A small city has recently discovered that one of its wells is contaminated with $200\frac{g}{L}$ TCE $($trichloroethene$,$

$C{l}_{3}H{C}_2).$ To continue using this well as a drinking water source, the TCE needs to be destroyed and the effluent

concentration of TCE cannot exceed $5\frac{g}{L}$ TCE. During normal pumping operations, the well produces water at

about $0\mathrm{.}025\frac{m^3}{s}.$ The concentration of bicarbonate $(HC{O}_3-)$ is $400m\frac{g}{L},$ the concentration of natural organic matter

$($NOM$)$ is $0\mathrm{.}7mg$ NOM$-$C$/$L$,$ and the $pH=7\mathrm{.}5.$ The physicochemical properties of TCE and NOM are as follows:

anote: For NOM, the units of the rate constant are: NOM$-$C $s.$ You can assume that the concentration

of carbonate $(C{O}_3^{2-})$ is negligible.

For simplicity, a proprietary AOP reactor system process$)$ will be used. It has been determined by

conducing tracer studies on the reactor that its hydraulic performance can be described using four CSTRs in$\_$series

$($each with a volume of $5500L).$

Determine the expected effluent concentration of TCE, given the following information:

$($i$)$ Assume that the $H_2{O}_2$ concentration is sufficiently large and that the pseudo first$-$order constant $(K_{\text{T}\text{C}\text{E}},s^{-1})$ can

be calculated using the Karimi equation provided below:

$K_{\text{T}\text{C}\text{E}}=\frac{K_{\text{T}\text{C}\text{E}\text{,}OH}*K_{L}a*[O_3{]}_{\text{t}\text{r}\text{a}\text{n}\text{s}\text{f}\text{e}\text{r}\text{r}\text{e}\text{d}}}{(k_{\text{H}\text{C}\text{O}3-,OH}*[HC{O}_3^{-}])+(k_{\text{N}\text{O}\text{M}\text{,}OH}*[NOM])+(k_{\text{T}\text{C}\text{E}\text{,}OH}*[\text{T}\text{C}\text{E}])}$

Where: $K_{\text{T}\text{C}\text{E}\text{,}OH}=$ second$-$rate constant of TCE with second$-$rate constants for the

reaction of the species e$.$g$.,HC{O}_3^{-},$ and $\{$:NOM$)$ with $*OH(L(mols)),$ and $K_{L}a=$ overall mass transfer coefficient

for $O_3(s^{-1}).$

$($ii$)$ The transferred $O_3$ dose is $3\mathrm{.}44m\frac{g}{L}.$

$($iii$)K_{L}a,$ at the working temperature, was measured to be $6{100}^{-4}{s}^{-1}.$

Note: You can use the following equation to calculate the TCE concentration $(C)$ in the effluent of the last CSTR

reactor:

$C=\frac{C_0}{(1+K_{\text{T}\text{C}\text{E}}*{)}^4}$

Where: $=$ Hydraulic retention time of a given reactor $($seconds$)$;

$Co=$ TCE concentration in the influent of the first reactor $(mo\frac{l}{L})$

$C=$TCE concentration in the effluent of the last reactor $(mo\frac{l}{L})$