EXAMPLE $12\mathrm{.}3-1.$ Scale$-$Up of Laboratory Adsorption Column

A waste stream of alcohol vapor in air from a process was adsorbed by activated carbon particles in a packed bed having a diameter of $4cm$ and length of $14cm$ containing $79\mathrm{.}2g$ of carbon. The inlet gas stream having a concentration $c_o$ of $600ppm$ and a density of $0\mathrm{.}00115\frac{g}{c}{m}^3$ entered the bed at a flow rate of $754c\frac{m^3}{s}.$ Data in Table $12\mathrm{.}3-1$ give the concentrations of the breakthrough curve. The break$-$point concentration is set at $\frac{c}{c_o}=0\mathrm{.}01.$ Do as follows.

$($a$)$ Determine the break$-$point time, the fraction of total capacity used up to the break point, and the length of the unused bed. Also determine the saturation loading capacity of the carbon.

TABLE $12\mathrm{.}3-1.$ Breakihrough Concentration for Example $12\mathrm{.}3-1$

$\backslash$table$[[$Time $h,\frac{c}{c_o},$Time, $h,\frac{c}{c_o}$