Reservoir Modeling with GSLIB
Case Studies / Modeling Tips
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Sequential Approach to Reservoir Modeling
Question / Answer Time
A Small Example
Glimpses of Case Studies
Centre for Computational Geostatistics - University of Alberta -
Edmonton, Alberta - Canada
Reservoir Modeling
Establish Stratigraphic Layering / Coordinates
Cell-based Lithofacies
Modeling
Object-Based Lithofacies
Modeling
Repeat for Multiple Realizations
Porosity Modeling
Permeability Modeling
Model Uses
1. Volumetric / Mapping
2. Assess Connectivity
3. Scale-Up for Flow Simulation
4. Place Wells / Process Design
Main geostatistical modeling flow chart: the structure and stratigraphy of each reservoir
layer must be established, the lithofacies modeled within each layer, and then porosity and
permeability modeled within each lithofacies.
Centre for Computational Geostatistics - University of Alberta -
Edmonton, Alberta - Canada
Introductory Example
Existing Vertical Well
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Top of Reservoir
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.
Centre for Computational Geostatistics - University of Alberta -
Edmonton, Alberta - Canada
Introductory Example Petrophysical Data
•Lithofacies 1
•Lithofacies 2
•Lithofacies 3
Permeability, md
10,000
Code
0
1
2
3
Lithofacies
Average Coefficient
Perm. of variation
Coal and Shale
1 md
0.00
Incised Valley Fill Sandstone 1500 md
1.00
Channel Fill Sandstone
500 md
1.50
Lower Shoreface Sandstone 1000 md
0.75
K v :K h
ratio
0.1
1.0
0.1
0.8
10
0
0.4
Porosity
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.
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.
Centre for Computational Geostatistics - University of Alberta -
Edmonton, Alberta - Canada
Simple Geologic Models
Layercake Model
Gaussian Simulation Model
Smooth Model
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.
Centre for Computational Geostatistics - University of Alberta -
Edmonton, Alberta - Canada
1000
1.0
Gas Oil Ratio
1600
Water Cut
Oil Production Ratio (m3/day)
Simple Geologic Models:
Flow Results
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3000
Time (days)
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3000
Time (days)
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3000
Time (days)
Flow results: layercake model - solid line; smooth model - long dashes; simple
geostats model -- short dashes.
Centre for Computational Geostatistics - University of Alberta -
Edmonton, Alberta - Canada
Better Geologic Model
(a) Geostatistical Model
(b) Geostatistical Model - Flow Grid
The first geostatistical realization shown on the geological grid and the flow
simulation grid
Centre for Computational Geostatistics - University of Alberta -
Edmonton, Alberta - Canada
Multiple Realizations
01
06
11
16
02
07
12
17
03
08
13
18
04
09
14
19
05
10
15
20
Centre for Computational Geostatistics - University of Alberta -
Edmonton, Alberta - Canada
Geologic Models - Flow Results
1.0
Gas Oil Ratio
2000
Water Cut
Oil Production
m3/day
10,000
0
3000
Time, days
0
Time, days
3000
0
Time, days
3000
Flow results from 20 geostatistical realizations (solid gray lines) with simple
model results superimposed
Centre for Computational Geostatistics - University of Alberta -
Edmonton, Alberta - Canada
Uncertainty
Cumulative Oil Production at 1000 Days
Time of Water Break Through
layercake
first sgsim
first sgsim
smooth
200
Cumulative Oil Production, x 10^3 m^3
layercake
Frequency
Frequency
smooth
800
1600
0
Water Break Through, days
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).
Centre for Computational Geostatistics - University of Alberta -
Edmonton, Alberta - Canada
Major Arabian Carbonate
Reservoir
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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 a
reason for building a new geological and flow
simulation models
Zone
Porosity %
Layer
3A
3B
3A
3B
Centre for Computational Geostatistics - University of Alberta -
Edmonton, Alberta - Canada
Modeling Process
Lithology
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Porosity
Matrix
Permeability
Large-Scale
Permeability
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
Centre for Computational Geostatistics - University of Alberta -
Edmonton, Alberta - Canada
Indicator Simulation of
Lithology
Vertical Indicator Variogram: Layer 8
Horizontal Indicator Variogram: Layer 8
120 degrees
0.25
0.25
γ
0
γ
Distance
0.8
0
30 degrees
Distance
100
Limestone
N
Dolomite
1 km
Presence / absence of limestone / dolomite was modeled with indicator simulation
(SISIM) on a by-layer basis
Centre for Computational Geostatistics - University of Alberta -
Edmonton, Alberta - Canada
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Gaussian Simulation of
Porosity
Variogram model for porosity in limestone:
Horizontal Porosity Variogram
Layer 8 (Limestone)
0
110 degrees
1.0
0.8
Variogram
Variogram
Vertical Porosity Variogram
Layer 8 (Limestone)
0
0.8
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20 degrees
0
Distance (m)
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10,000
Distance (m)
Variogram model for porosity in dolomite:
Horizontal Porosity Variogram
Layer 8 (Limestone)
0.8
0
Variogram
Variogram
Vertical Porosity Variogram
Layer 8 (Limestone)
0
0.8
Distance (m)
110 degrees
1.0
20 degrees
0
0
10,000
Distance (m)
Centre for Computational Geostatistics - University of Alberta -
Edmonton, Alberta - Canada
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
Centre for Computational Geostatistics - University of Alberta -
Edmonton, Alberta - Canada
Indicator Simulation of
Matrix Permeability
Group 1 - Limestone
Vertical Matrix k Variogram Layer 5 (Limestone)
Linear Transform:
Slope = 0.129
Intercept = -1.224
Permeability (md)
10,000
Variogram
2.0
Means:
Correlation:
Porosity = 21.57
Pearson = 0.73
Permeability = 295.7 Spearman = 0.70
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0
1.0
Stratigraphic Distance (m)
Horizontall Matrix k Variogram Layer 5 (Limestone)
2.0
Variogram
20 degrees
110 degrees
0.01
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40
Porosity (%)
0
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Numbers above x-axis are porosity class percentages
Numbers at corners are porosity/permeability class percentages
12000
Stratigraphic Distance (m)
Centre for Computational Geostatistics - University of Alberta -
Edmonton, Alberta - Canada
Gaussian Simulation of
Large-Scale Permeability
Vertical Large Scale Variogram Layer 5
Horizontal Large Scale Variogram Layer 5
2.0
2.0
Variogram
Variogram
isotropic
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0
1.0
Stratigraphic Distance
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12000
Stratigraphic Distance
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
Centre for Computational Geostatistics - University of Alberta -
Edmonton, Alberta - Canada
Gaussian Simulation of
Large-Scale Permeability
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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
Centre for Computational Geostatistics - University of Alberta -
Edmonton, Alberta - Canada
Datum Pressure (psi)
Flow Simulation: First
History Match
3400
1600
Water Cut (%)
100
0
1940
1995
1975
1980
1985
1990
1994
Year
Centre for Computational Geostatistics - University of Alberta -
Edmonton, Alberta - Canada
Datum Pressure (psi)
Flow Simulation: Fourth
History Match
3400
Water Cut (%)
1600
100
0
1940
1995
1975
1980
1985
1990
1994
Year
Centre for Computational Geostatistics - University of Alberta -
Edmonton, Alberta - Canada