Gamma ray logs

The radioactivity of rocks has been used for many years to help derive lithologies. Natural occurring radioactive materials (NORM) include the elements uranium, thorium, potassium, radium, and radon, along with the minerals that contain them. There is usually no fundamental connection between different rock types and measured gamma ray intensity, but there exists a strong general correlation between the radioactive isotope content and mineralogy. Logging tools have been developed to read the gamma rays emitted by these elements and interpret lithology from the information collected.

Conceptually, the simplest tools are the passive gamma ray devices. There is no source to deal with and generally only one detector. They range from simple gross gamma ray counters used for shale and bed-boundary delineation to spectral devices used in clay typing and geochemical logging. Despite their apparent simplicity, borehole and environmental effects, such as naturally radioactive potassium in drilling mud, can easily confound them.

Relating radioactivity to rock types

In Fig. 1, the distributions of radiation levels observed by Russell are plotted for numerous rock types. Evaporites (NaCl salt, anhydrites) and coals typically have low levels. In other rocks, the general trend toward higher radioactivity with increased shale content is apparent. At the high radioactivity extreme are organic-rich shales and potash (KCl). These plotted values can include beta as well as gamma radioactivity (collected with a Geiger counter). Modern techniques concentrate on gamma ray detection.

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  Fig. 1 – Distribution of relative radioactivity level for various rock types (from Bigelow after Russell).

Radioactive isotopes in rocks

The primary radioactive isotopes in rocks are potassium-40 and the isotope series associated with the disintegration of uranium and thorium. Fig. 2 shows the equilibrium distribution of energy levels associated with each of these groups. Potassium-40 (K⁴⁰) produces a single gamma ray of energy of 1.46 MeV as it transforms into stable calcium. On the other hand, both thorium (Th) and uranium (U) break down to form a sequence of radioactive daughter products. Subsequent breakdown of these unstable isotopes produces a variety of energy levels. Standard gamma ray tools measure a very broad band of energy including all the primary peaks as well as lower-energy daughter peaks. As might be expected from Fig. 2, the total count can be dominated by the low-energy decay radiation.

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  Fig. 2 – Gamma-ray energy levels resulting from disintegration of unstable isotopes (adapted from Tittman et al.).

The radionuclides, including radium, may become more mobile in formation waters found in oil fields. Typically, the greater the ionic strength (salinity), the higher the radium content. Produced waters can have slightly higher radioactivity than background. In addition, the radionuclides are often concentrated in the solid deposits (scale) formed in oilfield equipment. When enclosed in flow equipment (pipes, tanks, etc.) this elevated concentration is not important. However, health risks may occur when equipment is cleaned for reuse or old equipment is put to different application.

Table 1 lists some of the common rock types and their typical content of potassium, uranium, and thorium.

Potassium is an abundant element, so the radioactive K⁴⁰ is widely distributed (Table 2). Potassium, feldspars and micas are common components in igneous and metamorphic rocks. Immature sandstones can retain an abundance of these components. In addition, potassium is common in clays. Under extreme evaporitic conditions, KCl (sylvite) will be deposited and result in very high radioactivity levels. Uranium and thorium, on the other hand, are much less common. Both U and Th are found in clays (by absorption), volcanic ashes, and heavy minerals.

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  Table 1

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  Table 2

History of gamma ray tools

The gamma ray tool was the first nuclear log to come into service, around 1930 (see Fig. 3). Gamma ray logs are used primarily to distinguish clean, potentially productive intervals from probable unproductive shale intervals. The measurement is used to locate shale beds and quantify shale volume. Clay minerals are formed from the decomposition of igneous rock. Because clay minerals have large cation exchange capacities, they permanently retain a portion of the radioactive minerals present in trace amounts in their parent igneous micas and feldspars. Thus, shales are usually more radioactive than sedimentary rocks. The movement of water through formations can complicate this simple model. Radioactive salts (particularly uranium salts) dissolved in the water can precipitate out in a porous formation, making otherwise clean sands appear radioactive.

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  Fig. 3 – A timeline of nuclear logging highlights the introduction and evolution of commercial nuclear-logging measurements.

