history match with ensemble based methodstotal e&p uk - grc . distance to facies...
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HISTORY MATCH WITH ENSEMBLE BASED METHODS :
USE OF DISTANCE TO BOUNDARY PARAMETERIZATION TO ADDRESS UNCERTAINTY AND 4D SEISMIC
OBSERVATION
A. Abadpour, R. Piasecki and P. Bergey
Total E&P UK - GRC
DISTANCE TO FACIES PARAMETERIZATION
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Facies are represented by discrete non-sortable values in the reservoir model.
To be addressed by EnKF a re-parameterization scheme seems mandatory.
Level set method to calculate the closest distance to the facies boundary was proposed by IRIS (SPE 143031 – 2011)
UPDATING FACIES BOUNDARIES – WORKFLOW
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Distance Calculation
FIPNUM
4 full cube PERMX
PERMX
EnKF Update
Remap Facies
EnKF Update
New PERMX
New FIPNUM
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FIRST TEST CASE
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Model dimensions: (13,23,20) , all cells are active
Two wells: W22: Water injector and W27 Producer
4 facies type : shale, laminated shale, laminated sand and massive sand
Uncertain parameters : PERMX/PERMY, PORO, NTG, PERMZ(using Kv/KH ratio), FIPNUM(facies distribution)
Initial Ensemble:
• 100 realizations of facies maps and properties (4 times for the full cube)
• Updated petro-physical values would be asigned to the model taking the updated Facies map into account.
Shale
Laminated Shale
Laminated Sand
Massive Sand
W22 W27
HISTORY MATCH RESULTS
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Updating FIPNUM
No FIPNUM Update
WBHP W27
WWCT W27 WGOR W27 WBHP W27
WWCT W27 WGOR W27
CHANGE IN PARAMETERS
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Facies 4 Facies 3
Facies 1 Facies 2
TEST ON CHANNELIZED MODEL
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WWCT w27 WGOR w27
WGOR W27 WWCT W27
No FIPNUM Update
W22
W27
UPDATED PARAMETERS
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Updating Properties & FIPNUM Just updating properties
Change in PERMX (mD) – Initial Vs Rerun 8
W27 W27 W22
W22
ANTICLINE – COMPLEX GEOLOGY
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• Model dimensions: X = 70, Y = 140 and Z = 10 • 6 producer and 4 water injector (2 Producer and 1 injector penetrated in the channel)
• 4 facies type including the channel in the middle
K = 300 MD, NTG = 60% Poro = 15% (X correlated)
K = 800 MD, NTG = 80% Poro = 17% (X correlated)
K = 50 MD, NTG = 40% Poro = 10% (X correlated)
K = 2000 MD, NTG = 80% Poro = 15% (X correlated)
•2 x 4D survey, before and after water breakthrough
• Uncertainty in direction, widths, tortuosity and density of channel • Exercise objective: EnKF to find where the channel is
Complex geology
HISTORY MATCH RESULTS
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No FIPNUM Update With FIPNUM Update
30 % of Realizations are lost as a result
of convergence issues.
CHANGE IN THE PARAMETERS - PERMX
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Initial Map Final Map (No Facies Update)
Final Map (With Facies Update)
Truth
ANCJ1
ANCP1
ANCJ2
ANCP2
ANCP3
ANCP4
ANCJ4
ANCP5
ANCP6
ANCJ3
FACIES PROPORTION BEFORE AND AFTER ENKF
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ANCJ1
ANCP1
ANCJ2
ANCP2
ANCP3
ANCP4
ANCJ4
ANCP5
ANCP6
ANCJ3
ANCJ1
ANCP1
ANCJ2
ANCP2
ANCP3
ANCP4
ANCJ4
ANCP5
ANCP6
ANCJ3
Prior Models
Posterior Models Distance to interface
Posterior Models Variogram normalized distance to facies
White outline = True location of channels
VARIOGRAM INFORMATION INTO DISTANCE CALCULATION
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Using Variogram anisotropy and curvature to modify the distance calculation. Anisotropy to stretch the distance in
the 3D space.
Curvature is to normalize the distance and emphasis on the correlation length.
Facies map modification during assimilation steps
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Original Idea Today
Warning: current implementation still statistically biased (toward equi-proportion), being corrected.
