POCKET  PAL  INDEX 1.00 Integrated Petrophysics 1.01 What Is A Log? 1.02 Organizing Your Work 1.03 Calculators and the Math Hierarchy 2.00 The Step by Step Procedure 2.01 The Analysis Model 2.02 Formation Rock Model Definitions 2.03 The Log Response Equation 2.04 Using The Log Response Equation          – Seismic Modeling 2.05 Calibrating to Ground Truth 3.00 Eyeball Analysis - Crain’s Rules 3.01 General Rules For Picking Log Data 3.02 Selecting Log Analysis Parameters 4.00 Shale Volume 5.00 Pore Volume 5.01 Porosity From Sonic Log 5.02 Porosity From Density Log 5.03 Porosity From Neutron Log 5.04 Porosity From Complex Lithology           Density Neutron Crossplot 5.05 Porosity From Dual Water Density           Neutron Crossplot 5.06 Porosity From Photoelectric Density           Neutron Crossplot 5.07 Material Balance for Porosity            (Maximum Porosity) 5.08 Useful Porosity 5.09 Porosity From Nuclear Magnetic             Resonance Log 5.10 Fracture Porosity 5.11 Porosity from Old ES Logs 6.00 Lithologic Analysis of Matrix Rock 6.01 Lithology From Matrix Density 6.02 Lithology From Sonic Density              Neutron Data 6.03 Lithology From PE Density Neutron 6.04 Lithology From Spectral GammaRay 6.05 Lithology From Vp/Vs Velocity Ratio 6.06 Elastic Constants / Mechanical              Properties From Logs 7.00 Formation Water Resistivity 7.01 Water Resistivity From Catalog / DST 7.02 Water Resistivity From Water Zone 7.03 Water Resistivity From SP 8.00 Water and Hydrocarbon Saturation 8.01 Determination of Saturation               Parameters A, M, N 8.02 Saturation From Archie Method 8.03 Saturation From Simandoux Method 8.04 Saturation From Dual Water Method 8.05 Saturation From Buckles Number 8.06 Irreducible Water Saturation 8.07 Moveable Oil Saturation 9.00 Permeability and Productivity 9.01 Permeability From Wyllie-Rose 9.02 Permeability From Porosity 9.03 Permeability From Coates Method 9.04 Fracture Permeability 10.00 Summarizing Results 10.01 Cumulative and Average Reservoir                 Properties 10.02 Fluid Properties and Reserves 10.03 Productivity Index and Water Cut 11.00 Beyond Log Analysis 11.01 Productivity From Drill Stem Tests 11.02 Production Projection / Cash Flow 12.00 Case Histories 12.01 Cretaceous Glauconitic Sand 12.02 Triassic Dolomitic Sand 12.03 Devonian Carbonate Reef 12.04 Tar Sands 13.00 List of Abbreviations

1.00 Integrated PETROPHYSICS

This Handbook is designed to give you a starting point for learning integrated, quantitative, log analysis methods. It is a condensed version of Crain’s Petrophysical Handbook on CD-ROM, available at www.spec2000.net. You can use this book as a quick reference to quantitative petrophysical analysis, or as a self-directed study guide.

Petrophysics is the study of the physical and chemical properties of rocks and their included fluids, if any. Petrophysical data can be obtained from well logs and from laboratory data. Petrophysical data is used both qualitatively and quantitatively. Both forms are discussed in appropriate sections of this Handbook.

Although the word "petrophysics" was used by G. E. Archie in the 1940's, the word  has only become popular in the last 20 years. The terms "log interpretation" or "log analysis" are widely used in the literature (inaccurately) to mean the same thing.

Petrophysics is a more inclusive term, encompassing core analysis, sample descriptions, X-ray diffraction, petrography, scanning electron microscopy, and other forms of detailed laboratory data, in addition to well log data. lab data can also be considered as a "well log", because the depth of each sample is usually known.

Petrophysicists offer services in the areas of well logging supervision, log analysis and interpretation, computer analysis of logs, seismic modeling, synthetic seismograms, and reconciliations of log data with geological, geophysical and exploration prospects, field studies and simulations, reserves estimates, and submissions to regulatory agencies.

These services are essential functions in modern oil and gas companies and cannot be accomplished without input from trained petrophysicists. The financial health and long-term success of a company depends on the central role of petrophysicist in all aspects of the company’s exploration and development activities.

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.

 

Where petrophysics fits in the scheme of reservoir description (courtesy of GeoNeural)

This Handbook 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.
 

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.

 

A Typical Log, with curves from a sonic log on the left half and an image log of sonic waveform amplitude on the right  

 

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

Petrophysics is more than peering blindly into a black borehole

 

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 below. You should note the distinction between LOG ANALYSIS (data reduction to get answers) and LOG INTERPRETATION (understanding the answers) that is made here.
 

 

In this book, we distinguish between analysis and interpretation. Analysis is data reduction to achieve
answers. Answers plus local knowledge are then interpreted to achieve understanding. Analysis
techniques are relatively easy to learn; understanding what the answers means takes a little more skill
and daring.

 

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.

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, is 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

 

 

 

2.00 The Step By Step Procedure

Log analysis involves a series of logical steps, each necessary to proceed to the next step.  Like an athlete running  to win the 100 meter sprint, log analysis requires training, planning, focus, and concentration before the race starts. At race time, we proceed to the starting line, get Ready, Set, Go, and Finish. Then we critique the results – did we win or finish last?

 

 

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.

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 insufficient 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.

 

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 un-invaded zone.

 

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 >= Sw. The water saturation in the invaded zone between the flushed and un-invaded 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 = (DTCMA – DTC) / (DTCMA – DTCW)

WHERE: PHI = total porosity (including any clay bound water), DENS = density log values, DTC = 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 un-invaded 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

 

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 above, 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: DTC = Sum (DTCi * 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: DTCmod = PHIe * Sw * DTCW
                           + PHIe * (1 - Sw) * DTCHY
                           + Vsh * DTCSH
                           + (1 - Vsh - PHIe) * DTCMA

 

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 above

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.

 

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.

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.

 

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”.

 

 

 

Raw logs showing resistivity porosity overlay. Red shading indicates possible hydrocarbon zones. The density or density porosity (solid red curve) is placed on top of the deep resistivity curve (dashed red curve). Line up the two curves so that they lie on top of each other in obvious water zones. If there are no obvious water zones, line them up in the shale zones. If the porosity curve falls to the LEFT of the resistivity curve, as in Layers A and B, hydrocarbons are probably present.

 

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 above 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 is 24 %; Layer C is 19%. This is close to the final answer because there is not  much shale in these zones. 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!

 

Crossover on the density neutron log sometimes means gas (not seen on the above example). Watch for rough hole problems, sandstone recorded on a limestone scale, or limestone recorded on a dolomite scale, which can also show crossover – not caused by gas.

 

Water zones with high porosity and low resistivity are called “obvious water zones”. Fresh water may look like hydrocarbons, particularly in shallow zones. The lack of SP development will often help distinguish fresh water zones. Low porosity water zones may not be obvious.

 

Water saturation is usually calculated from the Archie equation or a shale corrected version of it. This is not easy to do with mental arithmetic. An easier estimate of water saturation can be made in obvious hydrocarbon zones by using a method attributed to Buckles, and it is commonly used by reservoir engineers in a hurry.

 

 

Visual determination of lithology (in addition to identifying shale as discussed earlier) is done by noting the quantity of density neutron separation and/or by noting absolute values of the photo electric curve. The rules take a little memory work.

 

You must know whether the density neutron log is recorded on Sandstone, Limestone, or Dolomite porosity scales, before you apply Crain’s Rule #5. The porosity scale on the log is a function of choices made at the time of logging and have nothing to do with the rocks being logged. Ideally, sand-shale sequences are logged on Sandstone scales and carbonate sequences on Limestone scales. The real world is far from ideal, so you could find any porosity scale in any rock sequence. Take care!

 

SANDSTONE SCALE LOG 

 Sand – shale identification from gamma ray and density-neutron separation. Small amounts of density neutron separation with a low gamma ray may indicate some heavy minerals in a sandstone. Most minerals are heavier than quartz, so any cementing materials, volcanic rock fragments, or mica will cause some separation.  Both pure quartz (no separation) and quartz with heavy minerals (some separation) are seen in Figure PP3.07.

 

LIMESTONE SCALE LOG

 Lithology identification is accomplished by observation of density neutron separation and the gamma ray response, along with a review of core and sample descriptions.

