CHAPTER FOUR: INTRODUCTION TO QUANTITATIVE METHODS

Table Of Contents
4.00 Introduction to This Chapter
4.01 What Does Quantitative Analysis Really Mean?
4.02 Quality Control Comes First
4.03 Visual Interpretation
4.04 Log Analysis as a System
4.05 The Analysis Model
4.06 The Environment Near the Borehole
4.07 Resistivity Distribution Around the Borehole
4.08 The Formation Rock Model
4.09 The Log Response Equation
4.10 General Rules For Picking Log Values
4.11 The Classic Examples
4.12 Selection of Log Interpretation Parameters
4.13 Organization of the Mathematical Algorithms
4.14 Arranging Algorithms Into Analysis Routines
4.15 Use of Abbreviations
4.16 Mathematical Operators
4.17 Mathematical Hierarchy
4.18 Mathematical Functions
4.19 Comments on Mathematical Notation
4.20 Use of Relational Operators
4.21 Units Conversions
4.22 In Conclusion
4.23 Exercises For Chapter Four
4.24 Bibliography For Chapter Four

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Publication History: This Chapter formed Chapter Four of The Log Analysis Handbook, Pennwell 1986. Only minor corrections were made for this electronic edition Feb 2001.

CHAPTER FOUR: INTRODUCTION TO
QUANTITATIVE METHODS

4.00 Introduction to This Chapter
This Chapter deals with a variety of concepts necessary for handling quantitative analysis, both conceptually and physically. Definitions of the log analysis model and its components are presented, along with step by step procedures for reviewing log data before analysis. Selection of analysis parameters and basic mathematics are also covered for those who may be a bit rusty in these subjects.

A rational method for writing useful algorithms and a procedure for combining these into working log analysis routines is described in detail. The approach is generic and can be applied to any programming language or log analysis software package that accepts user defined algorithms. They have even been used successfully in programmable calculators and electronic spreadsheets such as Excel or Lotus 1-2-3.

The field and office procedures outlined in Chapter Two, especially the quality control sections, should be thoroughly understood before embarking on any quantitative analysis.

Material is presented from two points of view; one as if the calculations are to be done by hand, the other assumes the data reduction will be done by computer. Both approaches require many of the same pre- and post-evaluation steps.

4.01 What Does Quantitative Analysis Really Mean?
Quantitative analysis is a matter of data reduction and summary. Analysis and interpretation should not be confused or construed to be one and the same. Some people use the words log evaluation to mean either or both analysis and interpretation. We prefer to think that analysis and evaluation mean data reduction and that interpretation involves trying to understand these results in light of the assumptions made, and other known facts not used in the analysis.

FIGURE 4.01: The Data Reduction/Analysis/Interpretation Model

Although some theoretical research has been done on log response, much work is based on observation and empirical relationships derived from correlation of measured rock properties versus well log readings of the same rocks. These empirical equations are the heart of quantitative analysis.

Unfortunately the formulae are often derived from very limited data sets. For example, one of the original papers on log response was by G.E. Archie. In it, he described 48 core samples and a corresponding number of porosity and resistivity measurements. Other analysts have run many more such samples through the lab, and have come up with different relationships, depending on where the samples originated. Archie's equation, and the interpretation parameters he suggested, are still in use nearly 60 years later, when it is known that the data is only an average result of a very limited local sample, not even a world-wide average.

The moral - log analysis parameters are not usually constants, although frequently referred to as such.

Not all methods outlined in this handbook, or elsewhere, apply in every instance. Nor is there time or data available to try every method on a particular zone. How to select a reasonable method is described in appropriate sections of each Chapter.

With the advent of modern, inexpensive, multi-function, programmable calculators, pocket computers, and desktop micro-computers, chart book methods are quickly disappearing. Charts are occasionally referred to when working in complex lithology, where the pattern or position of points on the chart or graph may be helpful - see Chapter Eleven. Even this can be quantified by appropriate equations.

For fast, practical analysis, preprogrammed methods for the calculator or computer are essential. They are provided in later sections of this handbook and are computer-ready. They do not need translation or modification to be used in virtually all computers with Basic, Fortran, or similar computer languages or interpreters. This may have made the equations a little harder to read, but easier to use.

