11, No. 6, pp. 723-736, but they took it from Henley and Rosen, “Materal and Energy Balance Computations”, Wiley, NY 1969 pg. 362.  Very similar to an earlier problem that we did from Cutlip and Shacham.

Problem Description:

We need to find the composition of a ‘batch distillation‘ as a function of time.  Essentially, we need to solve the following ODE:

dxw/dt = -[D/W(t)]*(y – xw)

t = time, hours

xw = liquid composition, dimensionless

W(t) = -D*t + W(0), total amount remaining in ‘pot’, kg

D = overhead rate, kg/hr

y = α*xw/[1 + xw *(α – 1)], vapor composition, dimensionless

α = relative volatility, dimensionless

Initial Conditions:

D = 10.o kg/hr

W(0) = 100 kg

What is the composition at t = 5 hr?   Not so bad, we just need to solve a single initial value ODE.  Piece ‘o cake.

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