 

The photoelectric effect is often a direct  mineralogy indicator. (PE is invalid on Figure PP3.08).

 

 

 

 

RULE EXCEPTIONS: High GR log readings coupled with density neutron log readings that are close together, are a sign of radioactive sandstone or limestone. To tell radioactive dolomite zones from shale zones, use a gamma ray spectral log, since the density neutron log will show separation in both cases. The PE value can help differentiate between radioactive dolomite and chlorite shale but not between dolomite and illite rich shale. High thorium values on the gamma ray spectral log indicate the shale.

 

 

 

To find signs of permeability, look for indications of 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.

 

 

To check for indications of fractures, look for sonic log skips, density neutron crossover in carbonates, hashy dipmeter curves, hashy resistivity curves, or caved hole in carbonates.

 

 

Computer systems are often provided to do the arithmetic and plot the answers. A diagram depicting the analysis steps in more detail is shown in Figure PP3.10. These steps cover only the data processing sequence involved in getting answers from the analysis of the raw data. Both novice and experienced analysts should review these illustrations to gain an understanding of how complex the processing and communication paths really are. If you use computerized log analysis, you should know how the program works.

Whether you use computer analysis software, spreadsheets, or calculators, you will be following the flow chart in this illustration. Looks complicated, but if you can see the step-by-step procedure streaming down the middle, and the feedback loops on both sides, you will understand the scope of the petrophysicist's job.

 

In any step by step procedure, there is a need to calibrate each step as it is performed. This reduces labor and dead end processing paths. The control data is usually the core, test, production, geological and engineering data available from a well or its nearby offsets.

 

Unfortunately, much of the needed control data is not available for many zones, so calibration is seldom perfect. Even when calibration data is available, the match to log analysis results may be weak, so be prepared to use good judgment to modify or reconcile your initial assumptions to improve the comparison.

Some "ground truth", such as core data, has its own data quality problems. It cannot and should not be used indiscriminately to force log analysis results to some preconceived solution.

3.01 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.

 

In computer aided log analysis, picks are made continuously with a digitizer or by reading magnetic tapes 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 tape-recorded data.

 

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. In thinner beds, 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. Pick peaks or valleys in thin beds to get the best possible values.

 

On thicker beds, draw a line through the average value of the curve. It is necessary to create a new bed or layer each time the porosity changes by 2% (porosity units), or when resistivity or gamma ray change by more than 10% (relative units)

 

The rule is to draw bed boundaries at the top and bottom of each clean zone, then draw boundaries at the porosity breaks within each clean zone. Finally draw any new boundaries needed to accommodate resistivity changes, which usually represent oil or gas water interfaces. The major interval between the top and bottom boundary of a relatively clean rock is called a ZONE. Each boundary inside a ZONE defines a LAYER of rock. Each layer will be analyzed separately by picking log values for each layer, called "Reading the Log"..

 

This concept is shown on the log at the right.

 

For thick layers, pick average values. For porosity, gamma ray, laterolog, and array induction logs, "thick" means more than 6 feet (2 meters). For older style induction logs, "thick means greater than 15 feet (5 meters).

 

 

 

 

In thick beds, pick average values
 (heavy black vertical lines)  ===>

 

 

 

 

 

 

 

 

 

 

 

 

 

Old style induction log, layer roughly
 15 feet (5 meters), pick peaks and valleys;
 other logs, pick averages ===>

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

<=== Thin beds, < 6 feet (2 meters), pick peaks on porosity logs. If there are high porosity streaks, treat them as individual layers. Average values will severely underestimate permeability and productivity. 90% of the production in this zone comes from layer B.

 

 

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.

 

 

Write the log values picked into a table or preprinted form so that you will have a record of the data you are using. Note that very shaly zones are not usually interpreted. Therefore, this data can be left off the table or marked as shale with no data values entered.

 

 

3.02 Selection of Log Interpretation Parameters

The method of selecting parameters varies depending on whether knowledge of fluid, matrix, or shale values are 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. Many values are published in tables or catalogs, and most necessary values are given in the PARAMETERS section following each mathematical method described in this book.

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. Most common values are listed in the PARAMETERS section with each method. More extensive lists are given in Section 13.02.

 

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 analyzed.

 

Matrix, fluid, and shale properties can sometimes be chosen from suitable crossplots. These techniques are described in more detail in Chapter Eleven of Crain’s Petrophysical Handbook.

With the shale lines, clean lines, and bed boundaries drawn, the logs become a series of “boxes”.  Inside each box, discrete values for each log can be picked (vertical black lines) using two basic rules: pick an average if the layer is “thick”, and either a peak or a valleys for layers that are “thin”. For porosity, GR, and SP logs, “thin” means less than 6 feet (2 meters). For older induction logs, “thin” means less than 16 - 20 feet (5 – 6 meters), but for newer induction logs and all laterologs, “thin” means less than 6 feet (2 meters). Note that the resistivity (RESD) for Layer B was picked on a peak and on a valley for Layer C, because the bed thickness is at the limit of the tool’s vertical resolution.

 

 

4.00 Shale Volume

Shale is an imprecise term used to describe a rock composed of clay, silt, and bound water. The clay type and silt composition can vary considerably from one place to another. These can be determined from appropriate cross plots of PE, thorium, and potassium logs. The bound water volume varies with clay type, depth of burial, and burial history. Some shales have not lost as much water as others at similar depths and are called overpressured shales. Most shales are radioactive due to potassium and thorium, and sometimes due to uranium.

 

Shale volume, shown in black, can be estimated from logs in a number of ways. The result is
 the average over the interval measured by a log and is independent of the shale distribution.

Shale distribution can vary, as shown above. The shale volume calculations shown below are insensitive to the shale distribution. However, porosity and water saturation are strongly affected by laminated shale, so the methods shown in Sections 5, 6, 7, and 8 in this handbook do not apply to laminated shaly sands.

 

*** PLEASE NOTE ***

You must choose the appropriate methods for each zone, but the minimum rule works well in most cases, provided the usage rules have been honored first.

 

Shale volume estimation is the first calculation step in a log analysis. All other calculations depend on the shale volume being known from this step.

 

STEP 1: Convert density log (gm/cc or Kg/m3) to porosity units if a density porosity log is not available (skip this step if density data is already in porosity units):

1: PHIDSH = (DENSSH – KD2) / (KD1 – KD2) – do this once in an obvious shale zone

2: PHID = (DENS – KD2) / (KD1 – KD2) – do this for every data level

 

Where:  KD1 = 1.00 for English units

 KD1 = 1000 for Metric units

 KD2 = 2.65 for English units Sandstone scale log

 KD2 = 2650 for Metric units Sandstone scale log

 KD2 = 2.71 for English units Limestone scale log

 KD2 = 2710 for Metric units Limestone scale log

 KD2 = 2.87 for English units Dolomite scale log

 KD2 = 2870 for Metric units Dolomite scale log

 

NOTE: The choice for KD2 must match the neutron log units – if neutron is in Limestone units, KD2 must be 2.71 for gm/cc or 2710 for Kg/m3 log scale.

 

STEP 2: Calculate shale volume from the three common  methods:

 3: Vshg = (GR - GR0) / (GR100 - GR0)

 4: Vshs = (SP - SP0) / (SP100 - SP0)

 5: Vshx = (PHIN - PHID) / (PHINSH - PHIDSH)

 

In tar sands or heavy oil, add the resistivity method:

6: Vshr = (logRESS - logRMAX) / (logRSH - logRMAX)

 

In radioactive sands, replace the gamma ray method with Thorium method if gamma ray spectral data is available:

7: Vshth = (TH - TH0) / (TH100 - TH0)

NOTE: Trim Vsh values between 0.0 and 1.0. If too many values fall outside this range, check the clean and shale parameters. Do not calculate methods which fail to pass all usage rules listed below.

STEP 3: Adjust gamma ray method for young rocks, if needed:

 8: Vshc = 1.7 - (3.38 - (Vshg + 0.7) ^ 2) ^ 0.5

 

STEP 4: Take minimum of available methods:

 9: Vsh = Min (Vshg, Vshs, Vshr, Vshx, Vshc)

 

 

 

USAGE RULES:

 

·         Use uranium corrected gamma ray (CGR) in preference to uncorrected GR

 

·         Do not use GR in radioactive sandstones or carbonates. Use Thorium curve from NGT for radioactive sandstone, and uranium corrected GR (CGR) curve for radioactive carbonates.

 

·         Do not use SP in fresh water formations, salt mud systems, high resistivity zones, or in carbonates.

