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®
GeoFrame 4.2
ELANPlus Theory
Index
Copyright and Trademark Information
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Copyright and Trademark Information
Copyright ©1991 - 2005 Schlumberger. All rights reserved.
Index
No part of this document may be reproduced, stored in an information retrieval
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Version and Program History
ELANPlus Theory
Version Date
Comment
4.2
Oct 2004
Updated for GeoFrame 4.2
4.0
May 2001
Updated for GeoFrame 4.0
3.7
July 1999
Update for GeoFrame 3.7
3.6
April 1999
Update for GeoFrame 3.6
3.5
July 1998
Update for GeoFrame 3.5
3.2
August 1997
Add APS Interpretation
3.1
March 1994
Upgrades for GF1.1 standards
3.0
June 1993
Commercial
2.0
July 1992
Beta
1.0
March 1991
First Version
2
How to Use This Manual
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How to Use This Manual
Electronic copies of this manual are distributed on the GeoFrame application CD.
This introduction gives you information for using the manual on-line.
Index
The files, which make up the Help system of an application, are distributed as .pdf
(portable document format) that are opened in the xpdf reader.
To print a hard-copy of a file, start xpdf, or open the file from the Help menu, or
Help button of an application and click on the Printer icon in xpdf.
Additional information on how to use this manual is covered in:
•
Typographical Conventions
•
Command Bar
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The blue buttons in the upper right-hand corner of the document window offer
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These options are:
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TOC — Move to the first page of the Table of Contents.
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Go Back
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paged forward or backward after jumping—you can return to the original jump
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Throughout the guide, there may be references to other chapters and to other
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When you click on one of these links, you either jump to the relevant section of
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either case, click on Go Back (
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the Previous Topic button) to return to your current location in the document.
ELANPlus Theory
3
Typographical Conventions
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Typographical Conventions
Following is a list of the typographical conventions used:
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MB1 is the left mouse button; MB2 is the middle mouse button; MB3 is the
right mouse button.
•
Boldface type indicates menus and menu commands (File, Print, et. al.), and
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A reference to another topic is in a blue typeface and, if you are accessing the
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with MB1 on Go Back [
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•
A series of boldface, italicized commands separated by greater than sign (>)
(for example, Borehole>Symbols) shows the menu from which the command
is accessed. For example, to choose Borehole>Symbols, move the pointer to
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Italics indicate special procedural instructions (Using the keyboard), or
keywords (focus).
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Courier font indicates characters that you type; for example, enter 10.0).
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In GeoFrame manuals, the following procedural words have a precise
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ELANPlus Theory
4
Index
Command Bar
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Command Bar
Most dialog boxes contain a row of buttons near the bottom. Each of these keys
has a standard function that is performed when you click on it with MB1.
Index
•
Click on the OK button to close the dialog box and to perform the function.
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Click on the Apply button to perform the function without closing the dialog
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•
Click on the Reset button to clear any entries and to return the dialog box to its
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•
Click on the Cancel button to close the dialog box without changing its state.
•
Click on the Help button to bring up the user documentation.
ELANPlus Theory
5
Table of Contents
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Table of Contents
How to Use This Manual . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
Index
Chapter 1 — ELANPlus Program Theory
The Purpose of the ELANPlus Application . . . . . . . . . . . . . . . . . . . . . .
Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Equations and Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Formation Components, Volumes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mnemonics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Model, Interpretation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Summation Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xxxx. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Assumptions of the ELANPlus Application . . . . . . . . . . . . . . . . . . . . . .
Borehole Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bound Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Curve Editing—Depth Correction, Depth Matching, Despiking, Patching
Environmental Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Flushed-Zone and Undisturbed-Zone Relationships . . . . . . . . . . . . . . . .
Lateral Continuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Neutron Porosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Qv_effective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Summation of Fluids. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Summation of Volumes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Vertical Continuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10
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12
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17
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Chapter 2 — Interpretation Models
Formation Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Response Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A Simple Response Equation Example . . . . . . . . . . . . . . . . . . . . . . . . .
Invasion Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The Overdetermined Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Global and Program Control Parameters . . . . . . . . . . . . . . . . . . . . . . . .
Binding Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Response Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Salinity Parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Temperature Correction of Parameter Values . . . . . . . . . . . . . . . . . . . . .
Parameter Calculator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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20
21
22
23
25
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28
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33
38
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Table of Contents
Building an ELANPlus Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Step 1 Select Formation Components . . . . . . . . . . . . . . . . . . . . . . . . . . .
Step 2 Select Response Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Step 3 Rationalize Formation Components and Response Equations .
Step 4 Choose Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Step 5 Label the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Step 6 Choose Model Combination Method . . . . . . . . . . . . . . . . . . . . . .
Step 7 Create Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Step 8 Set Parameter Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Step 9 Save Your Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Index
Chapter 3 — Response Equations
Wet and Dry Clay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Density Response Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
General Response Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Gamma Ray (GR) Response Parameters . . . . . . . . . . . . . . . . . . . . . . . .
SP Response Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sonic Response Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Slowness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Velocity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Neutron Response Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Linear NPHI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Noninear Neutron Response Parameters . . . . . . . . . . . . . . . . . . . . . . . . .
Recommendations for Using Neutron Data in ELANPlus Processing. .
Recommendations for APS Interpretation. . . . . . . . . . . . . . . . . . . . . . . .
Constant Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Parameter Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
49
50
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53
55
59
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73
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Chapter 4 — Conductivity Models
No Rxo Tool . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Oil and Gas Model with Rxo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Oil and Gas Model without Rxo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Water Saturation, Linear Conductivity . . . . . . . . . . . . . . . . . . . . . . . . . .
Conductivity Input, Hierarchy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
For Global Parameter Clay = Wet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
For Global Parameter Clay = Dry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Beware of CUDC_clai. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Conductivity Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Waxman Smits Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Dual-Water Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Linear Conductivity Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Indonesian and Nigerian Conductivity Equations. . . . . . . . . . . . . . . . . .
Simandoux Conductivity Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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90
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106
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Table of Contents
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Chapter 5 — Uncertainties
The ELANPlus Solution Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Balanced Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Conductivity, SP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Weight Multipliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Default Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Uncertainty Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Carbonate-Clay Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
107
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110
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111
112
115
Index
Chapter 6 — Constraints
Internal Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Predefined Inequality Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Maximum Porosity Constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Irreducible Water Constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sonic Clay Volume Constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Conductivity Constraint for Water-Based Mud (Sxo Sw) . . . . . . . . . . .
Conductivity Constraint for Oil-Based Mud (Sxo £ Sw) . . . . . . . . . . . . .
Sxo Constraint for Water-Based Mud (Sxo Sw) . . . . . . . . . . . . . . . . . . .
Sxo Constraint for Oil-Based Mud (Sxo £ Sw) . . . . . . . . . . . . . . . . . . . . .
User-Defined Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
117
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123
126
127
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Chapter 7 — Model Combination
Methods for Generating Combined Answer Sets . . . . . . . . . . . . . . . . . .
Individual Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Model Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
External Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Internal Probabilities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bad Hole Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Final Model Combination, Using Probabilities. . . . . . . . . . . . . . . . . . . . .
129
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Chapter 8 — Quality Control
Quality Control of the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Examples of Bad Hole Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Quality Control of the Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Reconstructed Logs Can Identify Model Problems . . . . . . . . . . . . . . . . .
Poor Reconstruction Means There Is a Problem . . . . . . . . . . . . . . . . . . .
A Good Reconstruction Can Go With a Wrong Answer . . . . . . . . . . . . .
Use Predicted Value to Check for Inconsistencies . . . . . . . . . . . . . . . . . .
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
137
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Appendix A — The Simandoux Conductivity Equation
(A historical perspective)
Glossary
Index
ELANPlus Theory
8
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Index
Chapter 1
ELANPlus Program Theory
This 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 in the ELANPlus User’s 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.
You can run the ELANPlus application and produce results—even meaningful
results—without 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. Finetuning parameter values will remain a frustrating hit-or-miss proposition. With a firm
theoretical understanding, though, you can make educated choices of model
components and parameter values that will quickly converge to a high quality result.
ELANPlus Theory
9
The Purpose of the ELANPlus Application
ELANPlus Program Theory
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The Purpose of the ELANPlus Application
The ELANPlus computer program is designed for quantitative formation evaluation
of cased and open-hole log level by level. Evaluation is done by optimizing
simultaneous equations described by one or more interpretation models. Single-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 so-called
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:
t
v
t = Rv
R
Petrophysical model used by the ELANPlus application.
In this diagram, the t represents the tool vector—all 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 fit between the
observed logging instrument readings and some believed formation component
ELANPlus Theory
10
Index
ELANPlus Program Theory
Conventions
volumes (often core results)?” A method for solving the calibration problem has not
been implemented in version 2.x of ELANPlus. The problem will be solvable in
Version 3.0.
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Index
☛
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 definitions of the additional output types rather than having the
definitions hard-coded in the program.
Chapters 2–8 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.
Conventions
To 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 first 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 fluids are likely to be present in the formation. These
minerals, rocks, and fluids are the formation components.
ELANPlus Theory
11
Conventions
ELANPlus Program Theory
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.
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 first
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 fluids 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.
ELANPlus Theory
12
ToC
Index
ELANPlus Program Theory
Conventions
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 specific
model are combined through the Combine process to produce a final answer for the
entire borehole interval being evaluated.
Summation Expressions
Many concepts are best described mathematically and involve a summation. To avoid
defining 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
nc
∑ Vi
i=1
even 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
The symbol nc represents the number of clays in a model, including all clays that
have specific names (ILLI, MONT, etc.) as well as the generic clays (CLA1, CLA2).
nf, nuf, nxf
The symbol nf represents the number of fluids in a model and includes all types of
fluids (water, hydrocarbon, irreducible, etc.) in both the flushed and undisturbed
zones. The symbol nuf applies to all fluids, regardless of type, in the undisturbed
zone only. The symbol nxf applies to all fluids, regardless of type, in the flushed zone
only.
nfc
The symbol nfc represents the number of formation components in a model. Unless
otherwise stated, nfc includes all solids—nonclay and clay alike—and all fluids.
However, note that since bound water (XBWA) is solved for as a dependent variable,
nfc does not include it.
ELANPlus Theory
13
ToC
Index
Conventions
ELANPlus Program Theory
ToC
ns
The symbol ns represents the number of solid formation components in a model,
including both clays and nonclays unless otherwise stated.
Index
Vi, Vi, CEC_j, WCLP_i, RHOB_i
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 nonspecific 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
specific 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 fill in appropriate mnemonics as
required by context.
For example, in “Equation uncertainty parameters, xxxx_UNC, should be set such
that ...,” the xxxx should be filled 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.
ELANPlus Theory
14
ELANPlus Program Theory
Assumptions of the ELANPlus Application
ToC
Assumptions of the ELANPlus Application
Most formation evaluation programs impose some sort of interpretation model—
assumptions about the depositional environment, clay properties, fluid 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—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, flushed-zone and
undisturbed-zone relationships, lateral continuity, neutron porosity, Qv_effective,
summation of fluids, 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 Editing—Depth 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 flushed and
undisturbed zones.
ELANPlus Theory
15
Index
Assumptions of the ELANPlus Application
ELANPlus Program Theory
If a model includes an undisturbed-zone fluid, the same type of fluid exists in the
flushed zone, even though the volume of the fluid might be zero in either or both
zones. For example, if a model includes undisturbed-zone oil (UOIL), it must also
contain flushed-zone oil (XOIL).
The volume of porosity in the flushed and undisturbed zones is the same, regardless
of the types of fluids filling the pore space.
Hydrocarbon density (gas/oil ratio) is the same in both zones.
Lateral Continuity
All solid formation components extend infinitely from the borehole at zero degrees
dip.
Fluid formation components exist in one of two annular zones—the flushed zone,
near the borehole, or the undisturbed zone, farther away from the borehole. That
allows for the concept of fluid invasion but uses the simplifying assumption of a step
invasion profile.
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 fluids in the flushed zone equals the sum of all fluids in the
undisturbed zone. This assumption is explicitly added as an equation along with the
other tools whenever a model includes both flushed and undisturbed-zone fluids. The
only user-settable parameter for the Summation of Fluids equation is the uncertainty,
VOLS_UNC (as in the Summation of Volumes equation).
ELANPlus Theory
16
ToC
Index
ELANPlus Program Theory
Assumptions of the ELANPlus Application
ToC
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.
ELANPlus Theory
17
Index
Assumptions of the ELANPlus Application
ELANPlus Program Theory
ToC
Index
ELANPlus Theory
18
ToC
Index
Chapter 2
Interpretation Models
An ELANPlus interpretation model has four parts: formation components, response
equations, parameters, and constraints.
1. Formation components are the constituents for which volumetric results are
desired.
2. Response equations are the equations to be solved and their associated input data
and uncertainties.
3. Parameters are the global and program control parameters, response parameters,
binding parameters, and salinity parameters.
4. 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 specified in a
separate Solve process. The final result is (typically) produced by mixing the results
from individual models (Solve processes) in a Combine process.
The Combine process is 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.
ELANPlus Theory
19
Formation Components
Interpretation Models
ToC
Formation Components
In 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 fluids. 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, SiO2, CaCO3, or
CaSO4. Because of their well-defined structure, it is usually possible to supply
default parameters for minerals.
Rocks are considered to be user-defined combinations of minerals, such as silt,
carbonate, and igneous rock. Rocks do not have default parameter values other than
Absent.
Fluids are pore-space-filling substances, including water, oil, gas, and other special
fluids. It is often possible to provide usable default values for fluids, 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 flushed-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.
Response Equations
A 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
nfc
measurement =
∑ Vi × Ri
(1)
i=1
where:
Vi =volume of formation component i
Ri =response parameter for formation component i
ELANPlus Theory
20
Index
A Simple Response Equation Example
Interpretation Models
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.
A Simple Response Equation Example
The 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 = φ × fluid density + ( 1 – φ ) × matrix density (2)
where:
φ = the volume of water-filled 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 = φ × 1.0 + ( 1 – φ ) × 2.71
(3)
Rearranging and solving for φ yields φ = 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
(4)
CALC = 1 – φ
The significance 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=1
Equation (5) is always added to all the other response equations in a model before
the set of equations is passed to the ELANPlus optimizer.
ELANPlus Theory
21
ToC
Index
Invasion Model
Interpretation Models
ToC
Invasion Model
Also implicit in the ELANPlus solution method is the assumption of a step invasion
profile consisting of a flushed zone, the X zone, and an undisturbed zone, the U zone.
All solid formation components and two particular fluid 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
influenced 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 influence comes from the X
zone. The remaining influence, 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 modifier, _xxx, represents the different forms of the nonlinear
conductivity equations (such as CXDC_DWA, CUDC_IND, and others).
Table 1 Curves Recognized by ELANPlus Application
Logs
ELANPlus Theory
Logs Assumed to
Measure Parts of
Both Zones
Logs Assumed to Measure
Only Flushed Zone
Assumed to
Measure Only
Undisturbed Zone
CCA
EATT
CUDC
BMK
CCHL
EQHY
CUDC_xxx
ENPA
CFE
EX1-EX10
SDPT
ENPU
CGDM
GR
SDPT_N
NPHI
CHY
PHIT
NPHU
CK
QVSP_N
RHOB
CSI
SIGM
CSUL
TPL
CTI
U
CT1 - CT6
VELC
22
Index
The Overdetermined Solution
Interpretation Models
ToC
Table 1 Curves Recognized by ELANPlus Application
CXDC
WWAL
CXDC_xxx
WWCA
DT
WWFE
DWAL
WWGD
DWCA
WWK
DWFE
WWTI
DWGD
WWSI
DWK
WWSU
DWMG
WWTH
DWSI
WWTI
DWSU
WWU
Index
DWTH
DWTI
DWU
The Overdetermined Solution
In 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.
The ELANPlus program allows specification 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.
ELANPlus Theory
23
The Overdetermined Solution
Interpretation Models
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 coefficients are
analogous to formation component volumes. shows the solution to the problem
when there are two points—a determined system.
B
A
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 fit to the data.
Often, the best-fit line is drawn so that the sum of the squares of the distances from
the data points to the line is minimized (). The technique of minimizing the squares
of distances from data points to a line is called least-squares minimization.
D
C
B
A
Overdetermined system.
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.
ELANPlus Theory
24
ToC
Index
Parameters
Interpretation Models
shows the same data as , but with points A and D assigned a weight of 1 and points
B and C assigned a weight of 100. The equally weighted fit is also shown for
reference.
ToC
Index
D
Points B and C
heavily weighted
C
B
A
Equal weighting
Overdetermined system with weights applied
Uncertainty is the inverse of weight, so the results illustrated in 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 final 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.
Parameters
ELANPlus 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.
ELANPlus Theory
25
Parameters
Interpretation Models
ToC
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 (briefly) 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
User’s Guide.
Clay
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 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.
ELANPlus Theory
26
Index
Interpretation Models
Parameters
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
Index
To be as general as possible, the ELANPlus program allows you to model formation
components with user-defined 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 userdefined fluids. 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 fluid in any process is applied to all processes in the session. Do
not try to combine special fluids from different processes if they have different
characteristics.
Similarly, the attribute chosen for the special fluid in the flushed zone (XSFL) and
the special fluid in the undisturbed zone (USFL) must be the same. The flushed zone
and undisturbed-zone special fluids 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.
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.
ELANPlus Theory
ToC
27
Parameters
Interpretation Models
ToC
Combination Method
Generally the more refined an ELANPlus model becomes, the more specific it
becomes. The key to efficient interpretation of long borehole intervals or multiple
wells in a field is the ability to splice together results from a library of well-refined
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 CT1–CT6 (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 26. 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 definition of each parameter that can derive its value
from either a zoned parameter or a curve.
Table 2 Parameters That Can Use Curve Input
GST Parameters
ELANPlus Theory
GST_PFAC
GST borehole partitioning factor
BCA
Borehole calcium
BCHL
Borehole chlorine
BFE
Borehole iron
BGD
Borehole gadolinium
28
Index
Parameters
Interpretation Models
ToC
Table 2 (Continued)Parameters That Can Use Curve Input
BHY
Borehole hydrogen
BK
Borehole potassium
BSI
Borehole silicon
BSUL
Borehole sulphur
BTI
Borehole titanium
Index
Saturation Parameters
M
Porosity exponent in Indonesia/Nigeria equation
M_DWA
Porosity exponent in Dual Water equation
M_WS
Porosity exponent in Waxman-Smits equation
N
Saturation exponent for nonlinear conductivities
Invasion Factor Parameters
BMK_IFAC
Bulk modulus invasion factor
ENPA_IFAC
Linear epithermal neutron invasion factor
ENPU_IFAC
Nonlinear epithermal neutron invasion factor
NPHI_IFAC
Linear thermal neutron invasion factor
NPHU_IFAC
Nonlinear thermal neutron invasion factor
RHOB_IFAC
Bulk density invasion factor
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 User’s Guide.
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.
ELANPlus Theory
29
Parameters
Interpretation Models
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
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 infinite amount of a particular
100% pure mineral, rock, or fluid.
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.
For more information about constant tool parameters, see "Constant Tools" on
page 75.
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.
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 flushed-zone equation and flushed-zone water, CXDC_DWA and
XWAT produce CXDC_XWAT. Note that for any given formation component all
conductivity equations for a specific zone (flushed 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.
ELANPlus Theory
30
ToC
Index
Parameters
Interpretation Models
ToC
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.
Index
There are three internal equations—Equal Hydrocarbon Ratio (EQHY), Summation
of Volumes, and Summation of Fluids—that do not have endpoint response
parameters that can be modified. Any values needed by those equations are set
within the program.
Formation-Component-Related Auxiliary Response Parameters
Table 3 lists the mnemonics and definitions for the formation-component-related
response parameters.
Table 3 Formation-Component-Related Response Parameters
Mnemonic
Definition
Applies to
ARHOB_xxxx
Actual density
All formation components
CBWA_xxxx
Apparent bound water conductivity
Clays only
CDPT_xxxx
Conductivity as seen by the Deep Propagation Tool
UWAT, UIWA, USFL
CEC_xxxx
Cation exchange capacity
Clays only
FLSOS_xxxx
Fluid/solid switch
Clays and XBWA
RSMSM_xxxx
Ratio of the skeleton modulus to the shear modulus
All formation components
WCLP_xxxx
Wet clay porosity
Clays only
Equation-Related Auxiliary Response Parameters
Table 4 lists the mnemonics and definitions 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
Archie A factor
Applies to
All conductivity equations
BCA
Borehole calcium
GST equations
BCHL
Borehole chlorine
GST equations
BFE
Borehole iron
GST equations
BGD
Borehole gadolinium
GST equations
ELANPlus Theory
Definition
31
Parameters
Interpretation Models
ToC
Table 4 Equation-Related Auxiliary Response Parameters
Mnemonic
Definition
Applies to
BHY
Borehole hydrogen
GST equations
BK
Borehole potassium
GST equations
BSI
Borehole silicon
GST equations
BSUL
Borehole sulphur
GST equations
BTI
Borehole titanium
GST equations
C_DWA
Dual water clay effect coefficient
CUDC_DWA, CXDC_DWA
C_WS
Waxman-Smits clay effect coefficient
CUDC_WS, CXDC_WS
DPT_DIS_EXP
Texture dispersion exponent
SDPT_N
DPT_DIS_FAC
Texture dispersion coefficient
SDPT_N
ERSH
Simandoux clay exponent
CUDC_SIM
ERSHO
Simandoux clay exponent
CXDC_SIM
EVCL
Indonesian clay exponent
CUDC_IND, CXDC_IND
EXC_FAC
Excavation effect factor
NPHU
EXPXO
Flushed-zone saturation exponent
CXDC_IND, CXDC_SIM
FLUID_PAR
Fluids add in parallel switch
BMK
GST_PFAC
GST borehole partitioning factor
GST equations
M
Archie porosity exponent
CUDC_IND, CUDC_SIM,
CXDC_IND, CXDC_SIM
M_DWA
Dual-water porosity exponent
CUDC_DWA, CXDC_DWA
M_WS
Waxman-Smits porosity exponent
CUDC_WS, CXDC_WS
MC2
Effective porosity exponent
CUDC_IND, CUDC_SIM,
CXDC_IND, CXDC_SIM
MVCL
Indonesian clay exponent
CUDC_IND, CXDC_IND
N
Undisturbed-zone saturation exponent
CUDC_DWA, CUDC_IND,
CUDC_SIM, CUDC_WS
CXDC_DWA, CXDC_WS
QV_HYD_FAC
QVSP hydrocarbon factor
QVSP_N
SOLID_PAR
Solids add in parallel switch
BMK
SONIC_POR_FAC
Sonic porosity factor
VELC
SWSHE
Water saturation shale effect
CUDC_SIM, CXDC_SIM
xxxx_IFAC
Invasion factor
BMK, ENPA, ENPU,
NPHI, NPHU, RHOB
xxxx_UBW
Undisturbed-zone bound-water conductivity
Undisturbed-zone
conductivity equations
xxxx_UNC
Response equation uncertainty
All equations, including
internal equations
xxxx_WM
Response equation weight multiplier
All equations, including
internal equations
xxxx_XBW
Flushed-zone bound-water conductivity
Flushed-zone conductivity
equations
ELANPlus Theory
Index
32
Parameters
Interpretation Models
ToC
Default Response Parameter Values
Every effort has been made to provide reliable default values for response
parameters. The minerals, which are well defined, all have reliable default values
with the exception of the GR_xxxx and SDPT_xxxx parameters.
Index
Fluids are less well defined. Some fluid response parameters have default values;
others contain only the Absent value. The values of fluid parameters that have default
values are usually a good starting point. Use the Parameter Calculator to calculate
fluid parameters that contain only the Absent value.
Because rocks are defined 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 fluid response parameters depend on the salinity of the fluids.
They will always have a default value of Absent. The ELANPlus program attempts
to help you, though, by calculating values for the salinity-dependent parameters
whenever possible.
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
CDPT_UWAT
CUDC_UWAT
CDPT_UIWA
CUDC_UIWA
CDPT_USFL*
CUDC_USFL*
*
CXDC_XWAT
EATT_XWAT
TPL_XWAT
CXDC_XIWA
EATT_XIWA
TPL_XIWA
CXDC_XSFL*
EATT_XSFL*
TPL_XSFL*
EATT_PARA
TPL_PARA
EATT_ISOL
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.
ELANPlus Theory
33
Parameters
Interpretation Models
ToC
Table 6 Parameters That Are a Function of Salinity
And a Weak Function of Temperature and Pressure
FCHL_XWAT
RHOB_XWAT
SIGM_XWAT
U_XWAT
FCHL_XIWA
RHOB_XIWA
SIGM_XIWA
U_XIWA
FCHL_XSFL*
RHOB_XSFL*
SIGM_XSFL*
U_XSFL*
Index
RHOB_UWAT
RHOB_UIWA
RHOB_USFL*
*
FCHL_PARA
RHOB_PARA
SIGM_PARA
U_PARA
FCHL_ISOL
RHOB_ISOL
SIGM_ISOL
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 progress—as 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 flushed-zone water, EATT_XWAT, and
(2) trying to compute the density of undisturbed-zone water, RHOB_UWAT, to show
how the rules apply to specific 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:
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
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34
Parameters
Interpretation Models
ToC
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 first:
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 value (not
Absent and greater than or equal to zero), it is used as the salinity value. For
example,
SALIN_XWAT = 50
SALIN_UWAT = 200
Absent 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 = 37.0
Computation 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.
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
ELANPlus Theory
35
Index
Parameters
Interpretation Models
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
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 first 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 definitions for the parameters found in the
Salinity Editor.
.
Table 7 Parameters of the Salinity Editor
SALIN_ISOL
Salinity of isolated porosity fluid
ELANPlus Theory
SALIN_PARA
Salinity of parallel porosity fluid
SALIN_UGAS
Salinity of undisturbed-zone gas
SALIN_XGAS
Salinity of flushed-zone gas
SALIN_UIWA
Salinity of undisturbed-zone irreducible water
SALIN_XIWA
Salinity of flushed-zone irreducible water
36
ToC
Index
Parameters
Interpretation Models
ToC
Table 7 Parameters of the Salinity Editor
SALIN_UOIL
Salinity of undisturbed-zone oil
SALIN_XOIL
Salinity of flushed-zone oil
SALIN_USFL
Salinity of undisturbed-zone special fluid
SALIN_XSFL
Salinity of flushed-zone special fluid
SALIN_UWAT
Salinity of undisturbed-zone water
SALIN_XWAT
Salinity of flushed-zone water
RMF
Resistivity of the mud filtrate
MST
Temperature of mud filtrate (mud sample temperature)
RW
Resistivity of formation water
RWT
Formation water temperature
BHT
Borehole temperature
ST
Surface temperature
GRADI
Earth temperature gradient
Index
Temperature Correction of Parameter Values
The value of some parameters changes significantly with temperature. That includes
all the parameters listed in Table 5 and Table 9.
Table 8 Fluid Parameters That Are Temperature Corrected
CDPT_UWAT
CUDC_UWAT
CDPT_UIWA
CUDC_UIWA
CDPT_USFL*
CUDC_USFL*
*
CXDC_XWAT
EATT_XWAT
TPL_XWAT
CXDC_XIWA
EATT_XIWA
TPL_XIWA
CXDC_XSFL*
EATT_XSFL*
TPL_XSFL*
EATT_PARA
TPL_PARA
EATT_ISOL
TPL_ISOL
— XSFL and USFL only if Special Fluids is Water or Immovable Water.
Table 9 Clay Parameters That Are Temperature Corrected
ELANPlus Theory
CBWA_CLA1
CUDC_CLA1
CXDC_CLA1
CBWA_CLA2
CUDC_CLA2
CXDC_CLA2
CBWA_CHLO
CUDC_CHLO
CXDC_CHLO
CBWA_GLAU
CUDC_GLAU
CXDC_GLAU
CBWA_ILLI
CUDC_ILLI
CXDC_ILLI
37
Parameters
Interpretation Models
ToC
Table 9 Clay Parameters That Are Temperature Corrected
CBWA_KAOL
CUDC_KAOL
CXDC_KAOL
CBWA_MONT
CUDC_MONT
CXDC_MONT
Index
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. The parameter values
and temperatures that you see in the Zoned Parameter Editor are never modified 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.
ELANPlus Theory
38
Constraints
Interpretation Models
ToC
Results from the Parameter Calculator are easily pasted into the Zoned Parameter
Editor. Use the Parameter Calculator!
Index
Constraints
Constraints let you impose absolute limits on the volumetric results of the program.
They are often used to eliminate physically impossible results.
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)
Solving the equations yields CALC = 1.01 and XWAT = -0.01. Both answers are
physically impossible—you cannot have more than 100% of a formation, and you
cannot have negative porosity—but 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 define 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
ELANPlus Theory
(8)
39
Constraints
Interpretation Models
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 .
ToC
Index
Volume of Montmorillonite
1.0
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 0.4
Solution space subject to constraints.
ELANPlus Theory
40
Interpretation Models
Building an ELANPlus Model
User-defined constraints can be very useful for adding local knowledge to the
ELANPlus model. However, just because some constraints are good, do not 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.
Building an ELANPlus Model
The term model means the way in which you present a problem to the
ELANPlus program; a model is simplified description of reality. Actually, all
formation evaluation problems are vastly underdetermined. It is unlikely that anyone
will ever have enough measurements, with sufficient 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 field. These natural subdivisions are the starting point for model
definitions.
ELANPlus Theory
41
ToC
Index
Building an ELANPlus Model
Interpretation Models
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 whatever—and 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 specific 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
significant quantity. Significance 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 superfluous 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.
ELANPlus Theory
42
ToC
Index
Building an ELANPlus Model
Interpretation Models
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 fluids 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
CALC
RHOB
U
ILLI
XWAT
GR
CXDC
NPHI
XOIL
∑ volumes
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
CALC
ILLI
XWAT
XOIL
RHOB
U
GR, NPHI
CXDC, NPHI
∑ 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.
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.
ELANPlus Theory
43
ToC
Index
Building an ELANPlus Model
Interpretation Models
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 quartz-plusorthoclase; 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)
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 prolific, 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 it. If you have
defined the constraint, you should also include the constraint definition. Rigorous
documentation may seem like excess work, but others cannot read our minds, and 6
weeks down the road you may find yourself spending just as much work trying to
decipher your own constraint syntax.
ELANPlus Theory
44
ToC
Index
Interpretation Models
Building an ELANPlus Model
ToC
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 specific 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 fine line between generality and specificity. If a model
is very general, it can be applied to more wells and larger borehole intervals, but it
often will have to be refined extensively when reapplied. If a model is very specific,
it usually will require little if any refinement when reapplied, but its reusability
suffers. Compromising on specificity 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 final 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 final 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.
For more information, see the Final Model Combination, Using Probabilities
section of Chapter 7, Model Combination.
ELANPlus Theory
45
Index
Building an ELANPlus Model
Interpretation Models
ToC
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 definitions that you
provide to compute additional outputs that may be written to the database.
See the ELANPlus User’s Guide 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 fine 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.
ELANPlus Theory
46
Index
Interpretation Models
Building an ELANPlus Model
ToC
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 file, the Session File, is invaluable to those trying to help you.
ELANPlus Theory
47
Index
Building an ELANPlus Model
Interpretation Models
ToC
Index
ELANPlus Theory
48
ToC
Index
Chapter 3
Response Equations
The 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 Clay
Fundamental 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 specifies the fraction of
bound water in the wet clay. The relationship between wet and dry clay values is best
shown and understood in the following formulations.
ELANPlus Theory
49
Wet and Dry Clay
Response Equations
ToC
Volume of dry clay
Volume of wet clay = -------------------------------------------------------1.0 – Wet clay porosity
(10)
Density of wet clay – Wet clay porosity
Density of dry clay = ----------------------------------------------------------------------------------------------1.0 – Wet clay porosity
(11)
Volume of dry clay × Wet clay porosity
Volume of bound water = ----------------------------------------------------------------------------------------------1.0 – Wet clay porosity
(11-1a)
= Volume of wet clay × Wet clay porosity
(11-1b)
Volume of wet clay = Volume of dry clay + Volume of bound water (12)
Throughout this text, unless otherwise specified, wet clay (Clay = Wet) is the default
for parameters and response equations. Response parameters signify dry clay values
only when Clay = Dry is specifically 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 signifies 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.
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.
ELANPlus Theory
50
Index
Wet and Dry Clay
Response Equations
RHOB = RHOB_QUAR × QUAR
+ RHOB_XWAT × XWAT
+ RHOB_ILLI × ILLI
ToC
(13)
Index
where:
RHOB_QUAR = density of quartz
RHOB_XWAT = density of flushed-zone water
RHOB_ILLI = density of illite
QUAR = volume of quartz
XWAT = volume of flushed-zone water
ILLI = volume of illite
When Clay = DRY, Equation (13) is used with the following substitution,
RHOB_ILLI WC = RHOB_ILLI DC × ( 1.0 – WCLP_ILLI )
+ RHOB_XBWA × WCLP_ILLI
(14)
where
WCLP_ILLI =wet clay porosity of illite
RHOB_XBWA =density of bound water
Inserting Equation (14) into Equation (13) for RHOB_ILLIWC yields
RHOB = RHOB_QUAR × QUAR + RHOB_XWAT × XWAT +
( RHOB_ILLI DC × ( 1 – WCLP_ILLI ) + RHOB_XBWA × WCLP_ILLI ) (15)
× ILLI WC
Most users set Clay = WET when running the ELANPlus program. An advantage of
setting Clay to Wet is that only one clay response parameter is needed for each
equation. (RHOB_ILLI is all that is needed when Clay = WET, but RHOB_ILLI and
RHOB_XBWA are required when Clay = DRY).
ELANPlus Theory
51
Wet and Dry Clay
Response Equations
ToC
General Response Equation
The simplest response equation is for linear measurements, such as the U (volumetric
photoelectric cross-section) tool. Equation (16) has the same form as Equation (13).
The difference is that it is for the U tool instead of the RHOB tool and has been
generalized to include XOIL and XGAS (flushed-zone oil and gas) in the porosity
analysis, plus all minerals with and without bound water.
U = U_XWAT × XWAT + U_XGAS × XGAS
ns
U_i × Vi
+ U_XOIL × XOIL +
∑
(16)
i=1
where:
ns = number of formation components that are solid
U_i = the response parameter for formation component i (if the
component is a clay, U_i is its wet clay response parameter)
Vi = the volume of component i (if the component is a clay
the Vi is its wet clay volume)
If Clay = WET, Equation (16) is used precisely as displayed. If Clay = DRY, the
general response equation is reformulated to look like Equation (15):
U = U_XWAT × XWAT + U_XGAS × XGAS
ns
U_i × Vi
+ U_XOIL × XOIL +
∑
i=1
(17)
nc
+
∑ ( U_ j × ( 1 – WCLP_ j ) + U_XBWA × WCLP_ j ) × V j
j=1
where:
ns = number of solid formation components, excluding clay
U_i = the response parameter for component i
Vi = the volume of component i
nc = the number of clays in the formation
ELANPlus Theory
52
Index
Gamma Ray (GR) Response Parameters
Response Equations
ToC
U_j = the dry clay response parameter for clay j
U_XBWA = the response parameter for bound water
Index
Vj =the volume of wet clay for clay j
Gamma Ray (GR) Response Parameters
The general form of the linear response equation is used for many tools. Although
straightforward, in practice it can be confusing to those not familiar with it. An
example is the following gamma ray response equation.
nfc
GR =
∑ GR_i × Vi
(18)
i=1
where:
GR = the gamma ray tool reading
GR_i = gamma ray response parameter for component i
For a sand-shale sequence, a commonly used equation for volume of clay from the
gamma ray is
GR – GR min
Volume of clay = -------------------------------------------GR max – GR min
(19)
where GRmin and GRmax are picked from the logs in a clean sand and a good shale,
respectively. Compare this to the ELANPlus equation (assuming a model that
contains only quartz, a clay, flushed-zone water, and flushed-zone oil):
GR = GR_QUAR × QUAR + GR_CLA1 × CLA1
+ GR_XWAT × XWAT + GR_XOIL × XOIL
(20)
Set GR_XWAT = GR_XOIL = 0, then solve for CLA1:
GR – GR_QUAR
CLA1 = -----------------------------------------GR_CLA1
(21)
In a clean sand, the volume of quartz is 1.0 minus the effective porosity
(1 – φe) and the volume of clay is zero, thus
ELANPlus Theory
53
Gamma Ray (GR) Response Parameters
Response Equations
GR – GR_QUAR × ( 1 – φ e )
CLA1 = -------------------------------------------------------------------GR_CLA1
ToC
(22)
Index
To get the same result as the conventional GR equation, one would set
GR min
GR_QUAR = -----------------1 – φe
(22-1a)
GR_CLA1 = GR max – GR_QUAR
(22-1b)
and
Note: The preceding equation assumes a similar porosity in the sands and the shales.
As an alternative, one could treat the fluids and clean sands as if they had the same
GR response and set
GR_QUAR = GR_XWAT = GR_XOIL = GR min
(23)
That could work better in areas where there are significant variations in porosity. The
fact that GR_XWAT and GR_XOIL are not equal to 0.0 is not intuitively obvious.
However, that is what is assumed with the traditional pick of GRmin from a clean
sand, where it represents the GR response of a mixture of quartz and fluids.
Picking consistent endpoints for the gamma ray can be difficult. There are no default
values for the GR tool. That is because the gamma ray signal comes from many
sources, only one of which is clay. Total GR (SGR for the NGS Natural Gamma Ray
Spectrometry tool) comprises a linear combination of thorium, potassium, and
uranium measurements:
SGR = 3.6 WWTH + 18.3 WWK + 9.5 WWU
(24)
In contrast to a total GR, there are defaults for thorium and potassium measurements.
Uranium, though, is a very mobile, water-soluble trace element whose presence
cannot be predicted. If all radioactive minerals present are being solved for, the
following values can be used. (CGR represents gamma ray data with uranium signal
removed.)
See Table 12 for more information.
ELANPlus Theory
54
SP Response Parameters
Response Equations
If a total GR measurement is being used, the values given require some boosting,
depending on the amount of uranium and potassium present.
ToC
Index
Table 12 Values to Use when All Radioactive Minerals Present
in Formation Are Included in Model
Thorium
Quartz
Potassium
CGR
0.0
0.0
0.0
Illite
18.0
4.0
138.0
Kaolinite
27.0
0.0
97.0
Smectite
15.0
0.5
63.0
5.0
10.0
201.0
Potassium Feldspar
SP Response Parameters
The SP measurement is not directly usable. It must first be transformed into a
Qv_effective by two programs, SPBOUNDARY and SPQV. (QVSP_N is the
ELANPlus input curve name for Qv_effective.)
The SPQV program requires a value for Qv_shale (or Static SP, SSP), the salinity of
filtrate and formation waters, and SP data. The SP used by these programs must have
its baseline set to 0.0.
The transform of SP to Qv_effective is an implementation of the work of L.J.M. Smits.
The work describes the SP deflection as a function of the contrast between the
wellbore and the formation salinities, and as a function of the contrast between the
electrical charges of the sands and the surrounding shales.
Qv
Q v_effective = ----------S xot
(24-1a)
Equation (24-1a) has been implemented as
Qv
Q v_effective = ----------------------------------------------------------------------------------S xot + QV_HYD_FAC ( 1 – S xot )
(24-1b)
where:
Sxot = total water saturation in the flushed zone
QV_HYD_FAC = the hydrocarbon correction factor for Qv
ELANPlus Theory
55
SP Response Parameters
Response Equations
QV_HYD_FAC is added to the original equation to allow you to adjust the
magnitude of hydrocarbon correction. The ELANPlus default is full hydrocarbon
correction: QV_HYD_FAC = 0. For no hydrocarbon correction, set QV_HYD_FAC
= 1.0.
The QVSP_N response equation used is
nxw
nxh
 nc


