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GeoFrame 4.0ELANPlus Theory

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1999 Schlumberger Schlumberger Austin Systems Center 8311 North FM 620 Road Austin, Texas 78726 U.S.A. All rights reserved. No part of this manual may be reproduced, stored in a retrieval system, or translated in any form or by any means, electronic or mechanical, including photocopying and recording, without the prior written permission of Schlumberger. Use of this product is governed by the License Agreement. Schlumberger makes no warranties, express, implied, or statutory, with respect to the product described herein and disclaims without limitation any warranties of merchantability or tness for a particular purpose.

Version and Program HistoryVersion 4.0 3.7 3.6 3.5 3.2 3.1 3.0 2.0 1.0 Date May 2001 July 1999 April 1999 July 1998 August 1997 March 1994 June 1993 July 1992 March 1991 Comment Updated for GeoFrame 4.0 Update for GeoFrame 3.7 Update for GeoFrame 3.6 Update for GeoFrame 3.5 Add APS Interpretation Upgrades for GF1.1 standards Commercial Beta First Version

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How to Use On-Line HelpThe Help menu on the right side of the title bar of major windows offers options such as Table of Contents, Index, On Context, Version, and Help, which activate hypertext links to the relevant pages of this document. If you click on the On Context button, the cursor becomes a question mark. Move the question mark to the item for which you want help and click the mouse button. The User Guide will open to the relevant page.

About This DocumentThis document contains the information you need to know to run this program. It is designed to be used both as a hardcopy document and to be accessed online by means of Hypertext. Click on any item in the table of contents to jump directly to the page on which that topic begins. Mouse Buttons These conventions are used to indicate which mouse button to click: MB1 Left mouse button MB2 Center mouse button MB3 Right mouse button If you are told to click on something, and you are not told which mouse button, use MB1. Hypertext Links In the users guide Contents, you can click on any heading to jump to that page. After you have jumped to a referenceeven if you have paged forward or backward after jumpingyou can return to the original jump point by pressing the GoBack button. Throughout this users guide, there are references to other sections in this guide and to other GeoFrame documents. These references are also active Hypertext links. When you click on a phrase that appears in blue, underlined Italic type, you jump to the section or document represented by that phrase. To jump to the beginning of the table of contents at any time click on the ToC ToC button.

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In addition, all items in the table of contents (though they are in black, not blue, type) are hyperlinked. Click on any TOC item to jump directly to the section of the document it represents. The Index button is not connected at this time. The Q (Quit) button closes the User Guide and quits FrameViewer (program used to view the Guide).

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Printing This GuideTo print this users guide from FrameMaker or FrameViewer on a PostScriptcompatible printer, you must have the proper Adobe PostScript printer drivers installed for your printer. 1 With the cursor anywhere in the document, press MB3 to display the MAKER or VIEWER menu, and select the Print option. The FrameMaker Print Document window appears. 2 Under the Print Page Range heading, verify that the All option is selected. 3 In the Printer Name eld, select the name of your printer. 4 Make sure that the Print Only to File button is not selected. 5 Click on the OK button to print the document. You may want to use the UNIX lpq command to check the printing status. See your system administrator or on-line man pages for information about this command.

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ContentsVersion and Program History How to Use On-Line Help About This Document Mouse Buttons Hypertext Links Printing This Guide

Chapter 1

ELANPlus Program Theory ..............................................................1The Purpose of the ELANPlus Application ..................................................1 Conventions ...................................................................................................3 Equations and Tools ................................................................................3 Formation Components, Volumes ...........................................................3 Matrices ...................................................................................................4 Mnemonics ..............................................................................................4 Model, Interpretation Model ...................................................................4 Summation Expressions ..........................................................................5 Units ........................................................................................................6 Vectors .....................................................................................................6 xxxx .........................................................................................................6 Assumptions of the ELANPlus Application .................................................6 Borehole Pressure ...................................................................................7 Bound Water.............................................................................................7 Curve EditingDepth Correction, Depth Matching, Despiking, Patching....................................................................................................7 Environmental Corrections ......................................................................7 Flushed-Zone and Undisturbed-Zone Relationships................................7 Lateral Continuity ....................................................................................8 Neutron Porosity ......................................................................................8 Qv_effective ............................................................................................8 Summation of Fluids ................................................................................8 Summation of Volumes ............................................................................8 Vertical Continuity ...................................................................................8

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Chapter 2

Interpretation Models ..........................................................................9Formation Components ...............................................................................10 Response Equations ....................................................................................10 A Simple Response Equation Example ................................................11 Invasion Model ......................................................................................11 The Overdetermined Solution ...............................................................13 Parameters ...................................................................................................16 Global and Program Control Parameters ..............................................16 Binding Parameters ...............................................................................18 Response Parameters .............................................................................20 Salinity Parameters ................................................................................24 Temperature Correction of Parameter Values .......................................30 Parameter Calculator .............................................................................31 Constraints ..................................................................................................31 Building an ELANPlus Model ....................................................................34 Step 1 Select Formation Components ...................................................35 Step 2 Select Response Equations ........................................................35 Step 3 Rationalize Formation Components and Response Equations................................................................................................35 Step 4 Choose Constraints ...................................................................37 Step 5 Label the Model ........................................................................38 Step 6 Choose Model Combination Method ........................................38 Step 7 Create Functions ........................................................................39 Step 8 Set Parameter Values..................................................................39 Step 9 Save Your Work ........................................................................40

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Chapter 3

Response Equations ............................................................................41Wet and Dry Clay ........................................................................................41 Density Response Equation ..................................................................42 General Response Equation ..................................................................44 Gamma Ray (GR) Response Parameters ....................................................45 SP Response Parameters .............................................................................47 Sonic Response Parameters .........................................................................51 Slowness ................................................................................................51 Velocity .................................................................................................52 Neutron Response Parameters .....................................................................56 Linear NPHI ..........................................................................................57

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Nonlinear Neutron Response Parameters ..............................................61 Recommendations for Using Neutron Data in ELANPlus Processing ...........................................................................66 Recommendations for APS Interpretation ............................................67 Constant Tools .............................................................................................69 Parameter Tables .........................................................................................71

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Chapter 4

Conductivity Models ...........................................................................75No Rxo Tool ................................................................................................78 Oil and Gas Model with Rxo ......................................................................79 Oil and Gas Model without Rxo .................................................................80 Water Saturation, Linear Conductivity ........................................................80 Conductivity Input, Hierarchy ....................................................................83 For Global Parameter Clay = Wet .........................................................84 For Global Parameter Clay = Dry ..........................................................84 Beware of CUDC_clai ............................................................................84 Conductivity Equations ...............................................................................85 Waxman-Smits Equation .......................................................................85 Dual-Water Equation .............................................................................89 Linear Conductivity Equation ...............................................................92 Indonesian and Nigerian Conductivity Equations .................................95 Simandoux Conductivity Equation .......................................................96

Chapter 5

Uncertainties ........................................................................................103The ELANPlus Solution Method ..............................................................103 Balanced Uncertainties .............................................................................104 Conductivity, SP ........................................................................................106 Weight Multipliers ....................................................................................106 Default Uncertainties ................................................................................107 Uncertainty Tables ....................................................................................108 Carbonate-Clay Example ..........................................................................111

Chapter 6

Constraints ...........................................................................................113Internal Constraints ...................................................................................113 Predened Inequality Constraints .............................................................114 Maximum Porosity Constraint ............................................................115 Irreducible Water Constraint ...............................................................115

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Sonic Clay Volume Constraint ............................................................116 Conductivity Constraint for Water-Based Mud (Sxo Sw) ..................119 Conductivity Constraint for Oil-Based Mud (Sxo Sw) ....................123 Sxo Constraint for Water-Based Mud (Sxo Sw) ................................123 Sxo Constraint for Oil-Based Mud (Sxo Sw) ..................................124 User-Dened Constraints ..........................................................................124

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Chapter 7

Model Combination ..........................................................................125Methods for Generating Combined Answer Sets .....................................125 Individual Models .....................................................................................127 Model Probabilities ...................................................................................127 External Probabilities ...........................................................................127 Internal Probabilities ............................................................................128 Bad Hole Probability............................................................................129 Final Model Combination, Using Probabilities ..................................130

