Logging Thermal Neutron Die-away

Thermal Neutron Die-away Logging

edited by P. Vass

Thermal Neutron Die-away Logging

The technical implementation of Thermal Neutron Die-away logging, also known as Thermal Decay Time (TDT) logging, is based on the application of a neutron generator as a source of high energy neutrons.

In this case the neutron generator is used in impulse mode.

By means of TDT logging, the macroscopic thermal capture cross section (

or simply ) of the formations is determined.

Its application is highly connected to the field of hydrocarbon exploration and production.

The method is mostly applied in cased holes for separating the oil-bearing zones from the water-bearing ones within the

reservoirs under investigation.

Not only qualitative but also quantitative results can be obtained

with respect to the water saturation.

The figure represents the timescale of free neutrons.

Two characteristic time intervals can be assigned to the characteristic distances (slowing-down length and diffusion length).

Interactions of neutrons with matter

Darwin V. Ellis, Julian M. Singer:

Well Logging for Earth Sciences

The slowing-down time gives how much time elapses averagely between the emission of fast neutrons (~4 MeV) and their slowing-down to the lower limit of epithermal energies (∼0.4 eV).

It primarily depends on the hydrogen concentration of the formation.

Its value is about 2 μs in water and 12 μs in non-porous formations.

The diffusion time gives how much time elapses averagely between the

thermalization of neutrons and their thermal capture.

It depends on the macroscopic thermal capture cross section of the medium.

Its value is of the order of 100 s.

The computed porosity dependence of slowing down length and diffusion length for clean limestone and sandstone formations is presented here.

Although a neutron spends much longer time in the diffusion phase than in the slowing-down phase during its lifetime, still the thermal diffusion length is always shorter than the slowing-down length in the same rock because of the significant difference in the velocity of neutron

propagation.

Interactions of neutrons with matter

O. Serra, L. Serra: Well Logging, Data Acquisition and Applications

Absorption phase

The energy of most thermal neutrons is already low enough for the nuclei of the medium to absorb the neutrons in this phase.

Two interactions are typical in this phase:

• thermal neutron capture,

• thermal activation.

Thermal neutron capture (n, )

During this interaction the incident thermal neutron is totally absorbed by the target nucleus, which becomes excited.

The excited state lasts a very short time because one or more gamma ray is emitted almost at once (prompt gamma ray), so the nucleus return to its ground state.

The energy of emitted gamma ray is characteristic of the target nucleus.

Interactions of neutrons with matter

Thermal neutron capture (n, ) The tendency of elements to absorb thermal neutrons is characterized by the

(microscopic) thermal capture cross section (its unit:

barn/neutron).

The most effective elements:

• chlorine (its concentration depends on the salinity of formation water),

• gadolinium (uncommon

element in formation water),

• boron (often connected to shales),

• lithium.

Interactions of neutrons with matter

O. Serra, L. Serra: Well Logging, Data Acquisition and Applications

Although hydrogen is a moderate absorber , still its effect on thermal neutron capture is significant when its concentration is high (formation water, oil) in porous formations.

The macroscopic (or volumetric) thermal capture cross section is the product of the microscopic thermal capture cross section and the number of target nuclei per unit volume.

It mainly depends on

• the lithology,

• porosity,

• salinity of formation water,

• water saturation,

• shale volume,

• and the types of clay minerals.

Interactions of neutrons with matter

Thermal Neutron Die-away Logging

If a short-time impulse of high energy neutrons is emitted from a neutron generator, the

neutrons penetrate into the medium and their energy gradually decrease with both the time elapsed from the emission and the distance from the source.

The figure illustrates the spread of neutrons coming from an impulsive source in the

formation, and the thermal neutron density at a detector as a function of time.

Here, t₁ symbolizes the time moment, when most of the neutrons have been thermalized.

By the time of t₂ most of the neutrons have entered the diffusion phase. The thermal neutron capture is responsible for the

decreases of neutron density near the source in this phase.

