Data Analysis and Property Modeling With SKUA-GOCAD Training Manual - Paradigm 15 [PDF]

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Data Analysis and Property Modeling with SKUA-GOCAD SKUA-GOCAD™ 15 - Paradigm® 15

Training Guide

© 1998–2015 Paradigm B.V. and/or its affiliates and subsidiaries. All rights reserved. The information in this document is subject to change without notice and should not be construed as a commitment by Paradigm B.V. and/or its affiliates and subsidiaries (collectively, "Paradigm"). Paradigm assumes no responsibility for any errors that may appear in this document. The Copyright Act of the United States, Title 17 of the United States Code, Section 501 prohibits the reproduction or transmission of Paradigm’s copyrighted material in any form or by any means, electronic or mechanical, including photocopying and recording, or by any information storage and retrieval system without permission in writing from Paradigm. Violators of this statute will be subject to civil and possible criminal liability. The infringing activity will be enjoined and the infringing articles will be impounded. Violators will be personally liable for Paradigm’s actual damages and any additional profits of the infringer, or statutory damages in the amount of up to $150,000 per infringement. Paradigm will also seek all costs and attorney fees. In addition, any person who infringes this copyright willfully and for the purpose of commercial advantage or private financial gain, or by the reproduction or distribution of one or more copies of a copyrighted work with a total retail value of over $1,000 shall be punished under the criminal laws of the United States of America, including fines and possible imprisonment. The following are trademarks or registered trademarks of Paradigm B.V. and/or its affiliates and subsidiaries (collectively, "Paradigm") in the United States or in other countries: Paradigm, Paradigm logo, and/or other Paradigm products referenced herein. For a complete list of Paradigm trademarks, visit our Web site at www.pdgm.com. All other company or product names are the trademarks or registered trademarks of their respective holders. Alea and Jacta software under license from TOTAL. All rights reserved. Some components or processes may be licensed under one or more of U.S. Patent Numbers 6,765,570 and 6,690,820. Some components or processes are patented by Paradigm and/or one or more of its affiliates under U.S. Patent Numbers 5,563,949; 5,629,904; 5,838,564; 5,892,732; 5,930,730 (RE 38,229); 6,055,482; 6,092,026; 6,430,508; 6,819,628; 6,820,043; 6,859,734; 6,873,913; 7,095,677; 7,123,258; 7,295,929; 7,295,930; 7,328,139; 7,584,056; 7,711,532; 7,844,402; 8,095,319; 8,120,991; 8,150,663; 8,582,825; 8,600,708; 8,635,052; 8,711,140; 8,743,115; 8,744,134; and 8,792,301. In addition, there may be patent protection in other foreign jurisdictions for these and other Paradigm products. All rights not expressly granted are reserved

Printed June 8, 2015

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Recommended Reading For further study after the class, we recommend the following: • Caers, Jef. Petroleum Geostatistics . Richardson, Texas: Society of Petroleum Engineers, 2005. • Deutsch, Clayton V. Geostatistical Reservoir Modeling. Oxford: University Press, 2002. • Deutsch, Clayton V., and Andre G. Journel. GSLIB: The Geostatistical Software Library. Oxford: University Press, 1998.

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Chapter 1 – Introduction to Data Analysis and Reservoir Modeling

Overview Before you begin building a reservoir model, you need to understand the main concepts and challenges of reservoir data analysis and reservoir modeling. A reservoir model is only as good as the parameters and data used to build it. • In order to build a consistent and robust reservoir model, we recommend that you use the Data and Trend Analysis Workflow to analyze the properties of interest first. This analysis establishes representative statistics and identifies the probable inconsistencies in your data. • Afterward, you can use the Reservoir Properties Workflow to populate a 3D reservoir grid with petrophysical properties using the data generated in the Data and Trend Analysis Workflow. These two workflows are used in conjunction with each other.

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Chapter 1 – Introduction to Data Analysis and Reservoir Modeling

Background • Huge investments in exploration and production, such as seismic acquisition campaigns, drilling programs, field development plans or enhanced oil recovery usage, are made on the basis of 3D numerical representations of the subsurface. • To be as precise as possible, numerical models need to integrate all the data and knowledge collected and interpreted by geoscientists, from geophysical interpretation to flow simulation. • These models support the representation of several elements of the subsurface: the reservoir structure and stratigraphy (that is, faults, horizons and their relationships and hierarchy), the rock property distribution and petrophysical content of the reservoir, and the fluid content of the reservoir.

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Introduction The construction of these realistic models that are economically optimal and consistent requires: • Integrating and combining: • Exploration data with geologic interpretation. For accurate models, we need to make sure that the interpretation is correct and that the geological model (at least) honors the input data. • Data from various sources (core data, well log data, outcrops, production data, seismicderived structural interpretation, 3D surveys, seismic-derived attributes=) and resolutions. • Expertise from different fields (geology, petroleum/reservoir engineering, economics..) • Accounting for the inherent uncertainty in the spatial distribution of reservoir properties and the structure. • Predicting rock properties at unsampled locations and forecasting the future flow behavior of the reservoir.

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Chapter 1 – Introduction to Data Analysis and Reservoir Modeling

Data and Modeling Scales One of the major challenges is to bring all data, each at its own scale of information, into a single numerical model: when you model a reservoir, you must define the intermediate geologic modeling scale, and then scale all input data to be consistent with that scale. For example, you must upscale your core and well logs while scaling down the larger-scale seismic data to the appropriate modeling resolution. The picture above [Jef Caers, Petroleum Geostatistics (Richardson, Texas: Society of Petroleum Engineers, 2005)] shows a comparison of the scale of observation, the typical resolution for geologic modeling (geocellular) and reservoir flow simulation models, and the operations between the various models. The reference unit resolution is the core support. If this reference resolution is on the order of 1, a 3D geocellular model is typically 6 orders of magnitude larger, a flow-simulation model is 8 orders of magnitude larger, and the entire reservoir is 12 orders of magnitude larger.

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Chapter 1 – Introduction to Data Analysis and Reservoir Modeling

3D Grid construction Despite the various natures of the reservoir models introduced previously, today geologists, reservoir modelers and engineers all tend to use the same 3D reservoir grid definition to construct their respective reservoir models. That grid is the pillar-based grid. Pillar Gridding Technique Pillars are defined as columns of grid cells and must respect two fundamental principles: • #1: Pillars must be aligned along faults, which implies that columns of cells cannot cross faults. • #2: Pillars must connect top and base horizons, which implicitly forces the same number of cells on the top and as at the base of the reservoir structure. Though this technique works well in simple, vertically faulted, layer-cake stratigraphy it raises many questions when geology becomes more complex.

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Chapter 1 – Introduction to Data Analysis and Reservoir Modeling

NOTE For more information about how to create structural and stratigraphic models, geologic grids and flow simulation grids with SKUA, sign up for the Modeling Reservoir Architecture with SKUA course.

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Chapter 1 – Introduction to Data Analysis and Reservoir Modeling

SKUA-GOCAD integrated product suite Since 2013, Paradigm GOCAD® and Paradigm SKUA® have been merged into one application, which is now available either as a standalone configuration or running on Paradigm Epos®. Projects from both GOCAD and SKUA can be loaded into the SKUA-GOCADTM application, and SKUA and GOCAD workflows can be shared.

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Chapter 1 – Introduction to Data Analysis and Reservoir Modeling

SKUA specific modules • SKUA Structure • SKUA Stratigraphy and Fault Analysis • SKUA Structure Uncertainty • SKUA Flow Simulation Grid GOCAD specific modules • GOCAD Structural Modeling • GOCAD Stratigraphy and Fault Analysis • GOCAD Rock Volume Uncertainty (Alea) • GOCAD 3D Reservoir Grid Builder

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Typical process of data analysis The objective of data analysis is to establish global statistics and modeling strategy. Such typical data analysis processes should be completed in order to ensure that your models are robust and representative.

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Challenges Oversampling must be identified and sampling bias removed by weighting raw data, in order not to establish biased scenarios (and biased estimates) that would lead to wrong strategies. Well data is also often too sparse to yield histograms representative of the underlying geologic phenomena. Smoothing data distributions allow you to remove artifacts (spikes, holes=) and provide representative information about a true underlying geologic distribution. Data blocking (upscaling) is recommended before performing stochastic simulation to: • Speed up algorithms • Enable verification of conditioning

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Chapter 1 – Introduction to Data Analysis and Reservoir Modeling

Data Trend Analysis (DTA) and Reservoir Properties (RP) workflows Both products are designed as workflows to: • Guide you systematically through the whole analysis/modeling process. • Audit trail of modeling decisions. • Ensure your models are robust and representative. Data Trend Analysis (DTA) DTA workflow provides tools for validating, organizing, analyzing, summarizing data as well as preparing input required by the various modeling algorithms. Reservoir Properties (RP) RP workflow offers many algorithms and options which can be combined for greater flexibility. This workflow enables: • Populating a grid with a complete petrophysical property model. • Accounting for both hard conditioning data and secondary information such as facies map, trends=

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What to remember
Why do we create property models? What are they used for? • OOIP and volumetrics • Reservoir management decisions
How can data analysis help you? • Identify inconsistencies between multiple types of data • Identify sampling bias (oversampling/sparse data) • Identify and capture geologic trends • Establish representative global statistics and define modeling strategy accordingly
How SKUA-GOCAD help the user to manage both data analysis and property modeling? • Integrated workflows-driven solutions • Use output from DTA as input for the Reservoir Properties workflow • Create and test alternative scenarios of models

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Chapter 2 – Raw Data Analysis

Overview When you model reservoir properties, it is important to know both the data and the geologic context of the area of interest. In this chapter, you will become familiar with the available data, geologic setting, and the process for analyzing raw data by using the Data and Trend Analysis Workflow.

