Gamma Theory

SECTION 4

GAMMA RAY

TABLE OF CONTENTS TABLE OF CONTENTS...............................................................................................i, ii BASIC PHYSICS............................................................................................................1

The Atomic Nucleus........................................... Nucleus.......................................................................................... ...................................................1 ....1 Alpha Decay..........................................................................................................2 Beta Decay.............................................................................................................2 Gamma Decay........................................................................................................4 Gamma Interaction With Matter............................................................................7 Pair Production............................ Production...........................................................................................7 ...............................................................7 Compton (Incoherent) Scattering................ Scattering....................................................... ................................................8 .........8 Photoelectric Effect.....................................................................................9 GAMMA RAY TOOLS.................................................................................................10

Natural Natural Gamma Ray Tools.................. Tools..................................... ..................................... ..................................... ............................10 .........10 Radioactivity Of Different Formations....................................................12 Volume Of Shale.................................................... Shale.......................................................................................12 ...................................12 Spectral Gamma Ray Tools..................................................................................13 Decay Sequence............................ Sequence........................................................................... ............................................................13 .............13

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Energy Spectrum................................. Spectrum......................................................................................1 .....................................................14 4

•

Potassium.................. Potassium........................................................... .....................................................................1 ............................1 4

•

Uranium................................ Uranium.................................................................. .........................................................15 .......................15

•

Thorium.............................. Thorium.......................................................................... ...........................................................1 ...............1 6

CALIBRATION.............................................................................................................1 7

Calibration Of The Natural Gamma Ray Tool.....................................................17 Calibration Of The Spectral Gamma Tool............................................................19

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

•

Gain Compensatio Compensation................... n.............................................. ..................................................... ............................20 ..20

•

Shop Calibration.. Calibration.......................... ................................................ ................................................ .............................20 .....20

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

•

Gain Compensatio Compensation................... n.............................................. ..................................................... ............................23 ..23

•

Calibration.... Calibration................................ ........................................................ ........................................................ ............................ 24

SPECTRAL GAMMA REAL TIME COMPUTATION.............................................26 STATISTICAL FLUCTUATION AND BED RESOLUTION...................................28

Depth Of Investigation Investigation.............................. ........................................................... ........................................................... ...............................28 .28 SCINTILLATION DETECTORS................................................................................29

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The Scintillating Crystal.......................................................................................30 The Photomultiplier Tube (PMT).........................................................................31 BOREHOLE EFFECTS................................................................................................31

Natural Gamma Tools...........................................................................................33 Spectral Gamma Tools...........................................................................................34 GEOLOGICAL CHARACTERISTICS.......................................................................35

Uranium................................................................................................................. 35 Thorium................................................................................................................. 36 Potassium.............................................................................................................. 36 Spectral Log Example...........................................................................................37 REFERENCES................................................................................................................ 38

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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 atomic number of the atom, the number of protons in the nucleus, is represented by the symbol Z. The number Z also represents the total number of electrons of the atom that determines its atomic and molecular properties. Atoms with the same atomic number often have markedly different nuclear characteristics because there can be different numbers of neutrons associated with a fixed number of protons. The total number of nucleons (protons and neutrons) in the nucleus is called the mass number, A. Nuclides having the same atomic number but different mass numbers, are called isotopes. Different isotopes of an element are chemically identical and can be distinguished by their different atomic weights or nuclear properties. An isotope is identified by naming the element and following that name with the number of the isotope. There is a more formal notation that sets the mass number (A) as a superscripted number in front of the symbol for the element and the atomic number (Z) as a subscripted number in front of the symbol. For any element (listed below as X), this formal notation is shown as: A

X

Z

As an example, the most common isotope of potassium has twenty neutrons and nineteen protons and is represented as follows: 39 K 19

or Potassium-39

The only radioactive isotope of potassium has twenty-one neutrons and nineteen protons. This element is represented as: 40 K 19

or Potassium-40

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

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Alpha Decay Certain radioactive nuclei, those for which Z > 82, spontaneously decay into a daughter nucleus (usually in an excited state) and a helium nucleus ( 24He). This helium nucleus consists of two protons and two neutrons that is called an alpha ( α) particle. Since the alpha particle has a very stable configuration of nucleons, it is perhaps not surprising that such a group of particles might exist within the parent nucleus prior to alpha decay. The laws of conservation of charge and of nucleons require that: 6-1.