ASSIMILATION ON 4D SEISMIC OBSERVATIONS – WORKFLOW
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Observed Front
Simulated Front
F. M.
F. M.
Hausdorff Distance to Front
Difference
Distance to Front
Mismatch term to be used in EnKF update equation
Minor error introduced due to
low FMM order
Remark: projection onto 1D space akin to streamline parameterisation
MATCH RESULTS – BENEFITS OF NEW APPROACH
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Initial map
Reference map
Final map – Front Position Final map – Cell Saturation
As for facies benefits are to be found more in respecting geology than obtaining match
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No 4D Assimilation With 4D Assimilation
MATCH RESULTS – BENEFITS FROM 4D ASSIMILATION
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Truth
No 4D
With 4D
MATCHING 4D-DERIVED FRONT – 1 REALIZATION – NO VARIO. NORM.
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MATCHING 4D-DERIVED FRONT – ALL REALIZATIONS
Truth
No 4D
With 4D
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VARIOGRAM NORMALISATION: NOT MUCH DIFFERENT
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Truth
No 4D
+ 4D
No 4D + 4D
Some failed simulations – Lower statistical validity
Vario normalization of facies without 4D input, improves 4D forecast a lot. Improvement by adding vario normalized 4D is marginal / non existent.
GEOLOGICAL REALISM
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All histograms fairly well maintained
Initial No vario Vario Truth
INITIAL(BLUE) vs. TRUTH (GREEN)
GEOLOGICAL REALISM
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All histograms fairly well maintained
Initial No vario Vario Truth
UPDATED (No Vario - BLUE) vs. TRUTH (GREEN)
GEOLOGICAL REALISM
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All histograms fairly well maintained
Initial No vario Vario Truth
UPDATED (Vario. Norm - BLUE) vs. TRUTH (GREEN)
TEST ON A REAL RESERVOIR MODEL
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North aquifer
South aquifer
Below aquifer
14 Gas head aquifers
Uncertain parameters: • Porosity • Permeability X • Permeability Z via the ratio Kv/Kh • Net to Gross • Facies ( 4 facies type) • Well Skin • Table of influence for Carter-Tracy aquifers • IP of the head gas aquifers • Pressure of head gas aquifers
• Dimensions: 171 * 151 * 40 (100m * 100m * 0-6m) • 4 producers, and 2 water injectors. • 8 years of production (May 2003 to July 2011)
Uncertain, unrealistic boundary condition
FACIES VS PETROPHYSICS
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GIR122
WCT BHP GOR
Not Matched Acceptable
Matched
GIR122
Just Facies Just Petro
WPR – 115
WPR – 124
WCT – 124
BHP – 124
BHP – 124
126 126
122 122
WCT – 115
126
115
124 127
126
115
124 127
FACIES UPDATE
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SIM 036
SIM 040
Initial Models
SIM 30
SIM 36
SIM 40
Final Models
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FACIES PROPORTION Initial Models Final Models
FACIES 1
FACIES 4
DATA ASSIMILATION ON MAP PROPERTIES – PHI/K EVOLUTION
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FACIES 1-2-3 – PERMX UPDATES
F1
F2
F3
Deviation in the Ensemble Correction term
Misfit term
UNUSED DATA & SPURIOUS CORRELATION
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Phi
BHP
Deviation in the Ensemble
All points
Red points • Spurious correlation with unused values might be the reason for high deviation.
• Taking just into account the used ones doesn't solve the problem because of under sampling .
• Bootstrapping inside the used ones might be the solution in general case.
CONCLUSION & WAY FORWARD
Distance to the boundary parameterization proved to be a powerful tool to deal with facies uncertainty as well as 4D seismic observation.
Results obtained seems a big step forward in respecting the complex geology.
To better respect the initial proportion of the facies distribution this information should be also included in the parameterization scheme.
A synthetic test case model with clearer 4D seismic image as well as less uncertainty in the position of the channel might be a better representative of the capability of the proposed workflow.
Proposed parameterization to deal with the facies showed interesting results on a real data set.
Handling both facies and petrophysical parameters remains still challenging for a highly uncertain problem far from the solution.
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