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Geologic setting and data overview Based on the various data types collected, geologists have defined a geologic conceptual model with the following specifications: • The reservoir thickness is approximately 30 meters. It is made up of two distinct geologic units, both deposited in siliciclastic environments: • UnitA: The top unit that is a marine deltaic system consisting of distributary channels with a main trend oriented west-southwest/ east-northeast. More specifically, delta front deposits with little tidal influence have been identified in southwestern and western parts of the area. 15 layers. • UnitB: The base unit that is a terrestrial system consisting of braided streams with a southsouthwest/north-northeast orientation. 20 layers. • The lithology studies identified the three facies categories indicated above.

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Chapter 2 – Raw Data Analysis

Open project and select modules 1. Start SKUA-GOCAD by one of the following methods, depending on your environment: • For Windows®, double-click the SKUA-GOCAD icon on the Windows desktop. • For Linux®, open a command prompt, and then type the command supplied by your instructor. 2. Select the project ReservoirModeling_SKUA15_Training.sprj or ReservoirModeling_GOCAD15_Training.sprj. 3. Select the Change modules before opening project check box and click OK. 4. In the Project Modules Selector, ensure the following modules are selected : • On the Geoscience tab: • 3D Viewer • Foundation Modeling and Editing • Map, Cross Section and Well Section • On the Reservoir Modeling tab: • Data and Trend Analysis • Reservoir Properties 5. Click OK. SKUA-GOCAD loads the selected modules and the project opens.

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Chapter 2 – Raw Data Analysis

Review geologic setting and data  Take a few minutes to review the data loaded in the project and discuss object classification and geologic settings with your instructor.

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Selecting data You can select different objects and choose more than one object property at the same time because the same property to analyse may have a different name in different objects. If more than one property is chosen and the same object has more than one of the properties, the workflow uses only the first property.

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Chapter 2 – Raw Data Analysis

Data representation Once both objects and object properties are selected, you need to specify where you assume that the data is valid: • As a point measurement (single data value) – valid only locally. You don’t know what happens in the interval and you don’t want to influence computations by missing data. • As a continuous interval – you consider the measured value that can be propagated along the well path below the point. You assume that what you measure is valid until the next measured point.

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Data representation: points or interval This slide introduces interpolation methods relating to the property type and the data representation. Segment length approximated by well points In the previous slide we said that when the Intervals option is selected, data points are weighted by the segment length below. SKUA-GOCAD does not exactly measure the segment length, rather it uses the well points to interpolate the value. Influence of Data Type (Continuous/Discrete) for Interval The way the value is interpolated depends on the data type: • Continuous property - All the well path points falling between two successive data points will take a value computed by using a linear interpolation between the two data values. • Discrete property - All the well path points falling between two successive data points will take the upper data value. Importance of well sampling Well sampling must be dense and regular in order to obtain relevant and accurate results.

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Create a new DTA workflow 1. Select the Workflows tab and do the following: a. In the Workflows browser right-click Data and Trend Analysis and select Create. b. Enter DTA_Training in the Workflow name box and click OK. c. Double-click the workflow study in the Scenarios browser to open it. NOTE If you select Create & Open, a workflow study is automatically created and opened. It is named after the workflow. Specify properties to analyze 2. In the Navigation panel, make sure Specify Properties to Analyze is selected. 3. In the Specify Properties to Analyze panel, click Insert a new row to insert a new property in the list. 4. To specify that you want to analyze lithology data: a. Double-click the Name box and type LITHOLOGY. b. Click the Type column, then under Discrete select the Facies classification. 5. Repeat step 3 and step 4 to specify that you plan to analyze porosity data as indicated below: • Name: POROSITY. • Property Type: Reservoir > Porosity. 6. Click Next.

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Specify data to associate with LITHOLOGY 1. In the Select Data panel, in the Properties to Analyze box, select LITHOLOGY. 2. In the Data objects box, select all wells. Tip: Use the filter in the object selector box to select only the wells. 3. In the Object properties box, select LITHO x32. 4. Keep Points selected. Specify data to associate with POROSITY 5. Repeat step1 to step 4 to associate POROSITY property with PORO well logs. What do you observe? 6. Click Edit Property Settings. 7. In the Edit Property Settings dialog box, assign the Reservoir > Porosity type to the PORO well logs and click OK. Make sure PORO x 32 is still selected in the Object Properties box. Select modeling grid and seismic data for blocking and trend analysis 8. In the Modeling grid box, select the DTA_PM_Field grid. 9. In the Seismic grid box, select the DTA_PM_Field grid. 10. Click Next.

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Specify the domain of analysis 1. In the Define Domains of Analysis panel, select the Units in stratigraphic column check box. 2. In the Column box, select the DTA_Training column and keep Eon selected in the Rank box. NOTE If you are working with the project ReservoirModeling_GOCAD15_Training, select the column chronostratigraphic_column. 3. In the list of stratigraphic units, select UNITA and UNITB. 4. Click Next.

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Histogram definition • For a discrete property the histogram shows the proportion of each category, i.e. the number of time a given category occurs divided by the total number of data points. • For a continuous property the histogram shows the number of data points that fall within each bin divided by the total number of data points. 3 ways for checking proportions • Read proportions in the Summary Statistics table • Rest the pointer on one of the bins to make a tooltip appear with the number of samples and exact proportion. • Double-click on one of the bins to print the tooltip content into an info message in the command terminal. You can edit plot size, axes, and graphic appearance for better visualization and in-depth data analysis as necessary. What would be a relevant plot for Lithology?

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Domain selection • Use all data option displays all data corresponding to the objects selected in the Select Data panel. • Use data from all selected domains option displays only data that corresponds to the domain of analysis specified in the Define Domains of Analysis panel. • Show by domain of analysis option lets you customize the display of the histogram and group the data by the specified domains of interest in the matrix plots. Plot layout specification The items that appear in the Horizontal and Vertical boxes correspond to the domains specified in the Define Domains of Analysis panel, the data objects, and any calculated discrete properties, selected in the Select Data panel. Data selection You can select: • Only one type of data to be plotted along the first dimension (vertical/or horizontal). • As many data types (sub-objects) as you want to be plotted along the second dimension.

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Calculate proportions for raw lithology data everywhere in the grid 1. In the Navigation panel, select Calculate Proportions. 2. In the Calculate Proportions panel, under Analyze the raw data and display the histogram and proportions, click Calculate and Display. 3. Explore the different ways to determine the exact proportions of a facies by doing the following: a. In the plot view, rest the pointer over a bin. After a moment, a tool tip displays the number of samples and exact proportion of the facies category. b. Double-click a bin to display the tool tip content on the status bar. c. Review proportions in the Summary Statistics table.

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Display proportions per grid region  Open the Edit Plot Layout dialog box and make adjustments to get plots similar to the plots above.

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Chapter 2 – Raw Data Analysis

Access the Calculate Vertical Proportions Curves panel 1. In the Calculate Proportions panel, click Next three times to access the Calculate Vertical Proportion Curves (LITHOLOGY) panel. NOTE You will analyze blocked data and apply weights in next chapter. Calculate and display the VPC 2. In the Calculate Vertical Proportion Curves panel, select Yes. 3. Under Select the data, ensure Raw is selected in the Data box. 4. Under Calculate vertical proportion curves, click Calculate and Display. The workflow displays the VPC calculated for the raw LITHOLOHY data in the Statistics view. 5. Analyze the computed VPC and try to identify the limit of the two stratigraphic units. Discuss the results with your instructor.

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Chapter 2 – Raw Data Analysis

Calculate raw porosity distribution for the entire model and per stratigraphic unit 1. In the Navigation panel, expand POROSITY and click Calculate Statistics to open the Calculate Statistics (POROSITY) panel. 2. Apply what you have learned to calculate and display the histograms for raw porosity data everywhere, and then per stratigraphic unit. What do you notice? What would you do next?

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Chapter 2 – Raw Data Analysis

Calculate and analyze raw porosity distribution per facies category and stratigraphic unit 1. Apply what you have learned to edit plot layout and display raw porosity distribution per stratigraphic unit and facies category. 2. Edit plot layout and display raw porosity distribution per facies category only. What can you observe? Discuss the results with your instructor. 3. After you are finished with your analysis, click Next until you reach the Calculate Vertical Trend Curves (POROSITY) panel.

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Chapter 2 – Raw Data Analysis

Calculate a Vertical Trend Curve (VTC) for raw porosity data 1. 2. 3. 4.

In the Calculate Vertical Trend Curves panel, select Yes. Under Select the data, ensure Raw is selected in the Data box. Click Calculate and Display to compute the VTC for raw porosity data everywhere in the grid. Apply what you have learned to edit the plot layout and display the VTC for raw porosity data per facies category, as illustrated above.

