CRAIN'S PETROPHYSICAL POCKET PAL
This is the Reader's Digest Condensed version of Crain's Petrophysical Handbook. The majority of the courses I give are based on the material contained in the PocketPal. In-house sessions and Instructor's Kits are available on request -  email us.-

TABLE OF CONTENTS

1.00 Introduction Quantitative Log Analysis 5
1.01 What Is A Log? 6
1.02 Organizing Your Work 7
1.03 Calculators and the Math Hierarchy 9
2.00 The Step by Step Procedure 10
2.01 The Analysis Model 11
2.02 The Formation Rock Model with Definitions 12
2.03 The Log Response Equation 15
2.04 Using The Log Response Equation – Seismic Modeling 17
2.05 Integration – Calibrating to Ground Truth 19
3.00 Eyeball Analysis Of Logs - Crain’s Rules 20
3.01 General Rules For Picking Log Data 29
3.02 Selection of Log Interpretation Parameters 29
4.00 Shale Volume 31
5.00 Pore Volume 33
5.01 Porosity From The Sonic Log 34
5.02 Porosity From The Density Log  36
5.03 Porosity From The Neutron Log 37
5.04 Porosity From The Complex Lithology Density Neutron Crossplot 40
5.05 Porosity From The Dual Water Density Neutron Crossplot 44
5.06 Porosity From The Photoelectric Density Neutron Crossplot 46
5.07 Material Balance for Porosity (Maximum Porosity) 47
5.08 Useful Porosity 48
5.09 Porosity From The Nuclear Magnetic Resonance Log 49
5.10 Fracture Porosity 50
5.11 Porosity from Old ES Logs 51
6.00 Lithologic Analysis of Matrix Rock Volume 52
6.01 Two Mineral Lithology From Matrix Density 53
6.02 Lithology From Sonic Density Neutron Data 54
6.03 Lithology From PE Density Neutron Log 55
6.04 Lithology From Spectral Gamma Ray Log 57
6.05 Lithology From Vp/Vs Velocity Ratio  61
6.06 Elastic Constants / Mechanical Properties From Logs 62
7.00 Formation Water Resistivity 62
7.01 Water Resistivity From Catalog or DST 63
7.02 Water Resistivity From Water Zone (Rwa) 65
7.03 Water Resistivity From Spontaneous Potential 66
8.00 Water and Hydrocarbon Saturation 67
8.01 Determination of Saturation Parameters A, M, N 68
8.02 Water Saturation from Archie Method 70
8.03 Water Saturation from Simandoux Method 71
8.04 Water Saturation from Dual Water Method 71
8.05 Water Saturation from Buckles Number 72
8.06 Irreducible Water Saturation 74
8.07 Moveable Oil Saturation 75
9.00 Permeability and Productivity 77
9.01 Permeability from the Wyllie-Rose Method 77
9.02 Permeability from Porosity 78
9.03 Permeability from the Coates Method 78
9.04 Fracture Permeability 79
10.00 Summarizing Results 80
10.01 Cumulative and Average Reservoir Properties 80
10.02 Fluid Properties and Reserves 81
10.03 Productivity Index and Water Cut 83
11.00 Beyond Log Analysis 85
11.01 Productivity From Drill Stem Tests 85
11.02 Production Projection and Cash Flow 88
12.00 Case Histories / Exercises 95
12.01 Cretaceous Glauconitic Sand 95
12.02 Triassic Dolomitic Sand 100
12.03 Devonian Carbonate Reef 108
12.04 Tar Sands 115
13.01 List of Abbreviations  117

1.00 Introduction To Quantitative Log Analysis
This Handbook is designed to give you a starting point for learning quantitative log analysis methods. It is a condensed version of Chapters 4 through 11 of Crain’s Petrophysical Handbook on CD-ROM, avail able at www.spec2000.net. When log analysis is combined with sample, core, test and production data, it is called Integrated Petrophysics or just plain “petrophysics”.

