Well-logging-methods_new................

Norbert Péter Szabó Ph.D., dr. habil.
university full professor
Department of Geophysics, University of Miskolc
norbert.szabo.phd@gmail.com
MSc in Earth Sciences Engineering

Petrophysics overview
Demonstration of the measuring environment
Basic petrophysical relationships
Principles of measurement techniques
Well log analysis, estimation of petrophysical parameters
Deterministic and statistical interpretation approaches
Special well-logging measurements
Well-logging inversion methodologies
Calculations using WellCad and MATLAB softwares
Well-logging methods Introduction

Serra O., 1984: Fundamentals of well-log interpretation, Elsevier.
Asquith G., Krygowski D., 2004: Basic well log analysis, Second
edition, American Association of Petroleum Geologists.
Ellis D. V., Singer J. M., 2007: Well logging for earth scientists, Second
edition, Springer.
Rider M. H., 2002: The geological interpretation of well logs, Second
Edition, Rider-French Consulting Ltd.
Schlumberger, 1989: Log interpretation principles/applications.
Schlumberger, 1989: Cased hole log interpretation
principles/applications

Well site, Drilling rig, Vehicle, Cable, Sonde,
Borehole, Drilling mud, Well log, Log header,
Observed quantity, Measuring range, Formation boundary, Petrophysical property

Depth (max. 488 m, sampling distance of 1 m)
„Carottage électrique” Pechelbronn oilfield, France (1927)
Specific resistivity (A is current electrode, M and N are potential electrodes)
Results of early scientific
research:

Ellis and Singer (2007)
Sonde used for measuring caliper with
multielectrode measuring pads on the
arms
Sonde used for measuring rock density
includes a gamma-ray source and a
gamma-ray detector
Sonde used for measuring acoustic
traveltime includes transmitters and
receivers for detecting sonic waves
Caliper sonde with one specific
resistivity rubber pad

Geological mapping by well-to-well correlation
Exploration of reserves, identification of productive zones
Determination of depth and bed thickness
Determination of lithology and mineral composition
Determination of porosity and pore geometry
Determination of water saturation and fluid type
Determination of permeability
Estimation of mineral resource and hydrocarbon reserves
Finding correlation between petrophysical properties, trend analysis
Determination of elastic parameters and in-situ stresses
Aid in calculating synthetic seismograms etc.

©Schlumberger
Caliper - the outer diameter of the
drill bit (normally 7-12 inches)
Drilling mud - to carry out drill
cuttings, to keep the drill bit cool
and lubricated, to prevent
formation fluids from entering into
the wellbore (mud column has
higher pressure than pore pressure
of the formation)
Mud filtrate - the drilling mud
invades into the porous and
permeable layers, shales and loose
formations are washed out
Mud cake - the solid particles of
the drilling mud (clay) accumulate
on the borehole wall
Well-logging methods Measuring environment

Flushed zone - the annular space
closest to the borehole, the original
pore content is flushed by the mud
filtrate, residual water and
hydrocarbon occupy the pore space
Uninvaded zone - the original pore
content is not contaminated by
mud filtrate
Invasion depth - radial distance to
which mud filtrate has invaded
(invasion diameter is normalized
with the hole diameter, in case of
the same amount of mud and
smaller porosity the invasion depth
is greater, even 10 times greater
than the hole diameter)
©Schlumberger
Well-logging methods Measuring environment

measured physical quantities
and reservoir parameters, they
are usually treated separately
from the matrix. Shale types
are disperse, laminar (thin
layers), structural
Rock matrix - the solid skeleton of the rock, which is built up from
grains (minerals) and cement. In case of simple lithology, it is
composed by one mineral, in complex lithology by the mixture of
minerals
Shale - minerals having grain sizes smaller than 0.004 mm. Clay is
composed by only clay minerals. Shale contains 50-60 % clay with
significant amount of silt and other minerals
Shale has a strong effect on the
Serra (1984)
Well-logging methods Petrophysics overview

Total porosity is the ratio of pore volume (void space between
the grains, capillary channels and bound water, cavities,
fractures, isolated pores) to the total volume of the rock
Effective porosity is the ratio of interconnected pore space
(where fluid can freely flow through the rock) to the total rock
volume, which does not contain the disperse shale volume (Vsh)
in sediments
(%)
100
V
V
t
p
t 


  (%)
100
V
1
Φ sh
t
e 




Primary porosity is the ratio of the intergranular (and inter-
crystalline) pore space generated during diagenesis to the total
rock volume (e.g. clastic rocks)
Secondary porosity is the ratio of the pore space generated after
diagenesis due to chemical or mechanical impacts (fractures,
caves) to the total rock volume (e.g. metamorphic and volcanic
rocks, carbonates)
where t, 1, 2 are total, primary and secondary porosity,
respectively
Mixed porosity is the combination of primary and secondary
porosity (e.g. in complex reservoirs)
(%)
100
)
Φ
(Φ
Φ 1
t
2 



Water saturation is the fraction of pore volume occupied by
formation water
Irreducible water saturation is the pore space filled with water
adsorbed to the clay particles and restrained in the capillaries and
brackets (Sw,irr). Its value is linearly proportional to the specific
surface (the smaller the grain size, the larger the specific surface)
Hydrocarbon saturation is the pore space filled with oil and/or gas
(%)
100
V
V
S
p
w
p,
w 

