gamma theory

44
SECTION 4 GAMMA RAY

Upload: jaggcc

Post on 04-Apr-2015

589 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Gamma Theory

SECTION4

GAMMA RAY

Page 2: Gamma Theory
Page 3: Gamma Theory

08/27/2001 TRAINING MANUAL i

TABLE OF CONTENTS

TABLE OF CONTENTS...............................................................................................i,ii

BASICPHYSICS............................................................................................................1

The AtomicNucleus..............................................................................................1

AlphaDecay..........................................................................................................2

BetaDecay.............................................................................................................2

GammaDecay........................................................................................................4

Gamma Interaction WithMatter............................................................................7

PairProduction...........................................................................................7

Compton (Incoherent)Scattering................................................................8

PhotoelectricEffect.....................................................................................9

GAMMA RAYTOOLS.................................................................................................10

Natural Gamma Ray Tools...................................................................................10

Radioactivity Of Different Formations....................................................12

Volume OfShale.......................................................................................12

Spectral Gamma RayTools..................................................................................13

DecaySequence........................................................................................13

Page 4: Gamma Theory

GAMMA RAY THEORY

ii TRAINING MANUAL08/27/2001

EnergySpectrum......................................................................................14

• Potassium.......................................................................................14

• Uranium.........................................................................................15

• Thorium.........................................................................................16

CALIBRATION.............................................................................................................17

Calibration Of The Natural Gamma Ray Tool.....................................................17

Calibration Of The Spectral GammaTool............................................................19

Compensated Spectral Natural Gamma Tool(CSNG)..............................20

• GainCompensation..........................................................................20

• ShopCalibration...............................................................................20

Spectral Gamma Ray Tool(SGR).............................................................23

• GainCompensation..........................................................................23

• Calibration........................................................................................24

SPECTRAL GAMMA REAL TIMECOMPUTATION.............................................26

STATISTICAL FLUCTUATION AND BED RESOLUTION...................................28

Depth OfInvestigation..........................................................................................28

SCINTILLATIONDETECTORS................................................................................29

Page 5: Gamma Theory

GAMMA RAY THEORY

08/27/01 TRAINING MANUAL 3

The ScintillatingCrystal.......................................................................................30

The Photomultiplier Tube(PMT).........................................................................31

BOREHOLEEFFECTS................................................................................................31

Natural GammaTools...........................................................................................33

Spectral GammaTools...........................................................................................34

GEOLOGICALCHARACTERISTICS.......................................................................35

Uranium.................................................................................................................35

Thorium.................................................................................................................36

Potassium..............................................................................................................36

Spectral LogExample...........................................................................................37

REFERENCES................................................................................................................38

Page 6: Gamma Theory
Page 7: Gamma Theory

GAMMA RAY THEORY

08/27/2001 TRAINING MANUAL 1

BASIC PHYSICS

The Atomic Nucleus

The basic building blocks of the atomic structure are the proton, neutron and electron.Each of these particles differs in the basic properties of charge and mass.

In the normal, stable atom, these are bound together into a hole that is electrically neutral.The neutrons and protons are joined to form the nucleus of the atom. The atomicnumber of the atom, the number of protons in the nucleus, is represented by the symbolZ. The number Z also represents the total number of electrons of the atom thatdetermines its atomic and molecular properties. Atoms with the same atomic numberoften have markedly different nuclear characteristics because there can be differentnumbers of neutrons associated with a fixed number of protons.

The total number of nucleons (protons and neutrons) in the nucleus is called the massnumber, A. Nuclides having the same atomic number but different mass numbers, arecalled isotopes. Different isotopes of an element are chemically identical and can bedistinguished by their different atomic weights or nuclear properties.

An isotope is identified by naming the element and following that name with the number ofthe isotope. There is a more formal notation that sets the mass number (A) as asuperscripted number in front of the symbol for the element and the atomic number (Z) asa subscripted number in front of the symbol. For any element (listed below as X), thisformal notation is shown as:

ZAX

As an example, the most common isotope of potassium has twenty neutrons and nineteenprotons and is represented as follows:

1939K or Potassium-39

The only radioactive isotope of potassium has twenty-one neutrons and nineteen protons.This element is represented as:

1940K or Potassium-40

The formal notation is used in formulas and in series descriptions, while the other notationis used in text material.

Page 8: Gamma Theory

GAMMA RAY THEORY

2 TRAINING MANUAL08/27/2001

Alpha Decay

Certain radioactive nuclei, those for which Z > 82, spontaneously decay into a daughternucleus (usually in an excited state) and a helium nucleus (2

4He). This helium nucleusconsists of two protons and two neutrons that is called an alpha (α) particle. Since thealpha particle has a very stable configuration of nucleons, it is perhaps not surprising thatsuch a group of particles might exist within the parent nucleus prior to alpha decay. Thelaws of conservation of charge and of nucleons require that:

6-1. ZA

ZAP D→ +−

−24 α

Where P and D are the parent and daughter nuclei, respectively. As an example ofequation 1, part of the decay sequence for Thorium-232 going to stable Lead-208 involvesthe decay of Bismuth-212 by alpha emission to Thallium-208 according to the equation:

6-2. 83212

81208Bi Tl→ + α

• Bi = Bismuth (parent)

• Tl = Thallium (daughter)

Beta Decay

Beta decay may be defined as that radioactive decay process in which the charge of anucleus is changed without a change in the number of nucleons. There are three types ofbeta decay. Two of these involve the emission of Beta particles. A ß- particle is anelectron emitted from an unstable nucleus when one of its neutrons' changes into a proton.The positron, ß+ (discovered in 1932) is emitted from an unstable nucleus when one of itsprotons' changes into a neutron. Except for its positive charge, a positron is identical toan electron. When a positron and an electron meet, they annihilate and their massesconvert into two γ rays. A parent to daughter representation of beta-electron decayobeys.*

*NOTE: In all the beta decay equations, the emitted neutrino is omitted since its existence is not

important (at this level) in understanding gamma spectroscopy theory.

Page 9: Gamma Theory

GAMMA RAY THEORY

08/27/01 TRAINING MANUAL 3

6-3. Beta-electron decay: ZA

ZAP D→ ++

−1 β

An example of this decay is found again in the decay sequence for Thorium-232. TheThallium-208 produced from the alpha decay depicted in(equation 6-2) next Beta decaysaccording to:

6-4. 81208

82208Ti Pb→ + −β

• Pb = lead (daughter)

The parent to daughter representation of beta-positron decay, in a similar fashion, obeysthe transformation.

6-5. Beta-positron decay: ZA

ZAP D → +−

+1 β

An example of this decay is shown in the transformation of unstable Nitrogen-12 toCarbon-12.