 You can use this book as a quick reference to quantitative petrophysical analysis or as a self-directed study guide. If you wish to take the exam at the end of this book to earn a certificate of proficiency, please go to my website at www.spec2000.net and click on the Learning Center tab.

To get maximum benefit from available well data, you must integrate logs, cores, samples, tests, seismic, geological, and engineering concepts into a coherent picture. Log analysis performed in isolation is pointless and can be a career-buster. However, learning log analysis methods can be done in relative isolation, as long as we appreciate the contributions available from other disciplines. It is really important to temper, and sometimes completely revise, the results of your log analysis by comparison to other sources of “ground truth”.

 Using productivity analysis based on accurate shale, porosity, lithology, saturation, and permeability calculations from log data, you can compare the quality of a zone with known production in your area. From this, you can decide if the well is worth completing or whether to drill more similar wells. You can also high-grade your drilling or completion prospects based on estimated flow capacity as well as the more usual net pay figures. This handbook provides the methods to extend conventional well log analysis to cover productivity and cash flow analysis.

The real question you must answer is not "What is the porosity and water saturation?"  but "Will the zone produce economically and at what rate?"  This goes considerably beyond conventional log analysis. That’s why my petrophysical software is called Meta/Log (Meta = Beyond). There are cases where you cannot get this far, either for lack of corroborative data or narrow-minded job descriptions, but it never hurts to try. The full spectrum techniques described here will help you find oil and gas more effectively from logs, complete discoveries more economically, and work-over wells with more confidence.

Crain’s Petrophysical Pocket Pal provides quantitative log analysis methods suitable for use by most geologists, engineers, and geophysicists who need to perform quick, complete, and accurate calculations of reservoir properties. The formulas presented are simple but adequate for all but the most detailed work. Usage rules for each method are described, based on the log suite available and the rock/fluid mixture expected. More complex methods are contained in Crain’s Petrophysical Handbook, the “big brother” to the Pocket Pal.

Although visual analysis, crossplots, and log overlay techniques have been widely used, this handbook provides a step by step numerical method which has worked reliably in most formations in many parts of the world. This computational approach minimizes the risk of bypassing lower quality zones, and improves your ability to estimate the quality of a zone. Finding zones of interest on a long log does require some form of visual  scanning. This topic is covered in Section 3.00, after we review the details of our log analysis model.

1.01 What Is A Log
A log is a record of something versus time or distance, such as a Ship’s Log or a travelog.  In oil and gas wells, a log is a recording versus depth of physical or chemical properties of the rocks and fluids penetrated by drilling the well.

FIGURE PP1.01: Recording a wireline log at a well site

The logs we usually think of are wireline logs run in open or cased hole, or logs run near the drill bit while drilling. Sample and core descriptions, core analysis results, as well as drill stem test and production test results are all forms of well logs.

Wireline logs are created by remote sensing equipment lowered into a hole drilled with a rotary or percussion drilling rig. Cased hole logs are run after the well is cased to assess the current state of the reservoir, to check the mechanical integrity of the casing, tubing, or cement, and to monitor fluid flow. Logging while drilling (LWD) provides many measurements similar to open hole wireline logs and are used in the same way as open hole logs.

Logs are created at the well site by a crew specially trained for this job. The equipment is highly specialized and expensive. A typical setup is shown in the illustration above.

FIGURE PP1.02: A Typical Log

The data is recorded, processed, and displayed by the logging service company with a specially designed computer graphics system. Here the data is transformed from the actual measurements into values we can use for analysis of the rocks and fluids traversed by the log. This pre-computation step reduces our labor, but introduces assumptions and procedures over which we have little control.

At right is a typical log, illustrating the standard three track presentation with numerous curves, or log traces, in each track and the usual log header, or scale insert, at the top. The analyst must become competent in reading, or picking, log values from these curves. This involves choosing the correct curve and scale combination, recognizing bed boundaries, and picking log curve values that appropriately represent the properties of the rocks.

Unfortunately, logs seldom measure directly what we want to know, like flow capacity or oil volume in place. Therefore, we have to analyze the values we can measure, and convert them into answers which will help us determine the quality of a hydrocarbon reservoir. To do this, the chosen data is put into equations, using charts, calculators, or computers, to obtain the answers we need.