Chapter 8

Quality Control ...................................................................................135Quality Control of the Model ....................................................................135 Examples of Bad Hole Models .................................................................138 Quality Control of the Results ..................................................................139 Reconstructed Logs Can Identify Model Problems ............................140 Poor Reconstruction Means There Is a Problem .................................140 A Good Reconstruction Can Go With a Wrong Answer .....................140 Use Predicted Value to Check for Inconsistencies...............................140 Summary ..............................................................................................141

Appendix-1

....................................................................................................................142 Simandoux Equation (A historical perspective)...................................142

Glossary .................................................................................................149

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Chapter 1

ELANPlus Program TheoryThis document presents theoretical concepts of the ELANPlus petrophysical interpretation program. Although the new user may wish to read this document in its entirety, it has been designed to be accessed in small, self-contained, single-topic segments, as well. As much as the ELANPlus Users Guide. This document often refers to ELANPlus editors such as the Global Parameter editor and Process Editor that are part of the human interface. Information on the editors is also found in the ELANPlus Users Guide. You can run the ELANPlus application and produce resultseven meaningful resultswithout the information presented in this document. However, until you understand the underlying concepts, theory, and assumptions of the ELANPlus program, it will remain a mysterious black box. If you do not understand the theory behind it, the ELANPlus program will sometimes appear to produce inconsistent, irreproducible, illogical results. Fine-tuning parameter values will remain a frustrating hit-or-miss proposition. With a rm theoretical understanding, though, you can make educated choices of model components and parameter values that will quickly converge to a high quality result.

The Purpose of the ELANPlus ApplicationThe ELANPlus computer program is designed for quantitative formation evaluation of cased and open-hole log level by level. Evaluation is done by

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optimizing simultaneous equations described by one or more interpretation models. Singe-well ELANPlus can be run anytime after preliminary data editing (such as patching, depth matching, environmental correction) is complete. Most users think the purpose of the ELANPlus application is solving the socalled inverse problem, in which log measurements, or tools, and response parameters are used together in response equations to compute volumetric results for formation components. In reality, that aspect of the program is only one side of a three-way relationship among tools, response parameters, and formation component volumes. The relationship is often presented in a triangular diagram, as in Figure 1.

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tt = Rv

v

RFigure 1 Petrophysical model used by the ELANPlus application.

In Figure 1, the t represents the tool vectorall logging instrument data and synthetic curves. The v is the volume vector, the volumes of formation components. R is the response matrix, containing the parameter values for what each tool would read, given 100% of each formation component. Given the data represented by any two corners of the triangle, the ELANPlus program can determine the third. In the inverse problem, t and R are used to compute v. As stated before, solution of the inverse problem is often considered the main job of the ELANPlus program. The forward problem, also known as log reconstruction, uses R and v to compute t. A log reconstruction problem is computed for each inverse problem, or Solve process. The reconstructed logs are compared against input data to determine the quality of volumetric results from the inverse problem. Using t and v to compute R is called the calibration problem. Here the question is, What response parameter value(s) should I use to obtain the best t between the observed logging instrument readings and some believed formation component volumes (often core results)? A method for solving the cal-

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ibration problem has not been implemented in version 2.x of ELANPlus. The problem will be solvable in Version 3.0. Note that the inverse problem solves for formation component volumes only. Other traditional log interpretation program results (such as water saturation, matrix grain density, and so on) are provided by the Function process. That approach allows the program user to control the denitions of the additional output types rather than having the denitions hard-coded in the program. Chapters 28 explain ELANPlus interpretation model concepts and tell how individual models can be combined for wide ranges of formation types, how the program produces its results, and how to check the quality of results.

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ConventionsTo fully understand the concepts behind the ELANPlus model, you must be aware of the conventions used in this document. If reading this section for the rst time, please read it completely. Though some terms may also be in the glossary, most of the material presented here will not be repeated. Equations and Tools Equation and tool will be synonymous in most cases. The more technically correct term is equations, or better, response equations. The term tool comes from the fact that most response equations obtain their input data from logging tools and often use the same mnemonic as the tool data. Also, the response equations and their associated data are used as tools to produce the desired results. Finally, the term tool has historical roots in the program. Generally, equation or response equation will be used when the intent is to focus attention on the structure of the equation. Tool will be used more conceptually in discussing interpretation models. Formation Components, Volumes When setting up an interpretation model, you must tell the ELANPlus program which minerals, rocks, and uids are likely to be present in the formation. These minerals, rocks, and uids are the formation components. Often the primary job of the ELANPlus program is to determine the relative quantities or volumes of the formation components that would most likely produce the set of measurements recorded by the logging instruments. Therefore, the terms volumes and formation components, or just components, are often used interchangeably.

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Usually components will be used in discussing interpretation models, where the constituent, but not the quantity thereof, is of prime importance. Volumes tends to be used in discussion of equations and output curves, where quantity carries more importance. Matrices Matrices are represented by upper case, bold characters, such as R. Mnemonics The mnemonics in this document will be those of the GeoFrame Interpretation Workstation. They are used (primarily in equations) to show how the theoretical concepts are related to the working program. Mnemonics will be explained when rst used. Model, Interpretation Model A model is a way to present information to the ELANPlus program to describe the problem to be solved. A model consists of a set of tools, or equations, a set of formation components, or volumes, and a set of constraints. Implicitly there are associated curves, response parameters, and other global and model-specific parameters. Abstractly, a model describes program input data and the solution space over which the ELANPlus optimizer can operate (the allowable results). The equations describe the logging data and supplementary response equations that are available. The formation components describe the minerals, rocks, and uids likely to be encountered in appreciable quantity and provide the geological description of the types of formations to which the model applies. The constraints let you set upper and lower limits on the output volumes. They are often used to establish a relationship between one formation component and another (or others). Constraints are a way of supplying the program with local knowledge. Often the term model is used interchangeably with Solve process, because a different Solve process is usually set up for each general set of equations, formation components, and constraints. Often, each model is given a name, such as Sand-Shale model, Carbonate model, Cotton Valley model, XYZ E&P Reservoir model. The results from each specic model are combined through the Combine process to produce a final answer for the entire borehole interval being evaluated.

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Summation Expressions Many concepts are best described mathematically and involve a summation. To avoid dening all summation elements and indices after each equation the most common ones are described once here. The summation indices are used in a unique way in this document. Assume a model which, among other formation components, includes the clays illite, kaolinite, and chlorite. In the expression

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Vii=1even though the summation index, i, is shown to start at 1 and index to nc, the number of clays in a model (in this example, nc = 3), i does not take on the values 1, 2, 3. Instead, it takes on the values ILLI, KAOL, and CHLO. Similarly, Vi represents volume of illite, volume of kaolinite, and volume of chlorite in the expanded summation.nc

nc

The symbol nc represents the number of clays in a model, including all clays that have specic names (ILLI, MONT, etc.) as well as the generic clays (CLA1, CLA2).nf, nuf, nxf

The symbol nf represents the number of uids in a model and includes all types of uids (water, hydrocarbon, irreducible, etc.) in both the ushed and undisturbed zones. The symbol nuf applies to all uids, regardless of type, in the undisturbed zone only. The symbol nxf applies to all uids, regardless of type, in the ushed zone only.nfc

The symbol nfc represents the number of formation components in a model. Unless otherwise stated, nfc includes all solidsnonclay and clay alikeand all uids. However, note that since bound water (XBWA) is solved for as a dependent variable, nfc does not include it.ns

The symbol ns represents the number of solid formation components in a model, including both clays and nonclays unless otherwise stated.

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Vi, Vi, CEC_j, WCLP_i, RHOB_i

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The notations Vi, Vi, CEC_j, WCLP_i, RHOB_i, and others are used primarily in summation expressions, where the i ( j, k, ...) indicates the ith ( jth, kth, ...) element of the summation. It is also used to refer to any nonspecic member of a volume, parameter, or similar group. For example, in The range of any output volume, Vi, is between 0.0 and 1.0 (0 to 100 p.u.), Vi is used generically to refer to, say, volumes in a nearby formula. As stated in the Summation Expressions section, the i, j, k, ... is not replaced with an integer, but with a mnemonic, so that NPHI_i refers to NPHI_QUAR, NPHI_CALC, or whichever formation components exist in a model. Units Examples are sometimes used to elucidate a concept. Unfortunately, the use of any specic numerical value at once raises the issue of units. Unless otherwise stated, porosities and other volumes will be given in v/v (decimal porosity), not p.u. (porosity units). In other situations where the units are not supplied and are not obvious from context, assume English units. Vectors Vectors are represented by a lower case bold letter, such as v. xxxx Most equation and formation component mnemonics contain four characters. The string xxxx is used to indicate that you are to ll in appropriate mnemonics as required by context. For example, in Equation uncertainty parameters, xxxx_UNC, should be set such that ..., the xxxx should be lled in with RHOB, NPHI, DT, TPL, or whatever equations are being used in a model. Similarly, in a sentence like Cation exchange capacities for the clays are entered using the parameter CEC_xxxx, the xxxx should be replaced by the mnemonics for the clays (ILLI, MONT, etc.) being used in a model.

