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A Plantwide Control Procedure Applied to the HDA Process

Antonio Araújo and Sigurd Skogestad

Department of Chemical EngineeringNorwegian University of Science and Technology (NTNU)Trondheim, Norway

November, 2006

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Outline

• General procedure plantwide control• HDA process• Active constraints• Self-optimizing variables• Maximum throughput mode• Regulatory control• Dynamic simulations

– comparison with Luyben

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General procedure plantwide control

y1s

y2s

Control of primary variables(MPC)

“Stabilizing” control:p, levels, T (PID)

Part I. “Top-down” steady-state approach - identify active constraints and primary controlled variables (y1)

– Self-optimizing control

Part II. Bottom-up identification of control structure – starting with regulatory (“stabilizing”) control layer.

– Identify secondary controlled variables (y2)

RTO. min J (economics). MV = y1s

u (valves)

Skogestad, S. (2004), “Control structure design for complete chemical plants”, Computers and Chemical Engineering, 28, 219-234.

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Part I. Top-down steady-state approach

Step 1. IDENTIFY DEGREES OF FREEDOMNeed later to choose a CV (y1) for each

Step 2. OPERATIONAL OBJECTIVES Optimal operation: Minimize cost J

J = cost feeds – value products – cost energy subject to satisfying constraints

Step 3. WHAT TO CONTROL? (primary CV’s c=y1)

What should we control (y1)?1. Active constraints2. “Self-optimizing” variables

These are “magic” variables which when kept at constant setpoints give indirect optimal operation by controlling some “magic” variables at– Maximum gain rule: Look for “sensitive” variables with a large scaled steady-state gain

Step 4. PRODUCTION RATE

y1s

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Part II. Bottom-up control structure design

Step 5. REGULATORY CONTROL LAYER (PID)

• Main objectives– “Stabilize” = Avoid “drift”– Control on fast time scale

• Identify secondary controlled variables (y2)

– flow, pressures, levels, selected temperatures– and pair with inputs (u2)

Step 6. SUPERVISORY CONTROL LAYER – Decentralization or MPC?

Step 7. OPTIMIZATION LAYER (RTO)– Can we do without it?

y2 = ?

u (valves)

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Two main modes of optimal operation for chemical plants

Depending on marked conditions:

Mode I: Given throughputWhen: Given feed or product rate

Optimal operation: Max. efficiency

Mode II: Maximum throughput (feed available). When: High product prices and available feed Optimal operation: max. flow in bottleneck

1. Desired: Same or similar control structure in both cases2. Operation/control: Traditionally: Focus on mode I But: Mode II is where the company may make extra money!

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Mixer FEHE Furnace PFR

Quench

Separator

Compressor

Cooler

StabilizerBenzeneColumn

TolueneColumn

H2 + CH4

Toluene

Toluene Benzene CH4

Diphenyl

Purge (CH4 + H2)

HDA process

Toluene + H2 = Benzenje + CH4

2 Benzene = Diphenyl + H2

References for HDA:McKetta (1977) ;

Douglas (1988) Wolff (1994)Luyben (2005)++....

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Mixer FEHE

Furnace

Reactor

Quencher

Separator

Compressor

Cooler

StabilizerBenzeneColumn

TolueneColumn

H2 + CH4

Toluene

Toluene Benzene CH4

Diphenyl

Purge (H2 + CH4)

1

2

3

64

7

5

1113

12 10 8

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Step 1 - Steady-state degrees of freedom

NEED TO FIND 13 CONTROLLED VARIABLES (y1)

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Step 2 - Definition of optimal operation

• The following profit is to be maximized:

-J = pbenDben + Σ(pv,iFv,i) – ptolFtol – pgasFgas – pfuelQfuel – pcwQcw – ppowerWpower - psteamQsteam

• Constraints during operation:– Production rate: Dben ≥ 265 lbmol/h.– Hydrogen excess in reactor inlet: Fhyd / (Fben + Ftol + Fdiph) ≥

5.– Reactor inlet pressure: Preactor,in ≤ 500 psia.– Reactor inlet temperature: Treactor,in ≥ 1150 °F.– Reactor outlet temperature: Treactor,out ≤ 1300 °F.– Quencher outlet temperature: Tquencher,out ≤ 1150 °F.– Product purity: xDben ≥ 0.9997.– Separator inlet temperature: 95 °F ≤ Tseparator ≤ 105 °F.– Compressor power: WS ≤ 545 hp– Furnace heat duty: Qfur ≤ 24 MBtu– Cooler heat duty: Qcool ≤ 33 MBtu– + Distillation heat duties (condensers and reboilers).