Algebra from various Chapters can be merged together and coded in calculator or computer language to give customized programs for the individual user. Once recorded and documented, they can be carried on the job as readily as a chart book.

The charts supplied in service company handbooks are generally easy to use, but it is essential to remember the limitations, restrictions, and assumptions which apply. Should you wish to use charts, a personal set may be assembled from this handbook or other sources. Keep the list of conditions for their use on the page next to each chart. Limitations given in this handbook are shown on the mathematical documentation pages, and apply to the corresponding charts. Very few charts perform shale corrections and few handle complex lithology (mixed mineral formations) or special cases.

4.02 Quality Control Comes First
On current drilling wells, the first items to tabulate are which service company ran the log, the engineer's name, who the log was run for, and who was the witness. In time, these names will become familiar and the particular failings or good points of the individuals involved will be helpful in solving future problems.

On projects, keep track of the service company, tool type, age of the logs, and mud system variations. These factors create differences in log response that may need to be accounted for.

Examine headings for any notes concerning tool problems or scale changes. Monitor log scales over the interval in question to ensure they are reasonable for the type of log being reviewed. Verify that calibrations have been run and are attached to the bottom of the log. In addition, check that the repeat section is present and that the log does repeat. On older logs, some of these features may be missing.

Following these basic quality control steps will ensure the logs contain reasonable information. Further details on quality control can be found in Chapter Two. Information on calibrations is presented in Chapter Five.

4.03 Visual Interpretation
Some knowledge of shale content, porosity, lithology, and hydrocarbon indications are required without resorting to chartbooks, calculators or computers, prior to starting a quantitative analysis. It is also needed when a quick decision must be reached, or as a preliminary analysis to find the most interesting zones in a well, prior to more detailed analysis. You can't analyze a log unless you know where and what to look for.

Therefore, it is recommended that a quantitative analysis be performed by first reviewing the entire set of logs, well history, well test information, and geologic setting.

The steps to follow for a visual interpretation prior to a quantitative analysis are listed below. They are covered in detail in subsequent Chapters:

1. Review local and regional geologic information, maps, formation descriptions, structural features, seismic data, existing oil or gas production, and well history data.

2. Correlate logs and pick formation tops, or mark tops provided by the well history, well information card or data base retrieval. Annotate the formation description on the log or on an accompanying sheet.

3. Mark all known drill stem test data, cored intervals, perforated intervals, initial or current production on the logs, or on an accompanying data sheet.

4. Edit the logs, fix spikes and skips, check scales, and compare with offsets. Decide which curves are good, which are bad, and list depth shifting problems. Record notes on the data sheet or on the logs.

5. If logs are to be used for geophysical purposes, mark velocity and density scales on the logs and verify that the resulting log is reasonable.

6. Scan the log for clean zones versus shale zones. That is, detect zones with low volume of shale (Vsh). This is done by examining the spontaneous potential (SP), gamma ray (GR) and density neutron response. This defines the zones of interest. Although a zone may be water bearing, it is still a useful source of log analysis information, and is a zone of interest at this stage. Low values of GR, highly negative values of SP and density neutron curves falling close to each other, usually indicate low shale volume. High GR values, no SP deflection and large separation on density neutron curves normally indicate high shale volume.

7. For zones of interest, review the porosity logs - sonic, density, and neutron. Identify zones which show the best, medium, poor or no porosity. Scale each porosity log based on the assumed matrix lithology. Discount coal beds, which appear as apparent porosity greater than 40%.

8. Select the shale base line on every log near each zone of interest.

9. Look for hydrocarbon indications and obvious water zones: High porosity and high resistivity usually indicate oil or gas. Crossover on the density neutron log usually means gas. Watch for rough hole problems or sandstone recorded on a limestone scale, which can also show crossover. Known DST, production or mud log indications of oil or gas are helpful.

Watch out for coal - unless you are looking for coal bed methane.. Water zones with high porosity and low resistivity should be obvious. Fresh water may look like hydrocarbons, particularly in shallow zones. The lack of SP development will often help distinguish fresh water zones.

