1 coordinator mpc for maximization of plant throughput elvira marie b. aske* &, stig strand...
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Coordinator MPC for maximization of plant throughput
Elvira Marie B. Aske*&, Stig Strand& and Sigurd Skogestad*
*Department of Chemical Engineering, Norwegian University of Science and Technology, Trondheim, Norway
&Statoil R&D, Process Control, Trondheim, Norway
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Outline
• Introduction• Modes of optimal operation• Maximum throughput• Bottleneck• Implementation of maximum flow• Coordinator MPC• Case study• Improvements
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1985
2005
20001993
2003
Case Study: Statoil/Gassco Gas Plant
Motivation for coordinator MPC: Plant development over 20 years
How manipulate feeds and crossovers?
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Control hierarchy
• Conventional real-time optimization
(RTO) offers a direct method of
maximizing an economic
objective function– Identifies optimal active constraints and optimal setpoints
• Challenge: Implement optimal solution in real plant with dynamic changes and uncertainty
• Special case considered here (very important and common in practice):– Maximize throughput
Regulatory control layer(PID, FF,..)
Stationaryoptimization
(RTO)
Planning
Supervisory control (e.g. MPC)
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Depending on marked conditions: Two main modes of optimal operation
Mode I. Given throughput (“nominal case”)Given feed or product rate
“Maximize efficiency”: Unconstrained optimum (“trade-off”) that may require RTO
Mode II. Max/Optimum throughput Throughput is a degree of freedom + good product prices
IIa) Maximum throughputIncrease throughput until constraints give infeasible operation
Do not need RTO if we can identify active constraints (bottleneck!)
IIb) Optimized throughput Increase throughput until further increase is uneconomicalUnconstrained optimum (with low efficiency...) that may require RTO
Operation/control:• Traditionally: Focus on mode I• But: Mode IIa is where we really can make “extra” money!
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Maximum throughput in networks
• Operation research community: max-flow min-cut theorem (Ford et.al (1962)): Maximum flow through the network is equal to the minimum capacity for all cuts
• Assumption: The mass flow through the network is represented by a set of units with linear flow connections
• Maximum throughput achieved by maximizing the flow through the bottleneck
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Bottleneck
• Definition: a unit is a bottleneck if maximum throughput is obtained by operating this unit at maximum flow
• 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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Bottlenecks in plantMax-flow min-cut
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Throughput manipulator (TPM)
Buckley (1964). Techniques of Process ControlPrice, Lyman and Georgakis (1994). Throughput manipulationin plantwide control structures. Ind. Eng. Chem. Res. 33, 1197–1207.
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Rules for achieving max throughput
1. Maximize flow through bottleneck at all times
2. Use TPM* for control of bottleneck unit
3. Locate TPM to achieve tight control at bottleneck
4. Back off: usually needed to ensure feasibility dynamically
yset point
Time
ymaxymeasure
Back off
*TPM = throughput manipulator
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Implementation of maximum flow
Bottleneck fixed*: - Single-loop control sufficient:
Use TPM to control bottleneck unit
- Best result (minimize back-off) if TPM permanently is moved to bottleneck unit
Bottleneck moves:1. Need to find bottleneck
2. Keep maximum flow at bottleneck, but avoid reassigning loops
Proposed solution: Coordinator MPC- Estimate of remaining capacity in each
unit is obtained from local MPCs
- Coordinator MPC manipulate TPMs and crossovers to maximize flow through bottlenecks
*Skogestad (2004) Control structure design for complete chemical plants Comp. Chem. Eng 28 p. 219-234
max
FC
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Coordinator MPC• Feeds and crossovers as
manipulated variables– affects throughput in each unit
• Local MPCs– Provide available capacity in each unit
• Decomposition – Local MPCs work as before– Coordinator uses extra DOFs
• Advantages:– dynamic – fast execution
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Identify bottleneck
1. Use RTO based on a detailed steady-state model of the plant2. Better: use local MPC to calculate remaining feed capacity in each unit!
Remaining feed capacity for unit k:
Jk – present feed to unit k
Jk,max – max feed to unit k within feasible operation, Obtained by solving “extra” steady-state LP problem in each local MPC:
Jk,max = max (Jk)subject to: satisfying existing CV& MV constraints + models in local MPC
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Coordinator MPC
• Degrees of freedom (MVs,u): feeds (TPMs) and crossovers.• Outputs (CVs, y): Remaining capacities in all units• Maximize throughput: Use “standard MPC” to solve LP problem:
max (throughput) subject to:
1. y > 0 + back off
2. umin < u < umax
3. Δumin < Δu < Δumax
4. Dynamic model from feedsand crossovers (u) to capacities (y)
Step response models for columns in 100-train
u
y
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Case study: Gas processing plant• Simulation study based on detailed dynamic model• Case: maximize throughput
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Coordinator MPC
• MVs (u):– Feed to train 100 and 300– Feed split from DPCU – Crossover from T100 to T300
• CVs (y):– Remaining feed capacity for each column (10 units)
– Sump level in ET-100 (to avoid loosing control due to crossover)
– Total plant feed (“trick” to use QP-MPC: high unreachable set point)
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Complete set ofStep response modelsin the coordinator
Feeds and crossovers (u, MVs)A
vaila
ble
capa
city
(y,
CV
s)
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• Simulations: – t=0: move the plant to maximum throughput– t=360 min: feed composition change in T100– t=600 min: change in CV high limit in butane splitter T100 MPC
(reducing the remaining feed capacity which is already operated at its maximum)
19Simulation results: CVs (available capacity)
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Simulation results: MVs (feeds and crossovers)
Train feed Train feed
Feed split
Feed split
Crossover
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Improvements (further work):Reduce back-off
1. Use inventories (buffer tanks) as additional MVs in the coordinator– MV closer to bottleneck: reduce back-off
2. Improve estimate of remaining feed capacity– column pressure drop not always a good indicator. More detailed
column capacity model?
3. Include feed forward, e.g from feed composition – Composition measurements at the pipelines into the plant
E.M.B. Aske and S. Skogestad, “Coordinator MPC with focus on maximizing throughput”,Proceedings PSE-ESCAPE’07, Garmisch-Partenkirchen, Germany, July 2007
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Conclusion
• Often: Optimal operation = max. throughput• Usually: Max. throughput = max. through bottleneck
• max-flow min-cut theorem
• Fixed bottleneck: Single-loop control• Moving bottleneck: Propose coordinator-MPC where
local MPCs estimate remaining capacity• Simulations promising• Implementation planned in 2007 • May later include inventories as dynamic degrees of freedom