2006 11 08 spe dl upscaling
TRANSCRIPT
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SPE DISTINGUISHED LECTURER SERIESis funded principally
through a grant of the
SPE FOUNDATION
The Society gratefully acknowledgesthose companies that support the program
by allowing their professionalsto 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 DistinguishedLecturer 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
Mr. Escalante, the Shekou Section, and other local SPE chapters worldwide for their
efforts in hosting these presentations
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Upgridding and Upscaling:
Current Trends and Future Directions
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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 To Avoid & What Works Well?
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
ChristieDW GOM
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Why Upscale?: CPU Time Reduction
Waterflood Field Example
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 Coarsen
Optimum Layering Coarsen
MCoarsen
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Upgridding and Upscaling: Context
Structure from well picks &/or
seismic horizons
Properties from well logs &/or seismic
attributes &/or field performance data
Geologic description from facies, analogues and field data
Performance prediction in the
absence of dynamic data
Starting point for a history matchwhen dynamic data is available
, upscalingwill
preserve the most important flow
characteristics of a geologic model
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Why Upscale?: Length & Area
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Kanaalkop: Tanqua Karoo basin, South Africa
Deepwater channel w/splay at top of photo
~15ft windmill
~10ft exposure
~250ft, which is about the size of a single cellin the areal direction of many simulation grids
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10ft thick exposure of channel
With 5 Components of a Bouma sequence
~10ft
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Why Upscale?: Thickness
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Reservoir Zones, Well Logs & Outcrop
No Vertical Exaggeration
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15 meters Geologist at Outcrop
30 geologic model layers
1-5 simulation model layers
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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 To Avoid & What Works Well?
Future Trends:
A Priori Error Analyses & Designer Grids
Summary: Best Practice in Upscaling
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LKCFLimit
OWC
MSM
Limit
Do We Have an Economic LKCF Waterflood Development?
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
-3400
Heat her / 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
-3400
Heat her / 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
-3400
Heat her / Brent
-3500
-3600
-3700
Yellow = Channel
Red = Margins
Blue = Non-pay
64x64x450 = 1,843,200 cells 50mx50mx0.5m
resolution
M LKCF
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Magnus LKCF
Waterflood Development Study
C ll P bili U li
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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)
Cell Permeability Upscaling:
Laboratory and Reservoir Model
Q
A
K P
L
Darcys Law:
1 2
3 4
S li i h U l d LKCF M d l
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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
Streamlines in the Upscaled LKCF Model
How Well Did 2x2x6 Upscaling Work?
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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600
200
0
0
500
600
0
300
300
0
0
300
0 0 600 0
Cell Permeability Upscaling
What Went Wrong?
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 thecontinuity 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 Upscaling
Streamline 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
C ll P bilit U li
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Cell Permeability Upscaling
Errors & More Subtle Errors
Sealed Side Boundary Conditions do not adequately represent fluid flow in the finescale model
Reservoir quality is not preserved
This is the most significant error
However, there are more subtle errors
Needless loss of spatial resolution
Transmissibility Upscaling
Well Productivity (or Injectivity) is not preserved
Well PI 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 To Avoid & What Works Well?
Future Trends:
A Priori Error Analyses & Designer Grids
Summary: Best Practice in Upscaling
B d C diti d
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Boundary Conditions and
Upscaled Permeability - 1/2
Upscale a simple sand/ shale reservoir
Sealed side BCs
expand barriers
Open linear pressureBCs allow barriers to
leak
Pizza box (Wide
BCs) allow global flow
tortuosity
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Tr n mi ibilit U ling 1/3
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Transmissibility Upscaling 1/3
Preserves Spatial Resolution
Transmissibility can be calculated by direct upscaling instead of from the harmonic averageof 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
21
2121
2
ii
i
iiDXDX
KXATX
121 )()( iii MinusKXKXPlusKX
i 1i
21i
Transmissibility Upscaling 2/3
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KX
Sealed Cell
KXY
Wide No
Shift
Transmissibility Upscaling 2/3
KX Streamline Flow Comparisons
KX
Wide
Shifted
KX
Sealed
Shifted
Transmissibility Upscaling 3/3
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Transmissibility Upscaling 3/3
Captures fine scale juxtaposition
0 MD 0 MD 38 MD 0 MD 50 MD50 MD
Well Productivity Upscaling
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Well Productivity Upscaling
Used to Preserve Reservoir Quality
Simulator well productivity calculated from sealed sidecoreflood permeability?
