46 • Basic Statistics Property Modeling Basic Statistics Part 1 – Exercises This exercise has a pre made Petrel project stored in the Projects folder Property Modeling 2010 pet Double click to open th[.]
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Basic Statistics Part 1 – Exercises
This exercise has a pre-made Petrel project stored in the Projects folder:
Property Modeling 2010.pet Double click to open the project.
Display and analyze a Histogram and a CDF curve
Exercise Steps
1 From the menu bar, open the Window menu, select New
histogram window.
2 Select the ‘Perm’ log from the Global well logs folder.
the Settings tab for the Histogram window and change the data range to [Min: 0.1, Max: 2000]
changes
6 Deselect the Min and Max and click OK to close the Show
viewport settings button.
7 Select to use a part of the data in the histogram by clicking the
Select using 1D range on X axis button On the Histogram window, create a filter to avoid the Permeability zero values, as shown in the figure below
8 The selection is stored as a filter ‘Permeability 1’ in the Input pane>Filter folder>User.
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Property Modeling Basic Statistics • 47
Now, use the Generic Filter to make permanent changes to the well log
9 Go to the Expl Wells sub-folder > right-click > Calculator
and use the Permeability_1 filter to remove the permeability
zero values Enter the expression shown below To insert the
filter, select it from the Filter folder and use the blue arrow in
the calculator
If a warning appears (cannot find the variable
Permeability_1), click OK and OK for all It is because the filter
does not exist as a variable in the Well logs variable list
10 In the Histogram window, deselect the Perm and select
Perm_temp from the Global well logs folder to visualize the
change
When you use a generic filter in the calculator, it is
recommended to filter the values that you want to
keep by setting the filter
equal to 1.
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11 The Perm_temp property will be continuously used in the
exercises for the next modules
Create a Normal Distribution from a Histogram
Exercise Steps
1 Open a New histogram window Under the main Wells folder, expand the ‘Expl Wells’ sub-folder and from well
DW3>Well logs, select the PHI log.
2 Open the PHI>right-click>Settings>Statistics tab and look for the Mean and Std dev values.
3 In the Histogram window>function bar select the Create
new distribution function button A Create
distribution function window will open Enter the Name of distribution, select the option Normal distribution and enter
the values of the Mean, Std and n.o points (number of
points), as shown in the figure below
4 Click on the Get from histogram button to specify the range
of the distribution and click Run to create the distribution.
5 The new distribution function is stored in the Input pane Analyze it in the Histogram window or open PHI Normal
The distribution
function can be interactively
edited by using the options
Select and edit/add points
and Select and edit line in
both windows (Histogram
and Settings>Function tab).
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Distribution > Settings > Function tab, where the
Probability of a PHI Normal Distribution with Mean=0.10 and
Std dev.=0.11 can be visualized
Display a Crossplot and calculate the Correlation
Coefficient
Exercise Steps
1 Open a New function window from the Window menu.
2 Under the main Wells folder, expand ‘Expl Wells’ sub-folder
and from well DW4>Well logs select PHI on the X-axis and
Perm_temp on the Y-axis (in the previous exercise, this was
edited to cut away all zero values, and will create a nicer
correlation coefficient)
3 Use the Facies log as a third variable (Z) to color and to see
how the distribution of facies relates to the
Permeability-Porosity To view the facies types, turn the Autolegend.
4 Display the Perm_temp (Y-axis) in logarithmic scale by
clicking the appropriate button in the function bar
5 Calculate the correlation coefficient between the two logs
by clicking the Make linear function from crossplot button
in the function bar The correlation coefficient is
The PHI Normal Distribution can also be automatically generated using the PHI parameters by
selecting the Method Fit
normal distribution to active histogram
.
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displayed in the pop-up window When clicking OK in this window, the linear function is stored at the bottom of the Input
pane
Optionally, the Function edit tools and Generic Filters can be used
1 Change the visual settings of the correlation line in
Settings>Style tab of the ‘Perm_temp_vs_PHI’ function.
2 In the Function window, the new function can be edited by
edit line buttons Open the ‘Perm_temp_vs_PHI’
Settings>Function tab and see the effect on the function line.
3 Now, filter part of the Well log data displayed in the crossplot
by clicking either the:
The selection is stored as a filter in the Filter folder>User in the Input pane.
