Case Studies / Modeling Tips - Mining Geology HQ · PDF fileCentre for Computational...
Transcript of Case Studies / Modeling Tips - Mining Geology HQ · PDF fileCentre for Computational...
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
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
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
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
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
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
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
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
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
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
Centre for Computational Geostatistics - University of Alberta - Edmonton, Alberta - Canada
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
Centre for Computational Geostatistics - University of Alberta - Edmonton, Alberta - Canada
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
Centre for Computational Geostatistics - University of Alberta - Edmonton, Alberta - Canada
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
Centre for Computational Geostatistics - University of Alberta - Edmonton, Alberta - Canada
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
Centre for Computational Geostatistics - University of Alberta - Edmonton, Alberta - Canada
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
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
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
Centre for Computational Geostatistics - University of Alberta - Edmonton, Alberta - Canada
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
Centre for Computational Geostatistics - University of Alberta - Edmonton, Alberta - Canada
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
Centre for Computational Geostatistics - University of Alberta - Edmonton, Alberta - Canada
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
Centre for Computational Geostatistics - University of Alberta - Edmonton, Alberta - Canada
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