Does not describe radial flow and
logarithmic pressure drop near a well
Instead, use three (hypothetical)X, Y, and Z wells for each coarse cell
w
ZZ
rr
HKYKXWI
0ln
2
w
Y
Y rr
HKZKXWI
0ln
2
w
XX
rr
HKZKYWI
0ln
2
Improved Upscaling:
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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
Improved Upscaling:
Well Index + Transmissibility
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
Coreflood Cell Permeability OR
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Coreflood Cell Permeability OR
Well 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 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 0 600 600 600 600 600 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
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
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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 To Avoid & What Works Well?
Future Trends:
A Priori Error Analyses & Designer Grids
Summary: Best Practice in Upscaling
LKCF Upscaling Validation
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LKCF Upscaling Validation
Well 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
Transmissibility Multipliers:
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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
Andrew Reservoir:
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Andrew Reservoir:
Validation & Impact of Thin Barriers
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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 to Avoid & What Works Well?
Future Trends:
A Priori Error Analyses & Designer Grids
Summary: Best Practice in Upscaling
Summary:
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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
Summary:
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Summary:
What Works Well
Preserve connectivity and flowwithinthe reservoir using flow based transmissibilityupscaling
Select boundary conditions to either preserve flow tortuosityorflow barriers
Preserve reservoir quality and flowbetweenreservoir and wells using algebraic well
index upscaling
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
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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 To Avoid & What Works Best?
Future Trends:
A Priori Error Analyses & Designer Grids
Summary: Best Practice in Upscaling
Future Trends:
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Assumption Source of Error(Missing Physics)
Pressure equilibrium withinthe coarse cell
Disconnected pay within the coarse cellwill 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
Future Trends:
A Priori Error Analyses & Designer Grids
Wouldnt it be nice to know if an upscaling calculation would be a goodapproximation beforeyou performed the upscaling calculation?
Sources of Upscaling Error
Error from Layer Coarsening:
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Error in the velocity distributionis 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
Error from Layer Coarsening:
Flood Front Progression
Fast
Slow
Medium
Fast
Slow
Medium
XW KSF *
Designer Grids within the Flow Simulator
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g
Static Boundary Conditions
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
%-Heterogeneity
0
2
4
6
8
10
12
14
16
18
20
RMSRe
gression-Error
Li & Beckner % Heterogeneity
% Heterogeneity ; B-Variation
% Heterogeneity: Uniform Coarsen
Diagonal Guide
Solution Total RMS Regression
Solution Weighted RMS Regression
Total RMS Regression
Weighted RMS Regression
Number of Coarse Layers
%-Heterogeneity
RMSRegressionErrorOptimal Layering
Uniform Coarsening: Not Efficient
Designer Grids within the Flow Simulator
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g
Upscale 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 Coarsening
Fine 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.
Ga
sProd.
(BCF)
Regular-CoarsenNextVar-OneStepNextVar-SequentialOptimal-12LOptimalLi-Map-12LLi-Ave-MaxLLi-Ave-12LMCOARSE
Fine Scale
Li and Beckner
UniformMCOARSE
Optimal
Layer Coarsening:
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y g
Waterflood Example
Waterflood Field Example:
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10%
20%
30%
40%
50%
60%
70%
80%
90%
00%
0 2000 4000 6000 8000 10000 12000
FineScale
Coarsen_54
Coarsen_22
Coarsen_22U
Coarsen_31
Coarsen_19
Coarsen_07
p
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 2000 4000 6000 8000 10000 1200
FineScale
Coarsen_54
Coarsen_22
Coarsen_31
Coarsen_19
Coarsen_07
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
FineScale
Coarsen_54
Coarsen_22Coarsen_31
Coarsen_19
Coarsen_07
1760
1780
1800
1820
1840
1860
1880
1900
1920
1940
1960
1980
0 2000 4000 6000 8000 10000 12000
FineScale
Coarsen_22
Coarsen_22U
Designer Grids within the Flow Simulator
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g
Static Boundary Conditions
Design 3D simulation grid to prevent different sands from merging
Designer Grids within the Flow Simulator
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g
Upscale 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 Coarsening
Fine 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.
Ga
sProd.