The basic results, or answers, we need from analysis of logs are porosity, water saturation, and permeability, as well as sums and averages of these values. The results are called petrophysical properties or reservoir properties. Geologists, geophysicists, engineers, managers, and shareholders are all interested in these quantities.  When transformed into productivity and reserves, the answers become more meaningful to non-professionals.

1.02 Organizing Your Work
The logical, step by step procedures presented here are simple and straight forward, and can be used by anyone with a modest knowledge of logs and reservoir geology.
The analysis style offered prevents circular reasoning, provides cross-checks of all major steps, assures completeness, and also significantly reduces labor. Following these steps does not guarantee a successful log analysis, but does offer the closest approximation possible.

Quantitative log analysis is mostly a matter of data reduction to obtain answers that are more manageable than the plethora of raw data. This process is followed by interpretation of the answers to obtain an understanding of the rocks and fluids. The concept is illustrated in Figure PP1.03. You should note the distinction between LOG ANALYSIS (data reduction to get answers) and LOG INTERPRETATION (understanding the answers) that is made here.

Analysis is based on a mathematical model called the Log Response Equation. It is determined by the complex mixture of rock minerals and fluids seen by the logging tools.

The most rational calculation sequence is shown in the test box above. This sequence has proved itself over the years, and is the most straight forward solution to a very complex problem. In many cases the lithology calculation is done concurrently with, or before, the porosity calculation, but the topics are discussed in the order shown. Economic calculations usually follow these steps, and are covered in Section 11.02.

FIGURE PP1.03: Data reduction and interpretation are separate entities

 There are many available methods for each calculation step. The analyst must choose the appropriate method from those presented for each of the topics. Recommended usage rules for each method are given, and depend to a large degree on the available log data and the rock/fluid mixture in the zone being analyzed. These rules may need to be adjusted to suit local conditions. Rules for calibrating results to ground truth are also given.

In the classroom or when starting work in a new area, you may want to try several methods, and see which matches core porosity the best. In an office environment, there is seldom enough time to try all methods on all zones. Unfortunately there is no standard logging program, so there is no single foolproof log analysis method.

For fast, practical analysis, pre-programmed methods for the calculator or computer are essential. The formulas provided in the following sections are "computer-ready" - if your calculator has round brackets, ( ), you can enter the equations just as they are printed. They do not need translation or modification and can be used in virtually all algebraic style calculators or any calculator or computer using Basic or Fortran. “Computer-ready” code may make the equations a little harder to read, but they are a lot easier to use.   

A shareware spreadsheet called META/ESP, using identical math to that contained in this Handbook, us available from the downloads tab at  www.spec2000.net .

Although a calculator or computer is considered essential to reduce labor and to improve accuracy, charts are available from logging service companies for some methods. Unfortunately, most chartbook solutions ignore shale effects, so results are often inaccurate. Computer program and spreadsheet solutions to these equations are also widely used and are commercially available. However, you should be familiar with hand calculator methods for jobs where no computer is available and to understand how different parameters influence computer derived results,

1.03 Calculators and the Math Hierarchy
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. In any case, you must obey the rules of mathematics, in particular the mathematical hierarchy.

Calculations are performed in a specific order by all mathematicians and all computers. Analysts using hand calculators or pencil and paper are obligated to use the same system or will get erroneous results. The order of the operations is called the mathematical hierarchy, and is defined as follows:

Operations at the highest priority are performed first, followed by the next lowest, and so on. If more than one type of operation is shown at one priority level, they are evaluated from left to right as found in the equation. The object of the hierarchy is to reduce the number of brackets needed to indicate the order of calculation.

EXAMPLES:

 A = B + C * D means multiply C by D then add to B

 A = B * C ^ D means take C to the power D then multiply by B

 A = (B + C) ^ 2 * D means add B and C, square it, then multiply by D

Log analysis also may be circular, or at least iterative, since the results from each step can often be compared to other sources of data and corrected if differences are found.