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Adding notes and generating a report As you progress through the workflow, you can create notes and comments to record your observations and share them with others in your group. You can use other applications to work on pictures and insert edited pictures in the note.

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Add a note to the Calculate Vertical Proportion Curves (LITHOLOGY) step 1. Access the Calculate Vertical Proportion Curves (LITHOLOGY) panel and click Report to open the Note related to DTA_Training dialog box. 2. In the Body area type in Big increase of proportions of Shale and ShalySand downward in UNITB. 3. Select the VPC view in the list of views available for snapshots. 4. Click Insert Image from View Snapshot. Notice how the dialog box updates. Generate an HTML report 5. Click Apply & Generate Report. An HTML document is created, automatically saved in your project folder and displayed in your internet browser. 6. Scroll the report until you see your note. 7. Close the report. NOTE In the Navigation panel, an icon appears to the right of the step to show that you have added a note.

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Chapter 2 – Raw Data Analysis

What to remember
What is the objective of defining a property in the first DTA panel (Specify Properties to Analyze panel)? • Definition of a container associated with a list of objects and properties that represent the data • Act as a filter
What is the difference between the Point and Interval representation? Is that synonymous with continuous and discrete properties? • The data representation depends on the way you want to extrapolate the local measurement • The continuous and discrete terms represent the nature of the property values
What are the different manners to display the statistics with DTA? • Per unit, facies= with the Plot Layout Manager
In our case study, we want to analyze the lithology, porosity and permeability distribution in the reservoir. In which order should you analyze these three properties? Why? • Porosity and permeability are influenced by the rock lithology • Permeability models are often built using porosity values

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Chapter 3 – Discrete Property Modeling

Overview Analyzing lithology is an important step in reservoir modeling because most of the properties of interest are highly correlated with the lithology facies. In this chapter, you will learn how to build a realistic 3D model of lithology that you can use later in making decisions and developing strategies regarding the reservoir.

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Chapter 3 – Discrete Property Modeling

More info about modeling lithology Lithology is a critical property to model because: • It defines reservoir and source rocks areas. • Most of properties of interest are highly correlated with facies category. The knowledge of lithology constrains the range of variability in porosity and permeability. Petrophysical properties are more homogeneous within each lithology than the reservoir as a whole. • A single algorithm is often not sufficient to capture the complexity of a reservoir, and multiple algorithms need to be combined in a way that mimics facies deposition. The variogram is the most widely used tool that helps quantify the spatial correlation of data and geological information such continuity, anisotropy or trends. • Interpolation algorithms will generate a property by estimating cell values using the specified hard data, producing an optimal and unique solution. Estimation models are said to be locally accurate in that they seek to minimize local errors independently of what the global map of estimates may look like. • Simulation algorithms will generate a property by using a probabilistic approach, producing equiprobable (multiple) solutions satisfying the selected parameters.The focus in simulation lies in reproducing a model that reflects as accurately as possible the patterns of the overall geological continuity of the actual reservoir. • Deterministic modeling is always preferred when there is sufficient evidence of the facies distribution to remove any doubt of the 3D distribution.

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Lithology Simulation Techniques • Cell-based simulation techniques are commonly applied when there are no clear geologic facies geometries and where the original depositional facies have complex variation patterns SIS: when the material is randomly distributed in depositional setting Truncated Gaussian: when there is a clear ordering of the facies (transition zone) and no obvious difference in their anisotropy • Object-based techniques are used when lithology appears to follow clear geometric patterns Shape of the geological structures can be described Proportions of the different objects can be quantified • Multiple Point Statistics are based on pattern recognition from a training image and enable to reproduce a spatial facies distribution as well as to honor well data

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Chapter 3 – Discrete Property Modeling

Property transfer and data blocking Data scale variation The property model is built at the geologic grid resolution. To create a representative and robust model, the geomodeler must deal with the differences in measurement scales [Fine scale: core and well log / Large scale: seismic]. Reservoir grid cells are at a much coarser resolution than at which well data is sampled. Blocking well data allows reconciling the well data resolution and the field extension. Modeling scale A too-small choice leads to large and inefficient computer use, which restricts the number of alternative scenarios and sensitivity runs that can be considered. A too-large choice could lead to incorrect flow results due to inadequate representation of important subgrid geological heterogeneities. Blocked data used as hard data for simulation Blocked data becomes conditioning data for property simulation and should be used as the reference data. Is it possible not to block data? When using interpolation (ex: kriging) it is recommended not to block data and directly use well data.

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Blocking methods for discrete properties The blocking method available depends on the property type (continuous or discrete). There are three blocking methods for discrete properties: • Nearest to cell center (1 on diagram): block the facies of the data point closest to cell center • Capture the fine features • Usually reproduce better the raw statistics • Largest Proportion (2 on diagram): block the most frequently occurring facies in a cell • May not preserve the heterogeneity of the reservoir • Random: block randomly one facies value in a cell Blocking challenge The challenge lies in determining the appropriate method to upscale well data that intersects the grid to grid resolution by blocking the values and calculating new statistics for those values. Capturing heterogeneity is much more important than reproducing raw statistics that will be input with global proportions or distribution.

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Data blocking options • NDV If data is sparsely sampled, cells lacking data must be considered and assigned an interpolated property value. • Include only cells that the well path intersects through opposite faces It is not recommended to exclude cells that the well paths do not intersect through opposite faces as it will lead to ignore many data points. • Calculate one value for each layer (Cell layer averaging) - When not selected (default setting): each individual cell contains an upscaled value. Successive cells in the same layer can have strong different values. Can lead to strong local artifacts when running a simulation. - When turned on: adjoining cells in the same layer are considered as a single one, and the mean computed for all these cells is assigned to the cell that contains the longest well path intersection. The others remain undefined. Such settings: • Affect the number of well data points which are used and locally assigned to the grid. See next slide. • Are especially relevant when working with deviated/horizontal wells.

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Impact of blocking options on simulation These options define which grid cells: • Will be assigned a value and will act as conditioning data for running the simulation. • Will remain undefined. Top pictures - When no option is selected, each individual cell will contain an upscaled value. Successive cells in the same layer could have strong different values, which would lead to strong local artifacts when computing the variograms and running a simulation. Middle pictures – When selected, the Include on cells that are intersected through opposite faces option avoids imposing features that might not be representative of the reservoir. Bottom pictures – When selected, the Calculate one value per layer option avoids high horizontal variations and allows you to reproduce the variogram. Conclusion: For the exact same well log, depending on the blocking options that are selected, the blocked data will be different, as will be the output model.

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Checking blocking scenarios in 2D and 3D As mentioned before, to validate one scenario you would take into account: • The amount of available data. • The knowledge of the geological area (discontinuity, flow barriers=). • The confidence in the model. Even after you test the best way to upscale your data, you still may not be satisfied with the blocked lithology category in some cells. You can change the value of a specific cell accordingly to better reproduce or delete a heterogeneity. Commands can be accessed by right-clicking the blocked data in the Objects browser or in the 3D Viewer. NOTE For more information watch the video Visualizing Blocked Data in 2D in SKUA-GOCAD available in Paradigm Online University under *Training SKUA-GOCAD > Video Learning Library.

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Data oversampling Determining the global proportions in the reservoir is not easy to do as we often have a view of only the over-sampled zones. Wells are drilled in areas with the greatest probability of high production (core are taken preferentially from good quality reservoir rock). Such data collection practices lead to the best economics and the greatest number of data in portions of the study area that are the most important. These practices should not be changed, but subsequent bias should be considered. → Oversampling must be identified and sampling bias removed by weighting raw data, in order not to establish biased scenarios (and biased estimates) that would lead to wrong strategies. In the figures above, the proportions calculated from well data (a) are not representative of the global proportions in the reservoir (b). We could even create a model that honors other global proportions (c) and the well data. That model would be valid if we don’t have other data.

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Methods to remove sampling bias Uncertainty on global proportions There are several methods to establish representative statistics that should be tested and combined. It is highly recommended to work with the geologists to estimate the global proportions of your model. Cell declustering The cell-declustering is a technique that tries to identify the clusters in data and weight statistics with the number of points that lie in an area. When there are a lot of points close together, their weight is reduced in proportion computation. In the figures above The 3 points circled in red are supposed to belong to the same area and therefore count for only one data point. Each point in the cluster is weighted by 1/3. This returns declustered proportion of sand = 50% instead of 70%. Other techniques Cell-declustering is only one method among others. Also polygonal-declustering: base weights on the volume (polygonal area) of influence of each sample. Algorithms that are CPU-intensive and somewhat unstable in 3D. Declustering weights are taken proportional to the areas of influence.

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Removing sampling bias: cell declustering Cell size The weights assigned by cell declustering depend on the cell size. If the cell size is set as very small, then every sample occupies its own cell and the result is equal weighting or the naïve sample distribution. If the cell size is very large, then all samples reside in the same and the result is once again equal weighting. Procedure When it is difficult to make a choice, a common procedure is to assign a cell size that maximizes or minimizes the declustered mean (the declustered mean is maximized if the data is clustered in lowvalued areas, and it is minimized if the data is clustered in high-valued areas). This procedure is applied when the sample values are clearly clustered in a low or high range. Automatically assigning the minimizing or maximizing cell size may lead to less representative results than simply using the original distribution. Choosing the optimal grid origin, cell shape and size requires some sensitivity studies. Cell size for declustering is assigned to an intermediate grid that is generally not the cell size used for geologic or flow modeling, but rather a size required for one datum to reside in the most sparse areas sampled. The histograms and summary statistics (mean, standard deviation=) are then calculated with these declustering weights to be representative of the entire volume of interest.

