In a laboratory experiment you are trying to create a system that can replicate the

advantages associated with a plug flow process for an activated sludge process to treat highly concentrated waste. As a result, you are using a series of $5$ aerated mixed reactors. Each reactor is $10$ m $3$ and the total flow into the system is $5$ m$3/$hr$.$ The first order reaction coefficient is $0\mathrm{.}4$ hr$-1.$ The inlet concentration of BOD is $985$ mg$/$L$.$

a$.$ If there is no recycled sludge, what is the expected BOD concentration in the

effluent.

b$.$ What is the ratio of this system $($effluent concentration$)$ compared to an ideal plug flow reactor of the same volume $($ignore the volume of piping in your system$).$

c$.$ You find that the answer in part a above cannot be achieved without sludge recycle because there are not enough microorganisms to achieve the reaction rate as specified. So in order to do so we install a sludge recycling system with a recycle flow rate of $1$ m $3/$hr$,$ a sludge effluent flow of $1$ L$/$hr and a $99\mathrm{.}99\%$ biomass removal efficiency in the secondary settling tank $($Note: Final BOD in effluent will change and it is recycled, therefore a mass balance is required$).$ Please plot the Biomass Production rate $($mg$/$L $/$ hr$)$ and BOD concentration versus the tank number $($ie $1-5).$ The Yield, Y$=0\mathrm{.}42$ mg$/$L Biomass $/$ mg$/$L BOD.

d$.($What is the Biomass concentration in the sludge effluent?