Applied geophysics Well logging Part 4

Applied geophysics

Well logging

Part 4

edited by P. Vass

for Petroleum Engineer MSc Students

There are three conventional porosity logging methods:

• density logging,

• neutron porosity logging,

• sonic or acoustic logging.

Two of them, the density and neutron logging, belong to the group of

radioactive and nuclear measurements.

Although they are called “porosity” logging methods, none of them

measures the porosity directly.

For all the three methods, the value of the measured quantity is affected by

not only the formation porosity but also other factors, such as shale or clay

volume fraction, fluid content, rock matrix. Thus, the corrections of these

disturbing effects are necessary for the estimation of formation porosity.

If the types of fluid and matrix are known or can be determined from other

log curves, the porosity of a clean (non-shaly) formation can be computed

easily from the porosity log data.

The depth of investigation is typically shallow (n x cm – n x 10 cm) for all

these methods, so most of the detected effects come from the flushed

zone.

Porosity measurements

Physical principles of the measurement

Medium-high energy gamma rays (0.2-2.0 MeV) are emitted from a

chemical source (usually Cesium 137), which is placed into the skid plate of

a density logging tool (the encapsulated source must be driven in a

threaded hole on the surface before lowering down the tool, and it must be

screwed off after the tool has been removed from the hole).

A focused beam of gamma rays penetrates into the formation and most of

the gamma photons interact with the atomic electrons of the formation.

Two interactions have important role from the point of view of formation

density logging:

• Compton scattering (Compton effect),

• photoelectric absorption (photoelectric effect).

For Compton scattering, a gamma photon of medium energy (0.5-1.5 MeV)

collides with one of the electrons of an atom. The gamma ray transfers a

portion of its energy to the electron and leaves the atom with reduced

energy in a modified direction. Both the energy and the direction of

propagation of gamma ray change due to the interaction. As a result of

successive scattering events, the energy of gamma photons gradually

decrease below 150 keV.

Density logging

If the energy level of a gamma photon decreases below 150 keV, the

occurrence of a photoelectric absorption will become more and more

probable.

In the course of a photoelectric effect, a low-energy gamma photon

collides with an atomic electron.

The electron absorbs the gamma ray, which disappears and transfers its

entire energy to the bound electron. If the energy of the incident gamma

ray is sufficiently high, the exited electron can leave the atom

(photoelectron).

Due to the gamma ray absorption, this interaction decreases the number

of gamma photons per unit volume in the formation.

Schematic of Compton scattering Schematic of photoelectric absorption

Density logging

As a result of these two interactions, both the number and the average

energy of gamma rays decrease with the distance from the source.

The rate of change depends on the properties of the formation (rock

matrix, porosity, fluid content etc.).

Two detectors (a near and a far detector) in the tool measure the number

of gamma rays backscattered from the rock formation in the unit of counts

per second (cps).

The higher is the average electron density (number of electrons per unit

volume) of the formation near the logging tool the lower is the detected

count rate (or counting rate). Namely, the electron density controls the

probability of both interactions to occur.

The ratio of near-to-far detector count rate relates to the average electron

density of the formation.

For the most frequent elements in the Earth’s crust, the electron density is

proportional to the atomic mass number and the mass density of materials.

Thus, the ratio of the near-to-far detector count rate can be converted into

the unit of bulk density (g/cm3) by means of a relationship coming from a

appropriate calibration procedure.

Density logging

An advanced variants of the conventional density logging is the so-called

spectral-density (Z-density logging or Litho-Density logging).

In a spectral density tool, both detectors measure the count rates of two

separated energy ranges simultaneously.

The count rates of higher energy gamma rays (coming from Compton

scattering) relates to the bulk density, while the count rates of lower

energy gamma rays are chiefly affected by the photoelectric absorption.

By means of the joint application of these detector count rates, not only

the bulk density but also the so-called photoelectric factor of the

formations can be estimated.

While the bulk density relates to the porosity of formation, the photoelectric

factor characterizes the lithology of the formation (it primarily depends on

the average atomic number of the elements forming the rock).

The photoelectric factor is just less dependent on the porosity and the fluid

type.