QVSP_N
Vi × WCLP_i +
V j + QV_HYD_FAC
Vk


i = 1
j=1
k=1 
∑
∑
∑
(25)
nc
=
∑ Vi ( 1 – WCLP_i ) ( CEC_i ) ( ARHOB_i )
i=1
where:
nxw = number of flushed-zone fluids that have a water attribute
Vj = the volume of water component j
nxh = number of flushed-zone fluids that have a hydrocarbon
attribute
Vk = the volume of hydrocarbon component k
CEC_i = cation exchange capacity of clay component i
ARHOB_i = actual density of clay component i
The parameters that control the effect of the SP on the final answer are Qv_shale (or
SSP), QV_HYD_FAC, and QVSP_UNC (SP uncertainty). Qv_shale and SSP are in
the preprocessing programs, and QV_HYD_FAC and QVSP_UNC are within the
program.
The Qv_shale (or SSP) parameter must be set correctly before the ELANPlus program
is run, or you will have to exit the program to make the appropriate corrections.
Calculating QVSP_UNC requires you to know that the processing of the
ELANPlus program internally multiplies QVSP_N by porosity.
For more information, see the Conductivity, SP section in Chapter5, Uncertainties.
We recommend that you use the value of Qv_shale, rather than SSP, as the input into
SPQV. It is easier to set the SP baseline to 0.0 and estimate Qv_shale than it is to
estimate SSP, especially when hydrocarbons are present.
ELANPlus Theory
56
ToC
Index
SP Response Parameters
Response Equations
ToC
One way to estimate the value of Qv_shale is as follows:
1. Use (Qv_shale = 1) and (Qv_shale = 4).
Index
170
Ec (mV)
160
Smits SP Chart
150
QvShale = 1
(meq/cm3)
140
130
120
110
100
Qv
(meq/cm3)
90
80
0.0
70
.04
60
SP
0.1
50
0.2
40
0.3
30
0.5
20
0.7
10
1.0
0
0.6
1
2
5
10
20
50
100
200
Salinity (ppk)
Chart showing Qv shale = 1
2. Enter the x-axis with the salinity of the mud filtrate and the salinity of connate
water.
3. Move each entry up to the line representing Qv_shale = 0,.
4. Move left to the y-axis (as in the example in ).
5. The difference is what the SP (-44 mV on ) should read in a clean water zone.
The chart that most closely fits the data approximates Qv_shale. The SPQV
program handles Qv_shale values continuously from 0.25 to 10.
A normal range of Qv_shale is from 1 to 4. A value of 1, or even lower, is common in
high-porosity rocks of the Gulf of Mexico. In older, more consolidated rocks, a value
of 4 will be more normal.
Another approach to approximating Qv_shale is the following chart:
1. Run the ELANPlus program with QVSP_N in a model that is not part of the final
answer. The program will create a reconstructed QVSP_N from the other tools.
ELANPlus Theory
57
SP Response Parameters
Response Equations
ToC
170
Ec (mV)
160
Smits SP Chart
150
QvShale = 4
(meq/cm3)
Qv
(meq/cm3)
140
Index
130
120
0.0
110
.04
100
0.1
90
0.2
80
0.3
70
0.5
60
0.7
50
1.0
40
1.5
30
2.0
20
10
4.0
0
0.6
1
2
5
10
20
50
100
200
Salinity (ppk)
Chart showing Qv shale = 4
2. Note the average value in shales. Exit the ELANPlus program.
3. Put the reconstructed QVSP_N into and run the SPQV program.
4. Use the QVSP_N output from SPQV in the ELANPlus program.
Either of those techniques may seem overly complex, but it is very important to have
the SP information balanced with the other tools used in the final solution. If it is not
balanced, the ELANPlus processing will try to justify the Qv_effective input by
altering one or more of the answer volumes.
An example of that is when the Qv_effective from the SP is much higher than the Qv
indicated by the other tools. If QV_HYD_FAC is anything but 1, the ELANPlus
processing will increase the volume of hydrocarbons in the flushed zone in an
attempt to correct the imbalance between the two sources of Qv. That will in turn
increase the volume of hydrocarbons in the deep zone (decreased Sw), even when the
deep conductivity tool computes 100% water.
Generally, the deep and shallow zones are linked mathematically by a Constant Tool,
which amplifies the problem (for example, XOIL = 0.2 UOIL , or in deep zone
terms, UOIL = 5 XOIL ). Because of that, we recommend that new users start with
QV_HYD_FAC = 1 (no hydrocarbon correction).
ELANPlus Theory
58
Sonic Response Parameters
Response Equations
ToC
Sonic Response Parameters
Because the sonic tool responds not only to the various mineral and fluid volumes
but also to the structure and texture of the rock, it less than ideal as a porosity tool.
Some uses for the sonic are
•
Mineral identification
•
Clay from dolomite differentiation
•
Porosity backup in bad hole
•
Hydrocarbon type identification
The response equations available for the sonic tool deal with either slowness (Wyllie
equation, DT input curve) or velocity (Hunt-Raymer-Gardner equation, VELC input
curve). Neither currently supports the presence of gas, because there is no industryaccepted way to handle it.
The concept of compaction correction in the Wyllie equation is not directly
supported. It must be entered by altering the fluid endpoint.
Shear velocities or slownesses also are not explicitly handled. Shear data must be
entered into equations used for compressional data, with appropriate parameter
changes.
Slowness
The slowness equation is simply the Wyllie Time Average equation.
DT – DT matrix
φ sonic = ---------------------------------------------------DT fluid – DT matrix
(26)
For a sand-water mixture this equation can be expressed in the form of a standard
ELANPlus linear equation as
DT = DT_XWAT × XWAT + DT_QUAR × QUAR
(27)
or more generally
nfc
DT =
∑ DT_i × Vi
(28)
i=1
where:
DT = the compressional slowness measurement
ELANPlus Theory
59
Index
Sonic Response Parameters
Response Equations
ToC
DT_XWAT = the compressional slowness of flushed-zone water
DT_QUAR = the compressional slowness of quartz
Index
DT_i = compressional slowness of component i
To include a compaction correction (CP), replace the fluid term (DT_XWAT) with
DT_XWAT_CP_corrected, as shown for a single mineral in
Equation (29).
DT_XWAT _CP_corrected = DT_XWAT × CP + DT_QUAR ( 1 – CP ) (29)
Velocity
The velocity expression can be derived from the simplified Hunt-Raymer-Gardner
equation for sonic porosity:
DT – DT matrix
φ sonic = 0.625  ---------------------------------------


