Geir Evensen
History matching reservoir models
using the EnKF/EnKS
Hydro: Aluminium and energy supplier
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Founded 1905
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36 000 employees in 40 countries
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Leading offshore oil producer
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Worlds third largest aluminium supplyer
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Pioneer in renewable energy and energy efficient solutions
Date: 2004-01-16 • Page: 2
Hydro Research Centre, Bergen
Programs
Improved
60%
Exploration
Recovery
Date: 2004-01-16 • Page: 3
Small Fields
Polar Regions
Climate &
Renewable
energy
Program: 60% Recovery
Extend lifetime of mature fields
mm
cm
m
Projects:
Seismic mapping
Reservoir geophysics
IOR Oseberg seismics
Reservoir characterization
km
Methods for tertiary recovery
Well and intervention technology
Unstable flow
Date: 2004-01-16 • Page: 4
Introduction
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Simulation model must be consistent with the reservoir production
history to be used for predicting future production.
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History matching = Tuning of model parameters or parameter
estimation.
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For history mathcing we must:
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Define the parameter space (porosity, permeability, reservoir structure,
transmissibilities,….).
Define a cost fuction (prior statistical weights, norm, etc.).
Chose a minimization method (gradient descent, Monte Carlo, EnKF).
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Minimization problem
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Highly nonlinear, multiple local minima.
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Hard to solve using traditional minimization methods.
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Data errors independent in time and model a Markov sequence:
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Reformulation as a sequence of minimization problems.
Each subproblem provides a prior for the next problem.
Equivalent to solving the full problem in one go for linear models.
Evensen 2005 (www.nersc.no/~geir)
Approach used by the EnKF/EnKS.
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Update procedure in EnKS/EnKF
d_1
d_2
Prediction
EnKF update
EnKS update
Updates
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d_3
Time
Nonlinear minimization problem
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Ensemble Kalman Filter (EnKF)
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Statistical method which solves the combined state and
parameter estimation problem.
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Monte Carlo version of the original Kalman Filter.
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EnKF home page: http://www.nersc.no/~geir/EnKF
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The EnKF is now used for ocean and weather prediction
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TOPAZ system: http://topaz.nersc.no
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Meteorological Service of Canada
Potential for history matching and reservoir management?
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Ensemble Kalman Filter (EnKF)
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Representation of uncertainty using an ensemble of model solutions
and randomized measurements:
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Uncertainty predictions by ensemble integration:
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Describes error covariances for the model estimate and measurements.
Each ensemble member is integrated using a stochastic version of the
dynamical model.
Includes the impact of model errors.
Model ensemble is updated from measurements using a variance
minimizing analysis scheme:
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Assumption about Gaussian error statistics for prediction.
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Measurements with
errors
True state
Initial state with errors
Time
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Measurements with
errors
True state
Model prediction
with errors
Time
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Measurements with
errors
True state
Updated estimate
with errors
Model prediction
with errors
Time
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Measurements with
errors
True state
New model prediction
with errors
Updated estimate
with errors
Time
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Measurements with
errors
True state
Updated estimate
with errors
Time
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EnKF-Eclipse Implementation at Hydro
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Suite of F90 programs controlled by unix script
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Simulation software for generation of the initial ensemble.
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Only used to integrate model states forward in time.
interface between ECLIPSE and the EnKF:
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Simulation of realizations based on statistical geomodel.
Conditioning on log and AI data.
Eclipse simulator is used as a “black box”:
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Modular and model independent implementation.
Based on generic EnKF distribution from http://www.nersc.no/~geir/EnKF/
Convert between ECLIPSE restart files and ensemble files.
Differentiate between dynamic and static variables.
EnKF analysis program.
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EnKF-Eclipse Implementation:
Initialization of ensemble
Eclipse
data file
eclipse
Statistical
geomodel
iniens
logobs.uf
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Grid and
restart info
Poro/perm
ensemble
EnKF
ens0F.uf
ens0S.uf
ens0A.uf
ens0S.uf
EnKF-Eclipse Implementation
Ensemble integration and update
For j=0, data_times
For i=1,nrens
ens{j}A.uf
ens{j}S.uf
Eclipse
restart file
interface
interface
Eclipse
restart file
ens{j+1}F.uf
ens{j+1}S.uf
done
ens{j+1}F.uf
EnKF
obs{j+1}.uf
done
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ens{j+1}A.uf
eclipse
Estimation of permeability using EnKF
Reference
First guess
Major structure of permeability field is recovered!
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Estimate 25 months
Estimation of permeability using EnKF
Permeability
Information from data
accumulates in time.
Result is consistent with
statistical input model.
Definition of initial statistical
model is crucial.
Cross section distance
Results from idealized experiments are very promising!
Date: 2004-01-16 • Page: 20
Some previous EnKF reservoir applications
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Nævdal, Mannseth and Vefring (2003), Near well reservoir monitoring
through EnKF, (SPE 75235).
Nævdal, Johnsen, Aanonsen and Vefring (2003), Reservoir monitoring
and continuous model updating using EnKF, (SPE 84372).
Gu and Oliver (2004), History matching of the PUNQ-S3 reservoir model
using the EnKF, (SPE 89942).
Gao, Zafari and Reynolds (2003), Quantifying uncertainty for the PUNQS3 problem in a Bayesian setting with RML and EnKF, (SPE 93324).
Liu and Oliver (2005), Critical evaluation of the EnKF on history matching
of geological facies, (SPE 92867).
Wen and Chen (2005), Real-time reservoir model updating using EnKF,
(SPE 92991).
All conclude positively regarding the use of EnKF for history matching.
All consider idealized experiments.
Date: 2004-01-16 • Page: 21
EnKF-Eclipse for Oseberg Alpha North
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Complex reservoir.
5 producers.
3 injectors.
Simulation model hard to match.
Uncertainty about faults, barriers,
channels, and communication with
other reservoirs.
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Some preliminary remarks
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Good match for GOR at wells started early in simulation.
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Poor match for wells started late in simulation.
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Easy to fit unconstrained model to the first production data.
Too large weight on early production data?
Neglected model errors?
Typical parameterization problem?
Possible to include faults, structural errors, transmissibilities?
Uncertainty in production data.
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10-20% or more?
QC of production data crucial.
Date: 2004-01-16 • Page: 24
Summary
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Ongoing field case with new Oseberg alpha north model:
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Includes pluri-gaussian facies representation.
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Assimilates production and 4D seismic data.
Ongoing field case for Rimfaks:
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Collaboration with Statoil.
Date: 2004-01-16 • Page: 25