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Assumptions of the ELANPlus ApplicationMost formation evaluation programs impose some sort of interpretation modelassumptions about the depositional environment, clay properties, uid interactions in pore space, and so on. Although the ELANPlus application was designed to be free of such assumptions, it is virtually impossible to design a working computer program without some sort of assumptions

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some imposed by physics, some resulting from incomplete knowledge of all variables that affect the solution sought. The assumptions implicit in the ELANPlus program are related to borehole pressure, bound water, curve editing, environmental corrections, ushed-zone and undisturbed-zone relationships, lateral continuity, neutron porosity, Qv_effective, summation of uids, summation of volumes, and vertical continuity. Borehole Pressure Borehole pressure is used in the computation of certain salinity-dependent parameter values. Borehole pressure (in psi) is assumed to be 0.465 times depth, in feet. Bound Water Clays are composed of dry clay mineral and associated (bound) water. The ratio of bound water to dry clay is constant for each clay. Curve EditingDepth Correction, Depth Matching, Despiking, Patching All input data curves have been properly depth corrected and matched with each other and have been edited to repair spurious effects such as data spikes or gaps. Environmental Corrections All input data curves are environmentally corrected. That is, they have had the effects of the borehole contents and geometry removed. One notable exception is that the salinity correction for the nonlinear neutron should not be done, because the salinity correction can be done properly only when the volumetric constituents are known, that is, during minimization. Flushed-Zone and Undisturbed-Zone Relationships Solid formation components exist in equal number and volume in both ushed and undisturbed zones. If a model includes an undisturbed-zone uid, the same type of uid exists in the ushed zone, even though the volume of the uid might be zero in either or both zones. For example, if a model includes undisturbed-zone oil (UOIL), it must also contain ushed-zone oil (XOIL). The volume of porosity in the ushed and undisturbed zones is the same, regardless of the types of uids lling the pore space. Hydrocarbon density (gas/oil ratio) is the same in both zones.

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Lateral Continuity All solid formation components extend innitely from the borehole at zero degrees dip. Fluid formation components exist in one of two annular zonesthe ushed zone, near the borehole, or the undisturbed zone, farther away from the borehole. That allows for the concept of uid invasion but uses the simplifying assumption of a step invasion prole. All formation components are azimuthally homogeneous, that is, the number and volume of formation components at one azimuth is the same as at all other azimuths. Neutron Porosity All neutron porosities are given in limestone units. Qv_effective Qv_effective (QVSP_N) is internally multiplied by porosity before use. That this multiplication occurs is particularly important to know in the computation of the QVSP_UNC (uncertainty) parameter. Default uncertainty is based on the assumption of a 0.3 (30 p.u.) porosity. Summation of Fluids The sum of all uids in the ushed zone equals the sum of all uids in the undisturbed zone. This assumption is explicitly added as an equation along with the other tools whenever a model includes both ushed and undisturbedzone uids. The only user-settable parameter for the Summation of Fluids equation is the uncertainty, VOLS_UNC (as in the Summation of Volumes equation). Summation of Volumes The sum of all formation components must equal 1.0. This assumption is always added along with the other tools in a model. The only user-settable parameter for the Summation of Volumes equation is the uncertainty, VOLS_UNC (as in the Summation of Fluids equation). Vertical Continuity The solution of one data level is completely independent from the solution at adjacent data levels. There is no vertical continuity logic in the ELANPlus program. The nonlinear optimizer does use results from the preceding level as a starting point when it can, but the solution is still determined only by the program data at each level.

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Chapter 2

Interpretation ModelsAn ELANPlus interpretation model has four parts: formation components, response equations, parameters, and constraints. Formation components are the constituents for which volumetric results are desired. Response equations are the equations to be solved and their associated input data and uncertainties. Parameters are the global and program control parameters, response parameters, binding parameters, and salinity parameters. Constraints are the limits that the volumetric results must obey. Additionally, the ELANPlus application includes methods by which individual models can be mixed and spliced to provide a combined model for more complex environments and large borehole extents. Each individual model is specied in a separate Solve process. The nal result is (typically) produced by mixing the results from individual models (Solve processes) in a Combine process. The Combine process will be discussed later in this chapter and also in a separate chapter. The discussion that follows considers only a single model and a single Solve process, as all remarks on a single Solve process apply equally to multiple Solve processes.

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Formation ComponentsIn most cases, the primary answer sought from the ELANPlus application will be the volumes of certain formation components at each data level. Formation components exist in three groups: minerals, rocks, and uids. The user must specify the components for which the program is to solve, by selecting them in the Process Editor. Minerals are solids described by a chemical formula; for example, SiO 2, CaCO3, or CaSO4. Because of their well-dened structure, it is usually possible to supply default parameters for minerals. Rocks are considered to be user-dened combinations of minerals, such as silt, carbonate, and igneous rock. Rocks do not have default parameter values other than Absent. Fluids are pore-space-lling substances, including water, oil, gas, and other special uids. It is often possible to provide usable default values for uids, though some defaults are better than others. A neutron porosity of 1.0 is pretty safe for water, but the default 0.8 gm/cc density of ushed-zone oil could vary appreciably from well to well. The formation components selected to be in a model should be only those expected to be present in appreciable quantity. The number of components to be solved can never exceed the total number of equations in use.

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Response EquationsA response equation is a mathematical description of how a given measurement varies with respect to each formation component. The simplest linear response equations are of the form

nfcmeasurement =

Vi Ri

(1)

i=1where: Vi = volume of formation component i Ri = response parameter for formation component i Although some linear equations include additional terms, and the nonlinear equations are more complex, the overall concept is the same: the total measurement observed is determined by the volume of each formation component and how the tool reacts to that formation component.

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A Simple Response Equation ExampleThe easiest way to discuss response equations is with a simple example. Assume that a formation consists of only calcite and water and that a density log was recorded through the formation. You can easily solve for the volume of water by using the density response equation written for a single matrix component: measured density = fluid density + ( 1 ) matrix density where: = the volume of water-lled porosity. Assume, also, that at some depth of interest the density log read 2.368 g/cm3. Using a density of 2.71 g/cm3 for calcite and a density of 1.0 g/cm3 for water, and substituting those values into Equation (2) yields 2.368 = 1.0 + ( 1 ) 2.71 (3) (2)

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Rearranging and solving for yields = 0.20 and, consequently, the volume of calcite (CALC) is 0.80. Something so obvious that it is frequently not stated is that Equations (2) and (3) assume that the volume of calcite is given by CALC = 1 (4)

The signicance of Equation (4) is that it points out an assumption implicit in all ELANPlus models: at every depth level, the sum of the volumes of all formation components present in a model must be 1.0. Expressed in ELANPlus terms, that is

nfc 1 =

Vi

(5)

i=1Equation (5) is always added to all the other response equations in a model before the set of equations is passed to the ELANPlus optimizer.