(%)
100
)
S
1
(
S w
hc 



The wetting phase (i.e. water) is
squeezed out by the non-wetting
fluid (e.g. petroleum)
Capillary pressure curves show
the relationship between the
amount of displaced water and the
applied pressure
By gradually increasing the
pressure, the water saturation
decreases down to a limiting value
(Sw,irr)
Irreducible water saturation
depends on the permeability of
the given rock in hydrocarbon
reservoirs
©Schlumberger
Sw,irr

Irreducible hydrocarbon saturation is the fraction of pore volume
filled with non-producible oil and/or gas (increases with viscosity)
Movable hydrocarbon saturation is the pore space filled with
producible oil and/or gas
The volume of hydrocarbon relative to the total volume of rock
  (%)
100
S
1
S x0
irr
hc, 


 
 
  (%)
100
S
S
S
S
S
S
1
S
S
1
S
w
x0
irr
hc,
hc
m
hc,
x0
irr
hc,
w
hc













hc
t
hc S
Φ
/V
V 


Vsh= Vcl +Vsi
Φ(Sw,mov+Sw,irr+Sg,mov+ Sg,irr +So,mov+So,irr)
Vma=ΣVma,i+Vcem
Φ +Vsh+Vma =1
Vt=1

Electric conductivity (σ) measures the ability of a rock to conduct an
electric current. Hydrocarbons, rock matrix, freshwater are
insulators, while brine conducts electricity
Electrical resistivity (ρ) is an intrinsic property of rocks that
quantifies how strongly a rock opposes the flow of electric current
where R(ohm) is electric resistance, A(m2) is cross-sectional area, L is
measured length (m), σ is electric conductivity (mmho/m)
Specific resistivity of a rock depends on porosity, resistivity and
amount of pore-fluids (i.e. saturation), salinity of pore-fluid, rock
type, texture (grain size and shape, sorting of grains, pore geometry)
(mS/m)
ρ
1000
σ
and
(ohmm)
L
RA
ρ 


Rock/fluid State Ra (ohmm)
Quartz 1012 – 3·1014
Marble 5·107 – 109
Clay/Shale 2 – 10
Sand
Brine 0.5 – 10
Oil 5 – 103
Limestone Compact 103
Sulfides <1.0
Graphite 0.1 – 10
Oil 2·1014
Distilled water 2·1014
Brine
150C, 2 kppm 3.40
150C, 10 kppm 0.72
150C, 100 kppm 0.09
150C, 200 kppm 0.06

Archie (1950)
Well-logging methods Basic petrophysical relations

Water saturation of a clean (Vsh=0) hydrocarbon reservoir can be
determined by the application of the relationship between the
resistivity of rock (R0) fully saturated with water (Sw=1) and the
resistivity of formation water (Rw)
where F is (resistivity) formation factor, Rt is true resistivity, a is
tortuosity coefficient, m is cementation exponent, n is saturation
exponent (a≈1, m≈n≈2)
The formula cannot be applied for rock matrices containing
electrically conductive mineral(s) and shaly layers
In case of high R0 and Rw (e.g. freshwater reservoirs) the formula
underestimates the formation factor
n
t
w
n
t
0
w
m
w
0
R
FR
R
R
S
Φ
a
F
and
FR
R 





Darcy’s law - the volume of fluid flowing through the rock per
unit time (in case of one phase)
where A (m2) is cross section of flow, L (m) is flow length, μ
(Ns/m2=Pa·s) is viscosity of fluid, ΔP (N/m2) is the pressure
gradient responsible for the flow, k (m2) is permeability
Kozeny equation - the amount of fluid flowing out from the
capillary per unit time (in case of small flow rate)
where r(m) is radius of capillary, L(m) is length of capillary
/s)
(m
ΔP
μL
A
k
Q 3

/s)
(m
μL
ΔP
8
π
r
Q 3
4


Permeability (K) depends on the grain size and pore geometry.
Kozeny equation derives (where a, b, c are site-specific constants)
Timur’s formula is a frequently used empirical relationship
We speak about absolute permeability if one fluid phase is present
in the pore space, effective permeability is the permeability of a
given fluid phase in the presence of other phases, relative
permeability is the ratio of effective and absolute permeability
)
m
10
(mD
S
Φ
136
.
0
K 2
15
-
2
irr
w,
4.4


b
w,irr
a
S
Φ
c
K 

With the increase of water
saturation the relative
permeability regarding to
the oil decreases, the
relative permeability for
the water increases
In case of the residual oil
saturation the relative
permeability for oil is 0,
then only water can be
produced from the
reservoir
©Schlumberger

Well Log Name Sensitive to Unit
SP Spontaneous potential mV
GR Natural gamma-ray intensity API
K Spectral gamma-ray intensity (potassium) %
U Spectral gamma-ray intensity (uranium) Lithology ppm
TH Spectral gamma-ray intensity (thorium) ppm
PE Photoelectric absorption index barn/e
CAL Caliper inch
CN Compensated neutron %
CD Compensated density Porosity g/cm3
AT Acoustic traveltime µs/ft
RMLL
RS
Microlaterolog
Shallow resistivity Saturation
ohmm
ohmm
RD Deep resistivity ohmm
Well-logging methods Principles of measurement techniques