A − 4

P→ Z − 2 D + α Z A

Where P and D are the parent and daughter nuclei, respectively. As an example of equation 1, part of the decay sequence for Thorium-232 going to stable Lead-208 involves the decay of Bismuth-212 by alpha emission to Thallium-208 according to the equation: 6-2.

212 83 Bi

→ 20881Tl + α

•

Bi = Bismuth (parent)

•

Tl = Thallium (daughter)

Beta Decay Beta decay may be defined as that radioactive decay process in which the charge of a nucleus is changed without a change in the number of nucleons. There are three types of beta decay. Two of these involve the emission of Beta particles. A ß - particle is an electron 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 its protons' changes into a neutron. Except for its positive charge, a positron is identical to an electron. When a positron and an electron meet, they annihilate and their masses convert into two γ rays. A parent to daughter representation of beta-electron decay obeys.*

*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 .

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A Z

6-3. Beta-electron decay:

P→ Z +A1 D + β −

An example of this decay is found again in the decay sequence for Thorium-232. The Thallium-208 produced from the alpha decay depicted in(equation 6-2) next Beta decays according to: 6-4.

208 81Ti

•

→

208 82 Pb

+ β−

Pb = lead (daughter)

The parent to daughter representation of beta-positron decay, in a similar fashion, obeys the transformation. 6-5. Beta-positron decay:

A Z

P → Z−A1 D + β

+

An example of this decay is shown in the transformation of unstable Nitrogen-12 to Carbon-12. 6-6.

12 7

N → 126 C + β

+

The third type of beta decay is electron capture. In electron capture, an atomic orbital electron combines with a proton of the nucleus to change it into a neutron. Again the number 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 daughter transformation for electron capture takes the form of: 6-7. Electron capture:

β

−

A A P + → capture Z Z −1 D

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

6-8.

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β

− capture

40 K → 40 + 19 18 Ar

•

K = Potassium

•

Ar = Argon

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Gamma Decay When a nucleus decays from a parent to daughter, the daughter is often left in one of a number of possible excited states. An excited state is not stable. The nucleus will therefore spontaneously drop to a lower energy excited state or the lowest energy ground state by emitting photons. A photon emitted from a nucleus in an excited state is called a gamma ray (γ ). Gamma ray photons represent the highest energy portion of the electromagnetic 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 the emitted 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

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Here the prime ( ′ ) denotes a lower excited state or ground state. Only those nuclear transitions that obey the conservation laws are permitted. In the downward transition from an upper nuclear energy state E U to a lower state EL, the emitted gamma ray (ignoring any recoil effect) has the energy: 6-11. E

γ

=h =E −E f

Here

u

L

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 of Potassium-40. From equation 6-8, Potassium-40 captures an electron and becomes Argon-40. The disintegration scheme is shown below. 40 19

Beta Electron Capture

K

Beta Electron Emision

11%

40 18 Ar*

89%

EU =1.46 MeV

40 20 Ca

(ground state)

E =1.46 Mev 40 Ar 18

EL =0 (ground state)

FIG: 1 Potassium Decay

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

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A more complex scheme is demonstrated by the decay of Thallium-208 to Lead-208 by beta-electron emission (equation 6-4). 208 81

Ti c

c

b

b

a

a

(not all states included) 3.198 MeV 2.614 Mev

E =2.614 Mev 208 82

Pb

0 (ground state)

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 emitted beta electron particles that cause the decay to the corresponding excited states (a, b and c). Notice that the de-excitation of lead-208 from the excited state "a" to the ground state produces 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 accelerated through a potential of one volt. The commonly used multiples of this unit are kiloelectron volts, keV, and Megaelectron volts, MeV. These represent multiples of 1,000 and 1,000,000 electron volts, respectively. Therefore, a gamma ray with an energy of 1 MeV would have the same striking power as an electron accelerated through a 1,000,000 volt potential.

