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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 Fo, F1, F2 and R are constant. Assume constant physical properties and a negligible time delay for the recycle line. Fo, Co R, C2 F1, C 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, C2 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 Ro), the transfer function derived in (b) becomes the transfer function of a single tank that has the volume eqto 2V and a gain of one. Hint: Recognize that F1 R+ F2 and Fo F2

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 Fo, F1, F2 and R are constant. Assume constant physical properties and a negligible time delay for the recycle line. Fo, Co R, C2 F1, C 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, C2 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 Ro), the transfer function derived in (b) becomes the transfer function of a single tank that has the volume eqto 2V and a gain of one. Hint: Recognize that F1 R+ F2 and Fo F2

Introduction to Chemical Engineering Thermodynamics
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
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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 Fo, F1, F2 and R are constant. Assume constant physical properties and a negligible time delay for the recycle line. Fo, Co R, C2 F1, C 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, C2 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 Ro), the transfer function derived in (b) becomes the transfer function of a single tank that has the volume eqto 2V and a gain of one. Hint: Recognize that F1 R+ F2 and Fo F2
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 Fo, F1, F2 and R are constant. Assume constant physical properties and a negligible time delay for the recycle line. Fo, Co R, C2 F1, C 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, C2 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 Ro), the transfer function derived in (b) becomes the transfer function of a single tank that has the volume eqto 2V and a gain of one. Hint: Recognize that F1 R+ F2 and Fo F2
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