SUBPRO Comparative study of Kalman Filterbased observers with

SUBPRO 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 christoph. backi@ntnu. no 21 st Nordic Process Control Workshop Åbo Akademi, Turku, Finland, January 18 th 2018 Backi, Skogestad – NPCW 2018

SUBPRO Outline 1. Introduction – Motivation and Scope – Problem Formulation 2. Mathematical Model – In-/outflow- and pressure dynamics – Droplet balances – Controller and Observer Design 3. Simulations 4. Conclusion and Future Work 2 Backi, Skogestad – NPCW 2018

1. Introduction Motivation and Scope SUBPRO 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 3 Backi, Skogestad – NPCW 2018

1. Introduction Motivation and Scope Subsea Factory Wells – Compression/Pumping – Separation – Power Source: Statoil 4 Backi, Skogestad – NPCW 2018 SUBPRO

1. Introduction Problem Formulation Gravity separator with different zones 5 Backi, Skogestad – NPCW 2018 SUBPRO

1. 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 6 Backi, Skogestad – NPCW 2018 SUBPRO

SUBPRO Outline 1. Introduction – Motivation and Scope – Problem Formulation 2. Mathematical Model – In-/outflow- and pressure dynamics – Droplet balances – Controller and Observer Design 3. Simulations 4. Conclusion and Future Work 7 Backi, Skogestad – NPCW 2018

2. Mathematical Model Assumptions SUBPRO 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 8 Backi, Skogestad – NPCW 2018

2. Mathematical Model In-/outflow and pressure-dynamics 9 Backi, Skogestad – NPCW 2018 SUBPRO

2. Mathematical Model Droplet balances Active separation zone 10 Backi, Skogestad – NPCW 2018 SUBPRO

2. Mathematical Model Droplet balances SUBPRO Stokes’ law Vertical residence time Horizontal residence time Residence-time based calculation of positions and numbers for each droplet class in each volumetric segment 11 Backi, Skogestad – NPCW 2018

2. 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” 12 Backi, Skogestad – NPCW 2018 SUBPRO

2. Mathematical Model Observer Designs SUBPRO 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 13 Backi, Skogestad – NPCW 2018

2. Mathematical Model Comparison EKF – LSO SUBPRO Classical differential Matrix Riccati Equation Differential Matrix Riccati Equation with forgetting factor* * M. A. M. Haring – Extremum-seeking control: convergence improvements and asymptotic stability. Ph. D Thesis, Norwegian University of Science and Technology, 2016. 14 Backi, Skogestad – NPCW 2018

2. Mathematical Model Full Observer Design 15 Backi, Skogestad – NPCW 2018 SUBPRO

2. Mathematical Model Cascaded Observer Design Observer 1 Observer 2 16 Backi, Skogestad – NPCW 2018 SUBPRO

2. Mathematical Model Cascaded Observer Design 17 Backi, Skogestad – NPCW 2018 SUBPRO

SUBPRO Outline 1. Introduction – Motivation and Scope – Problem Formulation 2. Mathematical Model – In-/outflow- and pressure dynamics – Particle balances – Controller and Observer Design 3. Simulations 4. Conclusion and Future Work 18 Backi, Skogestad – NPCW 2018

3. Simulations Parameters Gullfaks-A 1988 production rates 19 Backi, Skogestad – NPCW 2018 SUBPRO

3. Simulations Performance – Full EKF 20 Backi, Skogestad – NPCW 2018 SUBPRO

3. Simulations Performance – Full LSO 21 Backi, Skogestad – NPCW 2018 SUBPRO

3. Simulations Observer performance 22 Backi, Skogestad – NPCW 2018 SUBPRO

3. Simulations Performance – Cascaded EKF 23 Backi, Skogestad – NPCW 2018 SUBPRO

3. Simulations Performance – Full EKF 24 Backi, Skogestad – NPCW 2018 SUBPRO

3. Simulations Performance – Cascaded LSO 25 Backi, Skogestad – NPCW 2018 SUBPRO

3. Simulations Performance – Full LSO 26 Backi, Skogestad – NPCW 2018 SUBPRO

SUBPRO Outline 1. Introduction – Motivation and Scope – Problem Formulation 2. Mathematical Model – In-/outflow- and pressure dynamics – Particle balances 3. Simulations 4. Conclusion and Future Work 27 Backi, Skogestad – NPCW 2018

SUBPRO 4. 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 28 Backi, Skogestad – NPCW 2018

SUBPRO 4. 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-Papers. On. Line 50(1): 1632 -11638, 2017. 29 Backi, Skogestad – NPCW 2018

SUBPRO Acknowledgments 30 Backi, Skogestad – NPCW 2018