Torres-Verdín (2002)
Well-logging methods Principles of measurement techniques

Spontaneous potential (SP) is the
potential difference (mV) measured
between a surface electrode and an
electrode mounted on the sonde
Diffusion potential (Ed) - ions diffuse
into the more dilute solution (mud
filtrate when Rmf>Rw); for NaCl solution
the chloride ions have higher mobility
than sodium cations
Membrane potential (Esh≈5Ed) - shale is
an ion selective membrane, which lets
through only positive ions
Electrochemical potential is the
difference between Ed and Esh
Streaming potential (Emc, Esb) is caused
by the flow of mud filtrate through the
mud cake (or shale) as a result of
pressure difference, which is usually
negligible
Rmf>Rw
− +
Well-logging methods Spontaneous potential logging

SSP is the maximal
deflection of the SP curve
in a thick, clean, porous
and permeable bed
The theoretical value of
SSP is calculated
where Tf is the formation
temperature
C)
(
0.24T
65
k
(mV)
R
R
lg
k
SSP
0
f
w
mf





Rmf>Rw
− +

Measured SP value is affected
by
• Rmf /Rw ratio
• Layer thickness
• Resistivity of the layer (Rt)
• Resistivity of the adjacent
layer
• Borehole caliper
• Invasion parameters (Rx0, di)
• Clay/Shale volume
• Hydrocarbon content
Rmf>Rw
− +

Well-to-well correlation (made by the shape of SP curves)
Detection of permeable layers
Determination of the boundaries of permeable layers (at the
inflexion points of the SP curves) and layer thicknesses
Determination of resistivity of formation water (Rw)
Estimation of shale volume in permeable layers (Vsh)
Qualitative indication of the presence of hydrocarbons
Logging tool only works with conductive borehole fluid
It cannot be used in cased holes

Shale bed (with two sandy intervals)
Layer boundaries
Sand bed
(with thin shale layer at the bottom)
Shale base line
Sand line
Clean shale

Mark the SPSSP maximum for a
clean, water saturated, thick, porous
and permeable interval
Arps formula - correction of Rmf for
formation temperature
where Rmf,z is the measured resistivity
of mud filtrate at temperature Tz (0F)
(e.g. at the surface z=0), Tf is formation
temperature
Calculation of equivalent and true
value of Rw for the given interval
(ohmm)
6.77
T
6.77
T
R
R
f
z
z
mf,
mf



mf
mf,e
k
SSP
mf,e
w,e
w,e
mf,e
0.85R
R
,
10
R
R
R
R
lg
k
SSP 






©Reeves
Technologies

Formation temperature is required for
the determination of Rmf and Rw
In linear approximation the model is
where zf is formation depth, m is geothermal
gradient, T0 is surface average temperature
First slope m is calculated
where Tbh is temperature at the well bottom, ztd is depth of well
bottom, then Tf is estimated to arbitrary depths
Conversion from Fahrenheit to Celsius degree is T(0F)=1.8T(0C)+32
0
f
f
f T
mz
)
(z
T 

0
td
bh T
mz
T 


©Schlumberger

Pseudo Static Potential (PSP) is
the maximal SP deflection in a
shale contaminated permeable
formation
Estimation of shale volume
where α=(PSP/SSP) is the SP
reduction factor which can be
derived from observed SP
values with set of curves given
in chart books
Asquith and Gibson (1982)
(%)
100
α)
(1
Vsh 



When Rmf /Rw  1, no SP deflection develops (there can be some streaming potential
because of the different pressures of mud filtrate and formation water)
No characteristic shape of SP curves can be identified in modern hydrocarbon wells
drilled with synthetic-based muds
Normal SP - if Rmf > Rw, the permeable layer is detected by a negative value of SP (in
hydrocarbon reservoirs)
Reversed SP - if Rmf < Rw, the permeable layer is detected by a positive value of SP (in
shallow aquifers)
Shale base line shift - on longer intervals, it occurs because of the decrease of Rw
(increasing salt content) or the change in the mineral composition of shales (and the
increasing temperature)
SP currents avoid highly resistive formations and one obtains distorted SP curves
SP suppression is caused by the presence of hydrocarbons (qualitative
phenomenon, it is not suitable for the quantitative determination of hydrocarbon
saturation)
For the motion of ions causing SP phenomenon a minimal permeability (0.1 mD)
and porosity (1−2 %) are necessary, but there are no direct proportionality
between SP anomaly and these petrophysical quantities

Physical background: radioactive decay of atoms in rocks
Types of radiation are ,  and -radiation (emission of photons)
Gamma activity of rocks depends on the type and quantity of
radiating elements and rock density
Energy of photon (eV) is the amount of energy gained (or lost) by
the charge of a single electron moved across an electric potential
difference of 1 V
Gamma-ray sources in rocks are 40K, 238U, 232Th
Occurrence of potassium - evaporites, feldspars, clay minerals
(micas), granite, rhyolite, metamorphic rocks
Occurrence of uranium - uranium-oxides, uranium solutions, dark
limestone, organic materials (bituminous shale, coaly marl)
Occurrence of thorium - heavy minerals (monazite, zircon), clay (in
bound water)
Well-logging methods Natural -ray intensity logging