(BCF)
Regular-CoarsenNextVar-OneStepNextVar-SequentialOptimal-12LOptimalLi-Map-12LLi-Ave-MaxLLi-Ave-12LMCOARSE
Fine Scale
Li and Beckner
UniformMCOARSE
Optimal
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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 To Avoid & What Works Best?
Future Trends:
A Priori Error Analyses & Designer Grids
Summary: Best Practice in Upscaling
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Summary: Best Practice in Upscaling
Check transport properties in initial geologic model
By Facies: NTG, Porosity, Horizontal Permeability, Kv/Kh ratio
When upscaling 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
Chris Farmer
Kirk Hird
Lars Holden
Peter King
Dave MacDonald
Colin McGill
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
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Backup
Upscaling within the Flow Simulator
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p g
Dynamic Boundary Conditions
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
100x100x50 => 20x20x10 upscaling for a variogram-based fine scale model
Material provided by Lou Durlofsky (Stanford) & Yuguang Chen (Chevron)
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Future Trends:
Calculate your errors beforeupscaling
Designer simulation grids that minimize these errors
Best coarse layering
Best unstructured 3D grids
Upscaling in the Simulator (Static)
Transmissibility is calculated from the fine model by upscaling
Done at model initialization
Upscaling in the Simulator (Dynamic) Utilize well locations and well rates on the coarse grid to define the fine scale boundary
conditions
Iterative calculation per time step
A Priori Error:
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Lack of Pressure Equilibrium
Assumption Source of Error(Missing Physics)
Pressure equilibrium withinthe coarse cell Disconnected pay within the coarse cellwill not be in equilibrium
Fluid velocity is parallel tothe pressure drop
Flow may depend upon the transversepressure drop on the coarse grid
Single velocity within acoarse cell
Distribution of multiphase frontalvelocities replaced by a single value
Designer Grids within the Flow Simulator
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Static Boundary Conditions
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
eterogeneity
0
2
4
6
8
10
12
14
16
18
20
RMSRe
gression-Error
Li & Beckner % Heterogeneity
% Heterogeneity ; B-Variation
% Heterogeneity: Uniform Coarsen
Diagonal Guide
Solution Total RMS Regression
Solution Weighted RMS Regression
Total RMS Regression
Weighted RMS Regression
Number of Coarse Layers
%-Heterogeneity
RMSRegressionErrorOptimal Layering
Uniform Coarsening: Not Efficient
Designer Grids within the Flow Simulator
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Upscale 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 Coarsening
Fine 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.GasProd.
(BCF)
Regular-CoarsenNextVar-OneStepNextVar-SequentialOptimal-12LOptimalLi-Map-12LLi-Ave-MaxLLi-Ave-12LMCOARSE
Fine Scale
Li and Beckner
UniformMCOARSE
Optimal
Future Trends:
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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 thanwith uniform coarsening
Workflow Implications
Single Shared Earth Modelused for both static and
dynamic calculations
Negligible time spent building coarse grid
Extremely flexible grid design
Simulation speed improvement
comparable to model rebuild
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Complex Flow in a Vertical Cross-Section
In many ways, the unconfined boundary conditions are more typical of flow in the full three
dimensional model. For example, look at the flow patterns calculated by
as part of their work on Compositional Upscaling.
The detailed velocity field shows significant local variation, and only rarely aligns with the coarse grid
block boundaries.