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GAMMA RAY THEORY

Gamma Interaction With Matter After their creation, the gamma ray photons can interact with matter in different ways. In the 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 ways in 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 from the formation. Pair Production can only occur when the energy of the gamma ray is in excess 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, an electron and a positron appear, as shown in figure 3. Pair production (which cannot take place in a vacuum) obeys Einstein’s well know equation showing the convertibility of pure energy to matter E = M 0 c 2 ′ with E=photon energy. It should be noted that pair production is of little use in the evaluation of a formation.

Electron

e

e+

Incident Photon High Energy

Positron

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.

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COMPTON (INCOHERENT) SCATTERING The most important interaction to the bulk density measurement is called Compton Scattering. Compton Scattering is classified as incoherent scattering. Incoherent scattering involves a photon scattering off one electron at a time. In Compton Scattering the incident photon energy is assumed to be much greater than the binding energy of the electron. For this case the electron can be considered essentially free (i.e. not bound to the 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 likely been deflected along a different path. See figure 4. This scattering process will be repeated over and over (down scattering) as the gamma ray passes through the material, until the gamma ray has lost enough energy that it can be photoelectrically absorbed (i.e. less than about 100 keV). Since the gamma ray will undergo more collisions per unit distance in a high-density material than in a low-density material, 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 binding energy can not be ignored, binding-energy correction must be applied to the Compton interaction to obtain an accurate incoherent scattering across section. It should here be noted that if the energy to be imparted to the electron is not greater than the binding energy, compton scattering will not occur. Compton interaction is the dominant effect for gamma rays with energies between 100 keV to 10 MeV. Scattered Photon

e

Incident Photon Compton Recoil Electron

FIG: 4 The Compton effect

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PHOTOELECTRIC EFFECT The photoelectric effect becomes important when the gamma ray energy is only slightly greater than the binding energy of the electrons. For most rocks, this occurs at energies below about 100 keV. In the photoelectric effect one gamma ray photon is absorbed by one electron. In the process, all of the energy of the gamma ray is transferred to the electron, which then has enough energy to overcome the binding energy of the nucleus and escape. This interaction is shown below. Electron

e

Incident Photon

FIG: 5 The Photoelectric Effect

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GAMMA RAY TOOLS Natural formation gamma radiation comes from radioactive isotopes of uranium, thorium and potassium.* To record this radiation, there are presently two types of gamma ray tools 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 regard to the source, 2. The spectral gamma ray tool is a spectral analyzer that identifies the source and gives the contribution (concentration) of each of the elements (potassium, uranium and thorium) 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 a scintillation 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 basic gamma tool does not sort the pulses, it merely counts those above some discrimination level. Therefore the processed information is merely the count rate (counts/second) per depth sample. In order to output a standard result log, independent of tool systems, a unit of measurement called the API is used.**

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

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GAMMA RAY THEORY

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

FIG: 6 Gamma Ray Response In Typical Formations

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A major portion of the earth's radioactive potassium and uranium-thorium series elements was 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 any impurities from the quartz structure. Since sandstone’s are created from the erosion of quartz, they generally exhibit low radioactivity’s. Feldspars and micas contain a large portion of the earth's potassium fraction. This mineral group decomposes at a relatively rapid rate into the clay minerals. Clays have small individual particle size and a relatively open lattice structure that is characterized by weaker bonding. This open structure encourages the inclusion of impurities. During deposition, clays absorb heavy radioactive elements that are practically impossible to leach out. Since shales are composed of small clay particles, shales tend to be considerably higher in radioactivity than most common formations. Carbonate rocks were developed from calcareous marine life skeletal matter. Since little radioactivity is present in living organisms, carbonate rocks are generally low in radioactivity. Dolomite is formed from a chemical reaction between limestone and dissolved magnesium in migrating ground waters. This process is called dolomitization. Since ground waters contain dissolved radioactive isotopes, in the process of dolomitization some isotopes may be deposited. For this reason, dolomite has a small but higher amount of natural radiation with it than do limestones and may be radioactive, especially in vuggy and/or fractured intervals.