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Calculating proportions on weighted data With regards to the geologic knowledge of the area of interest you define the reference facies and define if it is under- or over- sampled. The reference facies generally represents the facies of interest in which wells tend to be preferentially drilled. If the reference facies is said to be oversampled, declustering will tend to minimize the proportion of this facies.

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Map data to grid 1. Access the Analyze Blocked Data (LITHOLOGY) panel and select Yes, block values from data objects and then calculate. 2. Click Map Data to Grid. After a few seconds the rest of the workflow panel is enabled and you can select blocking methods and options. Block well data to grid resolution 3. Under Specify options for blocking, do the following to create the first blocking model: a. Leave Discrete as the blocked data type to create. b. Leave Nearest to cell center as the blocking method. c. Leave None selected to specify there is no filtering for this model. 4. Under Calculate blocked proportions, click Calculate and Display. The blocked data is displayed in the Statistics view with the raw data for comparison. The blocked data is named Blocked-1. 5. Repeat step 3 and step 4 to create a second blocking model (Blocked-2), only this time choose Largest proportion as the blocking method, and no weighting. The Blocked-2 data displays in the Statistics view. 6. Compare and discuss the results with your instructor.

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Prepare your display 1. From the Windows menu select 3D Viewer 1. 2. In the 3D Viewer, show only deviated well Diamond-N22. 3. Show LITHO log and change log style to cylinder for better visualization. Tip: Open the Style Editor of the well, select Logs and then LITHO in the table. Change the Log Style for Cylinder, and the Scaling factor for 3. 4. Show LITHOLOGY>Blocked-1 data along Diamond-N22. What do you observe? Edit blocked cell value 4. In the 3D Viewer, right-click the blocked cell where indicated and select Edit Cell Value. 5. In the Edit Facies dialog box, select Shale in the New Facies box and click OK. In the 3D Viewer, the color of the cell changes from yellow to green to represent the new value of shale.

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Calculate weights by cell declustering and apply them to raw lithology data 1. Access the Apply Weights (LITHOLOGY) panel. 2. Select Calculate weights from cell-declustering. In this case, you do not have existing weights so you will use the workfow to calculate them using cell-declustering techniques. 3. Make sure Raw is selected in the Apply Weights on box. 4. Select Sand in the Reference facies box and make sure Over-sampled is selected. 5. Click Calculate and Display to display the histogram for the weighted proportions of lithology data everywhere in the grid.

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NOTE You can delete a model at any time. When you delete a model, the workflow deletes the row from the Summary Statistics table. But deleting models does not delete models saved as resources in the Object tree.

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NOTE You can also create 2D proportion maps from deposition azimuth or from facies boundaries outside the workflow, from the Resources browser.

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When you specify one map value per well, the values for the intersected cells are averaged and only one cell contains the averaged value. The location of that cell is the average aerial location of the intersected cells. For deviated wells, the location of the averaged cell will not necessarily be exactly at the well location.

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NOTE For more information about each method, please check the Online Help.

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Create a VPC model of Weighted-1 data 1. Open the Calculate Vertical Proportion Curves (LITHOLOGY) panel. 2. In the data box, select Weighted-1. 3. Under Calculate and display proportion curves, click Calculate and display to display the VPC for the Weighted-1 data. 4. Under Model vertical proportion curves, keep the default name VPC model in the Model Name box, then Click Create. What do you observe? You can edit the VPC model to correct or enhance the vertical trends you observe on the calculated VPC. Edit the VPC model 5. Under Edit Model Interactively, click Edit 6. In the Statistics view, drag the points to edit the curve to look like the figure above. Right-click when you are finished editing. 7. Under Smooth and Merge Models, select Weighted-1(LITHOLOGY) and click Smooth. Create a resource object from the VPC model 8. Click Create as Resource. The VPC is saved as resource. You can access it from the Resources browser > 1D Trend.

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Create a 2D proportion map from well data 1. Access the 2D Proportion Maps (LITHOLOGY) panel. 2. Select Yes, using well data. 3. Keep default map dimensions and select DSI as the interpolation method. 4. Under Create map, select the One map per unit and Only one map per well check boxes. 5. Click Create. Display your proportion map for each facies 6. Under Show Map, select the interpolated map for UNITA and Sand facies. 7. Use the Back and Next buttons to review the proportion of each facies. 8. In the 3D Viewer, right-click the map and click Show most probable facies. What can you observe? Tip All properties (most probable facies, random facies and facies proportions) are stored on the map. To change the display, open the map Style Editor, click Property in the left pane and select the property from the Display menu.

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Create a resource object from the interpolated proportion map for each unit 1. In the workflow panel: a. Select Raw(LITHOLOGY,UNITA)[192,227](single value)::DSI#1. b. Click Create as Resource. 2. Open the Resources browser and expand 2D Trend. 3. Right-click Raw(LITHOLOGY,UNITA)[192,227](single value) DSI#1 and select Rename. 4. In the Rename Statistic Object dialog box, do the following: a. Enter LithologyMap_DSI_UNITA as the new name and click Apply. b. Select Raw(LITHOLOGY,UNITB)[192,227](single value) DSI#1 as the Stratistic object and enter LithologyMap_DSI_UNITB as the New Name. c. Click OK.

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Combine your VPC and proportion map into a 3D proportion cube 1. Access the 3D Proportion Cubes (LITHOLOGY) panel and select Yes, 1D + 2D. 2. In the VPC box, select the VPC computed on raw data. 3. In the Map(s) box, select the maps you have calculated in the previous exercise with DSI interpolation. 4. In the table below, for each row, double-click the cell in the Units column and select the stratigraphic unit over which the map is valid. 5. Under Select method, leave Rescale vertical proportions (recommended) selected. 6. Under Create and show 3D proportions keep the default name and click Create proportions. 7. Use the Back and Next buttons to review the proportions of each facies. NOTE From the VPC and Map(s) boxes in the panel, you can either select the data object that was calculated in the workflow, or the one you saved as a Resource. Because their names are very similar, a good idea is to rename the Resources objects as you create them and as you just did in the previous exercise.

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Reservoir Properties workflow outline Typical process: • Specify general workflow parameters (reservoir grid, property type/name=) • For each property, specify conditioning "hard" data and simulation domains • For each modeling region: select the algorithm and options you want to use and enter all required parameters- filling methods, proportions of each facies category (any categorical property), variogram files for each category • Secondary data: proportion information to account for existing trend, if any (1D curve, 2D facies map, or 3D proportion cube) • Optionally define transition matrix, post-processing options=

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General workflow parameters The workflow is represented as a tree and displays all choices and parameters entered by user. It is dynamically updated as information is entered or modified. As with the DTA workflow, property dependencies require specific attention. You must define LITHOLOGY first as POROSITY will be simulated by lithology category. You must also create a realization for POROSITY if you want to use this property as a covariable when creating a PERMEABILITY model.

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Variogram parameters Definition The variogram (a spatial correlation function) is a measure of how geology varies with distance. Geologic properties at two locations are correlated if the distance that separates them is less than the range of the variogram. Advantage of using SIS The main advantage of SIS is that it allows you to have different variogram models for different property ranges. This means that it can better handle properties that show multiple correlation patterns. Geological facies is the most common example, where each property value has its own correlation pattern as it represents a distinctive sedimentary body or environment. SIS requires as input a variogram model for each facies category. Each facies may have a different variogram with different correlation lengths and anisotropy characteristics, reflecting the difference in spatial continuity of the various facies. Do you want the variogram parameters to vary spatially? The variogram parameters may vary locally within the modeling region. Although this variation may sometimes be difficult to infer from well data, it is important to be able to account for it because the variation may be an important feature of the conceptual geological model. The minimum and maximum ranges of correlation as well as the azimuth can be made to vary spatially.

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The Variogram: a spatial correlation function The variogram is the simplest way of looking at spatial continuity as it measures the degree of linear correlation between the values of a single property measured at any two locations separated by a certain 3D vector h and then plots that correlation versus h. It is the most widely used tool to investigate and model spatial variability of lithology, porosity, and other petrophysical properties. It is a quantitative measure (a function) of spatial correlation. It reflects our understanding of: • The geometry and underlying geological phenomena. • The continuity of reservoir properties. The variogram can be defined as a chart of the geological variability versus distance at a given direction. It measures the dissimilarity of a variable Z at 2 different locations. • Y axis: variability (‘geological difference’) • X axis: distance between locations ‘h’ The lack of data, which makes the variogram important, also makes it difficult to calculate, interpret, and model a reliable variogram. The available well data are too widely spaced to provide effective control on the numerical model. Seismic and historical production data provide large scale spatial constraints. The variogram provides the only effective control on the resulting numerical models.

