SECTION

NEUTRON
NEUTRON THEORY

TABLE OF CONTENTS

TABLE OF
CONTENTS.................................................................................................i

INTRODUCTION...........................................................................................................
.1

NEUTRON INTERACTIVE LIFE

CYCLE..................................................................1

Inelastic
Collisions..................................................................................................2

Elastic
Collisions.....................................................................................................3

Neutron Migration and

Absorption..........................................................................7

Slowing Down And Capture Cross

Sections............................................................8

Porosity And Characteristic

Length.........................................................................9

EPITHERMAL NEUTRON
TOOLS............................................................................13

THERMAL NEUTRON
TOOLS...................................................................................14

Thermal Neutron
Detector.....................................................................................15
CAPTURE GAMMA RAY
TOOLS..............................................................................16

Pulse Neutron
Logging...........................................................................................16
DUAL DETECTOR NEUTRON
TOOLS.....................................................................17
NEUTRON TRANSPORT THEORY............................................................................19

ENVIRONMENTAL EFFECTS ON POROSITY.......................................................26

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Lithology
Effects...................................................................................................26

Formation Fluid
Effects.........................................................................................28

Salinity
Effect........................................................................................................28

Gas
Effect..............................................................................................................29

Shale And Mineral

Effects....................................................................................29

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Borehole Effects................................................................................................30

Liquid Filled Boreholes.........................................................................30

Air Filled Boreholes...............................................................................30

ENVIRONMENTAL CORRECTIONS..............................................................................31

Open Hole..........................................................................................................31

Borehole Diameter Correction...............................................................31

Mudcake Correction..............................................................................32

Formation And Borehole Salinity Correction.......................................32

Mud Weight Correction.........................................................................32

Standoff Correction................................................................................32

BoreHole Temperature Correction.........................................................32

Cased Hole..........................................................................................................36

Casing Thickness Correction..................................................................36

Cement Thickness Correction.................................................................36

Gas Indication From Neutron/Density Overlay..................................................37

REFERENCES........................................................................................................................3
9

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INTRODUCTION
The neutron is a fundamental particle found in the nucleus of all atoms except hydrogen,
which contains only a proton. The neutron has approximately the same mass as the proton
but carries no electrical charge. These two properties, smallness of size and especially
electrical neutrality, make it an ideal projectile for penetrating matter. Neutrons pass
through brick walls and steel plates with the greatest of ease. They can pass through steel
casing and penetrate rocks. It was logical, therefore, that they should find a place in the
arsenal of logging tools.

Two categories of neutron sources are in the logging industry:

1. Chemical sources are composed of two elements, which are in intimate contact with
each other and react together to emit neutrons continuously. The chemical source
presently used by the industry is americium-beryllium. Chemical sources need to be
heavily shielded when not in use.

2. Pulsed sources incorporate an ion accelerator and a target and can be activated by
electronic means. Presently, pulsed neutron sources are used for pulsed neutron
logging (TMD) and (PSGT)

NEUTRON INTERACTIVE LIFE CYCLE

Table 1 shows how neutrons of various energies interact with nuclei. Particle reactions
such as (n, P) or (n, α) are neglected here.

Table 1 Energies interaction with Nuclei

Name Energy Interaction Comment Source

High Energy > 10 MeV Inelastic / Elastic TMD, PSGT Neutron

Absorption Neutrons Generator
14 MeV

Fast 10 MeV - 10 KeV Inelastic / Elastic DNS, CNS Chemical

Neutrons Am Be

4.6 MeV

Intermediate 10 KeV - 10 eV Elastic

Epithermal 10 eV - 0.1 eV Elastic

Thermal 0.025 eV Elastic / Absorption

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Near chemical sources, neutrons may be found with substantially all of their initial energy
of several MeV; these are called fast neutrons. Neutrons interact with other atoms in
several ways (which will be discussed later), and they lose energy with each collision and
move further from the source. After passing through an intermediate stage, the neutron
energy level drops to only a few eV; these neutrons are called epithermal neutrons.
After yet more interactions, a neutron will be slowed down to a point where it has the
same energy as the surrounding matter; this energy level is a direct function of the
absolute temperature. Such neutrons are called thermal neutrons. They have energies of
approximately 0.025 eV. It is at this stage that the neutron is ripe for capture. The
capturing nucleus will usually emit one or more gamma rays. These gamma rays are called
capture gamma rays.

The chemical source used by Halliburton is AmBe. The nuclear reaction involves the
americium producing alpha particles that combine with beryllium in the reaction below:

241
95 Am → 237
93 Np + 2 He + γ(60 KeV)
4

4
9-1. 2 He + 94 Be → 12
6C + 01 n + (5.71 MeV )
5.71 MeV is the reaction energy and is imparted to the carbon atom as recoil energy and
to the neutron as kinetic energy that sends it into flight. The neutrons have an initial
7
kinetic energy of about 4.6 MeV and a velocity of about 10 m/second. They are
produced at a rate of 4 x 10 neutrons/second in a 19 curie source.

The two main types of collisions that a neutron may undergo are:

1. Inelastic collisions

2. Elastic collisions

Inelastic Collisions
Inelastic collisions can only take place while the neutron is highly energetic. In this type of
collision, the kinetic energy of the system (neutron and struck nucleus) is not conserved.
The neutron collides with a nucleus, leaving the nucleus in a higher energy "excited" state.
The excited nucleus will return almost instantaneously to its ground state by emitting
gamma rays, which are called "inelastic gamma rays". Figure 1 illustrates this type of
collision.

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Target Nucleus
Target Target Nucleus returns to original state
Nucleus in an exited state

Fast Gamma
Neutron Rays

KE(before) = KE(recoil) + KE(scattered)

FIG: 1 Inelastic Collision

A large amount of energy is required to excite a nucleus out of its ground state. This is
why only neutrons at high energies can undergo inelastic collisions. With each inelastic
collision, the neutron loses the same amount of energy that the nucleus gains. This implies
that the neutron can lose a large amount of energy with each inelastic collision. After very
few inelastic collisions, the neutron is slowed down below the threshold required to excite
a nucleus and inelastic scattering cannot take place. In general inelastic scattering is only
important during the first few microseconds of a neutron's life.