DT
1 ⁄ VELC – 1 ⁄ VELC matrix
1.6φ = --------------------------------------------------------------------1 ⁄ VELC
⇒
⇒
⇒
⇒
1.6 × VELC matrix × φ = VELC matrix – VELC
(29-1a)
(29-1b)
(29-1c)
VELC = VELC matrix × ( 1 – φ ) – 0.6VELC matrix × φ
(29-1d)
VELC = VELC matrix × ( 1 – φ ) + SONIC_POR_FAC × φ
(29-1e)
When expressed as a general ELANPlus equation, the velocity equation looks like
VELC = SONIC_POR_FAC × ( XWAT + XGAS + XOIL + XIWA + XSFL )
ns
(30)
VELC_i × Vi
+
∑
i=1
where:
VELC = the compressional velocity measurement
SONIC_POR_FAC = sonic porosity factor
ELANPlus Theory
60
Sonic Response Parameters
Response Equations
ToC
VELC_i = compressional velocity of component i
Note that Equation (30) is different from the standard ELANPlus expression. The
minerals are a simple sum of the volumes times the endpoints. However, the fluids
are multiplied by a coefficient called the sonic porosity factor,
SONIC_POR_FAC.
is a plot of DT versus porosity for dolomite, calcite, and quartz. It compares the
simplified Hunt-Raymer-Gardner sonic transform to the ELANPlus response
equation.The response parameters used to generate the plot were assigned the
following values:
VELC_DOLO = 21,700 ft/sec
VELC_CALC = 19,800 ft/sec
VELC_QUAR = 18,000 ft/sec
SONIC_POR_FAC = –11.88
30
DOL
CLC
20
PHIT
QUA
10
0
40
60
80
100
DT
ELAN Response Equation
Simplified Hunt-Raymer-Gardner
1000
DT
nm
= VELC = SPORF x ( VXWA + VXGA + VXOI ) +
Σ VELCA.i x V.
i
i =1
DT versus porosity plotted for dolomite, calcite, and quartz.
In the solid curves represent the simplified Hunt-Raymer-Gardner transform. The
dotted curves represent the ELANPlus response equation. Although the two
transforms are similar, a different SONIC_POR_FAC is needed for each matrix to
mimic the Hunt-Raymer-Gardner equation exactly. In this example, the value of
SONIC_POR_FAC was chosen for calcite.
ELANPlus Theory
61
Index
Sonic Response Parameters
Response Equations
A crossplot of VELC versus total porosity (PHIT) is one technique for determining a
value for the compressional velocity of the matrix and the appropriate
SONIC_POR_FAC. is a crossplot of VELC versus PHIT in a limestone reservoir.
12
Index
VELC
14
16
18
20
22
0
5
10
15
20
25
PHIT
Crossplot of VELC versus total porosity (PHIT).
A line through the points (PHIT, VELC) = (0.0, 19.54) and (25.0, 13.1) was selected
to represent the best fit of the data. SONIC_POR_FAC was computed as follows:
VELC = SONIC_POR_FAC × φ + VELC_CALC × ( 1 – φ )
⇒
(30-1a)
VELC = ( SONIC_POR_FAC – VELC_CALC ) × φ + VELC_CALC (30-1b)
The curve is of the form y = slope × x + intercept. Evaluating it for the given data
yields
intercept = VELC_CALC = 19.54 (thousand) ft/sec
slope = (SONIC_POR_FAC – VELC_CALC)
∆y 13.17 – 19.54
= ------- = --------------------------------- = – 25.48
∆x
0.25 – 0.0
⇒ SONIC_POR_FAC = slope + VELC_CALC = –5.94
Do not be surprised to find SONIC_POR_FAC for calcite deviating from the default
value of – 11.88 . The default was selected for intergranular porosity. The formation
crossplotted in contained vugular porosity.
ELANPlus Theory
ToC
62
Neutron Response Parameters
Response Equations
VELC_CALC, on the other hand, was found to be quite close to the default value of
19,800 ft/sec. Observe that perfect agreement between porosity and velocity is
nonexistent because of variations in texture (secondary porosity) and trace minerals.
That example was for one mineral. Multiple-mineral, or complex-lithology,
parameter determination using a crossplot is awkward. It is difficult to determine
whether changes in velocity should be attributed to porosity or lithology. A
companion program, CALPAR (not yet released), solves for sonic parameter values
in complex lithology.
Sonic response parameters vary. Those calibrated in one area or zone may not apply
elsewhere. Table 13 shows how sonic velocities observed in the high-porosity, soft
rocks of Gulf of Mexico (GOM) differ from the default compressional velocities,
which are based on hard rock data. The shear parameters are included as a starting
point for the user; the program does not, at this time, explicitly recognize a shear
velocity as an input.
Table 13 Typical Gulf of Mexico Sonic Velocities
Parameter
SONIC_POR_FAC
Default
ELANPlus
Compressional
GOM
Compressional
GOM Shear
–11.8
–9
–5.5
VELC_QUAR
18.0
18
7.2
VELC_ILLI
10.0
8
4.3
VELC_KAOL
12.5
10
5.1
VELC_MONT
9.1
7
3.8
Neutron Response Parameters
Unlike the sonic, the nonlinear neutron is fairly well understood, although complex.
Understanding of the neutron response has improved with time.
The traditional neutron response was calibrated to field data and showed a larger
than expected matrix effect in dolomite. That lead to the classic curved dolomite line
shown in Schlumberger chart books from 1972 to 1986. The response was encoded
in the environmental correction programs and is still output on field logs as the curve
named NPHI.
ELANPlus Theory
63
ToC
Index
Neutron Response Parameters
Response Equations
The apparent dolomite effect was later understood to be related to formation salinity.
The neutron was recharacterized, and a new response and environmental corrections
were introduced in 1986 in SPE paper 15540, “Improved Environmental Corrections
for Compensated Neutron Logs,” by Gilchrist,
et al.
The field output is named TNPH (or NPOR if alpha processed). These new
response and environmental corrections also are encoded in the current
environmental correction program although the output is still called NPHI.
Note: The ELANPlus logic expects all neutron input to be in limestone units.
shows the response for the old and new neutron porosity transforms at a salinity of
50 ppk.
SS
30
LS
DOL
PHIT
20
10
0
–5
0
5
10
15
20
25
NPHI.LIM
TNPH Transform ( 50 ppk )
NPHI Transform
NPHI and TNPH porosity transforms at 50 ppk
In the ELANPlus processing there are linear and nonlinear response equations for the
neutron. The linear neutron equation is referred to as NPHI in the Session Editor and
uses data from the curve selected for NPHI in the Curve Editor. That can be either
the old or new neutron (NPHI or TNPH) with the endpoints picked appropriately.
The nonlinear equation is called NPHU and uses data bound to NPHU. It requires a
curve from an environmental correction program, to which all corrections except
salinity have been applied. Salinity corrections are part of the final solution.
ELANPlus Theory
64
ToC
Index
Neutron Response Parameters
Response Equations
ToC
Linear NPHI
The ELANPlus linear approximation of the nonlinear neutron response equation is
adequate for most applications. The approximation is accomplished by adjusting the
mineral endpoints NPHI_DOLO and NPHI_QUAR. Such an approximation is valid
only over a specific range of porosities and fluid saturations.
Computing Linear NPHI Mineral Endpoints
To compute NPHI_DOLO and NPHI_QUAR, use the following steps:
1. Observe the average true porosity range.
2. Enter the true porosity on the y-axis of Chart POR-13 of the Schlumberger chart
book.
3. Record the limestone porosity values on the x-axis assuming the matrix is
dolomite and sandstone.
4. Use these values together with the neutron response equation to solve for
NPHI_DOLO and NPHI_QUAR.
For example, assume that the average porosity in a dolomite reservoir is 8 p.u. The
chart book indicates the limestone neutron porosity is 15.6 p.u.
Note: Do not use the difference between the limestone neutron porosity and the true
porosity for NPHI_DOLO.
The calculations needed are
NPHI = NPHI_DOLO × DOLO + NPHI_XWAT × XWAT
⇒
(30-2a)
φ N_LS = NPHI_DOLO × ( 1 – φ ) + NPHI_XWAT × φ(30-2b)
⇒
φ N_LS – φ
NPHI_DOLO = ----------------------1.0 – φ
(30-2c)
⇒
0.156 – 0.08
NPHI_DOLO = ------------------------------ ≈ 0.083
1.0 – 0.08
(30-2d)
where φ N_LS = neutron porosity, expressed in limestone units.
The previous example is valid only in water and oil zones (NPHI_XWAT =
NPHI_XOIL = 1.00). In gas zones there must be an additional term on the right-hand
side of the equation, NPHI_XGAS. It lumps together the neutron value for gas and
the excavation correction.
ELANPlus Theory
65
Index
Neutron Response Parameters
Response Equations
For more information see the Nonlinear Neutron Response Parameters section in
Chapter 3, Response Equations.
You must solve the nonlinear excavation equation to determine a value for
NPHI_XGAS, or use the Parameter Calculator (selected from the Options menu in
the Session Manager), which requires as input the approximate porosity and water
saturation as seen by the neutron.
The neutron matrix value calculation is also encoded in the Parameter Calculator.
Having it there allows appropriate parameters for the neutron to be determined with
either transform.
Crossplot Porosity as Total Porosity
There are two exceptions to not putting the same information into a model twice in
different forms. They are both uses of crossplot porosity as total porosity (PHIT) in
carbonates.
In reservoirs that contain dolomite, the addition of PHIT can be very helpful.
Crossplot porosity (PXND) in dolomite is a nonlinear function of the density-neutron
tools.
Binding PHIT to the PXND curve enables the ELANPlus program to use PXND as
an apparent-PHIT tool and helps the ELANPlus processing overcome the
nonlinearity of the neutron tool by biasing the final answer with a crossplot
approximation of total porosity.
With PXND as an input, expect the Standard Deviation of Reconstruction, SDR, to
increase slightly in dolomites when there are large porosity variations. PHIT is also a
required input to the Sonic Clay Volume predefined constraint, which is designed to
assist interpretation in radioactive dolomites.
In sand-shale reservoirs PHIT is not recommended, because it adds little to the
solution. If the problem is underdetermined, adding the PHIT equation will not help.
For sandstones, PHIT is a near-linear combination of density and neutron data and,
especially in higher porosity, NPHI_QUAR varies little. Instead, select a value for
NPHI_QUAR that is representative of the average porosity and use the linear neutron
response equation.
Note: Set the PHIT response parameter for a mineral equal to a value that the input
PHIT data would read in the pure mineral.
Applying that to quartz, calcite, and dolomite yields PHIT_QUAR = 0.0,
PHIT_CALC = 0.0 and PHIT_DOLO = 0.0 when using density/neutron crossplot
porosity.
ELANPlus Theory
66
ToC
Index
Response Equations
Neutron Response Parameters
Be careful with clays and minerals that exhibit false crossplot porosity. Assume that
illite (ILLI) is used in a Solve process, that RHOB_ILLI has a value of 2.50 g/cm3,
and NPHI_ILLI has a value of 36 p.u. Crossplot porosity for 2.50 g/cm3 and 36 p.u.
is 24 p.u., so PHIT_ILLI should be set to 24 p.u. (assuming Clay = WET).
It is important to realize that PHIT_ILLI has nothing to do with the WCLP_ILLI
parameter. PHIT_ILLI is used solely in the PHIT response equation. WCLP_ILLI is
used to relate the volume of bound water to the volume of dry clay.
Crossplot porosity and the volume of bound water associated with clay are totally
different entities. One comes from a transform built to give accurate porosity when
the reservoir is composed of quartz, calcite, and dolomite. The other is related to the
ratio of the surface area to the density of the clay.
PXND reads 0 in most minerals. However, there are some minerals where it has a
nonzero value. Salt (26 p.u.) and gypsum (36 p.u.) are common examples.
Set PHIT_HALI = 0.26 or 26.0 p.u. and PHIT_GYPS = 0.36 or 36.0p.u. when
PXND is used as the input curve for the PHIT equation. The Parameter Calculator
provides the capability of computing any required crossplot porosities when the
density and neutron values of a mineral are known.
There is one more thing to watch out for if PXND is used as the PHIT tool:
If the density or neutron log gives an erroneous reading, setting the uncertainty
for RHOB (RHOB_UNC) or for the neutron (NPHI_UNC) to a high value is not
enough. You must also increase PHIT_UNC.
Noninear Neutron Response Parameters
lThe nonlinear neutron tool input curve is NPHU. The ELANPlus program assumes
that all environmental corrections already have been applied to NPHU except for
formation salinity, which is computed during the simultaneous solution.
Applying the salinity correction during optimization is more rigorous and more
correct than attempting to apply the salinity correction in an environmental
correction program before ELANPlus processing. Without a complete solution of the
volumes of formation water, filtrate, gas, and oil the salinity correction can only be
an approximation.
An even better way to apply the salinity correction is to use a measured sigma,
because sigma is a direct measurement of the salinity and absorber effects that
perturb the neutron. The only problem is that a usable sigma is seldom available.
The sigma measurement must be made at the same time the neutron log is recorded.
If it is run at a different time, the fluid volumes will have changed and it will no
longer reflect the effects as seen by the neutron log. The sigma correction is applied
before ELANPlus processing.
ELANPlus Theory
67
ToC
Index
Neutron Response Parameters
Response Equations
ToC
If the sigma correction is applied, then salinity parameters in the
ELANPlus program must be set to 0 to eliminate a double correction.
The nonlinear neutron response equation is given by the following equation:
Index
φ N = φ N_matrix × V matrix + φ N_fluid × V fluid + ∆φ N_ex
(31)
where:
φ N = the total neutron response
φ N_matrix × V matrix = the matrix response
φ N_fluid × V fluid = the fluid response
∆φ N_ex = the excavation effect
The matrix response (salinity and porosity dependent) is computed within the
ELANPlus program by the response equations as a function of effective salinity and
fluid volumes. Although the matrix response, fluid response, and excavation effect
will be reviewed in detail in the following sections, a few general comments are in
order. The basic assumptions are
1. For quartz, calcite, and dolomite the apparent matrix point, φ N_matrix ,
is not constant, but rather a function of the volume of pore fluids,
V fluid , and apparent fluid salinity, PPKfluid.
2. The response parameter for hydrocarbons can be modeled as a function of its
hydrogen index, HIhc. The hydrogen index of a hydrocarbon can be computed as
a function of the hydrogen density, as discussed in Schlumberger Interpretation
Principles. For a hydrocarbon with a density of ρhc and a chemical formula of
n(CHX), the hydrogen index is
9X
HI hc = ----------------ρ hc
12 + X
(32)
The hydrogen index value can be computed in the hydrocarbon section of the
Parameter Calculator and should be entered into the appropriate response parameter
(such as NPHU_XGAS or NPHU_UOIL). The response parameter for all waters
should be set to 100 p.u. The reduction in hydrogen index for water when salinity
increases are taken into account by using the matrix term.
ELANPlus Theory
68
Response Equations
Neutron Response Parameters
Following is a subset of the response parameters required for the nonlinear neutron
equation:
NPHU_QUAR,
NPHU_CALC,
NPHU_DOLO,
NPHU_ANHY,
NPHU_ILLI,
.
.
.
NPHU_XOIL
SALIN_XOIL,
NPHU_XWAT
SALIN_XWAT,
NPHU_UOIL
SALIN_UOIL,
NPHU_UWAT
SALIN_UWAT,
NPHU_ISOL
SALIN_ISOL,
NPHU_IFAC,
EXC_FAC.
Each mineral volume has an associated response parameter and default value. In
general, you should not modify the response parameter for quartz, calcite, dolomite,
or any water.
Also, each fluid term has an associated salinity parameter, SALIN_xxxx (in units of
ppk), that must be entered. The value for SALIN_xxxx can be supplied directly by
the user or computed by the program from an associated parameter.
For example, if the program finds that SALIN_UWAT is Absent, it will attempt to
compute a salinity from CUDC_UWAT. If CUDC_UWAT is also Absent, the
program will try to compute salinity from the formation water resistivity RW.
For more detail on how the program determines salinity values, see the section on
Rules for Initialization of Salinity-Dependent Parameters.
The invasion factor, NPHU_IFAC, represents the percentage that the neutron
response is influenced by the flushed zone. It has a range of 0 to 1. A value of 1.0
would indicate that the neutron tool is affected only by the flushed zone. A value of
0.0 would indicate influence from only the undisturbed zone. If both flushed and
undisturbed fluids are present in a model, a value of 0.4 would be typical.
The parameter EXC_FAC allows you to adjust the magnitude of the theoretical
excavation effect. It has a default value of 1.
For more information see The Neutron Excavation Term section.
ELANPlus Theory
69
ToC
Index
Neutron Response Parameters
Response Equations
ToC
The Neutron Fluid Term
The fluid response is defined by the following equation:
Index
nxf
φ N_fluid × V fluid = NPHU_IFAC ×
∑ NPHU_i × Vi
i=1
nuf
(33)
+ ( 1 – NPHU_IFAC ) ×
NPHU_ j × V j
∑
j=1
+ NPHU_ISOL × ISOL + NPHU_PARA × PARA
where:
NPHU_i = nonlinear neutron response parameter for flushed-zone
fluid i
Vi = volume of flushed-zone fluid i
NPHU_j = nonlinear neutron response parameter for undisturbed
zone fluid j
Vj = volume of undisturbed-zone fluid j
NPHU_ISOL = nonlinear neutron response parameter for isolated
porosity
ISOL = volume of isolated porosity
NPHU_PARA = nonlinear neutron response parameter for parallel
porosity
PARA = volume of parallel porosity
If the fluid is water, its response parameter should be set to equal 100 p.u. (the
default value). The response parameter for hydrocarbons should simply be set to the
hydrogen index computed in the Parameter Calculator.
The invasion factor, NPHU_IFAC, is used to define the percentage of the flushedzone and undisturbed-zone fluids influencing the neutron response. Because isolated
and parallel porosity (ISOL and PARA) are viewed as being the same in the flushed
and undisturbed zones, the invasion factor has no influence over them.
ELANPlus Theory
70
Neutron Response Parameters
Response Equations
ToC
The Neutron Excavation Term
For a simple mixture of hydrocarbons and water, Schlumberger Log Interpretation
Volume I—Principles approximates the excavation effect as
∆φ N_ex = 2K ( HI w V w + HI hc V hc ) [ ( 1 – HI w )V w + ( 1 – HI hc )V hc (34)
]
where:
K = a constant defined by the user
HI = hydrogen index of water
w
V w = volume of water
HI hc = hydrogen index of hydrocarbon
V hc = volume of hydrocarbon
It follows that the general case of fluid mixtures is handled as
nf
∆φ N_ex = 2K
nf
∑ HIi Vi × ∑ ( 1 – HIi )Vi
i=1
(35)
i=1
where:
nf = number of fluids, both water and hydrocarbon
HI = hydrogen index of fluid i
i
V i = volume of fluid i
In the ELANPlus program the excavation effect is implemented as
∆φ N_ex ≡ 2Kφ N_fluid V fluid ( V fluid – φ N_fluid V fluid ) (36)
where φ
N_fluid V fluid is the fluid term discussed earlier and
nxf
V fluid ≡ NPHU_IFAC ×
∑ Vi
i=1
nuf
+ ( 1 – NPHU_IFAC ) ×
V j + ISOL + PARA.
j=1
(37)
∑
The response parameter for the constant term, K, is called EXC_FAC. It has a
default value of 1.
ELANPlus Theory
71
Index
Neutron Response Parameters
Response Equations
ToC
The Neutron Matrix Term
The matrix response is defined by the following equation:
φ N_matrix V matrix =
Index
∑
φ N_matrix V j
j
j = QUAR, CALC, DOLO
(38)
ns, ns ≠ QUAR, CALC, DOLO
+
∑
i=1
φ N_matrix V i
i
In general, φ
N_matrix i values are modeled as constants for all minerals,
and they have the value of the response parameter NPHU_i. However, for
quartz, calcite, and dolomite, φ
N_matrix i is a function of porosity
and salinity.
The defining equation for φ
N_matrix i is
 ∆φ
 (V
, PPK fluid )
 N_matrix j fluid
(39)
φ N_matrix ( V fluid, PPK fluid ) = NPHU_ j + ----------------------------------------------------------------------------------------1 – V fluid
j
The NPHU_j term is a constant and generally should not be modified by
the user.
The ∆φ
N_matrix j term is a function of porosity and salinity.
It is selected to be consistent with TNPH data and salinity correction.
The matrix response for quartz, calcite, and dolomite is a function of the fluid
volumes and excavation effect; that is why the neutron response equation is
nonlinear.
ELANPlus Theory
72
Neutron Response Parameters
Response Equations
ToC
Recommendations for Using Neutron Data in ELANPlus Processing
TNPH is the preferred transform to use for the neutron equation (either linear or
nonlinear). Using it is no problem with new logs. For older logs, Schlumberger
recommends converting the traditional NPHI curve as input to TNPH.
Index
The nonlinear neutron (NPHU) is most correct for gas or for carbonates with salt
mud, or in large porosity variations. When using the nonlinear neutron, keep the
following points in mind:
Do not modify the default values for NPHU_QUAR, NPHU_CALC or
NPHU_DOLO (2.05, 0.0, and 0.63 p.u., respectively). The actual matrix response is
computed as porosity, and salinity varies.
All water response parameters should be set to 100.0 p.u. Changes resulting from
salinity are incorporated in the matrix terms.
The oil and gas values for NPHU can be computed in the Parameter Calculator. They
differ from the linear response parameters because the linear parameters have the
excavation effect built in. The parameter EXC_FAC should normally be left at 1.0
If a measured sigma is available, use it to make a formation salinity correction before
ELANPlus processing and bind the resulting NPOR_CRC to the NPHU equation.
Note: With sigma-corrected data, be sure to set all the SALIN_xxxx parameters to 0
when running the ELANPlus program.
Recommendations for APS Interpretation
Following are recommendations for APS interpretation.
Channels
The relevant output channels available from both the Maxis and PREAPS are shown
in Table 14.
Table 14 Available Maxis and PREAPS Output Channels
Channel
Description
Low Resolution
High Resolution
APLC
HALC
APS Near/Array Corrected Limestone Porosity
ENPI
HNPI
APS Near/Array Corrected Limestone Porosity except for
Formation Salinity (Linear)
ELANPlus Theory
73
Neutron Response Parameters
Response Equations
Do not use APLC or HALC in interpretation. The Near/Array porosity is an
epithermal measurement which responds almost linearly with hydrogen index. In salt
water the hydrogen index is reduced by the volume fraction of salt resulting in a
number less than one. APLC is equal to the measured porosity divided by the
hydrogen index of the salt water computed from the logging engineer’s input
parameter of FSAL, formation salinity.
The net result is that in a 20 pu salt saturated limestone formation the measured
porosity reads 18 pu but APLC is boosted to read 20 pu. The problem with this
approach is that in a 18 pu limestone and oil formation APLC will be boosted to
20 pu when in fact no boosting should occur. In shales, APLC is also incorrectly
boosted.
For this reason one should use either the ENPI or HNPI channel in interpretation. It
is identical to APLC/HALC but with no formation salinity boosting.
Response Equation
The response equation is identical to the linear neutron equation, NPHI.
ENPI =
# Minerals
# x fluids
+
ENPI_m
×
V
ENPI_IFAC
×
∑
∑ ENPI_x × V x(40)
m
m
x
# u fluids
+ ( 1 – ENPI_IFAC ) ×
∑ ENPI_u × V u
u
Matrix End Points
Parameters for the clean matrices quartz and dolomite may be computed from the
Neutron Matrix Computation of the ELANPlus Calculator. Simply enter the porosity
and salinity and the matrix end points are computed.
Water End Points
Typically one simply enters the parameters RMF, MST, RW and RWT and the
flushed and undisturbed zone water parameters are computed automatically. If at any
time one wishes to change the estimate of mud filtrate or formation water salinity,
use the X-Water or U-Water Parameters computation of the ELANPlus Calculator.
The corresponding ENPI parameters are computed.
ELANPlus Theory
74
ToC
Index
Constant Tools
Response Equations
ToC
Light Hydrocarbon End Points
In order to determine the correct gas parameters use the Hydrocarbon Parameters
computation of the ELANPlus Calculator and enter the density and either the weight
percent of hydrogen in the gas or the number of hydrogen molecules associated with
each carbon atom. For example, the gas methane has a density of 0.1 gm/cc at 150 F
and 2000 psi and has 4 atoms of hydrogen for each carbon atom. This results in a gas
parameter value of 22.5 pu.
Mineral End Points
Monte Carlo computations were performed to develop an algorithm which related
the density and chemical composition of compounds to the ENPI response. The
algorithm was used to compute the clay end points.
Table 15 shows the mineral end points for clays and other minerals. Note the large
positive value of 20.0 pu for salt.
Table 15 Mineral End Points
Mineral
ENPI
Mineral
ENPI
HALI
0.200
BIOT
0.086
ANHY
0.020
GLAU
0.245
GYPS
0.600
ILLI
0.254
PYRI
0.165
KAOL
0.430
SIDE
0.028
CHLO
0.410
MUSC
0.112
MONT
0.700
Constant Tools
Constant Tools provide a way to add more information to a model. Unlike most tools
within the ELANPlus application, they do not represent a curve bound to data. They
are a means of adding local knowledge to the model through equations.
The equation for a Constant Tool is in the standard form for the ELANPlus program:
nfc
CTn =
∑ CTn_i × Vi
(41)
i=1
where:
ELANPlus Theory
75
Index
Constant Tools
Response Equations
ToC
n = number of the Constant Tool (currently CT1 through CT6)
CTn_i =response parameter for Constant Tool n and formation
component i
Index
As with all other tools the user must supply an uncertainty ( CTn_UNC). The units
used in CTn_xxxx determine the units for CTn_UNC.
Although the units used for constant tools are arbitrary, it is easiest to think of them
as porosity units, especially when setting the uncertainty. If, for example, the
CTn_xxxx parameters have values like 20 and -100, then CTn_UNC would have a
value like 1.5. Similarly, if CTn_xxxx parameters had values of 0.20 and -1.00, then
CTn_UNC would be on the order of 0.015.
Unlike other tools, the value of the Constant Tool is supplied as a parameter (for
example, CT1 = 0), rather than a data-driven curve. Using Constant Tools is best
illustrated by the following examples, where spectral gamma ray data (from the NGS
tool) are available on one well but not on another. The model used for the well with
NGS tool data is summarized in Table 16.
Table 16 Model Using Data from NGS Tool
Model
QUAR
Tools
RHOB
NPHI
ORTH
ILLI
XWAT
XOIL
WWK
WWTH
CXDC
∑Volumes
On the well without NGS tool data, the thorium (WWTH) and potassium (WWK)
information must be replaced by external knowledge in order to solve for both illite
and orthoclase. One way of handling the problem is to replace QUAR and ORTH
with SAND to reflect a combination of quartz and orthoclase (so GR_SAND would
be higher for this well than GR_QUAR for the previous one).
An alternate approach is to use a Constant Tool. Assume that the orthoclase-to-quartz
ratio of the first well is about 20%, and the geology of the two wells is similar. That
knowledge can be entered into the ELANPlus program by means of a Constant Tool:
If
QUAR/ORTH = 20%
then
QUAR = 0.20 * ORTH
and
0 = QUAR – 0.20 * ORTH
or
ELANPlus Theory
76
Parameter Tables
Response Equations
ToC
0 = 100*QUAR – 20*ORTH
That is of the form
CT1 = CT1_QUAR × QUAR + CT1_ORTH × ORTH
(42)
The new model would be as shown in Table 17.
Table 17 Model Using Constant Tool and GR in Place of NGS
Model
QUAR
Tools
RHOB
NPHI
ORTH
ILLI
XWAT
XOIL
CT1
GR
CXDC
∑Volumes
In this example, potassium was replaced by a Constant Tool, and thorium was
replaced by the total GR. If a fairly constant value of uranium was observed in the
first well through zones of interest, then the GR parameters must be adjusted
accordingly. If the uranium varies significantly in zones of interest, this model will
be in error unless the GR was zoned to reflect the variations.
The following parameters were used: CT1 = 0, CT1_QUAR = 100, CT1_ORTH = 20, and CT1_UNC = 1.5. The interpretation model could be made more
sophisticated by determining an orthoclase ratio for the sands and shales and
defining different Constant Tools for each model.
Parameter Tables
The response equations previously described require fluid and rock or mineral
parameters to function. There are no default values for rocks and for many fluids.
Fluid parameters are dependent on hydrocarbon type and water salinity. The
Parameter Calculator should be used to determine the different fluid parameters.
Rocks (sandstone, shales, carbonates, etc.) are composed of undefined mixtures of
minerals. The classical interpretation techniques are based on rocks. The analyst
chooses the required parameters from some technique, such as crossplots.
Minerals, on the other hand, are more well known and generally have defined values.
For example, there is very little debate over the composition of quartz. Clay
minerals, though, are an exception.
Tables 18, 19, and 20 provide most of the parameter values needed to run a mineralbased interpretation, using the ELANPlus program. These are kept as default
parameter values in the ELANPlus data base.
ELANPlus Theory
77
Index
Parameter Tables
Response Equations
Some default values in the data base were updated according to work that was done
in Schlumberger-Doll Research center in Ridgefield, Connecticut, U.S.A., and
documented by M.M. Herron and A. Matteson in their paper, “Elemental
Composition and Nuclear Parameters of Some Common Sedimentary Minerals,”
Nuclear Geophysics, 1993, Vol. 7, No. 3, pp 383–406.
ToC
Index
Two sets of values are listed for chlorite and illite in the following tables. The second
sets are retained from previous version of this document for poorly ordered chlorite
and well-ordered illite.
Table 18 gives the Dry Elemental Weight Percent of various minerals commonly
found in sedimentary rocks.
Table 18 Common Sedimentary Minerals Dry Elemental Weight Percent
Si
Ca
Fe
46.75
0.20
0.60
30.00
30.00
0.00
0.00
0.00
0.40
21.16
18.20
23.09
20.80
14.00
13.30
0.10
39.40
21.60
0.10
2.30
29.44
23.28
0.00
0.28
0.10
0.20
0.49
0.10
0.70
0.20
0.00
0.10
0.30
0.10
0.10
0.00
0.00
46.55
39.98
1.30
13.56
15.52
0.40
20.80
16.28
24.80
24.40
0.50
0.36
4.80
3.90
0.00
0.00
4.50 10.50
5.50 14.20
Montmorillonite 26.40
1.40
2.00
0.00
0.66
Quartz
Calcite
Dolomite
Orthoclase
Albite
Anhydrite
Gypsum
Pyrite
Siderite
Muscovite
Biotite
Glauconite
Kaolinite
Chlorite
(poorly
ordered)
Illite
(well-ordered)
S
K
Al
Mg
weight %
0.00 0.00 0.00 0.00
0.00 0.00 0.10 0.20
0.10 0.00 0.10 12.30
0.00 10.20 9.90 0.10
0.00 0.50 11.80 0.10
23.55 0.00 0.00 0.00
18.62 0.00 0.00 0.00
53.45 0.00 0.00 0.00
0.00 0.00 0.70 3.01
0.00 7.80 19.10 0.10
0.00 7.20 6.03 7.72
0.00 5.94 4.35 2.10
0.00 0.10 20.40 0.10
0.00 0.40 9.60 4.80
0.00 0.03 9.58 12.10
9.10
Ti
Gd
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
1.48
0.09
1.10
1.30
0.00
0.00
0.50
1.30
0.30
0.20
0.00
0.00
0.00
0.50
0.00
0.20
4.20
4.30
4.80
1.20
1.69
0.50
0.30
3.70 12.30
4.80
-
-
2.20
0.10
7.80 26.00
-
Th
ppm
0.00
0.00
0.10
1.10
0.00
0.00
0.00
0.00
0.40
0.00
1.50
3.00
19.30
11.40
-
The General Parameters listed in Table 19 are the most frequently used parameters
that are required by the ELANPlus program. Some were derived from parameters
listed in Table 18.
Note: In Table 19, U represents the Volumetric Photoelectric Factor (unlike Table 18
and Table 20, where the U stands for Uranium).
ELANPlus Theory
78
U
0.10
1.40
0.90
0.40
0.00
0.50
0.30
0.00
0.50
0.70
0.70
5.40
3.20
3.60
-
7.10
Parameter Tables
Response Equations
ToC
Except for Wet Clay Porosities WCLP, no default values are provided for salinitydependent parameters. Use the appropriate formation water salinity or resistivity to
compute those parameters with the Parameter Calculator.
Index
Table 19 General Parameters
Quartz
Calcite
Dolomite
Halite
Orthoclase
Albite
Anhydrite
Gypsum
Pyrite
Siderite
Muscovite
Biotite
Glauconite
Kaolinite
Chlorite
(poorly
ordered)
Illite
(well-ordered)
Montmorillonite
ARHOB
g/cm3
2.65
2.71
2.85
2.05
2.57
2.62
2.96
2.32
5.00
3.93
2.86
3.09
2.96
2.63
3.01
2.82
RHOB
g/cm3
2.65
2.71
2.85
2.04
2.57
2.60
2.98
2.35
4.99
3.88
2.85
3.04
2.65
2.55
2.81
2.63
WCLP
p.u.
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
15.6*
5.8*
10.1*
11.1*
NPHI
p.u.
-6.0
0.0
1.8
-3.0
-1.0
-1.0
-2.0
54.0
0.8
18.4
24.0
13.4
41.0
50.7
58.3
59.6
ENPI
p.u.
-8.0
0.0
0.3
20.0
-1.0
-1.0
5.6
58.0
16.5
11.1
10.7
8.6
36.0
49.0
71.0
49.6
2.79
2.78
2.78
2.61
2.49
2.02
10.4*
15.6*
42.5*
35.2
47.9
65.0
28.0
37.9
60.0
U
5.0
14.1
9.1
9.7
8.7
5.6
14.95
9.46
82.06
71.6
11.5
21.6
16.5
5.1
21.7
14.96
SIGM
c.u.
4.7
7.4
6.92
750
15.3
11.4
11.1
20.0
90.0
54.2
95.3
54.1
90.0
21.9
43.7
34.0
EATT
dB/m
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
*
*
*
*
TPL
ns/m
7.2
9.8
8.7
8.2
7.6
7.6
8.4
6.8
8.9
8.9
7.8
12.0
11.0
11.0
11.0
9.9
7.55
4.4
41.0
66.0 †
20.0
*
*
*
14.0
14.0
16.0
* → Salinity-dependent parameters
† →
Marine source
The ARHOB values in Table 19 are the true dry mineral densities. The RHOB
values are the wet densities as measured by the density tools.
The thermal neutron NPHI values are only approximations because of the presence
of unpredictable neutron absorbers. The values were derived from the epithermal
neutron ENPI data by adding a maximum-thermal-absorber-effect of 10 p.u. to the
clay endpoints. That translates into a 10% to 20% correction in normal clay and
porosity ranges.
ELANPlus Theory
79
Parameter Tables
Response Equations
ToC
The Wet Elemental Weight Percent values in Table 20 are for spectral tools (NGT,
HNGS, ECS, RST, GST).
Table 20 Common Sedimentary Minerals Wet Elemental Weight Percent
Si
Ca
Fe
46.75
0.20
0.60
30.00
30.00
0.00
0.00
0.00
0.40
21.16
18.20
21.74
20.32
13.50
28.60
0.10
39.40
21.60
0.10
2.30
29.40
23.28
0.00
0.30
0.10
0.20
0.47
0.10
0.67
0.70
0.00
0.11
0.31
1.49
1.75
0.00
0.00
46.50
48.60
3.97
14.44
15.16
3.18
21.35
22.88
23.81
48.30
0.48
1.10
6.02
7.08
0.00
0.00
4.32 10.08
5.62 14.51
1.15
Montmorillonite 20.94
1.11
2.60
0.00
0.48
Quartz
Calcite
Dolomite
Orthoclase
Albite
Anhydrite
Gypsum
Pyrite
Siderite
Muscovite
Biotite
Glauconite
Kaolinite
Chlorite
(poorly
ordered)
Illite
(well-ordered)
ELANPlus Theory
S
K
weight %
0.00 0.00
0.00 0.00
0.07 0.00
0.00 10.20
0.00 0.50
23.60 0.00
18.62 0.00
53.50 0.00
0.00 0.00
0.00 7.80
0.00 7.20
0.00 5.55
0.00 0.10
0.00 0.67
0.00 3.00
Al
Mg
Gd
0.00
0.00
0.01
0.00
0.00
0.00
0.00
0.00
0.00
0.00
1.50
0.09
1.07
1.25
0.00
0.00
0.50
1.30
0.30
0.20
0.00
0.00
0.00
0.50
0.00
0.20
3.95
4.20
4.63
3.55 11.81
18.00
-
4.61
-
0.48
8.40
1.73
0.10
6.19 20.63
5.63
0.00 0.00
0.10 0.20
0.10 12.30
9.90 0.10
11.80 0.10
0.00 0.00
0.00 0.00
0.00 0.00
0.70 3.00
19.10 0.10
6.00 7.70
4.05 1.98
19.93 0.10
9.25 4.63
10.58
-
7.22
-
Th
ppm
0.00
0.00
0.10
1.10
0.00
0.00
0.00
0.00
0.40
0.00
1.50
2.82
18.86
10.99
15.00
Index
Ti
80
U
0.10
1.40
0.90
0.40
0.00
0.40
0.30
0.00
0.50
0.70
0.70
5.08
3.13
3.47
-
ToC
Index
Chapter 4
Conductivity Models
The ELANPlus program supports the water saturation equations listed in Table 21.
Table 21 Water Saturation Models
Saturation Model
Undisturbed Zone
Flushed Zone
Linear conductivity
CUDC
CXDC
Dual Water
CUDC_DWA
CXDC_DWA
Indonesia
CUDC_IND
CXDC_IND
Nigerian
CUDC_IND
CXDC_IND
Simandoux
CUDC_SIM
CXDC_SIM
Waxman-Smits
CUDC_WS
CXDC_WS
These equations represent different models for the correction of the effects of clay
conductivity on the calculation of water saturation. For each ELANPlus model
(Solve process) being used, choose the water saturation model with which you feel
most comfortable. To compare the effects of the different conductivity models of
Table 21, create several Solve processes, each of which differs from the others only
in the conductivity equation(s) used.
The Waxman-Smits and Dual Water models describe the same data base and
therefore have many similarities. There are differences in the saturation exponents a
and m, though the main difference is the way in which the two models describe clay
conductivity.
ELANPlus Theory
81
Parameter Tables
Conductivity Models
The Dual Water model uses clay-water conductivity (CUDC_UBWA) and claywater porosity (WCLP). The Waxman-Smits model uses cationic exchange capacity
of clays (CEC_xxxx). Both models, in their basic form, express clay conductivity in
Qv (charge per unit volume).
There is a WCLP parameter in the Waxman-Smits model for partitioning the wet and
dry clay fractions in the final output. This parameter does not affect the computation
of water saturation. Translation of parameters from the Waxman-Smits to the Dual
Water model and the reverse are supported in the Parameter Calculator.
The Linear Conductivity model is a simplification of the Dual Water model. It is
special in that it is the only model that allows for the concept of conductive minerals
that are nonclay minerals.
The Indonesian model and Nigerian model are very similar. Only two parameter
changes are needed to convert one equation to the other.
In ELANPlus processing, water saturation is not explicitly determined. Instead the
ELANPlus program solves for volumes of water and hydrocarbon, which can then be
converted to conventional water saturation through a Function process, using the
equation
UWAT + UIWA + USFL w
S w = ----------------------------------------------------------------------------------------------------------------------------------------- (43)
UWAT + UIWA + USFL w + UOIL + UGAS + USFL hc
where:
UWAT = volume of “free” water in the undisturbed zone
UIWA = volume of irreducible water in the undisturbed zone
USFLw = volume of special fluid with a water attribute in the
undisturbed zone
UOIL = volume of oil in the undisturbed zone
UGAS = volume of gas in the undisturbed zone
USFLhc = volume of special fluid with a hydrocarbon attribute in the
undisturbed zone
The relationship between the flushed zone and uninvaded zone can be confusing.
With Constant Tools the relationship is loosely fixed. With flushed-zone resistivity
(Rxo) and deep resistivity (Rt) measurements there can be strong disagreements
between the two solutions.
ELANPlus Theory
82
ToC
Index
Parameter Tables
Conductivity Models
•
In the volumetric display, moved hydrocarbons means that S
•
Negative moved hydrocarbons (moved water) means that S
ToC
w ≤ S xo .
w ≥ S xo .
The flushed zone can have a profound effect on the calculation of water saturation.
All log measurements, except deep resistivity and a few other deep reading devices,
are dominated by the flushed zone.
ELANPlus logic assumes that the volume of minerals and associated porosities are
the same in the flushed zone and the uninvaded zone, but it does not make any
assumption about the fluid volume relationships. Computing hydrocarbon volumes
in the uninvaded zone does not mean that hydrocarbons are present in the flushed
zone (as in the case of deep invasion).
Any interpretation system—and the ELANPlus system is no exception—must know
the volume and type of hydrocarbon in the flushed zone in order to make the proper
hydrocarbon corrections (especially gas corrections) to the porosity measurements.
There are two ways for the program to establish the flushed-zone volume and type of
hydrocarbon: (1) measurements such as Rxo and density-neutron that allow for the
direct solution and (2) Rxo information supplied by the user.
Warning: The ELANPlus program believes what the user tells it.
Flushed-zone computed values can have a dramatic effect on the uninvaded zone and
vice versa, especially when gas is part of the solution. One example is a model,
solving for gas in a gas zone, that finds no gas effect on the density-neutron
measurements yet has a Constant Tool defining a similar volume of hydrocarbons in
both flushed and uninvaded zones.
Using balanced uncertainties, the ELANPlus program will see two tools (density and
neutron) indicating no gas while the deep conductivity (CUDC) indicates gas. Two
against one in an optimized solution will have an answer weighted towards the two
tools that agree (no gas).
This is an example of a case in which the model does not fit the data. The ELANPlus
program will warn you that the tools are inconsistent in this case by showing a
reconstructed conductivity that does not match the measured conductivity.
For more information, see Chapter 8, Quality Control.
To correct the problem you can either correct the flushed-zone hydrocarbon model or
lower the uncertainty of the deep conductivity (CUDC_UNC). If CUDC_UNC is
lowered, the deep saturation will be more correct but the density-neutron will not
reconstruct and their “corrected porosity” values could be in error.
ELANPlus Theory
83
Index
No Rxo Tool
Conductivity Models
ToC
No Rxo Tool
If no shallow-resistivity device is available, the ELANPlus system still needs to know
the distribution of the flushed-zone fluids to accurately predict porosity. Computation
of the flushed-zone fluids can be done by assuming some relationship between
undisturbed-zone and flushed-zone fluids
One common relationship is the Tixier assumption that S
1⁄
5
xo = S w
In ELANPlus processing, an approximation of the Tixier assumption can be
formalized with the use of a Constant Tool (CTn).
Experience dictates that you should assume a hydrocarbon ratio of flushed-toundisturbed zone rather than water ratio. For example, assume that the ratio of
XOIL/UOIL is 0.2. That can be rewritten as
⇒
XOIL
-------------- = 0.2
UOIL
(43-1a)
XOIL = 0.2 × UOIL
(43-1b)
⇒
0 = – 1.0 × XOIL + 0.2 × UOIL
⇒
0 = CT1 = CT1_XOIL × XOIL + CT1_UOIL × UOIL(43-1d)
(43-1c)
Table 22 shows the relevant parameter values necessary to establish an
XOIL/UOIL ratio of 0.2 using the constant tool CT1. All other CT1 parameter values
would be 0.0.
Table 22 Constant Tool Parameter Values for an
XOIL/UOIL Ratio of 0.2
CT1
CTl_XOIL
CT1_UOIL
CT1_UNC
0.0
–1.0
0.20
0.015
The equation is equally valid if the signs are reversed, CT1_XOIL = 1.00 and
CT1_UOIL = –0.20. In addition, the same result is achieved if CT1_XOIL,
CT1_UOIL and CT1_UNC are multiplied by a constant such as 100. They would
then become –10.0, 20, and 1.5, respectively.
ELANPlus Theory
84
Index
Oil and Gas Model with Rxo
Conductivity Models
ToC
Oil and Gas Model with Rxo
When both flushed-zone and undisturbed-zone oil and gas are part of the model, two
additional equations are required. One defines the ratio between oil and gas; the
other defines the relationship of the oil and gas ratio in the flushed and the
undisturbed zones.
The neutron log is the conventional measurement used to distinguish between gas
and oil. (Deep conductivity describes the total amount of hydrocarbons.) However,
there is still a need to relate the oil and gas ratio between the flushed and uninvaded
zones.
That need is handled with an internal tool similar to a Constant Tool (no external
data curve used as an input). However, unlike a Constant Tool, this equation is
nonlinear. It is referred to as the Equal Hydrocarbon Tool, EQHY. It assumes that
the hydrocarbon density in the flushed and undisturbed zones is the same. In other
words, the gas-oil ratio (GOR) is the same.
XGAS
UGAS
---------------------------------------------------------- = ---------------------------------------------------------XGAS + XOIL + XSFL
UGAS + UOIL + USFL
(44)
To avoid a divide-by-zero problem at zero porosity, the equation is actually
implemented as follows:
0 = XGAS × ( UOIL + USFL ) – UGAS × ( XOIL + XSFL )
(45)
In Equations (44) and (45), special fluids in the flushed-zone (XSFL) and
undisturbed zone (USFL) are included only if they have a hydrocarbon attribute.
It should be emphasized that solving for gas, oil, and water at the same depth is a
tricky problem even under ideal conditions. The presence of clay in a shaly sand
environment causes the neutron-density to respond in a manner opposite that of gas.
Therefore, some other tool must accurately resolve the clay volume in order to
quantitatively distinguish between gas and oil. Experience has shown that EQHY
should be used only when an Rxo measurement is in the model.
Oil and Gas Model without Rxo
Previously when oil was in the model and no Rxo device was present, a constant
equation set the ratio of flushed-zone to undisturbed-zone oil. Likewise, when both
oil and gas are in a model, and there is no Rxo device, Constant Tools are needed.
Specifically, two Constant Tools are needed to replace CXDC and EQHY, as follows:
ELANPlus Theory
85
Index
Water Saturation, Linear Conductivity
Conductivity Models
ToC
CT1 = CT1_XOIL × XOIL + CT1_UOIL × UOIL
or
0 = – 1.0 × XOIL + k × UOIL
(46)
CT2 = CT2_XGAS × XGAS + CT2_UGAS × UGAS
or
0 = – 1.0 × XGAS + k × UGAS
(47)
Index
and
Note: Use the same ratio of flushed-zone to undisturbed-zone oil as is used for gas,
which is equivalent to the assumption made by the EQHY equation. Numerical
stability is not maintained when the EQHY equation is used without an Rxo device.
To stay out of trouble, stick with two constant equations.
For more information, see "No Rxo Tool" on page 84.
Water Saturation, Linear Conductivity
Following is a very simple example of how water saturation is formulated into a
conductivity equation. For the case of no clay, the linear conductivity equation can
be derived from the classic water saturation equation.
This derivation is written in deep conductivity terms (such as CUDC or UWAT). To
express it in flushed-zone terms, replace the U’s with X’s (CXDC, XWAT).
a × Rw
n
S wt = -------------------m
φ × Rt
(48)
Assuming a =1 and m = n = 2 yields
ELANPlus Theory
86
Water Saturation, Linear Conductivity
Conductivity Models
ToC
Rw
2
( φ × S w ) = -------Rt
(48-1a)
Index
Rw
UWAT = -----------Rt
⇒
1
1
---------- = ------------ × UWAT
Rw
Rt
⇒
⇒
(48-1b)
CUDC =
(48-1c)
CUDC_UWAT × UWAT
(48-1d)
Or in the general ELANPlus program form
nfc
CUDC =
∑
CUDC_i × Vi
(49)
i=1
where:
nfc = number of formation components
CUDC_i = conductivity of component i
Vi = volume of component i
The linear conductivity equation is used because the influence of each of the terms
on the volumetric results is more easily observed with this equation. However, what
is shown for the linear conductivity equation applies equally to the nonlinear
conductivity equations.
The complete equation with mineral conductivities included is
nf
CUDC =
∑
ns
CUDC_i
Vi × --------------------- +
a
i=1
∑ Vj ×
CUDC_ j
(50)
j=1
where:
nf = number of undisturbed-zone formation components that are
fluids
Vi = volume of undisturbed-zone fluid i
ELANPlus Theory
87
Water Saturation, Linear Conductivity
Conductivity Models
ToC
CUDC_i = conductivity of undisturbed-zone fluid i
a = the Archie fluid factor
Index
ns = number of formation components that are solids
Vj = volume of solid component j
CUDC_j = conductivity of solid component j
Note: Unlike any other saturation equation, linear conductivity allows any mineral to
have conductivity associated with it. An example would be the conductivity of pyrite
(CUDC_PYRI) or the conductivity of illite
(CUDC_ILLI). The conductivity value that was entered for the CUDC_xxxx
parameter represents the total conductivity of the rock and any associated fluids.
Often for a clay it is more convenient to supply a value for wet clay porosity
(WCLP) and apparent bound-water conductivity (CBWA) than it is to compute the
conductivity of a clay-water mixture. The ELANPlus application includes an
alternative formulation to allow clay conductivities to be specified in this manner.
For more information, see the Conductivity Input, Hierarchy.
Note that the ELANPlus program does not have WCLP parameters for nonclays.
nf
CUDC =
∑
ns
CUDC_i
Vi × --------------------- +
a
i=1
∑ Vj ×
CUDC_ j
j=1
(51)
nc
+
∑ Vk × WCLP_k ×
CBWA_k
-----------------------a
k=1
where:
ns = numberofsolidformationcomponents,includingclaysfor
valid CUDC_xxxx exists
which a
nc = number of clays that have no valid CUDC_xxxx, but have
WCLP_xxxx and CBWA_xxxx
valid
Vk = volume of clay k
WCLP_k = wet clay porosity of clay k
ELANPlus Theory
88
Water Saturation, Linear Conductivity
Conductivity Models
ToC
CBWA_k = apparent bound-water conductivity of clay k
a = the Archie fluid factor
This water saturation equation is good for illustration, but it is only an
approximation. Its validity is limited to when the conductivity of formation water
and clay water are similar or when there is no clay.
For more information see Linear Conductivity Equation.
In addition to the main saturation equation, the ELANPlus program applies internal
equations. One equation, which is always in effect, forces the sum of all volumes to
1.0:
nfc
1 =
∑ Vi = QUAR + ILLI + XOIL + XWAT + …
(52)
i=1
The other internal equation, applied only when undisturbed-zone fluids are present,
forces the sum of fluid volumes in the flushed zone and undisturbed zone to be equal:
nxf
0 =
nuf
∑ Vi – ∑ V j
i=1
(53)
j=1
where:
nfc = number of formation components
nxf = number of fluids in the flushed zone
nuf = number of fluids in the undisturbed zone
ELANPlus Theory
89
Index
Conductivity Input, Hierarchy
Conductivity Models
ToC
Conductivity Input, Hierarchy
There are several ways to enter conductivity of clays into the ELANPlus program.
They are listed later in this section for each water saturation equation, in their
hierarchical order.
When there are two possible input types, do not enter both. Those designated (A)
take precedence over those designated (B).
To ensure that a parameter is not used, insert the representation of an Absent value
used in the ELANPlus system. (The default is –999.25.) The parameter modifier,
_clai, represents either a generic clay, such as CLA1, or other clays, such as illite
(ILLI).
For Global Parameter Clay = Wet
For global parameter Clay = Wet, there are two groups of models: (1) WaxmanSmits, and (2) Dual Water, Linear Conductivity, Indonesian, Nigerian, and
Simandoux.
Waxman-Smits
There is only one possible input type for Waxman-Smits:
(A) CEC_clai
Dual Water, Linear Conductivity, Indonesian, Nigerian,
Simandoux
For the Dual Water, Linear Conductivity, Indonesian, Nigerian, and Simandoux
models, there are three possible input types:
(A) CUDC_UBWA
(B) CUDC_clai
(C) CBWA_clai, WCLP_clai
For Global Parameter Clay = Dry
For global parameter Clay = Dry, there are two models, Dual Water and Linear
Conductivity, with two possible input types:
(A) CUDC_UBWA
(B) CBWA_clai
ELANPlus Theory
90
Index
Conductivity Equations
Conductivity Models
ToC
Beware of CUDC_clai
Beware: CUDC_clai does not equal CBWA_clai because
Index
CUDC_clai is affected by both rock and fluids, similar to Rt.
CBWA_clai is defined by fluids only, like Rw. (Add WCLP_clai
and m, and it becomes CUDC_clai.).
Conductivity Equations
The nonlinear conductivity equations differ mostly in the way they handle clay. The
effect that clay has on the conductivity measurement has been the subject of
numerous publications. The effect is summarized in .
Linear Zone
Co
Nonlinear
Zone
X
an
e
“Cl
”
and
e
Lin
S
Cw
F
Cw
The effect of clay on conductivity.
At high salinities, the effect of clay is seen to shift the conductivity of the rock to a
higher value. The higher salinity range where the shift in conductivity is essentially
constant is called the linear region.
At low salinities the effect becomes highly nonlinear; given very fresh waters, the
effect is to lower the conductivity of the rock.
ELANPlus Theory
91
Conductivity Equations
Conductivity Models
In the equations in the following subsections the term USFL stands for Undisturbedzone Special FLuid. Although these equations are written in terms of the undisturbed
zone, you merely replace the U with an X (consistently, of course) to rewrite the
equation for the flushed zone, for example,
CUDC_UWAT ⇒ CXDC_XWAT.
Waxman Smits Equation
Equation (54) shows the theoretical form of the Waxman-Smits equation.
*
BQ v
1 m n 
C t = --- φ t S wt  C w + -----------
a
S wt 