Density logging

Operational conditions of density logging:

• the tool can be run either in open holes or in cased holes,

• it requires a decentralized position in the borehole because of its

shallow investigation depth (15-20 cm),

• there is no limit for the types of borehole fluids (gas or air, water or

water-based mud, oil or oil-based mud can be used).

http://www.gowellpetro.com/product/litho-density-logging-tool-ldlt.html

A DC motor actuated backup

arm opposite the skid plate

(including the sensors and

source) holds the density tool

against the borehole wall.

The movement of the arm is

calibrated to indicate borehole

diameter.

Density logging

Figure: Spectral density tool, SDL (Halliburton)

Daniel A. Krygowski: Guide to Petrophysical Interpretation

The ratio of the near-to-far detector count rate is

converted to density. The conversion is based on a

calibration procedure which requires calibrator

blocks with known mass densities (a magnesium

block with a density of 2.804 g/cm3, and an

aluminium block with a density of 1.78 g/cm3).

For density logging, it is important to distinguish the

• bulk density (b or RHOB),

• from the matrix density (ma).

The bulk density is the density of the entire formation

(includes solid and fluid parts) and indirectly

measured by the logging tool.

The matrix density is the density of the solid

framework of the rock (without any shale and clay

components).

The bulk density of a non-porous clean rock is

identical with the matrix density of the rock.

Density logging

Presentation of density log curve

The bulk density curve (RHOB in g/cm3) is displayed in the merged tracks

of 2 and 3 or separately in track 3.

A correction curve (DRHO in g/cm3) is also displayed with it.

This curve indicates the magnitude and the sign of the correction added to

the bulk density curve in order to decrease the effects of the borehole on

the measurement (primarily the effects of the mud cake thickness and

density are corrected).

The density correction curve is used as a quality control (QC) indicator of

the measurement.

Whenever the absolute value of the correction curve (DRHO) exceeds

0.15 g/cm3, the value of the bulk density (RHOB) is not reliable.

A density-derived porosity curve (DPHI) is sometimes presented along

with the bulk-density (RHOB) and correction (DRHO)

curves. This computed curve is not corrected for the effects of shale or

clay and low density fluids (e.g. gas).

Track 1 usually contains a gamma ray (GR) and a caliper log curve (CAL).

Density logging


Density logging

Interpretation goals

• determination of porosity (from bulk density, RHOB),

• lithology identification (with acoustic and/or neutron logs)

• gas indication (with neutron logs).

• production of synthetic seismograms (with acoustic logs).

• determination of formation mechanical properties (with full wave

acoustic logs).

• determination of clay content (shaliness) (with neutron logs).

• borehole size (from an attached caliper).

Determination of formation porosity

The measured bulk density (b) of a clean formation primarily depends on

the matrix density, the porosity, and the density of the fluid in the pores.

To determine the density-derived porosity of a clean formation, the matrix

density and the type of fluid in the formation must be known.

Density logging

The formula by which the density-derived porosity can be calculated is

based on the relationship below:

𝜌𝑏 = 𝜙 ∙ 𝜌𝑓𝑙𝑢𝑖𝑑 + (1 − 𝜙) ∙ 𝜌𝑚𝑎

where is the porosity, fluid is the density of the fluid in the pore space,

ma is the density of matrix, and b is the measured bulk density.

By the arrangement of the formula, we can calculate the density-derived

porosity of a clean formation saturated with a single fluid phase:

𝜙𝐷 =𝜌𝑚𝑎 − 𝜌𝑏

𝜌𝑚𝑎 − 𝜌𝑓𝑙𝑢𝑖𝑑

George Asquith and Daniel Krygowski: Basic Weil Log Analysis

Because the matrix density varies in a

wider range than the fluid density,

errors in estimating the matrix density

have a larger effect on the calculated

porosity.

Density logging

Correction for hydrocarbon

Where the depth of invasion is very shallow, the measured bulk density is

also affected by the formation fluid.

In the case of low density hydrocarbons, the density-derived porosity is

always greater than the actual porosity.