Elastic Collisions
The second type of collision, and the dominant mechanism by which a neutron loses
energy, is an elastic collision. Kinetic energy is conserved in these type of collisions. An
elastic collision is one in which the neutron collides with the nucleus of an atom but does
not excite the nucleus. The only energy transferred to the nucleus is kinetic (motion)
energy. This type of collision is illustrated in figure 2.

During an elastic collision, the neutron will lose a certain amount of energy and the struck
nucleus will gain that same amount of kinetic energy. The amount of energy that a
neutron loses in each collision depends on two factors:

1. The angle of collision

2. The mass of the struck nucleus

A neutron will lose more energy in a head-on collision with a nucleus than it will lose if the
neutron just grazes the nucleus. Also, the neutron will lose more energy in a collision with
a light nucleus than it will in the collision with a heavy nucleus.

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 NEUTRON THEORY

Scattered Neutron

= Scattering Angle
Incident Neutron

= Recoil Angle

Recoil Nucleus

KE(before) = KE(recoil) + KE(scattered)

FIG: 2 Elastic Collision

ε
The above suggests that a neutron will lose the most energy in a head-on ( = 0) collision
with a proton, since the proton has about the same mass as a neutron. The maximum
amount of energy the neutron can lose in an elastic, head-on collision is given by:

4M
9-2. ( FE ) max loss =
(1 + M ) 2

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Where ( FE ) max loss is the maximum fractional energy loss and "M" is the mass of the
struck nucleus in atomic mass units (AMU). The neutron and proton have a mass of 1
AMU. Using equation (2), Table 2 below shows the maximum fractional energy loss for
some common downhole elements.

Table 2 Maximum Fractional Energy Loss

Element Mass Max. Energy Loss
Hydrogen 1 AMU 100%
Carbon 12 AMU 28%
Oxygen 16 AMU 22%
Aluminum 27 AMU 14%
Lead 207 AMU 2%

For most elements, the maximum energy loss is low. A notable exception is the element
hydrogen (the nucleus contains one proton). A neutron that collides head-on with a
hydrogen nucleus can lose almost all of its energy in one collision. Not all neutrons will
lose this maximum amount of energy since most collisions will not be head-on. On the
average, neutrons will lose about 50% of their energy in each elastic collision with
hydrogen. The right-hand column of Table 3, shows the average number of collisions
required to slow a fast neutron (at 2 MeV) to the thermal level.

Notice the smaller the atom, the fewer collisions that are needed. This, therefore,
indicates that one of the most important factors affecting neutron theory is the presence of
hydrogen. Hydrogen is the most effective element in slowing neutrons down, because the
mass of hydrogen is about the same as the mass of a neutron.

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Table 3 Slowing Down and Capture Cross Sections for 2 MeV Neutrons
Element Collisions to 0.025
Symbol Cross Section eV
Capture Slowing
H 0.30 20.0 18
Be 0.01 6.1 87
B 700.00 3.0 105
C 0.00 4.8 115
N 1.88 10.0 130
O 0.00 4.1 150
Na 0.51 3.5 215
Mg 0.40 3.6 227
Al 0.23 1.5 251
Si 0.13 1.7 261
S 0.53 1.5 297
Cl 31.60 10.0 329
K 2.20 1.5 362
Ca 0.43 9.5 371
Fe 2.50 11.0 514
Cd 2500.00 5.3 1028

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Neutron Migration And Absorption

It should be mentioned here that at high energies, Si, O, Ca, etc., slow neutrons more
effectively than hydrogen. This is due to the fact that the hydrogen nucleus appears
relatively small to a fast neutron (i.e. at high neutron energies the slowing down cross
section for hydrogen is relatively small). At energy levels of 106 eV and below, hydrogen
becomes the most effective slowing element. Figure 3 shows these results for a clean sand
formation. The graph illustrates the slowing down power of different elements is primarily
a function of two factors:

1. The amount of energy loss which a neutron experiences upon making a collision
with a nucleus of a given mass.

2. The probability that a neutron will collide with this type of nucleus.

1
Clean Sand, Porosity = 15%

Hydrogen
10-1
Slowing
Down Oxygen
Power -2
10
Silicon

10-3
102 103 104 105 6 7
.1 1.0 10 10 10
Neutron Energy in Electron Volts

FIG: 3 Slowing Down Ability Of Different Elements

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 NEUTRON THEORY

Slowing Down And Capture Cross Sections

The ability of a nucleus to slow down or capture a neutron is governed by a property
known as its cross section. Cross section can be thought of as a measure of the
probability that a nuclear reaction will occur between a particle and a target. It is usually
expressed in terms of the effective area that a single target presents to the incoming
particle. In general, the slowing down cross section for any given nucleus may be quite
different from its capture cross section, i.e. although some elements may be good at
stopping neutrons, they may not be particularly hungry to swallow them once stopped.

To add to the complexities of the process of slowing down and capture, it should be noted
that cross sections are also a function of the neutron's kinetic energy before a collision.
Thus, an analysis of how fast neutrons are scattered in a subsurface formation and
eventually captured is a complex task. Referring back to Table 3, we have listed the main
elements found in the logging environment together with their slowing down and thermal
capture cross sections.

Two elements, hydrogen and chlorine, dominate the behavior of neutron tools.

1. Hydrogen provides the best material for slowing neutrons to a thermal level.

2. Chlorine is a voracious devoured of thermal neutrons, absorbing them a hundred

times faster than most other elements.

It should be noted that it is possible for neutrons to be absorbed at higher energy levels
(e.g. oxygen activation, resonance absorption), but that these absorption processes are
minor compared to thermal neutron capture. As previously mentioned, once captured the
new nucleus may very quickly drop to its ground state by emitting capture gamma rays.