(54)
If the term involving Qv is dropped, the Equation (54) reduces to the familiar Archie
water saturation equation. See Table 23 for the parameters used in it.
Table 23 Waxman-Smits Conductivity Parameters
Name
Unit
Default
Symbol
Description
A
—
1.0
a
Constant, a in Archie equation
ARHOB_clai
g/cm3
†
ρdcli
Actual density of dry clay i
CEC_clai
—
†
CECdcl
i
Cation exchange capacity of clay i
CUDC_UWAT
mho/m
Absent
Cuwa
Undisturbed-zone conductivity of formation water
CUDC_UIWA
mho/m
Absent
Cuiw
Undisturbed-zone conductivity of irreducible water
CUDC_USFL
mho/m
Absent
Cusf
Undisturbed-zone conductivity of special
fluid
M_WS
—
1.8
mws
Parameter for m* (Qv) computation
C_WS
—
1.0
cws
Parameter for m* (Qv) computation
N
—
2.0
n
Saturation exponent
WCLP_clai
p.u.
†
φ cli
Wet clay porosity of clay i
CUDC_UNC
mho/m
0.065
σ CUDC
Uncertainty of the CUDC curve data
†
→ See Table 24, Default Values Used for Clay.
Table 23 Notes:
1 All input data are at downhole conditions.
2 Replace any U or u with an X or x for the flushed-zone equation.
ELANPlus Theory
92
ToC
Index
Conductivity Equations
Conductivity Models
Clays are made up of molecular sheets of silica tetrahedrons (silica with four
oxygens and/or hydroxyls, whatever is needed to balance the structure) and
aluminum octahedrons (aluminum with six oxygens and/or hydroxyls). Within the
clay lattice there is substitution of Al+3 for Si+4 in the tetrahedron and Mg++ for
Al+3 in the octahedron, resulting in a net negative charge imbalance.
Additionally, there are broken bonds around the edges (at the end of the horizontal
sheets of silica tetrahedrons and aluminum octahedrons) of the clay particle,
contributing to the charge imbalance. The smaller the clay particle, the greater the
number of broken bonds.
Nature requires clays to be electrically neutral. Electrical neutrality is maintained by
positive ions (cations or counterions) being adsorbed on the exterior of the clay
particle. The cations are typically Ca++, Mg++, K+ or Na+. When submerged in
water, these ions are free to float about and exchange with other positive ions.
The counterion charge per unit pore space is defined as Qv.
ρ dcl V dcl CEC dcl
 meq
Counterions
Qv  ---------- = --------------------------------------------- = --------------------------------------φt
Total pore space
 cm 3
(54-1)
The unit meq stands for milli-ion equivalent and is a unit of charge. An ion
equivalent is the amount of charge in a mole of protons (6.023 × 1023 protons times
1.602 × 10-19 coulombs/proton).
The counterions per unit of pore space will depend on the amount of clay and the
type of clay, input to the program via the CEC_xxxx parameter for each clay. In
CEC you can set the units of meq per gram of dry clay.
Table 24 shows the default values for clay parameters used by ELANPlus logic:
Table 24 Default Values Used for Clay
Parameter
Illite
Glauconite
Kaolinite
Chlorite
Smectite
ARHOB
2.79
2.96
2.59
2.82
2.78
CEC
0.25
0.23
0.09
0.15
1.00
WCLP
15.6
15.6
5.8
10.1
42.5
As shown in Table 24, CEC is related to the WCLP (Wet Clay Porosity) parameter.
The wet clay porosity is part of the Dual Water model and will be discussed in the
following section.
ELANPlus Theory
93
ToC
Index
Conductivity Equations
Conductivity Models
The CEC values in Table 24 were determined by taking the average of the literature
values. To give you an idea of the precision of the CEC values, the literature values
for illite ranged from 0.1 to 0.4, resulting in an average value of 0.25.
The product BQV in Equation (54) is the conductivity of the clay counterions. The B
term is known as the equivalent conductivity, which is measured in units of mho/m
per meq/cm3. It is a function of temperature and the salinity of the water surrounding
the clay.
Juhasz, with Shell, developed the following empirical formula to use for the clay
counterion equivalent conductivity. Temperature is expressed in degrees Celcius.
2
– 1.28 + 0.225 Temp – 4.059 × 10 –4 Temp
B = -------------------------------------------------------------------------------------------------------------1.23
1 + R wa ( 0.045 Temp – 0.27 )
(55)
The equivalent conductivity is basically a quadratic function of temperature. For very
fresh waters the Rwa term in the denominator becomes very large, which causes the
equivalent conductivity to approach 0.
If you examine Equation (54), it appears that for the same porosity, adding clay to
the system can only increase the conductivity. Actually, that is not the case, because
of the parameter m*, which has been found to increase with the Qv of the formation.
The cementation factor varies much more strongly with the Qv of the formation when
using the Waxman-Smits model than with the Dual Water model. An empirical
algorithm relating the cementation factor to the Qv and porosity for the WaxmanSmits model is given by
m* = m ws + C ws ( 1.128Y + 0.22 ( 1 – e
– 17.3Y
))
(56)
Qvφ t
Y ≡ -------------1 – φt
(57)
As an example assume that the water resistivity is 0.04. (Conductivity is 25.0.) For a
20% porosity formation with no clay, the conductivity computes to be 1.38, using an
m* of 1.8.
Assume that the temperature is 60 C. The equivalent conductivity computes to be
10.75. Retain the same porosity, but change the matrix so that it is 20% dry clay.
Assume the clay is montmorillonite and has a CEC value of 1.0 and a density of
2.78.
ELANPlus Theory
94
ToC
Index
Conductivity Equations
Conductivity Models
The Qv and Y values are 2.78 and 0.695, respectively. That translates to an m* value
of 2.8. Using the new cementation value of 2.8, the conductivity computes to be
0.36, a much smaller value than the original 1.38.
Index
One more important factor needs to be mentioned about the Waxman-Smits
equation. Rather than using Equation (54) as it is written, the ELANPlus program
takes the square root of both sides.
Two advantages arise from taking the square roots. First, the square root makes the
variation with water volume closer to linear, resulting in a more numerically stable
and faster equation for the nonlinear solver. Second, the same uncertainty parameter
(CUDC_UNC) can be used for all conductivity equations. Because of these
advantages, the ELANPlus program not only takes the square root of Equation (54),
it takes the square root of all nonlinear equations.
Dual-Water Equation
The theoretical form of the Dual Water equation is
1 m n
C t = --- φ t S wt
a
 S – αV H Qv
wt
Q 
βQv
 ------------------------------------ C + ----------
 w S
S wt
wt