In this case, Generic Filters can be used for Wells or Properties to
filter the data of interest and to calculate its correlation coefficient by
using the Make linear function from crossplot icon Here, we will
use the filter, assuming it has filtered out the good reservoir part of the data:
4 In the Function window by displaying one of the Generic Filters
that you have generated previously, calculate the correlation
The Linear function
expression is stored in the
Comments tab under the Info
tab of the Settings of the
‘Perm_temp_vs_PHI’.
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coefficient using the Make linear function from crossplot
icon (restricted to one well at the time or a crossplot)
See an example in the figures below:
Comments
The Distribution Functions are useful in other processes, such as in
Facies modeling and Petrophysical modeling, to define the facies
probability distribution and properties distribution into the process
dialog respectively
The Correlation Coefficient analysis is helpful to define the
correlation between properties by zone (defined with the Filters tools)
In Facies and Petrophysical modeling, the Correlation Coefficient can be
applied for secondary data during modeling
Both processes are a useful quality control tool pre/post modeling
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the only reason for this is that these variogram settings must
be specified to run these processes
NOTE: You should never use the default settings unless you have
verified that they are appropriate for your field!
Basic Statistics Part 2 – Exercises
This exercise has a pre-made Petrel project stored in Projects folder:
Property Modeling 2010.pet If you did the last exercise, please use
the same project
Variograms are used as a method for describing spatial variation It is
based on the principle that closely spaced samples are likely to have a
greater correlation than those located far from one another, and that
beyond a certain point (range), a minimum correlation is reached and
the distance is no longer important
Of course, this spatial correlation can be anisotropic and several
variograms orientated in different directions may be required to
describe the variation in a property
Variogram map calculation of a point data set
By generating a variogram from input data, it is then possible to use the
variogram when modeling properties thus preserving the observed
spatial variation in the final model
In this simple exercise, you are given a point data set with two
attributes; depth and Acoustic Impedance (AI)
Exercise Steps
1 In the Input pane, go to the Variogram data set folder and
display the point data set Ac Impedance in a 2D window.
2 In the Settings>Variogram tab, select Horizontal
variogram map and change the settings under the XY range
tab according to the figure below The Search distance set in
the variogram settings defines the new Variogram map
extension
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3 Click the Run button The calculated variogram map will be stored at the bottom of the Input pane.
4 Open a Map window and display the Variogram map It is a
contour map (2D plot) of the sample variogram surface
complete Variogram map Determine the anisotropy direction
to be about 130 degrees by using the Measure distance
tool, positioning it on the map center and following the ellipse major axis The values will appear in the status bar at the bottom of the window
6 Keep the Variogram dialog open for the next exercise.
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Sample variogram calculation of point data set
Exercise Steps
1 Continue in the Variogram tab for the Ac Impedance point
data
2 Generate a Sample variogram and select the parameters as
shown below in the picture Use 20 lags and a horizontal
search radius of 26000 m In the Orientation tab, enter -39
degrees of orientation (it is the equivalent to the orientation
measured in the Variogram map) Click Run The Sample
variogram can be found at the bottom of the Input pane.
3 Display the Sample variogram in a Function window Under
Settings>Style tab of the Sample variogram, you can change
the display style for Points and Line.
4 As a test, in the Settings of the data, set the Ac Impedance,
go to the Variogram tab and change the parameters as shown
in the table below and inspect the various results:
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Orientation XY Range
No of Lags
XY Range
Horizontal Search Radius
Variogram Type
5 Calculate a new Sample variogram with an Orientation of
51 degrees Make sure that the check box Overwrite last is
NOT selected
6 Display the different variograms in a Function window and
notice the differences between variograms calculated with using parameters
Define a variogram model
The variogram model is a mathematical model used to describe the sample variogram
Exercise Steps
1 In the Function window, display the first calculated Sample
variogram of the major anisotropy axis (-39 degrees) that you
created in the last exercise
2 Click on the Make variogram for sample variogram button A Variogram model will be displayed, and the model
is also stored at the bottom of the Input pane.