6-6. 712

612N C → + +β

The third type of beta decay is electron capture. In electron capture, an atomic orbitalelectron combines with a proton of the nucleus to change it into a neutron. Again thenumber of nucleons is unchanged, but a proton is converted into a neutron, as in ß+ decay.No charged particle is emitted in the decay by electron capture. A parent to daughtertransformation for electron capture takes the form of:

6-7. Electron capture: β P Dcapture ZA

ZA−−+ → 1

An example of electron capture is observed in the transformation of radioactivePotassium-40 to Argon-40.

6-8. β K Arcapture− + →19

401840

• K = Potassium

• Ar = Argon

Page 10: Gamma Theory

GAMMA RAY THEORY

4 TRAINING MANUAL08/27/2001

Gamma Decay

When a nucleus decays from a parent to daughter, the daughter is often left in one of anumber of possible excited states. An excited state is not stable. The nucleus willtherefore spontaneously drop to a lower energy excited state or the lowest energy groundstate by emitting photons. A photon emitted from a nucleus in an excited state is called agamma ray (γ). Gamma ray photons represent the highest energy portion of theelectromagnetic spectrum (which includes X-rays and visible light). See Table 1.Referring to any parent to daughter decay (equation 6-1,6-3, 6-5, 6-7) and ignoring theemitted or capturing particles in the reactions, a general expression can be written:

6-9. P D→ *

Here, the asterisk (*) denotes an excited state. For gamma emission,

6-10. D D* '→ +γ

Table 1 Electromagnetic Spectrum

Page 11: Gamma Theory

GAMMA RAY THEORY

08/27/01 TRAINING MANUAL 5

Here the prime ( ′ ) denotes a lower excited state or ground state. Only those nucleartransitions that obey the conservation laws are permitted. In the downward transitionfrom an upper nuclear energy state EU to a lower state EL, the emitted gamma ray(ignoring any recoil effect) has the energy:

6-11. E h E Ef u Lγ

= = −

Here h = Planck's constant = 6.626 x 10-34 J/Hz

f = frequency

EU = nuclear energy of the upper state

EL = nuclear energy of the lower state

A simple practical example of our theoretical analysis is exemplified by the decay ofPotassium-40. From equation 6-8, Potassium-40 captures an electron and becomesArgon-40. The disintegration scheme is shown below.

K

Electron Capture

11%

E =1.46 MeVAr*

Ar E =0 (ground state)

4018

4018

U

L

E =1.46 Mev

4019

Electron Emision

89%

Ca (ground state)4020

Beta Beta

FIG: 1 Potassium Decay

From the above, figure Potassium-40 beta electron decays to Calcium-40 89% of the timewith no gamma emission (Calcium-40 is a stable element in its ground state). But 11% ofthe time Potassium-40 captures an electron to become Argon-40 in its excited state.

From equation 6-10, Argon-40 will de-excite itself by emitting a gamma ray whose energy(given by equation 6-11) is 1.46 MeV (1460 KeV).

Page 12: Gamma Theory

GAMMA RAY THEORY

6 TRAINING MANUAL08/27/2001

A more complex scheme is demonstrated by the decay of Thallium-208 to Lead-208 bybeta-electron emission (equation 6-4).

E =2.614 Mev

Ti20881

c

b

a

(not all states included)

3.198 MeV

2.614 Mev

0 (ground state)Pb20882

c

b

a

FIG: 2 Thallium Decay

The above figure shows Thallium-208 decaying to three of the excited states of Lead-208(there are actually more than just three excited states). ß-

a′ ß-b′ ß-

c′ represent the emittedbeta electron particles that cause the decay to the corresponding excited states (a, b andc). Notice that the de-excitation of lead-208 from the excited state "a" to the ground stateproduces a 2614 KeV gamma ray.

The traditional unit of measurement of atomic energy (nuclear energy) is the electron volt(eV), which is defined as the kinetic energy gained by an electron when it is acceleratedthrough a potential of one volt. The commonly used multiples of this unit are kiloelectronvolts, keV, and Megaelectron volts, MeV. These represent multiples of 1,000 and1,000,000 electron volts, respectively. Therefore, a gamma ray with an energy of 1 MeVwould have the same striking power as an electron accelerated through a 1,000,000 voltpotential.

Page 13: Gamma Theory

GAMMA RAY THEORY

08/27/01 TRAINING MANUAL 7

Gamma Interaction With Matter

After their creation, the gamma ray photons can interact with matter in different ways. Inthe discussion to follow it is important to remember the dual nature of these photons.Gamma rays, as all photons, travel and interact as waves and particles. Three of the waysin which gamma rays interact with matter are:

• Pair Production

• Compton Scattering

• Photoelectric Effect

PAIR PRODUCTION

Pair production serves to decrease the number of high energy gamma rays coming fromthe formation. Pair Production can only occur when the energy of the gamma ray is inexcess of 1.02 MeV (this is twice the rest mass of an electron or positron). In this case,the gamma ray photon passing near the nucleus of an atom vanishes. In its place, anelectron and a positron appear, as shown in figure 3. Pair production (which cannot takeplace in a vacuum) obeys Einstein’s well know equation showing the convertibility of pureenergy to matter E M c= 0

2 ′ with E=photon energy. It should be noted that pair

production is of little use in the evaluation of a formation.

Incident Photon

eElectron

High EnergyPositron

e+

FIG: 3 Pair Production

NOTE: For a more complete analysis of gamma interaction (including Rayleigh Scattering), refer to the“Density theory” section of this Manual.

Page 14: Gamma Theory

GAMMA RAY THEORY

8 TRAINING MANUAL08/27/2001

COMPTON (INCOHERENT) SCATTERING

The most important interaction to the bulk density measurement is called ComptonScattering. Compton Scattering is classified as incoherent scattering. Incoherentscattering involves a photon scattering off one electron at a time. In Compton Scatteringthe incident photon energy is assumed to be much greater than the binding energy of theelectron. For this case the electron can be considered essentially free (i.e. not bound tothe nucleus). In compton interaction the photon collides with an outer (weakly bounded)electron of an atom. Here the incident photon transfers some of its energy to the electron,which it knocks out of the atom. The scattered photon now has less energy and has likelybeen deflected along a different path. See figure 4.

This scattering process will be repeated over and over (down scattering) as the gamma raypasses through the material, until the gamma ray has lost enough energy that it can bephotoelectrically absorbed (i.e. less than about 100 keV). Since the gamma ray willundergo more collisions per unit distance in a high-density material than in a low-densitymaterial, the average distance travelled by a gamma ray (proportional to count rate)depends on the density of the material.