Darwin V. Ellis, Julian M. Singer:

Well Logging for Earth Sciences

Thermal Neutron Die-away Logging

The time interval of t

can be well approximated by the slowing- down time. The slowing-down time of fast neutrons primarily

depends on the hydrogen concentration of the formation and it is typically less than 15 s.

The time interval of t

, in turn, is related to the diffusion time.

The diffusion time of thermal neutrons generally lasts longer. It depends on the concentration of not only the hydrogen but also other elements having high microscopic thermal capture cross section (effective absorbers, e.g. chlorine) in the rock.

The possible range of diffusion time extends from about 5 s (rock salt) to 900 s (quartzite).

So, the theory of TDT logging is based on the fact that the average lifetime of neutrons in rocks depends on the chemical composition and reservoir parameters of the rocks.

Principally, the composition of fluid filling the pore space affects the

average lifetime of neutrons and has the most important role in the

TDT log response.

Thermal Neutron Die-away Logging

The average lifetime of neutrons is related to the macroscopic thermal capture cross section of the medium under investigation.

The change of number of neutrons (N) with time in a homogeneous medium is described by the following relationship:

𝑁(𝑡) = 𝑁

𝑒

,

where

N₀

is the number of neutrons emitted from the source and penetrated into the medium at t

v

is the average velocity of neutrons,

_a

is the macroscopic thermal capture cross section of the medium for neutrons propagating with velocity v in the medium.

t

is the time elapsed from the emission of neutron impulse at t

The relationship assumes that all the neutrons are in thermal

equilibrium with the surrounding medium.

Thermal Neutron Die-away Logging

A logging tool which is used for the measurement of macroscopic thermal capture cross section includes the following essential components:

• a neutron generator working in impulse mode (it is able to periodically emit impulses of fast neutrons),

• a detector whose operation can be controlled and limited to definite counting gates (time intervals).

A typical set of working parameters of a TDT logging tool (the exact values are different for different types of tools):

• the neutron generator periodically emits ~1000 impulses of neutrons in 1 s (essentially the frequency of neutron impulses),

• the time spacing between two neighbouring impulses is 1 ms ≈1000 s,

• the length of each impulse is ~30 s,

• the average number of emitted fast neutrons in an impulse is about 10⁵

• the length of a counting gate (an operating interval of the detector in which the thermal neutrons are detected in cps) is about 100 s,

Thermal Neutron Die-away Logging

t₁ is the time when the first counting gate starts within the time spacing of two neighbouring neutron impulses (e.g. 400 s),

t₂ is the time when the second counting gate starts (e.g. 700 or 800 s),

…

t_n is the time when the n^th counting gate starts.

Darwin V. Ellis, Julian M. Singer: Well Logging for Earth Sciences

Thermal Neutron Die-away Logging

If the thermal neutrons or the thermal capture gamma rays are

repeatedly detected within the time interval of neighbouring neutron impulses, the rate of decrease in the thermal neutron density can be measured.

This decay process can be characterized by a constant called half- time of neutrons (also known as neutron lifetime).

It gives the time which is necessary for reducing the number of neutrons in the medium from the initial amount (N

) to its half.

𝑁 =

2

= 𝑁

𝑒

If the velocity (v) of thermal neutrons is chosen to be 2200 m/s:

𝑡

≅

Σ_𝑎

[s] .

So, the half-time of neutrons (t

) depends on the macroscopic

thermal capture cross section of the medium (inverse proportionality).

Thermal Neutron Die-away Logging

If the half-time of neutrons is shorter in a rock, the decrease of neutron density with time is faster. It implies that the rock has a higher value of macroscopic thermal capture cross-section (_a).

So that _a can be expressed from Eq. 2, the initial number of neutrons (N₀) should be measured, but it is problematic.

An alternative solution, which is used in practice, is based on the

measurement of thermal neutron density at two or more different times (t₁, t₂, …) between two neighbouring neutron impulses.

When two counting gates with opening times of t₁ and t₂ are applied, two count-rates of thermal neutrons (N₁ and N₂) are detected

(in cps).

