1 Mineral Rights in Alberta Alberta Energy 2004 1 Alberta Department of Energy.
Case Studies / Modeling Tips - Mining Geology HQ · PDF fileCentre for Computational...
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Centre for Computational Geostatistics - University of Alberta - Edmonton, Alberta - Canada
Case Studies / Modeling Tips
• Sequential Approach to Reservoir Modeling• Question / Answer Time• A Small Example• Glimpses of Case Studies
Reservoir Modeling with GSLIB
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Centre for Computational Geostatistics - University of Alberta - Edmonton, Alberta - Canada
Reservoir Modeling
Main geostatistical modeling flow chart: the structure and stratigraphy of each reservoirlayer must be established, the lithofacies modeled within each layer, and then porosity andpermeability modeled within each lithofacies.
Cell-based LithofaciesModeling
Object-Based LithofaciesModeling
Establish Stratigraphic Layering / Coordinates
Porosity Modeling
Permeability Modeling
Repeat for Multiple Realizations
Model Uses1. Volumetric / Mapping2. Assess Connectivity3. Scale-Up for Flow Simulation4. Place Wells / Process Design
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Centre for Computational Geostatistics - University of Alberta - Edmonton, Alberta - Canada
Introductory Example
• Fashioned after a real problem and the geological data is based on outcrop observations • A horizontal well is to be drilled from a vertical well to produce from a relatively thin oil
column.• The goal is to construct a numerical model of porosity and permeability to predict the
performance of horizontal well including (1) oil production, (2) gas coning, and (3) water coning.
Top of ReservoirExisting Vertical Well
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Centre for Computational Geostatistics - University of Alberta - Edmonton, Alberta - Canada
Introductory Example -Petrophysical Data
Permeability characteristics of each lithofacies: the coefficient of variation is the average permeability divided by the standard deviation, Kv is the vertical permeability, and Kh is the horizontal permeability.
Code Lithofacies Average Coefficient Kv :Kh
Perm. of variation ratio0 Coal and Shale 1 md 0.00 0.11 Incised Valley Fill Sandstone 1500 md 1.00 1.02 Channel Fill Sandstone 500 md 1.50 0.13 Lower Shoreface Sandstone 1000 md 0.75 0.8Pe
rmea
bilit
y, m
d
•Lithofacies 1•Lithofacies 2•Lithofacies 3
Porosity0 0.4
10
10,000
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Centre for Computational Geostatistics - University of Alberta - Edmonton, Alberta - Canada
Flow Simulation
Gridding for flow simulation. For numerical efficiency, the vertical gridding is aligned with the gas-oil fluid contact and the oil-water fluid contact. The black dots illustrate the location of the proposed horizontal well completions. Representative three-phase fluid properties and rock properties such as compressibility have been considered. It would be possible to consider these properties as unknown and build that uncertainty into modeling; however, in this introductory example they have been fixed with no uncertainty.
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Centre for Computational Geostatistics - University of Alberta - Edmonton, Alberta - Canada
Simple Geologic Models
Three simple assignments of rock properties (a) a “layercake” or horizontal projection model, (b) a smooth inverse distance model, and (c) a simple Gaussian simulation.
Layercake Model
Smooth Model
Gaussian Simulation Model
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Centre for Computational Geostatistics - University of Alberta - Edmonton, Alberta - Canada
Simple Geologic Models: Flow Results
Flow results: layercake model - solid line; smooth model - long dashes; simple geostats model -- short dashes.
Time (days)
Oil
Prod
uctio
n R
atio
(m3/
day)
Time (days)
Wat
er C
ut
Time (days)
Gas
Oil
Rat
io
0 3000
10001.0
1600
0 3000 0 3000
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Centre for Computational Geostatistics - University of Alberta - Edmonton, Alberta - Canada
Better Geologic Model
The first geostatistical realization shown on the geological grid and the flow simulation grid
(a) Geostatistical Model (b) Geostatistical Model - Flow Grid
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Centre for Computational Geostatistics - University of Alberta - Edmonton, Alberta - Canada
Multiple Realizations
01
02
04
03
05
06
07
09
08
10
11
12
14
13
15
16
17
19
18
20
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Centre for Computational Geostatistics - University of Alberta - Edmonton, Alberta - Canada
Geologic Models - Flow Results
Flow results from 20 geostatistical realizations (solid gray lines) with simple model results superimposed
Wat
er C
ut
Time, days30000
1.0
Oil
Prod
uctio
nm
3 /day
Time, days30000
10,000
Gas
Oil
Rat
io
Time, days30000
2000
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Uncertainty
The cumulative oil production after 1000 days and the time to water breakthrough. Note the axis on the two plots. There is a significant difference between the simple models and the results of geostatistical modeling (the histograms).
