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SPE DISTINGUISHED LECTURER SERIESis funded principally
through a grant of the
SPE FOUNDATIONThe Society gratefully acknowledges
those companies that support the programby allowing their professionals
to participate as Lecturers.
And special thanks to The American Institute of Mining, Metallurgical,and Petroleum Engineers (AIME) for their contribution to the program.
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Acknowledgements
• SPE International for the opportunity to participate in the 2006-07 Distinguished Lecturer Program
• BP America, Inc. for permission, and the Professional Recognition Program which has provided the time and resources to prepare and present this material
• Colleagues whose work is represented
• Local SPE chapters worldwide for their efforts in hosting these presentations
Upgridding and Upscaling:Current Trends and Future DirectionsDr. Michael J. King
Senior Advisor, Reservoir Modelling and SimulationBP America, Inc.
SPE 2006-07 Distinguished Lecturer
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Outline
• Introduction: Change of Scale & Upscaling
• Case Study: Magnus LKCF
– Validation and Analysis: What Went Wrong?
• Improved Upscaling: Understanding Permeability
– Boundary Conditions and Permeability Upscaling
– Transmissibility: Yes, Permeability: No
– Maintain the Well Injectivity & Productivity
• Magnus LKCF & Andrew Reservoir Case Studies
• Summary: What Works Well & What To Avoid?
• Future Trends:
– A Priori Error Analyses & Designer Grids
• Summary: Best Practice in Upscaling
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Introduction: What is Upscaling?
What is Upscaling?
• Assign “effective” properties to coarse scale cells from properties on fine scale grid
• Capture flow features of fine scale model
Why Upscale?
• Reduce CPU time for uncertainty analysis and risk assessment
• Make fine-scale simulation practical
─ geological models: ~10 -100 million cells
Resolution?
Image from Mike Christie
DW GOM
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Why Upscale?: CPU Time ReductionWaterflood Field Example
CP
U R
atio
(C
oar
se S
cale
/ F
ine
Sca
le)
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
()
Uniform Layering CoarsenOptimum Layering CoarsenMCoarsen
Active Cell Ratio (Coarse Scale / Fine Scale)
Optimal Layer Coarsening
Uniform Layer Coarsening
Flexible 3D Coarsening
SPE 95759, King et.al.
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Upgridding and Upscaling: Context
Upgridding & Upscaling in the overall 3D Modelling Workflow
(After Roxar RMS)
• 3D Detailed Geologic Static Model
– Structure from well picks &/or seismic horizons
– Properties from well logs &/or seismicattributes &/or field performance data
– Geologic description from facies, analogues and field data
• Upscaled flow simulation model
– Performance prediction in the absence of dynamic data
– Starting point for a history match when dynamic data is available
• When done well, upscaling willpreserve the most important flow characteristics of a geologic model
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Why Upscale?: Length & Area
30 miles
30 miles
Lateral resolution of geologic and simulation grids are set by well
spacing
30 mile length of ACG reservoirs
with the London M25 loop used to
set the scale
Simulation Grid Cells: 200m x 200m or 100m x 100m
Geologic Grid Cells: 100m x 100m or 50m x 50m
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Kanaalkop: Tanqua Karoo basin, South AfricaDeepwater channel w/splay at top of photo
~15ft windmill
~10ft exposure
~250ft, which is about the size of a single cell in the areal direction of many simulation grids
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Why Upscale?: Thickness
Upscaling is dominated by loss of vertical resolution
Geologic grid will typically have 1 ft or 50 cm vertical resolution
Simulation grid may include only a single layer per geologic unit
600 ft section of a North Slope reservoir, with the 190 ft BP Anchorage office for scale
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Outline
• Introduction: Change of Scale & Upscaling
• Case Study: Magnus LKCF
– Validation and Analysis: What Went Wrong?
• Improved Upscaling: Understanding Permeability
– Boundary Conditions and Permeability Upscaling
– Transmissibility: Yes, Permeability: No
– Maintain the Well Injectivity & Productivity
• Magnus LKCF & Andrew Reservoir Case Studies
• Summary: What Works Well & What To Avoid?
