Transcript Slide 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
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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
management,
storage,
transport
economic
performance
criteria
disturbances
valve
settings
reservoir
model
reservoir
actual
flow rates,
seismics...
optimization
update
state
estimation
reservoir
model
- +
gain
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Two roles of reservoir models
management,
storage,
transport
Estimation
Prediction
economic
performance disturbances
criteria
reservoir
model
actual
flow rates,
seismics...
valve
settings
reservoir
optimization
update
disturbance + state
estimation
past
present
reservoir
model
future
- +
gain
• Reservoir model used for two distinct tasks: state
estimation and prediction.
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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
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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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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)
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Hierachy of decision levels
Reservoir optimization
Process control
market
scheduling
day
yrs
field
RTO
plant optimization
hrs
wks
well and reservoir
MPC
advanced control
min
hrs/day
production system
PID
basic control process
sec
sec
base control layer
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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
saturations, pressures
e.g. permeabilities
Model-based state estimation:
past data
state update
initial state
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Parameter and state estimation in data
reconciliation
If parameters are unknown, they can be estimated by
incorporating them into the state vector:
past data
state/parameter update
initial state/parameter
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 is
crucially dependent on initial state/model
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Parameter estimation in identification
Parameter estimation by
applying LS/ML criterion
to (linearized) model
prediction errors
e
H0(q)
v
u
G0(q)
G(q,)
e.g.
are
parameters that describe
permeabilities
+
+
-
y
+
presumed data
generating system
predictor model
H(q,)-1
(t)
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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 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)
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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.
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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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Goal oriented modelling
Well addressed in literature: “identification for control”
Identify reduced order model from i/o data to optimize the
closed-loop transfer:
disturbance
disturbance
output
input
process
Identification
Feedback
control system
reference
input +
output
controller
process
-
Feedback
Feedback control
control system
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)
disturbance
disturbance
output
input
process
Identification
Feedback
control system
reference
input +
output
controller
process
-
Feedback
Feedback control
control system
system
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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
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Steps from data to prediction
prior knowledge
+
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)
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Steps from data to prediction
prior knowledge
+
production
data
observability
to be optimized
controllability
Relevant phenomena for assessing the dominant
subspaces of the state space
[See presentation of Maarten Zandvliet, Wednesday]
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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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Handling model uncertainty
prior knowledge
+
production
data
to be optimized
+
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 on
100 realizations/scenario’s
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Challenge for next step: “learn” the most/less likely scenario’s
during 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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