1. 1 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

2. 2 Outline Introduction Modes of optimal operation Maximum throughput Bottleneck Implementation of maximum flow Coordinator MPC Case study Improvements

3. 3 1985 2005 20001993 2003 Case Study: Statoil/Gassco Gas Plant Motivation for coordinator MPC: Plant development over 20 years How manipulate feeds and crossovers?

4. 4 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,..) Stationary optimization (RTO) Planning Supervisory control (e.g. MPC)

5. 5 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 throughput Increase 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 uneconomical Unconstrained 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!

6. 6 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

7. 7 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

8. 8 Bottlenecks in plant Max-flow min-cut

9. 9 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, 1197–1207.

10. 10 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 y set point Time y max y measure Back off *TPM = throughput manipulator

11. 11 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

12. 12 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

13. 13 Identify bottleneck 1.Use RTO based on a detailed steady-state model of the plant 2.Better: use local MPC to calculate remaining feed capacity in each unit! Remaining feed capacity for unit k: J k – present feed to unit k J k,max – max feed to unit k within feasible operation, Obtained by solving “extra” steady-state LP problem in each local MPC: J k,max = max (J k ) subject to: satisfying existing CV& MV constraints + models in local MPC

14. 14 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. u min < u < u max 3. Δu min < Δu < Δu max 4. Dynamic model from feeds and crossovers (u) to capacities (y) Step response models for columns in 100-train u y

15. 15 Case study: Gas processing plant Simulation study based on detailed dynamic model Case: maximize throughput

16. 16 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)

17. 17 Complete set of Step response models in the coordinator Feeds and crossovers (u, MVs) Available capacity (y, CVs)

18. 18 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)

19. 19 Simulation results: CVs (available capacity)

20. 20 Simulation results: MVs (feeds and crossovers) Train feed Feed split Crossover

21. 21 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

22. 22 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