Invasion ModelAlso implicit in the ELANPlus solution method is the assumption of a step invasion prole consisting of a ushed zone, the X zone, and an undisturbed

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zone, the U zone. All solid formation components and two particular uid components, isolated porosity (ISOL) and parallel porosity (PARA), are assumed to exist in equal volume in both X and U zones. Shallow-reading log measurements are assumed to respond only to volumes of formation components in the X zone. Hence, their response equations contain terms for only the components that exist in the X zone. Similarly, deep-reading log measurements are assumed to respond only to volumes of formation components present in the U zone. Their response equations contain terms for only the components that exist in the U zone. Some tools, which have a medium depth of investigation, are assumed to be inuenced by both X and U zones, and their response equations contain terms for all formation components, regardless of zone, and contain a special factor, xxxx_IFAC, called the invasion factor, which controls how much inuence comes from the X zone. The remaining inuence, 1.0 - xxxx_IFAC, comes from the U zone. Table 1 lists all curves currently recognized by the ELANPlus application, grouped by zone. In Table 1 the modier, _xxx, represents the different forms of the nonlinear conductivity equations (such as CXDC_DWA, CUDC_IND, and others). Table 1 Logs and the Zones to Which They Respond L Logs Assumed to Measure Parts of Both Zones BMK ENPA ENPU NPHI NPHU RHOB

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Logs Assumed to Measure Only Flushed Zone CCA CCHL CFE CGDM CHY CK CSI CSUL EATT EQHY EX1-EX10 GR PHIT QVSP_N SIGM TPL

ogs Assumed to Measure Only Undisturbed Zone CUDC CUDC_xxx SDPT SDPT_N

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Table 1 (Cont.) Logs and the Zones to Which They Respond CTI CT1 - CT6 CXDC CXDC_xxx DT DWAL DWCA DWFE DWGD DWK DWMG DWSI DWSU DWTH DWTI DWU U VELC WWAL WWCA WWFE WWGD WWK WWTI WWSI WWSU WWTH WWTI WWU

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The Overdetermined SolutionIn any simultaneous solution of a system of equations, there must always be at least as many equations as unknowns. If there are exactly as many independent equations as there are unknowns, the system is said to be determined, or deterministic. In a determined system there is exactly one set of values for the unknowns that will satisfy the equations. If there are fewer equations than unknowns, the system is underdetermined and cannot be solved until the problem is reorganized by adding independent equations or by reducing the number of unknowns. If there are more independent equations than unknowns, the system is overdetermined, and some means must be employed to settle any disagreements among the equations.

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The ELANPlus program allows specication of determined and overdetermined systems. To envision how the program operates, consider the job of trying to draw a straight line through a collection of points. There are two unknowns to be solved: the slope and the intercept of the line. The points are analogous to tools in the ELANPlus program and the line coefcients are analogous to formation component volumes. Figure 2 shows the solution to the problem when there are two pointsa determined system.

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B A

Figure 2

Determined system.

It is generally impossible to draw a straight line through the data when more points are added, though, especially in any system where the measurements (points) may include some noise. A technique called linear regression is usually employed to determine a best t to the data. Often, the best-t line is drawn so that the sum of the squares of the distances from the data points to the line is minimized (Figure 3). The technique of minimizing the squares of distances from data points to a line is called leastsquares minimization.

D

C B A

Figure 3

Overdetermined system.

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Normal linear regression treats each point as having the same weight. It is like assigning equal trust to each point, but often we know that some points are more reliable than others. More sophisticated linear regression programs allow different weights to be assigned to each point. Figure 4 shows the same data as Figure 3, but with points A and D assigned a weight of 1 and points B and C assigned a weight of 100. The equally weighted t is also shown for reference.

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D Points B and C heavily weighted C B A Equal weighting

Figure 4

Overdetermined system with weights applied

Uncertainty is the inverse of weight, so the results illustrated in Figure 4 could be generated by assigning points A and D an uncertainty of 1.0 and points B and C an uncertainty of 0.01. The same results would also be obtained with the uncertainty of A and D set to 10 and the uncertainty of B and C set to 0.1. Note that the actual value of the uncertainty is not the most important part; the key is the relative value of the uncertainty of one point with respect to the rest. The ELANPlus program assigns an uncertainty to each response equation, including internal equations such as the Summation of Volumes equation or the Equal Hydrocarbon Ratio equation. After the program converts uncertainties to weights, it applies a second factor, a weight multiplier, to determine the nal weight to be applied to each equation in the least-squares optimization. It is up to you to set appropriate uncertainties and weight multipliers for the problem at hand. All equations have default values for the uncertainties and weight multipliers. Those values have been determined through both theory and experience. Schlumberger suggests that you use the default values to start and modify them only as conditions warrant. For more information see Chapter 5, Uncertainties.

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ParametersELANPlus program parameters give you control over how the program behaves, what results are produced, and which data are used. Although the program has over 3000 parameters, you will use only a small subset for any given model. Program parameters fall into four general groups: global and program control parameters, binding parameters, response parameters, and salinity parameters. Global and Program Control Parameters Global and program control parameters control which direction the program will take at certain major branches in the logic. You can think of them as determining in what mode the program will operate. Because they determine the environment in which the ELANPlus problem is set, program control parameters usually are global. That is, they take on a single value throughout the processing interval. Often they are set and never changed for an entire job. This and the following subsections cover (briey) only the program control parameters that affect the concept of an ELANPlus model: Clay, Uncertainty Channel, Special Fluid Attribute, and Weight Percentage Option. There are other program control parameters in the program, such as Pasteboard Option, Output Sample Rate, and Processing Mode, that are important but do not affect the petrophysical model. For detailed information on other program control parameters, see the ELANPlus Users Guide, available on line through the Help menu.Clay

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Q

The Clay parameter can be set to either Wet or Dry, using the Global Parameter Editor. By selecting Wet you tell the program that response parameters associated with clay will have values that represent a clay-water aggregate. By selecting Dry you tell the program that the clay parameters values represent only the clay mineral and that values for the clay-associated water will be entered with separate parameters. For more information see the Wet and Dry Clay section in Chapter 3, Presponse Equations.Uncertainty Channel

Response equation uncertainty values can be supplied to the ELANPlus program either through a zoned parameter (xxxx_UNC) or through a data curve. The uncertainty curve to be used with a given response equation is selected in

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the Binding Editor in the same way a curve is selected for use by a response equation. Setting the Uncertainty Channel toggle to True in the Global Parameter Editor tells the program to use any curves bound to the equation uncertainty parameter(s). Any uncertainty parameter that does not have a curve bound to it will use values from its corresponding zoned parameter, regardless of the setting of Uncertainty Channel. If Uncertainty Channel is set to False, the zoned values will be used for all equation uncertainties, whether or not there are curves bound to any uncertainty parameters.Special Fluids

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To be as general as possible, the ELANPlus program allows you to model formation components with user-dened characteristics. You simply give each solid formation component a generic name like carbonate or evaporite, and the program treats it like any other formation component. Fluids are a little more complex. You may wish to model, for example, a certain portion of the formation water, diesel invasion from oil-based mud, acid, a borax solution, or maybe carbon dioxide. Conductivity equations need to know a little bit more about how to treat such user-dened uids. The Special Fluids parameter provides the additional information. The options are Water, Hydrocarbon, Immovable Water, Immovable Hydrocarbon, and Other. Water is the default. You set the Special Fluids parameter in the Global Parameter Editor. The attribute chosen for a special uid in any process is applied to all processes in the session. Do not try to combine special uids from different processes if they have different characteristics. Similarly, the attribute chosen for the special uid in the ushed zone (XSFL) and the special uid in the undisturbed zone (USFL) must be the same. The ushed zone and undisturbed-zone special uids may have different densities, conductivities, or whatever, but if one is, for example, Immovable Hydrocarbon, so must the other be.Weight Percentage Option

After you select a Solve process that uses a dry weight percent curve such as DWSI or DWCA, set the Weight Percentage Option in the Process Editor. The value can be set to Linear, to direct the program to use the linear formulation for dry weight percentage data, or to Relative, to direct the program to use the relative equation formulation.

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Note that because the Weight Percentage Option is set from the Process Editor, rather than the Global Parameter Editor, different Weight Percentage Option values can be used for different Solve processes.Combination Method

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Generally the more rened an ELANPlus model becomes, the more specic it becomes. The key to efcient interpretation of long borehole intervals or multiple wells in a eld is the ability to splice together results from a library of well-rened models. Controlling the splicing of individual models is the purpose of the Combination Method. Unlike the other program control parameters, the Combination Method is zoned instead of global and is built with the Combine editor. Each entry in the list tells the ELANPlus program which model combination method to use for a given depth range. The zonation applied to the Combination Method parameter is separate from that of the response parameters. For more information see Chapter 7, Model Combination. Binding Parameters Binding parameters tell the ELANPlus program which data curve to use for any given purpose. You set them in the Binding Editor. All response equations used in a session must be bound to a data curve, except the constant tools CT1CT6 (each of which uses a zoned parameter), the Equal Hydrocarbon Ratio tool (EQHY), the Summation of Volumes equation, and the Summation of Fluids equation. Response equation uncertainty parameters may or may not be bound to curves, as described in the section Uncertainty Channel on page 16. Remember that even if equation uncertainties are bound to curves, the curve data will not be used unless the global parameter Uncertainty Channel is set to True. Finally, some special response parameters can also be bound to curves. Table 2 lists the mnemonic and denition of each parameter that can derive its value from either a zoned parameter or a curve.