(58)
which can be rewritten in bound-water terms as
1 m n
C t = --- φ t S wt
a
S wb
 S wt – S wb
 --------------------------- C w + C bw ----------S wt
S wt 

(59)
by using these substitutions
ELANPlus Theory
ToC
β
C bw ≡ ------------H
αV Q
(60)
H
XBWA
S wb ≡ ------------------ = αV Q Qv
φt
(61)
95
Conductivity Equations
Conductivity Models
ToC
See Table 25 for the parameters used in the equation.
Table 25 Dual Water Conductivity Parameters
Name
Unit
Default
Symbol
Description
A
—
1.0
a
Constant, a in Archie equation
ARHOB_clai
g/cm3
—
ρdcli
Actual density of dry clay i
CBWA_clai
mho/m
Absent
Cbwi
Bound-water conductivity for clay i
CUDC_clai
mho/m
Absent
Cucli
Conductivity of clay i
CUDC_UBWA
mho/m
Absent
Cubw
Undisturbed-zone bound-water conductivity
Used only when Clay = DRY
CUDC_UWAT
mho/m
Absent
Cuwa
Undisturbed-zone conductivity of formation water
CUDC_UIWA
mho/m
Absent
Cuiw
Undisturbed-zone conductivity of irreducible
water
CUDC_USFL
mho/m
Absent
Cusf
Undisturbed-zone conductivity of special fluid
CUDC_PARA
mho/m
Absent
Cupar
Undisturbed-zone conductivity of fluid
contributing parallel conductivity
M_DW
—
1.8
mdw
Parameter for m (Qv) computation
C_DW
—
1.0
Cdw
Parameter for m (Qv) computation
N
—
2.0
n
Saturation exponent
WCLP_clai
p.u.
†
φcli
Pure wet clay porosity of clay i
CUDC_UNC
mho/m
0.065
σ CUDC
Uncertainty of the CUDC curve data
†
Index
→ See Table 24 on page 93.
Table 25 Notes:
1 All input at downhole conditions.
2 Replace any U or u with an X or x, respectively, for the flushed-zone
equation.
The relationships between β, V Q , Qv and Cbw, Swb are more familiar to
the log analyst. The β has the same meaning as the B term of the Waxman-Smits equation, but it uses an algorithm that is a function of temperature only:
H
Temp ( °C ) + 8.5
β = ---------------------------------------22.0 + 8.5
ELANPlus Theory
(62)
96
Conductivity Equations
Conductivity Models
H
V Q is called the clay water volume factor.
ToC
It can be thought of as a volume of bound water per counterion charge. It has a value
of 0.28 cm3/meq at room temperature. In the Waxman-Smits equation B decreased
with decreasing salinity.
H
In the Dual Water equation V Q increases with decreasing salinity, causing the
conductivity of bound water to decrease. Both models predict a decreasing clay
conductivity at low salinities.
To compute the volume of bound water (XBWA) and the bound-water saturation
(Swb), ELANPlus processing uses the wet clay porosity parameter for each of the
clays:
nc
XBWA =
∑ Vi × WCLP_i
(63)
i=1
H
αV Q ρ dcl CEC dcl
i
i
WCLP_cla i = ------------------------------------------------------------H
1 + αV Q ρ dcl CEC dcl
i
i
(64)
As with Waxman-Smits, the m in the Dual Water equation is dependent on Qv,
although somewhat differently. The mdw has a default value of 1.8. To use a fixed m
= 2, set Cdw = 0 and mdw to 2.0.
m = m dw + C dw ( 0.258Y + 0.2 ( 1 – e
– 16.4Y
))
Qvφ t
Y ≡ -------------1 – φt
(65)
(66)
In ELANPlus terms, this is
nc
∑ Vi ( 1 – WCLP_i )CEC_i × ARHOB_i
i=1
Y ≡ ------------------------------------------------------------------------------------------------------1.0 – ( V hc + V wf + V bw )
(67)
where:
Vhc = sum of all fluids that are hydrocarbons
ELANPlus Theory
97
Index
Conductivity Equations
water
Conductivity Models
ToC
Vwf = sumofallfluidsthatarenonclaywaters,includingirreducible
Vbw = sum of all clay-bound waters
Index
The Parameter Calculator (selected from the Options menu of the Session Manager)
is a customized program used for computing parameters that are peculiar to
ELANPlus processing. It is capable of computing all of the relevant Dual-Water
parameters shown.
Once again, realize that the square root of the conductivity is used internally by the
nonlinear solver to improve numerical stability and speed.
Linear Conductivity Equation
The Linear Conductivity Equation in its theoretical form is
nc
Cw
 C bw

-------- × V w +
 ----------- × Vi × WCLP_i
a
a


i=1
∑
Ct =
(68)
which can be rewritten in ELANPlus terms as
nf
∑
CUDC =
ns
∑ (V j ×
 Vi × CUDC_i
--------------------- +


a
i=1
CUDC_ j ) (69)
j=1
In Equation (68) the term Vi × WCLP_i represents the quantity of bound
water associated with the various clay volumes defined in the model.
Equation (69) is the more general form of the equation.
Table 26 shows the parameters used in the linear conductivity equation.
Table 26 Linear Conductivity Parameters
Name
Unit
Default
Symbol
Description
A
—
1.0
a
Constant, a in Archie equation
CBWA_clai
mho/m
Absent
Cbwi
Bound-water conductivity for clay i
CUDC_i
mho/m
Absent
Cmini
Conductivity of nonclay component i
CUDC_clai
mho/m
Absent
Cucli
Conductivity of clay i
CUDC_UBWA
mho/m
Absent
Cubw
Undisturbed-zone bound-water conductivity Used
only when Clay = DRY
CUDC_UWAT
mho/m
Absent
Cuwa
Conductivity of undisturbed-zone free water
ELANPlus Theory
98
Conductivity Equations
Conductivity Models
ToC
Table 26 Linear Conductivity Parameters
CUDC_UIWA
mho/m
Absent
Cuiw
Conductivity of undisturbed-zone irreducible water
CUDC_USFL
mho/m
Absent
Cusf
Conductivity of undisturbed-zone special fluid
CUDC_PARA
mho/m
Absent
Cupar
Conductivity of undisturbed-zone fluid contrib-uting
parallel conductivity
M
—
2.0
m
Cementation exponent
N
—
2.0
n
Saturation exponent
WCLP_clai
p.u.
†
φ cli
Pure wet clay porosity of clay i
CUDC_UNC
mho/m
0.065
σ CUDC
Uncertainty of the CUDC curve data
†
→ See Table 24 on page 93.
Table 26 Notes:
1. All input data are at downhole conditions.
2. Replace any U or u with an X or x, respectively, for the flushed-zone equation.
The Linear Conductivity equation is an approximation of the Dual Water equation.
The derivation is presented below. Start with the Dual Water equation and assume
that the cementation factor, m, and the saturation exponent, n, are both 2.0.
1 m n
C t = --- φ t S wt
a
S wb
 S wt – S wb
-----------------------------------C
+
C