layercakefirst sgsim
smooth
Cumulative Oil Production at 1000 Days
Cumulative Oil Production, x 10^3 m^3
Freq
uenc
y layercake
first sgsimsmooth
Time of Water Break Through
Water Break Through, daysFr
eque
ncy
200 800 0 1600
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Major Arabian Carbonate Reservoir
• GOSP 2 & 7 Area study commissioned by Saudi Aramco
• SPE29869 paper Integrated Reservoir Modeling of a Major Arabian Carbonate Reservoir by J.P. Benkendorfer, C.V. Deutsch, P.D. LaCroix, L.H. Landis, Y.A. Al-Askar, A.A. Al-AbdulKarim, and J. Cole
• Oil production from wells on a one-kilometer spacing with flank water injection. There has been significant production and injection during the last 20 years
• This has had rapid and erratic water movement uncharacteristic of the rest of the field areason for building a new geological and flow simulation models
Zone Porosity % Layer
3A
3B
3A
3B
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Modeling Process
• Standard GSLIB software (because it was for Saudi Aramco)• Novel aspect was modeling permeability as the sum of a matrix permeability
and a large-scale permeability– fractures– vuggy and leached zones– bias due to core recovery
• Typical modeling procedure that could be applied to other carbonates and to clastic reservoirs
Lithology Porosity MatrixPermeability
Large-ScalePermeability
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Indicator Simulation of Lithology
Presence / absence of limestone / dolomite was modeled with indicator simulation (SISIM) on a by-layer basis
γγγγ
Vertical Indicator Variogram: Layer 8
Distance0
0.25
0.8
γγγγ
Horizontal Indicator Variogram: Layer 8
Distance0
0.25
100
30 degrees
120 degrees
Limestone
Dolomite
1 km
N
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Gaussian Simulation of Porosity
• Variogram model for porosity in limestone:Vertical Porosity Variogram Layer 8 (Limestone)
Horizontal Porosity Variogram Layer 8 (Limestone)
Var
iogr
am
Distance (m)
Var
iogr
am
Distance (m)
20 degrees
110 degrees
Vertical Porosity Variogram Layer 8 (Limestone)
Horizontal Porosity Variogram Layer 8 (Limestone)
Var
iogr
am
Distance (m)
Var
iogr
am
Distance (m)
20 degrees
110 degrees
0 0.8
• Variogram model for porosity in dolomite:
0.8 1.0
00 10,000
0
0 0.80
0 10,0000
0.8 1.0
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Gaussian Simulation of Porosity
Porosity models for limestone and dolomite were built on a by-layer basis with SGSIM and then put together according to the layer and lithology template
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Indicator Simulation of Matrix Permeability
Numbers above x-axis are porosity class percentagesNumbers at corners are porosity/permeability class percentages
Porosity (%)
Group 1 - Limestone
Perm
eabi
lity
(md)
Vertical Matrix k Variogram Layer 5 (Limestone)
Stratigraphic Distance (m)
Var
iogr
am
Horizontall Matrix k Variogram Layer 5 (Limestone)
Stratigraphic Distance (m)
Var
iogr
am
20 degrees110 degrees
0 400.01
10,000
Means:Porosity = 21.57Permeability = 295.7
Correlation:Pearson = 0.73Spearman = 0.70
Linear Transform:Slope = 0.129Intercept = -1.224
0 1.0
0 12000
0
2.0
0
2.0
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Gaussian Simulation of Large-Scale Permeability
• Matrix permeability at each well location yields a K•hmatrix• Well test-derived permeability at each well location yields a K•htotal• Subtraction yields a K•hlarge• Vertical distribution of K•hlarge scale on a foot-by-foot basis is done by
considering multiple CFM data
Vertical Large Scale Variogram Layer 5
Stratigraphic Distance
Horizontal Large Scale Variogram Layer 5
Stratigraphic Distance
Var
iogr
am
Var
iogr
am
0 120000
2.0isotropic
0 1.00
2.0
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Gaussian Simulation of Large-Scale Permeability
• Large-scale permeability models were built on a by-layer basis with SGSIM• Matrix permeability and large-scale permeability models were added together
to yield a geological model of permeability• A calibrated power average was considered to scale the geological model to
the resolution for flow simulation
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Flow Simulation: First History Match
Year
Wat
er C
ut (%
)D
atum
Pre
ssur
e (p
si) 3400
1600100
01940 1995 1975 1980 1985 1990 1994
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Flow Simulation: Fourth History Match
Year
Wat
er C
ut (%
)D
atum
Pre
ssur
e (p
si) 3400
1600
100
01940 1995 1975 1980 1985 1990 1994