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The Variogram: a spatial correlation function Variograms can be calculated for several directions in 3D space. The shapes of the experimental variograms depend on the direction along which they are calculated. Differences between XYZ and UVW domains In the figures above, we assume that the points A and Aw are correlated at the depositional time (Figure A). In the current reservoir geometry (Figure B): • In the XYZ space, the point A would be correlated with Az • In the UVW space, the point A will be correlated with Aw. Two points correlated at the depositional time must be correlated in the current reservoir geometry (geometric distances versus stratigraphic distances) Variograms must be modeled with respect to depositional patterns to preserve reservoir heterogeneities. Attempting variogram calculation prior stratigraphic transformation can lead to the erroneous conclusion that data has no horizontal correlation. As simulations are run in the parametric space, it is recommended to analyze and model your variogram in the parametric domain (UVW). • A UVW variogram model is unique to the grid that defines the UVW space. When geological sequences have been extensively folded, a more elaborate coordinate transform such as UVW which allows for following the curvilinear structure is required. In UVW (or XYW space) the distance is normalized between 0 and 1. • An XYW variogram is computed following the stratigraphy. The two selected horizons are used to define the Z interval at any given XY. Distance will be specified in W units. In the Areal variogram computation, the data will be divided into layers parallel to the two horizons and all related distances are given in XY units. • An XYZ variogram is computed with respect to top and base. It assumes proportional layering and vertical faults. All computations and modeling are carried out using the XYZ values.

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Top unit k-layer #2. Marine deltaic system in the top unit consisting of distributary channels with a main trend oriented WSW/ENE. More specifically delta front deposits with little tidal influence have been identified in SW and West parts of the area. Bottom unit k-layer #21. Terrestrial system in the base unit consisting of braided streams with a SSW/NNE orientation.

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Create a new Reservoir Properties Workflow 1. Apply what you have learned to create a Reservoir Properties workflow named RP_Training. Tip: Right-click the workflow and select Create to be able to name the study as appropriate. Define the general workflow parameters 2. In the Reservoir Grid/Voxet box, select DTA_PM_Field. 3. In the Number of Properties box, type 2 and press ENTER. 4. In the first Property Name box, type LITHOLOGY. 5. In the Type box, select Categorical. 6. Repeat steps 4 and 5 to name the second property POROSITY and define it as Continuous. 7. Click Next.

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Define the conditioning data for Lithology 1. In the Property: LITHOLOGY panel, click Yes because you want to use hard conditioning data. The panel expands for you to input additional information. 2. Because the data is already assigned to the grid, click Yes. 3. In the Blocked data type area, select Blocked Well. 4. In the Blocking Scenario, box, select DTA_Training. 5. In the Blocked Property box, select blocked data LITHOLOGY. 6. In the Blocked Method box, select nearest_neighbor. 7. Click Next. Define the simulation domain for Lithology 8. In the Simulation Domain for LITHOLOGY panel, click By Regions. 9. In the Available Regions box, select UNITA and UNITB. 10. Click Add Selected Regions to move both regions to the Regions Used box. 11. Click Next.

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Define filling method for UNITA 1. Access the Property: LITHOLOGY / Region: UNITA panel and specify simulation algorithm as indicated above (SIS with secondary data). Specify categorical properties for UNITA 2. In the Categorical Parameters panel, select the Data region check box and select UNITA, then click Initialize. 3. In the Proportion column, change the proportions for the three categories, as indicated above to use the proportions calculated from the weighted data, instead of the blocked data. 4. Click Create regions, then click Next. Specify the variograms for UNITA 5. In the Categorical Variogram Parameters panel, leave No selected because you do not want to use a single variogram model for all categories. 6. In the Available Variograms area, click Import from file. 7. In the Load Variogram dialog box: a. Browse to the Vario folder and double-click Litho_Shale_UNITA. b. Enter a name for the variogram and click Apply. c. Repeat step a and step b to load the two other variogram files for lithology in UNITA. 8. In the workflow panel: a. For the 1st category, select Litho_Shale_UNITA. b. For the 2nd category, select Litho_Sand_UNITA. c. For the 3rd category, select Litho_ShalySand_UNITA. 9. Leave No selected because you do not want the variogram parameters to vary spatially.

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Define secondary proportion data for UNITA In the Proportion Data panel: 1. Click Yes. 2. Click Proportion constraint already exists. 3. Click DTA_PM_Field and make sure Probability>DTA_Training is selected in the Property box. This represents the 3D proportions cube you have created by combining the VPC and the proportion map. 4. Keep Kriging with locally varying mean selected and click Next. 5. In the Facies Map panel, keep No selected because you do not have a facies map, then click Next. 6. In the Search Parameters panel, keep Yes selected because you want to use the default search parameters, then click Next. You have defined the parameters for the UNITA region. Next you copy the parameters to UNITB and make some adjustments. Define parameters for UNITB by copying and editing UNITA parameters 7. In the Navigation panel, under LITHOLOGY, drag UNITA to UNITB. The parameter settings are copied from UNITA to UNITB. 8. Using what you learned from defining the parameters for UNITA, edit the parameters for UNITB to make the changes as indicated in the table above. The remaining parameters stay the same as for UNITA. NOTE For training purposes, you will not define a transition between the two regions.

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Check the parameters 1. Access the Check LITHOLOGY Parameters panel and check all required parameters have been entered. A message in green should appear, indicating all parameters required for LITHOLOGY simulation have been specified. NOTE You can also review the parameters in the Navigation panel and make changes as necessary by clicking the task. Run the simulation and view the results 2. Access the Simulation Control Panel and for the LITHOLOGY row, click Process to run the simulation for lithology. This process may take a few minutes. As the simulation runs, the status bar at the bottom of the software window displays the progress. 3. After the simulation finishes running, click Show to visualize the result in the 3D Viewer. The command displays the reservoir grid and the simulation result (the LITHOLOGY1 property). 4. Compare the results for UNITA and UNITB. What do you observe? Discuss the model with your instructor.

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What you should remember
Why do we apply cell-declustering technique? • To remove sampling bias due to data collection practices • To avoid over/under-estimating subsequent property proportion
What is important to check when you upscale well data? • The property types • The data measurement interpretation • The well trajectories: Horizontal and deviated wells require specific attention
What is the difference between raw, weighted and blocked data, and when should you use each one? • Raw = initial • Weighted data = sampling bias has been removed from initial data • Blocked data = data has been upscaled to the grid resolution
What is the difference between interpolation and simulation? And between cell-based and objectbased algorithms? • Interpolation method = deterministic approach • Simulation method = stochastic approach

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Overview Because petrophysical properties within facies are more homogeneous than within the reservoir as a whole, these properties are usually modeled on a by-lithology basis. Even though non-net lithology (shale, for example) may be assigned arbitrary low values, porosity and permeability within most lithology must be simulated using geostatistical algorithms to reproduce the representative histogram, variogram, and correlation with related secondary variables when available. In this chapter, you will build realistic 3D models of porosity and permeability that you can use later in making decisions and developing strategies regarding the reservoir.

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Continuous properties: porosity and permeability Usually, reservoir properties: • Within the same lithology and different layers may have similar characteristics. • Within different lithology in the same layer often are significantly different and unrelated. Permeability Permeability can be more difficult to model than porosity as: • It can be highly variable (extreme values) • The continuity of extreme low/high values (flow barriers/conduits) is very important for subsequent flow modeling studies • It often has a highly skewed histogram Usually permeability is not computed directly with well logs, but: • Often estimated from Porosity • Measured on core data (chart of measured permeability vs porosity) Simulation methods Many simulation methods for simulating the spatial distribution of regionalized variables such as porosity and permeability are possible : • Basic methods such as porosity/permeability transforms (classical regression, conditional expectations, and simple Monte-Carlo simulation from porosity/permeability cross plots). • More advanced methods like Gaussian techniques and indicator techniques (in order of increasing complexity and flexibility). Indicator methods may be used to account for greater or lesser continuity of extreme values. They must be considered when permeability shows complex patterns of spatial variation such as exceptional continuity of extreme values. They are occasionally used when there are sufficient data to infer the complex required statistics.

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Blocking continuous properties The Nearest-to-Cell-center method is still proposed as it is one of the best methods for reproducing the fine features that may act as flow barriers/conduits. But it is often recommended to linearly average the porosity by using the Arithmetic Mean method. Nevertheless, with such averaging methods problems of robustness and consistency will likely occur in your resulting models as these methods take into account all the porosity data available to average the porosity in one given grid cell. As a result these methods randomly over/under estimate the blocked porosity. One may obtain a high porosity value in a cell with shaly facies. This is why additional options are recommended when averaging continuous properties such as Porosity. You can constrain/filter blocking by other (blocked or non-blocked) discrete logs. NOTE The Geometric Mean method is recommended to average the permeability as this method is sensitive to low values of permeability and would subsequently honor flow barrier.

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Blocking continuous property • In Figure A, the Blocked porosity value with the Arithmetic Mean method is 0.1531. High porosity values (that correspond to sand lithology category) are considered when averaging well data in shaly areas and the resulting porosity average is far higher than what could be expected in these areas. That is the reason why it is highly recommended to filter the porosity values before averaging and upscaling well data. • In Figure B, the Blocked porosity value with the Arithmetic Mean method and blocked facies used as a filter is 0.007. It is the same averaging method but with the blocked facies used as a filter. The averaged porosity is in accordance with the blocked facies. NOTE For a discrete property such as LITHOLOGY, a filtering option can be used if you previously blocked a depositional facies data: you would only block lithofacies values that correspond to the depositional blocked facies.