©
Halliburton
GR reads the natural gamma radiation of rocks in
units of cps or API (American Petroleum
Institute) based on an artificially radioactive
concrete block at the University of Houston, that
is defined to have a radioactivity of 200
(considered to be twice the radioactivity of a
typical shale)
Gamma detector is a scintillation counter
Integral measurement - the total gamma
radiation of rock is measured
Spectral measurement - gamma radiation is
measured in different energy windows
GR minimum - sand(stone), carbonates
GR maximum - clay, potassium-feldspar, mica,
sand(stone) containing glauconite or uranium
rich water

GR reading in open holes is influenced by
- Measuring instrument: statistical variation (rate of radioactive
decay varies in time), pulling speed of the sonde, dead time, length
of the detector, time constant, location of the sonde (central or
eccentric), diameter of the sonde
- Layer thickness
- Diameter of the borehole
- Density and composition of the drilling mud (e.g. bentonite mud is
radioactive)
GR reading in cased holes is influenced by
- Diameter of the casing
- Type, density and thickness of the cement sheath

Rider (2000)

Lithological classification (i.e. separation of shale and sand
layers)
Well-to-well correlation (by the shape of GR curves)
Determination of layer boundaries (at the inflexion points of GR
curves) and layer thicknesses
Estimation of shale volume (when there is not radioactive non-
clay minerals)
Determination of the types of clay minerals
Shale volume correction of probe response equations (for
quantitative interpretation)
Applicable in both open and cased holes, conductive and non-
conductive (oil-based) muds and air-drillings

Ellis
and
Singer
(2007)
Cavity
Shale
Mud cake
Sand
Layer boundary
Shale
Sand
Shale

Natural gamma-ray index
In linear approximation
In nonlinear approximation
(Larionov formula)
min
max
min
γ
GR
GR
GR
GR
i



γ
sh i
V 
 
 








older
1
2
0.33
tertiary
1
2
0.083
V
γ
γ
i
2
i
3.7
sh
Dennis and Lawrence (1984)

Ellis and Singer
(2007)
K-window
Th-window
U-window
Gamma rays of all radiating elements can be
detected in a given energy range
where I1, I2, I3 are the intensities measured
from the K-, U-, Th-window, r represents the
statistical error, a, b, c are calibration
constants of the windows (determined by
radiating rocks with known composition)
LSQ estimation of K-, U-, Th concentrations

















3
3
3
3
3
2
2
2
2
2
1
1
1
1
1
r
Th
c
U
b
K
a
I
r
Th
c
U
b
K
a
I
r
Th
c
U
b
K
a
I
 
 

 






3
1
i
2
i
i
i
i
3
1
i
2
i min
Th
c
U
b
K
a
I
r

Detection, identification and quantification of radioactive minerals
(K [%], U [ppm], Th [ppm])
Identification of clay minerals based on K−Th crossplot
Determination of shale volume in sandstones containing uranium
minerals, K-feldspar, mica, glauconite
Evaluation of potash deposits
Division of carbonate sequences based on uranium log (organic
material content)
Well-to-well correlation
Detection of fractured zones (fractures filled with shale, organic
material, uranium salt-rich thermal-water aquifers)
Determination of the composition of the crystalline basement
Detection of discordance-surfaces based on Th/K log

©Schlumberger

Neutron porosity (neutron-neutron) log
Density (gamma-gamma) log
Acoustic (sonic) traveltime log
Porosity estimation based on the individual use of
porosity sensitive logs
Simultaneous use of porosity sensitive logs for a more
accurate estimation of porosity and lithology (i.e.
crossplot techniques)
Nuclear magnetic resonance logging (effective porosity,
permeability determination), expensive method
Well-logging methods Porosity logging tools

Neutron porosity measurement employs a neutron source that
emits high-energy neutrons directed towards the formation
The reponse of the formation is measured in the form of either
neutron or gamma radiation
Neutrons according to energy are fast (>10 MeV), epithermic (0.4 eV
− 10 MeV), thermic (0.025 eV)
The neutrons interacts with the nucleus of elements of the rock
Elastic collision - the energy of the incident neutron is equal to the
sum of the kinetic energy of the scattered neutron and the nucleus
pushed away
Fast neutrons are slowed down the most intensively by hydrogen
atoms (water-filled pore space and clay), thermic neutrons are
generated and captured
Well-logging methods Neutron-porosity logging

Neutron source is either a neutron generator
which can be turned off or mixed chemical
source assuring a permanent stream of fast
neutron emission
Hydrogen concentration of the formation is
observed (high cps values, low rate of
scattering, less hydrogen, small porosity)
Measured signal and the depth of investigation
is inversely proportional to the porosity,
respectively
Neutron intensity depends on the type of
detector, energy of the incident particle,
transmitter-receiver distance (length of the
sonde), lithology (rock matrix composition)
Compensated neutron log measures the rate of
decrease of thermal neutron density by near
and far receivers, which is related to porosity
γ
n
C
Be
He 1
0
12
6
9
4
4
2 