Transmissibility Upscaling
http://../My%20Webs/3DKNOW/upscaling/spe37986/spe37986.htmlhttp://../My%20Webs/3DKNOW/upscaling/spe37986/spe37986.htmlhttp://../My%20Webs/3DKNOW/upscaling/spe37986/spe37986.htmlhttp://../My%20Webs/3DKNOW/upscaling/spe37986/spe37986.html -
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KX
Sealed Cell
KXY
Open Wide
No Shift
KX Streamline Flow Comparisons
KX
Open Wide
Shifted
KX
Sealed
Shifted
KY Upscaling Comparisons
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Streamline Flow Visualization
KY
Open
Wide
Shifted
KY
Sealed
Shifted
KY
Sealed
Cell
KYX
Open
Wide No
Shift
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Layer Coarsening:
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Waterflood Example
Waterflood Field Example:
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10%
20%
30%
40%
50%
60%
70%
80%
90%
00%
0 2000 4000 6000 8000 10000 12000
FineScale
Coarsen_54
Coarsen_22
Coarsen_22U
Coarsen_31
Coarsen_19
Coarsen_07
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 2000 4000 6000 8000 10000 1200
FineScale
Coarsen_54
Coarsen_22
Coarsen_31
Coarsen_19
Coarsen_07
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
FineScale
Coarsen_54
Coarsen_22
Coarsen_31
Coarsen_19
Coarsen_07
1760
1780
1800
1820
1840
1860
1880
1900
1920
1940
1960
1980
0 2000 4000 6000 8000 10000 12000
FineScale
Coarsen_22
Coarsen_22U
Tight Gas Example: Cum. Recoveryl
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Coarsening 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.GasProd.(BCF
)
Regular-CoarsenNextVar-OneStepNextVar-SequentialOptimal-12LOptimalLi-Map-12LLi-Ave-MaxL
Li-Ave-12LMCOARSE
Fine Scale
Li and Beckner
UniformMCOARSE
Optimal
k
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Backup
b l l
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Permeability Upscaling
Volume average of Darcys Law defines the effective permeability tensor for eachcoarse cell
Flow calculation region can be >> than averaging region
Results depend upon the choice of boundary conditions
Coarse grid superimposed on fine grid and fine
cell properties
Darcys Law:
Volume Averageof Darcys Law:
pku
pku *1
1 2
3 4
Boundary Conditions andU l d P b l /
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Upscaled Permeability - 2/3
Vertical permeability, with a 4x4 coarse
grid overlay
Kz varies from 0 to 150 mD
Open boundaries over-estimate flow
capacity
Calculations Courtesy of VoluMetrix FasTracker
What Works Well?T b l U l
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q
1
2
Transmissibility Upscaling
Upscale from coarse cell center to coarse cell center
Replaces harmonic average of permeability with link permeability
Captures fine scale juxtaposition of properties within the reservoir
21pp
q
p
qT
fEffective
q
1
2
Transmissibility UpscalingP S i l R l i
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Preserves 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
21
2121
2
ii
i
iiDXDX
KXATX
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Transmissibility UpscalingC t fi l j t iti
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Captures fine scale juxtaposition
0 MD 0 MD 38 MD 0 MD 50 MD50 MD
Permeability Upscaling does not preserve fine scaleti it
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connectivity
1x5 Upscaling Example
Arithmetic average for horizontal permeability
Harmonic average for vertical permeability
Horizontal flow over-represented: too much sweep
Arithmetic average of the transmissibility is preferred
Vertical permeability reduced by lower perms
Harmonic average preserves local barriers
KZ KZ
100 0.01
100 0.011 1
0.01 100
0.01 1
Harmonic Average
0.024873 0.024751
KX KX TX
100 0.01 0.019998
100 0.01 0.0199981 1 1
0.01 100 0.019998
0.01 1 0.019802
Average: 0.215959
Arithmetic Average
40.204 20.404 27.06977
Cell Permeability UpscalingM S btl E
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More Subtle Errors
Simulator well productivity calculated from
sealed side coreflood permeability
Does not describe radial flow and
logarithmic pressure drop near a well
Transmissibility could have been calculated by direct
upscaling instead of from the harmonic average of cell
permeabilities
Link Permeability doubles the lateral resolution of
the calculation
Harmonic average of a zero cell permeability is always
zero
w
ZZ
rr
HKYKXWI
0ln
2
11
2121
2
ii
ii
ii DXKXDXKX
DXKXDXKXATX
1
21
2121
2
ii
i
iiDXDX
KXATX
w
YY
rr
HKZKXWI
0ln
2
wX
Xrr
HKZKYWI0ln
2
What Works Well?W ll I d U li
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Well Index Upscaling
Three hypothetical directional wells (X, Y & Z) for each coarse cell
Algebraic upscaling preserves reservoir quality & continuity of pay
Use well index upscaling to define cell permeability in the simulator
Ensures that fluids correctly enter and leave the reservoir
ijk
ijk
ijk
ijkijk
Effective
DZDYDXNTG
DYDXDZNTGKYKX
KYKX
B k
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Backup
Upscaling Overview:In Review
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In Review
Understand, Validate and/or
Challenge the Reservoir Model
Gridding
Grid Alignment
Static Properties
Upscaling: Quality Control