10. Try to identify the matrix rock from the formation and sample descriptions. In carbonates, check the density neutron log. If there is separation between the curves, and the shale indicators show the zone is clean, suspect dolomite or anhydrite. Otherwise, limestone or sandstone is indicated. High shale content is shown on the GR log, density neutron log readings are close together, and hole conditions are a sign of radioactive sandstone or limestone. To distinguish radioactive dolomite zones from shale zones use a gamma ray spectrolog since the density neutron log will show separation in both cases.

11. Look for signs of permeability - indicators are porosity, mudcake shown by the caliper, separation on the resistivity log curves, known production or tested intervals, sample descriptions and hydrocarbon shows in the mud.

12. If necessary, estimate depositional environment.

13. Check for indications of fractures, such as sonic log skips, hashy dipmeter curves, hashy resistivity curves or caved hole in carbonates.

THEN AND ONLY THEN

14. Use charts, calculators, computers or mental arithmetic to refine your opinion by calculating shale corrected porosity and water saturation.

15. If results do not coincide with other facts, go back to Step 1 and refine assumptions.

16. Write a report discussing problems, results, sources of data and errors, discrepancies, areas for further work, and recommendations about the well.

FIGURE 4.02: The Ladder of Success for Log Analysis

I call the above picture my “Ladder to Success” - climb slowly, don’t skip any steps, and your log analysis will be successful. A consistent, step by step procedure will produce more reliable results with less chance for error. It tends to remove some of the mystery involved in log analysis, and reduces effort in the long run.

4.04 Log Analysis as a System
A log analyst should attempt to create a systematic analysis approach that is thorough, repeatable, and as accurate as possible. The step by step method described above, and the mathematical solutions provided later in this handbook, will help provide a basis for such a system. These methods are presented in the order in which the calculations are usually made, starting with the simplest and proceeding to the most complicated or least desirable in each section.

Virtually no analysis is based on just one or two log curves. Therefore, the entire complement of curves must be considered as a system and incorporated into the analysis as a complete set. When the proper algorithms from this book are selected, all available data will be used to gain the most knowledge about the well.

The system will not replace experience, research, and practical common sense. Since the results are seldom used directly by the analyst, the end user and management must be considered part of the system. Keep their needs and knowledge in mind when presenting results. The systems approach makes the step by step procedure not only necessary but attractive as well.

It usually requires the minimum long term effort, because you will not miss anything or have to analyze the data more than once. Quality control of your own work and the work of others is required for success as an analyst. Be fair, but be critical of all data, and rationalize the discrepancies as well as possible. When this is impossible, file the offending analysis for future study. New knowledge or experience may solve the apparently unsolvable.

Do not forget the limitations of the logging tools, analysis methods, and personal experience. The "Weasel Clause" applies to everyone.

4.05 The Analysis Model
Quantitative log analysis is based on a series of mathematical formulae, or models, derived from the experience of many analysts. Thus, literally thousands of methods exist. The most universal applications have been assembled in this handbook. Only a very few of the equations are original to the author.

The models used take into account two distinct problems:

1. Invasion of the formation by drilling mud filtrate.

2. The complex mixture of rock types and fluids that comprise the formation.

The model used in this handbook is described below. If you wish to apply a method not outlined in this book, remember that it may use a different rock or borehole environment model.

4.06 The Environment Near the Borehole
Variations in rock properties caused by the invasion of the drilling fluid into the rock play an important role in log analysis.

Invasion is a process whereby drilling mud fluid is forced into the rock due to differential pressure. The drilling mud is made up of solid particles and ions dissolved in water. This water displaces the native formation water to some degree, and mixes with formation water that is not displaced. The distance to which some displacement and/or mixing occurs is called the invasion diameter, and the zone so disturbed is termed the invaded zone. The zone nearest the borehole, or flushed zone, is the portion of rock where the maximum amount of displacement and mixing has occurred. The balance of the invaded zone is named the transition zone, where the transition between maximum flushing and no invasion occurs.

The invasion process leaves behind the solid particles of the mud, which collect on the borehole wall. The resulting material is called mud cake, and may be 3 to 4 inches thick or very thin and difficult to detect. The mud cake thickness by definition is one half the difference between the bit size and the borehole diameter. If the hole is enlarged by erosion beyond the bit size during drilling, the mud cake thickness may be impossible to determine.