Centralizer
Fast
neutron
source
Near
(epithermic)
detector
Far
(thermic)
detector
Gamma detector
Neutron
slow-down
Thermic
diffusion
Drilling mud
Borehole wall
Thermic
neutron
capture

Hydrogen-index (HI) measures the quantity of hydrogen atoms
in the given rock relative to the amount of hydrogen atoms in
pure water (HIw=1)
If the evaluated formation is limestone (HIma=0), then the
measured apparent (limestone) porosity is equal to the true
porosity
where HI is the measured hydrogen index, Hif is the hydrogen
index of the pore-filling fluid
Measured data must be corrected in case of a lithology
different from limestone
HI
Φ
Φ)HI
(1
ΦHI
HI N
ma
f 





Rock/Fluid Hydrogen Index
Pure water 1.0
Brine 0.90−0.92
Gas
(Low Temperature and Pressure)
0.002
Gas
(High Temperature and Pressure)
0.54
Heavy Oil > 0.9
Light Oil 0.55−0.9
Coal 0.66
Quartz, Calcite, Dolomite 0
Clay (In-Situ) 0.4−0.5
Shale (In-Situ) 0.2−0.4
Sandstone, Limestone 0
Metamorphic Rocks (In-Situ) 0.1−0.3

Borehole effect - the ratio of counts measured by the near and
fast detectors gives data corrected for the nominal borehole
diameter
Hole diameter and stand-off - their increase causes a decrease
of the measured counts (hydrogen-rich mud)
Salinity of mud - chlorine catches thermal neutrons
Density of mud - its increase decreases the hydrogen content
of the mud
Mud cake thickness - its increase decreases the measured
counts
Calibration is made in limestone, for a different lithology
further (rock matrix) correction is required

Rock Matrix Correction
Neutron sondes are calibrated in
limestone with known porosity
In case of clean sandstone the
number of thermic neutrons is
higher in the same distance from the
sonde, lower porosity is measured
than the true value (thus ΦN,lm=0
and ΦN,sd=−0.04)
In case of clean dolomite more
collisions are required to reach the
thermic energy level, the number of
observed thermic neutrons is
smaller, one obtains higher porosity
than the true one (ΦN,do=0.02)
Apparent neutron porosity of non-
porous gypsum (CaSO4+2H20) or
clays is high because of high
crystalline water content
Element
Number of Collisions
(from 2MeV to 0.025 eV)
Hydrogen 18
Silicon 257
Chlorine 329
Calcium 368
©Schlumberger

Hydrogens are present on the surface (bound water) and in
the crystal lattice (crystalline water) of clay minerals. The
neutron tool detects these hydrogens as part of the pore
space, therefore the apparent neutron porosity of clayey rocks
are greater than its true value
Neutron porosity corrected for shale
where Hish is the hydrogen index of the shale
(e.g. HIkaolinite=0.37, HImontmorillonite=0.17, HImuscovite=0.13)
sh
sh
N
(corr)
N HI
V
Φ
Φ 


Neutron absorbent elements influence the number of thermic
neutrons (e.g. Cl, B, Li). The most important is the NaCl content in
salty muds and formation water. These elements can occur in shales
as well
Hydrogen index of brine is less (≈0.92) than that of pure water
(HIw=1), thus the measured neutron porosity (N) decreases
Investigation depth of the neutron tool is in the flushed zone, the
hydrogen index of the mud filtrate (HImf) depends on salinity
where ρmf is density of mud filtrate, P is NaCl concentrate of mud
filtrate (10-6 ppm)
Detectors allow the counting of epithermal neutrons that are less
sensitive to salt content
 
P
1
ρ
HI mf
mf 


Hydrogen index of heavy oils is close to that of pore-water
In case of gas and light oil: HIhc<<HIw and ρch<< ρw, less hydrogen,
higher thermic neutron intensity is measured, derived neutron
porosity is smaller than its true value
In the flushed zone, mud filtrate and residual hydrocarbon
occupy the pore space
Hydrogen index of hydrocarbons can be calculated from density
hc
x0
mf
x0
hc
irr
hc,
mf
x0
f )HI
S
(1
HI
S
HI
S
HI
S
HI 












0.3
ρ
,
2.2ρ
0.8
ρ
0.3
0.3,
ρ
HI
ch
ch
ch
ch
hc

Still too small neutron porosity
can be measured in gas-
bearing rocks after completing
hydrocarbon correction
Neutron tool is sensitive to
hydrogen content, it can be
seen in the figure that for both
rock models the measured
neutron porosity is N=15%,
its reason is HIma≈HIgas≈0
Correction of neutron porosity
for excavation effect (K1 is a
lithological factor)
  
f
eff
f
2
eff
N
N,ex
N
(corr)
N HI
1
0.4Φ
HI
2Φ
K
Φ
ΔΦ
Φ
Φ 






In hydrocarbon-bearing zones, the observed (apparent) neutron
porosity (N) can be approximated by the following probe
response equation
where N,mf, N,hc,irr, N,sh, N,ma are the neutron porosities of
mud filtrate, residual hydrocarbon, shale, matrix, respectively, n
is the number of rock-forming mineral components
Neutron response function allows the calculation of
(theoretical) neutron porosity within the framework of forward
problem (see inverse modeling section)
 
