petrel-属性建模

Nugget: Degree of dissimilarity at zero • Vertical
distance.
Basic Statistics
Example of Experimental Variogram calculation Semi-variance for 1 Lag distance Semi-variance for 2 lag distance
- Determine Layer thickness - Determine directions/degree of Anisotropy - Determine correlation/connectedness of facies data
Used as Quality Control to compare data before and after modeling process
Variogram Map
Good for visualizing anisotropy and its direction.
Sample Variogram
Good for finding Major and minor Range horizont
Variogram Map – Theory
EXERCISE A WELL with a string of porosity values in depth steps of 1m: 3, 5, 7, 6, 4, 1, 1, 4. Calculate the variogram values for lags 1, 2, 3, and 4 m respectively. Plot the variogram. Is there a pattern?
Interpretative Process Should take geological knowledge into account
Vertical Variogram Model Usually plenty of data and easily estimated
Horizontal Variogram Model Can often not be calculated due to limited amount of data Can be derived from correlated data source or taken from analogous field / outcrop / geological knowledge
Variance
Basic Statistics
Variogram Model Types
Distance
Spherical: Good general algorithm Exponential: Produces the most “noisy” result Gaussian: Produces the smoothest result
Geostatistical techniques are indispensable part of reservoir management because quantitative numerical models are required for planning the field/reservoir development to optimize time, resources and economic gain
X axis
Y axis
Basic Statistics
Directional Variogram Analysis (search cone)
Because of irregular spacing of input points, a Search area (defined by a Search cone) must be defined in the search for points lying within the distance range given by the Lag.
Experimental Variogram Variogram Model
Basic Statistics
Why Variogram Modeling?
Requirement for geostatistical algorithms in Reservoir Modeling
Variograms are useful as Data Analysis tools
(h) 8
Sill 7
(4)=7.124
6
(3)=7.1
5
4
(2)=5.75
3
2
(1)=2.214
1
0 0
1
2 Ran3ge 4
h5
Gamma1 = 1 / (2* 7) * { (5-3)2 + (7-5) 2 + … } = 1/14 * {4 + 4 + 1 + 4 + 9 + 0 + 9} = 31/14 = 2.214
Basic Statistics
Applied Variogram Modeling
Variogram calculation process Calculate the Experimental Variogram Fit a Variogram Model to the Experimental Variogram Variogram model types could be Spherical, Gaussian or Exponential
Basic GeoStatistics in Property modeling
Basic Statistics
What is Geostatistics?
Geostatistics is a branch of applied statistics that places emphasis on the geological context of the data and the spatial relationship between the data
In the object Settings > Variogram tab, you will find the available options for generating a Horizontal variogram map and a Sample variogram for a property or correlated attribute.
other?
Basic Statistics
Variogram Parameters
Variance: A measure of how different
Sill
members of a collection are from eachother.
Lag distance: Separation distance between
Two main aspects of a variogram: 1. How similar are two values right next to each other? 2. How far apart are two points before they bear no relation to each
The Variogram can be calculated in 3 directions:
beyond which data points no longer exhibit
any statistical similarity.
• Horizontal Major • Horizontal Minor
points.
Nugget
Range
Sill: Variance at the point where the summary plot flattens out to random similarity.
Range: Correlation distance; distance
12
Separation 3 4 5 distance (lag)
Result of Experimental Variogram calculation
Semi-variogram
can be calculated experimentally as:
h
1 2Nh
Nh i 1
2
(ih) i
=3 =5 =7
=6 =4
=1 =1 =4
Y axis
Number of Y Lags
Y Range
Number of X Lags
X Range
Note: The variogram map has its center at coordinates (0,0) . It can therefore only be displayed in a Map window in Petrel
Basic Statistics
Variogram Concept
Variogram: A quantitative description of the variation in a property as a function of separation distance between data points Based on the principle that two points close together are more likely to have similar values than points far from each other
A Variogram Map is a way to present Variograms that have been computed in several different directions over a data set (in Petrel: A point data set, surface or 3D property). It produces a contour of the 2D variance surface (direction and extent of Anisotropy).
Basic Statistics
Anisotropy
Anisotropy is a characteristic of a data set, if there is a clear difference in how data values change in a preferred direction. If you suspect this kind of directional bias in your data set, incorporate that information in the variogram to get a more accurate model.
The variability of particle size across the channels will be much higher than along the channels
Basic Statistics
Variogram Maps and Sample Variograms in Petrel
1 2
…3
) )
) i
i1
…
((32--+21))22
+
… ( i+1 - i )2
+
…
h1
1 2 N1
N1 i 1
i1 i
2
1 2
)) 3
…
i
) i1
i2 …
( 3
-
2
1 )
(4 -+ 2 )2
+
…2
(i2 - i )
…+
h2
1 2N2
N2 i 1
i2 i
2
Basic Statistics
Angle=60o
X axis
Suggested Lag distance: Lateral = well spacing Vertical = cell thickness
Basic Statistics
Variogram Map – Anisotropy
Variogram Map:
Arrows show the Major and Minor direction of Anisotropy