 

·         Do not use density neutron crossplot when bad hole, gas, or heavy minerals are present.

 

·         Do not use the nonlinear young rock model unless there is some evidence that it is needed.

 

If log analysis porosity is too low, calculated shale volume may be too high (or vice versa).

The shale in the zone may not have the same properties as nearby shales seen on the log. Therefore, some adjustments to shale properties might be necessary.

Average effective porosity calculated from logs is pessimistic in thinly laminated sand shale series, and unconventional methods should be used to determine porosity and water saturation.

 

 

 

5.00 Pore Volume

The second calculation step in a log analysis is to find shale corrected porosity. Pore volume is the space in a rock filled with oil, gas, or water. Total porosity includes the bound water in the shale and is called PHIt. Effective porosity does not include bound water, and is called PHIe. When there is no shale, PHIe equals PHIt.

 

Logs read total porosity. All our analysis methods correct for shale, so the answers from any method presented below will give effective porosity. Some analysis methods NEED total porosity as an intermediate step, so you may also need to calculate it.

 

Raw log porosity, as presented in the field by the service company, does NOT take into account shale or lithology effects, so raw log readings should NEVER be used as answers. Log analysis MUST ALWAYS be done to find the correct porosity. All our analysis methods also account for matrix rock (lithology), but YOU may be required to define the rock type for some methods. Other methods will define the lithology for you.

 

YOU MUST choose a method that is appropriate for the available data and for the rock type being analyzed. The easiest methods are:

 

** Section 5.01: Porosity From The Sonic Log - use if density neutron combination is not available, or in bad hole when density log is no good.

 

** Section 5.02: Porosity From The Density Log - use in preference to sonic if available, lithology is well known, hole is good, and density neutron combination is not available.

 

** Section 5.03: Porosity From The Neutron Log - use if both sonic and density are not available.

 

** Section 5.04: Porosity From The Complex Lithology Density Neutron Crossplot - use in preference to a single log method except in bad hole where density is no good.

 

** Section 5.05: Porosity From The Dual Water Density Neutron Crossplot – use in quartz sands with no heavy minerals, otherwise use Complex Lithology method.

 

** Section 5.06: Porosity From The Photoelectric Density Neutron Crossplot - use in preference to complex lithology ONLY if mineral model end points are well known.

 

In all cases, the results must be trimmed to prevent too high a porosity in shaly zones and in bad hole by using Section 5.07: Material Balance for Porosity (Maximum Porosity). The META/ESP spreadsheet, available on the Downloads tab at www.spec2000.net, handles these models and makes the work relatively painless.

 

Unfortunately, there is no standard logging program, so there is no single foolproof log analysis method. Each method has its own usage rules. These rules may need to be adjusted to suit local conditions. 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.

 

 

 

5.01 Porosity From The Sonic Log

The sonic is a simple method and must be employed if more modern density neutron data is not available. The method shown is called the Wyllie time average equation. Other porosity methods are presented in following sections.

 

Other methods for the sonic have been proposed, but they are really specific to certain areas, although this is not clearly stated in the literature. For example, the Hunt-Raymer transform is appropriate for the US Gulf Coast, but a poor model for the Lower Cretaceous in Western Canada. The Wyllie approach, when calibrated to core, is universally applicable.

 

NORMAL CASES:

 

STEP 1: Calculate shale porosity (PHISSH), a constant for each zone:

 1: PHISSH = (DTCSH – DTCMA) / (DTCW – DTCMA)

 

DTCSH is a constant for the zone, chosen from the sonic log in a nearby shale.

 

STEP 2: Calculate porosity from sonic log (PHIsc) for each layer in the zone:

 2: PHIs = (DTC – DTCMA) / (DTCW – DTCMA)

 3: PHIsc = PHIs – (Vsh * PHISSH)

 

The sonic porosity (PHIsc), after all corrections are applied, is called the effective porosity, PHIe.

 

SPECIAL CASES:

 

CASE 1: Correct each layer for lack of compaction, ONLY IF DTCSH > 328 (Metric) or DTCSH > 100 (English)

 4: PHIe = PHIsc / KCP

 

CASE 2: Correct each layer for gas effect, ONLY IF PHIsc > PHItrue and gas is known or suspected

 5: PHIe = PHIsc * KS

 

USAGE RULES:

 

·         Use when density log is unavailable, or when density log is affected by bad hole.

 

·         Of the three "one-log" porosity methods, the sonic corrected for shale is the preferred one for wells that have no density log. However, crossplot methods or the density log corrected for shale are usually better if the log data is available.

 

·         If lithology is unknown, sonic log corrected for shale is better than density log because the lithology effect on the sonic is smaller.

 

·         Use the compaction correction KCP only if DTCSH > 100 usec/ft (for English units) or DTCSH > 328 usec/m (for Metric units). In western North America, this is normally required when above 3,000 - 4,000 feet (900 – l,200 meters).

 

  8: KCP = DTCSH / 100 (for English units)

  OR 9: KCP = DTCSH / 328 (for Metric units)

 

·         KCP is never less than 1.0.

 

·         Use the gas correction KS only if PHIsc is too high compared to other sources and if gas is known to be present. The need for this correction is common, but it is unlikely that a gas correction will be needed in very shaly sands since invasion should be relatively deep.

 

 10: KS = PHItrue / PHIsc

 

·         KS is never greater than 1.0.

 

·         Another way of making gas corrections is to change DTCW to a higher value, representing the travel time of sound in a mixture of gas and water. This value depends on water saturation in the invaded zone, pressure, temperature, and gas compressibility. Values in the range of 600 usec/ft (1900 usec/m) at shallow depths to 300 usec/ft (950 usec/m) at 6000 feet (2000 meters) are recommended as a starting point.

 

·         To calibrate to core porosity, adjust DTCMA, DTCW, DTCSH, KCP, KS, or Vsh to obtain a better match by trial and error. Appropriate crossplots may assist.

 

·         A newer method called the Hunt - Raymer equation has been proposed, but it seems to work well only in the Gulf Coast of USA. Shale corrected data should be entered to this equation (not mentioned in original paper).

 

 

For mixtures, take the average of two pure values as a starting point, eg: dolomitic sand, DTCMA = (144 + 182) / 2 = 163 usec/m, or prorate the values in proportion to the described mineral assemblage.

 

 

5.02 Porosity From The Density Log

Another "one-log" method uses the density log data, and is favored in shaly sands because the shale correction is quite small. In carbonates, the rock composition must be known accurately. This method is better than the sonic log, provided lithology is well known and the density log is not affected by bad hole. The density neutron combination is better than either sonic or density alone. Many people read the density log porosity directly from the log and call it effective porosity, PHIe. This is NOT a good idea, as you could be wrong by as much as 12 percent porosity in the worst case, and a few percent in most cases.

 

 

NORMAL CASES:

 

STEP 1: Calculate shale density (DENSSH) from shale porosity (a constant for each zone):

 1: DENSSH = PHIDSH * KD1 + (1 – PHIDSH) * KD2

 

PHIDSH is a constant for the zone, chosen from the density log in a nearby shale.

 

STEP 2: Translate density porosity of each layer into density units:

 2: DENS = PHID * KD1 + (1 – PHID) * KD2

 

Where:  KD1 = 1.00 for English units

 KD1 = 1000 for Metric units

 KD2 = 2.65 for English units Sandstone scale log

 KD2 = 2650 for Metric units Sandstone scale log

 KD2 = 2.71 for English units Limestone scale log

 KD2 = 2710 for Metric units Limestone scale log

 KD2 = 2.87 for English units Dolomite scale log

 KD2 = 2870 for Metric units Dolomite scale log

 

STEP 3: Calculate porosity of each layer with matrix and fluid of your choice:

 3: PHIDm = (DENS – DENSMA) / (DENSW – DENSMA)

 4: PHIdc = PHIDm – (Vsh * PHIDSH)

 

The density porosity (PHIdc), after all corrections are applied, is called the effective porosity, PHIe.

 

SPECIAL CASES:

 

CASE 1: Correct each layer for gas effect, ONLY IF PHIdc > PHItrue and gas is known or suspected

 5: PHIe = PHIdc * KD

 

USAGE RULES:

 

·         Do not use in bad hole conditions.

 

·         Use if neutron log is not available, otherwise use density neutron crossplot

 

·         Use in preference to sonic in shaly sands if both logs are available.

 

·         The density log corrected for shale AND lithology is a very good approximation to porosity, but the log was not common before 1965, so sonic or neutron methods may be necessary for wells drilled before that time.