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Porosity And Characteristic Length

You might expect that the more hydrogen present in the formation pore space (either in
the form of water, oil or gas, or a combination of the same) the more slowing down and
absorption would occur; thus the higher the porosity, the higher the count rate. For all
present neutron tools, however, the higher count rates are associated with lower porosity
(few hydrocarbons). Higher porosity is associated with low count rate. To understand
why this occurs, we need to examine the formation we are studying and the design of the
tool.
We first need to define some useful characteristic lengths used in migration theory:
• Slowing Down Length ( L s ) : (crudely speaking) the average distance traveled by a
fast neutron in going from the source energy at 4.6MeV to the energy level of 1.46eV.
Ls is mainly a function of hydrogen concentration.
• Thermalizing Length ( L e ) : (crudely speaking) the average distance travelled by a
neutron in going from an energy value of 1.46 eV to 0.025 eV.
• Thermal Diffusion Length ( L t ) : (crudely speaking) the average distance the
neutron travels from the point it first reaches the thermal level at 0,025 ev to its
capture still at the thermal level (0>025 ev). Lt is a function, not only of the hydrogen
content, but of the concentration of elements with high capture cross section, (e.g.
chlorine).
• Total Migration Length (M): (crudely speaking) the square of the three
characteristic lengths ( ( L s ), ( L e ), ( L t ) squared:

9-3. M 2 = (Ls ) 2 + (Le ) 2 + (L t ) 2

This length can be considered (crudely again) the total average distance the neutron
travels from source to capture.

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 NEUTRON THEORY

Table 4, below give Lt, Ls and M as a function of porosity for a water-filled sandstone.
Notice that salt water formations (high chlorine content) have Lt values less than those for
fresh water. The table gives Ls computed for neutrons degrading in energy from 4.6 MeV
to 0.025 eV.

Table 4 Neutron Characteristic Lengths

Porosity Slowing Down Thermal Diffusion Total Migration
% Length L s Length ( L t ) (cm) Length M (cm)
(cm) Fresh Water Salt Water Salt Water
3 21.0 9.8 8.6 23.9
11 15.4 8.0 5.6 17.6
23 12.3 6.3 3.7 13.9
34 10.8 5.4 2.9 12.2
50 9.6 4.4 2.1 10.6
100 7.8 2.8 1.2 8.3

As you can see, the lower the porosity the further the neutrons tend to travel. This means
that the thermal neutron density at any point in the borehole seen by the detector depends
on the porosity and how far the detector is from the source. Figure 4 shows a plot of
thermal neutron density versus the distance from the source, for four different porosities
(10, 20, 30, 40%).

Thermal neutron density for point source of Ra-Be neutrons in an infinite formation. These
curves were calculated using age theory that is know to apply poorly to hydrogenous media.
Thus they must be used as qualitative quides only.

FIG: 4 Thermal Neutron Density Vs Distance From Source

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Notice that close to the source the neutron density is very high. Also, by comparing the
10% and 40% porosity curves close to the source, we see that a higher count rate
indicates a higher porosity. However, as we move away from the source, this
proportionality fails as we go through the cross over zone. Moving further from the
source, the count rate versus porosity relationship reverses because neutrons can travel
further in lower porosity mediums. This means we would expect higher count rate in
lower porosity if our detector was more than about 30 cm from the source (in reality this
distance is substantially less than 30 cm).

Also notice that the greater the distance from the source, the greater the porosity
resolution. Of course, one disadvantage of this long spaced region is lower count rate.

Figure 5 illustrates the neutron migration profile "seen" by all present types of neutron-
porosity logging tools.

FIG: 5 Neutron Migration Profile

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 NEUTRON THEORY

At a point sufficiently removed from the source (i.e. the Long Spaced Region) formations
with decreased hydrogen content will have relatively more thermal, epithermal and capture
gamma rays. Since most hydrogen is located in the pore spaces of a formation the neutron
count rate can be related to a hydrogen index.

(grams hydrogen / cc formation)

9-4. H. I.=
(grams hydrogen / cc fresh water at STP)

φ
This hydrogen index can be considered the porosity; N = H.I*. This is true regardless of
whether the neutron tool measures thermal neutrons, epithermal neutrons, or capture
gamma rays. Again, a high count rate indicates a low hydrogen index and hence a low
porosity. A low count rate indicates a high hydrogen index and hence a high porosity.

Physically, the thermal neutron population can be represented by an expanding spherical

neutron cloud surrounding the source. For constant detector spacing, in lower porosity
formations the thermalized cloud density is greater farther away from the source (as
compared to higher porosity formation). Since the farther away we go from the source
the closer we get to the detector, a high count rate is then recorded because the thermal
neutrons have a shorter distance to travel to the detectors. This means their probability of
detection (before being captured by formation or borehole elements) is greater.

*Notice from equation 9-4, 100% porosity is only indicated for the case of fresh (pure) water. Since our
reference is fresh water, salt water environments cause problems.

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EPITHERMAL NEUTRON TOOLS

As previously mentioned, epithermal neutrons have energies just above the thermal range; these
neutrons avoid capture by strong thermal neutron absorbers such as boron, chlorine or the rare
earth minerals. Neutron Transport theory predicts the epithermal neutron intensity, or flux, to
be a function primarily of the neutron slowing down length, Ls. Since the epithermal neutron
distribution in the formation is not affected by differences in capture properties of the formation
nuclei (i.e. ∑ , ∑ ), this tool usually is less sensitive to lithology changes than tools
matrix fluid
measuring thermal neutrons or capture gamma rays. For the same reason, epithermal neutron
count rates are less sensitive to changes in formation or borehole chlorine (salinity) levels. The
bound water in shales will cause epithermal tools to indicate too high a porosity due to the
higher hydrogen concentration present, but the high capture cross section often associated with
these shales will not exaggerate this effect.

In principle, epithermal neutron tools, due to their insensitive to capture effects, are the most
accurate monitors of formation hydrogen index for any neutron tool employing only one
detector.

The primary drawback of epithermal neutron porosity devices is low count rate at the detectors.
This is due to two effects:

1. In any region of space there are just not that many epithermal neutrons around (as
compared to thermal neutrons).

2. The high energy level of epithermal neutrons make the probability of detection (i.e.
interaction with helium gas) less likely.