Oil (~0.8 g/cm3) has not a significant effect on the density-derived porosity,

but low pressure gas has (gas effect).

In the cases of formations saturated with gas in the vicinity of the

borehole, the substitution of actual density of gas (gas) in the porosity

formula as a density of fluid (fluid) is not enough to compensate the effect

of gas.

An apparent gas density (a,gas) must be computed by taking into account

the composition and the actual density of gas, as well as the formation

temperature and pressure.

Density logging

Malcolm Rider: The Geological Interpretation of Well Logs

Some typical density log responses

Neutron porosity logging


Neutron is a subatomic particle without electric charge.

Its mass is almost the same as that of a proton (slightly larger).

Normally, neutrons are located in the nuclei of atoms.

Generally, a chemical neutron source (a mixture of americium-beryllium,

Am-Be) is used for emitting high energy neutrons (4-6 MeV) with high

initial velocity (> 103 km/s) during the operation of neutron logging.

The emitted neutrons penetrate into the formation and collide with the

nuclei of atoms.

Due to the successive collisions, neutrons gradually lose their energy,

which entails their slowing down.

Below a certain energy level, the nuclei of atoms are already able to

absorb (or capture) the neutrons, which transmit the rest of their kinetic

energy to the nuclei.

From an energetic point of view, the „lifetime” of a free neutron (the length

of time between its emission and capture) in the formation can be divided

into the following phases:

• fast neutron phase,

• slowing-down phase,

• diffusion phase,

• and absorption phase.

All these phases generally lasts less than a millisecond.

The classification of neutrons is based on their energy:

high energy > 10 MeV

fast neutrons 10 keV – 10 MeV

intermediate 100 eV – 10 keV

slow 10 eV – 100 eV

epithermal 0.2 eV – 10 eV

thermal 0.025 eV

As a neutron is travelling farther from the source its energy is decreasing,

so the density of higher energy neutrons (number of neutron per unit

volume) decreases, but the density of lower energy neutrons increases

with the distance from the source.


Depending on the energy of neutron and the properties of a nucleus,

different types of interactions can occur between them.

In the fast neutron phase, the neutrons have sufficient energy to excite or

activate the nuclei.

The exited nuclei emit gamma rays with characteristic energies in order to

calm down. The activated nuclei decay into other isotopes, and gamma

ray emission also occurs.

In the course of inelastic scattering, an incident fast neutron collides with

a nucleus. The neutron transmits some part of its energy to the nucleus,

which gets into an excited state. The neutron leaves the atom with

reduced energy in a modified direction. After a while, the excited nucleus

emits a gamma photon. The energy of the gamma ray is specific to the

nucleus.


When the neutron has already lost the significant part of its initial energy

due to the successive inelastic collisions, it enters the slowing down

phase. In this phase, the typical interaction between neutrons and nuclei is

the so-called elastic scattering.

During elastic scattering, the incident neutron has not enough energy to

excite the nucleus, but it can increase the kinetic energy of the nucleus by

their collision.

After the collision, the neutron of reduced energy leaves the nucleus in a

modified direction.

As a result of the successive interactions, neutrons slow down to thermal

velocities corresponding to energies of around 0.025 eV within a few

microseconds.


Thermal neutrons are already in their absorption (or thermal capture)

phase.

In this phase, thermal neutrons propagate in the formation by diffusion.

They travel randomly without losing major energy until they have been

captured by the nuclei of atoms (such as chlorine, hydrogen, or silicon).

A nucleus which captures a low energy neutron gets into an excited state

(it has some extra energy).

Because the nucleus is not able to stay in such a state, calms down after

a while by releasing some plus energy in the form of gamma ray.

The energy of emitted gamma ray is specific to the emitting nucleus.


From the perspective of porosity

determination, the elastic scattering of

neutrons is the most important

interaction.

In this process, the relative mass of the

nucleus determines how much energy

the neutron loses due to the collision.

The smaller is the relative mass of the

(target) nucleus the greater is the

average energy loss per collision.

Because the nucleus of a hydrogen atom

is a single proton, whose mass is very

similar to that of a neutron, hydrogen has

the greatest slowing down power.