 

·         Use gas correction KD only if PHIdc is too high compared to other sources and if gas is known to be present.

 

 6: KD = PHItrue / PHIdc

 

·         KD is never greater than 1.0.

 

·         Another way of making gas corrections is to change DENSW to a lower value, representing the density in a mixture of gas and water. This value depends on water saturation in the invaded zone, pressure, temperature, and gas density. Values in the range of 0.25 g/cc (250 Kg/m3) at shallow depths to 0.70 g/cc (700 Kg/m3) at 6000 feet (2000 meters) are recommended as a starting point.

 

·         If density porosity data is in percent, rather than fractional, divide the data values by 100 before using them.

 

·         No compaction correction is made to density log data.

 

·         To calibrate to core porosity, adjust DENSMA, DENSW, DENSSH, KD, or Vsh to obtain a better match by trial and error. Appropriate crossplots may assist.

 

 

For mixtures, take the average of two pure values as a starting point, eg: dolomitic sand, DENSMA = (2870 + 2650) / 2 = 2760 Kg/m3 or prorate in proportion to mineral volumes.

 

 

 

 

5.03 Porosity From The Neutron Log

The third, and least accurate, "one-log" method is based on neutron log data. The method is used in old wells or cased holes where no other porosity data is available, or where the sonic log was not run and the density log suffers from bad hole conditions.

 

NORMAL CASES:

 

STEP 1: Adjust log values from each layer to correct for matrix rock:

 1: PHINm = (PHIN – PHINMA + KN1) / (PHINW – PHINMA)

 

Where:  KN1 = 0.028 for Sandstone units log

 KN1 = 0.000 for Limestone units log

 KN1 = -0.100 for Dolomite units log

 

This lithology approximation is not sufficient in low porosity and service company chartbooks should be used for the specific tool.

 

STEP 2: Apply shale corrections to each layer:

 2: PHInc = PHINm – (Vsh * PHINSH)

 

PHINSH is a constant for each zone, chosen from the neutron log in a nearby shale.

 

The neutron porosity (PHInc), after all corrections are applied, is called the effective porosity, PHIe.

 

SPECIAL CASES:

 

CASE 1: Old style GRN or unscaled neutron logs recorded in counts per second or API units

1: SLOPE = (log (PHIHI / PHILO)) / (CPSHI – CPSLO)

2: INTCPT = PHIHI / (10 ^ (CPSHI * SLOPE))

3: PHIn = INTCPT * (10 ^ (SLOPE * NCPS))

4: PHInc = PHIn – Vsh * PHINSH

 

Example of Porosity from Neutron Counts per Second - no shale correction

 

A large number of charts for specific tools, spacings, borehole conditions and rock types are available from service companies.

 

CASE 2: Apply gas correction to each layer, ONLY IF PHInc < PHItrue and gas is known or suspected

 1: PHIe = PHInc * KN

 

 

USAGE RULES:

·         Use only if sonic and density log are unavailable or unusable.

 

·         The neutron log corrected for shale is one of the least accurate methods in shaly sands and should only be used if no other porosity data is available. This is common for wells drilled prior to 1957 or for wells logged through casing or drill pipe.

 

·         Old style neutron logs recorded in counts per second need to be scaled logarithmically between a high and a low porosity point, calibrated by core or modern logs from offset wells.

 

·         Use the gas correction KN only if gas is known to be present and log reading is still too low after lithology corrections. This correction is very crude and not recommended.  KN = PHItrue / PHIN

 

·         KN is never greater than 1.0.

 

·         To calibrate to core porosity, adjust PHINMA, PHINW, PHINSH, KN, or Vsh to obtain a better match by trial and error. Appropriate crossplots may assist.

 

 

 

5.04 Porosity From The Complex Lithology Density Neutron Crossplot

The best method available for modern, simple, log analysis involves the density neutron crossplot. Several variations on the theme are common, but not all models are recommended. A crossplot method, called the shaly sand model was once widely used. It was found to be a poor model for any sandstone that contained other minerals in addition to quartz. The complex lithology model works equally well in quartz sands as in mixtures, so it is the preferred model today. Although the name of the method is complicated, the mathematics are not.

 

NORMAL CASES:

 

STEP 1: Shale correct the density and neutron log data for each layer:

 1: PHIdc = PHID – (Vsh * PHIDSH)

 2: PHInc = PHIN – (Vsh * PHINSH)

 

PHIDSH and PHINSH are constants for each zone, and are picked only once.

 

STEP 2: Check for gas crossover after shale corrections and calculate porosity for each layer from the correct equation:

 3: IF PHInc >= PHIdc, there is no gas crossover

 4: THEN PHIxdn = (PHInc + PHIdc) / 2

 

The density neutron crossplot porosity, PHIxdn, after all corrections are applied, is called the effective porosity, PHIe.

 

 Density Neutron Complex Lithology Crossplot - Oil and Water cases, or Gas zones with crossover.

 

Chartbook solutions are provided above. Shale corrected data must be entered.

 

SPECIAL CASES:

 

CASE 1: IF gas is known to be present AND gas crossover occurs after shale corrections, apply the following gas correction:

 6: IF PHInc < PHIdc, there is gas crossover

 7: THEN PHIxdn = ((PHInc ^ 2 + PHIdc ^ 2) / 2) ^ 0.5

 

CASE 2: IF gas is known to be present but no crossover occurs after shale corrections, this usually means gas in dolomite or in a sandstone with lots of heavy minerals, apply the following gas correction:

 8: PHIx = – PHIdc / (PHInc / 0.8 – 1) / (1 + PHIdc / (0.8 – PHInc))

 9: PHIxdn = PHIx + KD3 * (0.30 – PHIx) * (DENSMA / KD1 – KD2)

 

Where:  KD1 = 1.00 for English units

 KD1 = 1000 for Metric units

 KD2 = 2.65 for Sandstone scale log

 KD2 = 2.71 for Limestone scale log

 KD3 = 1.80 for Sandstone scale log

 KD3 = 2.00 for Limestone scale log

 

 Density Neutron Complex Lithology Crossplot - Gas zones with NO crossover. Enter shale corrected data and then slide data point to the right until it reaches the line representing the matrix density of the reservoir - travel parallel to the nearest heavy black line.

 

Do not use Dolomite scale log for this special case. Figure PP5.14 shows the effect of using this gas correction. Notice that computed porosity does not match core porosity unless the correct DENSMA is chosen. DENSMA should reflect the matrix density of the expected lithology. This can be predicted accurately if the PE curve can be used to determine mineral volumes in a two mineral model. Density and neutron data cannot be used for this purpose because the gas effect masks the mineral effect.

 

Chartbook solutions are provided below when gas is present. Shale corrected data must be entered.

 

CASE 3: IF rock is dolomite AND porosity is less than 5%, use the following instead of Equation 4 or 5:

 10: E = (4 - (3.3 + 10 ^ (-5 * PHInc - 0.16))

 11: PHIxdn = (E * PHIdc + 0.754 * PHInc) / (E + 0.754)

 

This option can be used instead of equation 4 as long as there is no gas crossover after shale corrections. It is slightly more accurate, but requires a computer or preprogrammed calculator.

 

CASE 4: IF Archie or dual water model is to be used for water saturation, the following is needed:

 12: BVWSH = (PHIDSH + PHINSH) / 2     (a constant for the zone)

 13: PHIt = (PHID + PHIN) / 2                      (one value for each layer)

 

CASE 5: IF zone is vuggy carbonate, calculate secondary porosity:

 14: PHIsec = PHIxdn - PHIsc

 

USAGE RULES:

   Use in preference to most methods if data is available, even in shaly sands to correct for heavy mineral content.

 

·         Do not use when density is affected by bad hole conditions.

 

·         No correction for log units (eg Sandstone or Limestone units) is needed for most cases, except gas in dolomite and low porosity dolomite. Use Limestone units log ONLY for these two special cases.

 

·         Answer porosity is accurate to +/- 1% porosity using the simplified rules.

 

·         For better accuracy, use Equations 10 and 11 with Limestone units logs instead of simpler rules, except gas rules must still be applied.

 

·         The matrix density required for the gas correction must be assumed from the sample descriptions or by calculating the lithology from the PE (photoelectric effect) log if it is available.

 

·         Shale corrections could create apparent gas crossover and this may be real or an artifact of excessive correction. Check against known data from the well if shale correction creates crossover.

 

·         Charts and math for sonic density and sonic neutron crossplots are provided in Chapter Seven of Crain’s Petrophysical Handbook.

