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[.]
Basic Statistics Part – 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 From the menu bar, open the Window menu, select New histogram window Select the ‘Perm’ log from the Global well logs folder Click the Show cdf curve button Click on the Show viewport settings button to open the Settings tab for the Histogram window and change the data range to [Min: 0.1, Max: 2000] Click the button and click Apply See how the cdf curve changes Deselect the Min and Max and click OK to close the Show viewport settings button 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 The selection is stored as a filter ‘Permeability 1’ in the Input pane>Filter folder>User 46 • Basic Statistics Property Modeling Now, use the Generic Filter to make permanent changes to the well log 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 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 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 Property Modeling Basic Statistics • 47 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 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 Open the PHI>right-click>Settings>Statistics tab and look for the Mean and Std dev values 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 Click on the Get from histogram button to specify the range of the distribution and click Run to create the distribution 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) 48 • Basic Statistics The new distribution function is stored in the Input pane Analyze it in the Histogram window or open PHI Normal Property Modeling Distribution > Settings > Function tab, where the Probability of a PHI Normal Distribution with Mean=0.10 and Std dev.=0.11 can be visualized The PHI Normal Distribution can also be automatically generated using the PHI parameters by selecting the Method Fit normal distribution to active histogram Display a Crossplot and calculate the Correlation Coefficient Exercise Steps Open a New function window from the Window menu 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) Use the Facies log as a third variable (Z) to color and to see how the distribution of facies relates to the PermeabilityPorosity To view the facies types, turn the Autolegend Display the Perm_temp (Y-axis) in logarithmic scale by clicking the appropriate button in the function bar 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 Property Modeling Basic Statistics • 49 The Linear function expression is stored in the Comments tab under the Info tab of the Settings of the ‘Perm_temp_vs_PHI’ 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 Change the visual settings of the correlation line in Settings>Style tab of the ‘Perm_temp_vs_PHI’ function In the Function window, the new function can be edited by using the Select and edit/add points and Select and edit line buttons Open the ‘Perm_temp_vs_PHI’ Settings>Function tab and see the effect on the function line Now, filter part of the Well log data displayed in the crossplot by clicking either the: a Select using 1D range on X axis button , b Select using 1D range on Y axis button , c Select using freehand draw button d Select using 2D rectangle button The selection is stored as a filter in the Filter folder>User in the Input pane or 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: In the Function window by displaying one of the Generic Filters that you have generated previously, calculate the correlation 50 • Basic Statistics Property Modeling 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 Property Modeling Basic Statistics • 51 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 – 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 In the Input pane, go to the Variogram data set folder and display the point data set Ac Impedance in a 2D window 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 Property Modeling Basic Statistics • 73 Click the Run button The calculated variogram map will be stored at the bottom of the Input pane Open a Map window and display the Variogram map It is a contour map (2D plot) of the sample variogram surface Click the View all in viewport button to see the 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 Keep the Variogram dialog open for the next exercise 74 • Basic Statistics Property Modeling Sample variogram calculation of point data set Exercise Steps Continue in the Variogram tab for the Ac Impedance point data 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 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 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: Property Modeling Basic Statistics • 75 Orientation XY Range No of Lags Horizontal Search Radius -39 -39 -39 -39 10 10 100 30 500 30000 30000 30000 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 XY Range Variogram Type Classical Classical Classical Classical Calculate a new Sample variogram with an Orientation of 51 degrees Make sure that the check box Overwrite last is NOT selected 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 In the Function window, display the first calculated Sample variogram of the major anisotropy axis (-39 degrees) that you created in the last exercise 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 Display the second Sample variogram as well (51 degrees) Now define the Variogram model range and nugget for both 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 76 • Basic Statistics displayed sample variograms interactively using the button or the button Notice, while editing the ranges interactively, one point will correspond to the major range and the other point to the minor range 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 