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

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Spectral Gamma Ray Tools The basic construction of a Spectral Gamma Ray Tool is essentially the same as the simple gamma tool. Although, the detector must be of the scintillation type to output voltage pulses proportional to gamma energy. Unlike the natural gamma tool, each pulse detected is now placed (counted) in a channel representing a certain energy level. There is at least 256 channels (corresponding to a spectrum utilizing an 8 bit analog to digital converter, 2 8 = 256 possible states or channels). To fully understand the usefulness of this spectral analyzer we need to elaborate more on the decay scheme and energy spectrum associated with formation radiation.

DECAY SEQUENCE Natural formation radiation is due primarily to radioactive isotopes of uranium (Uranium238), thorium (Thorium-232) and potassium (Potassium-40). These isotopes can be put into two categories: series and non-series. Uranium and thorium are in the series category, while potassium is part of the non-series group. The series isotopes, which all have high atomic numbers (Z = 81 to 92), are sets of isotopes that are found together, and which decay in sequence from one to another until reaching stable isotopes of lead. The non-series radioisotopes occur separately and decay directly to stable isotopes. Figure 7 shows the decay sequence for potassium, uranium and thorium.

FIG: 7 Decay Sequence

Notice the decay scheme shows potassium decaying non serially to argon by electron capture, 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.

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ENERGY SPECTRUM

• POTASSIUM There are three natural isotopes of potassium: Potassium-39, Potassium-40 and Potassium-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 10 9 years is the only radioactive isotope. It can decay (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 equation 6-10. The emitted gamma ray has an energy of 1.46 MeV. This is the only gamma emitted. Since potassium-40 decays into a stable isotope, there are no radioactive decay products. The energy spectrum for pure potassium is shown in Figure 8. The vertical line is the ideal case whereas the "mountain range" is the actual spectrum showing the effect of detector crystal resolution (the line becomes a peak) and Compton down scattering (the higher low energy portion). It should be mentioned that in the wellbore, a majority of the gamma rays coming from the formation have under gone many Compton interactions and have been degraded to energies of 50 to 200 KeV.

FIG: 8 Potassium Spectrum

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• 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 and 4.4 x 109 years, respectively. Uranium and most of its daughter isotopes emit gamma rays of not one, but several different energy levels. Most of the radioactivity actually measured by conventional gamma ray tools come not from uranium itself, but from the decay of one of its daughters, Bismuth-214 to Polonium-214 by beta-electron. The excited polonium nucleus emits gamma rays at over 50 distinct energy levels ranging from 63 KeV to 3.07 MeV. A very noticeable peak in this range is at 1.76 MeV. The spectrum for pure uranium is shown below:

FIG: 9 Uranium Spectrum

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• 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 Uranium238. Thorium-232 has a half life of 1.4 x 10 10 years and is most easily detected indirectly by the gamma rays emitted during the decay of one of its daughters, Thallium-208 to Lead-208 (Equation 6-4). The excited lead nucleus emits a number of distinct energy gamma rays. The most noticeable energy level (i.e. peak) occurs at 2.614 MeV. The spectrum for pure thorium is shown in the Figure below:

FIG: 10 Thorium Spectrum

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CALIBRATION Calibration Of The Natural Gamma Ray Tool One of the problems of gamma ray logging has always been the choice of a standard calibration system, since all logging companies use detectors of different sizes and shapes encased in tool housing of varying characteristics. On very old logs, the scales were calibrated in micrograms of radium per ton of formation. For many reasons, this was found to be an unsatisfactory calibration standard for gamma ray logs. In 1956 an American Petroleum Institute sub-committee was appointed for the purpose of designing a calibration system (and units) that would be an acceptable standard throughout the industry. It was decided to use a pit, with a bed of radioactive concrete situated between two zones of low radioactivity (concrete without the radioactive elements), and to define the API Gamma 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 presently consists of an "artificial shale" 8-ft thick and sandwiched between neat Portland cement. 4 Feet

Gamma Ray

5-1/2" J55 Casing Neat Portland Cement

200 API Units

Uranium 13 ppm Thorium 24 ppm

24 Feet

Potassium 4%

Neat Portland Cement

FIG: 11 API Test Pit

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The artificial shale is actually cement mixed with 13 ppm uranium, 24 ppm thorium and 4% potassium. The API standard defines the difference in radioactivity between the neat cement and the radioactive cement mixture as 200 API units. Any logging service company may place its tool in this pit to make a calibration. In doing so, a sensitivity factor, G', would be computed from the definition: [Tool Response (Hot) - Tool Response (Cool)] G ' = 200 API or 6-12.

