if the digester is modelled as a single well$-$mixed CSTR$,$ then the reaction rates $($for both substrate consumption and biomass generation$)$ are quite low, as the substrate concentration within the total digester volume is the same as that leaving the system $($i$.$e$.$ around $5$ mg $/$L to meet discharge requirements$).$ Rather than use a membrane bioreactor system, one commonly used means of reducing digester volume is to use internal baffles so that the digester effectively behaves like several CSTR$$s in series. In the extreme case, it is possible to envisage an infinite number of infinitely small CSTR$$s in series. This arrangement is equivalent to using a plug$-$flow reactor.

$1.$ Develop a mass balance model that describes the case where the aerobic digester consists of three well$-$mixed reactors in series. Assume that all reactors have the same volume. Clearly note any additional assumptions that you make.

$2.$ Estimate the total volume $($in m$3)$ of a three CSTR$$s in series digester that gives an exit substrate concentration of $5$ mg BOD$/$L

Note$-$ Use the image and notation used $in$ figure just change the reactor $to3cstr$ and build the equation accordingly.