Gamma ray logging tool

Before getting into how to use the log readings, let us consider the workings of the tool. Unlike all other nuclear tools (and, in fact, all other logging measurements), it is completely passive. It emits no radiation. Instead, it simply detects incoming gamma rays from the formation and (unfortunately) the borehole. Gamma rays are electromagnetic radiation, generally in the energy range 0.1 to 100 MeV. As light, this would correspond to very short wavelengths indeed. The difference between gamma rays and X-rays is largely semantic because they overlap in energy.

Originally, the detector was a Geiger-Müeller tube, just as in the Geiger counter. More recently, the detectors have been switched to solid-state scintillation crystals such as NaI. When a gamma ray strikes such a crystal, it may be absorbed. If it is, the crystal produces a flash of light. This light is "seen" by a photomultiplier staring into the end of the crystal. The photomultiplier shapes the light into an electrical pulse that is counted by the tool. Hence, like all nuclear tools, the raw measured quantity in a gamma ray log is counts. This means that the precision of gamma ray log measurements is determined by Poisson statistics. The precision is the square root of the total number of counts recorded at a given depth. Counts recorded are basically proportional to the volume of the detector crystal times its density (which determine the probability that a gamma ray will be captured within the crystal) times the length of time counted. As with all nuclear-logging measurements, the only part of this that the logger controls is the counting time. Because log measurements are depth driven, the length of time the logger counts is inversely proportional to the logging speed.

Historically, gamma ray sondes have recorded the total flux of gamma radiation integrated over all energies emanating from a formation as a single count rate, the gamma ray curve. Logging tools are not uniform in their energy sensitivity. No detector responds to all the gamma rays that impinge on it. Many pass through with no effect. The sizes of a detector, the solid angle it subtends, and its thickness, as well as its composition (particularly its density), all affect its efficiency for detecting gamma rays. The tool housing around the detector, the casing, and even the density of the borehole fluid can all filter the gamma rays coming from the formation. All these factors not only lower the overall tool efficiency, they also lead to variations in efficiency for gamma rays of different energies. In short, the count rate recorded in a particular radioactive shale bed is not a unique property of the shale. It is a complex function of tool design and borehole conditions as well as the actual formation’s radioactivity.

Common scale

Even though gamma ray readings are generally used only in a relative sense, with reservoir (clean) and shale values determined in situ, there are advantages to a common scale. In the US and most places outside the former Soviet Union, gamma ray logs are scaled in American Petroleum Institute (API) units. This harkens back to a desire to compare logs from tools of different designs. Tools with different detector sizes and compositions will not have the same efficiency and thus will not give the same count rate even in the same hole over the same interval. To provide a common scale, API built a calibration facility at the U. of Houston. It consists of a concrete-filled pit, 4 ft in diameter, with three 8-ft beds penetrated by a 5 1/2-in. hole cased with 17-lbm casing. The top and bottom beds are composed of extremely-low-radioactivity concrete. The middle bed was made approximately twice as radioactive as a typical midcontinent US shale, resulting in the zone containing 13 ppm uranium, 24 ppm thorium, and 4% potassium. The gamma ray API unit is defined as 1/200 of the difference between the count rate recorded by a logging tool in the middle of the radioactive bed and that recorded in the middle of the nonradioactive bed.

While it has served fairly well for more than 40 years, this is a poor way to define a fundamental unit. Different combinations of isotopes, tool designs, and hole conditions may give the same count rate, so the calibration does not transfer very far from the calibration-pit conditions. In contrast, Russian gamma ray logs are typically scaled in microroentgens (μR)/hr, which does correspond to a specific amount of radiation. Converting this to API units is a bit vaguely defined, but it is often suggested that the conversion factor is 1 μR/hr = 10 API units for Geiger tube detectors, but 15 μR/hr = 10 API for scintillation detectors. This falls in with the previous discussion of the many factors that can affect gamma ray readings. The problem is further aggravated in logging-while-drilling (LWD) measurements. The API unit provides a degree of standardization, but despite the best efforts of tool designers, one cannot expect tools of different designs to read exactly the same under all conditions. Fortunately, none of this is very important because gamma ray measurements are generally used only in a relative way.

