1. 1 Single-cycle mixed-fluid LNG (PRICO) process Part II: Optimal operation Sigurd Skogestad & Jørgen Bauck Jensen Qatar, January 2009

2. 2 Single-cycle mixed fluid LNG process Natural gas: Feed at 40 bar and 30 °C Cool to -157 °C (spec.) ΔP = 5 bar in main heat exchanger

3. 3 Single-cycle mixed fluid LNG process Refrigerant: Partly condensed with sea water Subcooled to ~ -157 °C Expansion to ~ 4 bar Evaporates in main HX Super-heated 10 °C Compressed to ~ 30 bar 30 bar -157 °C 26 bar 4 bar Sup 10 °C Sat. liquid Subcooled

4. 4 Degrees of freedom Manipulated variables: 1.Compressor speed N 2.Choke valve opening z 3.Turbine power 4.Sea water flowrate 5.Natural gas feed flowrate 6-9. Composition of refrigerant (4) 6-9

5. 5 Degrees of freedom Assumptions: 1.Assume maximum cooling in SW cooler Realized by fixing T=30 °C 8 degrees of freedom for optimization 4 degrees of freedom in operation –Assume 4 constant compositions in operation

6. 6 Operational constraints Some super-heating to avoid damage to compressor –But we find that super-heating is optimal anyway…. (constraint not active) Maximum compressor power 120 MW –active Maximum compressor rotational speed is 100 % –active Minimum distance to surge is 0 kg/s (no back-off) –active

7. 7 Optimal operation Minimize operation cost with respect to the 8 degrees of freedom (u) subject to the constraints c ≤ 0

8. 8 Optimal operation: Minimize cost Neglect income of turbine work –The main effect of the liquid turbines is the extra cooling effect, not the power production Neglect cost of cooling with sea water –Sea water requires pumping which is cheap in operation compared with compressors

9. 9 Two modes of operation Mode I: Given production rate (m feed ) Optimization problem simplifies to – Minimize compressor work (W s ) Mode II: Free production rate With reasonably high LNG prices: Optimization problem simplifies to – Maximize production rate (m feed ) while satifying operational constraints (max. compressor load)

10. 10 Two modes of operation

11. 11 Mode I: Nominal optimum Feed flowrate is given (69.8 kg/s) –8 - 1 = 7 steady-state degrees of freedom (incl. 4 compositions) Three operational constraints are active at optimum 1.Given temperature LNG (-157 °C) 2.Compressor surge margin at minimum (0.0 kg/s) 3.Compressor speed at maximum (100 %) Only the four degrees of freedom related to refrigerant compositions are unconstrained

12. 12 Nominal optimum

13. 13 Mode II: Nominal optimum LNG production is maximized –8 steady-state degrees of freedom (incl. 4 compositions) Four operational constraints are active at optimum 1.Given temperature LNG (-157 °C) 2.Compressor surge margin at minimum (0.0 kg/s) 3.Compressor speed at maximum (100 %) 4.Compressor work W s at maximum (120 MW) Note that two capacity constraints are active (3 and 4) Only the four constraints related to refrigerant composition are unconstrained

14. 14 Nominal optimum

15. 15 Nominal compressor operating point for mode II N=100% (max speed) N=50% N=10% * Surge limit

16. 16 Temperature profiles in heat exhanger (mode II) T NG -T C NG in LNG out

17. 17 Optimum with disturbances 4 operational degrees of freedom –Refrigerant composition is constant during operation Optimum with disturbances: 1.Given LNG temperature (all cases) 2.Given load (all cases) –Mode I: The production rate is given –Mode II: The compressor work is at maximum (W s = 120 MW) 3.Max. speed compressor (most cases) 4.Operate at surge limit (most cases)

18. 18 Optimum with disturbances Two additional degrees of freedom were at constraints at the nominal optimum –Compressor rotational speed at maximum (100 %) –Compressor surge margin at minimum (0.0 kg/s) We also find that controlling these constraints gives close to optimal operation with disturbance

19. 19 Optimum with disturbances Strictly speaking we would need to consider the following four regions: This is complicated and we prefer to have the same controlled variables in all four regions Control the nominal active constraints and

20. 20 Check Mode II (production vs. disturbance) Dots are re-optimized Lines are for different controlled variables constant Constant distance to surge (0.0 kg/s) (ALL CASES) N=N max gives highest production (CLOSE TO OPTIMAL) N=N max only feasible structure in increasing load direction

21. 21 Example of control structure TC Max cooling Max speed WC W s,max =120MW SC Δm surge =0 m Alternative: MPC

22. 22 Conclusion Maximum compressor speed and minimum distance to surge is nominally optimal for mode I and mode II –In practice one would have a back-off from surge, but this would still be an active constraint This is also close to optimal or optimal for all disturbance regions  Control the following variables: 1.Maximum sea water cooling (valve fully open) 2.T LNG = -157 °C 3.LNG flowrate = 69.8 kg/s (mode I) or W s = 120 MW (mode II) 4. 5.

23. 23 Additional material 1.Disturbances considered 2.Structure of model equations 3.Data used for the PRICO process

24. 24 Disturbances considered

25. 25 Structure of model equations

26. 26 Data used for the PRICO process