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 R&D, Process Control, Trondheim, Norway

2. 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

4. 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

5. 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.

6. 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)

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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:

13. Bottleneck Bottleneck Example – estimation of back off • Compare TPM at feed and at bottleneck • Feedback controller K tuned by Skogestad’s tuning rules, τc=3θeff • Disturbance rejection as function of frequency

14. Back off as a function of frequency • Peak unavoidable • Effect of disturbancesreduced

15. 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