Finding good models for model-based control and optimization

1. Delft Center for Systems and Control Finding good models for model-based control and optimization Paul Van den Hof Okko Bosgra Delft Center for Systems and Control 17 July 2007

2. Manipulated variables include: • Valve / production settings (continuous) • Well locations and investments (discrete)  Main point The goal Develop tools for supporting economically optimal operation and development of reservoirs on the basis of • plant models of dynamical behaviour, and • observations / measurements of relevant phenomena (pressures, temperatures, flows, production data, seismics)

3. Contents • Setting and basic ingredients of the problem • Three relevant modelling issues: • Estimation of physical parameters • Models for filtering/control/optimization • Handling model uncertainty • Conclusions

4. management, storage, transport economic performance criteria disturbances actual flow rates, seismics... reservoir model valve settings reservoir optimization update reservoir model + - state estimation gain Closed-loop Reservoir Management

5. management, storage, transport economic performance criteria disturbances Estimation Prediction actual flow rates, seismics... reservoir model valve settings reservoir optimization update past present future reservoir model + - disturbance + state estimation gain Two roles of reservoir models • Reservoir model used for two distinct tasks: state estimation and prediction.

6. The basic ingredients • Optimal economic operation Balancing short term production targets and long-term reservoir conditions requires accurate models of both phenomena (including quantifying their uncertainty) and performance criteria with constraint handling

7. The basic ingredients • Dynamic models • Starting from reservoir models: • Uncertain (continuous as well as discrete), large scale, nonlinear and hard to validate • Saturations are important states that determine long term reservoir conditions (model predictions) • State estimation and parameter estimation (permeabilities) have their own role

8. The basic ingredients • Optimization Gradient-based optimization over inputs, in shrinking horizon implementation Starting from: initial state pdf initial parameter pdf adjoint-based optimization Point of attention: constraint handling (inputs/states)

9. market scheduling plant optimization advanced control basic control process Hierachy of decision levels Reservoir optimization Process control field day yrs well and reservoir hrs RTO wks production system min hrs/day MPC base control layer sec sec PID

10. Points of attention in modelling • How to find the right physics? • Goal oriented modelling • Handling model uncertainty

11. Parameter and state estimation in data reconciliation saturations, pressures e.g. permeabilities Model-based state estimation: state update past data initial state

12. Parameter and state estimation in data reconciliation If parameters are unknown, they can be estimated by incorporating them into the state vector: state/parameter update past data initial state/parameter Can everything that you do not know be estimated?

13. In case of large-scale parameter vector: • Singular covariance matrix (data not sufficiently informative) • Parameters are updated only in directions where data contains information Result: data-based estimation; result and reliability is crucially dependent on initial state/model

14. Parameter estimation in identification Parameter estimation by applying LS/ML criterion to (linearized) model prediction errors e.g. are parameters that describe permeabilities

15. Starting from (linearized) state space form: the model dynamics is represented in its i/o transfer function form: with the shift operator:

16. Principle problem of physical model structures Different might lead to the same dynamic models This points to a lack of structural identifiability There does not exist experimental data that can solve this! • Solutions: • Apply regularization (additional penalty term on criterion) to enforce a unique solution (does not guarantee a sensible solution for ) • Find (identifiable) parametrization of reduced dimension

17. At a particular point the identifiable subspace of can be computed! This leads to a map with See presentation Jorn van Doren (wednesday) Structural identifiability A model structure is locally (i/o) identifiable at if for any two parameters in the neighbourhood of it holds that

18. Observations • Local estimate is required for analyzing identifiability. This “relates” to the initial estimate in data-assimilation. • Measure of weight for the relevance of particular directions can be adjusted. • Besides identifiability, finding low-dimensional parametrizatons for the permeability field is a challenge!(rather than “identify everything from data”) • Once the parametrization is chosen, input/experiment design can help in identifying the most relevant directions.

19. Points of attention in modelling • How to find the right physics? • Goal oriented modelling • Handling model uncertainty

20. Feedback control system Feedback control system disturbance reference input + output controller process - Goal oriented modelling Well addressed in literature: “identification for control” Identify reduced order model from i/o data to optimize the closed-loop transfer:

21. Feedback control system Feedback control system disturbance reference input + output controller process - • Some general rules for feedback control: • For tracking / disturbance rejection problems: • low-frequent model behaviour usually dominated by (integrating) controller • best models are obtained from closed-loop experiments (similar to intended application)

22. Identification for filtering / optimization Question: are these relevant and feasible problems? 1. Find the model that leads to the best possible state estimate of the relevant states (saturations, pressures) 2. Find the model that leads to the best possible future production prediction Problems might include: generation of experimental data

23. Shows dual role of model: state estimation and long term prediction Steps from data to prediction prior knowledge + to be optimized production data • Typical for the reservoir-situation: • current data only shows (linearized) dynamics of current reservoir situation (oil/water-front) • future scenario’s require physical model (permeabilities)

24. prior knowledge + to be optimized production data observability controllability Steps from data to prediction Relevant phenomena for assessing the dominant subspaces of the state space [See presentation of Maarten Zandvliet, Wednesday]

25. Points of attention in modelling • How to find the right physics? • Goal oriented modelling • Handling model uncertainty

26. Handling model uncertainty prior knowledge + to be optimized production data + uncertainty + uncertainty + uncertainty • Sources: • Different geological scenarios • Model deficiencies • ……….

27. First results (Gijs van Essen en Maarten Zandvliet) Robust performance (open-loop strategy) based on 100 realizations/scenario’s

28. Challenge for next step: “learn” the most/less likely scenario’s during closed-loop operation

29. Conclusions • Basic methods and tools have been set, but there remain important and challenging questions, as e.g.: • Complexity reduction of the physical models: limit attention to the esssentials • Structurally incorporate the role of uncertainties in modelling and optimization • Major steps to be made to discrete-type optimization/decisions: e.g. well drilling • Take account of all time scales (constraint handling)