G'=

200 A PI T o o l R e s p o n s e ( h ot ) - T o o l R e s p o n s e ( c oo l )

Here, Tool Response is usually in CPS, and Hot and Cool refer to the radioactive and non-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 the purpose of a standard calibration. Of course, in actuality not every gamma tool manufactured is calibrated in this test pit. The test is usually reserved for a particular type of "standard tool". Once calibrated in the pit, this standard tool is used to "calibrate" a radioactive source. This actually means we just record the API value of this source at a certain distance as seen by the standard tool. This source is then used for shop/field calibration of all tools manufactured "identically" to the standard tool. This radioactive source 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.

G =

Calibrator 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 test pit, the calculated G (which is proportional to G ') enables all field tools to give standard results (logs) in API units. Thus the modified log response is:

GR

18

Lo g

= G (Field Tool Response)


GAMMA RAY THEORY

Calibration Of The Spectral Gamma Tool The calibrations associated with the Spectral Gamma Tool are more complex than the Gross Gamma Tool.* This is due to the fact that each detected gamma must be placed in an appropriate channel based on its energy (voltage level). The channels and corresponding energies are directly proportional (i.e. the higher the channel value, the higher 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 each window is found by summing the total gamma count in the corresponding channels. Each window, while representing a specific channel range, also represents a specific energy range. To insure that all of the detected gamma’s is counted in the appropriate channels involves some gain control, (usually automatic) that takes into account the temperature effect (and any other miscellaneous drift) on the detector system. This temperature effect causes the voltage pulse height of the PMT (Photo Multiplier Tube) to change identical gamma inputs. 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 the Compensated Spectral Natural Gamma Tool (CSNG) and the other utilized by the Spectral Gamma Ray Tool (SGR).

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

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COMPENSATED SPECTRAL NATURAL GAMMA TOOL (CSNG)

• GAIN COMPENSATION Since the CSNG-A measures the energies of individual gamma rays, the gain of the detector must be held constant. This is accomplished by using an alpha-gamma ray coincidence technique. Near the main gamma ray detector is a much smaller detector that contains an embedded Americium-241 source. When Americium-241 decays to Np-237 by alpha emissions a 60 keV gamma ray and the high energy alpha particles are emitted essentially 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 are detected in the main gamma detector, since these gamma rays are coincident with the alpha particles, the stabilizer gamma rays can be spectrally separated from formation gamma’s with better than 99% efficiency. The peak value of the gamma stabilization spectrum is constantly monitored and the electrical bias on the detector adjusted to keep the peak at the same channel value (channel 47) 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 in software for all CSNG tools of identical design. Shop calibrations and field checks are performed in the districts and on location with the use of a Thorium-232 sleeve. This sleeve is wrapped, at the proper location, around the tool detector housing.

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During shop calibrations, window boundaries are determined in channel ranges for fixed energy ranges. The energy range of each window is fixed in the software, but the corresponding channel range varies slightly for each tool. Each window has an upper and lower energy value defining its width. The corresponding upper and lower channel values are computed from the linear expression: . 614.

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

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

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

FIG: 13 CSNG Cal Peaks

From the measured channels for the high spectrum above, the gain and offset are computed 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

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All CSNG tools have window 1 energy range from 2.480 MeV to 2.919 MeV. Using the gain and offset determined above, the corresponding channel range for this particular tool is defined by: Channel U = 81.2

Channel L = 81.2

Ch MeV Ch MeV

(2.919 MeV) + 2.7 Ch = 240 Ch

(2.480 MeV) + 2.7 Ch = 204 Ch

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 is maintained by constantly readjusting the window boundaries based on the measured channel of the formation potassium peak. The below figure shows how this peak varies with time (temperature).

