4 continuous stirred tank reactors cstrs of equal volume are often use

Question

4. Continuous stirred tank reactors (CSTRS) of equal volume are often used in series toperform reactions. (a)Show that the generalised design performance equation for a CSTR operating in series may be written as: \tau_{i}=\frac{C_{A(i-1)}-C_{A i}}{r_{i}} where t; is the residence time (s) in tank i, CA the concentration (mol m³) of raw material A and r; the reaction rate (mol m3 s). A second order reaction is conducted in such a CSTR train and the rate expression is given as: r = 0.02 + 0.0012[CĄ]? where r (mol m-3s-1) is the reaction rate and CA (mol m-3) is the concentration of raw material A. If the system is operating at steady state, the flow rate to first tank is 3.25 L s', the concentration of material A entering the reactor train is 9 mol m3, the total conversion is 88.9% and the concentration exiting the first tank is 6 mol m3, estimate: (b)The number of tanks required to perform this operation. (c)The residence time (seconds) in each tank. The volume (m³) of each of the tanks. A proposal has been made to use two tanks of non-equal size for the above reaction operation. Is this a sensible proposal and what would be the impact of this process change to the existing plant?