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

2 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) Manipulated variables include: Valve / production settings (continuous) Well locations and investments (discrete)  Main point

Delft Center for Systems and Control 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

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

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

Delft Center for Systems and Control 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

Delft Center for Systems and Control 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

Delft Center for Systems and Control 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)

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

Delft Center for Systems and Control 10 Points of attention in modelling How to find the right physics? Goal oriented modelling Handling model uncertainty

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

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

Delft Center for Systems and Control 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

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

Delft Center for Systems and Control 15 Starting from (linearized) state space form: the model dynamics is represented in its i/o transfer function form: with the shift operator:

Delft Center for Systems and Control 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

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

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

Delft Center for Systems and Control 19 Points of attention in modelling How to find the right physics? Goal oriented modelling Handling model uncertainty

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

Delft Center for Systems and Control 21 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) controllerprocess + - output reference input disturbance Feedback control system

Delft Center for Systems and Control 22 Identification for filtering / optimization 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 Question: are these relevant and feasible problems? Problems might include: generation of experimental data

Delft Center for Systems and Control 23 Steps from data to prediction production data to be optimized Shows dual role of model: state estimation and long term prediction 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) prior knowledge +

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

Delft Center for Systems and Control 25 Points of attention in modelling How to find the right physics? Goal oriented modelling Handling model uncertainty

Delft Center for Systems and Control 26 Handling model uncertainty production data to be optimized prior knowledge + uncertainty + uncertainty + uncertainty Sources: Different geological scenarios Model deficiencies ……….

Delft Center for Systems and Control 27 First results (Gijs van Essen en Maarten Zandvliet) Robust performance (open-loop strategy) based on 100 realizations/scenario’s

Delft Center for Systems and Control 28 Challenge for next step: “learn” the most/less likely scenario’s during closed-loop operation

Delft Center for Systems and Control 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)