$13\mathrm{.}6$ GAC design based on economic analysis: A treatability study was conducted for the treatment of $2,4-$dichloroaniline in an industrial waste stream being released from a dye manufacturing plant. The study was conducted in columns $5$ cm in diameter and $2$ m high. The pilot study was conducted at five different flow rates, which are listed below along with corresponding values for $\backslash ($ a $\backslash )$ and $\backslash ($ D $\backslash ).$

Using the pilot data, determine the dimensions of each of the full$-$scale GAC systems and the time until carbon exhaustion. $($Use the carbon exhaustion time as the time at which regeneration will take place.$)$ The full$-$scale flow rate is $\backslash (8000\backslash$mathrm$\{$~m$\}^\{3\}/\backslash )$ day. Because the value of $\backslash ($ D $\backslash )$ is small, design for one column.

Next, select the most cost$-$efficient design based on system cost. Cost data for the full$-$scale systems include:

Cost of GAC: $\backslash (\backslash$$ $1540/\backslash$mathrm$\{$m$\}^\{3\}\backslash ).$ The full quantity of GAC is purchased only at the beginning of the project. At each regeneration, $\backslash (10\backslash \%\backslash )$ of the carbon is lost and is replaced as part of the cost of regeneration $($listed below$).$

Cost of contactor including piping, distribution system, plenum support plate, etc.: $\backslash (\backslash$$ $12,820/\backslash$mathrm$\{$m$\}^\{3\}\backslash )$ of contactor.

Regeneration cost $($including transportation costs, cost of regeneration, and replacement of lost carbon$)$: $\backslash$$$2200($Round up regenerations$/$year to the nearest whole number$).$

Design life for system: $10$ years

$\backslash [$

i$=8\backslash \%$

$\backslash ]$