First Order Systems In Series, No Interaction

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First Order Systems In Series, No Interaction

• Two CSTRs in series

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CSTRs In Series, no interaction
FA, CA0
FA1, CA1
A
B
k
A
B
k
FA2, CA2
Initial Conditions are at t0----gt
CA2(t0)kp2kp1 CA0init CA1(t0) kp1
CA0init
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Impose a Disturbance on the Input Concentration
CA0
CA0(tgt0)
CA0init
t0
t
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Solution To the Problem
Observation of the governing material balance
equations clearly shows that the behavior of the
first tank depends on the changes imposed on the
input. It does not depend on the behavior of the
second tank.
Solution to this equation results to the already
known result of
Where ?1 is the characteristic time for the first
tank
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Response of First Tank
CA1
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Second Tank ?
The output of the first tank is now the input to
the second tank
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Solution
Can be easily solved using the integrating factor
method
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Interacting Systems in Series

• ChE 479

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Interacting Mixing Tank in Series
Key Feature Information from second process
effects the first process!
FA
FA2
h2
h1
FA1
Initial Conditions are at t0----gt h1(t0) h10
h2(t0) h20
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CSTR in Series With Recycle
R Percentage of Total Flow Rate that is recycled
A---gtB
FA, CA0
FA1, CA1
h1
FA2, CA2
h2
A---gtB
Initial Conditions are at t0----gt
CA1(t0)kp2kp1 CA0init CA2(t0) kp1
CA0init
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Dynamic Model of a Level in a Tank

• Model equation is based on dynamic conservation
  of mass, i.e., accumulation of mass in the tank
  is equal to the mass flow rate in minus the mass
  flow rate out.

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Dynamic Model for Tank Level

• Actuator on flow out of the tank.
  
• Process model
• Level sensor since the level sensor is much
  faster than the process and the actuator

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Model for Product Composition for CSTR with a
Series Reaction