To improve count rate efficiency, most epithermal neutron tools are limited to short source-to-
detector spacing. This, however, results in increased sensitivity to change in borehole diameter
and standoff and reduces the depth of investigation into the formation that, for medium porosity
formation, is approximately equal to the source-to-detector spacing. To improve the situation
somewhat, many epithermal neutron tools are pad mounted "sidewall neutron porosity" devices,
similar in many mechanical respects to density logging tools.

By incorporating source and detector collimation towards the formation into the pad design,
(azimuth collimation), borehole size effects can be minimized, especially in air filled boreholes.
Collimation and limited depth of investigation, however, make sidewall tools more sensitive to
mudcake thickness and severely restrict their utility in cased holes. They are also less effective
in fluid filled uncased wells where hole conditions prevent the pad from maintaining contact
with the formation, or where invasion restricts the utility of the log in identifying gas zones.

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 NEUTRON THEORY

Halliburton has developed a dual spaced epithermal neutron tools (DSEN). These tools are not
pad mounted and are used primarily in an air filled boreholes, where count rates are higher.
Thermal neutron tools do not work in an air filled boreholes.

Epithermal neutron detectors are usually constructed as thermal detectors wrapped with a
material that has a very high capture cross section for thermal neutrons. Cadmium wrapped He-
3 gas proportional counters are usually employed. The cadmium effectively absorbs all thermal
neutrons (see Table 3), so that only epithermal neutrons interact with the high pressure
3
2 He gas.

THERMAL NEUTRON TOOLS

Thermal neutron tools are usually desirable because of the high count rate at the detectors. For
this reason, tools employing thermal neutron detectors are not as limited by the spacing and
depth of investigation problems associated with epithermal neutron tools.

Thermal neutron detectors are, however, more sensitive to lithology and are affected by
borehole and formation salinity. Both thermal and epithermal tools have about the same
sand/lime/dolomite differences.

The thermal parameter Lt is inversely related to the capture cross sections of the specific
elements in the formation and borehole. Elements with high capture cross sections, such as
chlorine in the formation, borehole fluids, and boron in shales, will cause significant decreases
in thermal neutron count rate. Since these decreases are not porosity related, thermal neutron
tool data is often difficult to interpret quantitatively in highly saline or shaly downhole
environments.

Despite these problems, thermal neutron tools are in use today, primarily because of their high
count rate efficiency. Efficiency is especially needed in slim-hole (e.g. cased hole) versions
where only small detectors can be incorporated into the tool.

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Thermal Neutron Detector

To detect thermal neutrons, He3 gas proportional counters are used. These are cylindrical
tube type detectors that belong to the ionization chamber family. Neutrons interact with
the Helium-3 nucleus according to the reaction:

1
9-5. 0 n + 23He → 31H + 11H + (0.765 MeV)
The triton (3H) and proton (1H) are the products that ionize the gas. They share the
reaction energy of 0.765 MeV and as these positive charges move through the gas,
ionization occurs which causes a stream of electrons to flow to the center high voltage
anode.(see below)

ANODE

3 CATHODE
He GAS

FIG: 6 HE-3 Filled Proportional Counter

The streaming electrons will collide with orbital electrons causing secondary ionization.
This increased electron flow accumulates at the anode and moves on in the form of current
to cause a pulse outside the counter. The pulse height is proportional to the energy of the
neutron that initiated the ionization process.

A thermal detector is essentially 100% efficient for thermal neutrons when He3gas
pressure is 4 atmosphere or above. For epithermal neutrons, an increase in sensitivity is
achieved by increasing the gas pressure.

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 NEUTRON THEORY

CAPTURE GAMMA RAY TOOLS

Since capture gamma rays are emitted by nuclei following thermal neutron capture, the
spatial distribution of capture gamma rays in the formation is very similar to that of
thermal neutrons. By measuring capture gamma ray intensity, the tool in effect measures
the same formation characteristics as thermal neutron tools, in that each is sensitive to
both slowing down and diffusion effects. Count rates in capture gamma ray tools,
however, are also affected by changes in the energy and intensity distributions of the
gamma rays emitted, following neutron capture by the downhole nuclei. In some ways
these effects prove most beneficial. Chlorine, on the average, emits three gamma rays
following capture. Hydrogen, on the other hand, emits only one. Therefore, even though
the thermal neutron population is suppressed in saline formations, the large number of
gamma rays emitted by chlorine tends to compensate. The net results are small formation
and borehole salinity effects in most capture gamma ray tools, usually in the direction of
increasing count rate with increasing salinity.

The energy distribution of formation capture gamma rays is dependent on the elements
present. As an example, silicon will emit different energy gamma rays following capture
than will calcium or hydrogen. Since many scintillation type gamma ray detector systems
can be adjusted so that they are sensitive to gamma rays only in a pre-selected energy
range, it follows that relative borehole size and lithology sensitivity in capture gamma ray
tools will vary depending on tool design parameters. In general, hole size and lithology
effects for capture gamma ray tools are comparable to those for thermal neutron detector
tools.

Pulse Neutron Logging

The main use at present for capture gamma ray type tools, is in high energy pulse neutron
logging (TMD). With this type of logging, the emphasis in not on porosity determination,
but rather on determining, Σ, the thermal neutron capture cross section of the formation.
A dual detector system is usually employed to measure the decay rate of the thermal
neutron population (directly related to Σ) in the borehole, and formation by measuring the
"die out" rate of capture gamma rays. The presence of saline water (i.e. chlorine)
dominates the Σ response of the formation and borehole. Physically, the decay of capture
gamma rays is equal to the decay of thermal neutrons since the number of gamma rays
emitted in a given formation is proportional to the number of thermal neutrons present.

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For detection, a time gating method is used with the scintillation type detectors (usually
NaI or CsI). The advantages in detecting capture gamma rays rather than thermal
neutrons for Σ are:

1. Gamma rays can originate from deeper in the formation, i.e. detectors "see" events
from deeper in the formation;

2. Count rates are higher (multiple gamma rays for each capture);

3. Borehole effect dissipates faster in gamma ray detection versus neutron detection.

DUAL DETECTOR NEUTRON TOOLS

The count rate in a single detector neutron tool is affected significantly by hydrogen in the
borehole region, and by borehole size and rugosity, mudcake or cement thickness and tool
standoff. It is also affected by the neutron moderating and capture properties of other
elements within the formation and borehole. Since most of these parameters are usually
highly variable and/or poorly defined, it is often not possible to determine accurately if a
change in detector count rate is due to a change in formation porosity or to a change in
one of these other parameters.