• Future Trends:
– A Priori Error Analyses & Designer Grids
• Summary: Best Practice in Upscaling
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Summary:What Works Well…
• Preserve connectivity and flow within the reservoir using flow based transmissibility upscaling
– Wide “Pizza Box” BC’s preserve flow tortuosity
– &/or Sealed Side BC’s preserve flow barriers
• Preserve flow between reservoir and wells using algebraic well index upscaling
– Preserves reservoir quality
• This combination of techniques has worked well within BP & similarly elsewhere in the industry
• Streamline calculations provide detailed validation based on pressures, sweep, and time of flight
– Validation after upscaling is always necessary
1
2
3
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Do We Have an Economic LKCF Waterflood Development?
LKCFLimit
OWC
MSMLimit
1 2 A- 9M5 :C4M1 6 :A4
1 km
M1 2 :A5-2700
LKCF
-2800
UKCF
-2900
-3000
MSM C-G
-3100
MSM A
-3200
B Shale
-3300
-3400Heather / Brent
-3500
-3600
-3700
1 2 A- 9M5 :C4M1 6 :A4
1 km
M1 2 :A5-2700
LKCF
-2800
UKCF
-2900
-3000
MSM C-G
-3100
MSM A
-3200
B Shale
-3300
-3400Heather / Brent
-3500
-3600
-3700
1 2 A- 9M5 :C4M1 6 :A4
1 km
M1 2 :A5-2700
LKCF
-2800
UKCF
-2900
-3000
MSM C-G
-3100
MSM A
-3200
B Shale
-3300
-3400Heather / Brent
-3500
-3600
-3700
Yellow = ChannelRed = MarginsBlue = Non-pay
64x64x450 = 1,843,200 cells 50mx50mx0.5m resolution
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Cell Permeability Upscaling:Laboratory and Reservoir Model
• A laboratory coreflood
• In three dimensions, we have three numerical corefloods
– Coreflood follows the coarse cell shapes
– No flow side boundary conditions are the most common (others are possible)
QA
K PL
=µ∆
Darcy’s Law:
1 2
3 4
k*
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Streamlines in the Upscaled LKCF ModelHow Well Did 2x2x6 Upscaling Work?
• Time of Flight & Pressures after conventional 2x2x6 upscaling:
– Loss of 95% of effective permeability
– Loss of internal reservoir heterogeneity
Coarse Scale Time of Flight
Coarse Pressure
• 3D Streamlines, Time of Flight & Pressures calculated in the fine scale geologic model
– 2xInjectors & 2xProducers at a typical waterflood well spacing
– Fence diagram traced within the 3D geologic model
– Pressure constrained wells used to validate permeability
Fine Scale Time of Flight
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Cell Permeability UpscalingWhat Went Wrong?
600
200
0
0
500
600
0
300
300
0
0
300
0 0 600 0
KX Permeability0 100 200 300 400 500 600
0 0 0 0 600 600 600 600 600 0 0 0
0 0 0 0 600 600 600 600 600 0 0 0
0 0 0 0 600 600 600 600 600 0 0 0
0 0 0 0 600 600 600 600 600 0 0 0
0 0 0 0 0 600 600 600 600 600 0 0
0 0 0 0 0 0 600 600 600 600 600 0
300 300 300 0 0 0 600 600 600 600 600 0
300 300 300 0 0 0 0 600 600 600 600 600
300 300 300 300 300 0 0 600 600 600 600 600
300 300 300 300 300 300 0 0 600 600 600 600
300 300 300 300 300 300 0 0 600 600 600 600
300 300 300 300 300 300 0 0 600 600 600 600
• Sealed Side coreflood boundary conditions systematically expand barriers and reduce the continuity of pay
• Example 12x12=>4x4 (3x3 Upscaling):
• Continuous channel replaced by marginal sands
• Highly productive well replaced by poor producer
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Cell Permeability UpscalingStreamline Flow Visualization
• Each cell in isolation
• No cross-flow
• Equilibrium at cell faces
• Preserves & expands barriers
12x12 => 3x3
4x4 Upscaling Example
KX Cell Permeability KY Cell Permeability
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Cell Permeability UpscalingErrors & More Subtle Errors…
• Sealed Side Boundary Conditions do not adequately represent fluid flow in the fine scale model
– Reservoir quality is not preserved
– This is the most significant error
However, there are more subtle errors…
• Well Productivity (or Injectivity) is not preserved
– Well Index Upscaling
• Needless loss of spatial resolution
– Transmissibility Upscaling
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Outline
• Introduction: Change of Scale & Upscaling
• Case Study: Magnus LKCF
– Validation and Analysis: What Went Wrong?