𝑁₁ = 𝑁₀𝑒^{−𝑣Σ𝑎𝑡1} 𝑁₂ = 𝑁₀𝑒^{−𝑣Σ𝑎𝑡2}

The natural logarithm of their ratio gives the following relationship:

𝑙𝑛

𝑁₁

= −𝑣Σ

𝑡

− 𝑡

Thermal Neutron Die-away Logging

After converting the natural logarithm into common logarithm, the macroscopic thermal capture cross-section of the medium can already be obtained from the formula below :

Σ_𝑎 = ^10.5

Δ𝑡 𝑙𝑔 ^𝑁1

𝑁₂

[1/cm]

(Eq. 5)

where t is the difference between the opening times of counting gates (t

) in the unit of microsecond.

Thus, the measurement of 

is reduced to the measurement of time and detector count-rates.

This solution relies on the assumption that the thermal neutron

density near the detector is proportional to the detected count-rates of thermal neutrons.

Since the value of 

is regarded as constant for a given rock, it

results from Eq. 5 that the ratio of measured count rates increases

with t.

Thermal Neutron Die-away Logging

Essentially, 

characterizes the tendency of a material to capture thermal neutrons.

In well logging, the so-called capture unit (cu) is used to measure its magnitude instead of 1/cm (the latter is used in neutron

physics).

The capture unit is equal to 1000 times the unit of 1/cm.

In practice, not the thermal neutrons are detected in the counting gates, but the capture gamma rays.

The count-rates of the two "particles" are proportional at the same place and time.

Decreasing thermal neutron density entails decreasing intensity of thermal neutron capture, which results in less capture gamma ray flux within the same volume of a medium.

The decay of capture gamma ray flux follows the same

exponential function as does the decay of neutron density.

Thermal Neutron Die-away Logging

Advantages of detecting the capture gamma ray instead of thermal neutrons:

• the radial investigation depth of the logging tool is improved (n x 10 cm),

• the measurement is less sensitive to the unwanted effects of wells (workover fluid, casing, cement sheath etc.).

However, the effect of natural gamma radiation (coming from radioactive isotopes of the rocks) must be eliminated from the

measurement, because it does not come from thermal neutron capture.

The possible solutions of this problem.

1. Only the gamma rays having higher energy than a selected threshold (e.g. 2.2 MeV) are detected.

2. Another solution of the problem requires the separated measurement of natural gamma radiation during the logging operation. Essentially, a GR logging tool is combined with the TDT logging tool.

The effect of natural gamma radiation is minimized by subtracting the measured background radiation from the gamma ray count-rates

detected in the counting gates.

Thermal Neutron Die-away Logging

The background radiation is measured near the end of time interval between two neighbouring neutron impulses, because most of the

neutrons have been captured by then, so no or minimal capture gamma ray is emitted by the formation.

A short break can also be inserted after some periods of neutron

impulses, in which the neutron generator does not work and only the background radiation is detected and recorded.

The proposed logging speed of this measurement is 6 m/min (10 cm/s).

The time spacing between the neutron impulses is typically 1 ms. The tool runs about 0.1 mm in the wellbore during this time.

The displayed curves on the well log:

• the curves of thermal capture gamma rays in cps,

• and the curve of computed macroscopic thermal capture cross section in c.u.

The macroscopic thermal capture cross section is very sensitive to the hydrogen and the chlorine concentration of the formation fluid.

Thermal Neutron Die-away Logging

The figure represents how the number of thermal neutrons

decreases with the time elapsed from the emission of neutron

impulse in the case of sandstone samples filled with different

fluids.

The behaviour of oil and fresh water filled samples is the same since the hydrogen

concentration of these fluids are very similar, and there is no

appreciable chlorine content.

But the rate of thermal neutron capture is higher in the sample filled with salt water due to the presence of chlorine.

The difference in the rate of thermal neutron capture is reflected by the

different slopes of lines and half-time of neutrons (t_1/2).

Thermal Neutron Die-away Logging

The table shows the macroscopic thermal capture cross section

and the half-time of neutrons for some rocks and materials.

