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Question 12.6: It is proposed to use an existing distillation column, which...

It is proposed to use an existing distillation column, which is fitted with a dephlegmator (reflux condenser) which has 200 vertical, 50 mm i.d., tubes, for separating benzene from a mixture of chlorobenzenes. The top product will be 2500 kg/h benzene and the column will operate with a reflux ratio of 3. Check if the tubes are likely to flood. The condenser pressure will be 1 bar.

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The vapour will flow up and the liquid down the tubes. The maximum flow rates of both will occur at the base of the tube.

 

\text { Vapour flow }=(3+1) 2500=10,000 kg / h

 

\text { Liquid flow }=3 \times 2500=7500 kg / h

 

\text { Total area tubes }=\frac{\pi}{4}\left(50 \times 10^{-3}\right)^{2} \times 200=0.39 m ^{2}

 

Densities at benzene boiling point

 

\rho_{L}=840 kg / m ^{3}, \quad \rho_{v}=2.7 kg / m ^{3}

 

Vapour velocity (vapour flowing alone in tube)

 

u_{v}=\frac{10,000}{3600 \times 0.39 \times 2.7}=2.64 m / s

 

Liquid velocity (liquid alone)

 

u_{L}=\frac{7500}{3600 \times 0.39 \times 840}=0.006 m / s

 

From equation 12.55 for no flooding

 

\left[u_{v}^{1 / 2} \rho_{v}^{1 / 4}+u_{L}^{1 / 2} \rho_{L}^{1 / 4}\right]<0.6\left[g d_{i}\left(\rho_{L}-\rho_{v}\right)\right]^{1 / 4} (12.55)

 

\left[u_{v}^{1 / 2} \rho_{v}^{1 / 4}+u_{L}^{1 / 2} \rho_{L}^{1 / 4}\right]<0.6\left[g d_{i}\left(\rho_{L}-\rho_{v}\right)\right]^{1 / 4}

 

\begin{array}{c}{\left[(2.64)^{1 / 2}(2.7)^{1 / 4}+(0.006)^{1 / 2}(840)^{1 / 4}\right]<0.6\left[9.81 \times 50 \times 10^{-3}(840-2.7)\right]^{1 / 4}} \\{[2.50]<[2.70]}\end{array}

 

Tubes should not flood, but there is little margin of safety.

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