1. Coordinator MPC with focus on maximizing throughput
Elvira Marie B. Aske*,**
Stig Strand**
Sigurd Skogestad*
*Department of Chemical Engineering, Norwegian University of Science and Technology, Trondheim, Norway
** Statoil R&D, Process Control, Trondheim, Norway

2. Outline Background Bottleneck Back-off Remaining feed capacity
Coordinator MPC
Case study
Discussion
Conclusion

3. Background
Conventional real-time optimization (RTO) offers a direct method of maximizing an economic objective function
Identifies optimal active constraints and optimal setpoints
Special case considered here (very important and common in practice):
Maximize production (active constraint)
Challenge: Implement optimal solution in real plant with dynamic changes and uncertainty
Implementation of maximum production
Identify bottleneck
Minimize “back-off” at bottleneck

4. Often optimal: Set production rate at bottleneck!
"A bottleneck is an extensive variable that prevents an increase in the overall feed rate to the plant"
If feed is “cheap” and available: Optimal to set production rate at bottleneck
If the flow for some time is not at its maximum through the bottleneck, then this loss can never be recovered

5. Back-off Vmax Vmax-Vs = Back-off = Loss Vs
Back-off is required for robustness
Trade-off between robustness and acceptable loss
Can be placed on constraints, control targets, range changes etc.
Vmax Vs
Vmax-Vs = Back-off
= Loss

6. Key idea: Remaining feed capacity
Since location of the bottleneck may change, we suggest to monitor the remaining feed capacity in each unit (local MPC) of the plant
Estimate of the remaining feed capacity in unit k:
Jk – current throughput (feed) in unit k
Jk, max – found by solving a LP problem with unit constraints included
LP formulation:
Example Jk, max for a binary column:
x: vector of the MVs and DVs (reflux rate, boil-up, column feed)
b: vector of contraints (+back-off), (impurities, flooding limit )
A: from the MPC model for the unit

7. Coordinator MPC
Task: maximize an objective function
here: max feed rate
and make decisions involving several local MPC applications which handle smaller process units
Feedback on minutes basis
Coordinator MPC is placed on the top of the local MPC in the control hierarchy and coordinates the underlying MPCs
Smart decomposition
Avoid one large MPC application which will be over-complex for a complete chemical plant
Can operate both with and without an RTO layer.

8. Coordinator MPC MVs (not used by individual MPCs)
Feed to plant Fi
Feed crossovers / split fractions
Maximize weighted overall feed subject to capacity constraints:
G represents the dynamic influence from each MV to Rk
G typically obtained from step with MPCs in closed loop.

9. Case study: Coordinator MPC on Kårstø gas plant
Task: maximize plant throughput within feasible operation (=satisfy constraints)
Selected part of Kårstø plant: 2 separation train
D-SPICE whole plant simulator used as “real plant”
Local MPCs and coordinator MPC: Implemented in SEPTIC

10. Coordinator MPC MVs: train feed flows, feed splits and crossover CVs:
Each column has constraints on max. pressure drop, reflux rate, boilup, etc.
Vapor capacity in the columns limited by max. pressure drop corresponding to flooding
Potential problem: Pressure drop not always a good indicator of flooding
Coordinator MPC MVs: train feed flows, feed splits and crossover
CVs:
remaining feed capacity in each column (10 in total) > Back-off >0 ,
ET-100 sump level controller output in allowed range
Total plant feed (max.)
Experimental step-response model G obtained at 80-95% of the maximum throughput (typical flow rate)

11. Case study: Simulation
The coordinator performance is illustrated with three different cases
t = 0 min: Move the plant to maximum throughput
t = 360 min: Change in feed composition in T100
t = 600 min: Change in butane splitter T100 MPC CV limit (reducing the remaining feed capacity), which is operated at its maximum
Monitor the following:
Remaining feed capacity in each column (ET100, PT100, …..)
Sump level in ET100 (due to the crossover)
Total plant feed
MV valves

12. Case study: CVs in the coordinator MPC
T=0 min: ET100 and Stab1&2 bottlenecks at the optimal operation point. BS300 bottleneck, but uses crossover to reroute, removing the bottleneck
T=360 min: composition change gives ET100 more capacity, uses crossover to keep BST100 within its capacity, but not plant bottleneck yet, since there is still capacity for rerouting to T300
T=600 min: change in BST100 quality high limit (local MPC), gives less capacity. Reroute to T300, but must reduce T100 feed some.

13. Case study: MVs in the coordinator MPC
Train feed
Train feed
Crossover
Feed split
Feed split

14. Main potential improvement: Reduce back-off
Include feed forward, especially from feed composition changes
Composition measurements at the pipelines into the plant
Introduce level setpoints (buffer volume) as additional MVs for the coordinator
MV close to bottleneck, avoid loss

15. Discussion
With existing MPCs: Little extra work to implement coordinator MPC
Max throughput: Common in practice
Column pressure drop is not always a good indicator for flooding, a more detailed remaining feed capacity model may be needed in some cases
Express flow changes as relative (%) changes
All model gains (G) are then 1
Update nominal flows based on feed composition (“gain scheduling”)
If the feed is limited for a period, the economic optimum is not max. flow
RTO finds the optimal solution
No need to modify the coordinator MPC because we have used “trick”
Maximize feed realized through a (weighted) overall feed rate J as a CV with a high, not reachable set-point with lower priority

16. Conclusion
Designed and implemented a coordinator MPC with experimental step response models to follow the plant optimum, under influence by disturbances of dynamic character
Implemented on Kårstø Whole plant simulator, D-SPICE® software
Performs well on the simulated challenges
Improvements by including feed forward and manipulating buffer volumes