Mud cake is the sealing agent which slows down invasion. As a result, high permeability zones which allow quick buildup of mud cake, invade the least and low permeability zones invade the most or deepest. Non-permeable zones are not invaded.

Since the depth of investigation of logging tools varies, knowledge of the invasion profile is necessary in making assumptions about log analysis methods or parameters.

The resistivity log is the most severely affected by the invasion process. Sonic, density, neutron and spontaneous potential logs may also be influenced depending on the hydrocarbon type and density.

The abbreviations and definitions listed below describe conditions found within the borehole environment:

Abbreviation Definition

Rxo resistivity of the flushed zone
Ri resistivity of the invaded zone
Rt resistivity of the undisturbed zone
Ro resistivity of the undisturbed zone which is 100% water saturated
RZ resistivity of unknown mixture in the transition zone
RW resistivity of formation water
RM resistivity of mud
RMF resistivity of mud filtrate
RMC resistivity of mud cake
Dh borehole diameter
Di invasion diameter
Dj diameter of the flushed zone

FIGURE 4.03: Drilling Fluid Invasion Model

CAUTION: Many analysts and logging engineers use these abbreviations as nouns to replace the full definitions. This habit should be avoided, since few people understand their meanings.

4.07 Resistivity Distribution Around the Borehole
Resistivity distribution in a radial direction from the borehole determines the response of resistivity logs to various invasion conditions. Some typical profiles are shown in Figure 4.03.

FIGURE 4.04 Resistivity Response versus Depth of Investigation

Resistivity logs that measure different depths into the rock can be used to estimate the invasion profile. Results are used to judge the reliability of resistivity data, and to correct the log readings for the effects of invasion.

4.08 The Formation Rock Model
The formation rock model used for the interpretation methods described in this handbook is shown in the illustration below:

FIGURE 4.05: The Formation Rock/Fluid Model for Log Analysis

Here are the definitions that derive from the rock/fluid model shown above.

By definition, Vrock + PHIe + Vsh = 1.00

The mineral mixture can be quite complex and log analysis may not resolve all constituents.

The sum of the three water volumes is called clay bound water (CBW). CBW varies with shale volume and is zero when Vsh = 0.

By definition, Vsh = Vcl + Vsilt + CBW

Some of the “free water” is not free to move - it is, however, not “bound” to the shale.

BVI is sometimes called “bound water”, but this is confusing (see definition of clay bound water above), so “irreducible water” is a better term. Note that BVWm = BVW – BVI.

This definition is needed for the nuclear magnetic log (NMR, CMR, etc), since it cannot see BVWir. Non-useful porosity also occurs as tiny pores that do not connect to any other pores. They are almost invariably filled with immoveable water and do not contribute to useful reservoir volume or energy. Such pores occur in silt, volcanic rock fragments in sandstones, and in micritic, vuggy, or skeletal carbonates. The NMR may see some of this non-useful porosity – the jury is still out.

This is the standard definition of “water saturation”. Older books use this term to define total water saturation. Since all interpretation methods described here correct for the effects of shale, we are not normally interested in the total water saturation, except as a mathematical by-product. As effective porosity approaches zero, the water saturation approaches one (by edict, if not by calculus).

The amount of free water in the invaded zone is usually higher than in the un-invaded zone, when oil or gas is present. Thus Sxo >= Swe. The water saturation in the invaded zone between the flushed and un-invaded zone is seldom used.

All volumes defined above are in fractional units. In tables or reports, log analysis results are often converted to percentages by multiplying fractional units by 100.

4.09 The Log Response Equation
The response of an individual log to the model described above is defined by the log response equation. The usual log response equations are of the form:

This response equation will work for sonic travel time, density, or density porosity, neutron porosity, gamma ray (and the spectrolog curves - uranium, thorium and potassium), resistivity (if Sxo is replaced by Sw for deep resistivity logs), the electromagnetic propagation log, the thermal decay time log, and the photoelectric effect (if PE * DENS is used). It will also work for various derived logs described in later chapters of this handbook.

The response equations can be used in several ways. One is to find out what a log would read under a hypothetical set of circumstances. Another way is to calculate one unknown in the equation, for example porosity or shale volume, by using a log reading and assuming the other terms to be known or derivable from some other response equations. A third approach is to use sets of response equations simultaneously to determine as many unknowns as possible from the available log data.