Factors affecting readings

Because we use gamma ray logs as relative measures, precise calibration is not very important except as a visual log display feature. Environmental effects are much more important. Consider a radioactive volume of rock traversed by a borehole. Nuclear physics tells us that gamma rays are absorbed as they pass through the formation. For typical formations, this limits the depth of investigation to approximately 18 in. Considering only the geometry, the count rate opposite a given rock type will be much lower in a larger borehole in which the detector is effectively farther from the source of gamma rays. In an open hole, borehole size almost always has the greatest effect on the count-rate calibration. This problem can go well beyond changes in bit size. Especially if shales or sands are selectively washed out, borehole size can imprint itself of the expected gamma ray contrast between shales and sands. If the borehole is large enough, the density of the fluid filling the borehole can also impact the calibration by absorbing some of the gamma rays before they get to the tool.

Barite in the mud is another complication, filtering the incoming gamma rays. Thus, the gamma ray borehole size and fluid corrections are often very important and should be made if at all possible. Obviously, casing absorbs a large fraction of the gamma rays traversing it on their way to the borehole, so if the tool is run in a cased hole, casing corrections are very important. Tool design has a large impact on environmental corrections. The housing and location of the detectors all filter the incoming gamma rays. It is important to use the right environmental corrections for the tool being run. This is especially true for LWD tools that may consist of multiple detectors embedded in large, heavy drill collars that filter the incoming gamma rays in unique ways.

Interpreting gamma ray logs

Log analysis

Now that we know how the tools work, we are ready to discuss how gamma ray logs are used in log analysis. While the gamma ray log traditionally has been used primarily for well-to-well correlation, it also plays a role in quantitative log analysis. As mentioned at the outset, gamma ray logs are used primarily to define and quantify productive intervals. As discussed, above there are only three naturally occurring radioactive elements-potassium, uranium, and thorium (or K, U, and Th by their elemental symbols)—and all of these tend to be associated with shales, not clean matrix minerals (e.g., quartz sand, SiO₂, limestone CaCO₃).

The most common interpretation method is the simple bulk linear mixing law presented previously.

....................(1)

Even though we know that the distribution of clays in shales and reservoir rocks is quite complex, to first order, log analysts frequently simplify the linear bulk mixing law to the determination of shale volume:

....................(2)

Standard log analysis separates the log-analysis problem into a series of sequential, independent steps. Because shale-volume determination is usually the first step in the sequential process of formation evaluation from logs, porosity and fluid volumes are not yet known. As a result, the equation is further simplified to

....................(3)

Adding closure,

....................(4)

leads to the familiar formula for calculating shale volume from a borehole-corrected gamma ray log:

....................(5)

where the "clean" terms represent the lumped response to the matrix grains and the fluids in the porosity. Further complications arise because the shale values are taken from overlying shale beds. The clays distributed in the reservoir rock are almost certainly not simply dispersed versions of the shales, unless they occur as thin laminations. At the very least, there will be differences between shale, made up of clay minerals, clay bound water, and silt-size particles, and the clay minerals alone distributed in the matrix. Worse, because of differences in the processes at work when the shales were laid down vs. the shaly sands, the clay minerals in the sands may not be the same as those in the matrix. To compensate for this, numerous nonlinear relationships have been proposed. These have geologically significant-sounding names like Larinov older rocks but are simply empirical and have no physical basis. They are used to improve the correlation between gamma ray-derived shale volumes and other estimates of the shale volume, especially from core. The equations all start with the linear gamma ray index discussed above and reduce the intermediate values from there. Fig. 4 lists a few of the more common equations. Fig. 5 illustrates the degree of shale reduction that the various models afford. If one of these models must be used, select the one that best fits other available estimates of clay volume.

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  Fig. 4 – A summary of various nonlinear shale-volume models used to reduce the amount of shale below the linear, bulk mixing-law prediction.

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  Fig. 5 – Illustration of the amount of shale reduction predicted by various nonlinear shale-volume models listed in Fig 4.