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Index

Table 2 Parameters That Can Use Curve Input GST Parameters GST_PFAC BCA BCHL BFE BGD BHY BK BSI BSUL BTI GST borehole partitioning factor Borehole calcium Borehole chlorine Borehole iron Borehole gadolinium Borehole hydrogen Borehole potassium Borehole silicon Borehole sulphur Borehole titanium

Q

Saturation Parameters M M_DWA M_WS N Porosity exponent in Indonesia/Nigeria equation Porosity exponent in Dual Water equation Porosity exponent in Waxman-Smits equation Saturation exponent for nonlinear conductivities

Invasion Factor Parameters BMK_IFAC ENPA_IFAC ENPU_IFAC NPHI_IFAC NPHU_IFAC RHOB_IFAC Bulk modulus invasion factor Linear epithermal neutron invasion factor Nonlinear epithermal neutron invasion factor Linear thermal neutron invasion factor Nonlinear thermal neutron invasion factor Bulk density invasion factor

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If a curve that can be used for any of the parameters in Table 2 is present in the data base, it will be used whether or not a valid value exists for the corresponding zoned parameter. If such a curve is present in your data base, and you want to force the ELANPlus program to use the zoned parameter value, you must use the GeoFrame Process Manager DataItem Editor to change the name of the curve so that the name of the curve will be inappropriate for use by the parameter. For more information on using the Binding Editor and DataItem Editor, see the ELANPlus Users Guide, available on line from the Help menu. Response Parameters Response parameters can be roughly grouped into three main categories: those that represent pure formation component endpoints for each equation, auxiliary parameters that are related to certain formation components, and auxiliary parameters that are related to certain response equations. All response parameters must contain valid values prior to the beginning of computation. Any interval in which any response parameter has a value of Absent will produce results containing only Absent values for all formation components for that entire interval.Formation-Component-Endpoint Parameters

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Pure-formation-component-endpoint response parameters are the majority of all response parameters. Each endpoint parameter value is the value that would be read by a logging instrument if it were surrounded by an innite amount of a particular 100% pure mineral, rock, or uid. In the case of constant tools, the logging instrument is synthetic; you make up the endpoint values. The actual values are immaterial, as long as you maintain consistency within the equation and with the uncertainty of the equation. See Constant Tools on page 69 for more information about constant tool parameters. Pure-formation-component-endpoint response parameters usually have mnemonics of the form equation mnemonic_formation component mnemonic. For example, the mnemonic for the density of calcite is RHOB_CALC, the mnemonic for the dry weight percentage of silicon in illite is DWSI_ILLI. There are two exceptions to the rule: equation mnemonics containing an underbar, and GST response equations.

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Equation Mnemonics Containing an Underbar For equation mnemonics containing an underbar, drop the underbar and everything after it before adding the underbar and formation component mnemonic. For example, for the SP equation and kaolinite component you have the equation mnemonic QVSP_N and formation component mnemonic KAOL that combine to produce the response parameter mnemonic QVSP_KAOL. For the dual-water ushed-zone equation and ushed-zone water, CXDC_DWA and XWAT produce CXDC_XWAT. Note that for any given formation component all conductivity equations for a specic zone (ushed or undisturbed) share the same response parameter. For undisturbed-zone water, CUDC, CUDC_DWA, CUDC_IND, CUDC_SIM, and CUDC_WS all share the CUDC_UWAT response parameter. That is because there can be only one conductivity equation for each zone per model. GST Response Equations GST response equations have mnemonics that begin with C, for capture, and response parameters that begin with F, for fraction. For example, the GST capture silicon equation, CSI, uses response parameters FSI_QUAR, FSI_CALC, FSI_ILLI, and so on. There are three internal equationsEqual Hydrocarbon Ratio (EQHY), Summation of Volumes, and Summation of Fluidsthat do not have endpoint response parameters that can be modied. Any values needed by those equations are set within the program.Formation-Component-Related Auxiliary Response Parameters

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Table 3 lists the mnemonics and denitions for the formation-componentrelated response parameters.

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Index

Table 3 Formation-Component-Related Response Parameters Mnemonic ARHOB_xxxx CBWA_xxxx CDPT_xxxx CEC_xxxx FLSOS_xxxx RSMSM_xxxx WCLP_xxxx Actual density Apparent bound water conductivity Conductivity as seen by the Deep Propagation Tool Cation exchange capacity Fluid/solid switch Ratio of the skeleton modulus to the shear modulus Wet clay porosity Denition Applies to All formation components Clays only UWAT, UIWA, USFL Clays only Clays and XBWA All formation components Clays only

Q

Equation-Related Auxiliary Response Parameters

Table 4 lists the mnemonics and denitions of equation-related response parameters. For more information, see Chapter 3, Response Equations,and Chapter 4, Conductivity Models. Table 4 Equation-Related Auxiliary Response Parameters Mnemonic A BCA BCHL BFE BGD BHY BK BSI BSUL BTI Archie A factor Borehole calcium Borehole chlorine Borehole iron Borehole gadolinium Borehole hydrogen Borehole potassium Borehole silicon Borehole sulphur Borehole titanium Denition Applies to All conductivity equations GST equations GST equations GST equations GST equations GST equations GST equations GST equations GST equations GST equations

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Table 4 (Cont.) Equation-Related Auxiliary Response Parameters Mnemonic C_DWA C_WS DPT_DIS_EXP DPT_DIS_FAC ERSH ERSHO EVCL EXC_FAC EXPXO FLUID_PAR GST_PFAC M M_DWA M_WS MC2 MVCL N Denition Dual water clay effect coefcient Waxman-Smits clay effect coefcient Texture dispersion exponent Texture dispersion coefcient Simandoux clay exponent Simandoux clay exponent Indonesian clay exponent Excavation effect factor Flushed-zone saturation exponent Fluids add in parallel switch GST borehole partitioning factor Archie porosity exponent Dual-water porosity exponent Waxman-Smits porosity exponent Effective porosity exponent Indonesian clay exponent Undisturbed-zone saturation exponent Applies to CUDC_DWA, CXDC_DWA CUDC_WS, CXDC_WS SDPT_N SDPT_N CUDC_SIM CXDC_SIM CUDC_IND, CXDC_IND NPHU CXDC_IND, CXDC_SIM BMK GST equations CUDC_IND, CUDC_SIM, CXDC_IND, CXDC_SIM CUDC_DWA, CXDC_DWA CUDC_WS, CXDC_WS CUDC_IND, CUDC_SIM, CXDC_IND, CXDC_SIM CUDC_IND, CXDC_IND CUDC_DWA, CUDC_IND, CUDC_SIM, CUDC_WS CXDC_DWA, CXDC_WS QVSP_N BMK VELC CUDC_SIM, CXDC_SIM BMK, ENPA, ENPU, NPHI, NPHU, RHOB

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QV_HYD_FAC SOLID_PAR SONIC_POR_FAC SWSHE xxxx_IFAC

QVSP hydrocarbon factor Solids add in parallel switch Sonic porosity factor Water saturation shale effect Invasion factor

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Table 4 (Cont.) Equation-Related Auxiliary Response Parameters Mnemonic xxxx_UBW xxxx_UNC xxxx_WM xxxx_XBW Denition Undisturbed-zone bound-water conductivity Response equation uncertainty Response equation weight multiplier Flushed-zone bound-water conductivity Applies to Undisturbed-zone conductivity equations All equations, including internal equations All equations, including internal equations Flushed-zone conductivity equations

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Default Response Parameter Values

Every effort has been made to provide reliable default values for response parameters. The minerals, which are well dened, all have reliable default values with the exception of the GR_xxxx and SDPT_xxxx parameters. Fluids are less well dened. Some uid response parameters have default values; others contain only the Absent value. The values of uid parameters that have default values are usually a good starting point. Use the Parameter Calculator to calculate uid parameters that contain only the Absent value. Because rocks are dened by the user, it is impossible to provide default values for rock parameters. In a future release of the ELANPlus program, however, the Parameter Calculator will be improved to help compute rock response parameters. Salinity Parameters The values of some uid response parameters depend on the salinity of the uids. They will always have a default value of Absent. The ELANPlus program attempts to help you, though, by calculating values for the salinitydependent parameters whenever possible.