If a neutron tool has a second detector of similar design placed at a different distance from
the source, the ratio of count rates from the two detectors will retain porosity sensitivity
while minimizing sensitivity to most other environmental conditions.

As an illustrative example of the advantages of a two detector system, consider Figure 7

for a dual spaced thermal detector tool in a cased well. In the Figure we assume we have
two detectors, spaced 100 cm and 110 cm from the source. For a constant formation
porosity, we will vary the cement thickness to determine the effects on the count rates of
both detectors.

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 NEUTRON THEORY

FIG: 7 Dual Thermal Detector Effect Of A Cased Borehole

Let's look at how a single detector (A) will respond to changes in cement thickness with a
constant porosity of 10%.
Reading at A with 0" cement = 20
Reading at A with 1" cement = 5.9
Reading at A with 2" cement = 1.75

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From these readings we find a change in the count rate by a factor of more than 10, due
entirely to changes in cement thickness. This is the problem with the single detector
Epithermal tool in casing. The single detector does not have the resolution to determine
porosity behind casing. With the addition of a second detector, we can now establish a
ratio. If this ratio held fairly constant with changes in cement thickness, we could then use
this to define porosity. Looking at the ratios of A and B from Figure 7, we find:

A 20
Cement Thickness 0", ratio = = 2.0
B 10
A 59
.
Cement Thickness 1", ratio = = 197
.
B 3
A 175
.
Cement Thickness 2", ratio = = 195
.
B 09 .

This provides a nearly constant ratio for a constant porosity. In other words, by using a
ratio of the reading of two detectors, we can eliminate the effects due to the borehole,
casing and cement. After the ratio is normalized we can use it to derive porosity directly.
The porosity-ratio transform is usually determined from "fitting" the best curve to actual
data and has the form:
x
9-6. φ(R) = a o + a 1 R + a 2 R 2 +.... = ∑ a i R i
i =0

a i = constant coefficients, R = normalized ratio

NEUTRON TRANSPORT THEORY

The theoretical approach used to define the neutron intensity at some point "r" from the
source is referred to as the neutron transport theory. The results of this theory provide the
physical rationale governing the design and interpretation of neutron logging tools.

The theory assumes a two group system in a hydrogenous medium.

• The first group assumes the neutrons range in energy from the source energy down
to the epithermal level.

• The second group consists of thermal neutrons with the energy degraded
epithermal neutrons as a source.

Physically, both systems can be represented by diffusion equations. These are linear,
second order, differential equations with no time dependency (we assume no pulse
generator).

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For the first system (Epithermal group), the diffusion equation can be described as
consisting of three terms describing the neutron intensity through a unit volume sphere at
some distant "r" from the source.

• The first term is a diffusion term that simply says that the intensity of neutrons will
change as neutrons simply "move" away from the source and out of the volume.
This is the so called "diffusion effect" (neutron migration out of the unit volume is
somewhat offset by neutron migration into the volume).

• The second term is a removal effect and gives the probability that the neutrons will
be removed from the Epithermal group by degrading in energy to the thermal
group.

• The third term is the constant source strength (i.e., AmBe). The Epithermal
diffusion equation can simply be written as:
9-7. (Diffusion term)epi + (Removal term)epi+ (Source term)epi = 0
(no time dependency - from continuous source)

For the second system, a similar diffusion equation can be constructed for the thermal
neutron group. As before, there are three terms.

• The first term describes the diffusion effect.

• The second term is a removal term that gives the probability that thermal neutrons
will be removed from the thermal group by absorption by elements within the
volume.

• The third term is a source term whereby, the neutrons removed from the
epithermal group now become "source" neutrons for the thermal group. The
thermal diffusion equation can therefore also be simply written as:

9-8. (Diffusion term)thermal + (Removal term)thermal + (Source Term)thermal = 0

(no time dependency - from continuous source)

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NEUTRON THEORY

The solution to both diffusion equations can be explicitly solved. For the epithermal
group we have,

9-9.  Q  e − r/Ls
N e (r) =   Epithermal Solution
 4 πD s  r

WHERE: Ne(r) = epithermal density as a function of "r"

Q = source strength

Ds = diffusion constant

Ls = slowing down length

r = distance from source

For a single detector epithermal tool with a source to detector spacing r (see Figure 8),
d
the count rate is given by,

 Q  e − rd /Ls
Count Rate ∝ N e (rd ) =  
9-10.
π  r
 4 D
s d

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 NEUTRON THEORY

One can see why epithermal tools give the most accurate hydrogen index of all neutron
type tools. The count rate is shown to be primarily a function of Ls. As already
discussed, hydrogen dominates the slowing down process of neutrons, and therefore is the
primary element controlling Ls. From Equation (9-10) we see an increase in hydrogen,
which causes Ls to decrease, decreases the count rate that implies higher porosity. The
presence of strong neutron absorbers like chlorine will only effect Ls in the sense that
hydrogen atoms are replaced by chlorine atoms (thus increasing Ls). Equation (9-10) also
shows that Epithermal tools are less affected by changes in lithology in the sense that only
the matrix ability to slow neutrons is a factor, not its ability to absorb them once slowed
(no Lt effect).

FIG: 8 Single Detector Epithermal Tool

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NEUTRON THEORY

For the thermal group we get a solution to the diffusion equation of the form:

9-11. N (r) = QLt 2 (e − r/ L s − e − r / L t ) Thermal Solution

t
4 πD t (Ls 2 − Lt 2 ) r

Where:

N t (r) = thermal neutron density as a function of "r".