Property Modeling Property Modeling Basic Statistics • 77 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 Display the data set Ac Impedance in the 2D window You will find it in the Variogram data set folder in the Input pane Open the Make/edit surface process under Utilities in the Processes pane In the Main input, drop in the Ac Impedance point data, select AI as attribute and select the check box Name; enter “AI Kriging” Select the Geometry tab and select the User defined option, highlight the Ac Impedance data and click the Get limits from selected button Set the Grid increments X and Y to 200 94 • Kriging Property Modeling Go to the Algorithm tab and select Kriging from the dropdown menu Click Apply Property Modeling Kriging • 95 Now, calculate different surfaces using the variogram parameters from the table below: Range Major Dir 500 10000 10000 13000 If the Nugget seems wrong, it is because the Variogram is scaled to a Sill of 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’ Range Minor Dir 500 10000 10000 7000 Azimuth Nugget Model type 0 -40 0.1 0.1 0.9 0.1 Spherical Spherical Spherical Spherical 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 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 Basic Statistics Part - 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 96 • Kriging Property Modeling 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 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 116 • Gaussian Simulation Exercise Steps Display the point data set Ac Impedance in the 2D window Open the Make/edit surface process 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 Select the Geometry tab and select the User defined option, highlight the Ac Impedance data and click the Get limits from selected button Set the Grid increments X and Y to 200 Go to the Algorithm tab and select the Sequential Gaussian simulation as Method Leave the other settings as default and click Apply Property Modeling Display the surface on a 2D or Map window to visualize the result Now, switch to Gaussian random function simulation as method in the Algorithm tab 10 Calculate different maps using the following variogram parameters (defined under the Variogram sub-tab): Range Major Direction Range Minor Direction Azimuth Nugget Model Type 5000 5000 0.1 Spherical 500 500 0.1 Spherical 30000 30000 0.1 Spherical 30000 30000 0.9 Spherical 11 Observe the results on the AI Simulated surface that you have displayed in the 2D/Map window When recalculating 12 Continue in the Make/edit surfaces process to calculate a the surface to get a different output, the Result surface surface using the variogram model that you determined must be removed by previously in the Sample variogram exercises (Module Basic selecting it, Delete and to Statistics Part - Exercises) give a different Name (“AI Simulated GRFS”) A pop-up 13 Leave the previous settings, but remove the Result surface window ask to reset all the and enter a new Name settings, select No to keep 14 Select the Variogram model from the Input pane (“Sample the old parameters and only apply the changes needed Var from Ac Impedance (-39 deg)”) Property Modeling Gaussian Simulation • 117 15 Go to the Algorithm tab, select Sequential Gaussian simulation, in the Variogram sub-tab, click the button to get the parameters from the variogram model 16 Click Apply/OK to calculate the new surface and display it to compare with the previous results 17 Keep all parameters, but change the Seed number under Settings sub-tab>Specify seed, and recalculate the surface Optional Exercise: User defined Normal distribution for simulation Prior to Gaussian Simulation, the data is transformed to Normal distribution and the simulation results will be back-transformed You have limited control over the back transformation in the Settings folder: • Output data range - is typically the data range of the input data The CDF used for the back transformation covers the value range defined by this parameter • If you select the check box Distribution from input data, then the CDF used for the back transformation is calculated from the input data • Normal distribution – use this function if you have few or no data points and want a surface with normally distributed data Using the Output data range (Min and Max.), Mean, and Std., you control the data range of the output Use this option with great care, as it will have a massive influence on your result and you may lose all relationship with your input data Make sure the Mean is in the middle of the data range Also, the data range should be larger than Mean+/- Std Deviation Exercise Steps In the Make/edit surface process, delete the Result surface and select Yes in the pop-up dialog asking if you want to reset the settings Enter an output Name: “User def distribution” In the Geometry tab, activate the “AI Simulated” surface from the Input pane and click the Get limits from selected button 118 • Gaussian Simulation Property Modeling Go to the Algorithm tab and choose Sequential Gaussian simulation In the Variogram sub-tab, choose an isotropic variogram model with a range of 5000 m and a nugget of 0.1 In the Settings sub-tab, define the following parameters: • Choose an Output data range of –1000 / +1000 and select Absolute • Select Normal distribution • Select a Mean of and a Std of 10 Click Apply to calculate the surface In the surface Settings>Style tab, turn off the Contour lines Show check box before displaying the surface Also Adjust color table on selected button from the main toolbar Change the Std to and recalculate the surface Refresh the color table and observe the result Property Modeling Gaussian Simulation • 119