When the photon energy decreases to a sufficient level, such that the electron bindingenergy can not be ignored, binding-energy correction must be applied to the Comptoninteraction to obtain an accurate incoherent scattering across section. It should here benoted that if the energy to be imparted to the electron is not greater than the bindingenergy, compton scattering will not occur. Compton interaction is the dominant effect forgamma rays with energies between 100 keV to 10 MeV.

Incident Photon

Electron

e

ComptonRecoil

ScatteredPhoton

FIG: 4 The Compton effect

Page 15: Gamma Theory

GAMMA RAY THEORY

08/27/01 TRAINING MANUAL 9

PHOTOELECTRIC EFFECT

The photoelectric effect becomes important when the gamma ray energy is only slightlygreater than the binding energy of the electrons. For most rocks, this occurs at energiesbelow about 100 keV. In the photoelectric effect one gamma ray photon is absorbed byone electron. In the process, all of the energy of the gamma ray is transferred to theelectron, which then has enough energy to overcome the binding energy of the nucleusand escape. This interaction is shown below.

Incident Photon

eElectron

FIG: 5 The Photoelectric Effect

Page 16: Gamma Theory

GAMMA RAY THEORY

10 TRAINING MANUAL08/27/2001

GAMMA RAY TOOLS

Natural formation gamma radiation comes from radioactive isotopes of uranium, thoriumand potassium.* To record this radiation, there are presently two types of gamma raytools in use:

1. The gross (simple) gamma tool that is usually referred to as a natural gamma tool.The gross gamma tool records the total gamma activity in the wellbore without regardto the source,

2. The spectral gamma ray tool is a spectral analyzer that identifies the source andgives the contribution (concentration) of each of the elements (potassium, uranium andthorium) to the overall spectrum (count rate).

Natural Gamma Ray Tools

This simple gamma tool consists of a detector and a counter. The detector is usually ascintillation type that outputs a discrete electrical pulse for each gamma ray detected.Although the height of the pulses is proportional to incident gamma energy, the basicgamma tool does not sort the pulses, it merely counts those above some discriminationlevel. Therefore the processed information is merely the count rate (counts/second) perdepth sample. In order to output a standard result log, independent of tool systems, a unitof measurement called the API is used.**

*NOTE: The specifics of the decay sequences will be discussed in the Spectral Gamma Ray section.

**NOTE: See Calibration Section for definition of API.

Page 17: Gamma Theory

GAMMA RAY THEORY

08/27/01 TRAINING MANUAL 11

The basic gamma ray log is effective in distinguishing permeable zones by virtue of thefact that radioactive elements can be highly concentrated in the shale, which areimpermeable and much less concentrated in sands and carbonates, which are generallypermeable. Figure (6) shows some typical responses in different lithologies. The nextsection will explain the origin of the radioactivity of different earth formations.

FIG: 6 Gamma Ray Response In Typical Formations

RADIOACTIVITY OF DIFFERENT FORMATIONS

Page 18: Gamma Theory

GAMMA RAY THEORY

12 TRAINING MANUAL08/27/2001

A major portion of the earth's radioactive potassium and uranium-thorium series elementswas originally contained in igneous rocks. Igneous rocks generally consist of quartz,feldspars, micas and minor accessory minerals.

Quartz crystals have a strong well-ordered structure. This tends to eliminate anyimpurities from the quartz structure. Since sandstone’s are created from the erosion ofquartz, they generally exhibit low radioactivity’s.

Feldspars and micas contain a large portion of the earth's potassium fraction. This mineralgroup decomposes at a relatively rapid rate into the clay minerals. Clays have smallindividual particle size and a relatively open lattice structure that is characterized byweaker bonding. This open structure encourages the inclusion of impurities. Duringdeposition, clays absorb heavy radioactive elements that are practically impossible to leachout. Since shales are composed of small clay particles, shales tend to be considerablyhigher in radioactivity than most common formations.

Carbonate rocks were developed from calcareous marine life skeletal matter. Since littleradioactivity is present in living organisms, carbonate rocks are generally low inradioactivity.

Dolomite is formed from a chemical reaction between limestone and dissolved magnesiumin migrating ground waters. This process is called dolomitization. Since ground waterscontain dissolved radioactive isotopes, in the process of dolomitization some isotopes maybe deposited. For this reason, dolomite has a small but higher amount of natural radiationwith it than do limestones and may be radioactive, especially in vuggy and/or fracturedintervals.

VOLUME OF SHALE

Because thorium, potassium and (to a lesser degree) uranium is largely concentrated inclay minerals, the GR log can be used to estimate the shale content (Vsh) of a zone.Basically, the procedure is a matter of estimating the clean zone and 100% shale zone onthe log and interpolating between the two to determine Vsh in a partially shale interval.This is not a very precise technique, so other shale indicators are used as well (the spectralgamma ray provides better estimates of Vsh).

Page 19: Gamma Theory

GAMMA RAY THEORY

08/27/01 TRAINING MANUAL 13

Spectral Gamma Ray Tools

The basic construction of a Spectral Gamma Ray Tool is essentially the same as the simplegamma tool. Although, the detector must be of the scintillation type to output voltagepulses proportional to gamma energy. Unlike the natural gamma tool, each pulse detectedis now placed (counted) in a channel representing a certain energy level. There is at least256 channels (corresponding to a spectrum utilizing an 8 bit analog to digital converter, 28

= 256 possible states or channels). To fully understand the usefulness of this spectralanalyzer we need to elaborate more on the decay scheme and energy spectrum associatedwith formation radiation.

DECAY SEQUENCE

Natural formation radiation is due primarily to radioactive isotopes of uranium (Uranium-238), thorium (Thorium-232) and potassium (Potassium-40). These isotopes can be putinto two categories: series and non-series. Uranium and thorium are in the seriescategory, while potassium is part of the non-series group. The series isotopes, which allhave high atomic numbers (Z = 81 to 92), are sets of isotopes that are found together, andwhich decay in sequence from one to another until reaching stable isotopes of lead. Thenon-series radioisotopes occur separately and decay directly to stable isotopes. Figure 7shows the decay sequence for potassium, uranium and thorium.

FIG: 7 Decay Sequence

Notice the decay scheme shows potassium decaying non serially to argon by electroncapture, while the series isotopes (uranium and thorium) decay to stable isotopes of lead(lead-206 and lead-208 respectively) by repeated alpha and beta-electron emission.