Q = source strength

Dt = thermal diffusion coefficient

Ls = slowing down length

Lt = thermal diffusion length

r = distance from source

Since the count rate is proportional to N t (r) we see that at a distance "r" from the source,
the thermal neutron count rate at a detector is a function of both Ls and Lt. Thus, we see
a dependency not just on the presence of hydrogen but also on the presence of neutron
absorbers (which control Lt). An increase in the number of such absorbers, like chlorine,
decreases Lt.

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 NEUTRON THEORY

A compensated thermal neutron tool employs two detectors at a near and far distance rN
and rF respectively (see Figure 9 below). The two detectors give a ratio of count rates,
R, from equation (9-11).

CN N t (rN ) rF (e − rN /Ls − e − rN /Lt )

9-12. R = ∝ =
CF N t (rF ) rN (e −rF /Ls − e − rF /Lt )

Bowspring

Far Detector

rF Near Detector

rN
Source

Formation
Formation

FIG: 9 Compensated Thermal Neutron Tool

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NEUTRON THEORY

If we now realize that Ls > Lt and both rN and rF are relatively large, equation (12) can
be approximated by:

r − ( rN − r F ) / L s
9-13.
R≈ F
e Ratio of two thermal detectors count rate
r
N

Notice that equation 9-13 has the same form as the epithermal equation 9-10. This
demonstrates, theoretically, that a compensated thermal neutron ratio should be somewhat
independent of thermal neutron properties (salinity, etc.), because the dependency on Lt
vanishes. Unfortunately equation 9-13 only holds true for "r" values out of the physical
range of practical logging tool limits (the greater "r" the lower the count rate and the more
statistical the measurement). Nevertheless the approximation equation 9-13 still
demonstrates that a ratio method has a weaker dependency on Lt. Notice from equation
9-13 that as hydrogen content increases, Ls decreases and the ratio increases as it should
for higher porosity’s (φ α R).

Theoretically and realistically speaking, the intensity of capture gamma radiation resulting
from the absorption of thermal neutrons can be used to determine the thermal neutron
density N t (r) and therefore porosity or Σ. This is possible because, obviously, the count
rate for the capture gamma rays is proportional to N t (r). That is, as we have already
stressed, the more thermal neutrons in a volume, the more that will be captured, and the
greater the number of emitted gamma rays.

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 NEUTRON THEORY

ENVIRONMENTAL EFFECTS ON POROSITY

Although formation porosity is the most important determinant of any neutron tool, there
are several other variables which influence porosity determinations. Some cause
perturbation to the neutrons slowing down process and others to the thermal neutron
diffusion process. These perturbations can significantly affect the count rate in a neutron
tool and their ratio-porosity values.

Lithology Effects
Most matrix elements have different inelastic, elastic and thermal neutron capture
properties. Although the magnitudes of these effects are usually small relative to the
hydrogen effect, they do cause slight changes in the neutron slowing down length (Ls) and
the thermal diffusion length (Lt). For example, the neutron slowing down length (the
dominant factor affecting porosity) is always slightly larger in a sandstone (quartz)
formation than in a limestone (calcite) formation of the same porosity. Table (5) shows
the slowing down lengths for calcite, dolomite and sandstone. The slowing down lengths
correspond to neutron energy degraded from 4.6 MeV to 1.46 eV.

Table 5 Neutron Slowing down lengths

Mineral Composition Ls (cm) Porosity Compared to
4.6MeV to 1.46 ev O% Porosity Limestone
Dolomite CaMg(CO3)2 20.2 0.9

Calcite CaCO3 23.3 0.0

Quartz SiO2 28.7 -1.0

Anhydrite CaSO4 30.1 -1.0

Halite NaCl 36.8 -1.0

Gypsum CaSO4•2H2O 53

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NEUTRON THEORY

If a neutron tool moves from a limestone to a similar sandstone (same porosity) and the
log analyst is not aware of the change in lithology, he would incorrectly attribute the
increase in count rate to a decrease in porosity. By contrast, in going from limestone to a
similar dolomite a lower count rate would result because of the shorter Ls, thus indicating
a higher porosity. Lithology correction graphs like the one below for the DSNT (Dual
Spaced Neutron Tool) can be used to correct porosity for lithology effects. It should be
noted that graphs such as these assume certain values for sigma matrix (thermal neutron
capture cross section) that may not be correct.

FIG: 10 Neutron Lithology Response

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 NEUTRON THEORY

Lithology induced fractional errors in the indicated porosity will be larger for low porosity
formations. Here, the contribution of the matrix is greater.

Epithermal tools' lithology effect is smaller than that of thermal tools, because that small
portion of the matrix effect caused by neutron absorption (i.e., Lt) is eliminated.
Therefore, Epithermal type tools give better porosity estimates that are less sensitive to
lithology changes, especially at low formation porosities. This relative insensitivity to
lithology changes is also a disadvantage of the Epithermal type tools for use in lithology
cross-plot applications.

Formation Fluid Effects

The amount of hydrogen in water decreases as the salinity of the water increases since the
water molecules, and hydrogen atoms, are being displaced by the salt. The amount of
hydrogen in oil (which is rarely exactly the same as that of formation water), is a function
of its composition and its gas content. The amount of hydrogen in gas is lower than water
or oil. Before accurate porosity calculations can be made, the composition of the
formation fluid must be known. In practice, this is often very difficult to determine since
filtrate, residual hydrocarbons, irreducible connate water and bound water may all coexist
in the formation next to the well bore.

Salinity Effect
As stated earlier, chlorine is an excellent thermal neutron absorber compared to other
common downhole elements. In formations containing chlorine (i.e. salt water), the
thermal neutrons are quickly captured. This premature capturing reduces the number of
collisions a thermal neutron will have before being captured, and reduces the thermal
diffusion length, Lt. The net result is, at some fixed distance from the source, fewer
thermal neutrons will be present in saline formations compared to fresh formations of the
same porosity.

Since the standard tool reference for neutron tools assume fresh water is in the formation,
environmental correction charts must be used when saline water is present.

Capture gamma rays' intensity cannot be easily predicted in relation to formation water
salinity. Although the concentration of thermal neutrons is reduced in saline formations,
the resulting capture gamma ray intensity can even increase in some instances. This
offsetting effect occurs since chlorine emits more gamma rays following neutron capture
than most other downhole elements.