One disadvantage of the various empirical, nonlinear models is that they generally require core data for calibration or at least justification. This is a generic problem with more complex models; they require more parameters to characterize them. To set or calibrate those parameters in turn requires more independent log or core measurements.

It is also assumed that the clean reservoir material (the sum of the pore fluids and matrix minerals) has a fixed amount of radiation associated with it. As long as the gamma ray reading associated with the clean reservoir material is small compared to the shales, this assumption is safe. As the sands become hotter (more radioactive), lumping the fluids and matrix together becomes problematic, particularly if the porosity is large.

Precision

Consider briefly some details of how a standard, gross-count-rate gamma ray tool works. Most modern tools (in nuclear logging, "modern" means within the past 25 years) use a solid-state scintillator crystal (most often sodium iodide, NaI) to detect gamma rays. When a gamma ray strikes the crystal, there is some probability that it will be captured. That probability is mostly proportional to the size and density of the crystal. If it is captured, it gives off a flash of light. A photomultiplier mounted on one end of the crystal converts that light to an electrical pulse, which is then fed to an electronic pulse counter. To measure a count rate with a given precision in the laboratory, one counts until enough counts are registered to give the desired level of precision (see the discussion of counting statistics above). Then, one divides that number of counts by the time it took to get that many to obtain a count rate. Unfortunately, in a logging tool, all measurements are depth-based. To measure a count rate, the tool counts for the length of time it takes the tool to move 1/2 ft (or whatever the depth increment is), then divides by the length of time it took the tool to move that distance. This means that the precision of a nuclear-logging measurement in a given lithology is proportional to one over the square root of the logging speed. Remember that the number of counts received crossing a clean 1/2 ft will be much less than the number when crossing a shaly 1/2 ft.

Environmental distortion

The simple consideration of the discussion of radiation transport helps clarify which environmental effects most seriously distort the gamma ray log. Imagine what happens as borehole size increases. There is less of the radiating radioactive material near the detector, and the measured count rate goes down, even though the actual level of radioactivity in the formation remains the same. Further imagine the rather typical case in which the shales are eroded and broken out while the sands remain in gauge. This would suppress the apparent gamma ray count rate in the eroded shales much more than in the sands, suppressing the gamma ray contrast between eroded shales and sands. This is typically one of the largest environmental effects on the gamma ray count rate. Again from the discussion of radiation transport, heavier materials in the path that the gamma rays must follow from the formation through the detector will absorb more gamma rays than lighter materials (as will be seen in a later section, this is the basis for the bulk density log, but that is another story and a different log). Worse yet, barite is a big absorber of gamma rays. The lesson to carry away is that borehole size and fluid corrections are almost always important when running the gamma ray log.

Gamma ray interactions with formations

Gamma rays interact with formations in three different ways:

• Compton scattering
• Photoelectric absorption
• Pair production (to a limited extent)

One of these will dominate depending on the energy of the gamma ray, as Fig. 6 shows.

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  Fig. 6 – Illustration of dominant gamma-ray interactions with a formation as a function of gamma-ray energy.

Compton scattering

The most important interaction for logging measurements involving gamma rays is Compton scattering, which dominates in the middle energy range. The density log itself is designed to exploit Compton scattering. Compton scattering also controls the transport of natural gamma rays through a formation to the standard gamma ray tool. Compton scattering is scattering off an atomic electron. In the process, the gamma ray loses some of its energy to the electron. Compton scattering is the dominant form of gamma ray interaction with a formation, from several hundred keV (kilo electron volts, a unit of energy) all the way to 10 MeV (mega electron volts). The cross section for Compton scattering changes very little with energy. The loss of gamma rays is proportional to

....................(6)

where Z is the average atomic number of the formation. The attenuation law for gamma ray intensity falloff is then

....................(7)

For Compton scattering to be a true measure of bulk density, ρ_b, Z/A must be a constant. For almost all formation elements, Z/A = 1/2, and a measurement of gamma ray attenuation in the 1- to 10-MeV range can indeed be calibrated to bulk density. The notable exception is hydrogen, for which Z/A =1. Table 1 lists some density values for comparison.