  ma,i
N,
n
1
i
ma,i
sh
N,
sh
hc,irr
N,
x0
mf
N,
x0
eff
N Φ
V
Φ
V
Φ
S
1
Φ
S
Φ
Φ 







Determination of total (fluid) porosity
Qualitative identification of gas-bearing zones
In combination with other logs, it can be used to calculate porosity
more accurately, to estimate shale volume and to identify
lithology
Estimation of secondary porosity (2=t−1) together with sonic
porosity log (2N−S)
It can be used both in open and cased boreholes, in the latter case
the measured signal is influenced by the thickness of the casing,
and the thickness and quality of the cement sheath
In case of epithermal neutron detection, the presence of neutron
absorbent elements do not influence the measurement, therefore
it is more suitable for the evaluation of gas-bearing reservoirs

Gamma interactions are pair production (not measurable in
boreholes), Compton-scattering and photoelectric absorption
Rocks are exposed to gamma radiation, scattered gamma
radiation is observed
Photons emitted from the source interact with the electrons of
elements of the rock
Compton-scattering (0.5−1.5MeV) - the incident gamma photon
pushes out the electron of the atom and it travels forward with
the remained energy, the intensity of the scattered gamma
radiation is detected. In case of elements with low atomic
number the measure of scattering depends on electron density.
The measured apparent density is equal (with a good
approximation) to the bulk density of the rock
Well-logging methods Gamma-gamma logging

Source of medium energy gamma rays is used
(60Co or 137Cs of 662keV)
Intensity of scattered gamma radiation (I-) is
proportional to the bulk density of rocks (ρb)
where constant a depends on the energy of
source, constant b depends on source-
detector distance (length of the sonde) and
detector sensitivity
Sonde is pushed against the borehole wall,
which maximizes the information obtained
about the formation. The use of
compensated tools automatically corrects for
borehole effect (i.e. mud cake thickness)
Penetration depth  30−40 cm (flushed zone)
b
bρ
γ
γ ae
I 
 

On the spine and ribs plot, the
count rates measured by the
near and far detectors (beside
different mud cake thickness
and density) define one curve
Density can be determined
directly from the count rates
without knowing the values of
hmc and ρmc
Bulk density is defined by the
crossing point of the given rib
and the spine on the diagram
Ferenczy and Kiss (1993)

Photoelectric effect - when applying a soft gamma source (241Am of 62 keV)
the incident photon interacts with the electron causing its ejection from the
shell, the resulting photoelectron takes over all the energy of the photon,
the incident photon is absorbed and the atom is excited, which retains to
stable state by emitting characteristic gamma radiation
Intensity of the characteristic gamma radiation is proportional to the atomic
number Z
where Pe is photoelectric absorption (cross section) index, U is volumetric
photoelectric absorption index (cross section: intrinsic likelihood of event)
Pe is sensitive to lithology (pore-fluid influences it hardly)
Pe measurement is excellent for fracture detection using barite mud
Litho-Density tool allows the simultaneous measurement of density and Pe
(latter is proportional to the effective atomic number of rocks)
e
e
3.6
e ρ
P
U
/10
Z
P 


Rock/Fluid ρb (g/cm3) Pe (barn/e) U (barn/cm3)
Barite 4.50 266.8 1070
Calcite 2.71 5.08 13.77
Dolomite 2.87 3.14 9.00
Halite 2.16 4.65 9.65
Hematite 5.21 21.48 107
Pyrite 5.00 16.97 82.0
Quartz 2.65 1.81 4.79
Fresh Water 1.00 0.36 0.40
Brine (120 kppm) 1.09 0.81 0.96
Oil 0.85 0.11 0.11
Gas 0.25 0.09 0.04
Clean Sandstone 2.31 1.74 4.07
Contaminated Sandstone 2.39 2.7 6.52
Shale 2.4−2.8 3.42 9.05
Anthracite 1.70 0.16 0.28

Sonde responses (UPeρb) can be
used for quantitative interpretation
(when Uf0 and Φt is total porosity)
Volumes of three types of mineral
components can be estimated
With the Pe−ρb diagram, lithology
and porosity can be determined
)
Φ
U/(1
U
)U
Φ
(1
U
Φ
U
t
ma
ma
t
f
t



















1
V
V
V
ρ
ρ
V
ρ
V
ρ
V
U
U
V
U
V
U
V
ma,3
ma,2
ma,1
ma
ma,3
ma,3
ma,2
ma,2
ma,1
ma,1
ma
ma,3
ma,3
ma,2
ma,2
ma,1
ma,1
©Schlumberger