• Improved Upscaling: Understanding Permeability
– Boundary Conditions and Permeability Upscaling
– Transmissibility: Yes, Permeability: No
– Maintain the Well Injectivity & Productivity
• Magnus LKCF & Andrew Reservoir Case Studies
• Summary: What Works Well & What To Avoid?
• Future Trends:
– A Priori Error Analyses & Designer Grids
• Summary: Best Practice in Upscaling
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Boundary Conditions andUpscaled Permeability - 1/2
• Upscale a simple sand / shale reservoir
• Sealed side BC’s expand barriers
• Open linear pressure BC’s allow barriers to leak
• “Pizza box”(Wide BC’s) allow global flow tortuosity
One Cell
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Boundary Conditions andUpscaled Permeability – 2/2
Question: Which permeability is right?
Answer:
• Wide “Pizza Box” (or tortuous) boundary conditions provide the best representation of fluid flow capacity, but…
• Sealed side boundary conditions preserve barriers.
– Barriers are often very important for modelling gas displacement, especially for vertical permeability
– They are also important in preserving channel margins
• Both answers are useful
– Use your judgement as engineers
• What is most important in your reservoir processes?
– Use both choices of boundary conditions as a sensitivity
• Mix and match horizontal and vertical treatments?
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Transmissibility Upscaling – 1/3Preserves Spatial Resolution
• Transmissibility can be calculated by direct upscaling instead of from the harmonic average of cell permeabilities
• “Link Permeability” is upscaled from cell center to cell center and has double the lateral resolution compared to cell permeability upscaling
• Harmonic average of a zero cell permeability is always zero
( ) ( )( ) ( ) 1
12121
2
+
+++ +
⋅⋅=
ii
iiii DXKXDXKX
DXKXDXKXATX
1
212121
2
+
+++ +
⋅=
ii
iii DXDX
KXATX
121 )()( ++ == iii MinusKXKXPlusKX
i 1+i
21+i
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Transmissibility Upscaling – 2/3KX Streamline Flow Comparisons
KXSealed
Cell
KXWide
Shifted
KXSealed Shifted
KXYWide No
Shift
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Transmissibility Upscaling – 3/3Captures fine scale juxtaposition
0 MD 0 MD 38 MD 0 MD 50 MD50 MD
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Well Index UpscalingUsed to Preserve Reservoir Quality
• Well productivity / injectivity & sealed side coreflood permeability?
