1

Using Self-Optimizing Control on the Statoil Mongstad HEN

Daniel Greiner EdvardsenMay 27, 2010

NTNU

Confidential

2

Self-Optimizing Control

• Work by Professor Sigurd Skogestad

Self-optimizing control is said to occur when we can achieve an acceptable loss (in comparison with truly optimal operation) with constant setpoint values for the controlled variables without the need to reoptimize when disturbances occur.

Reference: S. Skogestad, “Plantwide control: The search for the self-optimizing control structure'', Journal of Process Control, 10, 487-507 (2000).

• Using offline analysis to find good controlled variables

3

Self-Optimizing Control

Acceptable loss ) self-optimizing control

4

Self-Optimizing Variable

• Properties– Maximizes Tend

– Relies only on cheap temperature measurement, i.e.:• No flow meaurements

• No technical data necessary (HE area, U-values, Cp etc.)

– Best for well designed processes• Because of ΔTlm approximation

5

Approximation

• If 1/1.4 < Θ1/ Θ2 < 1.4 the error is less than 1%

Source:

6

Some math

• where J = -Tend is the cost function and g is the steady-state model

• z = [u,x]T, u=MV’s (split) and x = temperatures that varies (Tout)

7

Some math

• If z is locally optimal then there exists Langrangian multiplier vectors λ such that the first order optimality conditions are satisified(*):

• These equations could be used for control but contain unkwown variables (x, d and λ) which must be eliminated

(*) Nocedal and Wright (2006): Numerical Optimization

8

Some math• Now define:

• Then, multiplying with the equation on the last slide we get:

• Controlling Jz,red = 0 and g = 0 fully specifies the system at the optimum– BUT: Jz,red still contains unkwown variables in x and d!– Sparse resultants are used to eliminate these.– In practive a toolbox in Maple is used.

λ is eliminated!

9

Our Self-Optimizing Variable- Case I: 2 heat exchangers in parallel

10

Our Self-Optimizing Variable- Case I: 2 heat exchangers in parallel

11

Our Self-Optimizing Variable- Case II: 2 heat exchangers in series and 1 in parallel

12

Our Self-Optimizing Variable- Case II: 2 heat exchangers in series and 1 in parallel

13

Mongstad HEN

• Can use both of the presented controlled variables

• Looks very promising

14

15

How to solve…• Earlier, only one split and the self-optimizing split (close to optimal)

could be presented like this

16

How to solve…• Another study with two splits

17

How to solve…• … where the result could be presented in this way:

18

How to solve…

• In the Mongstad HEN case we have 7 streams, i.e. 6 splits

19

234.0

214.0

215.7

210.9

213.4

204.7

234.5

175.2

157.5

192.8

145.4

156.7

P -41

C rude O il

T 0 = 132.9F 0 = 918.2

285.0

252.1

241.1

T o M ainF rac tio nato r

T en d = 266.4

358.6

295.8

275.6

300.4

175.2

178.0

270.3

232.2

245.4

145.4

226.2

175.5

273.8

181.5 223.4256.4

168.1

203.2

161.9

193.1

190.4262.6

244.1

167.5

161.8

A : 86.1

B : 174.6

C : 64.2

D : 128.2

E : 124.9

F : 236.1

G : 103.5

H

213.0H e a t e xc h an g e

248.1F *

20

How to solve…

• Hard to visualize the results like in the previous cases

• Used fmincon with the constraints:– ci = 0 (six controlled variables)

– Sum(splits) = 1

21

Controlled variables

Largest stream!

22

Results

23

Results

24

How much is a temperature increase of 0.81°C worth?

• Crude oil @ 213°C: Cp = 2696.8 J/kgK

• Flow rate = 918.2 tonne/h = 255.0 kg/s

• mCp = 688 kW/K

• mCp*0.81 = 557 kW

• Electricity price: 1 NOK/kWh

• Savings = 557 NOK/h = 4.9 million NOK/year

25

F* split

234.0

214.0

215.7

210.9

213.4

204.7

234.5

175.2

157.5

192.8

145.4

156.7

P -41

C rude O il

T 0 = 132.9F 0 = 918.2

285.0

252.1

241.1

T o M ainF rac tio n ato r

T en d = 266.4

358.6

295.8

275.6

300.4

175.2

178.0

270.3

232.2

245.4

145.4

226.2

175.5

273.8

181.5 223.4256.4

168.1

203.2

161.9

193.1

190.4262.6

244.1

167.5

161.8

A : 86.1

B : 174.6

C : 64.2

D : 128.2

E : 124.9

F : 236.1

G : 103.5

H

213.0H e a t e xc h an g e

248.1F *

26

F* split

Te

nd [

C]

Split, u0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

180

185

190

195

200

205

210

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-100

-80

-60

-40

-20

0

20

40

60

80

100

Co

ntr

olle

d v

ari

ab

le, c

[ C

]

SOC-split = 0.499RTO-split = 0.474

27

RES2-split also a DOF?

28

H split234.0

214.0

215.7

210.9

213.4

204.7

234.5

175.2

157.5

192.8

145.4

156.7

P -41

C rude O il

T 0 = 132.9F 0 = 918.2

285.0

252.1

241.1

T o M ainF rac tio nato r

T en d = 266.4

358.6

295.8

275.6

300.4

175.2

178.0

270.3

232.2

245.4

145.4

226.2

175.5

273.8

181.5 223.4256.4

168.1

203.2

161.9

193.1

190.4262.6

244.1

167.5

161.8

A : 86.1

B : 174.6

C : 64.2

D : 128.2

E : 124.9

F : 236.1

G : 103.5

H

213.0H e a t e xc h an g e

248.1F *

Assumed cold inlet temperature = Tmeasured + 0.81

29

H split

Te

nd [

C]

Split, u0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

262

264

266

268

270

272

274

276

278

280

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-60

-40

-20

0

20

40

60

80

100

120

Co

ntr

olle

d v

ari

abl

e, c

[ C

]

SOC-split = 0.55RTO-split = 0.43 = Optimal split

Flat optimum: Topt = 276.94°C and TSOC = 276.73°C

30

Conclusion

• Simple control structure

• Close to optimal operation– Demonstrated through several other case studies

• With well-tuned controllers good disturbance rejection can be achieved

31

To Discuss• Cp-values

• Type of heat exchangers– Flow patterns (correction factor, F)– Large deviations in heat exchangers B1, C1, C2, D1, D2, E1, F2 and H2

32

33

Thank you!