Throughput maximization by improved bottleneck control

1
Throughput maximization by improved bottleneck
control

• Elvira Marie B. Aske, Sigurd Skogestad and
  Stig Strand
• Department of Chemical Engineering, Norwegian
  University of Science and Technology, Trondheim,
  Norway
• Statoil RD, Process Control, Trondheim, Norway

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Outline

• Modes of optimal operation
• Maximum throughput
• Throughput manipulator (TPM)
• Max-flow min-cut theorem
• Realizing maximum throughput
• Single-loop
• MPC
• Back off
• Conclusions

3
Depending on marked conditions Two main modes of
optimal operation

• Mode 1. Given throughput (nominal case)
• Given feed or product rate
• Maximize efficiency Unconstrained
  optimum (trade-off)
• Mode 2. Max/Optimum throughput
• Throughput is a degree of freedom good
  product prices
• 2a) Maximum throughput
• Increase throughput until constraints give
  infeasible operation
• Constrained optimum - identify active
  constraints (bottleneck!)
• 2b) Optimized throughput
• Increase throughput until further increase is
  uneconomical
• Unconstrained optimum

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Mode 2a Maximum throughput

• Typical profit function
• Feed flows are set in proportion to F and assume
  constant efficiencies
• Leads to
• Maximize profit ? Maximize throughput F

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Throughput manipulator (TPM)
Buckley (1964). Techniques of Process
Control Price, Lyman and Georgakis (1994).
Throughput manipulation in plantwide control
structures. Ind. Eng. Chem. Res. 33, 11971207.
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From network theory Max-flow min-cut theorem
Maximum flow through the network is equal to the
capacity of the minimal cut (Ford and Fulkerson,
1962)
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Bottleneck

• Maximum throughput achieved by maximizing the
  flow through the bottleneck
• If the flow for some time is not at its maximum
  through the bottleneck, then this loss can never
  be recovered
• ? Maximum throughput requires tight control of
  the bottleneck unit

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Rules for achieving maximum throughput

• Maximize flow F through bottleneck at all times
• Use TPM for control of bottleneck unit
• Locate TPM to achieve tight control at bottleneck
• Back off usually needed to ensure feasibility
  dynamically

Fmax
F
Fset point
Back off
Time
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Realize maximum throughput
Best result (minimize back-off) if TPM
permanently is moved to bottleneck unit
Max bottleneck
Skogestad (2004) Control structure design for
complete chemical plants Comp. Chem. Eng 28
p.219-234
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Realize maximum throughput in more complex cases

• Bottleneck moves
• Multiple feeds and crossovers
• Proposed solution Coordinator MPC
• Estimate of remaining capacity in each unit is
  obtained from local MPCs
• Coordinator MPC manipulate TPMs ( crossovers) to
  maximize flow through bottlenecks

Aske et al. (2007) Coordinator MPC for
maximizing plant throughput Submitted to Comp.
Chem. Eng
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Coordinator MPC
- maximize throughput (CV with high, unreachable
set point with lower priority) - TPMs as MVs -
keep columns within their capacity (CV
constraints) - disturbances moves the bottlenecks
CV
CV
CV
CV
MV
MV
MV
CV
MV
CV
CV
CV
MV
CV
MV
CV
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Back off loss (in throughput)

• Back off can be reduced by
• Improved control (to some extent)
• Limited by network dynamics from TPM to
  bottleneck
• Obtain TPM closer to bottleneck
• Move TPM (Change in base control)
• Add buffer tanks to get dynamic TPMs (Design
  change)
• or use existing buffer volumes
• Estimate back off to find economic incentive
• Worst case amplification

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Example estimation of back off

• Compare TPM at feed and at bottleneck
• Feedback controller K tuned by Skogestads tuning
  rules, tc3?eff
• Disturbance rejection as function of frequency

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Back off as a function of frequency

• Peak unavoidable
• Effect of disturbances reduced

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Conclusions

• Tighter bottleneck control can reduce back off
• TPM should be used for control of the bottleneck
  unit to obtain maximum flow
• Bottleneck fixed ?single-loop control sufficient
• Bottleneck moves ? multivariable control
• Consider moving/adding TPM if back off is large