Page 20: Gamma Theory

GAMMA RAY THEORY

14 TRAINING MANUAL08/27/2001

ENERGY SPECTRUM

• POTASSIUM

There are three natural isotopes of potassium: Potassium-39, Potassium-40 andPotassium-41. Their respective proportions in the earth are 93.10%, 0.0199% and 6.88%.Potassium-40 with a half life of 1.3 x 109 years is the only radioactive isotope. It candecay (Figure 1) by electron capture to argon-40 according to equation 6-8. Argon-40,being in an excited state, de-excites itself by emitting a gamma ray according to equation6-10. The emitted gamma ray has an energy of 1.46 MeV. This is the only gammaemitted. Since potassium-40 decays into a stable isotope, there are no radioactive decayproducts. The energy spectrum for pure potassium is shown in Figure 8. The vertical lineis the ideal case whereas the "mountain range" is the actual spectrum showing the effect ofdetector crystal resolution (the line becomes a peak) and Compton down scattering (thehigher low energy portion). It should be mentioned that in the wellbore, a majority of thegamma rays coming from the formation have under gone many Compton interactions andhave been degraded to energies of 50 to 200 KeV.

FIG: 8 Potassium Spectrum

Page 21: Gamma Theory

GAMMA RAY THEORY

08/27/01 TRAINING MANUAL 15

• URANIUM

There are three natural isotopes of uranium and all are radioactive; Uranium-234,Uranium-235 and Uranium-238. Their respective proportions in the earth are 0.0057%,0.72% and 99.27%, respectively. Their half-lives are 2.5 x 105 years, 7.1 x 108 years and4.4 x 109 years, respectively. Uranium and most of its daughter isotopes emit gamma raysof not one, but several different energy levels. Most of the radioactivity actually measuredby conventional gamma ray tools come not from uranium itself, but from the decay of oneof its daughters, Bismuth-214 to Polonium-214 by beta-electron. The excited poloniumnucleus emits gamma rays at over 50 distinct energy levels ranging from 63 KeV to 3.07MeV. A very noticeable peak in this range is at 1.76 MeV. The spectrum for pureuranium is shown below:

FIG: 9 Uranium Spectrum

Page 22: Gamma Theory

GAMMA RAY THEORY

16 TRAINING MANUAL08/27/2001

• THORIUM

There is only one long-lived thorium isotope: Thorium-232. Other thorium isotopes(Thorium-234 and Thorium-230) are found in nature as daughter elements of Uranium-238. Thorium-232 has a half life of 1.4 x 1010 years and is most easily detected indirectlyby the gamma rays emitted during the decay of one of its daughters, Thallium-208 toLead-208 (Equation 6-4). The excited lead nucleus emits a number of distinct energygamma rays. The most noticeable energy level (i.e. peak) occurs at 2.614 MeV. Thespectrum for pure thorium is shown in the Figure below:

FIG: 10 Thorium Spectrum

Page 23: Gamma Theory

GAMMA RAY THEORY

08/27/01 TRAINING MANUAL 17

CALIBRATION

Calibration Of The Natural Gamma Ray Tool

One of the problems of gamma ray logging has always been the choice of a standardcalibration system, since all logging companies use detectors of different sizes and shapesencased in tool housing of varying characteristics. On very old logs, the scales werecalibrated in micrograms of radium per ton of formation. For many reasons, this wasfound to be an unsatisfactory calibration standard for gamma ray logs. In 1956 anAmerican Petroleum Institute sub-committee was appointed for the purpose of designing acalibration system (and units) that would be an acceptable standard throughout theindustry.

It was decided to use a pit, with a bed of radioactive concrete situated between two zonesof low radioactivity (concrete without the radioactive elements), and to define the APIGamma Ray unit as 1/200 of the difference in log reading between the "hot" zone and the"cool" zone. The test pit was constructed at the University of Houston. It presentlyconsists of an "artificial shale" 8-ft thick and sandwiched between neat Portland cement.

5-1/2" J55 Casing

Neat Portland Cement

Uranium 13 ppmThorium 24 ppm

Potassium 4%

Neat Portland Cement

4 Feet

24 Feet

Gamma Ray

200APIUnits

FIG: 11 API Test Pit

Page 24: Gamma Theory

GAMMA RAY THEORY

18 TRAINING MANUAL08/27/2001

The artificial shale is actually cement mixed with 13 ppm uranium, 24 ppm thorium and4% potassium. The API standard defines the difference in radioactivity between the neatcement and the radioactive cement mixture as 200 API units. Any logging servicecompany may place its tool in this pit to make a calibration. In doing so, a sensitivityfactor, G', would be computed from the definition:

[Tool Response (Hot) - Tool Response (Cool)] G' = 200 API

or

6-12. G2 0 0 A P I

T o o l R e s p o n s e ( h o t ) - T o o l R e s p o n s e ( c o o l )' =

Here, Tool Response is usually in CPS, and Hot and Cool refer to the radioactive andnon-radioactive zones respectively.

Once calibrated in the test pit, the tool's log response is now given by:

GRLog = G' (Tool Response)

And is independent of the type of tool and other instrumental factors, and thus satisfies thepurpose of a standard calibration. Of course, in actuality not every gamma toolmanufactured is calibrated in this test pit. The test is usually reserved for a particular typeof "standard tool". Once calibrated in the pit, this standard tool is used to "calibrate" aradioactive source. This actually means we just record the API value of this source at acertain distance as seen by the standard tool. This source is then used for shop/fieldcalibration of all tools manufactured "identically" to the standard tool. This radioactivesource is usually a Ra -226 test pill or a thorium -232 sleeve. With this calibration source,field calibration of all natural gamma tools involves determining a gain factor from:

6-13. GCalibrator value in API (as recorded by standard tool)

Calibrator value in field tool units=

Since the calibrator value was established by the standard tool calibrated in the API testpit, the calculated G (which is proportional to G') enables all field tools to give standardresults (logs) in API units. Thus the modified log response is:

GR G(Field Tool Response)Log

=

Page 25: Gamma Theory

GAMMA RAY THEORY

08/27/01 TRAINING MANUAL 19

Calibration Of The Spectral Gamma Tool

The calibrations associated with the Spectral Gamma Tool are more complex than theGross Gamma Tool.* This is due to the fact that each detected gamma must be placed inan appropriate channel based on its energy (voltage level). The channels andcorresponding energies are directly proportional (i.e. the higher the channel value, thehigher the energy it represents). A shop (or field) calibration is used to define the width(in channels) of certain computation "windows". Each spectral computation window(from 3 up) consists of a certain number of channels. The total gamma count within eachwindow is found by summing the total gamma count in the corresponding channels. Eachwindow, while representing a specific channel range, also represents a specific energyrange.

