$4\mathrm{.}12{?}^{b,d}.$ Pressure drop and mass$-$transfer coefficients in beds packed with fourth$-$generation random packings

A packed tower is to be designed for the countercurrent contact of a benzene$-$nitrogen gas mixture with kerosene to wash out the benzene from the gas.

Problems

$271$

The gas enters the tower at the rate of $1\mathrm{.}5\frac{m^3}{s},$ measured at $110$kPa and $298K,$ containing $5$mol$\%$ benzene. Essentially, all the benzene is absorbed by the kerosene. The liquid enters the tower at the rate of $4\mathrm{.}0k\frac{g}{s}$; the liquid density is $800k\frac{g}{m^3}$ and the viscosity is $2\mathrm{.}3cP.$ The packing will be metal Raschig SuperRings No$.2,$ and the tower diameter will be chosen to produce a gas$-$pressure drop of $275P\frac{a}{m}$ of irrigated packing. The gas viscosity, from Lucas method, is $1\mathrm{.}66{10}^{-5}k\frac{g}{m}-$s$.$

$($a$)$ Calculate the tower diameter to be used, and the resulting fractional approach to flooding.

Answer: $f=0\mathrm{.}82,D=0\mathrm{.}885m$

$($b$)$ Estimate the volumetric mass$-$transfer coefficients for the gas and liquid phases. Assume that $D_L=5\mathrm{.}0{10}^{-10}\frac{m^2}{s},D_G=8\mathrm{.}85{10}^{-6}\frac{m^2}{s}.$

Answer: $k_L{a}_h=0\mathrm{.}00621s^{-1}$

$($c$)$ Assume that for the diameter chosen, the irrigated packed height will be $5m$ and that $1m$ of unirrigated packing will be placed over the liquid inlet to act as entrainment separator. The blower$-$motor combination to be used at the gas inlet will have an overall mechanical efficiency of $60\%.$ Calculate the power required to blow the gas through the packing.

Answer: $3\mathrm{.}87kW$