This list looks pretty imposing, and a few steps might be skipped from time to time, but a consistent, step by step procedure will produce more reliable results. It tends to remove some of the mystery involved in log analysis, and reduces effort in the long run. You might consider the procedure to be a "Step Ladder to Success". Unfortunately, you may have to climb the ladder more than once if log analysis results do not compare to ground truth, such as core analysis, sample descriptions, or test results.

Review the available data before embarking on detailed analysis. Locate the well history files or well history cards, look at offset logs, review sample descriptions, formation tops, tests, cores, and production histories, and possibly structural or isopach maps of the target formations. Known gas-oil and oil-water contacts must be noted. If seismic maps or cross sections are available, review these as well.

On deep, remote, or offshore wells, a number of logs may be recorded while drilling, such as mud and hydrocarbon logs, or even gamma ray, resistivity, or other quantitative log curves. These should be added to the "Hopper of Knowledge".

Remember, however, that data from a new well may overturn all previous analysis results on older wells. Thus, some critical assessment of the old data is required in addition to that usually accorded the new data.

A data retrieval from a computer data base may reduce the labor in locating much of the needed information. Both commercial and in-house databases exist and appropriate software is available for most personal computers and workstations.

2.01 The Analysis Model
Quantitative log analysis is based on a series of mathematical formulas, 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.

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. These definitions are illustrated schematically in Figure PP2.04.

The invasion process leaves behind the solid particles of the mud, which collect on the borehole wall. The resulting material is called mudcake, and may be anywhere from 3 inches thick to very thin and difficult to detect. The mudcake 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 mudcake thickness may be impossible to determine.

Mudcake is the sealing agent which slows down invasion. As a result, high permeability zones which allow quick buildup of mudcake, invade the least, and low permeability zones invade the most or deepest. Non-permeable zones are not invaded. Since the mudcake is scraped off each time a drill pipe joint or the bit passes a formation, invasion of shallow zones may be repeated many times with many different fluids, thus making such zones difficult or impossible to analyze.

Figure PP2.04: The drilling fluid invasion model

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. Resistivity distribution in a radial direction from the borehole is determined by the invasion profile. The resistivity log reading in the formation depends on the response field of the logging tool and varies with the design of each tool. Resistivity logs which 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.

For example, if the ratio of the deep to medium resistivity log values is between 0.8 and 1.2, invasion effects are minimal and no correction to the deep resistivity is made. If the ratio falls outside this range, corrections should be applied using the appropriate service company "Tornado Chart". These charts are ONLY useful in water zones – they do VERY BAD THINGS in hydrocarbon zones.

Sonic, density, neutron, gamma ray, and spontaneous potential logs see the invaded zone and are thus influenced by those fluids. Most mathematical models include terms which account for invasion of mud filtrate into oil or water zones, but special models are needed for gas zones. These are noted as special cases in subsequent sections of this handbook.

2.02 The Formation Rock Model
All log analysis methods are based on a uniform, industry accepted model of the reservoir rocks and fluids.

FIGURE PP 2.05: The Formation Rock/Fluid Model for Log Analysis

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

DFN 1: The formation rock/fluid model is comprised of:
                 - the matrix rock (Vrock)
                 - the pore space (or porosity) within the matrix rock (PHIe)
                 - the shale content of the matrix rock (Vsh)

By definition, Vrock + PHIe + Vsh = 1.00

DFN 2: The matrix rock component (Vrock) can be subdivided into two or more constituents (Vmin1, Vmin2, ….), such as:
                 - limestone, dolomite, and anhydrite or
                  - quartz, calcite cement, and glauconite

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

DFN 3: The shale component (Vsh) can be classified further into:
                - one or more clays (Vcl1, Vcl2, …)
                 - silt (Vsilt)
                 - water trapped into the shale matrix due to lack of sufficient permeability to allow the water
                         to escape
                - water locked onto the surface of the clay minerals
                - water absorbed chemically into the molecules of the clay minerals

The sum of the three water volumes is called clay bound water (CBW). CBW varies with shale volume and is zero when Vsh = 0. Most shales are not pure clay and are really silts.