Sigma is often used in practice to simply refer to the macroscopic thermal capture cross section.

The sigma of rock matrices generally less than 10 cu.

(because of the lack of effective neutron absorbers).

So, the sigma of a rock formation primarily depends on the

porosity, water saturation and salinity of formation water.

Material _a[cu.] t_1/2 [s]

Limestone, ϕ=0 7 450

Water filled limestone,

ϕ=10% (10% NaCl) 12.1 262

Water filled limestone,

ϕ=30% (10% NaCl) 22.3 143

Sandstone, ϕ=0 3.5 912

Water filled sandstone,

ϕ=10% (10% NaCl) 8.9 354

Water filled sandstone,

ϕ=30% (10% NaCl) 19.8 159

Clay 20 - 40 160 - 80

Anhydrite, ϕ=0 12.1 262

Dolomite, ϕ=0 6.8 533

Fresh water 22.2 142

Oil 22.2 142

Salt water (3% NaCl) 31.7 100

Salt Water (10% Nacl) 56 56

Halite (NaCl) 726 4.3

Portland cement ~ 13 ~ 240

Iron 200 15.7

Thermal Neutron Die-away Logging

The sigma of oil is approximately the same as that of fresh water but it is less than that of salt water.

Consequently, if the formation water is salt water, increasing oil saturation decreases the value of sigma.

The range of sigma expected in well logging extends from 0 to 60 cu.

The graph shows how the sigma of

water depends on the salinity.

Thermal Neutron Die-away Logging

The most important applications:

•

determination of oil/salt water (O/W) contacts

•

indicating the places of salt water inflows,

•

estimation of salt water saturation of oil-bearing formations,

•

monitoring the change in the salt water saturation every half-year or year by means of succeeding TDT logging runs.

The contact between oil and water phases appears on the log when the formation water is salt water.

In salt water filled zones, the count-rate of capture gamma ray is less, and the macroscopic thermal capture cross section is greater because of the increased concentration of chlorine.

There are regions (e.g. Carpathian basin) and fields where the

salinity of formation water is not sufficiently high to exploit the

benefit of this logging method.

Thermal Neutron Die-away Logging

Minimum requirements for the reliable determination of water saturation from TDT logging:

• salinity of formation water  100 000 ppm (~100 g/l),

• formation porosity  15 %.

Water inflow is a natural consequence of the production after some time, because the production results in the gradual raise of O/W contact.

If TDT logging is performed in the same well between times (e.g. once or twice a year), the changes in the salt water saturation of reservoir zones can be investigated.

It is worth executing the first TDT logging in the open hole portions of the borehole (directly after drilling), because this log carries information about the original O/W contacts and water saturations of the reservoir zones.

A TDT log made in an open hole is regarded as the reference log for monitoring the change in levels of O/W contacts and salt water

saturation. This reference log records the initial conditions, and the logs made later are compared to it.

Thermal Neutron Die-away Logging

The original level of O/W contact appears on the resistivity logs made in the open hole portion. It is indicated by the arrows assigned to symbol A.

Ten years after the well

completion, the capture

gamma ray curves of

two counting gates

show the new raised

level of O/W contact at

the arrows assigned to

symbol B.

Thermal Neutron Die-away Logging

Response equations for quantitative evaluation

1. Clean porous formations filled with a single fluid phase:

Σ = 𝜙Σ_{𝑓𝑙𝑢𝑖𝑑} + 1 − 𝜙 Σ_𝑚𝑎



(or

) sigma of the formation coming from the TDT log

ϕ porosity of the formation coming from other logs (e.g.

CNL, DEN, ACL)

_fluid

sigma of the pore fluid

The type of fluid must be known (fresh water, salt water or oil). If there is a fluid sample from the reservoir (e.g. drill-stem test, formation tester), the identification is not problematic. The  values of different fluids are found in tables of logging tool responses.

The salinity of formation water should also be known for formations saturated with salt water, because it highly controls the value of _w. The salinity can be directly measured on fluid samples. Its indirect determination requires the calculation or measurement of resistivity of formation water (R_w).