Some terms in the response equation for certain logs go to zero. This is what makes it possible, for example, to calculate the shale volume from the gamma ray response. Both the water and hydrocarbon terms go to zero, since neither of these components has any gamma ray contribution. By re-arranging terms and further assuming that porosity is small, we get:

1. VSHgr = (GR - GRmatrix) / (GRshale - GRmatrix)

Here GR, GRshale, and GRmatrix are read from appropriate places on the gamma ray log to calculate shale volume.

In other cases, we sometimes lump two terms together, as for water and oil in the sonic log equation for porosity. This strategy eliminates the need to know water saturation prior to knowing porosity. This approach will fail if gas is present because the water and gas contributions are too dissimilar.

The algorithms in following chapters attempt to resolve as many of the unknowns as possible using these piecewise techniques. Where this is inappropriate, sets of two or three simultaneous equations are solved, with the final solution being given. It will not always be obvious that simultaneous response equations were used, but ALL log analysis methods rely on this approach. What we have done here is eliminate the repetitive derivation of the solution, and present instead the finished product, ready for inclusion in a calculator or computer program.

The borehole environment, invasion, and rock model define the log analysis problem. Logging tools define most of the data available to analyze the model. With many analysis methods to choose from, there are usually many possible answers. It is the analyst's job to select the method and model that best describe the problem to be solved. Adjustments to the basic model presented here are therefore plausible, and may be essential.

4.10 General Rules For Picking Log Values
In order to perform a log analysis, it is necessary to read or pick log values in the various zones of interest, and other key locations, such as in shale or water bearing zones. Selections should be made on a consistent basis from day to day to assist reproducibility of results. When using digital log data, the digits themselves will be used by the computer program, but the analyst must still pick numerous values by observation of log curves, crossplots, or data listings.

In computer aided log analysis, picks are made continuously with a digitizer or by reading magnetic tapes or discs created when the logs were recorded. Such data tends to be more accurate than hand picked values. Accuracy can be a hindrance on noisy logs, rounded bed boundaries, or in large or rough holes. Some editing or curve shaping may be required prior to digitizing, hand picking data, or using existing digitally recorded data. This subject is dealt with in Chapter Five.

To select a log value it is helpful, especially for the novice, to "box the log". Draw horizontal lines at each bed boundary, at the inflection points on each curve. Draw vertical lines on each curve at the peaks and valleys, thus transforming the log into a series of individual beds with a single specific log reading.

FIGURE 4.06: Picking Layers

With experience, it is possible to simply mark points at the peaks and valleys without drawing horizontal lines, as shown in the lower part of the figure shown above. When listing data values on a log interpretation form, as shown below, the top and bottom depth values can be estimated visually

FIGURE 4.07: Log Values Picked From Figure 4.06

Finally, experience will allow values to be picked without marking the log, although this practice may be continued for a lifetime. Clean copies of logs can always be obtained for future use.

Unless absolutely necessary, values should not be selected on slopes. Slopes indicate transition from one condition, such as porosity or hydrocarbon content, to another. Average values, halfway along the slope may be meaningful, but can also be misleading. Do not select values in thin beds unless you are also prepared to make bed thickness corrections.

Tables may require rewriting, since picking bed boundaries on other logs may produce additional zones not seen initially. When all values are picked, the analyst can proceed with calculations.

Note that very shaly zones are not usually analyzed. Therefore, this data can be left off the table or marked as shale with no data values entered.

Be sure to pick the correct curve, its appropriate scale, and edit any noise or bad hole conditions prior to finalizing values.

When using computers, log data is usually digitized at an increment much finer than the tool resolution. Thus answers are calculated even on slopes and in thin beds. Interpretation from such results usually requires some thought.

4.11 The Classic Examples
In order to demonstrate the methods described in later sections, a classic example has been prepared. The example is very simple, but illustrates the methods without ambiguity.

The logs available for the classic example are shown below.

4.12 Selection of Log Interpretation Parameters
The method of selecting parameters depends on whether knowledge of fluid, matrix, or shale values is desired.

Fluid values for various interpretation methods are generally obtained in a laboratory environment and adjusted for temperature, pressure, and salinity as required. They cannot generally be picked directly from logs. More information on this subject is located in Chapter Seven.