By definition, Vsh = Vcl + Vsilt + CBW

DFN 4: Bulk volume water of shale (BVWSH) is the sum of the three water volumes listed above in the definition of shale and is determined in a zone that is considered to be 100% shale.

By Definition, CBW = BVWSH * Vsh

DFN 5: Total porosity (PHIt) is the sum of:
                - clay bound water (CBW)
                - free water, including irreducible water (BVW)
                - hydrocarbon (BVH)

DFN 6: Effective porosity (PHIe) is the sum of:
                - free water, including irreducible water (BVW)
                - hydrocarbon (BVH)

DFN 7: Effective porosity is the porosity of the reservoir rock, excluding clay bound water (CBW).
                PHIe = PHIt – CBW
OR           PHIe = PHIt – Vsh * BVWSH

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

DFN 8: Free water (BVW) is further subdivided into:
                - a mobile portion free to flow out of the reservoir  (BVWm)
                - an immobile or irreducible water volume bound to the matrix rock by surface tension (BVI or BVWir)

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.

DFN 9: Hydrocarbon volume (BVH) can be classified into:
                - mobile hydrocarbon  (BVHm)
                - residual hydrocarbon (BVHr)

DFN 10: Free fluid index (FFI) is the sum of BVWm, BVHm, and BVHr. It is also called moveable fluid (BVM) or useful porosity (PHIuse).

     PHIuse = BVM = FFI = BVWm + BVHm + BVHr
OR            PHIuse = PHIe – BVI
OR            PHIuse = PHIe * (1 – SWir)

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.

DFN 11: Total water saturation (SWt) is the ratio of:
                - total water volume (BVW + CBW) to
                - total porosity (PHIt)

                  SWt = (BVW + CBW) / PHIt

DFN 12: Effective water saturation (Sw) is the ratio of:
               - free water volume (BVW) to
               - effective porosity (PHIe)

   Sw = BVW / PHIe

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).

DFN 13: Useful water saturation (SWuse) is the ratio of:
               - useful water volume (BVW - BVI) to
               - useful porosity (PHIuse)

SWuse = (BVW – BVI) / PHIuse

DFN 14: Irreducible water saturation (SWir) is the ratio of:
                - immobile or irreducible water volume (BVI) to
                - effective porosity (PHIe)

                 SWir = BVI / PHIe

DFN 15: Residual oil saturation (Sor) is the ratio of:
                - immobile oil volume (BVHr) to
                - effective porosity (PHIe)

                Sor = BVHr / PHIe

DFN 16: The water saturation in the flushed zone (Sxo) is the ratio of :
               - free water in the flushed zone, to 
               - effective porosity, which is assumed to be the same porosity as in the uninvaded zone.

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

DFN 17: Further constraints that should be remembered are:

                     PHIt >= PHIe >= PHIuse              SWt >= Sw >= SWuse.

                     PHIt = PHIe when Vsh = 0

                       SWt = Sw when Vsh = 0

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.

2.03 The Log Response Equation

The response of an individual log to the model described above is defined by the Log Response Equation, which takes 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. This is called forward modeling of log response, and is used to generate synthetic logs or to verify log analysis results. If the reconstructed log doesn’t match the recorded log, then something in the analysis model is wrong and must be fixed.

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:

Here GRlog, 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.

Calibration of log analysis results to “ground truth” is a normal step in checking your work, modifying parameters, or choosing alternate mathematical models..

 

2.04 Using The Log Response Equation – Seismic Modeling
The usual petrophysical application of the log response equation is to solve for shale volume, porosity, lithology, and water saturation from well log data recorded in open or cased holes. This is called inverse modeling, or more simply, plain ordinary “log analysis”.