To insure that all of the detected gamma’s is counted in the appropriate channels involvessome gain control, (usually automatic) that takes into account the temperature effect (andany other miscellaneous drift) on the detector system. This temperature effect causes thevoltage pulse height of the PMT (Photo Multiplier Tube) to change identical gammainputs. Therefore, to insure correct computed results:

1. The detector gain must be constantly monitored and adjusted.

2. Shop calibrations must be performed to set window boundaries.

To achieve this end, we will discuss two methods of calibrations; one used by theCompensated Spectral Natural Gamma Tool (CSNG) and the other utilized by theSpectral Gamma Ray Tool (SGR).

*NOTE: All Spectral Gamma Tools output a gross gamma curve calibrated like the natural gammatool for comparison purposes. This section deals with the calibrations associated with theelemental analysis feature.

Page 26: Gamma Theory

GAMMA RAY THEORY

20 TRAINING MANUAL08/27/2001

COMPENSATED SPECTRAL NATURAL GAMMA TOOL(CSNG)

• GAIN COMPENSATION

Since the CSNG-A measures the energies of individual gamma rays, the gain of thedetector must be held constant. This is accomplished by using an alpha-gamma raycoincidence technique. Near the main gamma ray detector is a much smaller detector thatcontains an embedded Americium-241 source. When Americium-241 decays to Np-237by alpha emissions a 60 keV gamma ray and the high energy alpha particles are emittedessentially simultaneously.

The alpha particle is detected with near 100% efficiency in the smaller alpha detector,whereas most of the 60 keV gamma rays escape. About 20% of these gamma rays aredetected in the main gamma detector, since these gamma rays are coincident with thealpha particles, the stabilizer gamma rays can be spectrally separated from formationgamma’s with better than 99% efficiency.

The peak value of the gamma stabilization spectrum is constantly monitored and theelectrical bias on the detector adjusted to keep the peak at the same channel value (channel47) that corresponds to 60 keV. See figure 12 (a)

• SHOP CALIBRATION

The primary calibration standards for all CSNG tools are the "KUT" (Potassium, Uranium,Thorium) calibration tanks, in the Nuclear Test Facility at HLS Headquarters in Houston,Texas. From this primary calibration, sensitivity coefficients are calculated and stored insoftware for all CSNG tools of identical design. Shop calibrations and field checks areperformed in the districts and on location with the use of a Thorium-232 sleeve. Thissleeve is wrapped, at the proper location, around the tool detector housing.

Page 27: Gamma Theory

GAMMA RAY THEORY

08/27/01 TRAINING MANUAL 21

During shop calibrations, window boundaries are determined in channel ranges for fixedenergy ranges. The energy range of each window is fixed in the software, but thecorresponding channel range varies slightly for each tool. Each window has an upper andlower energy value defining its width. The corresponding upper and lower channel valuesare computed from the linear expression:

. 6-14.

Channel Value = R (Energy Value) + B

R = slope

B = offset

Therefore, for any window whose width is defined by the upper and lower energy values,E'

U and E'L respectively, the corresponding channel range width is given by:*

CHANNEL U = R (E'U) + B

CHANNEL L = R (E'L) + B

Each window can be represented graphically as shown in figure 12 (b).

STABILIZER SPECTRUM CHANNEL RANGE VS ENERGY RANGE

(a) (b)

FIG: 12

Page 28: Gamma Theory

GAMMA RAY THEORY

22 TRAINING MANUAL08/27/2001

*NOTE: The prime denotes that these are not the same energy values associated with gamma decaydiscussed in a previous section.

The gain (R) and offset (B) is determined during shop calibration for a low and highspectrum (i.e., two slopes and two offsets are calculated). The thorium sleeve providesthe necessary four energy values (peaks). The Figure below shows the four centroids(peaks) used during calibration, along with the measured channels in which each centroidappears (for this particular tool).

FIG: 13 CSNG Cal Peaks

From the measured channels for the high spectrum above, the gain and offset arecomputed from the linear simultaneous equations.

215 Ch = R (2.614 MeV) + B

50 Ch = R (0.583 MeV) + B

Solving for R and B we obtain

R = 81.2 ch/MeV or .0812 ch/KeV

B = 2.7 channels

Page 29: Gamma Theory

GAMMA RAY THEORY

08/27/01 TRAINING MANUAL 23

All CSNG tools have window 1 energy range from 2.480 MeV to 2.919 MeV. Using thegain and offset determined above, the corresponding channel range for this particular toolis defined by:

ChChannel U = 81.2 ���� (2.919 MeV) + 2.7 Ch = 240 Ch

MeV

ChChannel L = 81.2 ���� (2.480 MeV) + 2.7 Ch = 204 Ch

MeV

Therefore:

Window 1 = 2.480 MeV ��� > 2.919 MeV

= Channel 204 ��� > Channel 240

SPECTRAL GAMMA RAY TOOL (SGR)

• GAIN COMPENSATION

Unlike the CSNG, the SGR contains no internal stabilization source, so gain control ismaintained by constantly readjusting the window boundaries based on the measuredchannel of the formation potassium peak. The below figure shows how this peak varieswith time (temperature).

FIG: 14 SGR Peak

Page 30: Gamma Theory

GAMMA RAY THEORY

24 TRAINING MANUAL08/27/2001

During logging a 256 channel spectrum is accumulated continuously over five-minutesperiods. At the end of each period the formation potassium peak (centroid) is found andthe measured channel is used to compute a new gain factor (R). The window boundariesare then readjusted using the new gain factor. This gain factor is computed from ourlinear expression (Equation 6-14) with the known energy level for potassium (see Figure8) and assuming a zero offset.

Channel Value = R(Energy)

6-15. R = Channel Value / Energy

or, for potassium:

Channel Value Measured Potassium Channel6-16. R(K) = ������������� = ��������������������������

Energy 1.460 MeV

The choice of potassium as the stabilization source is obviously due to its great abundanceas compared to uranium or thorium (i.e. it has the greatest likelihood of being present).

• CALIBRATION

The primary calibration standards for all SGR tools are three different simulated formationtanks. Each tank consists of a 6-inch, waterfilled borehole in a single-activity formation ofpotassium, uranium or thorium.

The tanks are used with the "standard" SGR tool to establish the computation coefficients,and window limits (in energy) stored in the software to be used by all tools manufacturedidentically (within close tolerances) to this "standard" tool.

In the field, a thorium calibrator is used to establish the window limits (in channels) thatare used for field checks and a gross gamma gain factor. The 2.614 MeV peak is used inequation (6-15). See Figure below.

