1 Finding good models for model-based control and optimization Paul Van den Hof Okko Bosgra Delft...

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Finding good models for model-based control and

optimization

Paul Van den HofOkko Bosgra

Delft Center for Systems and Control

17 July 2007


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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

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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

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Closed-loop Reservoir Management

reservoir

disturbances

valvesettings

actualflow rates,seismics...

management,storage,

transport

economicperformancecriteria

optimization

reservoirmodel

reservoirmodel

gain

+-

update

stateestimation

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Two roles of reservoir models

• Reservoir model used for two distinct tasks: state estimation and prediction.

past

Estimation

present future

Predictionreservoir

disturbances

valvesettings

actualflow rates,seismics...

management,storage,

transport

economicperformancecriteria

optimization

reservoirmodel

reservoirmodel

gain

+-

update

disturbance + stateestimation

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The basic ingredients

• Optimal economic operation

Balancing short term production targets and long-termreservoir conditions

requires accurate models of both phenomena(including quantifying their uncertainty)

and performance criteria with constraint handling

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• 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

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• Optimization

Gradient-based optimization over inputs, in shrinking horizon implementationStarting from:

initial state pdfinitial parameter pdf

adjoint-based optimization

Point of attention: constraint handling (inputs/states)

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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

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Points of attention in modelling

• How to find the right physics?

• Goal oriented modelling


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Parameter and state estimation in data reconciliation

Model-based state estimation:

past data

initial state

state update

saturations, pressurese.g. permeabilities

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Parameter and state estimation in data reconciliation

If parameters are unknown, they can be estimated byincorporating them into the state vector:

past data

initial state/parameter

state/parameter update

Can everything that you do not know be estimated?

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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 iscrucially dependent on initial state/model

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Parameter estimation in identification

G0(q)+++u yv

H0(q)

e

G(q,)+-

H(q,)-1

(t)

presumed datagenerating system

predictor model

Parameter estimation by applying LS/ML criterion to (linearized) model prediction errors

e.g. areparameters that describepermeabilities

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Starting from (linearized) state space form:

the model dynamics is represented in its i/o transfer function form:

with the shift operator:

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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

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Structural identifiability

A model structure is locally (i/o) identifiable at if for anytwo 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)

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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.

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Goal oriented modellingWell addressed in literature: “identification for control”

Identify reduced order model from i/o data to optimize the closed-loop transfer:

controller process+

-

outputreferenceinput

disturbance

Feedback control systemIdentification

processoutputinput

disturbance

Feedback control systemFeedback control system

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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)

controller process+

-

outputreferenceinput

disturbance

Feedback control systemIdentification

processoutputinput

disturbance

Feedback control systemFeedback control system

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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

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Steps from data to prediction

productiondata

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+

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Steps from data to prediction

Relevant phenomena for assessing the dominant subspaces of the state space

[See presentation of Maarten Zandvliet, Wednesday]

productiondata

to be optimized

observability controllability

prior knowledge+

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Handling model uncertainty

productiondata

to be optimizedprior knowledge+

+uncertainty

+uncertainty

+uncertainty

Sources:• Different geological scenarios• Model deficiencies• ……….

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First results (Gijs van Essen en Maarten Zandvliet)

Robust performance (open-loop strategy) based on100 realizations/scenario’s

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Challenge for next step: “learn” the most/less likely scenario’sduring closed-loop operation

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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)

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1 Finding good models for model-based control and optimization Paul Van den Hof Okko Bosgra Delft...

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