3 Display the second Sample variogram as well (51 degrees)
4 Now define the Variogram model range and nugget for both
displayed sample variograms interactively using the
interactively, one point will correspond to the major range and the other point to the minor range
5 Right-click on the stored Variogram model and select
Settings The parameters of the Variogram model for the
major and the minor anisotropy axis are stored there
Notice the option
with a Horizontal search
radius of 500; a Sample
variogram cannot be
generated because the
process does not find any
data in that small search
radius.
The Variogram model
type, the sill, and the nugget
must be the same for both
variograms However, the Sill
is of no importance for
kriging/simulation.
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Kriging – Exercises Influence of the variogram model parameters on Kriging results
The Kriging algorithm uses a variogram to express the spatial variability
of the input data The user can define the model type of function for the variogram (Exponential, Spherical or Gaussian) as well as the Range, Orientation and Nugget
This exercise has a pre-made Petrel project stored in Projects folder:
Property Modeling 2010.pet If you did the last exercise, please use
the same project
Exercise Steps
1 Display the data set Ac Impedance in the 2D window You will find it in the Variogram data set folder in the Input pane.
2 Open the Make/edit surface process under Utilities in the
Processes pane.
3 In the Main input, drop in the Ac Impedance point data, select AI as attribute and select the check box Name; enter
“AI Kriging”.
4 Select the Geometry tab and select the User defined option, highlight the Ac Impedance data and click the Get limits
from selected button.
5 Set the Grid increments X and Y to 200.
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6 Go to the Algorithm tab and select Kriging from the
drop-down menu Click Apply.
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96 • Kriging Property Modeling
7 Now, calculate different surfaces using the variogram parameters from the table below:
Range Major
Dir Range Minor Dir Azimuth Nugget Model type
8 Display the results in a 2D or Map window When the
surface is recalculated with new parameter settings, the old result will be overwritten and the display automatically updated
Hint: When recalculating the surface to get a different output,
the Result surface must be removed by selecting it, deleting
it and it giving it a different Name A pop-up window ask to reset all the settings, select No to keep the old parameters and
only apply the necessary changes
9 Change the model type from Spherical to Gaussian and
Exponential Compare the results of all the models.
10 Continue in the Make/edit surfaces process to calculate a
surface using the variogram model that you determined previously in the Sample variogram exercises (Module 2 Basic Statistics Part 2 - Exercises)
11 Leave the previous settings, but remove the Result surface output and give a new Name (“AI Kriging - Model Variogram”).
12 Select the Variogram model from the Input pane (“Sample
var from Ac Impedance (-39 deg)”)
13 Go to the Algorithm tab In the Variogram sub-tab, click the
button to get the parameters from the variogram model
14 Click Apply/OK to calculate the new surface and display it to
compare with the previous results
If the Nugget seems
wrong, it is because the
Variogram is scaled to a Sill
of 1 in the Make/edit
surface, while it may be
different in the created
Variogram model Go to the
Variogram model settings
and toggle ‘Force sill to be
equal to 1.0’.
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Gaussian Simulation – Exercises
Sequential Gaussian simulation is a stochastic method based on Kriging It can honor input data, input distributions, variograms and trends
During the simulation, local highs and lows will be generated between input data locations which honor the variogram and the input
distribution A random number, supplied by the user or the software, will determine the positions of these highs and lows Because of this, multiple representations may be generated to gain an understanding of uncertainty
This exercise has a pre-made Petrel project stored in Projects folder:
Property Modeling 2010.pet If you did the last exercise, please use
the same project
Influence of variogram model parameters on Gaussian Simulation
Exercise Steps
1 Display the point data set Ac Impedance in the 2D window.
2 Open the Make/edit surface process.
3 Enter a new Name for the output: “AI Simulated” If there is
a name in the Result surface field, delete it If a pop-up window asks you to reset all settings, then click Yes to this.
4 Select the Geometry tab and select the User defined option, highlight the Ac Impedance data and click the Get limits
from selected button.
5 Set the Grid increments X and Y to 200.
6 Go to the Algorithm tab and select the Sequential Gaussian
simulation as Method
7 Leave the other settings as default and click Apply.
Before you display
the surface, open the
Settings window for it (RMB
click on the “AI Simulated”
surface) and de-select the
Show: Contour Lines option
under the Style tab This is
due to the random character
of the simulation giving a
high number of contour lines