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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