– Does not describe radial flow andlogarithmic pressure drop near a well
• Instead, use three (hypothetical)X, Y, and Z wells for each coarse cell
( )( )w
ZZ rr
HKYKXWI0ln
2 ⋅=
µπ
( )( )w
YY rr
HKZKXWI0ln
2 ⋅=
µπ
( )( )w
XX rr
HKZKYWI0ln
2 ⋅=
µπ
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Improved Upscaling:Well Index + Transmissibility
• Lack of pay continuity resolved through Well Index Upscaling
– Preserves injectivity and productivity of horizontal and vertical wells
– But, expands channels and removes barriers
• Contrast and barriers reintroduced through Transmissibility Upscaling
– Repeat in all three directions for 2x2x2=8-fold factor of improved flow resolution compared to cell permeabilities
KX Permeability0 100 200 300 400 500 600
0 0 0 0 600 600 600 600 600 0 0 0
0 0 0 0 600 600 600 600 600 0 0 0
0 0 0 0 600 600 600 600 600 0 0 0
0 0 0 0 600 600 600 600 600 0 0 0
0 0 0 0 0 600 600 600 600 600 0 0
0 0 0 0 0 0 600 600 600 600 600 0
300 300 300 0 0 0 600 600 600 600 600 0
300 300 300 0 0 0 0 600 600 600 600 600
300 300 300 300 300 0 0 600 600 600 600 600
300 300 300 300 300 300 0 0 600 600 600 600
300 300 300 300 300 300 0 0 600 600 600 600
300 300 300 300 300 300 0 0 600 600 600 600
600
467
200
200
533
600
0
300
300
200
67
300
0 400 600 0
600
467
200
200
533
600
0
300
300
200
67
300
0 400 600 0
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Coreflood Cell Permeability ORWell Index + Transmissibility Upscaling
• Coreflood Cell Permeability Upscaling
• Well Index + Transmissibility Upscaling KX Permeability0 100 200 300 400 500 600
600
200
0
0
500
600
0
300
300
0
0
300
0 0 600 00 0 0 0 600 600 600 600 600 0 0 0
0 0 0 0 600 600 600 600 600 0 0 0
0 0 0 0 600 600 600 600 600 0 0 0
0 0 0 0 600 600 600 600 600 0 0 0
0 0 0 0 0 600 600 600 600 600 0 0
0 0 0 0 0 0 600 600 600 600 600 0
300 300 300 0 0 0 600 600 600 600 600 0
300 300 300 0 0 0 0 600 600 600 600 600
300 300 300 300 300 0 0 600 600 600 600 600
300 300 300 300 300 300 0 0 600 600 600 600
300 300 300 300 300 300 0 0 600 600 600 600
300 300 300 300 300 300 0 0 600 600 600 600
600
467
200
200
533
600
0
300
300
200
67
300
0 400 600 00 0 0 0 600 600 600 600 600 0 0 0
0 0 0 0 600 600 600 600 600 0 0 0
0 0 0 0 600 600 600 600 600 0 0 0
0 0 0 0 600 600 600 600 600 0 0 0
0 0 0 0 0 600 600 600 600 600 0 0
0 0 0 0 0 0 600 600 600 600 600 0
300 300 300 0 0 0 600 600 600 600 600 0
300 300 300 0 0 0 0 600 600 600 600 600
300 300 300 300 300 0 0 600 600 600 600 600
300 300 300 300 300 300 0 0 600 600 600 600
300 300 300 300 300 300 0 0 600 600 600 600
300 300 300 300 300 300 0 0 600 600 600 600
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Outline
• Introduction: Change of Scale & Upscaling
• Case Study: Magnus LKCF
– Validation and Analysis: What Went Wrong?
• Improved Upscaling: Understanding Permeability
– Boundary Conditions and Permeability Upscaling
– Transmissibility: Yes, Permeability: No
– Maintain the Well Injectivity & Productivity
• Magnus LKCF & Andrew Reservoir Case Studies
• Summary: What Works Well & What To Avoid?
• Future Trends:
– A Priori Error Analyses & Designer Grids
• Summary: Best Practice in Upscaling
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LKCF Upscaling ValidationWell Index + Transmissibility
• 3D Streamlines & Time of Flight
• Comparison of:
– Fine Scale Model
– Coreflood Cell Perm Upscaling
– WI + Transmissibility Upscaling
Fine Scale Time of Flight
Coarse Scale Time of Flight
Coarse Pressure
Coarse Scale Time of Flight
Coarse Pressure
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Transmissibility Multipliers:Double the Spatial Resolution
• A transmissibility multiplier can represent a barrier without using a cell
• In contrast, zero vertical permeability prevents flow both up AND down and impacts flow in three layers
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Andrew Reservoir:Validation & Impact of Thin Barriers
Well Index + Transmissibility upscaling tracks
fine scale prediction &
early field performance
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Outline
• Introduction: Change of Scale & Upscaling
• Case Study: Magnus LKCF
– Validation and Analysis: What Went Wrong?
