Postaeration$$ tanks are CFSTRs that are designed to

increase the oxygen concentration of a wastewater

after biological treatment and before discharge to a

receiving water. In a typical design situation, the

oxygen concentration in the influent to the postaeration system and the required effluent concentration

would both be known, along with the liquid flow rate.

Assume that this oxygen transfer is accomplished

by an air diffuser system.

$($a$)$ Develop an expression for the minimum volume

of a CFSTR that could achieve a specified postaeration goal $($i$.$e$.,$ a specified dissolved oxygen

concentration$),$ using an aeration system with

known KLaL $.$ Your result should be an algebraic

expression for the volume in terms of known

quantities. Indicate how each of those quantities

is known $($i$.$e$.,$ what in the description above

allows you to know each quantity of interest?$).$

Assume that all oxygen demands $($i$.$e$.,$ reactions

that consume oxygen$)$ have been exerted in

treatment prior to the postaeration tank, so

that the only reaction that occurs is gas $($oxygen$)$

transfer. Assume also that gas transfer is kinetically limited$.$

$($b$)$ What is the required volume if two equi$-$sized

CFSTRs in series are used, each equipped with

the same type of diffuser system as considered

in part $($a$)?$ What is the ratio of the volume

required for the two$-$reactor system to that

required for the one reactor system?