Matrix rock values are normally available from handbooks or data tables. The numbers usually represent log readings for pure minerals, which rarely exist in real situations. The values may also be found by inspecting logs if relatively pure, zero porosity zones are present. Some crossplots may assist in finding matrix parameters, see Chapter Eleven.

Due to varying shale compositions, shale values are not as well known or as constant as for other rock minerals. They are often found by inspecting logs in a shale bed near the zone being interpreted. Some crossplots may assist in finding matrix parameters, see Chapter Eleven.

In order to pick a parameter, the expected values must be known approximately. Only then is it possible to determine if the value seen on the log or the crossplot is reasonable and representative of the parameter required. This may involve evaluating several wells to gain confidence in making assumptions. Expected parameter values are found in Chapter Seven.

Suggested methods for selecting parameters through log inspection are illustrated in Figures 4.19 through 4.21 and the following discussion. Note - Figures 4.13 through 4.18 have been omitted to reduce confusion.

1. Shale resistivity is the average value of the deepest resistivity curve reading in shale, (two or more feet thick), below the zone in question. Generally, this is a minimum value, and the correct value may be 1.5 to 2.5 times higher. It is used to correct the water saturation equation for shale.

2. Resistivity in a water zone is the lowest value of the deepest resistivity curve reading in a water zone, (20 feet or more thick), below the zone to be interpreted. The value will generally be slightly to 2 or 3 times too high. It is used to determine water resistivity for water saturation calculations.

3. Matrix values for the sonic, density, and neutron logs are used to correct for the effects of the varying lithology. Find the lowest consistent value of sonic travel time, lowest density, porosity, (or highest density), and lowest neutron porosity in the zone to be interpreted. If these values are close to the expected matrix value for the known lithology, they may be used with caution. If lithology is unknown, start with pure mineral values from tables.

4. Shale values for sonic, density, and neutron are determined from the average value of logs in shales, (20 or more feet thick), below the zone to be interpreted. This applies to clean logs without skips, spikes, and rough or large holes. Caution should be used since shale properties can vary widely within a short interval. Data is used for shale corrections to porosity calculations. Therefore, corrections may be inaccurate if shale properties vary or are poorly chosen.

5. The gamma ray and SP clean sand and shale points are all required to find the shale volume for use in shale corrections to porosity calculations. To determine the maximum clean line value, find the cleanest or least shaly zone in the entire well. Lower this value to suit the known shale content in other zones. Caution - never push the clean line into more than 5% of the data points. To find the shale line, draw a line through the average data value in thick shale zones. Do not include very radioactive zones which are generally caused by uranium, and not shale minerals. Up to 10% of the data points may be above the shale line.

If base line methods are difficult, certain crossplots may be helpful. See Chapter Eleven - Use of Crossplots for further information. Some analysts prefer the crossplot method although it requires an extra computer step and is not appropriate for visual or quick look interpretation.

Again, the reader should verify that he or she can pick similar values to those shown in Figures 4.19 to 4.21 and the tables in Figures 4.12 and 4.18. Additional methods for computing rock properties are found in Chapter Seven. These methods are necessary where the needed matrix and fluid values are not directly available from logs or tables, but can be calculated from other known data.

Abbreviations used on the example logs and data tables are discussed later in this Chapter.

Picking log values and analysis parameters from logs is THE most important step in quantitative log analysis. Mathematics cannot compensate for poor selections. Few comments on this subject are found in service company training manuals. As a result, beginners often find it difficult to start with valid data, or assume the task is easy and requires no thought or knowledge.

Analysts may have different opinions on log picks, analysis parameters, and methods, but an individual should be fairly consistent and able to duplicate answers.

4.13 Organization of the Mathematical Algorithms
An algorithm is a set of mathematical operations impressed upon the log data, assumed parameters, and possibly on the results of previously applied algorithms, which produces one or more easily defined numerical results. A series of algorithms make up a routine, and a series of routines make up a computation. Algorithms presented here are self contained units and do not rely too heavily on previous algorithms, so some internal duplication exists, especially in the area of units conversions.

The layout of all algorithms in this book has been specially designed to allow a text editor or language interpreter program to convert the information into a working program. This has been achieved by using a very brief pseudo-programming language with few keywords, and yet it retains many components of the English language to increase readability.