Epithermal neutron intensity will not be significantly affected by formation salinity.

Epithermal neutrons have sufficient energy to be unaffected by the thermal capture
properties of the formation (equation 10).

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NEUTRON THEORY

Gas Effect
Replacement of liquid by gas in the pore space of a rock lowers the hydrogen density of
the pore fluid. As a result the neutron tool, that is calibrated for liquid-filled porosity,
indicates abnormally low porosity (i.e. it sees gas as water occupying a smaller
volume).

In the case of formations with considerable gas saturation’s, another effect is present.
This is known as the "excavation effect". Consider a formation with 10% porosity
completely saturated with gas having a hydrogen index of 0.1. This formation will contain
the same amount of hydrogen as a fresh water filled formation with a 1% porosity. The
count rate observed in the gas filled formation will be greater.

The 1% porosity fluid filled formation has 99% rock matrix, while the 10% porosity gas
filled formation only has 90% rock matrix. In the case of the gas filled formation, 9% less
rock matrix is present to absorb, scatter and attenuate neutrons and gamma rays. The shift
in the count rate due to the excavation effect is larger for higher porosity zones with
intermediate gas saturation’s.

Shale And Mineral Effects

Many shales contain chemically bound water (especially montmorillonite). Shaly zones
contain hydrogen in the pore space and in the bound water. The amount of bound water a
shale contains depends on the type of shale, its age, and the pressure exerted on the shale.
Older shales normally have less bound water than younger shales or clays.

Neutron tools respond only to the total amount of hydrogen in a formation. Since shales
contain hydrogen that is not part of the porosity, any porosity estimates in shaly zones will
be too optimistic. This is also true of gypsum since it contains bound water of
crystallization.

In addition to bound water effects, there are an additional lowering of thermal neutron and
capture gamma ray intensities in shaly zones due to their unusually large capture cross
sections. Most shales contain trace concentrations of elements with extremely high
thermal neutron capture cross sections. The most important of these is boron. Boron has
a capture cross section almost 25 times larger than chlorine. Even small concentrations of
boron (typically 100 parts per million in shales) can cause a large increase in the overall
formation capture cross section.

Rare earth minerals present in trace amounts can cause similar effects: porosities may
appear optimistic due to abnormally low count rates. Of course, the magnitude of the
effect depends upon the specific minerals present and the type of detectors used.

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 NEUTRON THEORY

The capture gamma ray intensity, which is only slightly sensitive to salinity due to the
offsetting effects described earlier, is very sensitive to shaliness. Boron, unlike most other
formation elements, does not emit high energy gamma rays following thermal neutron
capture. Instead, boron emits non-penetrating alpha particles (helium nuclei) and low
energy gamma rays that are usually unable to reach the detector. This reduces the count
rate in a gamma ray detector and results in an optimistic porosity calculation.

Borehole Effects
LIQUID FILLED BOREHOLES
Changes in the borehole environments also produces changes in neutron and capture
gamma ray count rates. Since neutron tools are calibrated to a standard conditions, any
departure from these standards must be quantified and corrected. In the open hole the
perturbation effects include those due to: the presence of mud and mud cake, the size of
the hole, the eccentricity (standoff) of the tool, the presence of chlorine, the pressure of
weighting materials and borehole temperature. In the cased hole the neutron and capture
gamma ray distribution is also effected by the presence of the iron casing and surrounding
cement.

The "Environmental Correction" section will elaborate more on these effects and define
the type of correction needed.

AIR FILLED BOREHOLES

In air or gas filled boreholes, the neutrons are not appreciably moderated, scattered or
attenuated by the borehole. The borehole essentially acts as a waveguide, channeling the
neutrons and gamma rays up and down the wellbore. Because of this, much higher count
rates are observed in air-filled boreholes as compared to fluid filled boreholes.

The relationships between hole size and observed count rate are opposite for air and liquid
filled holes. In an air filled borehole, the observed count rate increases with increasing
borehole diameter. The net result of all known borehole phenomena is a very significant
reduction in the effectiveness of most neutron tools in air filled holes. As previously
mentioned epithermal tools are the only recommended neutron porosity devices for
air filled holes.

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NEUTRON THEORY

ENVIRONMENTAL CORRECTIONS
Open Hole
The basic neutron porosity response represents "true" formation porosity only if the
borehole and formation conditions are "standard". When non-standard conditions are
encountered, corrections must be applied to the porosity values. We shall discuss the
correction applied to a dual spaced thermal neutron tool. Although the corrections may
be numerous, they are much smaller in magnitude than corrections for a single-detector
neutron porosity tool and, in many cases, tend to cancel algebraically (see Figure 11). The
physical rational for the direction of each correction (positive or negative) will be
explained. Although performed on the thermal neutron tool, the same rationale and
direction of each environmental correction is also correct for epithermal type tools; only
the magnitudes of the corrections are different.

Since the porosity is a function of the ratio of the near to far detector count rate [φ (R) = φ
(N/F)] , the far detector count rate essentially controls porosity estimates. This is due to
the fact that it changes much more dramatically than the near, i.e. an increase in porosity is
essentially due to the far detector count rate decreasing significantly while the near
decreases less dramatically (fractionally speaking). For the DSNT-A, a change in porosity
from 10% to 40% shows the near count rate decreases by 43%, while the far decreases by
81%. As with all present neutron type tools, both thermal detectors are placed at a
sufficient distance to give an inverse relationship between count rate and porosity.

BOREHOLE DIAMETER CORRECTION

The effect of a change in borehole size is to change the amount of hydrogen near the tool.
An increase in hydrogen near the tool will slow the source neutrons more readily. This
will lead to a reduction in count rate and an increase in the porosity. Therefore, a negative
correction is applied for an increase in borehole size above the standard (8") and a positive
correction is applied if the borehole is smaller than the standard.

The magnitude of the borehole effect increases as the apparent porosity increases. As the
apparent formation porosity increases, a greater fraction of neutrons from the source are
thermalized and captured within the formation and, do not reach the detectors. The count
rate from the borehole, however, remains relatively constant. As φ (R) increases, the
fraction of total tool response from the borehole increases. This means that at high
apparent formation porosities, the borehole tends to dominate the tool response; thus the
borehole correction becomes greater as φ (R) increases.

