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Specialization Project 2012:
Optimal Operation of Parallel Systems
Stian Aaltvedt
Supervisors: Sigurd Skogestad
Johannes Jäschke
Stian Aaltvedt, Optimal Operation of Parallel Systems, Dec 13 2012
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THE JÄSCHKE TEMPERATURE
OPTIMAL OPERATION OF
HEAT EXCHANGER NETWORKS
?
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Optimal Operation of
Heat Exchanger Networks …
• Objective function ?
• Equality constraints ?
• Inequality constraints ?
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Optimal Operation of
Heat Exchanger Networks …
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Optimal Operation of
Heat Exchanger Networks …
Equality constraints:
Jäschke
Temperature
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Optimal Operation of
Heat Exchanger Networks …
Equality constraints:
Jäschke
Temperature
Inequality constraints:
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Case Studies …
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Case Studies …
Disturbances:
• Inlet cold stream temperature T0
• Inlet cold stream heat capacity w0
•
•
Inlet hot stream temperature Thi
Inlet hot stream heat capacity whi
Manipulated variable:
• Stream split (w1 or w2)
Controlled variables:
• Outlet temperature Tend
• Heat exchanger size UAi
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The procedure …
INITIAL
DISTURBANCES
Optimize subject to object
function and constraints
OPTIMAL DESIGN
Outlet temperature from
optimal design
=
outlet temperature from
optimal opreation
?
Optimized
UA values
JÄSCHKE
OPTIMAL OPERATION
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The Jäschke Temperatures …
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Case 1 Results
GIVEN DATA
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Case 1 Results
GIVEN DATA
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Case 1 Results
GIVEN DATA
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Case 2 Results
GIVEN DATA
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Case 3 Results
GIVEN DATA
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Case 3 Results
GIVEN DATA
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Conclusions and Further Work
For steady state parallel systems:
• The Jäschke Temperature showed good
results compared to the optimal design
For real, dynamic systems:
• Further investigation needed, including
dynamic simulations
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Thank you!