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Disturbances

D1 Fresh toluene feed rate [lbmol/h] 300 285

D2 Fresh toluene feed rate [lbmol/h] 300 315

D3 Fresh gas feed rate methane mole fraction 0.03 0.08

D4 Hydrogen to aromatic ratio in reactor inlet 5.0 5.5

D5 Reactor inlet pressure [psi] 500 520

D6 Quencher outlet temperature [oF] 1150 1170

D7 Product purity in the benzene column distillate 0.9997 0.9960

Typical disturbances :• Feeds• Utilities• Constraints

Caused by: implementation error or change

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Step 3: What to control?

• 13 steady-state degrees of freedom• 70 Candidate controlled variables

– pressures, temperatures, compositions, flow rates, heat duties, etc..

• Number of different sets of controlled variables:

• Cannot evaluate all !

1370 70!4.75 10

13 57!13!

æ ö÷ç ÷= = ×ç ÷ç ÷çè ø

OPTIMAL OPERATION:1. Control active constraints!

Find from steady-state optimization (step 3.1)

2. Remaining unconstrained DOFs: Look for “self-optimizing” variables (step 3.2)

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Operation with given feedMode I

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Step 3.1 – Optimization distillation• Distillation train:

– Optimized separately using detailed models– Generally: Most valuable product at its constraint– Other compositions: Trade-off between recovery and energy– Results:

Stabilizer

xD,benzene 1 · 10-4

xB,methane 1 · 10-6

Benzene column

xD,benzene 0.9997

xB,benzene 1.3 · 10-3

Toluene column

xD,diphenyl 0.5 · 10-3

xB,toluene 0.4 · 10-3

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Step 3.1 – Optimization entire process

• Reactor-recycle part• With simplified distillation section (constant compositions)

Distillation compositions

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Step 3.1 – Optimization: Active Constraints

7911

Mixer FEHE

Furnace

Reactor

Quencher

Separator

Compressor

Cooler

StabilizerBenzeneColumn

TolueneColumn

H2 + CH4

Toluene

Toluene Benzene CH4

Diphenyl

Purge (H2 + CH4)

8

1

4

2

610

4

3

5

1. Max. Toluene feed rate 2. Min. H2/aromatics ratio3. Min. Separator temperature4. Min. quencher temperature5. Max. Reactor pressure6. Max. impurity product

+ 5 distillation purities

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Step 3.2: What more to control?

• So far: Control 6 active constraints + 5 compositions (“self-optimizing”)

• What should we do with the 2 remaining degrees of freedom?– Self-optimizing control: Control variables that

give small economic loss when kept constant

• But still many alternative sets

• Prescreening: Use “maximum gain rule” (local analysis) for prescreening– Maximize σ(S1·G2x2·Juu

-1/2).– Optimal variation and implementation error enters in S1

59 59!1711

2 57!2!

æ ö÷ç ÷= =ç ÷ç ÷çè ø

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σ(S1·G2x2·Juu-1/2) = 2.33·10-3 Average Loss (k$/year)

Mixer outlet inert (methane) mole fractionQuencher outlet toluene mole fraction

15.39

σ(S1·G2x2·Juu-1/2) = 2.27·10-3 Average Loss (k$/year)

Mixer outlet inert (methane) mole fractionToluene conversion at reactor outlet

26.55

σ(S1·G2x2·Juu-1/2) = 2.25·10-3 Average Loss (k$/year)

Mixer outlet inert (methane) mole fractionSeparator liquid benzene mole fraction

31.39

• Linear model• All measurements: σ(S1Gfull·Juu

-1/2) = 6.34·10-3

• Best set of two measurements involves two compositions:

c1c2

Step 3.2 – “Maximum gain rule”

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Step 3 - Final selection in mode I

c1 c2

Mixer FEHE

Furnace

Reactor

Quencher

Separator

Compressor

Cooler

StabilizerBenzeneColumn

TolueneColumn

H2 + CH4

Toluene

Toluene Benzene CH4

Diphenyl

Purge (H2 + CH4)

8

1

4

2

7

6

9

10

11

4

3

5

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Step 3: What to control in Mode II ?