Multiphase Flow & Pseudoization
Iteration & Learning
Future Trends:Upgridding and Upscaling
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Upgridding and Upscaling
Design of the simulation grid at run-time
Fine scale model initialized in the simulator
Resolution chosen as required by calculation
Error estimates used to design grid
Regular grid
Layer grouping
Unstructured grid
Designed composite corner point grids in
3D
How to Combine Well Index & Transmissibility Upscaling
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How to Combine Well Index & Transmissibility Upscaling
Well Index upscaling defines cell permeability
Algebraic average (close to arithmetic average)
Adjust transmissibility at cell faces according to flow-based upscaling calculations
Retain two flow calculations as sensitivities
Pizza Box boundary conditions will preserve tortuosity
Sealed side barriers will preserve local barriers
1
1212121
2222
ii
iiiii
DXKXDXKXDXKXDXKXATMXTX
Face Property Cell Properties
Backup
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Backup
Magnus LKCFWaterflood Development Study
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Waterflood Development Study
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LKCF Upscaling Streamline Validation
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LKCF Upscaling Streamline Validation
-10.0%
-5.0%
0.0%
5.0%
10.0%
15.0%
20.0%
25.0%
30.0%
2x2x6 2x2x4 2x2x2 1x1x6 1x1x4 1x1x2
Upscale ( NX * NY * NZ)
Error on injection rate
Error on connected volume
CPU time scale =1 x1.8 x2.4 x3.7x6.8 x15.6
42285 active cells 152734 active cells
Backup
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Backup
A h A
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Arithmetic Average
Think of all of the reservoir re-stacked and placed immediately adjacent to a well.
All the rock feels the same pressure gradient
K1
KN
P
L
PAKQ jj
H A
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AQ
KLP
j j
j
Harmonic Average
Think of all of the reservoir sliced and stacked into one amazingly long core.
All the flow must run through each piece of rock.
K1 KNP
U li E i Fl Pi
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Upscaling Exercise: Flow Pictures
Geometric Average: Permeability follows a log normal distribution. In others words, the logarithm of
permeability follows a Gaussian distribution, and the average of the data provides an unbiased
estimate of the mean.
Important Exceptions:
What if we lose all of our unconsolidated core samples?
What if we never make permeability measurements of our muds?
Log PermPerm
Fre
que
ncy
Mode,
Median& Mean
A i h i H i
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Arithmetic-Harmonic
Harmonic followed by Arithmetic: Turn off all cross-flow between layers. Now you
have the sum of many core floods!
P
H i A i h i
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Harmonic-Arithmetic
Arithmetic followed by Harmonic: Think of perfect vertical pressure equilibrium. This
generates mixing at each column of the model, and a single average core flood
P1 PN
Coarsen in 3D:Preserve Pay/Non-Pay in Each Column
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Preserve Pay/Non Pay in Each Column
Tight Gas Field ExampleLayer Coarsening Analysis
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Layer Coarsening Analysis
1715 Geologic Layers Coarsened to 1 Simulation Layer
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
%-Heterogeneit
y
0
2
4
6
8
10
12
14
16
18
20
RMSRegression-Error
Li & Beckner % Heterogeneity
% Heterogeneity ; B-Variation
% Heterogeneity: Uniform Coarsen
Diagonal Guide
Solution Total RMS Regression
Solution Weighted RMS Regression
Total RMS Regression
Weighted RMS Regression
Effective Vertical PermeabilityImpact of Boundary Conditions
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pac o ou da y Co d o s
Upscale shales on a
sand background
Sealed sides capture
local flow barriers
Linear pressure allows
barriers to leak
Pizza box allows
global flow tortuosity
Summary:What to Avoid
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Flow based upscaling for cell permeabilities
Sealed side boundary conditions used for flow based upscaling of permeability
Using the same upscaled flow based permeability to calculate both well indices and
intercell transmissibility
Linear pressure (open) boundary conditions used for flow based upscaling of
permeability
Unfortunately, these steps describe the most common upscaling approaches in the
industry
Summary:What Works Well
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Use different upscaling techniques to extract different flow characteristics from the
fine scale geologic model
Well Index Upscaling preserves continuity of pay and provides a measure of the reservoir
quality
Transmissibility Upscaling provides higher spatial resolution
Different boundary conditions preserve either flow tortuosity or flow barriers
This combination of techniques has worked well within BP & elsewhere in the industry
Streamline calculations provide detailed validation based on pressures, sweep, and
time of flight
Validation after upscaling is always necessary