FIG: 14 SGR Peak

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During logging a 256 channel spectrum is accumulated continuously over five-minutes periods. At the end of each period the formation potassium peak (centroid) is found and the measured channel is used to compute a new gain factor (R). The window boundaries are then readjusted using the new gain factor. This gain factor is computed from our linear expression (Equation 6-14) with the known energy level for potassium (see Figure 8) and assuming a zero offset. Channel Value = R(Energy) 6-15.

R = Channel Value / Energy or, for potassium:

6-16. R(K) =

Channel Value Energy

=

Measured Potassium Channel 1.460 MeV

The choice of potassium as the stabilization source is obviously due to its great abundance as 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 formation tanks. Each tank consists of a 6-inch, waterfilled borehole in a single-activity formation of potassium, 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 manufactured identically (within close tolerances) to this "standard" tool. In the field, a thorium calibrator is used to establish the window limits (in channels) that are used for field checks and a gross gamma gain factor. The 2.614 MeV peak is used in equation (6-15). See Figure below.

FIG: 15 Thorium Peak

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GAMMA RAY THEORY

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

216 Ch 2.614 MeV

= 82.6 Ch/MeV

All SGR tools have the thorium window from 2.30 MeV to 2.80 MeV. From the gain factor calculated above, the corresponding channel range for this particular tool is determined from: Channel U = 82.6

Channel L = 82.6

Ch MeV Ch MeV

(2.80 MeV) = 231 Ch

(2.30 MeV) = 190 Ch

Therefore: Thorium Window = 2.30 MeV = Channel 190

> 2.80 MeV > Channel 231

For the gross gamma gain factor, a Ra-226 calibrator is used and counts are measured in the gross gamma window. The gain factor is computed from Equation (6-13). Field checks are performed with a doughnut-shaped fixture with known amounts of thorium, potassium and uranium. By estimating the specific concentrations, the checks verify 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, a new gain factor (R) is computed from (Equation 6-16). This gain factor is used to establish the initial windows for logging. At all other times (during logging) the windows are computed from the downhole formation potassium peaks.

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GAMMA RAY THEORY

SPECTRAL GAMMA REAL TIME COMPUTATION For any Spectral Gamma tool (SGR or CSNG), the measured count rate in any one of the windows 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: C1 = a1Th MTh + a1U MU + a1K MK C2 = a2Th MTh + a2U MU + a2K MK

6-18.

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: 3

6-19. C =

∑ a ij M j

j=1

Here

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

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Matrix algebra provides a neat compact way of writing our system of simultaneous linear equations (Equation 18). 6-20. [C] = [A] [M] where

[A] is a n x 3 sensitivity matrix with elements' a ij. The elements of [A] are computed from the primary calibration and stored in software. Although it may appear rather complicated to solve for the unknown concentrations (M Th, MU, Mk ), the complexity of the solution is reduced somewhat by considering down scattering effects. Compton down scattering states that gamma’s emitted at one energy level can be degraded to lower levels by Compton scattering. This implies that a "narrow" window around the main thorium peak at 2.614 MeV would not receive any potassium gamma’s, since these have an initial energy of 1.460 MeV and cannot gain energy. The gamma’s from potassium can be expected in a window around 1.460 MeV (the extent being a function of crystal resolution) and any lower energy window. Because of Compton down scattering, some of the coefficients of the potassium terms (a ik ), can be taken to be zero. Down scattering effects 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 windows uses a stripping algorithm while the CSNG with 13 windows uses a weighted least square technique.

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GAMMA RAY THEORY

STATISTICAL FLUCTUATIONS AND BED RESOLUTION Nuclear logs never repeat exactly. Some of the small wiggles on the logs are statistical variations (fluctuations) that do not represent true lithology variations. When reading any gamma log, averaging the results over a 3-4 foot interval is advisable. When the bed is less than 3 ft thick, the peak reading should be taken. The source of statistical fluctuation is the random nature of nuclear events. The number of 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 the difference will decrease if the time interval is increased to obtain more counts. A measure of 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 to infinity, the percentage fluctuation goes to zero. Typical shales usually show a count rate around 300 cps while that of carbonates and clean sands can be about 50 cps (for a natural gamma tool). Using equation (21) with an averaging time of 2 sec we can get the percentage fluctuations,

Typical shale:

% f =

Carbonates or Clean Sands:

% f =

100 300(2 ) 100 50(2)

= 4%

= 10%

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

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

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GAMMA RAY THEORY

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 scintillating transparent 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 photon energy (light) strikes a photo-sensitive surface or cathode causing electron emission. The electrons so produced are accelerated to an anode which upon impact, releases additional electrons that are directed to another anode.