• Improved Upscaling: Understanding Permeability
– Boundary Conditions and Permeability Upscaling
– Transmissibility: Yes, Permeability: No
– Maintain the Well Injectivity & Productivity
• Magnus LKCF & Andrew Reservoir Case Studies
• Summary: What Works Well & What to Avoid?
• Future Trends:
– A Priori Error Analyses & Designer Grids
• Summary: Best Practice in Upscaling
40 of 57
Summary:What Works Well…
• Preserve connectivity and flow within the reservoir using flow based transmissibility upscaling
– Wide “Pizza Box” BC’s preserve flow tortuosity
– &/or Sealed Side BC’s preserve flow barriers
• Preserve flow between reservoir and wells using algebraic well index upscaling
– Preserves reservoir quality
• This combination of techniques has worked well within BP & similarly elsewhere in the industry
• Streamline calculations provide detailed validation based on pressures, sweep, and time of flight
– Validation after upscaling is always necessary
41 of 57
Summary:What to Avoid…
• Flow based ‘coreflood’ upscaling for cell permeabilities
– Sealed side boundary conditions will not preserve flow tortuosity & will under-estimate reservoir quality
– Open linear pressure boundary conditions will not preserve reservoir barriers
• A single upscaling calculation cannot be used to preserve:– Reservoir quality
– Reservoir barriers
– Tortuosity of reservoir fluid flow around barriers
• Unfortunately, using coreflood permeability upscaling is the most common practice in the industry…
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Outline
• Introduction: Change of Scale & Upscaling
• Case Study: Magnus LKCF
– Validation and Analysis: What Went Wrong?
• Improved Upscaling: Understanding Permeability
– Boundary Conditions and Permeability Upscaling
– Transmissibility Yes, Permeability No
– Maintain the Well Injectivity & Productivity
• Magnus LKCF & Andrew Reservoir Case Studies
• Summary: What Works Well & What To Avoid?
• Future Trends:
– A Priori Error Analyses & Designer Grids
• Summary: Best Practice in Upscaling
43 of 57
Future Trends:A Priori Error Analyses & Designer Grids
• Wouldn’t it be nice to know if an upscaling calculation would be a good approximation before you performed the upscaling calculation?
• Sources of Upscaling Error
• Designer Grids: Upscale in the Simulator at Initialization
– Calculate Transmissibility and Pore Volume for Composite Cells
Assumption Source of Error (Missing Physics)
• Pressure equilibrium within the coarse cell
• Disconnected pay within the coarse cell will not be in equilibrium
• Fluid velocity is parallel to the pressure drop
• Flow may depend upon the transverse pressure drop on the coarse grid
• Single velocity within a coarse cell
• Distribution of multiphase frontal velocities replaced by a single value
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Error from Layer Coarsening:Flood Front Progression
• Error in the velocity distribution is introduced while upscaling
• Different fluid velocities are replaced by a single value
• F’(S) Kx/Phi is the frontal speed in each layer
– This is the property whose heterogeneity we will analyze
– Analysis applies to the net sands
• Vertical equilibrium within each coarse cell
FastSlow
MediumFastSlow
Medium
( ) ( )φXW KSF ⋅′ *
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Designer Grids within the Flow SimulatorStatic Boundary Conditions
• Source of A Priori Error: Multiphase frontal velocities are replaced by a single value
– Design simulation layering from 3D geologic model to minimize variation in local multiphase frontal velocities
249, 80% 336, 86%
0
10
20
30
40
50
60
70
80
90
100
0 200 400 600 800 1000 1200 1400 1600
Model Layers