A common log analysis calculation is to calculate apparent porosity from density and sonic logs, as here:
            1: PHID = (DENSMA – DENS) / (DENSMA – DENSW)

            2: PHIS = (DELTMA – DELT) / (DELTMA – DELTW)

WHERE: PHI = total porosity (including any clay bound water), DENS = density log values, DELT = sonic log values, and the subscripts MA and W represent values for matrix rock and water respectively.

These equations are very widely used in the industry, but cause many problems because the shale term in the response equation is missing, and the choice of matrix rock values are often poorly selected. Log analysis methods described in this Handbook will show you how to use the response equation correctly, in order to handle these two concerns.

An alternate use is to calculate what a log should have read. By using the log response equation in this forward model, we can reconstruct bad logs – logs that failed due to bad hole condition or other problems. We could also create a synthetic log to replace a missing log curve. All we need is a satisfying log analysis result from the good log curves and, from this, calculate the missing or faulty data. Many modern log analysis software packages have this capability for editing and repair of logs.

Be careful to use flushed zone water saturation (Sxo) while creating these synthetic logs.

Geophysicists have a similar but subtly different application. They need to reconstruct the logs for bad hole and missing data, but they also need to replace the invaded zone fluids with the native reservoir fluids. Since the seismic signal sees uninvaded reservoir properties, there is not much sense using invaded zone log data to calibrate seismic sections, seismic inversions, or offset versus amplitude interpretations. The problem is most serious in shallow gas sands, but may be important in thicker light oil zones as well. The process of correcting for invasion is called “fluid replacement editing”.

The important but subtle difference between petrophysical log modeling and geophysical log modeling is that the geophysical model needs the actual water saturation (Sw) instead of the flushed zone saturation (Sxo).

Another use of forward modeling is to create hypothetical logs, sometimes called “rock replacement editing”. Sometimes this can be done by cut and paste of existing log data, for example thinning out a reservoir to a pinchout or adding a reef to a known geological sequence. Other hypothetical models merely change a water bearing reservoir to a gas or oil zone, or change the porosity or shale volume, to see “what if?” scenarios.

The log response equation is the best way to do fluid or lithology replacement. A spreadsheet to perform this math, called META/MODL,  is available from the Downloads tab at www.spec2000.net .

1. Density Log Response
The response of a density log can be described rigorously by a volume weighted summation of the densities of the individual components in the rock. The usual form of this equation is:
    0: DENS = Sum (DENSi * Vi)

The expansion for well logging situations is:
     1: DENSmod = PHIe * Sw * DENSW
                           + PHIe * (1 - Sw) * DENSHY
                           + Vsh * DENSSH
                           + (1 - Vsh - PHIe) * DENSMA

FIGURE PP2.06: Density of gas at reservoir conditions – default approximation

This equation can be used to calculate what a density log would read given a hypothetical rock/fluid mixture, thus modeling of various formation alternatives is a straight forward mathematical process. It is preferable to guessing or estimating from previous experience.
This equation is rigorous and can be used with real hydrocarbon densities based on the temperature, pressure, and phase relationship of the fluid in question. A chart showing approximate gas density versus depth is shown in Figure PP2.06, based on average pressure and temperature data for the western Canadian basin. No correction for vuggy porosity is needed.

Corrections for the fact that density logs respond to electron density, and not bulk density, can be made, and may be necessary especially in the case of coal or salt beds. We usually do not make these corrections, because the accuracy needed for computing seismic response does not warrant the effort.

2. Sonic Log Response
An equation similar to that for density can be generated for sound velocity of mixtures. However, it is a summation of travel time weighted by volume and not a summation of velocity components:
     0: DELT = Sum (DELTi * Vi)

This is called the Wyllie time average equation and is true for many situations where the components are not very compressible, such as water, sandstone, and shale. It does not work too well with gas under low pressure. It is an empirical relationship and is not rigorous. However, the Biot model for sound velocity in mixtures is rigorous, and reduces to Wyllie's equation in most situations (ie: compressibility is very low).