Optical Grease Coupling Scintillation Crystal Photons

P

e-

Pre-Amp

ee-

e-

e- e

e-

e- e-

e-

Photocathode

Radiation Cathode

e-

e-

+ High Voltage ee-

High Vacuum

Dynodes

Glass Tube

e- Electrons P

Protons

Photomultiplier Tube FIG: 16 Scintillation Detector

Those anodes are called Dynodes and they are supplied with progressively higher voltages by an internal or external resistor divider chain. There are several stages of such multiplication that finally yield a sufficiently high flow of electrons to be measured and recorded as an indication of the incident gamma ray radiation. Proper manipulation of this electronic signal results in a voltage signal that is nearly proportional to the energy deposited in the crystal by the detected photon. Let's take a more in depth look at the two components of a scintillation detector - the scintillation crystal and the photomultiplier tube.

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The Scintillating Crystal The operation of the scintillation detector depends on the fact that certain materials, called phosphors, emit visible light when struck by particles (e.g. photons). The mechanism by which this happens is a well understood quantum phenomenon that involves pair production, Compton scattering and photoelectric effects. As a photon enters the crystal it produces electrons and positrons by the above interactions. These particles excite the crystal into generating flashes of light (scintillation’s). The sum of the intensity of these scintillation’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, liberating electrons via the photoelectric effect. The tube amplifies the electronic charge and provides a voltage signal strong enough to be analyzed. In the logging industry, inorganic scintillators (phosphors) are employed. In these types of scintillators, the scintillation process depends on the energy states determined by the crystalline lattice of some materials classified as insulators or semiconductors. The "Band Theory" approach states that in these crystals, the electrons have available only discrete bands of energy (i.e. they can occupy only discrete energy levels). The lower band, called the valence band represents those electrons bound to form the lattice, whereas the conduction 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 the pure crystal. The electrons and positrons generated by the incident photon excite the crystal valence electrons into the conduction band by electrostatic interactions. The return of 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's emission (invisible light). To increase the probability of visible light emission during the de-excitation, small amounts of impurities are added. These impurities, called activators, modify the energy band structure creating states within the forbidden gap through which the electron can de-excite with lower energy involved and therefore longer wavelength. If the activator is properly chosen, the energetic transition can be in the visible range.

Conductive Band

e-

Forbidden Gap Photon Valence Band

FIG: 17 Band Theory

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The most widely applied scintillators is alkali halide crystals (NaI, CsI, LiI) of which sodium iodide is the favorite. Common activators are Thallium (Tl), Sodium (Na) and Europium (Eu). Today, a suitable cylindrical shape scintillator compatible with commercial photomultipliers is found mostly in the NaI(Tl) style. The Compensated Spectral Natural Gamma (CSNG) uses a NaI (T1) detector. The Spectral Gamma Ray tool (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-multiplier structure (Dynodes) (see Figure 16). The photocathode can be made sensitive to almost any region of the electromagnetic spectrum. For logging tools we are interested in having PMs with peak sensitivities around 400 nano-meters (10 -9 m) (blue) to match the emission spectra of the NaI (T1) scintillation crystals. The electron multiplying network (through the process of secondary emission) greatly increases the number of electrons with each dynode stage. A typical scintillation pulse will give rise to 10 7 - 1010 electrons. The output voltage pulse from the photomultiplier tube is very nearly proportional to the energy of the photon that initiates scintillation in the crystal; then not only can photons be detected 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 standard borehole conditions. When non-standard conditions are encountered, the intensity as well as the spectral shape changes due to variations in the scattering and absorption properties of the borehole. Therefore, corrections need to be applied if we are to obtain useful and quantitative formation data. In general, these corrections reflect variations in: hole size mud density tool position casing diameter casing weight cement thickness

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Figure (18) shows how the intensity (proportional to count rate) and shape of a high energy 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 the normalization 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 down scattering 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), additional borehole/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 the photoelectric energy portion of the gamma ray spectrum of the CSNG tool.

