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

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

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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.

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4 Maximum gain rule Optimal control problem: NCO:

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

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

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7 Cyclic operation of a CO 2 removal plant

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

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

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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

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

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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

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13 Optimal transition paths

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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

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15 Scorecard 1: Direct measurement OutputOptimal variation Implementation error (assumed) SpanP2P GainScaled gain X ppm1 ppm3.23 ppm X ppm1 ppm3.59 ppm N144.9 kmol5 kmol49.9 kmol N244.9 kmol5 kmol49.9 kmol ……………… N932.3 kmol5 kmol43.7 kmol L4.45 kmol/min 1 kmol/min5.45 kmol10.183

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

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17 Output 10 8 x Optimal variation Implementation error (linear app.) SpanP2P GainScaled gain X14/N X14/N x15/N X15/N

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18 Loss evaluation (Constant set point policy) Candidate CVAverage absorbent usage Loss [%] X14/N X14/N X15/N X15/N

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19 CO2 comp. Performance check Absorbent feed Controlled variable

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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

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