Observed bulk density (ρb) depends on porosity and densities
of rock matrix (ρma) and pore fluids (ρf) including mud filtrate,
water and hydrocarbon
Density-derived porosity of clean porous formations
Porosity decreases with increasing rock density. When ρmaρb,
negative porosity is obtained, which allows the indication of
heavy minerals
f
ma
b
ma
D
ρ
ρ
ρ
ρ
Φ



ma
f
b Φ)ρ
(1
Φρ
ρ 



Density of shales are different (2.2ρsh2.65), the density of
interbedded (laminar) shale is usually greater, than that of shale
dispersed in the pore space. Density difference between the shale
and matrix specifies the amount of shale correction
Observed bulk density of shaly rocks can be approximated
Normally dispersed clay slightly decreases the measured density
(ρma−ρsh ≤ 0.15 g/cm3) and increases the apparent porosity
Shale corrected bulk density is calculated
ma
sh
eff
sh
sh
f
eff
b )ρ
V
Φ
(1
ρ
V
ρ
Φ
ρ 




 
sh
ma
sh
ma
eff
f
eff
b ρ
ρ
V
)ρ
Φ
(1
ρ
Φ
ρ 




 
sh
ma
sh
b
(korr.)
b ρ
ρ
V
ρ
ρ 



Density of hydrocarbons (especially gas) has lower density than
formation water
Observed bulk density is lower in a hydrocarbon-bearing rock
than in the same rock occupied by water
Apparent bulk density measured with the density tool should be
corrected
Correction is applied using an approximate formula
Density-derived porosity in oil-bearing intervals is higher, in gas-
bearing zones it is much higher, than the true porosity
b
a
b ρ
ρ
ρ 


 
 
hc
mf
hc,irr
eff
b 1.23ρ
ρ
0.16P
1.19
S
1.07Φ
Δρ 



In hydrocarbon-bearing zones, the observed (apparent) bulk
density (b) can be approximated by the following probe
response equation
where mf, hc, sh, ma are densities of mud filtrate, residual
hydrocarbon, shale and matrix, respectively, n is the number of
mineral components
Density response function allows the calculation of
(theoretical) bulk density within the framework of forward
problem (see inverse modeling section)
 
  ma,i
n
1
i
ma,i
sh
sh
hc
x0
mf
x0
e
b ρ
V
ρ
V
ρ
S
1
ρ
S
Φ
ρ 







Estimation of porosity (best performance in oil and water
reservoirs)
Lithological composition is determined in combination with
other porosity sensitive logs
Evaluation of shaly sand(stone) formations
Detection of gas-bearing zones
Identification of evaporite minerals
Identification of heavy minerals (ores, anhydrite)
Identification of coals (low rock density)
Determination of composition of rocks in a complex lithology
Determination of secondary porosity together with the sonic log
(2D−S)

Gas-bearing formations
Well logs:
SP - Spontaneous potential
CAL - Caliper
GR - Natural gamma-ray
CNL - Compensated neutron
ATL - Acoustic traveltime
DEN - Density
©
MOL
Group
Well-logging methods Porosity logs

Sonde is equipped with
ultrasonic transmitter(s)
and two or more
piezoelectric receivers
Transit time of acoustic
(elastic) wave propagating
through 1 m (or 1 ft)
interval in the wall rock is
measured
Observed parameter is the
acoustic interval time (∆t)
in units of μs/m unit (i.e.
refracted P wave
slowness)
t2
t3
t4
t5
t1
4
R
R
5
4
2
1
R
3
2
1
R
t
t
t
Δt
t
t
t
t
t
and
t
t
t
t
1
2
2
1










Well-logging methods Sonic logging

First arrival - longitudinal (compressional)
wave, which propagates from the transmitter
to the rock in the mud, than it refracts in the
rock, finally returns to the receiver as
compressional (pressure) wave
Shear wave - it propagates from the
transmitter to formation as compressional
wave, as transverse wave in the rock and
back to the receiver as compressional wave
Mud wave - it propagates from the
transmitter to the receiver directly in the
mud column with the velocity corresponding
the compressional wave velocity of mud
(hard to differentiate in the full waveform)
Stoneley wave - it is a dispersive surface
wave propagating on the mud-rock surface
with smaller velocity than the mud wave. Its
velocity depends on frequency, hole caliper,
shear wave velocity of the formation, density
of mud and formation, velocity of mud wave
(used for permeability estimation and
detecting the location of fractures)

©Baker Hughes SPWLA glossary

Rock / Fluid ∆tp (μs/ft)
Sandstone 56
Limestone 49
Dolomite 44
Clay 56−164
Salt 66.7
Coal 115
Casing 57
Fresh water, Mud filtrate 189
Brine, Mud filtrate 185
Oil 230
Gas (Methane) 602

Because of the inclined (eccentric)
sonde position (inclined drilling)
and different hole sizes,
compensated acoustic sonde is
generally used (min. 2 transmitters
and 2 pairs of receivers)
In case of the conventional tool (1
transmitter and 2 receivers) the
observed quantity is ∆tt4 as t3t5
Solution is the use of more
transmitters with 2 receivers per
transmitter (BHC sonde)
Corrected acoustic interval time
data is obtained by calculating the
arithmetic mean of individual
traveltime data
Ferenczy and Kiss (1993)

Because of the wave absorption
the far receiver detects higher
propagation time than the true
one (e.g. in unconsolidated
formations, gas reservoirs,
fractured rocks)
Cycle slipping - the far receiver
does not detect the first arrival,
a subsequent phase is detected
Traveltime stretching - the far
receiver detects within one
period, but not at the same
place, as the near receiver
Spikes appear on the acoustic log
Serra (1984)

