We want to assess the effectiveness of disinfection by chlorine (in HClO form) of several different configurations of the same chlorination tank. The chlorine concentration in water is noted C (mg/l). It is used to destroy, in water that must be made drinkable, several types of microorganisms, whose concentrations are referred to by the letter N (number/l). The data relating to the tank are as follows:

Cylindrical tank

Diameter = 20 m

Water height = 3.2 m

Inlet flow rate = outlet flow rate = 1000 m3/h

The tank may be equipped with baffles (inner walls) making it possible, at least in theory, to divide it into a series of n perfectly mixed reactors placed in series. The applied chlorine dose is 3 mg/l and the immediate demand for chlorine by water (due to the oxidation of organic compounds) is estimated at 1 mg/l (the chlorine concentration at the inlet of the tank is 2 mg/l). The decomposition of chlorine in water results in a disappearance of chlorine according to a first order kinetics with respect to the chlorine concentration (kinetic constant k of 0.02 min-1): rC = -k C. When entering the tank, the water contains several types of microorganisms with concentrations (Ne) presented in the table below. The maximum authorized concentrations of these microorganisms at the exit of the tank are also given in the table below.

	Ne (nb/l)	Max. authorized (nb/l)	k (l/min/mg)
Escherichiacoli	100 000	2	100
Gardia	100	2	0,09

It is assumed that the degradation kinetics of a given type of microorganisms by chlorine, noted rN and expressed in number of microorganisms destroyed per liter and per minute, can be calculated according to the following kinetic law: rN = -k' N C where k is a kinetic constant (depending on the microorganism type), given in the table above, for each considered microorganism type.

Questions. In how many perfectly mixed zones placed in series and of the same volume should the tank be divided so that sanitary standards are respected? Propose a schematic representation of a division by baffles of the tank making it possible to reach (at least in theory) such a number of perfectly mixed zones in series. For n (number of perfectly mixed zones in series) tending to infinity, what is the limit of the Gardia concentration at the outlet of the tank?