Consider the following cascade connection of isothermal reactors. A first-order reaction A †’ B occurs in both reactors, with reaction rate constant k. The volumes of liquid in the reactors,V, are constant and equal; the flow rates F₀, F₁, F₂and R are constant. Assume constant physical properties and a negligible time delay for the recycle line.

(a) Write a mathematical model for this process.
(b) Derive a transfer function model relating the output concentration of A, C₂ to the inlet concentration of A, C₀.
(c) Verify that, in the limit of no recycle (R †’ 0), the transfer function derived in (b) is equivalent to the transfer function of the two tanks connected in series.

Fo, Co R, C2 F2, C2 F1, C1 Figure E6.19