 

·         To calibrate to core porosity, adjust DENSMA, PHIDSH, PHINSH or Vsh to obtain a better match by trial and error. Appropriate crossplots may assist, or regression of PHIxdn vs core porosity may be used.

 

Effect of DENSMA on density neutron crossplot porosity with gas in heavy minerals. Core porosity (square black lines) and log analysis porosity (smooth black curves) show a good match when DENSMA was set at
2710 - 2740 Kg/m3. Log analysis shows near zero porosity if DENSMA set at 2650 for this heavy sandstone.

 

 

5.05 Porosity From The Dual Water Density Neutron Crossplot

Another version of the density neutron crossplot is the dual water, or bulk volume water method. This form should be used only in shaly sands with no heavy minerals. The simplified equations (5a and 6a) account for heavy minerals and are recommended over the original, more complex formulation which was meant for quartz sands ONLY.

 

For people who prefer chartbook solutions instead of calculators, a graph must be made manually for each zone to be analyzed. This is not recommended, so dig out the calculator and get at it.

 

NORMAL CASES:

 

STEP 1: Adjust log values for each layer to correct units. If in limestone units, put logs into sandstone units:

 1: PHID = PHID – 0.03

 2: PHIN = PHIN + 0.04

 

STEP 2: Calculate neutron dry clay (PHINDC) from PHIDDC, and shale bound water (BVWSH), which are constants for the zone

 3: PHIDDC = (DENSDC – KD2) / (KD1 – KD2)

 

Where:  KD1 = 1.00 for English units

 KD1 = 1000 for Metric units

 KD2 = 2.65 for English units Sandstone scale log

 KD2 = 2650 for Metric units Sandstone scale log

 

 4: PHINDC = 1.00 - (1.00 - PHIDDC) * (1.00 - PHINSH) / (1.00 - PHIDSH)

 5: BVWSH = (PHINDC * PHIDSH - PHIDDC * PHINSH) / (PHINDC - PHIDDC)

 

These are constants for each zone. PHIDDC is usually negative, so watch the minus sign when using the above equations.

 

STEP 3: Calculate total porosity for each layer:

 6: PHIt = (PHINDC * PHID – PHIDDC * PHIN) / (PHINDC – PHIDDC)

 

An easier approximation is:

 5a: BVWSH = (PHIDSH + PHINSH) / 2 (a constant for the zone)

 6a: PHIt = (PHID + PHIN) / 2 (one value for each layer)

 

STEP 4: Calculate effective porosity in each layer:

 7: PHIbvw = PHIt – (Vsh * BVWSH)

 

SPECIAL CASES:

 

If matrix offset is required for heavy minerals, apply the offset to all neutron and density values including shale points, then use the above equation.

 

Nothing special is done in gas zones, as the values computed for PHIt and PHIe are reasonable even if gas crossover occurs. If this rule seems uncomfortable use:

 8: PHIbvw = ((PHInc ^ 2 + PHIdc ^ 2) / 2) ^ 0.5

 

The dual water density neutron crossplot porosity PHIbvw, after all corrections are applied, is called the effective porosity, PHIe.

 

USAGE RULES:

 

·         Use in shaly sands without heavy minerals. If heavy minerals are present, the complex lithology density neutron crossplot is preferred.

 

·         The method is also called the bulk volume water (BVW) method and is the basis of many wellsite and office computer programs.

 

·         If the simplified equations 5a and 6a are used, the results are numerically identical to the Complex Lithology Model, except that no special cases are covered.

 

·         To calibrate to core porosity, adjust DENSDC, PHIDSH, PHINSH or Vsh to obtain a better match by trial and error. Appropriate crossplots may assist, or regression of PHIbvw vs core porosity may be used.

 

 

 

 

5.06 Porosity From The Photoelectric Density Neutron Crossplot

This method assumes that lithology is known from a UMA - DENSMA 3 mineral model or some other method that will determine mineral volumes accurately. The method can also be used if V1 and V2 (and V3 if desired) are derived from sonic density neutron (Mlith/Nlith or DTCMA/DENSMA), core description, or sample description.

 

NORMAL CASES:

 

STEP 1: Calculate shale density from shale porosity (a constant for each zone):

 1: DENSSH = PHIDSH * KD1 + (1 – PHIDSH) * KD2

 

PHIDSH and DENSSH are constants for each zone, chosen from the density log in a nearby shale.

 

STEP 2: Translate density porosity for each layer to density units:

 2: DENS = PHID * KD1 + (1 – PHID) * KD2

 

Where:  KD1 = 1.00 for English units

 KD1 = 1000 for Metric units

 KD2 = 2.65 for English units Sandstone scale log

 KD2 = 2650 for Metric units Sandstone scale log

 KD2 = 2.71 for English units Limestone scale log

 KD2 = 2710 for Metric units Limestone scale log

 KD2 = 2.87 for English units Dolomite scale log

 KD2 = 2870 for Metric units Dolomite scale log

 

STEP 3: Calculate matrix density from lithology results:

 3: DENSma = (Vmin1 * DENS1 + Vmin2 * DENS2 + (1 – Vmin1 – Vmin2) * DENS3) * (1 – Vsh)

+ Vsh * DENSSH

 

STEP 4: Calculate porosity from density response equation:

 4: PHIped = (DENS – DENSma) / (DENSW – DENSma)

 

The photoelectric density neutron crossplot porosity, after all corrections are applied, is called the effective porosity, PHIe.

 

SPECIAL CASES:

 

Cannot be used in gas zones or in bad hole.

 

 

USAGE RULES:

 

·         Use when data is available, but use care since errors in lithology calculation are exaggerated into the porosity equation.

 

·         Do not use in bad hole conditions or in gas zones.

 

·         This method is equivalent to a 4 mineral model where one mineral is considered to be porosity. Shale, which is calculated separately, is a fifth mineral.

 

·         The model can be rephrased as a two mineral model by setting V3 to zero (ie V1 + V2 = 1.0.

 

·         To calibrate to core porosity, adjust DENS1, DENS2, DENS3, DENSSH or Vsh to obtain a better match by trial and error. Appropriate crossplots may assist, or regression of PHIped vs core porosity may be used.

 

 

 

5.07 Material Balance for Porosity (Maximum Porosity)

Bad hole, high shale volume, and statistical variations can cause erratic results in both very low and high porosities. Values from any method used should be trimmed by the following:

 1: IF PHIe < 0

 2: THEN PHIe = 0

 3: IF PHIe > PHIMAX * (1 - Vsh)

 4: THEN PHImx = PHIMAX * (1 - Vsh)

 5: AND PHIe = Min (PHIe, PHImx)

 

USAGE RULES:

 

·         Use always to trim excessive porosity due to wet shales or bad hole conditions.

 

·         This material balance prevents the sum of shale volume, porosity, and rock matrix from exceeding 100%, and prevents porosity in the sand fraction of a shaly sand from reaching ridiculous values.

 

·         It is also useful for estimating porosity in shaly sands where only an SP or gamma ray log is available. Bear in mind that this approach provides a porosity value based only upon the shale content and the analyst's assumed maximum possible porosity. With offset well data for control this is not a bad approach for wells with a very limited log suite. It is often used in computer analysis of ancient logs. Because of its gross assumptions, a warning note should be annotated on the results, if the method is used in this manner.

 

The figure below shows results from a number of different porosity techniques, all of which have been trimmed by PHIMAX. A spreadsheet called META/ESP is available on the Downloads tab at www.spec2000.net  that makes the work relatively painless.

 

 Comparison of results from various porosity methods. It is fairly easy to calibrate any method to match core porosity but more difficult to match perfectly in shaly sands.

 

 

5.08 Useful Porosity

There is a recent trend among petrophysicists and engineers to partition porosity into a useful and a non- useful fraction. The concept of useful porosity, as opposed to effective porosity, is helpful where very small pores exist. These tiny pores do not connect to other pores and thus do not contribute to useful reservoir volume or reservoir energy. They are invariably water filled and nothing flows from them or through them. The tiny pores are called micro porosity; the larger, more effective, pores are called macro porosity. Thus:

1: PHIuse = PHIe – PHImicro

 

In sandstones, micro porosity is often associated with volcanic rock fragments that are part of the sandstone mineral mixture. In carbonates, micro porosity is associated with micrite, matrix, or pin point vugs. 

