6.19 Consider the following cascade connection of isothermal reactors. A first-order reaction A Boccurs in both reactors, with reaction rate constant k. The volumes of liquid in the reactors, V, are constant and equal; the flow rates Fo, Fi, F2 and R are constant. Assume constant physical properties and a negligible time delay for the recycle line. Fo. Co R, C F1, C1 Figure E6.19 (a) Write a mathematical model for this process. (b) Derive a transfer function model relating the output con- centration of A, C2 to the inlet concentration of A, C (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 Ro), 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 FRF2 and FoF2
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6.19 Consider the following cascade connection of isothermal reactors. A first-order reaction A Boccurs in both reactors, with reaction rate constant k. The volumes of liquid in the reactors, V, are constant and equal; the flow rates Fo, Fi, F2 and R are constant. Assume constant physical properties and a negligible time delay for the recycle line. Fo. Co R, C F1, C1 Figure E6.19 (a) Write a mathematical model for this process. (b) Derive a transfer function model relating the output con- centration of A, C2 to the inlet concentration of A, C (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 Ro), 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 FRF2 and FoF2
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