A collision with a nucleus of a heavy

atom changes rather the direction of

neutron propagation than its kinetic

energy.


The table shows how many elastic collisions with the nuclei of different

elements are needed, on average, for a neutron with an initial energy of 2

MeV to slow down to thermal energy of 0.025 eV.

Chemical

element

Atomic number

(Z)

Average number of

elastic collisions

hydrogen 1 18

carbon 6 114

oxygen 8 150

silicon 14 257

chlorine 17 329

calcium 20 368

The table unambiguously indicates that slowing down of neutrons

primarily depends on the amount (concentration) of hydrogen in the

formation.


In the case of a widely used (borehole)

compensated neutron logging tool geometry (CNL),

two detectors with different distance from the

neutron source are located in the tool.

Both the near and the far detector counts the

number of backscattered thermal neutrons in unit

time.

The detector count rates are inversely proportional

to the hydrogen concentration of the formation.

Assuming that all the hydrogen resides in the pore

space of the formation (as water or hydrocarbons),

the hydrogen concentration relates to the formation

porosity.

Operational conditions:

The tool can be run in both open holes and cased holes.

But, it requires a decentralized position in the borehole, which is

implemented by means of a steel bow spring.

It can be used with any type of borehole fluids (gas or air, water or water-

based mud ,oil or oil-based mud).


Calibration

The primary calibration standard for the neutron porosity logging tools is the

API test pit of the University of Houston.

It contains four zones with different but known porosities:

• a zone of pure water, which represents a porosity of 100%,

• a zone of Carthage Marble with a porosity of 1.9%,

• a zone of Indiana Limestone with a porosity of 19%,

• a zone of Austin Limestone with a porosity of 26%.

In the test pit, the manufacturers calibrate their neutron tools in the so-

called limestone (or neutron) porosity unit. The secondary workshop

standards (water-filled calibrating tanks by which environments with different

porosities can be simulated) are also constructed for the logging tools to

replace the test pit when repeated calibrations become necessary.

Wellsite verification of the tools is also performed before and after logging by

means of a portable calibrator providing a known thermal neutron count rate.

For other lithology (not limestone), the measured limestone porosity value

can be converted to a porosity value of a given rock matrix by using

correction data from lithology tables.


Presentation of neutron porosity logs

Neutron porosity curves are commonly displayed in porosity units (% or

volume fraction) in the merged tracks of 2 and 3 or separately in track 3.

Generally, the scale is from 45% (0.45) to -15% (-0.15).

Figure: the structure of the API test pit

used as a primary calibration standard for

neutron logging tools.

The measured porosity value of a

calibrated CNL tool is only valid for a clean

(non-shaly), water-filled limestone

formation.

In other cases, the measured value has to

be corrected for the effects of the factors

(e.g. lithology, hydrocarbon, shale or clay).



Presentation of neutron porosity logs

Since a neutron tool are generally run

with combination of a density tool, the

neutron porosity (NPHI) and the bulk

density (RHOB) or density-derived

porosity (DPHI) log curves are

displayed together.

Track 1 usually contains a gamma ray

(GR) and a caliper log curve (CAL).



Interpretation goals:

• porosity determination,

• lithology identification (with sonic and/or density logs),

• gas indication (with density logs),

• determination of clay content (shaliness) (with density logs),

• correlation (especially in cased holes).

Porosity determination

The neutron slowing down power of a given material is quantified by the so

called hydrogen index of the material (HI).

It gives how rate the unit volume of a given material slows down the

neutrons by elastic scattering compared to the unit volume of pure water at a

temperature of 24 °C.

Its value ranges from 0 to 1 (pure water has the value of 1).

For materials containing hydrogen, the value of HI mainly depends on their

hydrogen concentration.

But HI also depends on the atomic number of elements, namely HI

decreases with the increase of atomic number.


Porosity determination

In the case of clear, water-filled limestone formations, the measured

(limestone calibrated) neutron porosity (NPHI or N) gives the estimation of

the true porosity ().