 

The quantity of micro porosity cannot always be found directly from logs but is usually assessed as a constant fraction, KM1, of the effective porosity. This constant can be found by examination of thin section visual porosity. Where micro porosity is associated with silt  or a volcanic mineral (Vmin2) in a quartz sandstone:

2: KM1 = Vsilt / (Vqrtz + Vsilt)

OR       2A: KM1 = Vmin2 / (Vqrtz + Vmin2)

            3: PHIuse = PHIe * (1 – KM1)

 

In some cases, the micro porosity is assumed to be a constant, PHIoffset, over an interval (ie, PHImicro is not proportional to effective porosity). This appears to happen in carbonates with unconnected pin point vugs (PHIppv), micritic carbonates (PHImict), or carbonates with matrix porosity (PHImatr). In all three cases, PHIoffset is found by comparing visual porosity in thin sections to log analysis porosity.

            4: PHIuse = PHIe - PHIoffset

 

In log analysis terminology, matrix porosity usually means effective porosity (PHIe). However, in petrographic (thin section) analysis, matrix porosity (PHImatr) is non-useful porosity contained in the very fine grained matrix material deposited between the granular or crystalline rock structure.

 

PHIppv, PHImict, and PHImatr may be varied according to rules developed by the analyst for the zone. A crossplot of visual porosity from thin section analysis versus PHIe from logs is a useful tool for determining the appropriate correction to obtain PHIuse. Typical rules might be:

            5: PHIuse = PHIe – PHIsec        (This is pretty pessimistic)

            6: PHIuse = PHIsec                   (This may be optimistic)

            7: PHIuse = PHIe – KMATR * (1 – PHIe) / (1 - KMATR)

            8: PHIuse = PHIe – PHIsc * KMICT / PHISavg

 

KMATR and KMICT would be in the range 0.01 to 0.08, averaging 0.04, and cannot exceed PHIt.

 

 

5.09 Porosity from Nuclear Magnetic Log

The Log Response Equation for modern nuclear magnetic logs is the same as for all other logs. The difference between the NMR and other porosity logs is that the Log Response Equation is solved by the service company at logging time, instead of by the analyst after the logs are delivered.  This transform is illustrated below.

 

The matrix and dry clay terms of NMR response are zero. An NMR log run today can display clay bound water (CBW), irreducible water (capillary bound water, BVI), and mobile fluids (hydrocarbon plus water, BVM), also called free fluids or free fluid index (FFI). On older logs, only free fluids (FFI) is recorded and some subtractions, based on other open hole logs, are required.

 

Nuclear Magnetic Resonance Response to Fluids

For modern logs:

1: PHIt = CBW + BVI + BVM

2: PHIe = BVI + BVM

3: PHIuse = BVM
            4: SWir = BVI / PHIe

 

Some or all of the sums defined above may be displayed on the delivered log. Log presentation is far from standard for NMR logs. In some situations, mobile water can be separated from hydrocarbon, and sometimes gas can be distinguished from oil, by further (experimental) processing of the original signal. However, the depth of investigation and measurement volume are tiny, so the hydrocarbon indication is from the invaded zone.

 

For the same reason, PHIt and PHIe from NMR do not always agree with that derived from density neutron methods, which see much larger volumes of rock.

 

For older logs:

            1: PHInmr = FFI

            2: SWir = KBUCKL / PHInmr

3: PHIe = FFI / (1 – SWir)

            4: BVWSH = (PHINSH + PHIDSH) / 2

            5: PHIt = PHIe + Vsh * BVWSH

IF  PHIe is known from some other log:
            6: BVI = PHIe - FFI
            7: SWir = BVI / PHIe

 

PHIe and PHIt should be compared to density neutron or other methods defined earlier.

 

KBUCKL is in the range 0.010 to 0.100, with a default of 0.040.

 

 

5.10 Fracture Porosity

There are a number of techniques published for calculating fracture porosity from conventional open hole logs. All were developed before the processing of formation micro-scanner data for fracture aperture became common. These older methods over-estimate fracture porosity. The only correct method is to use fracture aperture and frequency data from FMI/FMS processed logs:

            1: PHIfrac = 0.001 * Wf * Df * KF1

 

Where:      KF1 = number of main fracture directions

                        = 1 for sub-horizontal or sub-vertical

                        = 2 for orthogonal sub-vertical

                        = 3 for chaotic or brecciated

            PHIfrac = fracture porosity (fractional)

            Df = fracture frequency (fractures per meter)

            Wf = fracture aperture (millimeters)

 

Fracture porosity is exceedingly small and seldom is larger than 0.25% (0.0025 fractional). This is well below the noise level of conventional open hole logs. Fracture aperture from cores or thin section may be exaggerated due to stress release, so be cautious using this data. Some “fracture-related” porosity, such as solution porosity near the fracture face, will be seen by conventional logs, which is why some older fracture porosity methods give quite high values for fracture porosity.

 

 

5.11 Porosity from Old ES Logs

There are a number of techniques for handling ancient logs like the old electrical survey (ES). The simplest is to use the shallow resistivity and assume that the flushed zone water saturation is near 1.0.

1: PHIxo = (A / ((RXO / RMF@FT) * (SXO ^ N))) ^ (l / M)

This is pretty nearly a last resort. Old style neutron logs (Section 5.03) and the maximum porosity methods (Section 5.07) may work better,

 

The microlog can also be used:

1: IF RES2 > RES1
             2: THEN PHIml = 0.614 ((RMF@FT * KML) ^ 0.61) / (R2 ^ 0.75)
             3: OTHERWISE PHIml = 0

 

 

6.00 Lithologic Analysis of Matrix Rock Volume

The third step in a log analysis is to calculate the volume of each component of the matrix rock. A large number of minerals exist and you must choose a set of likely minerals appropriate to the rocks present in the zone. The minerals present must be differentiable with sufficient resolution to provide useful results. Minerals with similar properties are often lumped together.

 

We can solve for the volume of one mineral for each porosity indicating log over the zone. Thus a sonic, density, neutron combination or photoelectric effect, density, neutron combination can provide volumes for either two or three mineral models. YOU must choose the correct two or three minerals for the end points of the model. Choosing the wrong end points may lead to mathematically feasible results which are not correct.

 

If additional lithology indicating curves are available, for example the natural or induced spectral gamma ray logs, one more mineral may be added to the model for each useable curve. Such models cannot be computed by hand, and computer programs are required. {n some software, porosity can be one of the “minerals”.

 

When gas is present, only the photo electric effect (two mineral model) is useful for hand calculated lithology analysis. If only one porosity indicating log is present, the lithology will be, by definition, the lithology you imposed on the porosity calculation done earlier.

 

The PE density neutron method can be used to define clay mineralogy in shales and shaly sands.

 

 *** PLEASE NOTE ***

 

YOU MUST choose a method AND the end points that are appropriate for the available data and for the rock type being analyzed. The easiest methods are:

 

** Section 6.01: Two Mineral Lithology From Matrix Density - the most common method because the density neutron log is very common in modern wells; cannot be used in gas zones.

 

** Section 6.02: Lithology From Sonic Density Neutron Data - used for either two or three mineral models when data is available; photo electric effect is better method than sonic for most rock mixtures, if it is available.

 

** Section 6.03: Lithology From PE Density Neutron Log - preferred method for two or three mineral models when data is available.

 

The META/ESP spreadsheet, available on the Downloads tab at www.spec2000.net, handles these models and makes the work relatively painless.

 

 

 

6.01 Two Mineral Lithology From Matrix Density

This is the easiest and most common lithology method and is widely used in wellsite and office computer programs.

 

 

NORMAL CASES:

 

STEP 1: Calculate shale density from shale porosity (a constant for each zone):

 1: DENSSH = PHIDSH * KD1 + (1 – PHIDSH) * KD2

 

PHIDSH and DENSSH are constants for each zone, chosen from the density log in a nearby shale.

 

STEP 2: Translate density porosity for each layer to density units:

   2: DENS = PHID * KD1 + (1 – PHID) * KD2

 

Where: 
             KD1 = 1.00 for English units

 KD1 = 1000 for Metric units

 KD2 = 2.65 for English units Sandstone scale log

 KD2 = 2650 for Metric units Sandstone scale log

 KD2 = 2.71 for English units Limestone scale log

 KD2 = 2710 for Metric units Limestone scale log

 KD2 = 2.87 for English units Dolomite scale log

 KD2 = 2870 for Metric units Dolomite scale log

 

STEP 3: Calculate matrix density:

 3: DENSma = (DENS – PHIe * DENSW – Vsh * DENSSH)
                                / (1 – PHIe – Vsh)

 

STEP 4: Calculate rock volumes:

 4: Min1 = (DENSma – DENS2) / (DENS1 – DENS2)

 5: Min2 = 1.0 – Min1

 

SPECIAL CASES:

Cannot be used in gas zones.