Available feed and good product pricesMaximum throughput

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Optimization in mode II: Maximum throughput• 14 steady-state degrees of freedom (one extra) • Reoptimize operation with feedrate Ftol as parameter:

– Find same active constraints as in Mode I.– At Ftol = 380 lbmol/h: Compressor power constraint active.– At Ftol = 390 lbmol/h: Furnace heat duty constraint active.– Further increase in Ftol infeasible: Furnace is BOTTLENECK!

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Step 3 - Controlled variable mode II• 8 active constraints (including WS and Qfur )

• + 5 distillation compositions• One unconstrained degree of freedom:

– To reduce the need for reconfiguration we control x-methane

– Average loss 68.74 k$/year

c1

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Step 4 – Throughput manipulator

• Mode I: Toluene feedrate (given)• Mode II: Optimal throughput manipulator is

furnace duty (bottleneck)– Minimizes back-off– But furnace duty is used to stabilize reactor– So use toluene feedrate also in mode II

c1

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Part II: Bottom-up designstarting with regulatory layer

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Step 5: Regulatory layer - Stabilization• Control reactor temperature and liquid levels in separator and

distillation columns (LV configuration).

LC01

LC11LC21LC31

LC32 LC22 LC12

TC01

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Regulatory layer - Avoiding drift I: Pressure control

LC01

LC11LC21LC31

LC32 LC22 LC12

PC01

PC11PC22PC33

TC01

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Regulatory layer - Avoiding drift II: Temperature control

LC01

LC11LC21LC31

LC32 LC22 LC12

PC01

PC11PC22PC33

TC02

TC03

TC22

TC11

#20

#3#5

TC33

TC01

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Regulatory layer - Avoiding drift III: Flow control

LC01

LC11LC21LC31

LC32 LC22 LC12

PC01

PC11PC22PC33

TC02

TC03

TC22

TC11

#20

#3#5

TC33

FC01

FC02

TC01

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Step 6: Supervisory layer – Mode I

LC01

LC11LC21LC31

LC32 LC22 LC12

TC01

PC01

PC11PC22PC33

TC02

TC03

TC22

TC11

#20

#3#5

TC33

FC01

FC02

RC01

CC01

CC02

CC21

CC22

CC32

CC31

CC12

CC11

Decentralized control (PID-loops) seems sufficient

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Step 6: Supervisory layer – Mode II

LC01

LC11LC21LC31

LC32 LC22 LC12

TC01

PC01

PC11PC22PC33

TC02

TC03

TC22

TC11

#20

#3#5

TC33

SETPOINT=Max.fuel-backoff

FC02

RC01

CC01

CC21

CC22

CC32

CC31

CC12

CC11

FixedDecentralized control (PID-loops) seems sufficient

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Dynamic simulations – Mode IDisturbance D1: +15 lbmol/h (+5%) increase in Ftol .

Ours Luyben’s

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Dynamic simulations – Mode IDisturbance D2: -15 lbmol/h (-5%) increase in Ftol .

Ours Luyben’s

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Dynamic simulations – Mode IDisturbance D3: +0.05 increase in xmet.

Ours Luyben’s

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Dynamic simulations – Mode IDisturbance D4: +20 psi increase in Prin.

Ours Luyben’s

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Conclusion

Procedure plantwide control:

I. Top-down analysis to identify degrees of freedom and primary controlled variables (look for self-optimizing variables)

II. Bottom-up analysis to determine secondary controlled variables and structure of control system (pairing).