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Declustering continuous properties • For a continuous property, declustering tends to minimize the average of the property if the high property values are set to be over-sampled. • The statistics of the weighted distribution are displayed near the statistics of the raw data so that you can evaluate quantitatively how the cell-declustering process affected the data statistics. As with discrete properties, values are also displayed in the Summary Statistics table. • When several histograms are displayed, you can focus on the histogram of interest by hiding others temporarily using the shortcuts or the Data Display tab. • After a histogram is calculated and displayed with the DTA workflow you can: o Overlay the histogram’s calculated cumulative distribution function (CDF). o Use the legend to edit the fill color for a continuous property (or apply a pattern if the property is discrete).

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Summary statistics table In the Summary Statistics table you can: • Specify the columns of information you want included in the table: right-click any column heading and then select or clear the item on the shortcut menu. • Copy the data and paste it into another program, or export the data as a file for importing into another program. Right-click any data cell (but not a column heading) and then: a. Click Export to and select a file format and the location for saving the file. b. Click Select all/Copy to copy summary statistics data to the clipboard and then paste it into another program. To paste the data into a spreadsheet program, use the Paste Special command. NOTE The Copy command copies the cell data only, not the column heading. Tab characters separate the data so it will format easily when you paste it into a text editor or spreadsheet program.

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Fitting and smoothing histograms Fit and Smooth Histograms options allow the effective removal of holes and unrealistic spikes from raw, weighted or blocked histogram data, by fitting a parametric distribution to the data or by smoothing the histogram. It is recommended to try each one and see which one gives you the best results. • Yes, fit existing models- Overlay stored histogram models on the existing histogram. • Yes, fit parametric models- Choose the parametric distribution with the shape closest to the histogram, and the DTA workflow will create a model with parameters that match the parameters of your data. • Yes, smooth distribution. Smooth out unrealistic spikes and ‘fill in’ the holes in the histogram. Can also edit the smoothing parameters to improve the match to your data. Kernel functions algorithm Calculates a distribution based on the sum of several Gaussian functions. Replaces each datum with a parametric probability distribution with a mean equal to the datum value and a small variance. The resulting distribution (model) does not in general simultaneously honor the mean, variance and important quantiles of the sample data. If you want to use data derived directly from any object selected in the Select Data panel (such as wells), select Raw. If you want to use sample data representing statistics expected throughout the entire volume, select Weighted-2.

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Working with 2D trends Using the map editing tools, you can interactively edit the map that you created (only if you used the DSI interpolation method). You can add iso-value lines to further constrain the trend. After you add the iso-value lines, the workflow automatically recomputes the DSI interpolation and updates the map to take into account the additional constraints.

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Block porosity data without applying a filter 1. In the Data Trend Analysis workflow, create a new blocking model for the raw porosity data, using Arithmetic mean as the blocking method and no filters or weights. Apply filter and create a new blocked model 2. Still in the Analyze Blocked Data (POROSITY) panel, select LITHOLOGY>Blocked-1 (nearest to cell center) as a filter and create a new blocked model (blocked-4). 3. Review and discuss the results with your instructor. When you use the blocked lithology data as a filter, only the porosity data values that correspond to the facies blocked in each grid cell are considered for the average computation. This prevents from overestimating or underestimating the porosity value that is assigned to each grid cell and subsequent inconsistencies in the output models. • Min/Mean/Max Blocked-3 values increase in Shale lithology. Property value in this region is overestimated. • Min/Mean/Max Blocked-3 values decrease in Sand lithology. Property value is underestimated. • Min/Mean/Max Blocked-4 values are more relevant within each lithology category.

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Calculate weights by cell-declustering and apply them to raw porosity data 1. Use what you have learned to calculate and display raw porosity histogram weighted by celldeclustering assuming high property values are over-sampled. 2. Discuss the results with your instructor. Is the distribution shifted to the lower values?

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Smooth the porosity distribution for each lithology facies 1. In the Navigation panel, under POROSITY, click Fit and Smooth Histograms. 2. In the Fit and Smooth Histogram panel, click Yes, smooth distribution. 3. In the Display histogram area, select Weighted-2 as the data you want to display, then click Calculate and Display Histogram. 4. If necessary, use the Edit Plot Layout dialog box to ensure that the histogram displays statistics per lithology facies. 5. In the Specify smoothing algorithm area, click Kernel functions. 6. In the Calculate and Display smoothed models area, click Calculate and Display. Notice how the Statistics view updates. The smoothed distribution is named Weighted-2Kernel#1. Create resources from smoothed distributions 7. In the Manage model(s) area: a. Select all three smoothed kernel models in the Select models box. b. Click Create as Resources. 8. Check that the three models are listed in the Resources browser. NOTE With the kernel functions algorithm, the resulting distribution (model) does not simultaneously honor the mean, variance, and important quantiles of the sample data.

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Create a 2D trend map from well data 1. In the Navigation panel, under POROSITY select 2D Trend Maps and specify that you will calculate trend maps using well data. 2. Choose DSI as interpolation method. 3. Under Create map, select One map per unit and click Create. 4. Apply what you have learned to show the map in UNIT A. Edit trend map by digitizing isovalue lines 5. Under Edit Map, type in 0.1 in the Isovalue box and click Draw an open isovalue line. Tip: Rest the pointer over a button to make a tool tip appear. 6. In the 3D Viewer, digitize lines as indicated in figure B-Edited trend map in UNIT A. 7. Repeat step 5 and step 6 as necessary to practice editing your map. NOTE Indicated isovalues are unitless.

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SGS with simple kriging Simple kriging This method assumes that the property is stationary and that its mean is constant throughout the domain. Beyond the range of correlation, the estimated value will be equal to the mean of the property. Other special forms of kriging exist to take into account secondary information such as: • The soft constraints provided by the data points interpreted from seismic • More complex trends NOTE See the Online Help for a more detailed description of the other forms of kriging.

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Transition between regions The Transition Between Regions panel is available only if you chose to perform the simulation By Regions. NOTE When no transition zone is defined, the random paths used for SGS will be separate for each region (i.e. there will be 1 random path within region 1, and another one in region2). When a transition zone is defined between these two regions, then the random path for SGS will cover both these regions. Both regions will be calculated simultaneously.

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Top unit Marine deltaic system in the top unit consisting of distributary channels with a main trend oriented WSW/ENE. More specifically delta front deposits with little tidal influence have been identified in SW and West parts of the area. Bottom unit Terrestrial system in the base unit consisting of braided streams with a SSW/NNE orientation.

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Define the conditioning data and simulation domains 1. Use what you have learned in previous sections to define the conditioning data and simulation domains for porosity with the information provided in Table A. Define filling parameters for Sand region 2. Use what you have learned in previous sections to define the filling parameters for ShalySand with the information provided in Table B. No secondary data is used. Define filling parameters for Shale and ShalySand regions 3. In the Navigation panel, under POROSITY, drag ShalySand to Sand, then drag Sand to Shale to copy the parameters defined for the Sand region to the other regions. 4. Click Sand and make the following changes: a. Select Weighted-2(POROSITY, Sand)::Kernel#1 as the external histogram. b. Select Poro_Sand as the variogram. 5. Click Shale and make the following changes: a. Select Weighted-2(POROSITY,Shale)::Kernel#1 as the external histogram. b. Select Poro_Shale as the variogram. Tip: Check in the Navigation panel, Value column that all the parameters you selected or entered are correct.

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Check the parameters 1. Access the Check POROSITY Parameters panel and verify that all required parameters have been entered. A message in green should appear, indicating that all parameters required for POROSITY simulation have been specified. Tip You can make changes in the Navigation panel as necessary by clicking the task. Run the simulation and view the results 2. Access the Simulation Control Panel and for the POROSITY row, click Process to run the simulation. Again, as the simulation runs, the status bar at the bottom of the software window displays the progress. 3. After the simulation finishes running, click Show to visualize the result in the 3D Viewer. The command displays the reservoir grid and the simulation result (the POROSITY1 property). 4. Compare the results for UNITA and UNITB. What can you observe? Discuss the results with your instructor.

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NOTE Bivariate analysis is also required as permeability is usually correlated with porosity and models of permeability must also account for any relationship with porosity. Usually, the logarithm of permeability is used because of the approximately lognormal character of many permeability histograms. Based on this advanced analysis, alternative scenarios of models can be considered and compared in order to determine which modeling method would best fit your data and context.

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Create a new Data and Trend Analysis Workflow and define the new properties 1. Create a new Data and Trend Analysis Workflow named K_Core_Analysis. 2. Create new properties and select input data as indicated in the table above.

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Calculate raw and weighted statistics for permeability data 1. In the Calculate Proportions (Litho_Core) panel, calculate and display the raw statistics everywhere in the grid for Litho_Core. Notice that there is no value for Shale. 2. In the Calculate Statistics (K_Core) panel, calculate and display the raw statistics everywhere, then use the Edit Plot Layout dialog box to display the statistics: a. Per grid unit b. Per (Sand and ShalySand) region 3. Calculate the declustered statistics for Sand and ShalySand assuming that the high permeability values are oversampled. Your display should look similar to the figure above.