The neutron tool response equation for that case:

𝜙𝑁 = 𝜙 ∙ 𝐻𝐼𝑊 + (1 − 𝜙) ∙ 𝐻𝐼𝐿𝑀

where HIw is the hydrogen index of water (=1) and the HILM is the hydrogen

index of limestone (~ 0).

If the rock matrix is different from limestone, the effect of the rock matrix

must be corrected by means of a graph similar to the one below.

Malcolm Rider: The Geological

Interpretation of Well Logs


For the neutron porosity corrected for the effect of lithology (N,corr), the

following equation can be written:

𝜙𝑁,𝑐𝑜𝑟𝑟 = 𝜙 ∙ 𝐻𝐼𝑓𝑙𝑢𝑖𝑑 + 1 − 𝜙 ∙ 𝐻𝐼𝑚𝑎

where HIfluid is the hydrogen index of pore fluid and the HIma is the

hydrogen index of the given matrix.

By the arrangement of the equation, the porosity of the formation can be

calculated:

𝜙 =𝜙𝑁,𝑐𝑜𝑟𝑟 − 𝐻𝐼𝑚𝑎

𝐻𝐼𝑓𝑙𝑢𝑖𝑑 − 𝐻𝐼𝑚𝑎

The formula enables us to take into account the effect of fluids whose HI is

different from that of the pure water (e.g. salt water, oil, gas).

However, for gas bearing formations, the application of additional correction

is needed to obtain a reliable porosity value.

The decrease in measured neutron porosity caused by the presence of gas

is called gas effect.

Because shale minerals contain hydrogen in their crystal lattice and are

able to adsorb lots of water on their surface, the shale or clay content

increases the measured neutron porosity compared to the true porosity.

Therefore, the shale correction is very important for shaly formations.


Some typical neutron porosity log responses


Negative values of the neutron

porosity indicate that the slowing

down power of the rock is less

than that of the rock used for the

calibration (limestone).

In this case, the measured values

must be corrected for the lithology.

Neutron porosity values marked by

an asterisk refer to fresh water

filled formations and the

Schlumberger CNL tool.

Acoustic wave theory

Rocks can be considered as elastic bodies from the perspective of

acoustic wave propagation.

The acoustic logging method is based on the fact that high frequency

(tens of kHz) ultrasonic waves coming from a transmitter are able to

propagate through rocks.

During the acoustic wave propagation spatial and temporal variations

in the states of mechanical stress and strain (deformation) is taking

place within the medium (rock), which entails kinetic energy transfer.

The states of stress and strain are in close relation. They mutually

modify each other within the medium when a wave is produced at a

given point (the force acting on the point suddenly changes).

It is important to note that not the particles travel through the medium

during the propagation of an elastic wave, but the perturbation in the

states of stress and strain.

The particles of a medium are oscillating about their equilibrium

positions during the wave propagation.

Sonic or acoustic transit time logging

There are two principal types of elastic waves:

• body waves

• and interface or surface waves.

Body waves travel three-dimensionally within an elastic medium.

Interface or surface waves propagate along and near by the interfaces of

two different media (e.g. along the borehole wall).

Body waves

Two types of body waves are distinguished according to the deformation

patterns propagating through the medium.

When periodic alternations of contraction and expansion are taking place

during the wave propagation, the particles are oscillating along axes

parallel to the direction of the wave propagation.

That type of body wave is called compressional wave or P-wave (primary

wave).


Body waves

The compressional wave belongs to the group of longitudinal waves.

Compressional wave motion entails both volume change and deformation.

It can propagate in both solids and fluids.

http://www.geo.mtu.edu/UPSeis/waves.html

The figure illustrates the deformation

pattern during the propagation of a

compressional wave.


Body waves

The other type of body waves is called shear wave or S-wave (secondary

wave)

In the case of a shear wave only the shear component of the stress field

plays role in the shear wave motion.

The particles of the medium are oscillating along axes perpendicular to the

direction of wave propagation.

This type of wave belongs to the group of transverse waves.

The propagation of shear waves entails only deformation without any

volume change in the medium.

A shear wave cannot propagate in fluids because fluids are not able to

resist shear forces.