%-H
eter
ogen
eity
0
2
4
6
8
10
12
14
16
18
20
RM
S R
egre
ssio
n - E
rror
Li & Beckner % Heterogeneity% Heterogeneity ; B-Variation% Heterogeneity: Uniform CoarsenDiagonal GuideSolution Total RMS RegressionSolution Weighted RMS RegressionTotal RMS RegressionWeighted RMS Regression
Number of Coarse Layers
%-H
eter
og
enei
ty
RM
S R
egre
ssio
n E
rro
rOptimal Layering
Uniform Coarsening: Not Efficient
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Designer Grids within the Flow SimulatorUpscale During Initialization (Static)
• General trend shows that uniform coarsening does not perform well
• “Optimal” (293 layers) is the best layering scheme
• Flexible 3D grid (MCOARSE) provides even better results
Tight Gas Layer CoarseningFine Scale Model 22x23x1715 (Geological Scenario 5)
0
5
10
15
20
25
30
0 200 400 600 800 1,000 1,200 1,400 1,600 1,800
Model Layers
Cum
. Gas
Pro
d. (B
CF)
Regular-CoarsenNextVar-OneStepNextVar-SequentialOptimal-12LOptimalLi-Map-12LLi-Ave-MaxLLi-Ave-12LMCOARSE
Fine Scale
Li and Beckner
UniformMCOARSE
Optimal
UniformCoarsening
OptimalLayering
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Layer Coarsening:Waterflood Example
Fine Scale124 Layers
Optimal22 Layers
7 LayersToo Coarse
22 Uniform LayersToo Coarse
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Waterflood Field Example:Oil Recovery and Watercut
• Optimal Simulation Model has 22 layers– 7 layers and 22 uniform layers are each too coarse
0%
5%
10%
15%
20%
25%
30%
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
FineScaleCoarsen_54Coarsen_22Coarsen_31Coarsen_19Coarsen_07
0%
5%
10%
15%
20%
25%
30%
0 2000 4000 6000 8000 10000 12000
FineScaleCoarsen_54Coarsen_22Coarsen_31Coarsen_19Coarsen_07
Oil Production
Time
Oil Production
PVINJ7 Layers7 Layers
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0 2000 4000 6000 8000 10000 12000
FineScaleCoarsen_54Coarsen_22Coarsen_22UCoarsen_31Coarsen_19Coarsen_07
@
1760
1780
1800
1820
1840
1860
1880
1900
1920
1940
1960
1980
0 2000 4000 6000 8000 10000 12000
FineScaleCoarsen_22Coarsen_22U
Average Reservoir Pressure
Time
WaterCut
Time
7 Layers
22 Uniform Layers
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A Priori Error:Lack of Pressure Equilibrium
Assumption Source of Error (Missing Physics)
• Pressure equilibrium within the coarse cell
• Disconnected pay within the coarse cell will not be in equilibrium
• Fluid velocity is parallel to the pressure drop
• Flow may depend upon the transverse pressure drop on the coarse grid
• Single velocity within a coarse cell
• Distribution of multiphase frontal velocities replaced by a single value
50 of 57
Designer Grids within the Flow SimulatorUpscale During Initialization (Static)
• Source of A Priori Error: Pressure equilibrium in the coarse cell is not present on the fine grid
– Design 3D simulation grid to prevent different sands from merging
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Designer Grids within the Flow SimulatorUpscale During Initialization (Static)
• General trend shows that uniform coarsening does not perform well
• “Optimal” (293 layers) is the best layering scheme
• Flexible 3D grid (MCOARSE) provides even better results
Tight Gas Layer CoarseningFine Scale Model 22x23x1715 (Geological Scenario 5)
0
5
10
15
20
25
30
0 200 400 600 800 1,000 1,200 1,400 1,600 1,800
Model Layers
Cum
. Gas
Pro
d. (B
CF)
Regular-CoarsenNextVar-OneStepNextVar-SequentialOptimal-12LOptimalLi-Map-12LLi-Ave-MaxLLi-Ave-12LMCOARSE
Fine Scale
Li and Beckner
UniformMCOARSE
Optimal
FlexibleCoarsening
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2-point Geostat Model, 100×100 → 10x10
