1 Using Self-Optimizing Control on the Statoil Mongstad HEN Daniel Greiner Edvardsen May 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, (2000). Using offline analysis to find good controlled variables

3 Self-Optimizing Control Acceptable loss ) self-optimizing control

4 Self-Optimizing Variable Properties –Maximizes T end –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 ΔT lm approximation

5 Approximation If 1/1.4 < Θ 1 / Θ 2 < 1.4 the error is less than 1% Source:

6 Some math where J = -T end is the cost function and g is the steady-state model z = [u,x] T, u=MV’s (split) and x = temperatures that varies (T out )

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 J z,red = 0 and g = 0 fully specifies the system at the optimum –BUT: J z,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

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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

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20 How to solve… Hard to visualize the results like in the previous cases Used fmincon with the constraints: –c i = 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 213°C: Cp = J/kgK Flow rate = tonne/h = 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

26 F* split SOC-split = RTO-split = 0.474

27 RES2-split also a DOF?

28 H split Assumed cold inlet temperature = T measured

29 H split SOC-split = 0.55 RTO-split = 0.43 = Optimal split Flat optimum: T opt = °C and T SOC = °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

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33 Thank you!