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The following tables list the salinity-dependent parameters whose values can be calculated automatically by the program. Table 5 lists all salinity-dependent parameters whose values are a strong function of temperature. Table 5 Parameters That Are a Function of Salinity And a Strong Function of Temperature CXDC_XWAT CXDC_XIWA CXDC_XSFL* CDPT_UWAT CDPT_UIWA CDPT_USFL* CUDC_UWAT CUDC_UIWA CUDC_USFL* EATT_PARA EATT_ISOL*

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EATT_XWAT EATT_XIWA EATT_XSFL*

TPL_XWAT TPL_XIWA TPL_XSFL*

TPL_PARA TPL_ISOL

XSFL and USFL only if Special Fluids is Water or Immovable Water

Table 6 lists salinity-dependent parameters whose values are a weak function of temperature and pressure.

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Index

Table 6 Parameters That Are a Function of Salinity And a Weak Function of Temperature and Pressure FCHL_XWAT FCHL_XIWA FCHL_XSFL* RHOB_XWAT RHOB_XIWA RHOB_XSFL* RHOB_UWAT RHOB_UIWA RHOB_USFL* FCHL_PARA FCHL_ISOL*

Q

SIGM_XWAT SIGM_XIWA SIGM_XSFL*

U_XWAT U_XIWA U_XSFL*

RHOB_PARA RHOB_ISOL

SIGM_PARA SIGM_ISOL

U_PARA U_ISOL

XSFL and USFL only if Special Fluid is Water or Immovable Water

The program will compute a value for any of the parameters in Table 5 and Table 6 if the parameter value is Absent and the associated salinity value is known. The main difference between the two groups is that in addition to being initialized by the program, the parameters in Table 5 have their values updated periodically as computations progressas the borehole temperature changes. The values of the parameters in Table 6 are not updated. Another difference is that the parameters in Table 6 have a small pressure dependence. The pressure (in psi) used to compute their values is 0.465 times the depth in feet. In the following discussion of the salinity initialization hierarchy, the examples are (1) trying to compute the EPT attenuation for ushed-zone water, EATT_XWAT, and (2) trying to compute the density of undisturbed-zone water, RHOB_UWAT, to show how the rules apply to specic parameter values. Assume a formation temperature of 125 F. Salinities are expressed in ppk.Rules for Initialization of Salinity-Dependent Parameters

The rules for initialization of salinity-dependent parameters are as follows:

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Not Computing Parameter Values Other Than Absent If a parameter has a value other than Absent, its value is not computed. For example, EATT_XWAT = 1700 RHOB_UWAT = 1.15 Parameter Value of Absent Requires a Valid Salinity Value A parameter that has a value of Absent will be computed by the program if it can determine a valid salinity value for the parameter. The salinity for each parameter is determined by whichever of the following occurs rst: 1 Finding a valid value for SALIN. 2 Finding an absent value for SALIN but a valid conductivity value associated with the parameter. 3 Computing salinity from RMF, RW, and RWT. 4 Leaving the value as Absent.Valid Value for SALIN_xxxx. If the SALIN_xxxx parameter has a valid

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value (not Absent and greater than or equal to zero), it is used as the salinity value. For example, SALIN_XWAT = 50 SALIN_UWAT = 200Absent Value for SALIN_xxxx but Valid Conductivity Value. If the

SALIN_xxxx parameter has an Absent value, but the parameter has an associated conductivity parameter that has a valid value, the conductivity parameter value and temperature are used to compute salinity. (However, salinities are not computed from conductivities for parallel porosity (PARA) and isolated porosity (ISOL).) For example, SALIN_XWAT = Absent; CXDC_XWAT = 12.3 SALIN_UWAT = Absent; CUDC_UWAT = 37.0Computation of Salinity from RMF, MST, RW, and RWT. If the first two

tries fail, the program makes a final attempt to compute values for the xxxx_XWAT and xxxx_UWAT parameters. Either (1) resistivity of the mud filtrate (RMF) and mud sample temperature (MST) or (2) resistivity of the formation water (RW) and formation water temperature (RWT) can be used to compute salinity.

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Both RMF and MST must be present to compute SALIN_XWAT, and both RW and RWT must be present to compute SALIN_UWAT. Though this is the method of last resort, it is actually the most frequently used method. For example, SALIN_XWAT = Absent; CXDC_XWAT = Absent; RMF = 0.13; MST = 75 F SALIN_UWAT = Absent; CUDC_UWAT = Absent; RW = 0.027; RWT = 125 F Leaving the Parameter Value as Absent. If the program cannot perform at least one of the three actions (1, 2, or 3), the parameter value is left as Absent.Borehole Temperature

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Temperature plays an important part in salinity computations. The ELANPlus program must know the borehole temperature to compute proper salinity and parameter values. Usually a temperature curve already exists in the data base by the time the program is run. If the curve exists, you simply bind it, using the Binding Editor. The program automatically attempts to bind a curve named TEMP to the temperature. If no temperature curve is bound by the time that the program rst needs one, the program will compute a temperature from parameter values. The parameters that it uses are borehole temperature (BHT), surface temperature (ST), and gradient (GRADI). If BHT, a zoned parameter, contains valid values, then temperature is linearly interpolated between the values. The temperature between the shallowest depth entered in BHT and the surface is interpolated, using the shallowest BHT value and ST. If BHT contains only Absent values, ST and GRADI are used together to estimate the temperature.Salinity Editor

Because the program needs to know salinities before it can perform some other operations, such as giving the Zoned Parameter Editor proper values, the ELANPlus program has a special editor, the Salinity Editor, for entering salinity-related parameter values, including those needed to compute a temperature, if necessary. Table 7 lists the parameter mnemonics and denitions for the parameters found in the Salinity Editor.

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.

Index

Table 7 Salinity Parameters SALIN_ISOL SALIN_PARA SALIN_UGAS SALIN_XGAS SALIN_UIWA SALIN_XIWA SALIN_UOIL SALIN_XOIL SALIN_USFL SALIN_XSFL SALIN_UWAT SALIN_XWAT RMF MST RW RWT BHT ST GRADI Salinity of isolated porosity uid Salinity of parallel porosity uid Salinity of undisturbed-zone gas Salinity of ushed-zone gas Salinity of undisturbed-zone irreducible water Salinity of ushed-zone irreducible water Salinity of undisturbed-zone oil Salinity of ushed-zone oil Salinity of undisturbed-zone special uid Salinity of ushed-zone special uid Salinity of undisturbed-zone water Salinity of ushed-zone water Resistivity of the mud ltrate Temperature of mud ltrate (mud sample temperature) Resistivity of formation water Formation water temperature Borehole temperature Surface temperature Earth temperature gradient

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Temperature Correction of Parameter Values The value of some parameters changes signicantly with temperature. That includes all the parameters listed in Table 5 and Table 9. Table 8 Fluid Parameters That Are Temperature Corrected CXDC_XWAT CXDC_XIWA CXDC_XSFL* CDPT_UWAT CDPT_UIWA CDPT_USFL* CUDC_UWAT CUDC_UIWA CUDC_USFL* EATT_PARA EATT_ISOL*

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Q

EATT_XWAT EATT_XIWA EATT_XSFL*

TPL_XWAT TPL_XIWA TPL_XSFL*

TPL_PARA TPL_ISOL

XSFL and USFL only if Special Fluids is Water or Immovable Water.

Table 9 Clay Parameters That Are Temperature Corrected CBWA_CLA1 CBWA_CLA2 CBWA_CHLO CBWA_GLAU CBWA_ILLI CBWA_KAOL CBWA_MONT CUDC_CLA1 CUDC_CLA2 CUDC_CHLO CUDC_GLAU CUDC_ILLI CUDC_KAOL CUDC_MONT CXDC_CLA1 CXDC_CLA2 CXDC_CHLO CXDC_GLAU CXDC_ILLI CXDC_KAOL CXDC_MONT

Because the parameter values change with temperature, the ELANPlus program periodically updates the values (does a temperature correction). The temperature correction is applied only internally, during the computations.

