Case Studies / Modeling Tips - Mining Geology HQ · PDF fileCentre for Computational Geostatistics - University of Alberta - Edmonton, Alberta - Canada Reservoir Modeling Main geostatistical

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


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


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


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


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.


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


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


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


Multiple Realizations

01

02

04

03

05

06

07

09

08

10

11

12

14

13

15

16

17

19

18

20


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


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


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


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


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


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


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


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


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


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


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


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

Documents

Case Studies / Modeling Tips - Mining Geology HQ · PDF fileCentre for Computational Geostatistics - University of Alberta - Edmonton, Alberta - Canada Reservoir Modeling Main geostatistical