 

To use this method for sonic neutron crossplot, replace all DENSxx terms in Equations 3, 4, and 5 with their corresponding DTCxx terms. Equations 1 and 2 are not needed.

USAGE RULES:
 

·         If Min1 and Min2 are to be plotted in a volumetric track with Vsh and PHIe, multiply by Vrock before plotting, where Vrock = 1 – PHIe – Vsh.

 

·         Use any time data is available, but not in bad hole conditions or when gas is present. Methods using PE or UMA are usually better.

 

·         This equation will break down when PHIe plus Vsh approaches 1.0, so we limit the use of the equation to those cases where PHIe + Vsh < 0.8.

 

 

 

 

 

6.02 Lithology From Sonic Density Neutron Data

This is usually called the M-N method in the literature. This method provides two different two-mineral and one three-mineral models.

 

YOU must choose the model which gives the best resolution for the mineral end points you have chosen. Resolution is better when the values for the end points have the largest absolute difference.

 

NORMAL CASES:

 

STEP 1: Shale correct log data:

 1: PHIdc = PHID – (Vsh * PHIDSH)

 2: PHInc = PHIN – (Vsh * PHINSH)

 

If PHIN is in sandstone units, subtract 0.03 before using it.

 3: PHIsc = (DTC – (1 – Vsh) * 47.3 – (Vsh * DTCSH)) / (KS1 – 47.3)

 

Note: DTC must be in English units (us/ft).

 4: DENSc = PHIdc * KD1 + (1 – PHIdc) * 2.71

 5: DTCc = PHIsc * KS1 + (1 – PHIsc) * 47.3

 

Where: 
              KD1 = 1.0 for fresh drilling mud

 KD1 = 1.1 for salty drilling mud

 KS1 = 200 for fresh drilling mud

 KS1 = 188 for salty drilling mud

 

STEP 2: Calculate lithology factors:

 6: Mlith = 0.01 * (KS1 – DTCc) / (DENSc – KD1)

 7: Nlith = (1.00 - PHInc) / (DENSc – KD1)

 8: Klith = Mlith / Nlith

 9: Alith = 1 / Nlith

 

STEP 3: Calculate two mineral rock volumes from MLITH factor:

 10: Min1 = (Mlith – MLITH2) / (MLITH1 – MLITH2)

 11: Min2 = 1.0 – Min1

 

STEP 4: Calculate two mineral rock volumes from NLITH factor:

 12: Min1 = (Nlith – NLITH2) / (NLITH1 – NLITH2)

 13: Min2 = 1.0 – Min1

 

STEP 5: Calculate three mineral rock volumes from Mlith and Nlith:

 14: D = (Mlith * (NLITH2 – NLITH1) + Nlith * (MLITH1 – MLITH2)

 + MLITH2 * NLITH1 – MLITH1 * NLITH2) / (MLITH1 * (NLITH3 – NLITH2)

 + MLITH2 * (NLITH1 – NLITH3) + MLITH3 * (NLITH2 – NLITH1))

 

 15: E = (D * (NLITH3 – NLITH1) – Nlith + NLITH1) / (NLITH1 – NLITH2)

 16: Min1 = MAX(0, 1 – D – E) / (MAX(0, 1 – D – E) + MAX(0, D) + MAX(0, E))

 17: Min2 = MAX(0, E) / (MAX(0, 1 – D – E) + MAX(0, D) + MAX(0, E))

 18: Min3 = 1 – Min1 – Min2

 

SPECIAL CASES:

 

Cannot be used in gas zones.

 

To use DTCma and DENSma instead of Mlith and Nlith, replace all Mlith terms with DTCma terms, and all Mlith with DENSma terms in Equations 15 and 16. Equations 1 thru 14 are not needed, but DTCma and DENSma must be derived as shown in Section 6.01.

 

 

 

USAGE RULES:

 

·         If Min1 and Min2 are to be plotted in a volumetric track with Vsh and PHIe, multiply by Vrock before plotting, where Vrock = 1 - PHIe – Vsh. For examp;e Vmin1 = Min1 * Vrock.

 

·         Nlith gives about the same answer as the matrix density method, because both methods use density and neutron data. Do not use in bad hole conditions or when gas is present.

 

·         Mlith uses sonic and density data. Do not use in bad hole conditions or when gas is present.

 

·         Alith and Klith can be used to calculate 2 or 3 mineral models by replacing all Mlith and Nlith terms in Equations 10 through 18 with corresponding Alith and Klith terms.

 

·         Klith uses sonic and neutron data and can be used in bad hole where Mlith and Nlith are no good.

 

·         For the available two or three mineral models in this section, choose the method with the most resolution for the mineral pair you have chosen. This means that the numerical distance between the end points is as large as possible.

 

·         Mlith and Nlith are usually called M and N, but they can be confused with the cementation exponent M and the saturation exponent N, so we have changed their names to reduce confusion.

 

 

To calculate MLITH and NLITH parameters for salt mud case, use Equations 6 and 7 with KD1 and KS1 for salt mud.

 

 

6.03 Lithology From PE Density Neutron Data

This is the best method for calculating lithology if the data is available. This method provides two different two-mineral and one three-mineral models.

 

YOU must choose the model which gives the best resolution for the mineral end points you have chosen. Resolution is better when the values for the end points have the largest absolute difference.

 

NORMAL CASES:

 

STEP 1: Calculate shale density and shale capture cross section (a constant for each zone):

 1: DENSSH = PHIDSH * KD1 + (1 – PHIDSH) * KD2

 2: USH = PESH * DENSSH

 

STEP 2: Translate density porosity to density units for each layer:

 3: DENS = PHID * KD1 + (1 –  PHID) * KD2

 

Where:  KD1 = 1.00

 KD2 = 2.65 for Sandstone scale

 KD2 = 2.71 for Limestone scale

 

NOTE: Density data is needed in English units (gm/cc).

 

STEP 3: Calculate matrix capture cross section for each layer:

 4: Uma = (PE * DENS – Vsh * USH) / (1 – PHIe)

 

STEP 4: Calculate two mineral rock volumes from UMA:

 5: Min1 = (Uma – UMA2) / (UMA1 – UMA2)

 6: Min2 = 1.0 – Min1

 

STEP 5: Calculate two mineral rock volumes from PE:

 7: Min1 = (PE – PE2 – PESH * Vsh) / (PE1 – PE2)

 8: Min2 = 1.0 – Min1

 

STEP 6: Calculate three mineral rock volumes from Uma and DENSma:

 9: D = (Uma * (DENS2 – DENS1) + DENSma * (UMA1 – UMA2)

            + UMA2 * DENS1 – UMA1 * DENS2) / (UMA1 * (DENS3 –  DENS2)

            + UMA2 * (DENS1 – DENS3) + UMA3 * (DENS2 –DENS1))

 

 10: E = (D * (DENS3 – DENS1) – DENSma + DENS1) / (DENS1 – DENS2)

 11: Min1 = MAX(0, 1 – D – E) / (MAX(0, 1 – D – E) + MAX(0, D) + MAX(0, E))

 12: Min2 = MAX(0, E) / (MAX(0, 1 - D - E) + MAX(0, D) + MAX(0, E))

 13: Min3 = 1 – Min1 – Min2

 

SPECIAL CASES:

 

Only the PE 2 mineral model can be used in gas zones.

 

To use DTCma instead of Uma, replace all Uma terms with DTCma terms in Equations 9 and 10. Equations 1 thru 8 are not needed, but DTCma and DENSma must be derived as shown in Section 6.01.

 

USAGE RULES:

 

·         If Min1 and Min2 are to be plotted in a volumetric track with Vsh and PHIe, multiply by Vrock before plotting, where Vrock = 1 - PHIe – Vsh.For example, Vmin1 = Min1 * Vrock.

 

·         Use the Uma method any time data is available, but not in bad hole conditions or when gas is present.

 

·         Use the PE method any time data is available, but not in bad hole conditions. However it can be used when gas is present.

 

·         There may be three mineral combinations where the sonic density neutron methods have better resolution. Check the shape of the mineral triangles.

 

·         Porosity can also be obtained from the PE response equation. Since resolution is poor, this method is not recommended – the density/PE combination is better.

 

·         If this method is used to find the fraction of clay minerals present in a shale, Uma is found from Uma = PESH * DENSsh / (1 - BVWSH).  Then the two or three mineral model is applied.