Observations • Trans upscaling is better than k*• T* (open) > T* (restricted)• Linear pressure B.C. not good• Line/ point average good
λx = 1.0λy = 0.1σlogk = 1.735dx = 10.0 ftdy = 10.0 ft
-30% -20% -10% 0% 10% 20%ConstantPrePeriodicBCLinearPreConstantPre, vlConstantPre, lnConstantPre, ptPeriodicBC, vlPeriodicBC, lnPeriodicBC, ptLinearPre, vl
LinearPre, lnLinearPre, pt
Error to Fine-Scale Model Flow Rate, Qy = 7.02
restrictedopen
-15% -10% -5% 0%ConstantPrePeriodicBCLinearPreConstantPre, vlConstantPre, lnConstantPre, ptPeriodicBC, vlPeriodicBC, lnPeriodicBC, ptLinearPre, vl
LinearPre, lnLinearPre, pt
Error to Fine-Scale Model Flow Rate, QX = 47.8
restrictedopen
T*
K*
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Upscaling within the Flow SimulatorDynamic Boundary Conditions
• Source of A Priori Error: Fluid flow may depend upon the transverse pressure drop on the coarse grid
– Utilize actual well positions, flow rates and an iterative global solution on the coarse simulation grid to provide local pressure boundary conditions for the upscaling calculation, including the transverse pressure drop
Cell Permeability Transmissibility + Well PI Global Flow Rates
• 100x100x50 => 20x20x10 upscaling for a variogram-based fine scale model
• Material provided by Lou Durlofsky (Stanford) & Yuguang Chen (Chevron)
54 of 57
Future Trends:Upscale in the Simulator (Static)
• 3x3x3 ‘coarsen’ used to reduce run-time
• Resolution re-introduced to preserveFault block boundariesResolution near wellsFluid contactsHeterogeneity via statistical measures
• More accurate flow simulation than with uniform coarsening
Workflow Implications
• Single ‘Shared Earth Model’used for both static anddynamic calculations
• Negligible time spent building coarse grid
• Extremely flexible grid design
• Simulation speed improvement comparable to model rebuild
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Outline
• Introduction: Change of Scale & Upscaling
• Case Study: Magnus LKCF
– Validation and Analysis: What Went Wrong?
• Improved Upscaling: Understanding Permeability
– Boundary Conditions and Permeability Upscaling
– Transmissibility Yes, Permeability No
– Maintain the Well Injectivity & Productivity
• Magnus LKCF & Andrew Reservoir Case Studies
• Summary: What Works Well & What To Avoid?
• Future Trends:
– A Priori Error Analyses & Designer Grids
• Summary: Best Practice in Upscaling
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Summary: Best Practice in Upscaling
• Ensure that the fine and coarse grids are aligned– Many to 1 logical relationship is very important
• Check transport properties in initial geologic model– By Facies: NTG, Porosity, Horizontal Permeability, Kv/Kh ratio
• Conserve volumes when upscaling static properties & saturations– Bulk Rock Volume, Net Rock Volume, Pore Volume, Fluid Volumes
– Both 3DGeo => 3DSimulation and 1DLog => 1DGeo (blocked wells)
• When upscaling transmissibility (or permeability)– Preserve reservoir quality
– Preserve reservoir barriers
– Preserve flow around reservoir barriers
• Streamline-based flow validation after upscaling– Iteration: Is there a need to change resolution?
– Future trends: A Priori Error analysis & “Designer Grids”
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Summary: A Personal Literature Review
• Individuals whose work and questions have shaped my understanding of permeability & upscaling
• John Barker
• Karam Burns
• Dominic Camilleri
• Tianhong Chen
• Mike Christie
• Lou Durlofsky
• Don Peaceman
• Jens Rolfsnes
• Kefei Wang
• Chris White
• John K Williams
• Mike Zerzan
• Chris Farmer
• Kirk Hird
• Lars Holden
• Peter King
• Dave MacDonald
• Colin McGill
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