FIG: 15 Thorium Peak

Page 31: Gamma Theory

GAMMA RAY THEORY

08/27/01 TRAINING MANUAL 25

Using Equation 6-15 we can obtain a gain factor for this particular tool,

216 Ch R = ��������� = 82.6 Ch/MeV

2.614 MeV

All SGR tools have the thorium window from 2.30 MeV to 2.80 MeV. From the gainfactor calculated above, the corresponding channel range for this particular tool isdetermined from:

Ch Channel U = 82.6 ������ (2.80 MeV) = 231 Ch

MeV

Ch Channel L = 82.6 ������ (2.30 MeV) = 190 Ch

MeV

Therefore:

Thorium Window = 2.30 MeV ��� > 2.80 MeV

= Channel 190 ��� > Channel 231

For the gross gamma gain factor, a Ra-226 calibrator is used and counts are measured inthe gross gamma window. The gain factor is computed from Equation (6-13).

Field checks are performed with a doughnut-shaped fixture with known amounts ofthorium, potassium and uranium. By estimating the specific concentrations, the checksverify the response of the Spectral Gamma tool over the entire formation spectrum.During the field checks, a peak search routine is performed for potassium. Once found, anew gain factor (R) is computed from (Equation 6-16). This gain factor is used toestablish the initial windows for logging. At all other times (during logging) the windowsare computed from the downhole formation potassium peaks.

Page 32: Gamma Theory

GAMMA RAY THEORY

26 TRAINING MANUAL08/27/2001

SPECTRAL GAMMA REAL TIME COMPUTATION

For any Spectral Gamma tool (SGR or CSNG), the measured count rate in any one of thewindows is related to the elemental concentrations by the general expression:

6-17. C = aTh MTh + aU MU + aK MK

Here C = measured count rate in window in cps

MTh = elemental concentration of thorium in ppm

MU = elemental concentration of uranium in ppm

MK = elemental concentration of potassium in %

aTh = sensitivity coefficient for the element thorium (in CPS/ppm)

aU = sensitivity coefficient for the element uranium (in CPS/ppm)

aK = sensitivity coefficient for the element potassium (in CPS/%)

For n windows the above equation must be expanded to:

6-18.

C1 = a1Th MTh + a1U MU + a1K MK

C2 = a2Th MTh + a2U MU + a2K MK

C3 = a3Th MTh + a3U MU + a3K MK

Cn = anTh MTh + anU MU + anK MK

Notice that any one of the Equations (18) above can be written as:

6-19. C = a Mj=1

3

ij j∑

Here i = the window index

j = the elemental concentration index (1 = Th; 2 = U; 3 = K)

Page 33: Gamma Theory

GAMMA RAY THEORY

08/27/01 TRAINING MANUAL 27

Matrix algebra provides a neat compact way of writing our system of simultaneous linearequations (Equation 18).

6-20. [C] = [A] [M]

where

[A] is a n x 3 sensitivity matrix with elements' aij. The elements of [A] are computed fromthe primary calibration and stored in software. Although it may appear rather complicatedto solve for the unknown concentrations (MTh, MU, Mk), the complexity of the solution isreduced somewhat by considering down scattering effects. Compton down scatteringstates that gamma’s emitted at one energy level can be degraded to lower levels byCompton scattering. This implies that a "narrow" window around the main thorium peakat 2.614 MeV would not receive any potassium gamma’s, since these have an initialenergy of 1.460 MeV and cannot gain energy. The gamma’s from potassium can beexpected in a window around 1.460 MeV (the extent being a function of crystalresolution) and any lower energy window. Because of Compton down scattering, some ofthe coefficients of the potassium terms (aik), can be taken to be zero. Down scatteringeffects in all lower energy windows are incorporated in the values for the coefficients.

In real time processing for the elemental concentration, the SGR with only three windowsuses a stripping algorithm while the CSNG with 13 windows uses a weighted least squaretechnique.

Page 34: Gamma Theory

GAMMA RAY THEORY

28 TRAINING MANUAL08/27/2001

STATISTICAL FLUCTUATIONS AND BEDRESOLUTION

Nuclear logs never repeat exactly. Some of the small wiggles on the logs are statisticalvariations (fluctuations) that do not represent true lithology variations. When reading anygamma log, averaging the results over a 3-4 foot interval is advisable. When the bed isless than 3 ft thick, the peak reading should be taken.

The source of statistical fluctuation is the random nature of nuclear events. The numberof gamma rays counted in any time interval will differ from that counted in a successive,but identical time interval, even though the detector is stationary. The amount of thedifference will decrease if the time interval is increased to obtain more counts. A measureof the percentage fluctuation is given by:

6-21. % f =100

N

Here N is the average number of counts in the measuring interval. Notice as N goes toinfinity, the percentage fluctuation goes to zero.

Typical shales usually show a count rate around 300 cps while that of carbonates andclean sands can be about 50 cps (for a natural gamma tool). Using equation (21) with anaveraging time of 2 sec we can get the percentage fluctuations,

Typical shale: %( )

f = =100

300 24%

Carbonates or Clean Sands: %( )

f = =100

50 210%

We see that the log can be expected to show a 4% fluctuation around the mean reading inshales and up to 10% either side of the mean in clean sands or carbonates. Absolutemagnitudes will be in the range + (5 - 10) API units in typical shales and + (2 - 4) APIunits in clean formations.

Depth Of Investigation

About 90% of the measured gamma rays recorded from a borehole tool originate withinthe first six inches of the formation being investigated. Generally, the accepted depth ofinvestigation for any gamma tool is about one foot from the borehole wall. The effect ofintroducing additional media, such as cement and casing, only reduces the total quality ofgamma rays otherwise available for measurement. In general, this does not distract fromthe useful information provided by the gamma ray measurement.

Page 35: Gamma Theory

GAMMA RAY THEORY

08/27/01 TRAINING MANUAL 29

SCINTILLATION DETECTORS

To detect gamma rays, most gamma tools use scintillation type detectors. Figure (16)shows the basic components of a typical scintillation counter (detector). A scintillatingtransparent crystal, normally sodium iodide, is optically coupled to a photomultiplier tube.The crystal will give off a minute burst of light when struck by a gamma ray. The photonenergy (light) strikes a photo-sensitive surface or cathode causing electron emission. Theelectrons so produced are accelerated to an anode which upon impact, releases additionalelectrons that are directed to another anode.

Optical Grease Coupling

Scintillation CrystalPhotons

Cathode

RadiationGlass Tube

Photomultiplier Tube

Dynodes

e-

e- e-e-

e-

e-

e-

e-e- e-e-

e-

e-

e-P High Vacuum

+ High Voltage

Pre-Amp

Photocathodee Electrons

ProtonsP

-

FIG: 16 Scintillation Detector

Those anodes are called Dynodes and they are supplied with progressively higher voltagesby an internal or external resistor divider chain. There are several stages of suchmultiplication that finally yield a sufficiently high flow of electrons to be measured andrecorded as an indication of the incident gamma ray radiation. Proper manipulation of thiselectronic signal results in a voltage signal that is nearly proportional to the energydeposited in the crystal by the detected photon. Let's take a more in depth look at the twocomponents of a scintillation detector - the scintillation crystal and the photomultipliertube.