The deformation pattern of the propagation of a shear wave.

http://www.geo.mtu.edu/UPSeis/waves.html



High frequency (tens of kHz) acoustic pulses are emitted periodically

from a transmitter installed in the logging tool.

First the impulse-like ultrasonic wave packet (or wave trains)

propagates through the mud (mud wave) and arrives at the borehole

wall (which is a boundary between two media of different elastic

properties).

Here, it changes into different types of acoustic waves which travel on

their own way within the rock or along the borehole wall. In fact the

energy of incident mud wave divides into different parts propagating in

the forms of different waves.

From porosity determination point of view the critically refracted

compressional wave has essential importance.

The critically refracted compressional wave propagates within the rock

formation. Its velocity depends on the density and elastic properties of

the rock. The direction of wave propagation is parallel to the borehole

wall, and the wave-motion causes small vibrations along the borehole

wall.



Thus, the points of the borehole wall act as secondary sources of waves,

which means that secondary waves are generated and propagate in the

mud toward the sonic logging tool.

These secondary waves are detected by the receiver located at some

distance from the transmitter in the logging tool.

The time elapsed between the generation of the wave and the detection of

the first wave arrival at the receiver is recorded. This one-way time is

called (first) arrival time.

The simplest form of a sonic logging tool contains two receivers located at

different distances from the transmitter (3' and 5' or 2' and 4').

It is clear that the sonic wave arrives later at the farther receiver, so the

arrival time of the far receiver is greater than that of the near one.

The difference of the two arrival times is compared with the distance

between the receivers (span), and the ratio of time difference to distance is

called interval transit time or interval travel time. The word interval is often

omitted in texts when the term is frequently used. The usual notation of

this inverse velocity is t or DT, the applied unit is s/ft or s/m.



So, the interval transit time gives the time necessary for the compressional

wave to travel one foot (or metre) distance in the formation collaterally to

the borehole wall.

As the interval transit time is actually the reciprocal of the wave velocity, it

is also called slowness.

If a new acoustic pulse is generated by the transmitter, a synchronizing

signal is sent to each receiver to start listening.

By selecting long enough time between two successive acoustic pulses,

the detection of a wave coming from a previous pulse after the next has

been generated can be avoided.

When not only the first arrival but the entire acoustic waveform belonging

to a generated acoustic pulse is recorded by the receivers, arrival times

and amplitude attenuations (energy decrease) of additional wave

components can also be investigated.


The different parts of a full waveform represent different types of acoustic

waves.

The most important ones are the following:

• compressional wave or P wave (it gives the standard interval transit

time, because it is the fastest of all waves, DTC),

• shear wave or S wave (it generally follows the compressional wave in

most cases, DTS),

• and Stoneley wave (it is an interface wave propagating along the

borehole wall, and generally slower than the shear wave).


Acoustic pulse generation

• a single pulse typically ranges from 100 to 200 s depending on the

type of logging tool,

• the time gap between two neighbouring pulses is about 50 ms (at least

250 times longer than the duration of a pulse,

In practice, more than one pulse is used to determine a single (average)

interval transit time value for a given depth level.



Full acoustic waveform recorded by a receiver

Conventional acoustic logging used for porosity determination records only

the first arrival time of the waveform, which belongs to the compressional

wave.



Borehole-compensated acoustic tool geometry (BHC)

It has two transmitters located at the lower and upper parts of the logging

tool (T1, T2).

Two receivers belong to each transmitter (R1 & R3 T1, R2 & R4 T2)



The receiver which is closer to its transmitter is called near

receiver, and the farther one is the far receiver.

The first arrival of the far receiver is detected later than that of

the near receiver.

The time difference gives how much time is necessary for the

compressional wave to run a distance identical with the span

of receivers in the formation collaterally with the borehole wall.

The time difference divided by the span of receivers gives the

interval transit time of compressional wave (or compressional

slowness).

By using two pairs of transmitters , two independent interval

transit times are measured for each depth level.

If the diameter varies near the logging tool and/or the logging

tool is not centralized perfectly, the values of interval transit

time will not be identical.