 

·         If natural gamma ray spectral log data is available, other two and three mineral models can be solved in similar fashion as for PE density neutron – compare Figures PP6.16, PP6.17 and PP6.18.

 

·         If clay is to be one of the minerals to be found along with two matrix rocks, then do not shale correct the Uma equation, and use PHIt instead of PHIe in Step 2.

 

 

Matrix Density – Matrix Cross Section Crossplot for Lithology

 

 

6.04 Lithology From Spectral Gamma Ray Data

Many other two and three mineral models can be made using combinations of sonic, density, neutron, PE and spectral gamma ray log curves, such as potassium or thorium or potassium/thorium ratio. Typical crossplots are shown on the following page.

 

A comparison of various lithology methods is shown on Figure PP6.19. Notice that some models could not resolve for three minerals so the anhydrite zone is not portrayed correctly.

 

PE vs Th/K Ratio Crossplot for Lithology. X Axis Th/K (ppm/%)

 

 PE vs Potassium Crossplot for Lithology.  X Axis is K (%).

 

 

Comparison of Lithology Methods. Note that the 2-mineral model will give silly results in a 3-mineral environment, as shown here in the anhydrite layer, unless appropriate parameters and zoning are applied.

 

6.05 Lithology From Vp/Vs Velocity Ratios

The dipole shear sonic log provides compressional and shear travel time values that can be used for lithology estimation.

 

1: Vp/Vs = DTS  / DTC

 

Where DTC = compressional travel time (usec/ft or usec/m)

            DTS = shear travel time (usec/ft or usec/m)

            Vp/Vs = velocity ratio (unitless)

 

This ratio is used in seismic calibration and interpretation as a guide to lithology. Vp/Vs is relatively independent of porosity and fluid type (little gas effect).

 

RECOMMENDED PARAMETERS:

Sandstone Vp/Vs = 1.50 – 1.70

Dolostone Vp/Vs  = 1.65 – 1.80

Limestone Vp/Vs  = 1.80 – 2.00

 

 

6.06 Elastic Constants / Mechanical Properties

The elastic properties of rocks depend on their acoustic velocity and density. These values can be derived from log data or measured in the laboratory. Elastic properties are needed for stress studies in fractured reservoirs, hydraulic fracture design, and seismic data analysis. Reservoir simulation engineers also use  compressibility values, but few are aware that log analysis can provide this information.

 

There are a number of problems correlating log derived values with lab data, but results can usually be calibrated to actual fracture pressures measured in the field.

 

In the following definitions, stress is the applied pressure and strain is the change in size of the rock.

 

1. Shear modulus is defined as the applied stress divided by the shear strain.

2. Poisson's Ratio is the lateral strain divided by longitudinal strain.

3. Bulk Modulus is the hydrostatic pressure divided by volumetric strain.

4. Bulk Compressibility is the inverse of Bulk Modulus.

5. Biot's Constant is the ratio of the volume change of the fluid filled porosity to the volume change of the rock when the fluid is free to move out of the rock (ie. the hydraulic pressure remains unchanged).

6. Young's Modulus is applied uni-axial stress divided by normal strain.       

 

Here are the basic equations – a spreadsheet called META/MECH is available on the Downloads tab at www.spec2000.net  that makes the work relatively painless.

 

Shear modulus N, also abbreviated G or S or u (mu)

For rock with porosity:

      1: N = KS5 * DENS / (DTS ^ 2)

For rock with no porosity:

     2: No = KS5 * DENSMA / (DTSMA ^ 2)

 

Where: 
    KS5 = 13400 for English units
    KS5 = 1000 for Metric units

 

Density is in gm/cc, travel time is in usec/ft, and N is in psi * 10^6 for English units. Density is in Kg/m3, travel time is in usec/m, and N is in Giga-Pascals (10^9 Pa or GPa) for Metric units.

 

Poisson's ratio PR, also abbreviated with the Greek letter NU (v) or SIGMA
For rocks with porosity:

      2: R = DTS / DTC

      3: PR = (0.5 * R^2 - 1) / (R^2 - 1)

 

For rocks with no porosity:

      2: Ro = DTSMA / DTCMA

      3: PRo = (0.5 * Ro^2 - 1) / (Ro^2 - 1)

 

Bulk modulus Kb (also abbreviated B or L)

For rock with porosity:

      1: Kb = KS5 * DENS *(1 / DTC^2 - 4/3 * (1 / (DTS^2)))

For rock with no porosity:

      2: Km = KS5 * DENSMA *(1 / DTCMA^2 - 4/3 * (1 / (DTSMA^2)))

 

Bulk compressibility Cb

For rock with porosity:

      1: Cb = 1 / Kb

For rock with no porosity:

      2: Cm = 1 / Km

 

Biot's Constant

For rock with porosity:

      1: ALPHA = 1 - Kb / Km

For rock with no porosity, Kb = Km

      2: ALPHA = 0

 

Young's modulus Y (also abbreviated E)

For rocks with porosity:

      1: Y = 2 * N * (1 + PR)

For rocks with no porosity
      1: Yo = 2 * No * (1 + PRo)                                              Sample log analysis with elastic properties answers

 

Modulus of compressibility Kc

For rock with porosity,

      1: Kc  = Km + 4/3 * N

 

Overburden and Pore Pressure

Normal Gradient  OBG = 22.8 KPa (0.98 psi/ft)    PPG =  9.81 KPa  (0.43 psi/ft)

      1: Po = OBG * DEPTH

      2: Pp = PPG * DEPTH

 

Fracture Closure Stress

Typical Tectonic Stress  Pext = 1000 KPa  Tensile Strength Ts = 1000 KPa

 

      1: Px = (PR / (1 – PR)) * Po + (1 – (PR / (1 – PR))) * Pp * ALPHA + Pext

      2: Py = (PR / (1 – PR)) * Po + (1 – (PR / (1 – PR))) * Pp * ALPHA

 

Fracture pressure and fracture pressure gradient are:

      3: Pf = 3 * Px – Py + Ts

      4: FPG = Pf / DEPTH

 

 

7.00 Formation Water Resistivity

The fourth step in a log analysis is to determine the water resistivity since most methods for computing water saturation require knowledge of this value. Water resistivity data can be sparse or overwhelming, depending on where you are working at the moment.

 

 

 *** PLEASE NOTE ***

YOU must choose a water resistivity method appropriate to the available data:

 

** Section 7.01: Water Resistivity From Catalog or DST Recovery - use when drill stem test recoveries of water, in your well or nearby wells, have been analyzed for chemical content and water resistivity in the laboratory, or when a water catalogue, published by your local well logging or geological society, is available. Measured values are the preferred source.

 

** Section 7.02: Water Resistivity From Water Zone (R0 Method) - use when a clean (non shaly) water zone is present - sometimes called the Rwa method.

 

** Section 7.03: Water Resistivity From Spontaneous Potential - use when a clean (non shaly) water zone is present; less reliable in hydrocarbon zones.

 

 

7.01 Water Resistivity From Catalog or DST Recovery

Catalogs and lab reports usually provide results at 77'F (25'C) and this value must be transformed to a different value based on the formation temperature.

 

STEP 1: Calculate formation temperature:

 1. GRAD = (BHT – SUFT) / BHTDEP

 2: FT = SUFT + GRAD * DEPTH

 

STEP 2: Calculate water resistivity at formation temperature:

 3: RW@FT = RW@TRW * (TRW + KT1) / (FT + KT1)

 

Where:  KT1 = 6.8 for English units

 KT1 = 21.5 for Metric units

 

If water salinity is reported instead of resistivity, as may happen in reporting direct from the well site, convert salinity to resistivity with:

 4: RW@FT = (400000 / FT1 / WS) ^ 0.88

 

NOTE: FT1 is in Fahrenheit

 

In some cases, salinity is reported in parts per million Chloride instead of the more usual parts per million salt (NaCl). In this situation convert Chloride to NaCl equivalent with:

 5: WS = Ccl * 1.645

 

To convert a downhole RW to a surface temperature, reverse the terms in equation 3:

6: RW@SUFT = RW@FT * (FT + KT1) / (SUFT + KT1)

 

Where:  KT1 = 6.8 for English units

 KT1 = 21.5 for Metric units

Sometimes, it is nice to know what the resistivity log would read in a water zone (R0). For quick look work, use the following:
            7: R0 = RW@FT ‘ (PHIe ^ 2)

 

For example, If RW@FT = 0.10 and PHIe = 0.20, then R0 = 0.10 / (0.20^2) = 2.5 ohm-m.

 

USAGE RULES:

·         Use in preference to other methods if data is available.

 

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