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 NEUTRON THEORY

MUDCAKE CORRECTION
The effect of the mudcake on the recorded porosity depends on a complicated relationship
between mud, mudcake and if the log porosity is auto caliper corrected. An increase in
mudcake thickness will increase the amount of hydrogen near the tool. This reduces the
count rate and increases the apparent porosity. Mud cake effects usually require a
negative correction.

FORMATION AND BOREHOLE SALINITY CORRECTION

An increase in the salinity of a fluid gives two competing effects.

• First, the added NaCl increases the thermal neutron capture cross section of a fluid.
This tends to reduce neutron count rates.

• Second, the added NaCl decreases the hydrogen index of water.

With formation salinity, the increased capture cross section of the formation water is the
dominant effect. As the salinity of the formation fluid increases, the count rate decreases
,and the apparent porosity is too high. A negative correction is usually required.

With the borehole, the decrease in hydrogen index of the borehole fluid is the dominant
effect. This is due to the fact that the borehole's largest influence is with neutrons as they
leave the source. These high energy neutrons are not affected by the capture properties
of the borehole fluid. Overall, an increase in borehole fluid salinity will increase count
rates and yield a recorded porosity that is too low. A positive correction is required.

MUD WEIGHT CORRECTION

An increase in mud weight reduces the hydrogen index of the mud since the weighting
material displaces some water molecules. This tends to increase the count rates.
Increased mud weights make the recorded porosity lower than it should be. A positive
correction is required.

It should also be mentioned that the type of mud must also be considered. Barite mud,
due to the higher density of the solid material, will have a higher hydrogen index than
natural mud of the same weight. As an example, 16 lb/gal barite mud has approximately
the same hydrogen index as 12 lb/gal natural mud. The correction should be the same for
both.

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NEUTRON THEORY

STANDOFF CORRECTION
An increase in tool standoff from the formation places more hydrogen between the tool
and formation. This tends to reduce count rates and increase the apparent porosity. A
negative correction is required.

The magnitude of the standoff correction increases with standoff distance until the tool is
centralized within the borehole and then begins to decrease. This effect can be illustrated
as follows. Recall that the neutron tool is not collimated. Assume that we have a 3.5"
O.D. tool in a 5.0" borehole. A 0.5" standoff will produce a negative correction. Yet as
the standoff is increased to 1.5", the tool is actually against the opposite side of the
borehole wall and, by definition, the correction must be zero. All standoff corrections
must, therefore, be a function of borehole diameter as well as standoff distance in order to
by physically meaningful.
BOREHOLE TEMPERATURE CORRECTION
As the temperature of a fluid increases, the density of that fluid (and its hydrogen index)
will decrease. An increase in pressure increases the hydrogen index of a fluid. Higher
temperatures will increase the count rate and reduce apparent porosity. Higher pressures
have the opposite effect but to a much smaller extent. The temperature correction
includes a pressure correction that assumes an increase in pressure with an increase in
temperature. A positive correction is the result. If the pressure and temperature
corrections are performed separately, the pressure correction would be negative, while the
temperature correction would be positive. Figure 11 and 12 show the corrections that are
applied to the neutron response in the open hole.

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 NEUTRON THEORY

Figure 11

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NEUTRON THEORY

Figure 12

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 NEUTRON THEORY

Cased Hole
In addition to the borehole diameter (before casing), borehole salinity, formation salinity,
mud weight and borehole temperature effects, additional corrections are required in the
cased hole due to the presence of steel casing and cement.
CASING THICKNESS CORRECTION
Iron is a good thermal neutron scatterer and absorber. An increase in the casing thickness
above the standard increases the amount of iron between the formation and the tool. The
iron tends to reduce the neutron intensity within the borehole. This reduces count rate and
makes the apparent porosity too high. The correction applied is therefore negative. The
correction is positive for casing thickness less than the standard.

CEMENT THICKNESS CORRECTION

Cement contains bound water and has a relatively high hydrogen index. An increase in
cement thickness above the standard affects the recorded porosity like an increase in tool
standoff. As cement thickness increases, count rate decreases which makes the apparent
porosity too high. A negative correction is required. The correction is positive if the
cement thickness is less than the standard.

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NEUTRON THEORY

Gas Indication From Neutron/Density Overlay

Since the neutron tool “sees” gas as low porosity, a good combination for identifying a
possible gas zone is the neutron/density log. Gas is indicated when the different porosities
show opposite (or mirror images) responses with φ N < φ D . In most cases, gas will
produces the famous “cross over” effect. Figure 13 shows the gas effect on a neutron -
density overlay. In the figure both φ N and φ D were calculated using the correct
lithology (sandstone) and are displayed on identical scales.

FIG: 13 Gas Effect On Neutron/Density Log

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 NEUTRON THEORY

Choosing the wrong lithology can give a false gas effect (i.e., choosing limestone when the
actual matrix is sandstone). Figure 14 shows a neutron - density log using a limestone
matrix. Notice the false gas effect through the sand section.

FIG: 14 False Gas Effect

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NEUTRON THEORY

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

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

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

4. Dewan, John T., Essentials of Modern Open-Hole Log Interpretation, Penn Well
Publishing Company, Tulsa Oklahoma, 1983

5. Perkins, Donald H., Introduction to High Energy Physics, Addison-Wesley Publishing

Company, Reading, Mass., 1972

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

7. Smith, Mike P., "Calibration, Checking and Physical Corrections for a new Dual-
Spaced Neutron Porosity Tool", SPWLA Symposium, June, 1986

8. Density Logging and Neutron Logging, Gearhart Publication, WS-7602-85

9. Arnold, D.M. and Harry D. Smith, "Experimental Determination of Environmental

Corrections for a Dual-Spaced Neutron Porosity Log", SPWLA Twenty-Second
Annual Logging Symposium, June, 1981

10. Thermal Multigate Decay Logging, Welex Publication, WTS-2-315

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