Borehole-compensated acoustic tool geometry

By computing the average of two interval transit times, the unwanted

effects of the borehole geometry (asymmetrical shape of the borehole) and

logging tool position (sloped tool axis) can be eliminated.



Δ𝑡1 =𝑡1,3 − 𝑡1,1

𝐿1,3t1,3 first arrival time measured by R3

t1,1 first arrival time measured by R1

L1,3 distance between R1 and R3

t1 interval transit time for T1

Δ𝑡2 =𝑡2,2 − 𝑡2,4

𝐿2,4t2,2 first arrival time measured by R2

t2,4 first arrival time measured by R4

L2,4 distance between R2 and R4

t2 interval transit time for T2

Δ𝑡 =Δ𝑡1 + Δ𝑡2

2t borehole-compensated interval transit time

(compressional slowness)


Operational conditions of borehole-compensated acoustic logging (BHC):

• the sonic porosity logging can be applied only in open holes,

• it requires centralization in holes smaller than 16 inches (frequently

used with a three-arm caliper tool),

• it requires decentralization in holes larger than 16 inches (to minimize

the signal attenuation),

• the tool must not push to the borehole wall (some stand-off is needed)

to avoid the generation of acoustic noise during the movement of the

tool,

• liquid filled borehole is required (water or water-based mud, oil or oil-

based mud) so that the coupling of acoustic waves between the logging

tool and the borehole wall will be provided.

• in air- or gas-filled borehole the measurement can not be implement.

Remark:

a simpler sonic tool geometry with a single transmitter and two receivers is

used for cement bond logging (CBL) in cased and cemented holes.


Interpretation goals

• determination of porosity (from interval transit time, DT),

• lithology identification (with density and/or neutron logs),

• production of synthetic seismograms (with the density log),

• determination of formation mechanical properties (from the full acoustic

waveform, with density log),

• detection of zones with abnormal formation pressure,

• permeability identification (from the full acoustic waveform),

• determination of cement bond quality (in a cased hole after cementing).

Presentation of conventional acoustic log data

Interval transit time (DT) is usually displayed in tracks 2 and 3 of a log.

A computed, sonic-derived porosity curve (SPHI or ϕS) is sometimes

displayed in tracks 2 and 3, along with the DT curve.

Track 1 usually contains a caliper (CALI), a gamma ray (GR) and a

spontaneous potential (SP) curve.




The main factors influencing the value of interval transit time:

• the mineral composition of the rock matrix,

• the porosity and the type of fluids filling the pore space,

• the rock microstructure (includes the texture and the small scale rock

structures),

• the vertical effective stress acting on the rock,

• the temperature.

The composition of rock matrix

The velocity of compressional wave in a rock depends on the density and

the elastic properties (bulk modulus, shear modulus) of the minerals

building up the solid rock framework.

If the rock matrix is made up of more than one mineral, the effect of a

component on the interval transit time of the entire rock matrix is

proportional to its volume fraction and its own interval transit time.


It can be described by the following formula:

Δ𝑡𝑚𝑎 = 𝑉1 ∙ Δ𝑡𝑚𝑎1+ 𝑉2 ∙ Δ𝑡𝑚𝑎

2+…+𝑉𝑛 ∙ Δ𝑡𝑚𝑎

𝑛

The interval transit time of minerals with higher density have lower interval

transit time in general (it means that the compressional wave propagates

faster inside them).

The interval transit time of the most important minerals are known from

laboratory measurements, and the values can be looked up in tables.

The effect of porosity and the type of fluids filling the pore space

As the porosity of the rock increases, the interval transit time also

increases.

This is because fluids filling the pore space have significantly higher

interval transit time than have the solid components of a rock.

Namely, the interval transit time of fluids primarily depends on their density

similarly to the solid materials.

So, the natural gas (because of its lowest density) increases the interval

transit time of a porous rock in the greatest measure.


Velocities of compressional wave and interval transit times for different

rock matrix and fluids.

George Asquith and Daniel Krygowski: Basic Well Log Analysis


The effect of rock microstructure

The propagation of acoustic waves in a porous rock is influenced by

among other things:

• the grain size distribution of the sediment,

• the shapes and arrangement of grains,

• the type of porosity,

• the pore size distribution.