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Establish representative statistics by smoothing distribution 1. Access the Fit and Smooth Histograms panel. 2. Using what you have learned, calculate and display a smoothed model for permeability using the following parameters : • Data: Weighted-1 data • Smoothing algorithm: Kernel functions 3. Analyze the data and compare the statistical variations between the model (Weighted-1-Kernel#1) and experimental data (Weighted-1). Remember that using a kernel function algorithm does not always honor the values of your data. If the proposed model does not honor the values that you wanted, you can edit the model to better match the displayed histogram. Edit the smoothed model 4. In the Statistics view, right-click the histogram and select Statistic Style Editor. 5. Select the Display category, then type 20 in the Number of bins box and press ENTER. Notice how the display updates. 6. In the Fit and Smooth Histograms (K_Core) panel, under Edit models, click Edit. 7. In the Statistics view, click the histogram model where you want to edit and drag the curve to the new value. Notice that when you edit the model, the workflow updates its values in the Summary Statistics table. During editing, the curve automatically adjusts to guarantee that the area under the curve is equal to one. Create a resource object from the smoothed distribution in ShalySand 8. Apply what you have learned to create new resource objects from the smoothed distributions in Sand and ShalySand.

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Display the porosity and permeability data in a crossplot 1. In the Application toolbar click Show Cross Plot to open the Multivariate Statistics window. 2. Display a crossplot of porosity versus permeability on core data by doing the following: a. In the Object box, select Core_Data. b. In the X-Axis property area, select PORO_CORE in the Property box. c. In the Scale function box, select normal_score. d. In the Y-Axis property area, select K_CORE in the Property box. e. In the Scale function box, select normal_score. f. In the Color property area, select LITHO_CORE in the Property box. Visualize the results for Sand 3. Select the Region check box, then select Sand. 4. Note the bivariate distribution and record the correlation coefficient. Visualize the results for ShalySand 5. Repeat step 3 and step 4 to record correlation coefficient of PORO_Core and K_Core in ShalySand facies.

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Cloud transform The cloud transform allows the conversion of one property (porosity) to another property (permeability) via a calibration scatterplot. A scatterplot is a 2D crossplot between an independent variable X and a dependent variable Y. It is presented as an ascii file of data pairs with no headers: for a given X, several Y values. It provides the correlation between the input data and the dependent property. The key element is that for a given input property value, there are several possible outcomes (converted property values). The output property value is obtained through sampling a number of possible values (instead of a one-to-one conversion). This approach: • Preserves the uncertainty in the relationship between the two types of data. • Allows to reproduce nonlinear relationships between two properties. Figure Step #A: The number of bins depends on the dispersion of the data. Usually 10 or more bins are differentiated. Three options to bin the input property: number of bins, number of data points per bin, and discrete independent variable (when input data is a discrete property). Figure Step #B: For each bin, a CDF is constructed using the data pairs from the scatterplot.

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Figure Step #3: At each cell the input grid property value (number 1 in Figure Step #C) is used to determine which CDF to sample (number 2 in Figure Step #C) and the simulated p-field value (probability number generated for that cell ) (number 3 in Figure Step #C) is used to draw the transformed property (Permeability) value from the selected CDF (number 4 in Figure Step #C). • The p-field can be generated by conditional or unconditional SGS. Either way you must provide a variogram model. Usually, the variogram is derived from the input property. • The p-field will have values uniformly distributed between 0 and 1. • The p-field advantage is that it honors the variogram, so the drawn values will be continuous. There are a number of numerical methods that are suited to fast simulation of uncorrelated spatial fields. Process The permeability value at a location can be drawn by Monte-Carlo (p-field) simulation from the conditional distribution of permeability given the porosity at that location. A series of conditional distributions are constructed. In general, 10 or more conditional distributions are used. The histogram of permeability and the full scatter between porosity and permeability is reproduced with this approach.

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Modeling permeability in the sand region • The bivariate distribution shown in the normal score porosity and permeability crossplot does not appear to have the elliptical probability contours required of Gaussian techniques because they are not bivariate Gaussian. • The Cloud Transform method preserves the uncertainty in the relationships between the two types of data: for a given input property value, the output property value (converted value) is obtained through sampling a number of possible values (instead of a one-to-one conversion). The ‘possible values’ of the output property for any given input value are provided by an ascii file (scattergram or 2D Cross-plot). • The p-field generated by SGS also ensures continuity and geological trend in the transformed property values between neighboring cells.

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Modeling permeability in the shaly sand region The SGS with collocated cokriging method uses a secondary property in addition to the original data to estimate the primary property at unsampled locations. A correlation coefficient between the primary and secondary properties must be specified. The porosity is treated as a covariable, i.e. a variable that has a statistical relationship with permeability. A correlation coefficient is calculated by crossplotting core data. NOTES • The permeability variability usually follows the porosity variability. • The term kriging is traditionally reserved for linear regression using data with the same attribute as the one being estimated. For example, an unsampled porosity value is estimated from neighboring porosity sample values defined on the same volume support. • The term cokriging is reserved for linear regression that also uses data defined on different attributes. For example, the porosity value may be estimated from a combination of porosity samples and related accoustic impedance values.

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Define general workflow parameters for PERMEABILITY property Apply what you have learned to: 1. Add a new PERMEABILITY property in the current Reservoir Properties workflow. 2. Specify that no conditioning data will be used. 3. Select each facies as a simulation domain. Define filling parameters for PERMEABILITY in the Shale region 4. Apply what you have learned to specify that you will use a constant value equal to 0.001 for Shale region as Shale lithology acts as flow barriers. Define filling parameters for PERMEABILITY in ShalySand region 5. Apply what you have learned to select the parameters you will use to model PERMEABILITY in the ShalySand region as indicated below: a. Filling method: Simulation > SGS > Collocated coKriging b. External histogram :Weighted-1 (K_Core,ShalySand) Edited Kernel#1 1 c. Variogram: PERM_ShalySand d. Collocated property: POROSITY1 e. Domain for normal score transformation: ShalySand only. f. Correlation Coefficient: 0.6 g. Markov approximation: MM1

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Define filling parameters for PERMEABILITY in Sand region Apply what you have learned to select the parameters you will use to model PERMEABILITY in the Sand region as indicated below: 1. Filling method: Simulation > Cloud Transform 2. P-field: generate 3. Variogram: PERM_Sand 4. Define the secondary data as described below: a. Collocated property: POROSITY1 b. Binning option: NumberOfBins c. Number of bins:7 d. Cloud computation method: Cloud from Well Data so the software calculates the CDF for each bin from the core data. e. Object: Core_Data f. Region: Sand g. Secondary Property: PORO_CORE h. Primary Property: K_CORE

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Check the parameters 1. Access the Check PERMEABILITY Parameters panel and verify that all required parameters have been entered. A message in green should appear, indicating all parameters required for PERMEABILITY simulation have been specified. NOTE You can also review the parameters in the Navigation panel and make changes as necessary by clicking the task. Run the simulation and view the results 2. Access the Simulation Control Panel and for the PERMEABILITY row, click Process to run the simulation. Again, as the simulation runs, the status bar at the bottom of the software window displays the progress. 3. After the simulation finishes running, click Show to visualize the result in the 3D Viewer. The command displays the reservoir grid and the simulation result (the PERMEABILITY1 property). 4. Compare the results for UNITA and UNITB. What do you observe? Discuss the results with your instructor.

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Create a crossplot for bivariate analysis purposes 1. In the K_Core_Analysis workflow, access the Bivariate Analysis (K_Core) panel and click Yes, with another primary property. NOTE You may have to click Next from where you last were to activate the panel. 2. Select Raw and Poro_Core in the Data and Secondary property boxes respectively. 3. Click Calculate and Display. 4. Edit plot layout to show statistics in Sand and ShalySand facies only. Fit regression curve to data and save trend lines as resources 5. Under Calculate regression curve: a. Click Parametric curve and select Power as the curve type. b. Click Create. 6. Change curve type to Polynomial of 3rd degree and click Create again. 7. Under Smooth and manage regression curve(s): a. Select Raw(K_Core.Poro_Core,@[email protected])::Fitted Power in the Model box. b. Click Create as Resource. 8. Repeat step 7 to create a resource for Raw(K_Core.Poro_Core,@[email protected])::Fitted Power. Save residual histograms as resources 9. In the Statistics view, right-click the residuals histogram for the Power model and select Create All Related Residuals as Resources.

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Propagate permeability residuals into your model Apply what you have learned to: 1. Define a new Residuals_Perm continuous property in the current RP_Training workflow. 2. Define conditioning data and simulation domains as indicated in Table A. 3. Define filling methods and parameter as indicated in Table B. 4. Create a new realization for Residuals_Perm. NOTE A new variogram should be computed with the residuals data. However, for training purposes existing permeability variograms are used here.