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The parameter values and temperatures that you see in the Zoned Parameter Editor are never modied by the temperature correction unless you insert or move a zone boundary. Temperature corrections are made under the following conditions: At every zone boundary. The reference temperature for the parameter is the temperature at the bottom (deeper) depth of the zone. At every 100 foot interval if all response equations in the process are linear. That is, the temperature corrections are performed whenever the depth in feet is evenly divisible by 100. If a processing interval bottom depth were 7615, temperature corrections would be applied at 7600, 7500, and so on, not at 7515, 7415, 7315. To ensure consistency, the temperature correction interval is based on feet, regardless of the depth unit used. At every depth level if any response equation in the process is nonlinear. Parameter Calculator Use the Parameter Calculator! Its use is a key to self-consistent results with the ELANPlus application. Those who do not use it will find that the convergence to a believable answer takes much longer than if the input data are obtained from the Parameter Calculator. The Parameter Calculator can be used to compute Water parameter values and salinities (if salinity is not entered) Linear neutron dolomite and quartz endpoint values to approximate nonlinear effects and excavation correction Gas density and apparent neutron porosity as well as FHY_XGAS Hydrocarbon density from chemical formula Wet clay to dry clay conversions Most computations are bidirectional. You can supply a conductivity to obtain a salinity, or a salinity to obtain a conductivity. You can convert wet clay values to dry clay, or dry clay values to wet clay, and so on. Results from the Parameter Calculator are easily pasted into the Zoned Parameter Editor. Use the Parameter Calculator!

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ConstraintsConstraints let you impose absolute limits on the volumetric results of the program. They are often used to eliminate physically impossible results.

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Consider a formation modelled as calcite and water. Assuming a calcite density of 2.71, a water density of 1.0, and a measured density of 2.737, you can easily compute the volumes of calcite and water, using the following system of equations: 2.737 = 2.71 CALC + 1.0 XWAT sum of volumes = 1.0 = 1.0 CALC + 1.0 XWAT (6)

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Solving the equations yields CALC = 1.01 and XWAT = -0.01. Both answers are physically impossibleyou cannot have more than 100% of a formation, and you cannot have negative porositybut they lie within the uncertainty of the equations. To avoid such situations, the ELANPlus program imposes nonnegativity constraints on all formation component volumes and a constraint on the Summation of Volumes. Constraints are brick walls; there is no uncertainty associated with any constraint. When applied to the results of equations (2-6) and (2-7), the ELANPlus internal constraints would result in CALC = 1.0 and XWAT = 0.0. The imposition of constraints has an interesting side effect. When the forward problem is run to build the reconstructed logs for the example problem, the result is RHOB_REC = 2.71 1.0 + 1.0 0.0 = 2.71 (7)

Note that neither the input density, RHOB, nor the reconstructed density, RHOB_REC, is constrained; it is the formation component volumes that are constrained. It is the result of the volumes being constrained that causes RHOB_REC to lie between 1.0 and 2.71. Think of constraints as limiting the volume space available for an answer. You can also dene constraints. For example, you might constrain the results to match results known from some other source, such as core analyses. One such constraint might be an illite-montmorillonite relationship: ILLI 0.4 ---------------------------------- 0.6 ILLI + MONT (8)

The interaction of the constraint in Equation (8), the nonnegative volume constraints, and the Summation of Volumes constraint results in an available solution space shown as the clear area in Figure 5.

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Index

Q

1.0 Volume of Montmorillonite

0.5

0.0 0.0 0.5 1.0

Volume of Illite

Volume of illite greater than or equal to zero Volume of montmorillonite greater than or equal to zero Sum of volumes less than or equal to one ILLI/(ILLI + MONT) less than or equal to 0.6 ILLI/(ILLI + MONT) greater than or equal to 0.4Figure 5 Solution space subject to constraints.

User-dened constraints can be very useful for adding local knowledge to the ELANPlus model. However, just because some constraints are good, do not

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assume that lots of constraints are better. If a model requires a lot of constraints, chances are that your time would be better spent reviewing your choice of response equations, formation components, and parameter values rather than writing more constraints. Also, be wary of your source of local knowledge. A known pure limestone may turn out to have a large amount of microcrystalline quartz, for example. Modelling only calcite or using a constraint to force zero quartz in that case will make the result of the computation match the local knowledge. Unfortunately, all of the answers will be skewed, including porosity and hydrocarbon volumes. Be especially cautious about core results. Core results are usually measured by weight; ELANPlus computations are usually in volumes. Valid comparisons can be performed only after one set of measurements is converted to be consistent with the other. Also, core measurements are made on a very small volume, compared to logging measurements. That is not to say that one measurement is better than the other, but that they are simply different. You should not place too much emphasis on a small number of core results. Look for trends. Remember that there is often a depth difference between core results and log results. For more information, including a set of constraints that have already been written for you, see the User-Defined Constraints section of Chapter 6, Constraints.

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Building an ELANPlus ModelThe term model means the way in which you present a problem to the ELANPlus program; a model is simplied description of reality. Actually, all formation evaluation problems are vastly underdetermined. It is unlikely that anyone will ever have enough measurements, with sufcient accuracy and resolution in all dimensions, to fully describe the near-wellbore environment. Instead you will settle for a model, a subset of reality. The following discussion of a methodology for building ELANPlus models assumes that you do not already have a library of models available. By no means is this the only way to go about building models, and not every well will lend itself to it. It is only a suggested method, based on experience. Before ever sitting down to the computer, take time to think about the well. Each well has its zones of interest and distinct geological subdivisions, many of which will be common across a eld. These natural subdivisions are the starting point for model denitions.

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Often it is impossible and undesirable to try to describe long wellbore intervals with a single model. The ELANPlus application allows you to create several Solve processes (models)each of which describes a distinct depositional environment, time sequence, or whateverand then combine the results of the models to cover the entire interpretation interval. Using the model-combination capability of the ELANPlus application, you can build more specic and accurate models that can be saved and reused as you encounter the same geological conditions in other wells. Step 1 Select Formation Components For each model, select the formation components that you think may be present in signicant quantity. Signicance may depend on the mineral. The presence of pyrite, for example, can be important in volumes as low as a few percent. Solving for a feldspar in a quartz sand formation is probably unnecessary unless the volume of feldspar reaches double-digit percentages. Do not try to trim the list too much at this point. The more general a model, the wider its applicability. It is usually advisable to include a hydrocarbon in a model to be used for clean, wet formations. Sometimes nature provides little surprises. You can always eliminate superuous components later. Step 2 Select Response Equations The available selection of response equations is primarily determined by the logging suite recorded in the well. Select logs that are sensitive to at least one of the formation components you have selected. Do not select response equations that are inappropriate for the model. It does no good to include the gamma ray equation in a calcite-anhydrite-dolomite model. Those minerals are not radioactive, and the gamma ray tool has the same response (or lack thereof) to each of them. In a bad hole model, it is inappropriate to select any borehole-wall contact tools, such as bulk density or EPT attenuation. An exception might be made either if the uncertainty of the tool is being driven by a curve at least partly determined by hole rugosity, or if you very carefully zone the uncertainty parameter. Step 3 Rationalize Formation Components and Response Equations To produce a unique solution, your model must contain at least as many response equations as formation components. That is a mathematical fact of life, but it represents only the minimum requirement. Each response equation in the model must also be sensitive to at least one of the formation components in the model.

Index

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When you count response equations, remember to include the Summation of Volumes equation, which is always present, and the Summation of Fluids equation, which is present if undisturbed-zone uids exist in the model. The Summation of Volumes and Summation of Fluids equations are added automatically by the program. You do not have to select them, but they must be counted. Most tools are more sensitive to one formation component, or group of components, than others. You can use that fact to help establish good, stable models. Many log analysts who have experience with the ELANPlus program write models an the same form as the one in Table 10. Table 10 Rationalized Formation Components and Response Equations QUAR RHOB CALC U NPHI ILLI GR XWAT CXDC

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volumes

XOIL

There are no hard and fast rules. For example, rather than leaving the NPHI equation unassigned, you might write the model as in Table 11. Table 11 An Alternate Method QUAR RHOB CALC U ILLI GR, NPHI XWAT CXDC, NPHI XOIL

volumes

The main point is to write the model so that you can see which equation affects which formation component. In reality, all response equations affect all formation component volumes, but it is often helpful to think of a particular tool as solving for a particular component. Look at Table 10 again and consider what would happen if the sand were arkosic and you wanted to include orthoclase in the model. Where would it go? Even though there are enough response equations to solve for the number of formation components, which tool would be responsible for the orthoclase? Certainly not the neutron. Orthoclase and quartz may as well be the same as far as it is concerned.