bw S
S wt  w

wt
(70)
⇒
1
C t = --- ( V w + V bw ) × ( C w × V w + C bw × V bw )
a
⇒
2
2
C w × V w ( C w + C bw ) × V w × V bw C bw × V bw
C t = ----------------------- + ----------------------------------------------------------------- + ------------------------------ (72)
a
a
a
(71)
The term ( 2 ⁄ a ) × C × C
w
bw × V w × V bw is added to and subtracted from both sides to get
ELANPlus Theory
99
Index
Conductivity Equations
Conductivity Models
ToC
⇒
2
2
C w × C bw
Cw × Vw
C bw × V bw
C t = ----------------------- + 2 ------------------------------ × V w × V bw + -----------------------------a
a
a
(73)
C w + C bw – 2 C w × C bw
+ ------------------------------------------------------------------a
Neglecting the last term results in
⇒
2
1
C t = --- × ( C w × V w + C bw × V bw )
a
(74)
Cw
C bw
-------- × V w + ----------- × V bw
a
a
(75)
or
⇒
Ct =
The last equation is the Linear Conductivity equation used in ELANPlus processing.
It is equivalent to the Dual Water equation, provided the formation is totally clean or
100% bound water, or if
C w + C bw
C w × C bw ≈ -------------------------2
Relation (76) is satisfied when C
(76)
w ≈ C bw .
Indonesian and Nigerian Conductivity Equations
The theoretical form of the Indonesian and Nigerian equations is identical. They
differ only in the numerical values used for the EVCL and MVCL parameters. The
Indonesian equation, the default, uses EVCL = 1.0 and MVCL = 0.5. The Nigerian
equation uses EVCL = 1.4 and MVCL = 0.0.
Ct =
( evcl – mvcl V cl )
C uwa
C ucl V cl
+ ------------------- φ e
a
ELANPlus Theory
n---0.5 ( m + ( mc2 ⁄ φ ) ) V uwa 2
e
---------------φ
(77)
e
100
Index
Conductivity Equations
Conductivity Models
ToC
See Table 27 for the parameters used in the equation.
Table 27 Indonesian and Nigerian Conductivity Equation Parameters
Name
Unit
Default
Symbol
Description
A
—
1.0
a
Constant, a in Archie equation
CBWA_clai
mho/m
Absent
Cbwi
Bound-water conductivity for clay i
CUDC_clai
mho/m
Absent
Cucli
Conductivity of clay i
CUDC_UWAT
mho/m
Absent
Cuwa
Conductivity of undisturbed-zone formation water
CUDC_UIWA
mho/m
Absent
Cuiw
Conductivity of undisturbed-zone irreducible water
CUDC_USFL
mho/m
Absent
Cusf
Conductivity of undisturbed-zone special fluid
M
—
2.0
m
Cementation exponent
MC2
—
0.0
mc2
Porosity correction for cementation factor
EVCL
—
1.0
evcl
Exponent of Vcl in saturation equation
MVCL
—
0.5
mvcl
Vcl multiplier for exponent of Vcl
N
—
2.0
n
Saturation exponent
WCLP_clai
p.u.
†
φ cli
Pure wet clay porosity of clay i
CUDC_UNC
mho/m
0.065
σ CUDC
Uncertainty of the CUDC curve data
†
Index
→ See Table 24 on page 93.
Table 27 Notes:
1 All input data are at downhole conditions.
2 Set EVCL = 1.4 for Nigerian equation.
3 Set MVCL = 0.0 for Nigerian equation.
4 Replace any U or u with an X or x, respectively, and N with EXPO
for the flushed-zone equation.
The flushed-zone Indonesian Conductivity equation is the same for an undisturbed
zone, except that the water saturation exponent parameter is expo rather than n. In
addition, the water and clay parameters require an x rather than a u; for example,
Cxwa, Vxwa rather than Cuwa, Vuwa.
Default values for EVCL and MVCL are 1.0 and 0.5, respectively. To use the
Nigerian equation you must manually change them to 1.4 and 0.0.
ELANPlus Theory
101
Conductivity Equations
Conductivity Models
Observe that the equation blows up when Vcl is 100%, because water and effective
porosity will be zero, so that the equation contains a zero-divided-by-zero term.
Experience has shown that it is a good idea to write a constraint to force the volume
of water to be greater than about 0.5 p.u. when using the Indonesian or Nigerian
equation.
Simandoux Conductivity Equation
The actual form and derivation of the “Simandoux”equation as quoted
and used in ELAN has a long and tortuous history. Enquiring minds
who refer to the original Simandoux paper of 19631 (and can read
French) will find that the paper is in fact a report on laboratory
experiments to measure the complex dialectric constant at 1MHz of
material samples that relate the dialectric constants and losses to water
saturations; and resistivity to porosity, clay content and clay resisitivity,
but for water filled formations only, by the following equations:
K – C∗
2
ζε 1 + ε′ = ζε 1 + εδ + ASw + BSw = Kζε 1 -------------------------------------------------2
( K – C∗ ) 2 + ( G ∗ ⁄ ω )
and
(EQ 1)
G∗ ⁄ ω
1
2
ε″ = --- ( ASw + BSw ) = Kζε 1 -------------------------------------------------2
µ
( K – C∗ ) 2 + ( G∗ ⁄ ω )
(EQ 2)
1
1
p
---- = ------- + -------R
R m R sh
(EQ 3)
and
Where:
ε1 = Dialectric constant of apparatus walls
ε’ = Real dialectric constant of the sample
ε” = Dialectric losses of the sample
δ = Thickness of the ionic double layer
ζ = Dimensionless coefficient, describing the ratio between the active
capacity of the apparatus walls and that of the sample = (K/ε1)/C0
C0= Active capacity of apparatus cell.
ω = Angular frequency of the current 2πf
ELANPlus Theory
102
ToC
Index
Conductivity Equations
Conductivity Models
ToC
µ = Proportionality of the coefficient between ε’and ε”
K= Capacity of the apparatus insulating walls
Index
C*= Apparent capacity of the cell-sample combination
G*= Apparent conductance of the cell-sample combination
A= Constant
B= Constant
p= Clay content of the sample
R= Radius of apparatus external walls in the case of a cylindrical cell
Rm= Resistivity of the equivalent clean formation
Rsh= Clay particle resistance
Sw= Water saturation
It may be seen from the form that the above equation is strictly valid for
laminated layers of clean sand and shale only.For this reason many, in
fact most, saturation models that are variations of a laminated model are
termed “Simandoux”equations.
The actual form of the equation in ELANPlus is based on the same
concept as Simandoux of laminated sand-shale layers but originally
derived from an equvalent parallel resisitor model. This gives:
n
m
φ e Sw
1
Vsh
------ = ( 1 – Vsh ) ----------------------------------- + --------m
Rt
Rsh
aRw ( 1 – V sh )
(EQ 4)
This equation was first modified for a reduced effect in hydrocarbon
bearing formations:
n
m
φ e Sw
˙
Vsh
1
------ = ( 1 – Vsh ) ------------------------------------------ Sw
+
m
Rt
Rsh
aRw ( 1 – V sh )
(EQ 5)
And then for the non-laminar behaviour of real clays:
ELANPlus Theory
103
Conductivity Equations
Conductivity Models
m
ToC
n
c
φ e Sw
Vsh
1
------ = ---------------------------------------------------+
Sw
m–1
c
Rt
Rsh
aRw ( 1 – V sh )
(EQ 6)
Index
This equation was first published in the 1972 Schlumberger Log
Interpretation Principles2 book with the assumption of m=n=2. In his
1985 review of saturation equations Paul Worthington3 classifies the
original Simandoux equation as a “Type 1”, which means it has a form
of Phi x Sw plus linear Vclay, whereas the above equation is classified
as a “Type 2” where Sw is raised to a power and Vclay contains an Sw
term.He attributes this equation to Schlumberger, 1972, with no
reference to Simandoux. However, the 1972 Schlumberger Log
Interpretation Principles book directly references the original
Simandoux paper as the basis of the 1972 equaiton, and also the paper
by Poupon et al4 in 1967 as the development of the model.
Considering that Shale is a mixture of clay and silt, the 1972 Log
Interpretation Principles book uses the standard R0=aRw/φm to obtain:
R clay
R clay
( V sh = V silt + V cl ) → ( I Silt = V silt ⁄ V Sh ) → R sh = -------------------------x = ------------------------------ (EQ 7)
( 1 – V silt ⁄ V sh )x
( 1 – V silt )
where x is empircally found to range between 1.4 and 2.4, depending on
clay distribution type, and Vsilt is the silt index or volume. Combining
equations 6 and 7 and using m, n, and a instead of 2,2 and 1 :
m
n
x
φ e Sw
V cl
1
------ = ---------------------------------------------------------------- Sw
- + ---------------------------------------------(x – c)
c m–1
Rt
R
(
V
+
V
)
aRw ( 1 – ( V cl + V silt ) )
cl
cl
silt
(EQ 8)
‘x’ and ‘c’ were usually taken equal to 2 for practical reasons: it allows
reduction of the equation to a quadratic form that may be solved using a
slide rule or simpe calculator.
With the x = ‘ersh’ and the c = ‘swshe+1’in ELANPlus terminology,
three further assumptions were made :
ELANPlus Theory
•
1) The difference between the exponent of (m-1) and 1.0 for shale
term in the first denominator is not significant enough to consider for
shaley sand, and therefore (m-1) is assumed 1.0.
•
2) The Sw in the second term should be to the power of n/2, not unity.
104
Conductivity Equations
Conductivity Models
•
ToC
3) ‘m’ may vary with porosity as per the Shell formula. The usual
value assumed for mc2 is 0.19.
This produces the form of the equation as implemeted, and with
conductivity replacing resistivity, the Simandoux Conductivity Equation
is written:
Index
n
--2
V
( m + ( mc2 ⁄ φ e ) )  V uwa n
ersh  uma
C ucl V cl  ---------------
 ---------------
C uwa φ e
 φe 
 φe 
C t = -------------------------------------------------------------------------------- + -------------- ------------------------------------------------------------------------- (78)
a
( swshe + 1 )
( ersh – swshe – 1 )
1 – ( V cl + V silt )
( V cl + V silt )
See Table 28 for the parameters used in the equation.
Table 28 Simandoux Conductivity Equation Parameters
Name
Unit
Default
Symbol
Description
A
—
1.0
a
Constant, a in Archie equation
CBWA_clai
mho/m
Absent
Cbwi
Bound-water conductivity for clay i
CUDC_clai
mho/m
Absent
Cucli
Conductivity of clay i
CUDC_UWAT
mho/m
Absent
Cuwa
Conductivity of undisturbed-zone formation water
CUDC_UIWA
mho/m
Absent
Cuiw
Conductivity of undisturbed-zone irreducible water
CUDC_USFL
mho/m
Absent
Cusf
Conductivity of undisturbed-zone special fluid
M
—
2.0
m
Cementation exponent
MC2
—
0.0
mc2
Porosity correction for cementation factor
ERSH
—
1.0
ersh
Exponent to compute Cush from Cucl
SWSHE
—
0.5
swshe
Simandoux shale effect
N
—
2.0
n
Saturation exponent
WCLP_clai
p.u.
†
φ cli
Pure wet clay porosity of clay i
CUDC_UNC
mho/m
0.065
σ CUDC
Uncertainty of the CUDC curve data
†
→ See Table 24 on page 93.
Table 28 Notes:
1. All input data are at downhole conditions.
2. Replace any U or u with an X or x, ERSH with ERSHO, and N with EXPXO for
the flushed-zone equation.
ELANPlus Theory
105
Conductivity Equations
Conductivity Models
The ELANPlus default values for ersh and swshe are 1.0 and 0.5, which correspond
to an ‘x’of 1.0 and a ‘c’of 1.5. This essentially assumes that by default in ELANPlus
the silt behaves in the same manner as clay in relation to the conductivity. The
expected range for ersh was given above as 1.4=>2.4, and that of swshe as 0=>1.0.
The default value of mc2 is 0.0. In tight formations for which this was developped
(actually very low prosity limestones!), the value is usually taken as 0.19 .
The reader is refered to the refernces below and other referecnes in the literature,
such as the SPWLA Shaly Sand Reprint, to determine the applicability of the
equation outside the strict model of a laminated shaley sand, and also the range of
industry accepted values for the above exponents beyond those quoted.
References
1) Simandoux, P., 1963, Measures diélectriques en milieu poroux. Revue de l’I.F.P.,
pp 193-215
2) Schlumberger Log Interpretation Principles/Applications, 1989, pp 8-14,8-15
3) Worthington, P. F. , 1985, The evolution of shaly-sand concepts in reservoir
evaluation. The Log Analyst 26(1) 23-40.
4) Poupon, A., Strecker, I., and Gartner, J., A review of Log Interpretation Methods
used in the Niger Delta. SPWLA Symposium, 1967.
ELANPlus Theory
106
ToC
Index
ToC
Index
Chapter 5
Uncertainties
Uncertainties are a difficult concept for many users, but without some knowledge of
uncertainties you will have a difficult time reaching a believable answer. For a given
situation the correct uncertainties often require a subjective decision by the user.
Actually, there may be more than one mathematically valid answer.
The ELANPlus Solution Method
The ELANPlus program solves the inverse problem by creating the
incoherence function and standard deviation:

1  ( RHOB_REC – RHOB ) × RHOB_UNC_WM 2
incoherence = ---  --------------------------------------------------------------------------------------------------------------- + . . . .  (79)
2
RHOB_UNC × Largest Weight

standard deviation = sqrt [ 2.0 × incoherence ⁄ ( num of tools ) ] × Largest Weight(80)
where:
RHOB = density input curve (bound to RHOB equation)
NPHI = neutron porosity input curve (bound to NPHI equation)
xxxx_REC = xxxx curve, reconstructed from output formation
components
xxxx_UNC = uncertainty of the xxxx curve
ELANPlus Theory
107
Balanced Uncertainties
Uncertainties
ToC
RHOB_UNC_WM =Weight Multiplier
Largest Weight = Maximum Weight of all weights encountered
For more information on Standard Deviation, see the Quality Control of the Results
section in Chapter 8, Quality Control.
There is one term in the summation for each equation used in the Solve process. The
program selects as its solution the volumes that minimize Equation (80).
Uncertainties do not include the volume of the mineral. In other words, the
uncertainty of QUAR is dependent on the response of the various tools to quartz and
to the uncertainties of the various tools, but not to the actual volume of quartz being
computed. Because the volume uncertainties are independent of the volumes, the
uncertainties can be computed and used for quality control before the volumes are
actually computed.
The fact that the volume uncertainties do not depend on the absolute value of the
volume means that balanced uncertainties can be created.
Balanced Uncertainties
Calculating solution uncertainties is difficult. Theoretically, solution uncertainties are
made up of two parts: tool uncertainty, and model uncertainty.
Tool uncertainty can be illustrated with the induction and density tools. The absolute
accuracy of the induction log is excellent (in the proper fresh mud environment), but
the density log is influenced by counting statistics and rough borehole.
Uncertainties resulting from counting statistics and rough borehole can be quantified
through modelling and laboratory experiments. However, quantifying the uncertainty
of a saturation model for induction versus a porosity model for RHOB is quite
difficult. Uncertainties in this discussion relate specifically to the tool uncertainties.
Either uncertainty parameters or uncertainty data channels (or both) can be used to
put uncertainties into the ELANPlus program. The environmental correction
programs have uncertainty channels as output, but those channels may not be
appropriate for ELANPlus processing without rescaling.
In addition, the user cannot adjust channel input (short of exiting the
ELANPlus program and functioning the channels), aside from a zonable weight
multiplier.
ELANPlus Theory
108
Index
Balanced Uncertainties
Uncertainties
Finally, opening additional data channels increases the program execution time.
Thus, most log analysts use the uncertainty parameters (RHOB_UNC, NPHI_UNC,
and so on) and take on the responsibility of choosing the correct uncertainties for a
given situation.
The suggested approach is to start with balanced uncertainties. That means that each
tool in the model affects the resultant volumes equally.
For linear equations, the balanced uncertainty value can be determined easily by the
following steps:
1. Assign an uncertainty value to the Summation of Volumes equation
(VOLS_UNC). Remember that the absolute uncertainty value is not important.
What is important is its value relative to the others. The volume summation
equation has a range of 0 to 1.0 (100 p.u.); the default uncertainty is 0.015 (1.5
p.u.).
2. Determine the range for all the other equations from the minimum and
maximum response parameters of the major minerals and fluids in the model.
For a quartz-calcite-dolomite model, the minimum for the density tool would be
the density of the water in the pore space (RHOB_XWAT), which is about 1.05.
The maximum would be the density of dolomite, RHOB_DOLO = 2.85. Those
values reflect the values from 100% porosity to 100% dolomite.
If the mineral exists only in trace quantities (for example, a trace amount of
pyrite), do not use it for the maximum or minimum value.
3. The uncertainty value that leads to a mathematically balanced set of equations
can be determined by
MAX tool – MIN tool
Balanced Uncertainty = -------------------------------------------------- × VOLS_UNC (81)
MAX vols – MIN vols
For the preceding density equation and quartz-calcite-dolomite model
(expressing the summation of volumes in p.u.), that would be
2.85 – 1.05
RHOB_UNC = --------------------------- × 1.5 ≈ 0.027
100.0 – 0.0
(82)
Using balanced uncertainties is, in effect, a technique to scale the broad variety
of input data so that they are weighted equally in the final answer.
ELANPlus Theory
109
ToC
Index
Conductivity, SP
Uncertainties
Balanced uncertainties are useful for two reasons. First, balanced uncertainties result
in a model with the minimum resolution number for a given combination of tools,
volumes, and endpoints. Second, all the tools will equally affect the results when you
run the ELANPlus program. Your job is to evaluate those results and modify the
uncertainties to improve the final result.
Conductivity, SP
The conductivity equation is special. Within the ELANPlus system the
square root of conductivity is used for all water saturation equations.
Therefore, the expression MAXtool – MINtool becomes
MAX tool – MIN tool. More specifically, for the deep conductivity equation (CUDC) would be
CUDC_UWAT – 0.0
CUDC_UNC = ------------------------------------------------------- × 1.5
100.00 – 0.0
(83)
with a similar expression for the flushed-zone equation.
The SP also is special because the input is multiplied by porosity. Therefore, MAXtool – MINtool becomes (Qv_shale – 0)(φ). The SP measurement
is most useful in areas of high porosity; therefore a value of φ = 0.3 is
used in the default computation.
Weight Multipliers
Before use, ELANPlus uncertainties have incorporated within their computation an
additional term, a multiplier that is based on log analyst experience. A multiplier
value of 1.0 means that the tool will influence the answer as strongly as the Volume
Summation tool. An understanding of how a tool can affect the results and a
knowledge of tool physics is required to select the multiplier values.
Consider the following scenario, if the borehole was in good shape, and the log
analyst wants the density and neutron tools to determine the porosity. He gives
these tools a multiplier value of 1.0. He gives UCUDC a multiplier value of 0.75 so
that it does not affect the estimation of porosity as much as the density-neutron. He
gives UCXDC a multiplier value of 0.50, because he has selected the SXO > SW
constraint and if a conflict between CUDC and CXDC arose, the log analyst has
more confidence in CUDC. Since the U tool is formed by multiplying the PEF
and RHOB measurements, it has a multiplier value of 0.50 to account for the
increased statistics present when two tools are multiplied together.
ELANPlus Theory
110
ToC
Index
Default Uncertainties
Uncertainties
ToC
The ELANPlus program uses the following algorithm:
1. Take the xxxx_UNC value supplied by the user or a default table.
Index
2. Convert to internal representation (units), if necessary.
3. Limit the value (to avoid dividing by zero).
4. Invert the uncertainty to produce a weighting factor.
In the process, the program keeps track of the largest weight encountered, and when
all weights have been calculated, the program normalizes the largest weight to a
value of 1.0. Finally, each weight is multiplied by the user-zonable parameter
xxxx_WM to produce the weight actually used by the solver.
1.0 ⁄ xxxx_UNC
Weight = --------------------------------------- × xxxx_WM
Largest Weight
(84)
Weight multipliers allow modification of balanced uncertainties in a consistent way
without any computations. They are particularly convenient to use when the input
uncertainties are obtained from uncertainty curves.
Also, some users would rather work with laboratory-established values for tool
uncertainties. Weight multipliers allow them to modify the theoretical uncertainty
values to produce balanced results.
Using laboratory-based and theory-based uncertainties is in fact a conceptually
cleaner way to handle uncertainties. To use that method, however, you must be very
familiar with the meaning of the laboratory uncertainties, the eigenvalues and
principle components, and the ELANPlus solution method.
Default Uncertainties
Table 29, Table 30, and Table 31 show the basis for the default uncertainties used in
the ELANPlus program.
Note: the MIN/MAX values used are the full expected range of the measurement, not
just what is seen on the log. If a log value is used as a reference range for one of the
tools, then all tools must be rescaled appropriately.
Uncertainty is the inverse of a weighting factor. A small weight multiplier applied to
the balanced uncertainty means that the equation is not being weighted as heavily as
an equation with a larger multiplier. Default weight multipliers are based on
experience in using ELANPlus processing to solve various problems.
ELANPlus Theory
111
Uncertainty Tables
Uncertainties
Dividing the multiplier by four is close to having the tool ignored in the solution.
Truthfully, one can never completely turn the tool off with uncertainties. To be totally
out of the solution, the equation must be removed from the model (Solve process).
GR and SDPT values have been added to the table as a guide. The default within the
ELANPlus program is Absent because these logs have such a high degree of
variability. For the gamma ray, if an assumption is made that there is seldom more
than 50% clay in shales, then the MAX value used in the uncertainty computation
should be at least twice the observed log value in shales.
Uncertainty Tables
Table 29 contains the default uncertainties and weight multipliers for the ELANPlus
linear equations. It also shows the values used to derive the uncertainties.
Table 29 Linear Uncertainties
Equation
Uncertainty
MIN
MAX
CUDC_UNC
0.0
CXDC_UNC
0.0
20.0
Balanced
Uncertainty
Weight
Multiplier
0.065
0.67
20.0
0.065
0.5
43.0
189.0
2.250
0.75
EATT_UNC
0.0
2500.0
37.500
0.5
ENPA_UNC
0.0
1.0
0.015
1.0
GR_UNC*
0.0*
6.000*
0.3
NPHI_UNC
0.0
1.0
0.015
1.0
PHIT_UNC
0.0
1.0
0.015
0.5
RHOB_UNC
1.0
2.8
0.027
1.0
SIGM_UNC
10.0
50.0
0.600
1.0
TPL_UNC
7.2
50.0
0.600
0.5
U_UNC
0.4
15.4
0.225
0.5
VELC_UNC
–12.0
20.0
0.500
0.7
VOLS_UNC
0.0
100.0
1.500
1.0
DT_UNC
400.0*
* GR uncertainty has no default value within the ELANPlus program because of high variability. The values shown are only suggested as a starting point.
ELANPlus Theory
112
ToC
Index
Uncertainty Tables
Uncertainties
Table 30 contains the default uncertainties and weight multipliers for the ELANPlus
nonlinear equations. It also shows the values used to derive the uncertainties.
ToC
Table 30 Nonlinear Uncertainties
Equation
Uncertainty
MIN
MAX
Balanced
Uncertainty
Index
Weight
Multiplier
BMK_UNC
0.0
10.0
0.15
0.5
CUDC_xxx_UNC
0.0
20.0
0.065
0.67
CXDC_xxx_UNC
0.0
20.0
0.065
0.5
ENPU_UNC
0.0
1.0
0.015
1.0
NPHU_UNC
0.0
1.0
0.015
1.0
QVSP_UNC
0.0
8.0 × 0.3
0.036
0.5
SDPT_UNC*
0.0*
9.0*
0.14*
1.0
EQHY_UNC
0.0
0.1
0.0015
1.0
* SDPT_N uncertainty has no default value within the ELANPlus program because of high
variability. The values shown are suggested only as a starting point.
Unlike the other ELANPlus equations, those used on elemental concentrations do not
lend themselves to simple MIN/MAX calculations to determine the proper balanced
uncertainties. Table 31, Geochemical Uncertainties, shows the default uncertainties
and weight multipliers for the elemental equations.
Table 31 Geochemical Uncertainties
ELANPlus Theory
Equation
Uncertainty
Balanced
Uncertainty
Weight
Multiplier
DWAL_UNC
0.0028
1.0
DWCA_UNC
0.011
1.0
DWFE_UNC
0.0018
1.0
DWGD_UNC
0.7
1.0
DWK_UNC
0.0026
1.0
DWMG_UNC
0.021
1.0
DWSI_UNC
0.016
1.0
DWSU_UNC
0.0515
1.0
DWTH_UNC
0.5
1.0
DWTI_UNC
0.002
1.0
DWU_UNC
Absent
1.0
113
Uncertainty Tables
Uncertainties
ToC
Table 31 (Continued)Geochemical Uncertainties
ELANPlus Theory
Equation
Uncertainty
Balanced
Uncertainty
Weight
Multiplier
FCA_UNC
0.031
1.0
FCHL_UNC
0.010
1.0
FFE_UNC
0.020
1.0
FGD_UNC
0.065
1.0
FHY_UNC
0.010
1.0
FK_UNC
0.125
1.0
FSI_UNC
0.028
1.0
FSUL_UNC
0.019
1.0
FTI_UNC
0.05
1.0
WWAL_UNC
0.00256
1.0
WWCA_UNC
0.01
1.0
WWFE_UNC
0.0016
1.0
WWGD_UNC
0.64
1.0
WWK_UNC
0.00235
1.0
WWMG_UNC
0.019
1.0
WWSI_UNC
0.0145
1.0
WWSU_UNC
0.047
1.0
WWTH_UNC
0.45
1.0
WWTI_UNC
0.0018
1.0
WWU_UNC
Absent
1.0
Index
114
Carbonate-Clay Example
Uncertainties
ToC
Carbonate-Clay Example
The following carbonate-clay example illustrates how uncertainties affect the answer.
The user set DT_UNC = 10 (4.4 times normal, turning it off) in the carbonate
section. The job was run without zoning.
shows the result in the clay section where there was bad hole. The same effect could
have been obtained by setting DT_WM = 4.4 and not changing the DT_UNC default.
4.0
0
2.0
UNPHI = 2.0
2.8
120
RHOB
NPHI
4.0
DTT
ROBT
NPHT
0
2.0
,,,,,
,,,,,
,,,,,
,,,,,
,,,,,
,,,,,
,,,,,
60
DT
2.8
URHOB = 0.016
120
60
UDT = 10.0
Carbonate-Clay Example with DT_UNC = 10
Zoning DT_UNC to 1.0 (0.44 of normal) to overcome the problem of invalid
density-neutron data in the washed-out zone yields the results shown in
. The same result would be obtained by setting DT_WM to 0.44 and not changing
the DT_UNC default value.
ELANPlus Theory
115
Index
Carbonate-Clay Example
Uncertainties
4.0
0
2.0
UNPHI = 4.0
2.8
120
RHOB
NPHI
4.0
DTT
ROBT
NPHT
0
2.0
,,,,
,,,,
,,,,
,,,,
,,,,
,,,,
,,,,
ToC
Index
60
DT
2.8
URHOB = 0.48
120
60
UDT = 1.0
Carbonate-Clay Example with DT_UNC = 1.0
ELANPlus Theory
116
ToC
Index
Chapter 6
Constraints
Constraints are absolute minimum and/or maximum limits on ELANPlus formation
component volumes. Constraints typically are used for imposing geological or
petrophysical information, limiting anomalous tool response (for example, bad hole),
and constructing minimum clay indicators.
Unlike constant tools, which are weighted by uncertainties, constraints are absolute
limits. Constraints fall into three categories:
1. Internal constraints
2. Predefined constraints
3. User-defined constraints
Internal Constraints
Internal constraints are imposed by the program on the optimized solution and
cannot be changed by the user. They are based on physical limits, such as a volume
not having a negative value, and the sum of all volumes not being greater than 1.
The positive volume constraint is always used by the program. It is written as
follows:
Vi ≥ 0.0
ELANPlus Theory
(85)
117
Internal Constraints
Constraints
Another constraint always used by the program is the Summation of Volumes
constraint. It is actually implemented as a pair of constraints, one limiting the sum of
volumes to be less than or equal to 1.0, the other limiting the sum to be greater than
or equal to 1.0:
nfc
∑ Vi ≤ 1.0
(85-1a)
i=1
nfc
∑ Vi ≥ 1.0
(85-1b)
i=1
where nfc = number of formation components in the model, excluding any
undisturbed-zone fluids. The effect of the constraint pair is that the sum of volumes
must be exactly equal to 1.0.
Finally, two more internal constraints are used whenever a model contains both
undisturbed-zone and flushed-zone fluid volumes. Used together, these constraints
ensure that the sum of the fluid volumes in the flushed zone is equal to the sum of the
fluid volumes in the undisturbed zone.
nxf
nuf
∑ Vi – ∑ V j ≤ 0.0
i=1
j=1
nxf
nuf
∑ Vi – ∑ V j ≥ 0.0
i=1
(85-2a)
(85-2b)
j=1
As with the sum of volumes constraints, a pair of inequality constraints is used to
establish an equality.
ELANPlus Theory
118
ToC
Index
Predefined Inequality Constraints
Constraints
ToC
Predefined Inequality Constraints
Predefined constraints are commonly used constraints available in the
ELANPlus program. Note that the predefined constraints are not automatic but are
made available at the user’s discretion. There are seven such constraints:
1. Maximum Porosity Constraint
2. Irreducible Water Constraint
3. Sonic Clay Volume Constraint
4. Conductivity Constraint for Water-Based Muds ( S
5. Conductivity Constraint for Oil-Based Muds ( S
6. Sxo Constraint for Water-Based Muds ( S
7. Sxo Constraint for Oil-Based Muds ( S
xo ≥ S w )
xo ≤ S w )
xo ≥ S w )
xo ≤ S w )
Maximum Porosity Constraint
The maximum Porosity Constraint limits the sum of the flushed-zone fluid volumes
to be less than or equal to the zonable parameter PHIMAX.
nxf
∑ Vi ≤ PHIMAX
(86)
i=1
The main application of the Maximum Porosity Constraint is to control excess
porosity, which might be caused by bad hole. Set PHIMAX to the maximum porosity
observed in the good hole. Setting PHIMAX to less than 1.0 (0.5, perhaps) also helps
the nonlinear solver to be more stable and run faster.
Irreducible Water Constraint
The Irreducible Water Constraint limits the sum of all waters in the undisturbed zone
to be greater than or equal to the minimum of either the zonable parameter BVIRR
or the input curve PHIT. The same constraint is applied to the flushed zone.
UWAT + UIWA + USFL ≥ minimum ( BVIRR, PHIT )
(86-1a)
XWAT + XIWA + XSFL ≥ minimum ( BVIRR, PHIT )
(86-1b)
where:
ELANPlus Theory
119
Index
Predefined Inequality Constraints
Constraints
ToC
UWAT = undisturbed-zone water
UIWA = undisturbed-zone irreducible water
USFL = undisturbed-zone special fluid if the global parameter Special Fluids
is set to Water or Immovable Water
XWAT = flushed-zone water
XIWA = flushed-zone irreducible water
XSFL = flushed-zone special fluid if the global parameter Special Fluids is
set to Water or Immovable Water
BVIRR = value of the bulk volume irreducible zoned parameter
PHIT = value of the curve bound to PHIT
The PHIT limit is for very low porosity carbonates and will be active only when
there is an input PHIT curve. The Irreducible Water Constraint is applied to prevent
the computation of unrealistically low water saturations, as can happen in low
porosity or when the resistivity tool is spiking to high values.
Sonic Clay Volume Constraint
The Sonic Clay Volume Limit Constraint limits the sum of all the clays
to less than or equal to a clay volume that is based on a sonic matrix
velocity
(Vmatrix) versus matrix volumetric photoelectric cross-section (Umatrix)
relationship.
nc
∑ VDCi ≤ A × U + B × VELC + C – D × PHIT
(87)
i=1
where:
VDCi = volume of dry clay for clay i
U = value of the volumetric photoelectric cross-section curve
VELC = value of the sonic velocity curve
A, B, C, and D = coefficients computed from response parameters
ELANPlus Theory
120
Index
Predefined Inequality Constraints
Constraints
The concept of the Sonic Clay Limit Constraint relies on the fact that, in a carbonate,
the sonic velocity is sensitive to the amount of clay in the matrix. The constraint has
very useful applications in distinguishing between clay and radioactive dolomite,
especially when a computed gamma ray, CGR, (gamma ray minus uranium) is
unavailable. Observe the crossplot of Vmatrix versus Umatrix in .
24
DOLOMITE
Vmatrix
22
CALCITE
20
18
16
ILLITE
14
6
8
10
12
14
16
Umatrix
Matrix velocity versus matrix photoelectric cross-section.
The equation of the line connecting the limestone and dolomite points is given by
0 = a × U matrix + b × V matrix + c
(88)
where:
a=
1.0
U_CALC – U_DOLO
b = –  ----------------------------------------------------------------------------
 VELC_CALC – VELC_DOLO
U_CALC × VELC_DOLO – U_DOLO × VELC_CALC
c = ---------------------------------------------------------------------------------------------------------------------------------------VELC_CALC – VELC_DOLO
ELANPlus Theory
121
ToC
Index
Predefined Inequality Constraints
Constraints
The fraction of the matrix rock that is illite (FILLI) is given by the ratio of the
distance from the point (Umatrix, Vmatrix) to the limestone-dolomite line to the
distance from the illite point (U_ILLI, VELC_ILLI) to the limestone-dolomite line.
a × U matrix + b × V matrix + c
ILLI
F ILLI = -------------- = ---------------------------------------------------------------------------------1 – φt
a × U_ILLI + b × VELC_ILLI + c
Index
(89)
where:
ILLI = volume of illite (wet clay)
φt = total porosity
U – φ t × U fluid
Umatrix = -------------------------------------1 – φt
VELC – φ t × SPORF
Vmatrix = --------------------------------------------------1 – φt
Introduce the following definitions:
DC ≡ a × U_ILLI + b × VELC_ILLI + c
(89-1a)
a
A ≡ -------DC
(89-1b)
b
B ≡ -------DC
(89-1c)
c
C ≡ -------DC
(89-1d)
Then Equation (89) can be written
ILLI
-------------- = A × U matrix + B × V matrix + C
1 – φt
(90)
Expanding the definitions of Umatrix and Vmatrix yields
 U – φ t × U fluid
 VELC – φ t × SPORF
ILLI
-------------- = A ×  -------------------------------------- + B  --------------------------------------------------- + C(91)
1 – φt
1 – φt
1 – φt




