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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










Future Trends:



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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

C ll P bili U li

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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

C ll P bilit U li

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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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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










Future Trends:



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


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KX

Sealed Cell

KXY

Wide No

Shift


KX Streamline Flow Comparisons

KX

Wide

Shifted

KX

Sealed

Shifted


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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










Future Trends:



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

Pressure


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









Summary: What to Avoid & What Works Well?

Future Trends:



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






Transmissibility Yes, Permeability No



Summary: What To Avoid & What Works Best?

Future Trends:



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:


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


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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


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g


Design 3D simulation grid to prevent different sands from merging


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g







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)


Fine Scale

Li and Beckner

UniformMCOARSE

Optimal

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Outline






Transmissibility Yes, Permeability No



Summary: What To Avoid & What Works Best?

Future Trends:



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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


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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




Diagonal Guide





Number of Coarse Layers

%-Heterogeneity

RMSRegressionErrorOptimal Layering

Uniform Coarsening: Not Efficient


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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)


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.

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

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FineScale

Coarsen_54

Coarsen_22

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Coarsen_07

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FineScale

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FineScale

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Coarsen_22U

Tight Gas Example: Cum. Recoveryl

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Coarsening Results

Tight Gas Layer CoarseningFine Scale Model 22x23x1715 (Geological Scenario 5)

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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


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

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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%

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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%

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%-Heterogeneit

y

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RMSRegression-Error




Diagonal Guide





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

2006 11 08 spe dl upscaling

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