An EnKF formulation that better respects atmospheric balance
upstream and technical services - UiS Laura Dovera IOR_Norway.pdf · upstream and technical...
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upstream and technical services
Polymer injection optimization using ensemble methods Laura Dovera
IOR Norway 2015 28-29 April, Stavanger
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upstream and technical services
§ Reservoir modelling study to implement a chemical Enhanced Oil Recovery (EOR) pilot in a giant on-shore brown field
§ quantification of EOR benefit: incremental oil and associated cash flow
§ confidence interval accounting for geological/engineering
uncertainties
§ Integrated workflow with Ensemble Kalman filter (EnKF) and Ensemble Optimization (EnOpt) § Automatic integration of production data (history match)
§ Forecast optimization of chemical injection parameters
§ Uncertainty quantification with multiple models
Introduction
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The field and the pilot area
§ Giant brown field § Moderate recovery factor § Onshore sandstone
environment § Oil viscosity 3-8 cP § About 200 prod. and 40 inj. § Unfavorable mobility ratio
§ Multilayered field with 12 stacked reservoirs § Turbiditic and deltaic sandstones with intercalations of shales and evaporites § Production start-up in 1953 § Current production strategy is peripheral water injection
IOR/EOR actions Why IOR/EOR?
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Polymer flooding
§ Polymer flooding is one of the selected EOR techniques polymer vs. water injection
− Higher viscosity µ polymer >> µW
− Rock adsorption i.e. Krw reduction
à Lower mobility ratio
§ Actual mobility 6.5 à expected 1-0.5, with 3-6 cP target polymer
viscosity
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Project activities
§ Selection of suitable area for pilot test § Good petrophysical properties § Current low recovery factor § Possibility of implementing a dispersed injection scheme § Short producers-injectors distance
§ New core data acquisition
§ Laboratories analyses § Routine and special core analyses § Chemical study for ad hoc polymer
§ Sector model construction § Geological and dynamic model § History match § Definition and optimization of forecast strategy
wellspolymer injectorpolygon for local updating in the sector model
Legend
The pilot area
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Sector model
Pilot area sector § High resolution model
§ 22 total wells
§ 14 wells in commingle
§ 6 producers, 2 injectors to match
§ Complex history match
§ 60 years production
§ Few pressure data
§ Communication with the rest of the field
§ Challenges:
§ Define multiple models to represent uncertainty
§ Automatic multiple history match with EnKF
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§ The Ensemble Kalman filter is a sequential data assimilation method to update dynamic systems
§ Monte Carlo approach: representation of initial uncertainty using an ensemble of models § Geostatistics and/or parameters sampling
§ Forward step: evolution of uncertainty by forward ensemble models in time § Eclipse simulation
§ Assimilation of measurements using an error minimizing update § Update parameters and state variables
The Ensemble Kalman Filter (Evensen, 2006)
SEQUENTIAL ASSIMILATION
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upstream and technical services
The EnKF idea
Water Cut
Time
Measurements with errors
Original prediction
Models prediction
Updated estimate
New models prediction
Updated estimate
New models prediction
Updated estimate
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EnKF on pilot area – Ensemble generation
§ NTG
§ Porosity
§ Permeability
§ Water Saturation = fun(Porosity)
Multiple porosity grid Multiple permeability grid
• Spatial variables • Generated using geological workflow
§ Water rel. perm.