The expansion of this formula for log analysis parallels the density formula:
     1: DELTmod = PHIe * Sw * DELTW
                           + PHIe * (1 - Sw) * DELTHY
                           + Vsh * DELTSH
                           + (1 - Vsh - PHIe) * DELTMA

FIGURE PP2.07: Sonic “pseudo” travel time in gas at reservoir conditions – default approximation

The Wyllie equation provides the opportunity to compute the sonic travel time (and the seismic velocity) of any hypothetical formation by describing the quantity of rock matrix, shale, water, and hydrocarbon. The equation works for either compressional or shear waves, as long as the appropriate fluid and rock properties are used.

The relationship is usually not true when gas fills the pore space, or is even a small fraction of the pore space. For this reason, we use a "pseudo-travel-time" in gas zones to reaffirm that it represents a velocity which may not be the same as the velocity of the gas at the temperature and pressure of the formation.

The hydrocarbon "pseudo-travel-time" is derived empirically by comparing results from synthetic seismograms and properly processed field data. A very rough approximation of hydrocarbon "pseudo-travel-time" versus depth, which has given reasonable results in the western Canadian basin, is shown in Figure PP2.07.

Proper editing of density and sonic data for fluid replacement and bad hole condition is an absolute prerequisite before using the log for any seismic application. Appropriate values for water, oil, and matrix rock are found in sections 5.02 and 5.01 of this Handbook.
 

2.05 Integration – Calibrating to Ground Truth
All log analysis methods depend on numerous assumptions made by the analyst and on parameters derived by observation or statistical analysis of the available log data. Assumptions and parameters may be adjusted by comparing log analysis results to “ground truth”, such as sample descriptions, core analyses, well tests, and production histories from the zone of interest in the current well or in offset wells. This is called “Integrated Petrophysics” when all sources of data are combined to obtain a clear reservoir description.

The coarsest log available is merely a list of formation names and their top depths from a well history file. The formation names are often clues to their basic lithology. For example, the Halfway Sand, Leduc Reef, Austin Chalk, Ardlee Coal, Delaware Shale suggest a lot, even to a novice. In time, we “know” that the Rex and Sparky are sandstones, and the Doig and Charlie Lake formations are mostly dolomite.

Sample descriptions provide the basic framework for developing a model of the formations to be analyzed.  The primary sedimentary rocks (sandstone, limestone, dolomite, anhydrite, shale, salt, coal) and accessory minerals (calcite, siderite, glauconite, pyrite, etc.) are usually described in some detail, in words or as a descriptive log. Visual porosity, hydrocarbon shows, fluorescence, porosity type, rock texture, and layer boundaries give the petrophysicist valuable insights into what to expect from analysis results.

Sample descriptions are provided at a coarse sample rate of 1 to 10 meters, so there is some need to exercise good judgment when comparing logs to samples. Samples may be contaminated by cavings from above the current sample depth. Core descriptions are also used, but here the depth increment of the data is finer than the log resolution.

Core analysis porosity and permeability are used directly to calibrate petrophysical results. The finer sample rate needs to be considered, but a good log analysis should match the core data, within reason. Bear in mind that the core analysis is performed on a piece of rock the size of a soda-pop can (whole core) or the size of a pill bottle (core plugs or sidewall cores). Logs see a piece of rock the size of a 45 gallon barrel.

Special core data, such as capillary pressure relative permeability, and electrical properties measurements are used to calibrate water saturation calculations from logs.

Gas logs, sometimes called mud logs or measurements while drilling (MWD), record gas shows in the drilling mud. Good shows on this log sometimes indicate a hydrocarbon bearing interval that ought to be visible on the log analysis results. Gas shows in the mud are not very quantitative indicators so there are many false-positive and false-negative indications.

The driller’s log is often combined with the gas and sample description logs. It shows rate of penetration, weight on bit, torque, and drilling mud properties. Lost circulation zones are noted here. All of this “stuff” can help untangle difficult interpretations or narrow the focus to specific zones of interest.

