1. Christoph J. Backi and Sigurd Skogestad
Comparative study of Kalman Filter-based observers with simplified tuning procedures
Christoph J. Backi and Sigurd Skogestad
Department of Chemical Engineering
Norwegian University of Science and Technology
21st Nordic Process Control Workshop
Åbo Akademi, Turku, Finland, January 18th 2018

2. Outline Introduction Mathematical Model Simulations
Motivation and Scope
Problem Formulation
Mathematical Model
In-/outflow- and pressure dynamics
Droplet balances
Controller and Observer Design
Simulations
Conclusion and Future Work

3. Introduction Motivation and Scope
Oil and gas production require several processing stages
Separate gas and liquid phases
Separate water from oil
Pump liquids / compress gases for distribution
Reinject gas / water into the reservoir for pressure increase
Problem: Move production, processing and storage from platforms / FPSOs to the seabed  Subsea production and processing  Subsea Factory
Aim: Purify gas, water and oil for direct distribution via pumps and compressors

4. Introduction Motivation and Scope
Subsea Factory
Wells – Compression/Pumping – Separation – Power
Source: Statoil

5. Introduction Problem Formulation
Gravity separator with different zones

6. Introduction Problem Formulation
Information about process variables desired
Inflows of gas and liquid
Anticipate slugs (counter-action to protect downstream equipment)
Information about separation
Measurement of multiphase flows
Expensive
Inaccurate (certain flow regimes / calibration)
Use available measurements (level and pressure) for estimation of inflows / disturbance variables

7. Outline Introduction Mathematical Model Simulations
Motivation and Scope
Problem Formulation
Mathematical Model
In-/outflow- and pressure dynamics
Droplet balances
Controller and Observer Design
Simulations
Conclusion and Future Work

8. Mathematical Model Assumptions
Several assumptions are made
Static distribution of droplet sizes
No gas droplets in liquid phase and vice versa
Plug flow with average velocity in horizontal direction for each phase (including droplets)
Water and liquid levels instantly level out wrt. changes in in- and outflows
No dense-packed (emulsion) layer

9. Mathematical Model In-/outflow and pressure-dynamics

10. Mathematical Model Droplet balances
Active separation zone

11. Mathematical Model Droplet balances
Stokes’ law Vertical residence time Horizontal residence time Residence-time based calculation of positions and numbers for each droplet class in each volumetric segment

12. Mathematical Model Controller Design
Level and pressure control using PI controllers Integrating processes without time-delay Bounds on MVs and their rates of change Tuned with SIMC* tuning method * ”Skogestad IMC”

13. Mathematical Model Observer Designs
Observers are based on Extended Kalman Filter formulations
EKF vs. least squares observer with forgetting factor
Both in full and cascaded (dual) formulations
By measuring the 3 dynamic states (water level, total liquid level and pressure)
Estimate the liquid and the gas inflows
Estimate the effective split ratio
Receive filtered signals for the measurements

14. Mathematical Model Comparison EKF – LSO
Classical differential Matrix Riccati Equation Differential Matrix Riccati Equation with forgetting factor*
* M.A.M. Haring – Extremum-seeking control: convergence improvements and asymptotic stability.
PhD Thesis, Norwegian University of Science and Technology, 2016.

15. Mathematical Model Full Observer Design

16. Mathematical Model Cascaded Observer Design

17. Mathematical Model Cascaded Observer Design

18. Outline Introduction Mathematical Model Simulations
Motivation and Scope
Problem Formulation
Mathematical Model
In-/outflow- and pressure dynamics
Particle balances
Controller and Observer Design
Simulations
Conclusion and Future Work

19. Simulations Parameters
Gullfaks-A 1988 production rates

20. Simulations Performance – Full EKF

21. Simulations Performance – Full LSO

22. Simulations Observer performance

23. Simulations Performance – Cascaded EKF

24. Simulations Performance – Full EKF

25. Simulations Performance – Cascaded LSO

26. Simulations Performance – Full LSO

27. Outline Introduction Mathematical Model Simulations
Motivation and Scope
Problem Formulation
Mathematical Model
In-/outflow- and pressure dynamics
Particle balances
Simulations
Conclusion and Future Work

28. Conclusion
We compared four estimation strategies for inflow estimation in a three-phase gravity separator
EKF vs. LSO
Both in full and cascaded formulations
PI control
Observer performance
Disturbance estimation works quite well for all cases
LSO has better noise suppression
Cascaded EKF design shows improvements

29. Future Work Incorporate coalescence and breakage into the model
Linearization around estimated state trajectories  Optimality of estimation / guaranteed stability?
E.g. Double Kalman Filter*
Feedforward control using estimated variables
Utilize knowledge about effective split ratio?
Test simulations versus real data
* Abdellahouri et al. – Nonlinear State and Parameter Estimation using Discrete-Time Double Kalman Filter.
IFAC-PapersOnLine 50(1): , 2017.

30. Acknowledgments