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Apply permeability regression curve to porosity model In this exercise you apply the trend, by regions, to the simulated property POROSITY1. 1. In the Resources browser, under Bivariate Analysis right-click Raw(K_Core.Poro_Core,@[email protected]) Fitted Power and select Apply on Property. 2. In the Create a Property by Transforming Another Property dialog box: a. Type in Trend_permeability in the Property name box. b. Select DTA_PM_Field and POROSITY1 in the Object and Property to transform boxes respectively. c. Select the Region check box and select Sand. d. Ensure that Raw(K_Core.Poro_Core,@[email protected]) Fitted Power is selected in the Regression curve box. e. Click Apply. 3. Repeat step 2 with ShalySand as the region and Raw(K_Core.Poro_Core,@[email protected]) Fitted Power as the regression curve. 4. Close the dialog box. At this stage you have created a new permeability property in the grid using the trend applied to the porosity property POROSITY 1. The property is defined in the region Sand and ShalySand. In the region Shale there is only No Data Value (NDV) for the moment. You set the NDV to 0.001 in the following task, and add the residuals to the results.

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Combine permeability trend and permeability residuals into a new permeability model 1. In the Objects browser, under DTA_PM_Field, right-click properties and select Apply script. 2. In the Properties Script Editor: a. Make sure DTA_PM_Field is selected in the Objects box and that the Check no-data values automatically check box is selected. b. Type in the script as indicated in the figure above. c. Click Define Variables4 and specify the property settings of Permeability (category and type) as appropriate. d. Check script and click OK to apply it.

This script enables you to add the residuals to the results, set the values of Permeability to 0.001 in the region Shale (this is where No Data Value NDV have been defined), and clip the values to zero.

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Compare the two permeability models  Compare PERMEABILITY1 and Permeability properties in your reservoir grid. NOTE Make sure you have set the property type of PERMEABILITY1 to Reservoir > Permeability before comparing the two properties.

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Why is it recommended to apply a filter when blocking porosity data? • To avoid under/over-estimating statistics during the linear averaging process • Average only high porosity value in good-porosity lithology, and vice-versa
What is the purpose of smoothing a histogram? • Remove unrealistic spikes and holes to output a distribution representative of the underlying geological phenomenon
Why is it recommended to complete a bivariate analysis? • To quantify relationships between two variables • To identify and remove trends, and compute property residuals
What are the most significant advantages of Gaussian techniques? • The simplest way to honor local data, external histogram, variogram • Different mapping (kriging) methods allow considering different secondary data

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Overview In this chapter, you will learn how to compute reservoir volumes based on the simulated properties of interest, your understanding of geology, and your knowledge of the reservoir. You will also learn about the post-processing functionality so you can compute parameters of significant interest for decision-making purposes.

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You can easily run a calculation, update parameters, and then re-compute at any time to see how the volumes have been updated. All the requested volumes are computed on the fly for each of the specified regions and in the desired units.

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Define the input parameters and specify the volumes to compute 1. On the Application toolbar, click Compute Reservoir Volumes to open the window. 2. In the Reservoir grid box, make sure DTA_PM_Field is selected. 3. On the Parameters tab, do the following to define the Net/Gross property: a. Select the Define check box for Net/Gross. b. In the Constant column, click the radio button, then type 0.7 and press ENTER. 4. Do the following to define the Porosity property: a. Click the Define check box for Porosity. b. In the Variable column, click the option button and select POROSITY1. 5. Define the Swater property (water saturation) using a constant value of 0.2 as you did in step 3. 6. In the top area of the tab: a. Select the Net and Pore check boxes in the Rock row to calculate the net rock volume and net porous volume for each fluid zone. b. Select the Oil check box in the Reservoir In Place row to calculate the OIP volume in reservoir conditions. Define the regions of computation and fluid phases 7. Select the Define zones tab and do the following: a. In the Region box, select Sand, ShalySand, UNITA and UNITB. b. Under Phase contacts select the Oil and Water check boxes, then click Surface in the Oil/Water Contact row and select OWC. NOTE If you cannot see OWC in the list it means that it has not been assigned to a feature. Use the Assign Data to Geologic Features dialog box, accessible from the Objects or Unassigned Objects browser to define the surface as Oil-Water Contact.

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Compute volumes and save the results as a text file 1. Click Compute at the bottom of the window to compute the volumes and display the results in the Compute area. 2. Click Save as Text, then in the Save as dialog box keep the default name and click Save. NOTE In this course you keep the default settings on the Reporting tab.

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Creating and post-processing multiple realizations Post-processing steps are optional but in order to validate models and optimize production strategies it is recommended to: • Compute relevant summary statistics • Identify which cells within a specific region are connected • Compute the probability that cell values are less than or equal to a specified threshold • Calculate the probability that cell values are within specified threshold interval ranges

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Nesting simulations A nesting column is available for use only if the user has a Reservoir Risk Assessment license. However, the Reservoir Risk Assessment module doesn’t need to be loaded. In cases where two properties are to be simulated: • If the Reservoir Risk Assessment module is available, then the two properties can be nested, meaning that they can be simulated one after the other in one go. All will use a different random path and yield different results. • If the Reservoir Risk Assessment module is not available, you cannot launch nested simulations, and you must perform each property simulation separately.

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Post-processing • Summary statistics are allowed for simulated properties or any scalar properties. Postprocessing operations are not allowed on vectorial properties. • When you perform the computation, the result is stored in a new grid property with the specified name. Default names can be changed as necessary.

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Post-processing: Summary statistics • The Compute Most Frequent Occurrence option compares the input realizations and calculates which categorical value occurs most frequently in each cell. If there is a tie between two or more categories for the most frequent occurrence, the category with the lowest value prevails. For example, if you had selected six realizations of Facies as input and there were three Shale (value 0) and three Sand (value 1), the result would be Shale. • The Compute Proportions option computes the proportions of the input realizations in each cell. Unlike the other computations, the result is a vectorial, rather than scalar, property. For example, assuming five realizations of LITHOLOGY, if Shale occurred in one cell four times and Sand occurred once (0 0 0 0 1), the proportion would be 80 percent Shale and 20 percent Sand. This result would be expressed as 0.8, 0.2. The first element of the vector is displayed. In this case, the cell would be drawn as 80 percent Shale.

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Post-processing: connectivity analysis • The purpose of the Define regions from property range panel is to define a region inside the grid containing only the cells belonging to a certain range of a property. • The purpose of the Connectivity computation panel is to look at the connectivity of the cells within the selected region. You process after choosing the required regions and your type of connectivity (type of connection for the workflow to use to compute the geobodies). Enter the name of the new property in the Geobody volume box. This property will be used to store the total volume of the cells belonging to a same geobody. Connectivity type: • Faces: Two adjacent cells are considered to be connected if they share a common cell face. • Edges: Two adjacent cells are considered to be connected if they share a common edge (grid line). • Nodes: Two adjacent cells are considered to be connected if they share a common node (cell corner point). If you want to save the geobody volume: Select the Save geobody volume check box.

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Generate multiple realizations of the lithology model 1. Open the RP_Training Reservoir Properties workflow and access the Simulation Control Panel. 2. In the Number of Realizations column, type 5 in the LITHOLOGY row and press ENTER. 3. Run the five concurrent simulations. This may take a few minutes. 4. In the Objects browser, expand Geological Models and expand DTA_PM_Field. Notice that there are five properties named LITHOLOGYx where x is the realization number. These multiple realizations represent equally probable results, and the results are all in accordance with the variogram and the well data analyzed using the Data and Trend Analysis Workflow and selected as input.

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Select post-processing operations 1. In the Navigation panel, click Post Processing. 2. In the Post Processing of Multiple Realizations panel, select the following check boxes: a. Summary Statistics b. Connectivity Analysis 3. Click Next. Select the input realizations 4. In the Summary Statistics – Input Realization panel: a. In the Reservoir Grid or Voxet box, select DTA_PM_Field. This is the grid that contains the simulated properties. b. Keep everywhere selected in the Region box. c. Select Categorical. d. Select the five lithology realizations in the table (LITHOLOGY1 to LITHOLOGY5 included). 5. Click Next. Define and calculate the summary statistics 6. In the Summary Statistics panel: a. Select the Compute Most Frequent Occurrence check box and keep the default property name: most_frequent_occurence. b. Select the Compute Probabilities check box and keep the default property name: probabilities. c. Click Process to perform the calculations. You can see the results in the 3D Viewer by selecting each property in the Objects browser. 7. Click Next twice.

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Define region for connectivity analysis from property range 1. In the Define regions from property range panel, do the following to define the property you will use to create your region: a. Make sure DTA_PM_Field and POROSITY1 are selected in the Reservoir Grid or Voxet and Input Property boxes, respectively. b. Enter 0.2 and 0.3 as the minimum and maximum values. c. Keep all other default settings. d. Click Process to perform the calculations. Three new regions POROSITY1_between0_2And0_3, POROSITY1_GreaterThen0_3 and POROSITY1lessThan0 are created and are listed in the table below. 2. Click Next. Compute connectivity 3. In the Connectivity computation panel, select POROSITY1_between0_2And0_3 in the Region for connectivity computation box. 4. In the Geobody rank property box, leave the default name selected. 5. Leave the Save geobody volume check box cleared. 6. In the Connectivity type area, leave Faces selected. 7. Click Process to perform the calculations. Next you visualize the connectivity of the cells within the selected region.

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Visualize the connectivity 1. In the 3D Viewer, show: a. The grid b. The POROSITY1_between0_2And0_3 region and region volume c. The geobody_rank property 2. Change the display style of the property by doing the following: a. Change colormap to rainbow1. b. Set High Clip to 11 and make high clip transparent. 3. Discuss your results with your instructor. 4. Save your project.

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