Drill stem tests (DST), run in open hole either before or after logging, may assist in predicting production characteristics. Many tests fail to produce anything, so log analysis shows may be completed, even in the face of  a negative test result. If a test produces water or hydrocarbons, it is usual to see the same prediction on the log analysis. However, formation damage, natural fractures, and depth control problems may give a false show that cannot be confirmed by the log analysis. Production tests through casing are also aids to log analysis calibration – it is always nice to have a good hydrocarbon show on the logs when the test makes oil-to-surface!

Production history data shows the rates and cumulative values for oil, gas, and water, giving a view of how these change over time. If productivity predictions are made from petrophysical analysis, they can be loosely calibrated to the first 90 or 120 days of production. 

Petrographic data from thin section photography, X-ray diffraction, scanning electron microscopy, and other petrology methods are used to understand pore geometry, diagenetic history, and mineralogy. This can often explain differences in interpretation between test results, core data, and log data.

Where this data is available, it is provided as part of the Case Histories and Exercises in this Handbook.

3.00 Eyeball Analysis Of Logs – Crain’s Simplified Rules
You should know the basic rules for eyeball analysis of log curves to help you climb the “Ladder to Success”. The common rules are described below with reference to Figures PP3.06A through PP3.06D. A more elaborate set of rules follows in Section 3.01. Lets start the race.

FIGURE PP3.06A: The left half of this image shows a resistivity log with spontaneous potential (SP) in Track 1 and shallow, medium, and deep resistivity (RESS, RESM, RESD) on a logarithmic track to the right of the depth track. The right half of the image shows a density neutron log with gamma ray (GR) and caliper (CAL) in Track 1. Photo electric effect (PE) is in Track 2 with neutron porosity (PHIN) and density porosity (PHID) spread across Tracks 2 and 3.

FIGURE PP3.06B: To find clean zones versus shale zones, examine the spontaneous potential (SP) response, gamma ray (GR) response, and density neutron separation. Low values of GR, highly negative values of SP, or density neutron curves falling close to each other usually indicate low shale volume. High GR values, no SP deflection, or large separation on density neutron curves normally indicate high shale volume.

 Very shaly beds are not “Zones of Interest”. Everything else, including very shaly sands (Vsh < 0.50) and even obvious water zones, are interesting. Although a zone may be water bearing, it is still a useful source of log analysis information, and is still a zone of interest at this stage.

FIGURE PP3.06C: For zones of interest, draw bed boundaries (horizontal lines). Then review the porosity logs: sonic, density, and neutron. All porosity logs deflect to the left for increased porosity. If density neutron data is available, estimate porosity in clean sands by averaging the two log values. In shaly sands, read the density porosity. IMPORTANT: This is just an estimate and not a final answer.

Scale the sonic log based on the assumed matrix lithology. Mark coal and salt beds, which appear to have very high apparent porosity. Identify zones which show high medium, low, or no porosity. Low porosity, high shale content, coal, and salt beds are no longer “interesting”.

FIGURE PP3.06D: Raw logs showing resistivity porosity overlay. Red shading indicates
possible hydrocarbon zones.

To find hydrocarbon indications and obvious water zones, compare deep resistivity to porosity, by mentally or physically overlaying the density porosity on top of the resistivity log. High porosity (deflections on the density log to the left) and high resistivity (deflections to the right) usually indicate oil or gas, or fresh water. See cross-hatched area on resistivity track of Figure PP3.06C.

Layer A on Figure PP3.06 is a shaly sand and has medium porosity. Layers B and C are clean sands and have high porosity. All other layers are shale with no useful porosity.

The average of density and neutron porosity in Layers B and C  is 24 %. This is close to the final answer because there is not  much shale in the zone. The average in Layer A is 16 % - much higher than the truth due to the influence of the shale in the zone. The density porosity is about 11%, pretty close to the core data. Therefore all our analysis must make use of shale correction methods.

Low resistivity and high porosity usually means water, as in Layer C. Known DST, production, or mud log indications of oil or gas are helpful indicators.

Layer B and Layer A show crossover when the porosity is traced on the resistivity log, so these zones remain interesting. In fresher water formations, it is often difficult or impossible to spot hydrocarbons visually. If it was easy, log analysts would be out of work!