Finally, multiply both sides by 1 − φt to get
ELANPlus Theory
ToC
122
Predefined Inequality Constraints
Constraints
ILLI = A × U + B × VELC + C – φ t × ( A × U fluid + B × SPORF + C )(92)
The value computed for ILLI in Equation (92) is the value used as the upper limit for
the sum of all dry clay volumes in the Sonic Clay Volume Constraint.
In order to evaluate the Sonic Clay Volume Constraint, the program requires values
for all of the parameters and tools in Table 32.
Table 32 Parameters and Tools Required by the
Sonic Clay Volume Constraint
Parameters
Tools
U_CALC
VELC_CALC
U
U_DOLO
VELC_DOLO
VELC
U_ILLI
VELC_ILLI
PHIT*
U_XBWA
PHIT_ILLI
U_XWAT
SPORF
WCLP_ILLI
*PHIT is required input!
If the global parameter Clay is set to Wet, the illite wet clay parameters are converted
to matrix values according to Equation (89). The Sonic Clay Volume Constraint is
normally used in carbonates. No harm is done if it is used in shaly sands, because the
limiting value is generally greater than the volume of clay computed by the
ELANPlus program.
Conductivity Constraint for Water-Based Mud (Sxo ≥ Sw)
The Conductivity Constraint for Water-Based Mud (Sxo Sw) can be confusing. It is
best explained by reviewing an example of effective porosity, undisturbed-zone
water, and flushed-zone water in a clean formation (). Notice that flushed-zone water
spikes to a value less than that of the undisturbed-zone water.
The Conductivity Constraint for Water-Based Mud is designed to limit the volume of
water computed in the flushed zone by the volume of water computed in the
undisturbed zone, assuming that the undisturbed-zone water is correct.
For water-based muds, the invading fluid is water. Therefore, the water saturation of
the flushed zone is expected to be greater than or equal to the undisturbed-zone-water
saturation.
ELANPlus Theory
123
ToC
Index
Predefined Inequality Constraints
Constraints
ToC
Index
Undisturbed-zone water volume
0.25
0.0
Flushed-zone water volume
0.0
0.25
Effective porosity
0.25
0.0
Porosity contents in a clean zone with no constraints applied
Use the Conductivity Constraint for Water-Based Mud when (a) the flushed-zone
tools (EPT, MSFL) are considered to be less accurate than the undisturbed-zone
conductivity (as in rough hole or unusual mudcake conditions) and (b) you wish to
force the Sxo ≥ Sw condition, using only conductivity data. Otherwise, use the Sxo
Constraint for Water-Based Mud.
As indicated by its name, the Conductivity Constraint for Water-Based Mud relies
exclusively on the deep conductivity (CUDC) for the limit. Conceptually, the
constraint can be written as
Xwater ≥ Uwater + PHI_OFFSET
(93)
where:
Xwater = the sum of all flushed-zone water volumes
Uwater = the sum of all undisturbed-zone water volumes
PHI_OFFSET = a small offset to Uwater
The form in which it is implemented can be derived as follows:
1. Start with the linear deep conductivity response equation.
ELANPlus Theory
124
Predefined Inequality Constraints
Constraints
ns
CUDC =
∑(
nuf
CUDC_i × Vi ) +
∑ 
ToC
CUDC_ j
---------------------- × V j (94)

a
j=1
i=1
Index
where:
ns = number of solid formation components
CUDC = value of the deep conductivity measurement
a = the Archie porosity factor
Assuming that the effect of undisturbed-zone irreducible water
and special fluid is negligible compared to undisturbed-zone water
yields
ns
CUDC =
∑(
CUDC_UWAT
CUDC_i × Vi ) + ------------------------------------- × UWAT(95)
a
i=1
2. Solve for the undisturbed-zone water.
ns
CUDC –
∑(
CUDC_i × Vi )
i=1
UWAT = ---------------------------------------------------------------------------------CUDC_UWAT
------------------------------------a
(96)
3. Substitute the right hand side of Equation (96) for Uwater into the constraint,
Equation (93), and expand Xwater to a formal summation.
ns
nxf
CUDC –
∑(
CUDC_i × Vi )
i=1
+ PHI_OFFSET
∑ Vk ≥ ---------------------------------------------------------------------------------CUDC_UWAT
k=1
(97)
------------------------------------a
4. Finally, rearrange to isolate the conductivity measurement.
ns
 nxf

CUDC_UWAT


Vk – PHI_OFFSET × ------------------------------------- +
( CUDC_i × Vi ) ≥ CUDC(98)


a
k = 1

i=1
∑
ELANPlus Theory
∑
125
Predefined Inequality Constraints
Constraints
ToC
Equation (98) is the form in which the constraint exists in the program. The
conductivity from the solids summation term
ns
∑i = 1 ( CUDC_i × Vi )
Index
usually is exclusively from clays. If other conductive rocks or minerals are present,
they will be included.
allows you to compare the results of applying the Conductivity Constraint for WaterBased Mud with PHI_OFFSET = -0.02 to the data from .
undisturbed-zone water volume
0.25
0.0
Flushed-zone water volume
0.0
0.25
Effective porosity
0.0
0.25
UWAT + PHI_OFFSET
0.25
0.0
Porosity contents in a clean zone with the Conductivity Constraint for Water-Based Mud
applied
ELANPlus Theory
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Predefined Inequality Constraints
Constraints
ToC
Conductivity Constraint for Oil-Based Mud (Sxo ≤ Sw)
When oil-based mud is used, the invading fluid is a hydrocarbon. Therefore, the
water saturation of the flushed zone is expected to be less than or equal to the
undisturbed zone. As in the water-based constraint, the limit is based on deepreading conductivity.
Index
The derivation of the constraint is the same as for the water-based constraint. The
only difference is that the direction of the inequality is reversed.
Xwater ≤ Uwater + PHI_OFFSET
(99)
Sxo Constraint for Water-Based Mud (Sxo ≥ Sw)
The Sxo Constraint for Water-Based Mud is more commonly used than the
Conductivity Constraint for Water-Based Mud, because it better reflects standard
constraints. The Sxo Constraint for Water-Based Mud limits the volume of water in
the flushed zone to greater than or equal to the volume of undisturbed water, on the
basis of the normal response equations.
The Sxo Constraint differs from the Conductivity Constraint in that a single tool does
not determine the undisturbed water used to constrain the flushed-zone water. Its
application is similar to the Conductivity Constraint but it can be applied more
generally.
Sxo Constraint for Oil-Based Mud (Sxo ≤ Sw)
The Sxo Constraint for Water-Based Mud limits the volume of water in the flushed
zone to less than or equal to the volume of undisturbed water on the basis of the
normal response equations. This constraint differs from the Conductivity Constraint
for Oil-Based Mud in that a single tool does not determine the undisturbed water
used to constrain the flushed-zone water. Its application is similar to the Conductivity
Constraint, but it can be applied more generally.
ELANPlus Theory
127
User-Defined Constraints
Constraints
ToC
User-Defined Constraints
User-defined constraints are created by the user to constrain volume solutions as a
function of the input tools, the constants, and a combination of tools and constants.
The constraints are defined in a syntax much like that of the C programming
language.
The syntax includes the most common arithmetic operators and logical comparisons.
Any curve available in the current data focus and any user-accessible variable known
to the ELANPlus application can be used.
In addition to program variables, you can create and use as many convenience and
intermediate variables as you desire. User-defined constraints are a very powerful and
flexible means of controlling volumetric results.
☛
For details on syntax and user-defined constraints, see the ELANPlus User’s Guide..
ELANPlus Theory
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Index
ToC
Index
Chapter 7
Model Combination
An ELANPlus model can never solve for more formation components than the
number of response equations (including any internal response equations) in the
model. Since the number of logging measurements available from any given well is
often small, it might seem that wells with widely varied geology cannot be evaluated,
but they can.
Previous programs have handled the complex lithology problem with internally
defined geological models. If the data did not match the prebuilt models, the problem
could not be solved.
Only the ELANPlus program can explicitly define and process multiple models in a
single pass, optimizing each model for a particular geology or even a specific
formation. The volumes for each model are solved independently, each potentially
with different formation components, response equations, parameter values, and
constraints.
The results from the individual models can then be combined in a variety of ways.
The models can be combined after individual fine tuning or while the Solve
Processes are being executed.
Methods for Generating Combined Answer Sets
To combine results of different processes (models) you must first create a Combine
process and associated dependencies, using the Session Editor. For example, if three
models, Shaly_Sand, Carbonate, and Bad_Hole, were being combined, the Session
Editor might look like .
ELANPlus Theory
129
Methods for Generating Combined Answer Sets
Model Combination
ToC
Shaly_Sand
Carbonate
Bad_Hole
S1
S2
S3
Index
Combine
C1
Three Solve processes being combined.
Once a Combine process exists, the Combine Editor can be activated. To do that,
click on the Combine process icon; then select the Process option from the Edit
menu.
The Combine Editor is the means by which the order and method of model
combination are controlled. It contains a list of zones (maybe only one zone at the
start) and zone boundaries.
Zone boundaries can be added, deleted, or modified. The zone boundaries in the
Combine Editor are different from the boundaries used by the zoned parameter
editor. For each zone, a combination method is chosen.
Models can be combined by two main methods: individual models and probabilities.
Probabilities can be determined from an external source or computed internally.
The results of probability combination depend on whether the probability maximum
or probability average method is used. All together, there are five possibilities for the
combination method:
1. Individual model
2. External maximum
3. External average
4. Internal maximum
5. Internal average
Only one method can be chosen for each zone, but any combination of methods can
be used in different zones.
ELANPlus Theory
130
Individual Models
Model Combination
ToC
Individual Models
When an individual model is selected as the combination method for a zone, the
results are from that model used exclusively for that zone.
Index
For example, for the session depicted in , assume that there are five zones. Using
individual models, the models might be combined as Zone 1, Shaly_Sand; Zone 2,
Carbonate; Zone 3, Bad_Hole; Zone 4, Shaly_Sand; Zone 5, Shaly_Sand. At each
zone boundary there is an instantaneous change from the volumes computed by one
model to those computed by the next model in the list.
The individual model method provides direct control of the appearance of the
combined results. It reflects the fact that, in nature, abrupt facies changes are
common.
Model Probabilities
Sometimes, gradual transitions occur. Sometimes, abruptly alternating environments
make manually zoning and selecting models impossibly tedious. Model probabilities
are well suited to either problem.
A model probability is a value between 0.0 and 1.0, inclusive, assigned to a model to
indicate its suitability according to volumetric results and/or curve data. A value of
0.0 indicates that the model does not fit; a value of 1.0 indicates suitability.
The volumetric data can come from any model in the session for which results are
available. The curve data can come from any available database curve.
External Probabilities
The ELANPlus program allows computation of model probabilities by an external
source. The source might be a facies identification program, some custom or
proprietary code, or even a previous run of the ELANPlus program. Whatever the
source of the probabilities, the curves are bound to PRB1 for probability of model 1,
PRB2 for probability of model 2, and so on.
At each data level, the model assigned to be model 1 takes on the probability value
from the curve bound to PRB1. Model 2 takes on the probability value from the
curve bound to PRB2 and others. If the probability value of any model lies outside
the range 0.0 to 1.0, it is clipped. Model combination then proceeds as discussed in
the Final Model Combination, Using Probabilities section.
RHOB_UNC_WM =Weight Multiplier
Largest Weight = Maximum Weight of all weights encountered
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Model Probabilities
Model Combination
ToC
Internal Probabilities
Internal probabilities are computed from probability expressions entered in the
Combination Probability Expression section of the Combine Editor. The entries can
be obtained from an ASCII file or typed in. Good model probability expressions are
something of an art but are well worth the effort, particularly when the formation is
highly laminated.
Suppose that you wanted the Carbonate model of to have zero probability when the
volume of calcite computed by that model is less than or equal to 40%, and have a
probability of 1.0 when the volume of calcite exceeds 65%. The values required for a
probability expression required to impose those conditions can be computed from the
system of equations
0.0 = 0.40x + y
1.0 = 0.65x + y
(100)
from which the values x = 4.0, y = −1.6 result. The probability expression that you
would enter in the Combine Editor would be
prob(SOL.2, 4.0*CALC_VOL.SOL2 - 1.6)
The keyword prob indicates the introduction of a probability expression. The entry
SOL.2 indicates that the probability is to be applied to Solve Process number 2.
Note that the Carbonate model in is marked S2, indicating the Solve Process
number.
The 4.0 and -1.6 are the coefficients that were computed from the system of
equations (100). Finally, CALC_VOL.SOL2 indicates that the mineral volume used
is the calcite volume from Solve Process number 2.
When internal probabilities are used, any model that does not have a probability
expression is assigned a probability of 0.0.
Once all probabilities are computed, model combination proceeds.
For more information see the Final Model Combination, Using Probabilities
section in Chapter 7, Model Combination.
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Index
Model Probabilities
Model Combination
ToC
Bad Hole Probability
Bad hole data (data corruption by enlarged or rough hole) is a common problem in
log analysis. Many techniques have been developed to handle it.
In programs using optimization solvers, like the ELANPlus program, often the
weighting on one tool or another changes as a function of hole size. That works
sometimes, but in reality tools are seldom just a percentage bad. Their measurements
are usually good or bad (unrecoverable).
To allow for the problems caused by bad hole, the ELANPlus application includes
the concept of a bad hole model. In addition to probabilities for individual models,
there exists a special bad hole probability. It is used to switch over to a specific
model when certain conditions are met. A bad hole model usually uses a subset of
available logging measurements, eliminating tools that would respond poorly in bad
hole, such as RHOB, TPL, and so on.
Since fewer tools are available, bad hole models typically use a limited number of
formation components as well. Because of the way the final model combination is set
up, the bad hole model takes precedence over all others.
For more information see the Final Model Combination, Using Probabilities
section in Chapter 7, Model Combination.
For example, assume a bad hole probability based on the hole rugosity curve,
HRUG_CH, and differential caliper curve, DCAL_CH. The desired result is to have
the bad hole probability high if the hole is washed out (large DCAL_CH) or if the
borehole wall is rough (high HRUG_CH), regardless of hole size.
Assume that the probability based on differential caliper should be zero when
DCAL_CH reads 1.5 (inches) or less and the probability should be 1.0 when it reads
2.5 or higher. Probability based on hole rugosity will be set to zero when HRUG_CH
reads 0.2 or less, and the probability will be 1.0 when it reads 0.3 or higher.
The bad hole probability may then be computed as
PCAL = (DCAL_CH - 1.5)/(2.5 - 1.5)
PRUG = (HRUG_CH - 0.2)/(0.3 - 0.2)
prob (BADHOLE, min(max(PCAL, PRUG, 0.0),
1.0))
where min and max are the minimum and maximum functions provided by the
expressions parser. The parser provides many other useful functions as well, such as
a linear transform that could have been used in place of the explicit arithmetic in the
PCAL and PRUG expressions.
For details on probability expression syntax, see the ELANPlus User’s Guide.
ELANPlus Theory
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Index
Model Probabilities
Model Combination
ToC
Final Model Combination, Using Probabilities
Once the individual and bad hole probabilities have been computed (whether
externally or internally), the individual model results are combined, using rules based
on these:
1. Combination order
2. Whether Probability Maximum or Probability Average is selected
3. Bad hole probability
Combination Order
Part of the Combine Editor is dedicated to something called Combine Order. It is an
ordered list of the processes feeding into a combine process. Each process involved
in the model combination is assigned a combination order number based on its
position in the list. The order is used in the final stage of the internal average and
external average combination methods. It is also used for resolving ties.
In general, the primary geological model should be the last process in the Combine
Order. If a bad hole model exists, it should always be assigned the first position in the
Combine Order.
Probability Maximum
If the chosen combination method is external maximum or internal maximum, the
individual model probabilities are examined, and the model with the largest
probability value is selected as the sole model to be used for the current data level. If
there is a tie between probabilities, the primary geological model wins.
Probability Average and the Bad Hole Model
When either the external average or internal average method is selected, the final
probability of a model is based on:
•
Its original probability
•
Its position in the Combine Order list
ELANPlus Theory
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Index
Model Probabilities
Model Combination
Let us consider the example shown in the session in ) . There are three processes
Shaly_Sand (S1), Carbonate (S2) and Bad_Hole (S3) feeding into the Combine
process. The order in which these models are listed in the combine order is shown in
the figure below.
Shaly_Sand(S1) the main geological model is listed at the bottom of the list and
Bad_Hole(S3) the badhole model is on the top. The final probability of the badhole
model (first in the list) is given by
prob ( SOL3 ) = prob ( SOL3 ) 0 + prob ( BAD ) × ( 1 – prob ( SOL3 ) 0 )
(101)
where:
prob(SOL3) = the new probability of model S3
prob(SOL3)0 = the original probability of model S3
prob(BAD) = the bad hole probability
The following relationship between prob(3) and prob(BAD) results from
Equation (101):
prob ( SOL3 ) 0 , if prob ( BAD ) = 0.0
prob ( SOL3 ) = 

