$4\mathrm{.}12$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.The gas enters the tower at the rate of $1\mathrm{.}5$ m$3/$s$,$ measured at $110$ kPa and $298$ K$,$

containing $5$ mol$\%$ benzene. Essentially, all the benzene is absorbed by the

kerosene. The liquid enters the tower at the rate of $4\mathrm{.}0$ kg$/$s; the liquid density is

$800$ kg$/$m$3$ and the viscosity is $2\mathrm{.}3$ cP$.$ The packing will be metal Raschig SuperRings No$.2,$ and the tower diameter will be chosen to produce a gas$-$pressure drop

of $275$ Pa$/$m of irrigated packing. The gas viscosity, from Lucas method, is $1\mathrm{.}66\backslash$times

$105$ kg$/$m$-$s$.($a$)$ Calculate the tower diameter to be used, and the resulting fractional approach$$to flooding.

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

$($b$)$ Estimate the volumetric mass$-$transfer coefficients for the gas and liquid phases. Assume that D$$L $=5\mathrm{.}0\backslash$times $1010$ m$2/$s$,$ DG $=8\mathrm{.}85\backslash$times $106$ m$2/$s$.$

Answer: k$$Lah $=0\mathrm{.}00621$ s$1($c$)$ Assume that for the diameter chosen, the irrigated packed height will be $5$ m$$and that $1$ m 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: $3\mathrm{.}87$ kW

$4\mathrm{.}13$b$,$d$.$ Pressure drop in beds packed with structured packings

Redesign the packed bed of Problem $4\mathrm{.}12$ using Montz metal B$1-200$ structured packing. Estimate the corresponding mass$-$transfer coefficients. For this$$packing$,$ CS$,$T $=3\mathrm{.}116,$ CF$,$T $=2\mathrm{.}339,$ a $=200$ m$1,\backslash$epsi $=0\mathrm{.}979,$ Ch $=0\mathrm{.}547,$ Cp $=0\mathrm{.}355,$C$$L $=0\mathrm{.}971,$ and CV $=0\mathrm{.}390($Seader and Henley, $1998$; Billet and Schultes, $1999).$Answer: D $=0\mathrm{.}961$ m; k$$y$$a$$h $=0\mathrm{.}250$ kmol$/$m$3$s Please do $4\mathrm{.}13!$