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GAMMA RAY THEORY

Natural Gamma Tools Charts are available for correcting the gamma tool for borehole effects. For a Natural Gamma Tool, these charts are used to correct for the total count in the borehole, which results in a corrected API gamma curve. For these basic tools, the simplest charts usually provide corrections based on variations in hole diameter and mud density, for both centralized and excentralized tools in the open hole. More sophisticated charts simultaneously correct for variations in borehole diameter, casing diameter, mud weight, cement weight, cement thickness and casing thickness (casing weight) for two, one or zero strings of casing. Figure 19 shows on of these simple charts.

FIG: 19 Natural Gamma Borehole Correction Chart

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GAMMA RAY THEORY

Spectral Gamma Tools For Spectral Gamma tools, charts are designed to provide correction to the apparent concentration of the elements, potassium, uranium and thorium. Figure (20) shows the effects of hole size and mud density on the estimated concentrations. As is to be expected, 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 during the drilling operations may cause erroneously high values for the apparent K.U.T. concentrations in the formation. Bentonite is a clay mineral containing significant amounts of thorium and uranium that is used as a gel-additive. Potassium salts such as potassium chloride (KC1) is frequently used for clay stabilization of the mud system. The presence of these radioactive elements causes an increase in the gamma radiation (count rate) in the borehole. This effect can be eliminated by identifying and subtracting the borehole contribution from the total signal.

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GAMMA RAY THEORY

GEOLOGICAL CHARACTERISTICS Uranium The average concentration of uranium in the Earth's crust is about 3 ppm. The original sources, 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 the presence of organic matter and sulfides. Because of its water solubility, uranium can be a very mobile element. Uranium is insoluble in acidic or reducing environments and can be absorbed 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, due to leaching. Waters are oxidizing and often alkaline in these environments. Uranium rich percolating waters may deposit uranium in permeable, reducing and/or acidic reservoirs. This is especially true in the presence of organic matter or H 2 S . Uranium can be present along paths of vertical water migration, i.e. along faults, in unconformable 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 through the bed since this zone leached at surface. Uranium may appear at oil/water contacts, especially in high sulfur crudes since it precipitates out of water in the presence of sulfur. Trends toward increasing uranium at increasing depths may imply a trangressive sequence since 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 to oxidation conditions.

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Thorium The average concentration of thorium in the Earth's crust is about 12 ppm. The original sources, or parent rocks, of thorium are, like uranium, the silicic igneous rocks in which it exists as a number of minerals. Its average concentration in igneous rocks is 3.5 to 4 times that of uranium and the thorium/uranium ratio is quite constant. Thorium is generally insoluble in water and is stable with respect to oxidation conditions. Because of this, it can be present in all marine deposition environments. Thorium has a tendency to concentrate in residual minerals such as bauxite and clay minerals. Significant concentrations are also found in heavy minerals such as monazite. Most clays seem to contain thorium. However, some montmorillonites have a low thorium content. The amount of thorium fixed in clay minerals remains constant in spite of 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 original sources, or parent rocks, are chiefly the silicic igneous rocks where it is present as potassium feldspars (orthoclase, microcline), micas (muscovite, biotite) and a number of other minerals. The average K 2O 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 upon the degree of weathering, one of the following clay minerals may be produced; illite, interlayered illite-montmorillonite, montmorillonite, chlorite and kaolinite. A small part of the total potassium concentration enters into the formation of some of those minerals, but the major part is dissolved by water. In arid regions, this large part tends to remain with the products of alteration (residuals). In other regions, it is transported by rivers to the sea. In water, the potassium ion has a very weak ionic potential and can stay in real solution under a wide range of pH. Generally, during transportation, most of the potassium is absorbed 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 average potassium concentration of 380 ppm. One fraction of the potassium is dissolved in sea water 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. These minerals represent the maximum concentrations of potassium in rocks.

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GAMMA RAY THEORY

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

FIG: 21 Spectral Log Example

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