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  Table 1

Photoelectric (PE) absorption

Not surprisingly, the PE log is based on the photoelectric absorption of gamma rays, the scattering process that dominates at low energy. In this process, the incoming gamma ray is absorbed by an atomic electron, giving up all its energy to the electron in the process. If the gamma ray is energetic enough, the added energy causes the electron to break free from its atom. As another electron falls into the vacancy, a characteristic X-ray, generally less than 100 keV, is emitted. These X-rays are too low in energy to contribute to logging measurements.

The PE cross section falls off very strongly as the energy of the incoming gamma ray increases. The cross section is proportional to

....................(8)

It is a significant factor in gamma ray scattering only for energies less than 100 keV. This means that it is easy to separate the effects of PE absorption from those of Compton scattering by simply windowing the energies of the gamma rays detected. The same tool can make both measurements simultaneously. By examining the falloff of low-energy gamma ray flux, a logging tool can be calibrated to measure the PE factor (PEF). The PEF, in turn, is primarily sensitive to the average atomic number, Z, of the formation. Because hydrocarbons and water have very low Z values, they contribute very little to the average PE of a formation. Conversely, because the major rock matrices have very different Zs, the PE factor is a nearly porosity-independent lithology indicator.

Pair production

The final process by which gamma rays interact with a formation needs only a passing comment because its impact on logging measurements is minimal. This process, pair production, occurs only at very high gamma ray energies. It is another absorption process, with a threshold of 1.022 MeV. The incoming gamma ray interacts with the electric field of the nucleus and is absorbed if it has enough energy. This generates an electron-positron pair. The positron (actually just an antimatter electron) is quickly annihilated, yielding two 511-keV gamma rays. This has little impact on passive gamma ray or gamma-scattering density measurements but does play a role in the appearance and analysis of gamma ray spectra from neutron-induced gamma ray logs.

Applications

Gamma ray logs have a number of niche applications. For example, injected fluids can be tagged with radioactive tracers and their progress through a field monitored with gamma ray logs in wells adjacent to the injection site. The most common applications are described below.

Determining lithology

Gamma ray log character is one of the primary methods used to correlate the stratigraphic section. For most engineering and geophysical applications, the gamma ray log is primarily used to extract lithologic, mineralogic, or fabric estimates.

The log response depends on the radiation, tool characteristics, and logging parameters. A 30-cm sodium iodide scintillation crystal with a photomultiplier tube is a common detector configuration. Thin, highly radioactive beds may be detected, but cannot be resolved below about 0.25 m. Radiation is damped primarily by formation material electron density and Compton scattering. This limits the depth of investigation to around 30 cm, although it will depend on the energy levels. Because the radioactive decay is a statistical process, slower logging rates produce better results. The low number of counts resulting from logging too fast cannot be increased by logging rate correction factors. Most tools are usually out of calibration if they are not centered in the borehole. Heavy barite mud can also lower the overall count rate, particularly for low-energy gamma rays.

Rather than merely measuring total gamma radiation, the energy levels can be detected separately. This allows the concentrations of K, U, and Th to be derived as independent parameters. Fig. 7 shows the energy windows used in a Baker-Atlas tool. This would allow, for example, the feldspars in immature sands to be separated from clays with adsorbed U or Th.

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  Fig. 7 – Gamma-ray energy windows used for spectral gamma-ray logging (from Bigelow).

Identifying shale volumes

The most common use of gamma ray logs is to estimate the shale "volume" in rocks. It is important to remember that the tool measures radioactivity, and the correlation to shale content is empirical. Shales are presumed to be composed of clay minerals. Thus, the gamma ray level is assumed to be correlated with grain size. In reality, shales may be composed of 30% or more of quartz and other minerals. The clays within the shales may not be radioactive, and the adjacent sands may contain radioactive isotopes. However, radioactivity levels typically are related to grain size, as seen in Fig. 8. Here, core plugs were analyzed for median grain size and radioactivity level measured directly; crosses are fine-grained sands, while dots are silts and clay-rich rocks.

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  Fig. 8– Measured mean grain size vs. gamma-ray levels (calibrated to API value) for clastic samples. The rough correspondence of gamma ray value can be seen, but relationship is not simple (data from Georgi et al.).