1.0
if prob ( BAD ) = 1.0
(102)
Remember that prob(BAD) = 0.0 if no bad hole probability expression exists.
Once the bad hole probability has been applied to the first model, the remaining
probabilities are readjusted as follows (again using the example in ).
ELANPlus Theory
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ToC
Index
Model Probabilities
Model Combination
ToC
Using the cascading scheme of in Table 33, the higher-numbered models take
precedence over lower-numbered models.
Table 33 Probability
Cascading Used for
Final Probability Values
prob(SOL3) = (prob(SOL3))
prob(SOL2) =
(prob(SOL2)0) ×
(1.0 – prob(SOL3))
prob(SOL1) =
1.0
×
(1.0 – prob(SOL2))
Index
×
(1.0 – prob(SOL3))
For example, assume that before final combination prob(1) = 1.0, prob(2) = 1.0,
prob(3) = 0.0, and prob(BAD) = 0.0. When the final combination is applied, model 2
will receive 100% of the final probability, and model 1 will receive 0%.
No probability expression is required for model 1(the last model in the list). It gets
whatever remains after the models listed above it have removed their share of the
probability.
It may seem backwards that the primary geological model is accorded only the
leftovers of the secondary models. The idea is that in most cases, the models listed
earlier in the list are exceptions. As such, their probabilities are zero or low most of
the time. The primary model gets all or most of the probability until an exceptional
condition occurs. At such point a specialized model takes over.
If no probability expressions exist, all individual model probabilities are zero. In that
case, the probability cascading method causes all volumetric results to be obtained
from the last model in the list, since its probability will be 1.0 as a result of the
cascade.
The final volumetric results are obtained as
nmod
Vi =
∑
Vi ( j ) × prob ( j )
(103)
j=1
where:
Vi = volume of the ith component in the union of all formation com- ponents
from all models
nmod = number of models being combined
prob(j) = final, cascaded probability of model j
ELANPlus Theory
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ToC
Index
Chapter 8
Quality Control
ELANPlus quality control consists of developing appropriate models and controlling
the quality of the results.
Quality Control of the Model
Model development involves taking known information about the geological area and
building appropriate ELANPlus models. Although the ELANPlus program has no
knowledge of how appropriate a model is geologically, two pieces of information can
be computed that provide an indication of the mathematical validity of the model:
resolution number, and relative volume uncertainties.
Resolution number is the average sensitivity of the results to small changes in the
parameters or tool response. A value of less than 4 indicates good resolution. A value
greater than 6 indicates poor resolution.
A relative volume uncertainty is the uncertainty for an individual volume,
normalized so that the smallest uncertainty has a value of 1.0. When all relative
volume uncertainties are less than 10, the results warrant a high level of confidence.
The resolution number and relative volume uncertainties are derived from the
response matrix and can be computed only for linear models, but the same concept
can be applied to nonlinear models. Neither the resolution number nor the relative
volume uncertainties are output by the program. They are used here to show how
changes to a model affect the mathematical stability of results.
ELANPlus Theory
137
Quality Control of the Model
Quality Control
A poor resolution number or poor relative volume uncertainties may be the result of
an unbalanced uncertainty matrix, which can result when one tool is weighted much
more heavily than the others. While there are good reasons to weight a tool more
heavily in a particular well (for example, sonic in bad hole), during model
development you should keep the uncertainty matrix balanced. The balanced
uncertainty matrix discussed earlier provides the lowest resolution number for any
given model
For more information see the Balanced Uncertainties section of Chapter 5,
Uncertainties.
For a model with balanced uncertainties, the best way to improve the resolution is to
add an additional measurement that responds to a volume being solved. For example,
consider the model in Table 34.
Table 34 An Example Model
Components
QUAR
Equations
RHOB
NPHI
ILLI
XWAT
XOIL
GR
CXDC
ΣVolumes
Resolution Number = 2.86
QUAR = 3.4741
ILLI = 4.3235
XWAT = 1.0000
XOIL = 1.8322
Now extend the model by adding orthoclase feldspar (ORTH), as shown in Table 35.
Table 35 Model with Orthoclase Added
Components
QUAR
ORTH
ILLI
XWAT
XOIL
Equations
RHOB
NPHI
GR
CXDC
ΣVolumes
Resolution Number = 6.36
QUAR = 210.28
ORTH = 189.95
ILLI = 36.865
XWAT = 1.0000
XOIL = 16.404
Obviously the solution of Table 35 is not very believable. To solve for orthoclase
requires an additional measurement.
ELANPlus Theory
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ToC
Index
Quality Control of the Model
Quality Control
Extend the model by adding the potassium measurement (WWK), as shown in Table
36.
ToC
Table 36 Model with Orthoclase and Potassium Added
Components
QUAR
Equations
RHOB
NPHI
ORTH
ILLI
XWAT
XOIL
WWK
GR
CXDC
ΣVolume
Resolution Number = 2.89
QUAR = 2.1606
ORTH = 1.2834
ILLI = 4.0862
XWAT = 1.0000
XOIL = 1.7494
Note that the models of Table 34, Table 35, and Table 36 are all possible. That is,
the number of unknowns is less than or equal to the number of equations.
Table 34 is a quartz-clay model. In Table 35 orthoclase was added. Note that the
resulting resolution number and the relative volume uncertainties are very poor. That
suggests that the tools provided do not have sufficient resolution for the model, so
the results obtained from ELANPlus processing would be very poor. Adding the
potassium measurement in Table 36, however, again results in a well-defined model.
Neither tools nor volumes can be arbitrarily added or subtracted from a model. The
choice must come from external knowledge in one of three basic forms:
•
Adding more individual models and limiting the types of minerals found by
each model.
•
Adding additional information in the form of constant equations.
•
Constraining the results of an individual model to a known solution space.
ELANPlus Theory
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Index
Examples of Bad Hole Models
Quality Control
ToC
Examples of Bad Hole Models
In rough hole conditions, some models lose their validity. Often, bad hole is limited
to a single facies (as perhaps only the shales wash out). Thus, a model needs to be
defined with a more limited number of volumes and tools. A bad hole model example
is shown in Table 37.
Table 37 A Bad Hole Model
Components
Equations
QUAR
ILLI
XIWA
UIWA
XIWA=UIWA
DT
GR
CUDC
ΣVolumes
CT1
Note that hydrocarbons are not included in this model! Therefore, the model is
appropriate only when the bad hole is in sections believed to be nonproductive.
Notice that the model is overdetermined because of the relationship established by
the constant tool, CT1. Thus, a similar model could be built even when no DT data
are available. (The CUDC equation can be an excellent rough-hole porosity tool in
zones where clearly there are no hydrocarbons.)
In cases where the bad hole is in more than just one facies, consider using the
constant tools. Take, for example, a sand-shale section; the primary model for the
sands is shown in Table 38.
Table 38 Sand-Shale Model
Components
QUAR
Equations
RHOB
NPHI
ORTH
ILLI
XWAT
XOIL
WWK
WWTH
CXDC
ΣVolumes
If there are some sections where hole rugosity causes the RHOB and CXDC
equations to be in error, you can define a second model where those measurements
are replaced with constant equations, as for example in Table 39.
Table 39 Sand-Shale Model for Rough Hole
Components
Equations
QUAR
CT1
NPHI
ORTH
ILLI
XWAT
XOIL
WWK
WWTH
CT2
ΣVolumes
CT2 controls an average moved hydrocarbon ratio; CT1 controls an average porosity
for the sands. The actual values for CT1, CT2 and their parameters are determined in
good hole. The basic model and the bad hole model are combined using ELANPlus
model combination logic.
Another way of handling bad hole is through the use of a constraint. An example is
limiting volumes such that the reconstructed density is greater than 2.15:
constraint(Min_Density,
2.5*ILLI+2.65*QUAR+2.71*CALC+2.85*DOLO+1.0*XWAT
2.15)
ELANPlus Theory
140
Index
Quality Control
Quality Control of the Results
If density is less than 2.15, the constraint will affect the answer as if the density had a
value of 2.15.
Quality Control of the Results
Index
The primary quality control mechanism for ELANPlus results is the use of
reconstructed logs. Reconstructed log quality information is available in two forms:
the curve SDR (standard deviation of the reconstruction), and the individual
reconstructed logs, themselves.
SDR provides an overall indication of how well the logs reconstruct. For a
determined model, SDR could theoretically approach 0. With real data the value of
SDR may be low but will not reach 0.
For an overdetermined model, an SDR greater than 0 theoretically means that one or
more of the logs do not agree with the other logs. To determine which logs are being
affected, the ELANPlus processing provides a set of logs reconstructed from the
volumetric results of each Solve or Combine process in the session.
Reconstructed logs are an important tool for quality control of ELANPlus results.
Here are some points to remember about reconstructed logs.
Reconstructed Logs Can Identify Model Problems
Reconstructed logs can identify model problems such as data outside the model or
inconsistency within models.
Data Outside the Model
Reconstructed logs can help identify problems caused by data outside the model. For
example, a problem is indicated in a sand-shale model when RHOB_REC = 2.5, but
RHOB = 2.8. The high density must be rationalized. The most likely cause is the
presence of a heavier mineral, perhaps a dolomite stringer.
After model tuning is complete, the density log should reconstruct (unless there is
bad hole). If it does not, there is a problem.
Inconsistency Within Models
Reconstructed logs can help identify problems caused by inconsistency within
models. For example, oil parameters input for NPHI and gas parameters for RHOB.
ELANPlus Theory
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141
Quality Control of the Results
Quality Control
ToC
Poor Reconstruction Means There Is a Problem
Poor reconstruction means that there is a problem that may lie with the log that does
not reconstruct, another log, a constraint, invalid data (for example, bad hole data),
the selection of one or more parameters (for example, Rw, hydrocarbon type).
A Good Reconstruction Can Go With a Wrong Answer
A good reconstruction does not necessarily mean that the answer is correct. It means
the data fit the model. An example is an average carbonate model, which is
underdetermined, that will compute a very geologically questionable 50% dolomite
and 50% clay in shaly zones. The user must make sure that the chosen model makes
petrophysical sense for the area being interpreted.
Use Predicted Value to Check for Inconsistencies
Using the predicted value for a log (reconstructing a log from a model that does not
use the log directly) is a powerful technique to check for parameter inconsistencies
such as wrong Rw and to check the validity of a particular log. There are two
methods: use the log from one model with the volume from other models, and set the
uncertainty very high.
Using the Log from One Model and the Volumes from Others
Have the log in one model and use the Combine Editor to choose the volumes from
other models to use for reconstruction.
Setting the Uncertainty Very High
Set the uncertainty very high for the log in question (assuming the original model
was overdetermined). Setting the value very high only de-emphasizes the input; it
never completely eliminates the influence of the data in the final answer. A common
way to run the first ELANPlus pass is to have
CUDC_UNC high to see if there is an Rw problem; then balance for the final
computation.
Summary
In summary, the SDR curve will point out areas in which log reconstruction is poor.
It is then up to you to determine the cause of the inconsistency. Remember that a
good SDR does not always mean good results. As a final check, always ask, “Do the
volumetric results make sense?”
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Index
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Index
Appendix A
The Simandoux Conductivity Equation (A historical perspective)
The actual form and derivation of the “Simandoux”equation as quoted and used in
ELAN has a long and tortuous history. Enquiring minds who refer to the original
Simandoux paper of 19631 (and can read French) will find that the paper is in fact a
report on laboratory experiments to measure the complex dialectric constant at
1MHz of material samples that relate the dialectric constants and losses to water
saturations; and resistivity to porosity, clay content and clay resisitivity, but for water
filled formations only, by the following equations:
K – C∗
2
ζε 1 + ε′ = ζε 1 + εδ + ASw + BSw = Kζε 1 -------------------------------------------------2
( K – C∗ ) 2 + ( G∗ ⁄ ω )
(EQ 9)
and
G∗ ⁄ ω
1
2
ε″ = --- ( ASw + BSw ) = Kζε 1 -------------------------------------------------2
µ
( K – C∗ ) 2 + ( G∗ ⁄ ω )
and
1
1
p
---- = ------- + -------R
R m R sh
(EQ 10)
(EQ 11)
Where:
ε1 = Dialectric constant of apparatus walls
ε’ = Real dialectric constant of the sample
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Quality Control of the Results
Quality Control
ToC
ε” = Dialectric losses of the sample
δ = Thickness of the ionic double layer
ζ = Dimensionless coefficient, describing the ratio between the active capacity of the
apparatus walls and that of the sample = (K/ε1)/C0
C0= Active capacity of apparatus cell.
ω = Angular frequency of the current 2πf
µ = Proportionality of the coefficient between ε’and ε”
K= Capacity of the apparatus insulating walls
C*= Apparent capacity of the cell-sample combination
G*= Apparent conductance of the cell-sample combination
A= Constant
B= Constant
p= Clay content of the sample
R= Radius of apparatus external walls in the case of a cylindrical cell
Rm= Resistivity of the equivalent clean formation
Rsh= Clay particle resistance
Sw= Water saturation
It may be seen from the form that the above equation is strictly valid for laminated
layers of clean sand and shale only.For this reason many, in fact most, saturation
models that are variations of a laminated model are termed “Simandoux”equations.
The actual form of the equation in ELANPlus is based on the same concept as
Simandoux of laminated sand-shale layers but originally derived from an equvalent
parallel resisitor model. This gives:
n
m
φ e Sw
1
Vsh
------ = ( 1 – Vsh ) ----------------------------------- + --------m
Rt
Rsh
aRw ( 1 – V sh )
ELANPlus Theory
(EQ 12)
144
Index
Quality Control of the Results
Quality Control
ToC
This equation was first modified for a reduced effect in hydrocarbon bearing
formations:
n
m
φ e Sw
˙
Vsh
1
------ = ( 1 – Vsh ) ------------------------------------------ Sw
+
m
Rt
Rsh
aRw ( 1 – V sh )
Index
(EQ 13)
And then for the non-laminar behaviour of real clays:
n
m
c
φ e Sw
Vsh
1
------ = ------------------------------------------- + ----------- Sw
m–1
c
Rt
Rsh
aRw ( 1 – V sh )
(EQ 14)
This equation was first published in the 1972 Schlumberger Log Interpretation
Principles2 book with the assumption of m=n=2. In his 1985 review of saturation
equations Paul Worthington3 classifies the original Simandoux equation as a “Type
1”, which means it has a form of Phi x Sw plus linear Vclay, whereas the above
equation is classified as a “Type 2” where Sw is raised to a power and Vclay contains
an Sw term.He attributes this equation to Schlumberger, 1972, with no reference to
Simandoux. However, the 1972 Schlumberger Log Interpretation Principles book
directly references the original Simandoux paper as the basis of the 1972 equaiton,
and also the paper by Poupon et al4 in 1967 as the development of the model.
Considering that Shale is a mixture of clay and silt, the 1972 Log Interpretation
Principles book uses the standard R0=aRw/φm to obtain:
R clay
R clay
( V sh = V silt + V cl ) → ( I Silt = V silt ⁄ V Sh ) → R sh = -------------------------x = -----------------------------( 1 – V silt ⁄ V sh )x
( 1 – V silt )
(EQ 15)
where x is empircally found to range between 1.4 and 2.4, depending on clay
distribution type, and Vsilt is the silt index or volume. Combining equations 6 and 7
and using m, n, and a instead of 2,2 and 1 :
m
n
x
φ e Sw
V cl
1
------ = ---------------------------------------------------------------- Sw
- + ---------------------------------------------(x – c)
c m–1
Rt
R cl ( V cl + V silt )
aRw ( 1 – ( V cl + V silt ) )
ELANPlus Theory
(EQ 16)
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Quality Control
‘x’ and ‘c’ were usually taken equal to 2 for practical reasons: it allows reduction of
the equation to a quadratic form that may be solved using a slide rule or simpe
calculator.
With the x = ‘ersh’ and the c = ‘swshe+1’in ELANPlus terminology, three further
assumptions were made :
1) The difference between the exponent of (m-1) and 1.0 for shale term in the first
denominator is not significant enough to consider for shaley sand, and therefore (m1) is assumed 1.0.
2) The Sw in the second term should be to the power of n/2, not unity.
3) ‘m’ may vary with porosity as per the Shell formula. The usual value assumed for
mc2 is 0.19.
This produces the form of the equation as implemeted, and with conductivity
replacing resistivity, the Simandoux Conductivity Equation is written:
n
--2
V
( m + ( mc2 ⁄ φ e ) )  V uwa n
ersh  uwa
C ucl V cl  ---------------
 --------------- (EQ 17)
C uwa φ e
 φe 
 φe 
C t = -------------------------------------------------------------------------------- + -------------- ------------------------------------------------------------------------a
( swshe + 1 )
( ersh – swshe – 1 )
1 – ( V cl + V silt )
( V cl + V silt )
See Table 28 for the parameters used in the equation.
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Index
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Glossary
alpha processed, alpha processing Alpha processing is a signal processing technique that uses
high frequency information from a short spacing detector on a multidetector tool to enhance the vertical resolution of the tool. An alpha-processed curve is a curve that has undergone alpha processing.
absent
A special numerical value, recognized by the ELANPlus program as representing invalid data. The Absent value has historically been -999.25, a
value that is unlikely to occur in borehole data from logging tools and
that produces a specific, easily recognizable bit pattern on certain computers. If necessary, Absent cane set to any number.
Note: an Absent curve is not the same as a missing curve. An Absent
curve is a curve in the database that contains only Absent values. A missing curve simply does not exist in the database.
balanced uncertainties Equation uncertainties chosen so that each equation has approximately
the same relative influence on the volumetric results.
calibration problem
ELANPlus Theory
In a linear algebra expression of the type Ax = b, the calibration problem
is that of determining A, when b and x are known. Contrast with inverse
problem.
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constraint
Glossary
A limit imposed on the volumetric results of the ELANPlus optimizer. A
constraint can be used to impose an absolute upper or lower limit on an
output volume (for example, volume of flushed-zone water ≥ 0.03) or it
may establish a relationship among volumes (for example, volume of
montmorillonite ≤ 0.25 times the volume of illite).
curve (data curve)
A depth-indexed array of real-valued data such as logging data or environmentally corrected data.
Combine process
A part of the ELANPlus application that provides the capability to combine the results of several Solve process computations into a single set of
answers.
formation component One of a set of minerals, rocks or fluids assumed to be present to some
degree in a borehole interval under study.
forward problem
In a linear algebra expression of the type Ax = b, the forward problem is
that of determining b, when A and x are known. Contrast with inverse
problem.In the ELANPlus program, the forward problem is also called
log reconstruction.
Function process
The part of the ELANPlus application that takes input and produces output according to one or more predefined or user-defined functions.
hypertext
A system of links between parts of a document or documents that allows
the user to click on a link in one document to display the relevant information in (and to navigate among) other documents and return to the
same place in the original document.
incoherence function
A mathematical expression based upon the deviation of reconstructed
tools from the true tool reading, taking also into consideration the uncertainty of each tool. It is this function that the optimizer tries to minimize
to achieve the most probable answer.
inverse problem
In a linear algebra expression of the type Ax = b, the inverse problem is
that of determining x, when A and b are known. It is named for the fact
that the matrix A must be inverted to obtain the solution.
In the ELANPlus program, the linear response equations can be written
in this form and are usually written t = Rv, where t is the tool, or log data,
vector, R is the matrix of response parameters and v is the formation
component volume vector. The object of the inverse problem is to obtain
v, given t and R. The concept of the inverse problem applies whether the
equations are linear or nonlinear.
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Glossary
local knowledge
Quality Control of the Results
Information specific to a localized area, usually a well or field, which is
taken as truth. When properly provided to the ELANPlus program, local
knowledge such as “We know that the XYZ sand contains no more than
20% calcite cementing,” can help produce a more accurate interpretation.
log measurements
The data obtained from instruments lowered into a borehole, sometimes
referred to as tools.
level by level
An analysis in which data from input curves are all obtained from the
same depth, with no consideration to the data values at adjacent levels.
When computations for the current depth level are complete, results are
written to a file (either in memory or on disk) at the same depth as the
input data.
model
A set of response equations, formation components, constraints, and
parameters that define the problem to be solved by the ELANPlus program.
nc
The number of clays in a model, including all clays that have specific
names (ILLI, MONT, etc.) as well as the generic clays (CLA1, CLA2).
nf
The number of fluids in a model, including all types of fluids (water,
hydrocarbon, irreducible, etc.) in both the flushed and undisturbed zones.
nfc
The number of formation components in a model. Unless otherwise
stated, nfc includes all solids—nonclay and clay alike—and all fluids.
However, note that since bound water (XBWA) is solved for as a dependent variable, nfc does not include it.
nuf
The number of fluids in a model, including all types of fluids (water,
hydrocarbon, irreducible, etc.) in both the flushed and undisturbed zones.
Applies to all fluids, regardless of type, in the undisturbed zone only.
nxf
The number of fluids in a model, including all types of fluids (water,
hydrocarbon, irreducible, etc.) in both the flushed and undisturbed zones.
Applies to all fluids, regardless of type, in the flushed zone only.
ns
The number of solid formation components in a model, including both
clays and nonclays unless otherwise stated.
parameter
A numeric or alphanumeric value, that can be set by the user and is used
by the program in the evaluation of expressions, in the selection of inputs
and outputs, or to control program flow.
process
A computation component specified by the user for an ELANPlus session. A process can be of type SOLVE, COMBINE, or FUNCTION, and
each type of process performs a specific type of computation.
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p.u.
reconstructed logs
Glossary
Porosity Unit. Internally, the ELANPlus program always works in decimal porosity, that is, values ranging between 0.0 and 1.0, inclusive.
Porosity units are 100 times the decimal units, or values between 0.0 and
100.0.
Output curves that are generated from computed formation components
and from response parameters using ELANPlus response equations.
Reconstructed logs are mathematical reconstructions of measured logs.
relative volume uncertainty The uncertainty for an individual volume, normalized so that the
smallest uncertainty has a value of 1.0. When all relative volume uncertainties are less than 10, the results warrant a high level of confidence.
resolution number
A number that represents the relative degree to which the equations
selected in a model respond to the selected formation components.
Strictly speaking, for any response matrix, the resolution number is the
base 10 logarithm of the ratio of the largest eigenvalue of the response
parameter matrix to the smallest eigenvalue. A value in the range of 3 to
4 generally indicates that the input logs are sensitive to the selected formation components. A value greater than about 6 indicates that at least
one formation component exists for which the input logs all react in a
similar way.
For a formation composed of calcite and water, using the equations for
gamma ray, thorium, and potassium (alone) would result in a very high
resolution number, even though there are more than enough equations,
since these logs are insensitive to any differences between calcite and
water. Using density and conductivity, on the other hand, would produce
a low resolution number.
response equations
A mathematical expression whose form is known to the ELANPlus application. A response equation relates a set of measured logs such as density,
gamma ray, etc., to a set of formation volumes such as quartz, water, oil.
response parameters
A parameter, usually zonable, whose value represents the reading of a
tool when surrounded by 100% pure formation component. There are
therefore (number of tools) times (number of formation components)
response parameters available in the ELANPlus program. The mnemonic
for a response parameter consists of its tool mnemonic and its formation
component mnemonic, joined by an underbar (for example,
RHOB_QUAR, DT_XWAT, CT1_USFL ...).
Solve process
A part of the ELANPlus application that uses input logs to compute the
volumes, reconstructed logs, and Standard Deviation of Reconstruction
(SDR).
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tools
Measurements from logging devices, such as bulk density, gamma ray,
and deep conductivity. In addition to log measurements, tools may also
be constant or zoned values.
uncertainty
The numerical value expressing the level/degree of uncertainty of how a
response equation will contribute to the final solution of an instantiated
ELANPlus model.
volumes
Values assigned to formation components such as quartz, illite, oil, and
bound water. These values are calculated from logging measurements
and response parameters. The term volumes is often used interchangeably with formation components.
zoned parameter
A parameter whose value varies with the depth interval in which it is
defined. A zone can be defined by a top depth and a bottom depth or by
a top depth and an interval.
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Index
ABCDEFGHIJKLMNOPQRSTUVWXYZ
C
T
Choose, meaning 4
Command Bar 5
Table of Contents
using hyperlinks in 3
typographical conventions 4
E
Enter, meaning 4
Equation, Simandoux Conductivity 145
X
xpdf reader 3
G
GoBack button 4
H
hypertext link, using 4
M
mouse button usage 4
P
pdf (portable document format) 3
Previous Topic button 3
S
Select, meaning 4
Simandoux Conductivity Equation
A historical perspective 145
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