Thermal Neutron Die-away Logging

Response equations for quantitative evaluation

Remember that R

can be estimated from SP curves under certain conditions. The concentration of NaCl can be read from a nomogram representing the quantitative relationship among the resistivity of formation water, the formation temperature and the salinity.

_ma

sigma of rock matrix

If the type of rock matrix is known, the

is found in a table of logging tool responses.

If it is not known a priori,

can be calculated in a water-filled zone (S

Σ_𝑚𝑎 = Σ − 𝜙Σ_𝑤 1 − 𝜙

Thermal Neutron Die-away Logging

Nomogram for determining the NaCl concentration

Schlumberger: Log interpretation charts 2009 edition

Thermal Neutron Die-away Logging

Response equations for quantitative evaluation

2. Clean porous formations filled with two different fluid phases (oil &

salt water):

Σ = 𝜙𝑆_𝑤Σ_𝑤 + 𝜙 1 − 𝑆_𝑤 Σ_𝑜 + 1 − 𝜙 Σ_𝑚𝑎

_w sigma of formation water

It can be measured on a fluid sample taken from the reservoir. It can also be derived from the calculated salinity of formation water in a water-filled zone of the reservoir (S_w= 100%)

_o sigma of oil

It can be measured on fluid samples or obtained from tables.

The (salt) water saturation of an oil-bearing zone:

𝑆_𝑤 = Σ − 𝜙Σ_𝑜 − (1 − 𝜙)Σ_𝑚𝑎 𝜙(Σ_𝑤 − Σ_𝑜)

Thermal Neutron Die-away Logging

Response equations for the quantitative evaluation

3. Shaly formations filled with two different fluid phases (oil & water):

Σ = 𝜙𝑆_𝑤Σ_𝑤 + 𝜙 1 − 𝑆_𝑤 Σ_𝑜 + 𝑉_𝑠ℎΣ_𝑠ℎ + 1 − 𝜙 − 𝑉_𝑠ℎ Σ_𝑚𝑎

V

shale volume fraction coming from the evaluation of other logs (e.g. GR),

_sh

sigma of shale taken as a representative value of TDT log opposite adjacent shale beds.

The (salt) water saturation of an oil-bearing zone:

𝑆

= Σ − 𝜙Σ

− 𝑉

Σ

− (1 − 𝜙 − 𝑉

)Σ

𝜙(Σ

− Σ

)

Thermal Neutron Die-away Logging

Determination of the change in water saturation between two runs of TDT logging made in different times (reservoir monitoring)

Σ₁ = 𝜙𝑆_𝑤1Σ_𝑤 + 𝜙 1 − 𝑆_𝑤1 Σ_𝑜 + 1 − 𝜙 Σ_𝑚𝑎 Σ₂ = 𝜙𝑆_𝑤2Σ_𝑤 + 𝜙 1 − 𝑆_𝑤2 Σ_𝑜 + 1 − 𝜙 Σ_𝑚𝑎

Σ₂ − Σ₁ = 𝜙 𝑆_𝑤2 − 𝑆_𝑤1 Σ_𝑤 − Σ_𝑜 Δ𝑆_𝑤 = ΔΣ

𝜙(Σ_𝑤 − Σ_𝑜)

₁

comes from the first TDT log,

₂

comes from the second TDT log made some months or years after the previous one.

Notice that the last formula which gives the change in water

saturation does not require the knowledge of

Thermal Neutron Die-away Logging

Example

Two zones were separated within a reservoir. The lower zone (zone A) is water-bearing without hydrocarbon content.

The upper zone (zone B) is oil-bearing, but it contains some amount of water, as well.

TDT logging was made in the well. The following data are known from the cased hole logging and the evaluation of former open hole logging operations.

