1. 1 Rapid transition control of a CO 2 capture plant Håkon Dahl-Olsen and Sigurd Skogestad

2. 2 High performance with low complexity Control Philosophy Summarizing key properties Step response Gain Rule Reactive absorption column Rapid throughput change Case study

3. 3 Control philosophy Skogestad and Postlethwaite (2005): Multivariable feedback control – analysis and design, Wiley Self-optimizing control (soc) is when acceptable performance is achieved with feedback control with pre-computed set points without the need to re-optimize when disturbances occur.

4. 4 Maximum gain rule Optimal control problem: NCO:

5. 5 Maximum gain rule Hamiltonian Loss: A second-order approximation yields:

6. 6 P2P Gains – Simple Look at step responses for the time-scale that is relevant for economic control:

7. 7 Cyclic operation of a CO 2 removal plant

8. 8 Column Lean absorbent L Sour gas feed Purified gas y CO2 ≤ 0.005 CaCO 3 (s), H 2 O, Ca(OH) 2 (aq) TC 0.02 ≤ y CO2 ≤ 0.06 Rich absorbent, L N Power plant

9. 9 Modeling VLE described by Henry’s law for CO2/water system : Reaction in water phase: Assumed first-order kinetics:

10. 10 Modeling XLVNHkθ Mole fraction in water phase Liquid flow Vapor flow (feed) Tray holdup (moles) Henry’s law constant Reaction constant Tray hydraulics parameter Variable definitions

11. 11 Optimal steady-state operation Minimize absorbent usage while maintaining y ≤ 0.5% (active)

12. 12 Optimal transition paths Objectives: minimum time and limited absorbent usage Constraint y < 0.5% at all times This constraint is active for the transition phase Constraint not measureable Can measure dissolved CO 2, but threshold on x = 5 ppm

13. 13 Optimal transition paths

14. 14 Implementation Open-loop implementation of VCandidate CV’s: CO2 composition where xmin > 5 ppm Tray holdups Absorbent feed rate L Functions of available measurements? Evaluation method: Maximum gain rule Table of different measures

15. 15 Scorecard 1: Direct measurement OutputOptimal variation Implementation error (assumed) SpanP2P GainScaled gain X142.23 ppm1 ppm3.23 ppm0.4350.134 X152.59 ppm1 ppm3.59 ppm0.4310.120 N144.9 kmol5 kmol49.9 kmol10.00.219 N244.9 kmol5 kmol49.9 kmol9.940.217 ……………… N932.3 kmol5 kmol43.7 kmol6.260.120 L4.45 kmol/min 1 kmol/min5.45 kmol10.183

16. 16 Can we use ratio control to limit the span of the CV? Approximate span propagation by linearization

17. 17 Output 10 8 x Optimal variation Implementation error (linear app.) SpanP2P GainScaled gain X14/N10.140.0300.175.5332.5 X14/N20.140.0310.175.5332.5 x15/N10.130.0530.235.9025.6 X15/N20.130.0640.256.1224.5

18. 18 Loss evaluation (Constant set point policy) Candidate CVAverage absorbent usage Loss [%] X14/N116091.9 X14/N216595.0 X15/N116102.0 X15/N216605.1

19. 19 CO2 comp. Performance check Absorbent feed Controlled variable

20. 20 Discussion Point-to-point gain Step response required Gain rule simplification Consider several measures Optimal variation, implementation error, sensor range… Can include functions of measurements Scorecard Ratio controller found in systematic way Near-optimal performance with constant set-point Transition control