Post on 17-Jan-2016
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Using Self-Optimizing Control on the Statoil Mongstad HEN
Daniel Greiner EdvardsenMay 27, 2010
NTNU
Confidential
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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
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Self-Optimizing Control
Acceptable loss ) self-optimizing control
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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
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Approximation
• If 1/1.4 < Θ1/ Θ2 < 1.4 the error is less than 1%
Source:
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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)
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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
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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!
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Our Self-Optimizing Variable- Case I: 2 heat exchangers in parallel
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Our Self-Optimizing Variable- Case I: 2 heat exchangers in parallel
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Our Self-Optimizing Variable- Case II: 2 heat exchangers in series and 1 in parallel
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Our Self-Optimizing Variable- Case II: 2 heat exchangers in series and 1 in parallel
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Mongstad HEN
• Can use both of the presented controlled variables
• Looks very promising
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How to solve…• Earlier, only one split and the self-optimizing split (close to optimal)
could be presented like this
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How to solve…• Another study with two splits
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How to solve…• … where the result could be presented in this way:
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How to solve…
• In the Mongstad HEN case we have 7 streams, i.e. 6 splits
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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 *
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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
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Controlled variables
Largest stream!
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Results
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Results
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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
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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 *
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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
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RES2-split also a DOF?
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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
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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
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Conclusion
• Simple control structure
• Close to optimal operation– Demonstrated through several other case studies
• With well-tuned controllers good disturbance rejection can be achieved
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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
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Thank you!