a$)$ A diffused aeration system has Ka $=0\mathrm{.}150$ min$^-1$ for oxygen transfer. Assuming that the ratio kc$/$k for this system is $3\mathrm{.}0,$ compute the gas$-$ and liquid$-$phase mass transfer coefficients, ka and kl$,$ for oxygen, as well as the fraction of the total gas$-$transfer resistance that resides in each phase. For the given solution at the temperature of the test, Hec for oxygen is $30$ L$/$LG$.$

b$)$ As in the Onda correlations, assume that ka is proportional to D$^0\mathrm{.}5,$ and that kl is proportional to D$^0\mathrm{.}667.$ Using the following information, estimate:

$($i$)$ the liquid$-$ and gas$-$phase mass transfer coefficients for TCE

$($ii$)$ the overall mass transfer coefficient for TCE

$($iii$)$ the fraction of the total resistance in each phase for TCE.

D $($cm$/$s$)$ DG $($cm$/$s$)$ Hec $($Vi$/$Vc$)$

Oxygen $2\mathrm{.}03$ x $10^5$ TCE $1\mathrm{.}07$ x $10^5$

$0\mathrm{.}2190\mathrm{.}088$

$300\mathrm{.}32$

c$)$ The gas transfer equipment characterized in parts $($a$)$ and $($b$)$ is installed in an activated sludge reactor that operates as a steady$-$state CFSTR with a detention time of $2$h$.$ What fractional removal of TCE is expected to occur by stripping, assuming that the biological activity has no effect on TCE or gas transfer, and that TCE transfer is limited by interfacial transport $($i$.$e$.,$ it is kinetically or microscopically limited$).$

d$)$ Air is supplied to the activated sludge at a rate of $0\mathrm{.}05$ mG$/$m$.$min. Using this value in the full expression for the rate of gas transfer, find the value of k that, in essence, replaces K in the overall mass balance. Re$-$do part $($c$)$ with this new kinetic expression, and compare your answers.