Page 36: Gamma Theory

GAMMA RAY THEORY

30 TRAINING MANUAL08/27/2001

The Scintillating Crystal

The operation of the scintillation detector depends on the fact that certain materials, calledphosphors, emit visible light when struck by particles (e.g. photons). The mechanism bywhich this happens is a well understood quantum phenomenon that involves pairproduction, Compton scattering and photoelectric effects. As a photon enters the crystalit produces electrons and positrons by the above interactions. These particles excite thecrystal into generating flashes of light (scintillation’s). The sum of the intensity of thesescintillation’s is related to the energy deposited in the crystal by the bombarding photons.The light flashes fall on the photocathode surface of a photomultiplier tube, liberatingelectrons via the photoelectric effect. The tube amplifies the electronic charge andprovides a voltage signal strong enough to be analyzed.

In the logging industry, inorganic scintillators (phosphors) are employed. In these types ofscintillators, the scintillation process depends on the energy states determined by thecrystalline lattice of some materials classified as insulators or semiconductors. The "BandTheory" approach states that in these crystals, the electrons have available only discretebands of energy (i.e. they can occupy only discrete energy levels). The lower band, calledthe valence band represents those electrons bound to form the lattice, whereas theconduction band represents those with sufficient energy to be free to migrate throughout.Intermediate levels are called the forbidden gap where electrons are never found in thepure crystal. The electrons and positrons generated by the incident photon excite thecrystal valence electrons into the conduction band by electrostatic interactions. The returnof the electrons back to the valance band results in the emission of photons. See Figure(17) below.

For pure crystals, the process is inefficient and usually results in higher energy photon'semission (invisible light). To increase the probability of visible light emission during thede-excitation, small amounts of impurities are added. These impurities, called activators,modify the energy band structure creating states within the forbidden gap through whichthe electron can de-excite with lower energy involved and therefore longer wavelength. Ifthe activator is properly chosen, the energetic transition can be in the visible range.

e-Photon

Conductive Band

Valence Band

Forbidden Gap

FIG: 17 Band Theory

Page 37: Gamma Theory

GAMMA RAY THEORY

08/27/01 TRAINING MANUAL 31

The most widely applied scintillators is alkali halide crystals (NaI, CsI, LiI) of whichsodium iodide is the favorite. Common activators are Thallium (Tl), Sodium (Na) andEuropium (Eu). Today, a suitable cylindrical shape scintillator compatible withcommercial photomultipliers is found mostly in the NaI(Tl) style. The CompensatedSpectral Natural Gamma (CSNG) uses a NaI (T1) detector. The Spectral Gamma Raytool (SGR) uses a CsI(Na) crystal because of its high density.

The Photomultiplier Tube (PMT)

The two major elements of the PMT are the photocathode and the electron-multiplierstructure (Dynodes) (see Figure 16). The photocathode can be made sensitive to almostany region of the electromagnetic spectrum. For logging tools we are interested in havingPMs with peak sensitivities around 400 nano-meters (10-9 m) (blue) to match the emissionspectra of the NaI (T1) scintillation crystals. The electron multiplying network (throughthe process of secondary emission) greatly increases the number of electrons with eachdynode stage. A typical scintillation pulse will give rise to 107 - 1010 electrons.

The output voltage pulse from the photomultiplier tube is very nearly proportional to theenergy of the photon that initiates scintillation in the crystal; then not only can photons bedetected with a scintillation detector, but also their energies can be measured.

BOREHOLE EFFECTS

All gamma tools (spectral and natural) are referenced to an arbitrary set of standardborehole conditions. When non-standard conditions are encountered, the intensity as wellas the spectral shape changes due to variations in the scattering and absorption propertiesof the borehole. Therefore, corrections need to be applied if we are to obtain useful andquantitative formation data. In general, these corrections reflect variations in:

hole size

mud density

tool position

casing diameter

casing weight

cement thickness

Page 38: Gamma Theory

GAMMA RAY THEORY

32 TRAINING MANUAL08/27/2001

Figure (18) shows how the intensity (proportional to count rate) and shape of a highenergy spectrum is affected by changes in some of the variables above (i.e. hole size,casing diameter, casing weight and cement thickness). All of the curves were normalized(i.e. made to overlay) at the 1.460 MeV peak. A gain factor, N, is used in thenormalization such that the larger the N, the less intense the original 1.460 MeV peak.Notice the appreciable separation in the curves on the lower end, due to Compton downscattering effects.

Because of changes that occur in the total spectral shape over the entire energy spectrum,along with the primary log for the apparent concentrations (K, U, Th), additionalborehole/formation information can be obtained from the more "sensitive" spectral Tools.*

FIG: 18 Gamma Ray Spectrum Versus Borehole Effects

*NOTE: We can obtain information on casing thickness or lithology using data from thephotoelectric energy portion of the gamma ray spectrum of the CSNG tool.

Page 39: Gamma Theory

GAMMA RAY THEORY

08/27/01 TRAINING MANUAL 33

Natural Gamma Tools

Charts are available for correcting the gamma tool for borehole effects. For a NaturalGamma Tool, these charts are used to correct for the total count in the borehole, whichresults in a corrected API gamma curve. For these basic tools, the simplest charts usuallyprovide corrections based on variations in hole diameter and mud density, for bothcentralized and excentralized tools in the open hole. More sophisticated chartssimultaneously correct for variations in borehole diameter, casing diameter, mud weight,cement weight, cement thickness and casing thickness (casing weight) for two, one orzero strings of casing. Figure 19 shows on of these simple charts.

FIG: 19 Natural Gamma Borehole Correction Chart

Page 40: Gamma Theory

GAMMA RAY THEORY

34 TRAINING MANUAL08/27/2001

Spectral Gamma Tools

For Spectral Gamma tools, charts are designed to provide correction to the apparentconcentration of the elements, potassium, uranium and thorium. Figure (20) shows theeffects of hole size and mud density on the estimated concentrations. As is to beexpected, the denser the material in the borehole, the greater the magnitude of the applied(positive) correction.

FIG: 20 SGR Borehole Correction Chart For A Centralized Tool

It should be mentioned that certain mud additives used to stabilize the mud system duringthe drilling operations may cause erroneously high values for the apparent K.U.T.concentrations in the formation. Bentonite is a clay mineral containing significant amountsof thorium and uranium that is used as a gel-additive. Potassium salts such as potassiumchloride (KC1) is frequently used for clay stabilization of the mud system. The presenceof these radioactive elements causes an increase in the gamma radiation (count rate) in theborehole. This effect can be eliminated by identifying and subtracting the boreholecontribution from the total signal.

