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
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
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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Transcribed Image 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
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