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The same is true for density and conductivity. The gamma ray tool responds to orthoclase, but you are already counting on the gamma ray for the illite. The best solution is to provide an additional tool. Perhaps the gamma ray tool could be replaced with thorium and potassium. If it is known from some other source that the orthoclase volume is, say, roughly 20%of the quartz volume, a constant tool could be added. If you cannot add another equation, you may need to model the quartz-orthoclase mixture as a single rock. To do that, assume a ratio of quartz to quartzplus-orthoclase; call it K. Replace QUAR with SAND in the model. Then compute each of the SAND response parameters as xxxx_SAND = K xxxx_QUAR + ( 1.0 K ) xxxx_ORTH (9)

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Q

You could, of course, simply modify the xxxx_QUAR parameter values in the same manner as Equation (9), but that is not recommended, because it could be misleading. Quartz is silicon dioxide and nothing else. A quartz-whatever mixture should be modelled as a rock. Whenever you include a rock in an ELANPlus model, document its composition. The interpretation makes sense only when everyone can understand what went into it. Step 4 Choose Constraints If you wish to restrict the volume space available in the solution, you may wish to set some constraints. For now, simply remember that constraints are absolute limits and that they are not substitutes for equations. For more information see Chapter 6, Constraints. When you use a constraint, you begin to draw the result. Use constraints with care. It is a good idea to run the computation at least once without any constraints to see how it looks before you start imposing your idea of what the solution should be. For example, some log analysts dislike seeing porosity or hydrocarbon shows in shales. It would be easy to build constraints to limit porosity and to force hydrocarbon volumes to zero. But consider that the shale might be a source rock. Suppressing the hydrocarbon hides important information from a geologist. Even worse, the minor shows might be a tip-off that a potentially prolic, thinly bedded pay zone is present. Never apply a constraint for the sake of aesthetic effect. Whenever you do apply a constraint, document it. Include the name of the constraint, the depth intervals for which it applies, and the reason for applying

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it. If you have dened the constraint, you should also include the constraint denition. Rigorous documentation may seem like excess work, but others cannot read our minds, and 6 weeks down the road you may nd yourself spending just as much work trying to decipher your own constraint syntax. Step 5 Label the Model The ELANPlus program allows you to provide your own label for processes in a session. Use that capability to give your model a name that will be meaningful not only to you but to those who follow. Be as specic as the model. Use words that tell what sets this model apart from other, maybe similar, ones. Your efforts will be rewarded on subsequent jobs when you can quickly choose desired models from your stored work. Step 6 Choose Model Combination Method Up to now, nearly all remarks have been on individual models that exist as individual Solve processes. Now it is time to enlarge the scope to that of a session. Good model-building walks a ne line between generality and specicity. If a model is very general, it can be applied to more wells and larger borehole intervals, but it often will have to be rened extensively when reapplied. If a model is very specic, it usually will require little if any renement when reapplied, but its reusability suffers. Compromising on specicity can cause a single well interpretation to require many individual models. A separate editor, the Combine process editor, is used to specify how the individual models will come together to provide the nal interpretation for the entire wellbore interval. The zonation that controls the depth interval over which a certain combination method will be used is unique. Modifying zone boundaries in the Combine process editor has no effect on response or other zoned parameters. The nal combined result may come from Any one of the individual models exclusively. A weighted combination of all of the models, based on probabilities computed from expressions that you supply to the program. A weighted combination of all of the models, based on probabilities that were computed externally to the ELANPlus program If you use internally computed probabilities for any model combination interval, you need to select (or create) probability expressions to be used.

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Q

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For more information, see the Final Model Combination, Using Probabilities section of Chapter 7, Model Combination. Step 7 Create Functions The ELANPlus program computes results in formation component volumes. Usually it is desirable to create functions of those component volumes as output data types such as water saturation or grain density. The ELANPlus application lets you specify any number of Function processes, which may be driven by data from other processes and from curves present in the data base. A Function process uses the data along with function denitions that you provide to compute additional outputs that may be written to the database. See the ELANPlus Users Guide (available on line through the Help menu in the single-well section of the ELANPLus program) for details concerning function definition creation and syntax. Step 8 Set Parameter Values Parameters come in four types: global and program control parameters, binding parameters, response parameters, and salinity parameters. For more information, see the Parameters section of Chapter 2, Interpretation Models. When you set parameter values, you set them for all processes to which they apply. The lone exception is the Weight Percentage Option, which can be set model by model. It is especially important to remember that one parameter value applies to all processes when you are ne tuning response parameters. Changing a response parameter value might improve one model but adversely affect another, which might or might not be important. Remember, too, that those same response parameter values may affect constraint limits, model probabilities, and function results. Use the Parameter Calculator to help you set parameter values. The Parameter Calculator helps ensure consistency among parameter values and generally results in a quicker convergence to a believable answer. Use the Zoned Parameter Editor to help you review the values of selected groups of response parameters. All response parameters can be zoned. When a zone boundary is created for one response parameter, it will exist for all response parameters. Since response parameters are used in the evaluation of some constraints, the zonation of response parameters affects the zonation of constraints.

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Step 9 Save Your Work Select Save As from the File menu in the main title bar and give your work a meaningful name. You will be able to call it up later for use. If you have problems, the saved le, the Session File, is invaluable to those trying to help you.

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Q

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Index

Q

Chapter 3

Response EquationsThe types of response equations discussed in this chapter include Wet and Dry Clay, Gamma Ray Response Parameters, SP Response Parameters, Sonic Response Parameters, Neutron Response Parameters.

Wet and Dry ClayFundamental in understanding ELANPlus response equations is a knowledge of how clay is handled and the concept of wet versus dry clay. Many log analysts treat wet and dry clays as the same, even though they can be quite different. The most common source of dry clay information is core results. Such results are often used to judge the log analysis, which normally is in wet units, making the comparison less than ideal. The ELANPlus program allows you to work in either domain. There will be an additional program (GEOPOST) that converts back and forth between the two domains. ELANPlus logic makes use of the Dual Water Model formulation for clays, where wet clays are composed of dry clay and associated (bound) water. The ratio of bound water to dry clay is assumed to be constant for each clay. The ELANPlus program lets you enter parameters independently for the clay and the bound water by setting Clay = Dry in the Global Parameter editor. Alternatively, by setting Clay = Wet, you can enter parameter values for the clay-water combination and another parameter, WCLP (wet clay porosity), which species the fraction of bound water in the wet clay. The relationship

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between wet and dry clay values is best shown and understood in the following formulations. Volume of dry clay Volume of wet clay = ------------------------------------------------------1.0 Wet clay porosity Density of wet clay Wet clay porosity Density of dry clay = ---------------------------------------------------------------------------------------------1.0 Wet clay porosity Volume of dry clay Wet clay porosity Volume of bound water = ----------------------------------------------------------------------------------------------1.0 Wet clay porosity = Volume of wet clay Wet clay porosity (10)

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Q

(11) (11-1a) (11-1b) (12)

Volume of wet clay = Volume of dry clay + Volume of bound water

Throughout this text, unless otherwise specied, wet clay (Clay = Wet) is the default for parameters and response equations. Response parameters signify dry clay values only when Clay = Dry is specically stated. Mnemonics that have a subscript of DC also denote dry clay values. When one or more clays is present in a model (Solve process), the ELANPlus program automatically creates a bound water output curve (XBWA). The volume of clay in each output clay curve (ILLI, MONT, etc.) is a dry clay mineral volume. The bound water from each clay is summed into the XBWA curve. Occasionally, the subscript WC will be used to emphasize that a particular parameter or volume is a wet clay value. Keep in mind, though, that referring to a volume in a response equation signies wet clay values irrespective of the value of the Clay switch. Regardless of whether parameters are input as wet or dry values, the ELANPlus program always works internally with wet clay values, converting them whenever necessary. Density Response Equation The density response equation is the same for clay and nonclay minerals. The program solves for the volume of wet clay (dry clay plus its water). Then Equation (11-1b) is used to separate the total volume into volume of dry clay and volume of bound water. Note: If Clay = Wet, the program expects the clay response parameter values to be wet clay values and a WCLP_xxxx value for each clay in the model is required. If Clay = Dry, the response parameter values must be input as dry clay values, plus each equation requires a value for the bound-water parameter, xxxx_XBWA.

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Assume that Clay = WetT and the volumes of illite, quartz, and water are being solved; then the linear response equation needs to be formulated in wet clay terms. That is done for the density tool (RHOB) in the following equation. RHOB = RHOB_QUAR QUAR + RHOB_XWAT XWAT + RHOB_ILLI ILLI where: RHOB_QUAR = density of quartz RHOB_XWAT = density of ushed-zone water RHOB_ILLI = density of illite QUAR