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
Delft Center for Systems and Control
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Delft Center for Systems and Control
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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Delft Center for Systems and Control
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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Delft Center for Systems and Control
Closed-loop Reservoir Management
reservoir
disturbances
valvesettings
actualflow rates,seismics...
management,storage,
transport
economicperformancecriteria
optimization
reservoirmodel
reservoirmodel
gain
+-
update
stateestimation
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Delft Center for Systems and Control
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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Delft Center for Systems and Control
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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Delft Center for Systems and Control
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
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Delft Center for Systems and Control
The basic ingredients
• 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
• Handling model uncertainty
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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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Delft Center for Systems and Control
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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Delft Center for Systems and Control
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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Delft Center for Systems and Control
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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Delft Center for Systems and Control
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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Delft Center for Systems and Control
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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Delft Center for Systems and Control
Points of attention in modelling
• How to find the right physics?
• Goal oriented modelling
• Handling model uncertainty
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Delft Center for Systems and Control
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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Delft Center for Systems and Control
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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Delft Center for Systems and Control
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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Delft Center for Systems and Control
Points of attention in modelling
• How to find the right physics?
• Goal oriented modelling
• Handling model uncertainty
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Delft Center for Systems and Control
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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Delft Center for Systems and Control
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)