§ Faults Transmissibility
• Scalar variables • Sampled within uncertainty ranges
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§ EnKF updating: realizations are adjusted adding data mismatch weighted by the Kalman Gain matrix
Localization
Permx‘ = Permx + (dobs-dsim)
Kalman gain weights for permeability in layer 5 Probable spurious
correlations
Probable true correlations
Pressure data Assimilation well I2
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upstream and technical services
§ EnKF updating: realizations are adjusted adding data mismatch weighted by the Kalman Gain matrix
Localization
Kalman gain weights for permeability in layer 5
= *
Localization region Localized Kalman gain
Pressure data Assimilation well I2
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upstream and technical services
EnKF on the pilot area – Summary
Multiple porosity realizations Multiple permeability realizations § Ensemble size: 100
§ Ensemble generation using 3 spatial and 6 scalar parameters
§ Match of 8 wells § Localization for each well and each measurements
§ Run EnKF for 42 assimilation steps § Rerun of the final updated realizations
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upstream and technical services
EnKF on the pilot area - History match for PROD P4 PROD P4 PROD P4
PROD P4
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EnKF application – Final properties update
Initial average Lnk map - layer 5 Final average Lnk map - layer 5
§ Geological coherence is preserved
§ No manual modifications
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Robust (on multiple models) optimization
§ EnKF output: ensemble of 100 matched models that represent the current geological uncertainty
§ Single scenario optimization: major risk of underestimating uncertainty, even the P50 could be a very unlikely model!
§ Can we perform a robust optimization - where the target is to improve the statistical outcome of the models ?
Optimization of a single profile
Robust Optimization of a profile distribution
p90
p10
p50
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Ensemble Optimization (Chen, 2008)
§ Define optimization parameters and objective § polymer concentration, rates, … § cash flow, cumulative oil, …
§ Generate an ensemble of controls and couple it with the ensemble of realizations
§ Use the ensemble to investigate the objective
§ Compute gradient with the ensemble
§ Move the ensemble towards the maximum
),( jujNPVg xy=
),,( 1 cNxx …=xeNjj
uj 1},{ =xy
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Polymer flooding optimization with EnOpt
Polymer injector
§ Optimize polymer injection to increment Cash Flow § Over 10 years § For the TARGET wells
§ Optimization parameters:
§ Polymer slug concentrations (kg/sm3) § Slug cycles (time) § 3 different slugs
§ Comparison to § Natural depletion scenario § Water injection scenario
Target wells
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upstream and technical services
Polymer flooding optimization – Results
Actual Development Strategy
Water Injection Strategy
Polymer Injection Strategy
Polymer injection profiles guarantee the highest oil
rates
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upstream and technical services
Polymer flooding optimization – Results
P50 profiles
1st Polymer slug viscosity 3 cP
Initial water pre-flush
2nd Polymer slug viscosity 6.5 cp Driving water
injection
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upstream and technical services
Polymer flooding optimization – Results
P50 profiles Polymer injection average incremental recovery equal to 16%
Water injection average incremental recovery equal to 10%
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upstream and technical services
Polymer flooding optimization – Results
P50 profiles Produced water is reduced by 11% using polymer with respect to
the water injection scenario
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upstream and technical services
Polymer flooding optimization – Summary
Development scenario
Additional Oil Production at 2023
(P50)
Additional technical Cash Flow at 2023
(P50)
% %
No Injection - -
Water Inj. + 10 % + 3 %
Polymer Inj. + 16 % + 8 %
§ Reference values for technical cash flow evaluation § Oil price: 90 $/bbl § Treated water cost: 1 $/bbl § Polymer cost: 4.25 $/kg § CAPEX polymer pilot: 2.0 $ million
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Current status of project
§ Dispersed water injection implemented in the pilot area
§ Polymer plant commissioned
§ Start-up of polymer injection planned for Q3/2015
§ Injection strategy will be implemented according to optimization results
§ A proper monitoring plan is on going
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Conclusions
§ Multiple sector models § Integrated workflow from static to dynamic
§ Multiple history matching using the EnKF § Good quality history match § No manual modifications
§ Robust optimization of polymer flooding § Polymer flooding is cost-effective § Average cumulative oil = +16% § Average Cash Flow = +8%
§ Closed loop workflow § First iteration: ensemble HM and optimization § Interesting way forward - Close the loop: update the ensemble with
most recent data and use it for continuos real time monitoring and optimization
The closed loop