c) Using deviation variables, derive the response when the inlet concentration increase in a step by 1 kg m-³. Again the solution is the one we obtained during the lecture, although in this case with specific numerical values for the time constant and steady-state gain. c* (t) = 1 50 [1 – exp(-2.5t)]
c) Using deviation variables, derive the response when the inlet concentration increase in a step by 1 kg m-³. Again the solution is the one we obtained during the lecture, although in this case with specific numerical values for the time constant and steady-state gain. c* (t) = 1 50 [1 – exp(-2.5t)]
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
Related questions
Question
A continuous stirred tank reactor is used to break down a chemical in an irreversible first-order reaction. The reactor has a volume of 10 m3 and nominal inlet and outlet concentrations of the chemical of 5 kg m-3 and 0.1 kg m-3 respectively. The flowrate through the reactor is perfectly controlled at 0.5 m3 h -1 .
a) Derive a dynamic model for the reactor.
b) By considering steady state, calculate the reaction rate constant.
c) Using deviation variables, derive the response when the inlet concentration increase in a step by 1 kg m-3
COULD SOMEONE SHOW HOW TO REACH ANSWER FOR PART C I HAVE ATTACHED WORKING AND FEEDBACK TO HELP
PLEASE DONT COPY AND PASTE FROM OTHER ANSWERS
Transcribed Image Text:A)
B)
VdCA
de
Steady State
K=
dcA
dt
0 = FCAIN
=0
vdCA =
dt
1+ke=0
FCA
CAIN CA- KOCA
=
-
CAN-CA
SA
FLA-FCA - KVCA
dca = CAIN- CA
dt
CA = CA -
CAM: CA
FCAIN - FCA -KVCA
- KOCA
= CAN-CA (1+10)
I+KO
deviation variables:
tdcA= K CAIN- CA
dt
↑
- CASS
Idea = KCAIM-
dt
KVCA
2.45hr
CAMM
tdC₁ = K (C₁²76) - (C₂² + cx₂) |
de
CAK
toca = Kean-Cat
dt
des
KCAIM-CA
C²(t) = KCAM
dt
exp
XEAN (1 - 200 (- =))
K(AS) - CAS
in
![a) Derive a dynamic model for the reactor.
The model is the same as the one we found during the lecture.
b) By considering steady state, calculate the reaction rate constant.
Set the accumulation term to zero for steady-state. Sub in the steady-state
values of concentration that were provided and rearrange for k. Pay attention
that the units of k are consistent with the order of reaction.
Ꮎ ;
V
F
= 20 h k
c* (t)
=
-
c) Using deviation variables, derive the response when the inlet concentration
increase in a step by 1 kg m-³.
1
1 Cin - Css
0 Css
Again the solution is the one we obtained during the lecture, although in this case
with specific numerical values for the time constant and steady-state gain.
50
4.9
0.1 × 20
= 2.45 h-¹
[1 – exp(-2.5t)]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fde55ad6b-27eb-44c5-bca1-afdb32f2dfc7%2F937ae3fa-c63c-4fa9-ae55-8fbdd3ac42aa%2Fqoovdrb_processed.png&w=3840&q=75)
Transcribed Image Text:a) Derive a dynamic model for the reactor.
The model is the same as the one we found during the lecture.
b) By considering steady state, calculate the reaction rate constant.
Set the accumulation term to zero for steady-state. Sub in the steady-state
values of concentration that were provided and rearrange for k. Pay attention
that the units of k are consistent with the order of reaction.
Ꮎ ;
V
F
= 20 h k
c* (t)
=
-
c) Using deviation variables, derive the response when the inlet concentration
increase in a step by 1 kg m-³.
1
1 Cin - Css
0 Css
Again the solution is the one we obtained during the lecture, although in this case
with specific numerical values for the time constant and steady-state gain.
50
4.9
0.1 × 20
= 2.45 h-¹
[1 – exp(-2.5t)]
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