More than one algorithm may appear under a single Chapter subheading. Conversely some Chapter subheadings may contain no algorithm.

The algorithms are written in a pseudo computer language using structural programming style. The key words are:

IF
AND IF
OR IF
THEN
OTHERWISE (ELSE is used in many computers)
AND
FOR ...TO ...ENDLOOP

Each keyword follows the algorithm line number, and only one keyword can be on a line. For example:
1: IF X > Y
2: THEN Z = 36

A more complicated IF statement might use several lines:
1: IF X > Y
2: AND IF Z > 36
3: OR IF SWITCH$ = "ON"
4: THEN W = 14
5: AND Q = 8
6: OTHERWISE W = 15
7: AND Q = 9

Using this style eliminates the need for the END IF statement and allows one to read the program in English without difficulty. It also lends itself to automatic translation into Basic or Fortran by a simple interpreter program or the Find/Replace function of a word processor. Some language interpreters will insist that the complete IF..THEN..ELSE be on one program line. Some care is required to keep the AND and OR statements sorted out when you convert this pseudo-code. Some languages will insist on different punctuation or parentheses to compile correctly. Read your language manuals carefully to determine what you need to do to translate the algorithms.

An example will illustrate this point more clearly:

The end of an algorithm is signaled by the beginning of the next one or by the next Chapter section.

4.14 Arranging Algorithms Into Analysis Routines
We define a routine as a series of algorithms arranged end to end to perform a complete analysis of a data set. The routine is often a standard one, such as a shale volume routine, or a shaly sand analysis routine. Branches between algorithms based on tests of other data, such as bore hole conditions may be included.

Recommended routines are given in each Chapter where required. For example:

The algorithm name, input curve names, and output curve names match those found in the desired algorithm. The Transferred To column represents the renaming of an output curve so that it will match the required name of an input curve name in a subsequent algorithm. Conditions and limits should be placed on the use of an algorithm, such as not using one which requires density data in bad hole. Care should be taken so that an alternative algorithm is allowed and constrained to the balance of the conditions eliminated in the first case.

The input, output, and transferred-to curve names can be considered as pass parameters in Basic or Fortran subroutines. All analysis parameters required by an algorithm are considered to be Global or Common to the entire system, and therefore must be spelled uniquely.

4.15 Use of Abbreviations
The policy of this handbook concerning the spelling of abbreviations is as follows:
1. Measured or assumed values are spelled in capital letters.
2. Derived or computed values are spelled in capital and lower case letters.
3. Spelling should suggest the English word or English spelling of traditional Greek symbol for the term.
4. Lower case letters often refer to the subscript traditionally used in the literature.
5. No real subscripts or superscripts are allowed.
6. Only the twenty-six letters of the English alphabet and the numerals zero through nine, are permitted.
7. No spaces are allowed within variable names.
8. No spelling which is a legal operator, function, or reserved word in Basic or Fortran is allowed.
9. Abbreviations should be reasonably short.
10. Abbreviations for a curve name or constant must be unique within the context in which they will be used.
11. Abbreviations for variables containing character strings end with the dollar sign ($). Numeric variables cannot use the dollar sign.
12. Abbreviations for log curve names end with square brackets []. Other variables cannot use the square brackets.

These rules were developed to allow easy translation of the algorithms into computer programs, while allowing traditional English and Greek terminology.

4.16 Mathematical Operators
For consistency, the mathematical notation in this handbook is that used in many computer languages. This notation is easily translated into Basic, Fortran, spreadsheet programs, or programmable calculators.

The mathematical operations allowed by modern computers and calculators are defined below.

1. Assignment
Different computer languages use varying symbols to indicate assignment:

Only the single equal sign is used in this book.

2. Arithmetic

3. Relational
Relational operators compare two variables and return either true (1) or false (0).

NOTE: Some languages do not permit all the above variations, or use alternate spellings (such as NOT.EQ. in Fortran).

4. Logical
Logical or Boolean operations return true (1) or false (0) depending on the truth or falsity of one or more variables.

TRUTH TABLE FOR LOGICAL OPERATORS
Where: T = non-zero value or 1 = True, 0 = False