To extract the shale content in rocks, a linear or near-linear relation is used to convert a gamma ray index, I_gr, to shale volume V_sh. Because local sands can contain radioactive components, and the shales may vary with depth, local baseline levels are chosen near the zone of interest.

....................(9)

where R is the measured radiation level, R_cleansand is the baseline level through a reference sand, and R_shale is the baseline through a representative shale. Several relations have been developed to derive shale volume (Fig. 9). A linear relation simply sets the shale content equal to the gamma ray index.

....................(10)

Other proposed relations shown in Fig. 9 are defined in Table 3. Several assumptions are made in these evaluations:

• Compositions of sand and shale components are constant.
• Baselines are chosen on representative "shales" and "clean" sands (although these terms are very subjective).
• Simple mixture laws apply.
• Fabric is not important.

Many of these assumptions may be poor approximations.

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  Fig. 9 – Reported gamma-ray index to shale volume conversions (from Bigelow).

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  Table 3

A more likely presumption is that the radiation level is dependent on the mixture densities and not volumes (Wahl and Katahara). In this case, a fabric analysis can also be performed. Katahara modeled the shale component of shaly sands as existing in three forms:

• Structural—an original depositional granular form.
• Dispersed—clay distributed through the rock and pore space.
• Laminated—thin layers of shale cutting the sand beds.

In Fig. 10, his results show a surprisingly simple form. The conclusion is that in most cases, the simple linear relation is appropriate.

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  Fig. 10 – Modeled gamma-ray response to different clay distributions within a shaley sand series (modified from Katahara).

As an example of this process, the shale content of a zone in a Gulf of Mexico well is estimated. In Fig.11, a sand-shale sequence gives a gamma ray range of approximately 20 to 90 API units. A baseline of approximately 25 is chosen through the sand, and a baseline of approximately 98 is chosen for the shale. Using the relations in Eqs. 9 and 10 result in the shale volume estimates scaled at the bottom of the logged zone.

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  Fig. 11 – Typical shale volume extraction from a Gulf of Mexico log. 100% “sand” and 100% “shale” lines are locally established; then, shale content is a linear interpolation between the two.

Correlating cores with logged depth

Gamma radiation levels can also be measured on core. This technique provides a profile of levels along the length of the core. The primary use is to correlate core depths to logged depths. An example is shown in Fig. 12. This procedure can be used to identify log features or positioning of the cored interval. Especially when core recovery is poor, this method is very useful in tying the core fragments to true depths. Core plugs can also be measured, although special equipment must be used to record the low levels of radiation associated with the small samples. In general, property correlations to the measured gamma ray levels are much better for cores than for the log because of the depth averaging in the log.

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  Fig. 12 – A measured core gamma-ray profile vs. logged data in a carbonate section. Comparison of peaks shows the offset in measured depth (adapted from Core Labs data).

Nomenclature

A	=	atomic weight
EGR	=	gamma ray energy
NA	=	Avogadro’s number = 6.02 × 10 23 molecules/gram molecular weight
Vcn	=	volume of clean formation
Vf	=	volume of fluid
Vi	=	volume of a particular constituent (mineral or fluid) of a formation
Vma	=	volume fraction of matrix mineral
Vsh	=	volume of shale
Z	=	average atomic number
γ	=	gamma ray tool reading in API units
γf	=	gamma ray flux from 100% fluid
γcn	=	gamma ray flux from 100% clean formation component
γma	=	gamma ray flux from 100% matrix
γns	=	gamma ray tool reading in nonshale
γsh	=	gamma ray tool reading in 100% shale
ρb	=	bulk density
σco	=	Compton scattering cross section
Σi	=	capture cross section of ith formation component

Subscripts

GR	=	gamma ray
i	=	item count or index

Noteworthy papers in OnePetro

Use this section to list papers in OnePetro that a reader who wants to learn more should definitely read

See also

Spectral gamma ray logs

Rock failure relationships

Nuclear log interpretation

Nuclear logging

Nuclear logging while drilling

Density logging

PEH:Nuclear_Logging