Christoph J. Backi and Sigurd Skogestad

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Presentation transcript:

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

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

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

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

Introduction Problem Formulation Gravity separator with different zones

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

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

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

Mathematical Model In-/outflow and pressure-dynamics

Mathematical Model Droplet balances Active separation zone

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

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”

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

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.

Mathematical Model Full Observer Design

Mathematical Model Cascaded Observer Design

Mathematical Model Cascaded Observer Design

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

Simulations Parameters Gullfaks-A 1988 production rates

Simulations Performance – Full EKF

Simulations Performance – Full LSO

Simulations Observer performance

Simulations Performance – Cascaded EKF

Simulations Performance – Full EKF

Simulations Performance – Cascaded LSO

Simulations Performance – Full LSO

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

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

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): 1632-11638, 2017.

Acknowledgments