The reaction A → B takes place in two reactors in series as shown in the image. The reactors are well-mixed but are not at steady-state. The unsteady-state mass balance for each stirred tank reactor is shown below: dc A1 dC₁₁ = 1½-½ (CA0 - C₁₁) - KC A1 dt dC B1 dt τ AO A1 C=C1+kCA dC A2 dt dC dt B2 = = τ B1 τ - (C1-C2) KC A1 (C1-C2)- KC τ B1 B2 A2 B2 where CA0=concentration of A at the inlet of the first reactor CAI= concentration of A at the outlet of the first reactor (and inlet of the second) CA2= concentration of A at the outlet of the second reactor CBI = concentration of B at the outlet of the first reactor (and inlet of the second) CB2= concentration of B in the second reactor T= residence time for each reactor k = rate constant for reaction of A to produce B If CA is equal to 20 mol/L, find the concentrations of A and B in both reactors during their first 10 minutes of operation using 4th order Runge-Kutta Method, with At = 0.10. Use k = 0.12/min and T = 5 minutes, and assume that the initial conditions of all the dependent variables are zero. In addition, make concentration profiles by plotting all the concentrations as a function of time for each chemical species.
The reaction A → B takes place in two reactors in series as shown in the image. The reactors are well-mixed but are not at steady-state. The unsteady-state mass balance for each stirred tank reactor is shown below: dc A1 dC₁₁ = 1½-½ (CA0 - C₁₁) - KC A1 dt dC B1 dt τ AO A1 C=C1+kCA dC A2 dt dC dt B2 = = τ B1 τ - (C1-C2) KC A1 (C1-C2)- KC τ B1 B2 A2 B2 where CA0=concentration of A at the inlet of the first reactor CAI= concentration of A at the outlet of the first reactor (and inlet of the second) CA2= concentration of A at the outlet of the second reactor CBI = concentration of B at the outlet of the first reactor (and inlet of the second) CB2= concentration of B in the second reactor T= residence time for each reactor k = rate constant for reaction of A to produce B If CA is equal to 20 mol/L, find the concentrations of A and B in both reactors during their first 10 minutes of operation using 4th order Runge-Kutta Method, with At = 0.10. Use k = 0.12/min and T = 5 minutes, and assume that the initial conditions of all the dependent variables are zero. In addition, make concentration profiles by plotting all the concentrations as a function of time for each chemical species.
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:The reaction A → B takes place in two reactors in series as shown in the image. The reactors are
well-mixed but are not at steady-state. The unsteady-state mass balance for each stirred tank reactor is
shown below:
dC
A1
dt
dC
B1
dt
dC
A2
dt
dC
B2
=
dt
=
=
1
-+-+-(CA0 - CA1) - KC A1
T
AO
=
+/+CB₁+kC
KC
B1
T
1
+(CB₁ - CB2) - KC B2
B1
where CAO concentration of A at the inlet of the first reactor
A1
+-+-+-(CA₁ - CA₂) - KC A2
A1
CAL = concentration of A at the outlet of the first reactor (and inlet of the second)
CA2= concentration of A at the outlet of the second reactor
CBI concentration of B at the outlet of the first reactor (and inlet of the second)
=
CB2= concentration of B in the second reactor
T = residence time for each reactor
k
=rate constant for reaction of A to produce B
If CAO is equal to 20 mol/L, find the concentrations of A and B in both reactors during their first 10
minutes of operation using 4th order Runge-Kutta Method, with At = 0.10. Use k = 0.12/min and
T = 5 minutes, and assume that the initial conditions of all the dependent variables are zero. In
addition, make concentration profiles by plotting all the concentrations as a function of time for each
chemical species.
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