In the case of rocks with low primary porosity (< 5-10%), mostly the rock

matrix determines the interval transit time of the rock.

For unconsolidated near-surface sediments with high porosity (40-50%),

the measured interval transit time characterizes the fluid filling the pore

space rather than the solid components.

Acoustic logging is not sensitive to the secondary porosity of rocks,

because acoustic waves are able to pass round the larger cavities and

fractures during their propagation through the rock.

So, the porosity derived from acoustic logs estimates the primary porosity

of rocks.


The influence of vertical effective stress acting on the rock

The effective vertical stress is the difference between the lithostatic (or

overburden) pressure and the pore pressure at any given depth.

𝑃𝑒𝑓𝑓 = 𝑃𝑙𝑖𝑡ℎ𝑜 − 𝑃𝑝𝑜𝑟𝑒

Because the vertical effective stress compresses the rock, it influences the

compaction of the rock and the size of the surface by which the grains are

in direct contact with each others.

With increasing vertical effective stress, the compressional wave

propagates faster in the rock (the interval transit time becomes shorter),

and the wave velocity approaches an asymptotic upper limit (velocity limit).

The effect of temperature

It was proven by the results of laboratory measurements that the velocity

of compressional wave decreases with increasing temperature.

The change in wave velocity depends on the type of rock, the porosity and

the fluid content of the pore space.


Determination of porosity (from interval transit time, DT)

The equation used for calculating the total, primary porosity is based on a

very simple rock model which is made up of a homogeneous rock matrix

and a single fluid phase filling the pore space:

Δ𝑡𝑙𝑜𝑔 = 𝜙 ∙ Δ𝑡𝑓𝑙𝑢𝑖𝑑 + 1 − 𝜙 ∙ Δ𝑡𝑚𝑎

porosity, tlog interval transit time in the formation, tma interval transit

time in the solid rock matrix, tfluid interval transit time in the fluid.

From the linear equation above, we can derive the so-called Wyllie time-

average equation (Wyllie et al., 1958):

𝜙𝑆 =Δ𝑡𝑙𝑜𝑔 − Δ𝑡𝑚𝑎

Δ𝑡𝑓𝑙𝑢𝑖𝑑 − Δ𝑡𝑚𝑎

where S is the sonic-derived porosity.

The formula is valid for clean, water-filled, consolidated rocks with primary

porosity.


Relation between interval transit time and porosity in

a dolomite formation


Correction for unconsolidated rocks

If the value of vertical effective stress at a given depth is not enough for

the compressional wave to approach the (upper) velocity limit of the rock,

the rock is regarded as unconsolidated.

Unconsolidated rocks are characterized by interval transit times greater

than 100 s/ft (~330 s/m).

These high measured values results in higher sonic-derived porosity than

the true one.

In order to correct the effect of unconsolidated rocks, an empirical

compaction factor (Cp) must be added to the Wyllie equation:

𝜙𝑆 =Δ𝑡𝑙𝑜𝑔 − Δ𝑡𝑚𝑎

Δ𝑡𝑓𝑙𝑢𝑖𝑑 − Δ𝑡𝑚𝑎⋅1

𝐶𝑝The compaction factor is obtained from the following formula:

𝐶𝑝 =Δ𝑡𝑠ℎ𝑎𝑙𝑒 ∙ 𝐶

100tsh is the interval transit time in a shale adjacent to the formation of

interest,

C is the compaction coefficient of shale (a constant which is normally 1.0)


Correction for hydrocarbon

The presence of hydrocarbon in the pore space increases the interval

transit time of a formation.

If the effect of hydrocarbons is not corrected, the sonic-derived porosity

will be higher than the actual porosity.

The following empirical corrections are proposed to eliminate the effect of

hydrocarbon on the sonic-derived porosity (Hilchie,1978):

= S 0.7 (for gas)

= S 0.9 (for oil)


Some typical acoustic log responses


Date post:	30-Dec-2021
Category:	Documents
Upload:	others
View:	5 times
Download:	0 times

Applied geophysics Well logging Part 4

Documents