Fo, CoR, C2V.F1, C1F2, C2Figure E6.19(a) Write a mathematical model for this process.(b) Derive a transfer function model relating the output con-centration of A, C, to the inlet concentration...

Extracted text: 6.19 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 F, F,, F, and R are constant. Assume constant physical properties and a negligible time delay for the recycle line. 1> Fo, Co R, C2 V. F1, C1 F2, C2 Figure E6.19 (a) Write a mathematical model for this process. (b) Derive a transfer function model relating the output con- centration of A, C, to the inlet concentration of A, Co. (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. (d) Show that when k = 0 and a very large recycle flow rate is used (i.e., the limit as R 0), the transfer function derived in (b) becomes the transfer function of a single tank that has the volume equal to 2V and a gain of one. Hint: Recognize that F, = R+ F, and F, F,. %3D -> %3D