Zone A

Count rate of gamma ray in the first counting gate: N_1=6600 cps Count rate of gamma ray in the second counting gate: N_2=1300 cps Time difference between the two counting gates: t=300 s

Level of background gamma ray: N_bk=400 cps Porosity of the zone: _A=26 %  0.26

Resistivity of formation water: R_w=0.049 m at T=68 °F

Thermal Neutron Die-away Logging

Zone A

The equivalent salinity of formation water is determined from the resistivity and temperature data by means of an appropriate nomogram.

c_{eq_NaCl}=210 000 ppm

The sigma of water (_w) can be obtained from the salinity since the relationship is known from laboratory measurements:

_w=98 cu.

This value is also valid for zone B since both zones belong to the same reservoir.

Zone B

Count rate of gamma ray in the first counting gate: N_1=12 000 cps Count rate of gamma ray in the second counting gate: N_2=5150 cps Time difference between the two counting gates: t=300 s

Level of background gamma ray: N_bk=400 cps Porosity of zone: _B=28 %  0.28

The sigma of oil is also known:

_o=22.2 cu.

Thermal Neutron Die-away Logging

Task 1

Let us calculate the water saturation in zone B. (S_w=?)

In order to determine the water saturation in zone B, the sigma of rock matrix (_ma) is needed to know. The value of this parameter can be obtained from a water-filled zone (zone A).

Step 1

Calculating the sigma of zone A Σ_𝐴 = 10.5

Δ𝑡 𝑙𝑔 𝑁_{𝛾1𝑐𝑜𝑟𝑟}

𝑁_{𝛾2𝑐𝑜𝑜𝑟} = 10.5

300 𝑙𝑔6200

900 = 0.0293 1

𝑐𝑚 = 29.3 𝑐𝑢

where N_1corr and N_2corr the count rates of gamma ray corrected for the background radiation: N_corr= N_-N_bk

The sigma of rock matrix can be calculated by means of the response equation:

Σ_𝑚𝑎 = Σ_𝐴 − 𝜙Σ_𝑤

1 − 𝜙 = 29.3 − 0.26 ∙ 98

1 − 0.26 = 5.2 𝑐𝑢

Thermal Neutron Die-away Logging

Task 1 Step 2

Calculating the sigma of zone B Σ_𝐵 = 10.5

Δ𝑡 𝑙𝑔 𝑁_{𝛾1𝑐𝑜𝑟𝑟}

𝑁_{𝛾2𝑐𝑜𝑜𝑟} = 10.5

300 𝑙𝑔11600

4750 = 0.0136 1

𝑐𝑚 = 13.6 𝑐𝑢

Now the water saturation can be calculated by means of the response equation:

𝑆_𝑤 = Σ_𝐵 − 𝜙Σ_𝑜 − (1 − 𝜙)Σ_𝑚𝑎

𝜙(Σ_𝑤 − Σ_𝑜) = 13.6 − 0.28 ∙ 22.2 − (1 − 0.28) ∙ 5.2 0.28 ∙ (98 − 22.2)

= 0.172 → 17.2%

The reservoir was logged a year after, and the data of TDT logging for zone B are the following:

N_1=11 000 cps N_2=5000 cps t=300 s N_bk=400 cps.

Task 2

Let us calculate the change in water saturation between the two runs of TDT logging.

Thermal Neutron Die-away Logging

Task 2 Step 1

Calculating the sigma of zone B for the second run Σ_𝐵2 = 10.5

Δ𝑡 𝑙𝑔 𝑁_{𝛾1𝑐𝑜𝑟𝑟}

𝑁_{𝛾2𝑐𝑜𝑜𝑟} = 10.5

300 𝑙𝑔 10600

4600 = 0.0127 1/𝑐𝑚 = 12.7 𝑐𝑢 The change in sigma of zone B:

_B = _B1 - _B2 =13.6 - 12.7 = 0.9 cu Step 2

Calculating the change (increase) in water saturation : Δ𝑆_𝑤 = ΔΣ_𝐵

𝜙(Σ_𝑤 − Σ_𝑜) = 0.9

0.28 ∙ (98 − 22.2) = 0.042 → 4.2%

So, the water saturation at the second logging operation is:

S_w2 = S_w1 + S_w = 17.2 + 4.2 = 21.4 %