Page 41: Gamma Theory

GAMMA RAY THEORY

08/27/01 TRAINING MANUAL 35

GEOLOGICAL CHARACTERISTICS

Uranium

The average concentration of uranium in the Earth's crust is about 3 ppm. The originalsources, or parent rocks, are the silicic igneous rocks (granite, granodiorite, syenite,rhyolite, etc.) in which uranium exists as a number of accessory minerals.

Uranium is water soluble in alkaline or oxidizing environments and less soluble in thepresence of organic matter and sulfides. Because of its water solubility, uranium can be avery mobile element. Uranium is insoluble in acidic or reducing environments and can beabsorbed into iron compounds. Uranium will precipitate with variations in temperature,pH, pressure and flow conditions.

Since it is water soluble, uranium is not found in surface rocks, especially carbonates, dueto leaching. Waters are oxidizing and often alkaline in these environments. Uranium richpercolating waters may deposit uranium in permeable, reducing and/or acidic reservoirs.This is especially true in the presence of organic matter or H S2 .

Uranium can be present along paths of vertical water migration, i.e. along faults, inunconformable layers and in fracture zones. This is because uranium salts, being soluble,can be transported by liquid movement. This is especially true in deeper (reducing)environments. Low uranium below an unconformity implies little fluid movement throughthe bed since this zone leached at surface.

Uranium may appear at oil/water contacts, especially in high sulfur crudes since itprecipitates out of water in the presence of sulfur.

Trends toward increasing uranium at increasing depths may imply a trangressive sequencesince deeper waters tends to be more reducing (hence the uranium would precipitate out).This is especially true when compared to thorium since thorium is stable with respect tooxidation conditions.

Page 42: Gamma Theory

GAMMA RAY THEORY

36 TRAINING MANUAL08/27/2001

Thorium

The average concentration of thorium in the Earth's crust is about 12 ppm. The originalsources, or parent rocks, of thorium are, like uranium, the silicic igneous rocks in which itexists as a number of minerals. Its average concentration in igneous rocks is 3.5 to 4times that of uranium and the thorium/uranium ratio is quite constant. Thorium isgenerally insoluble in water and is stable with respect to oxidation conditions. Because ofthis, it can be present in all marine deposition environments. Thorium has a tendency toconcentrate in residual minerals such as bauxite and clay minerals. Significantconcentrations are also found in heavy minerals such as monazite.

Most clays seem to contain thorium. However, some montmorillonites have a lowthorium content. The amount of thorium fixed in clay minerals remains constant in spiteof thermal diagnoses. In shale series, this amount usually ranges from 8 to 20 ppm,depending on the clay content.

Potassium

The average concentration of potassium in the Earth's crust is about 2.6%. The originalsources, or parent rocks, are chiefly the silicic igneous rocks where it is present aspotassium feldspars (orthoclase, microcline), micas (muscovite, biotite) and a number ofother minerals. The average K2O concentration of igneous rocks is equal to 3.13%compared to 2.87% for sediments.

During the alteration process, feldspars and micas are largely destroyed. Depending uponthe degree of weathering, one of the following clay minerals may be produced; illite,interlayered illite-montmorillonite, montmorillonite, chlorite and kaolinite. A small part ofthe total potassium concentration enters into the formation of some of those minerals, butthe major part is dissolved by water. In arid regions, this large part tends to remain withthe products of alteration (residuals). In other regions, it is transported by rivers to thesea.

In water, the potassium ion has a very weak ionic potential and can stay in real solutionunder a wide range of pH. Generally, during transportation, most of the potassium isabsorbed by clays and extracted from the water by plants.

Thus, only a small part of the original potassium arrives at the sea, which has an averagepotassium concentration of 380 ppm. One fraction of the potassium is dissolved in seawater and extracted by organisms like algae. Another part reacts with clay minerals (e.g.with kaolinite to give illite). At least several potassium minerals (e.g. sylvite, langbeinite,kainite) can crystallize directly from sea-water brines to give potassium evaporates. Theseminerals represent the maximum concentrations of potassium in rocks.

Page 43: Gamma Theory

GAMMA RAY THEORY

08/27/01 TRAINING MANUAL 37

A CSNG log example is shown in figure 21. The uranium, potassium and thoriumconcentration are in tracks 2 and 3. Notice that the uranium and thorium concentrationsare in ppm while potassium is in percent (%). The selected ratio curve in track 4 is usedfor casing thickness and lithology information.

FIG: 21 Spectral Log Example

Page 44: Gamma Theory

GAMMA RAY THEORY

38 TRAINING MANUAL08/27/2001

REFERENCES

1. Smith, Harry D., Nuclear Logging Lectures, (1981)

2. Bateman, Richard M., Open-Hole Log Analysis and Formation Evaluation, IHROL,Boston, 1985

3. Gadeken, L.L., D.M. Arnold and H.D. Smith, Jr., "Applications of the CompensatedSpectral Natural Gamma Tool" SPWLA 25th Annual Symposium, Paper JJJ, June1984

4. Interpretation of the Spectral Gamma Ray, Gearhart Publication, G-1963 6-86

5. Dewan, John T., Essentials of Modern Open-Hole Log Interpretation, Penn WellPublishing Company, Tulsa, Oklahoma, 1983

6. Weidner, Richard T., Robert L. Sells, Elementary Modern Physics, Allyn and Bacon,Inc., Boston, 1972

7. Perkins, Donald H., Introduction to High Energy Physics, Addison-Wesley PublishingCompany, Reading Mass, 1972

8. Sears, Francis W., Mark W. Zemansky and Hugh D. Young, University Physics,Addison-Wesley Publishing Company, Reading, Massachusetts, 1977

9. Knoll, Glenn F., Radiation Detection and Measurement, John Wiley and Sons, NewYork, 1989

10. Log Interpretation, Volume 1 - Principles, Schlumberger Publication, C-11759

11. General Radiation and Gamma Ray, Gearhart Publication, WS-451-1-85

12. Smith, H.D., Jr., C.A. Robbins, D.M. Arnold, L.L. Gadeken and J.G. Deaton, "AMulti-Function Compensated Spectral Natural Gamma Ray Logging System", SPE58th Annual Technical Conference and Exhibition, San Francisco, CA, Oct. 1983

13. Welex Log Interpretation Chart Book, Welex Publication, 1985

14. CSNG Interpretation, Welex Publication