Estimation of primary porosity in clastic rocks and secondary porosity (2N−S) in
fractured rocks (According to the Fermat principle the path taken between two points
by a wave is the path that can be traversed in least time. The propagation time in
fractures is maximal, therefore the wave avoids them. The acoustic measurement gives
information only about primary porosity)
Permeability estimation from Stoneley wave travel times
In-situ determination of elastic moduli from the travel times of P and S waves
Qualitative determination of reservoir fluid (e.g. based on cycle slipping)
Aid for seismic interpretation (together with the density log the calculation of acoustic
impedance and synthetic seismograms for improving the seismic velocity model
Cement Bond Log (CBL) informs on the quality of bond of the cement to the casing and
formation
Variable Density Log (VDL) detects gas-bearing zones and control the cement quality
Cross dipole measurements (stress direction analysis, mapping of fracture systems,
estimation of permeability)
Circumferential Borehole Imaging Log (CBIL) is used for borehole-wall imaging and
checking the casing conditions

Acoustic traveltime is a function of formation porosity and lithology
Wyllie time average equation assumes an empirical relation
between porosity and acoustic travel time
where vf, ∆tf, vma, ∆tma, vsh, ∆tsh are the velocities and acoustic
interval times of the pore fluid, rock matrix and shale, respectively
Sonic log-derived porosity in clean formations
ma
f
ma
f
Δt
Φ)
(1
ΦΔt
Δt
v
Φ
1
v
v
1








ma
f
ma
S
Δt
Δt
Δt
Δt
Φ




Wyllie formula is only valid in consolidated sandstones with primary
porosity and carbonates
Overburden pressure causes the underlying rocks to be compacted, the
velocity increases up to a limit ( 3000 m/s)
In poorly consolidated (loose) rocks, until the velocity limit is not reached
(∆tsh>330 μs/m), the observed value of ∆t and sonic porosity calculated
from the Wyllie formula is higher than the true value
Empirical correction is applied to correct Wyllie’s porosity data
where cp is the compaction correction factor, ∆tsh is the acoustic travel time
of shale (usually ∆tsh>∆tma), C is a compaction coefficient of shale (0.8−1.2)
0)
V
1,
(S
Φ
Φ
Φ
Φ
Φ
Φ
c
or
330
Δt
C
c
c
1
Δt
Δt
Δt
Δt
Φ
sh
w
N
S
D
S
R
S
p
sh
p
p
ma
f
ma
S












Given value of compaction correction factor is uncertain, which strongly
influences the calculation of porosity
No need for the compaction correction if the porosity is considered as a non-
linear function of ∆t
Sonic porosity can be calculated
empirically
where  is between 0.6−0.7
 
Δt
Δt
Δt
α
Φ
Δt
Φ
1
Δt
Φ
Δt
1
ma
S
ma
2
f





RHG equation gives a better
estimate than the Wyllie
formula on a wider range of
porosity Raymer et al. (1980)

Assuming the same rock composition and porosity, the observed acoustic
travel time of oil or gas saturated rocks is higher than that of water
saturated rocks
Hydrocarbon effect is small in consolidated and low porosity rocks; effect of
residual hydrocarbons being in the flushed zone is negligible
Empirical correction is used in unconsolidated rocks with high porosity
(shallow invasion of mud)
Travel time of hydrocarbons is given empirically in the sonic response
function
where ∆to and ∆tg are the acoustic travel time of oil and gas, respectively
oil)
for
(
Φ
9
.
0
Φ
gas)
for
(
Φ
7
.
0
Φ
S
(corr)
S
(corr)




 
 /0.9
Δt
ρ
0.95
t
0.05)Δ
(ρ
Δt g
hc
o
hc
hc 




Necessary in shaly rocks (Vsh≠0), where the acoustic travel time of
shales (∆tsh) is usually higher (the velocity is lower) than that of the
rock matrix, thus, porosity is higher than the true one
Modified Wyllie equation for consolidated formations with shale
laminae
where Φs,sh is the sonic porosity of shale
Modified Wyllie equation for consolidate formations with dispersed
shale content
sh
,
s
sh
ma
f
ma
ma
f
ma
sh
sh
ma
f
ma
S
sh
sh
ma
sh
f
V
Δt
Δt
Δt
Δt
Δt
Δt
Δt
Δt
V
Δt
Δt
Δt
Δt
Δt
V
Δt
)
V
Φ
(1
ΦΔt
Δt

















 
sh
ma
f
ma
S
ma
sh
f
sh
V
Δt
Δt
Δt
Δt
Δt
)
V
Φ
(1
Δt
V
Φ
Δt











In hydrocarbon-bearing zones, the observed acoustic travel time (∆t)
can be approximated by the following probe response equation
where ∆tmf, ∆thc, ∆tsh, ∆tma are the acoustic travel times of mud
filtrate, hydrocarbon, shale, matrix, respectively, n is the number of
mineral components
In unconsolidated formations the compaction correction factor
should also be taken into account
Sonic response function allows the calculation of (theoretical)
acoustic travel time within the framework of forward problem (see
inverse modeling section)
 
  ma,i
n
1
i
ma,i
sh
sh
hc
x0
mf
x0 Δt
V
Δt
V
Δt
S
1
Δt
S
Φ
Δt 







In impermeable rocks, the theoretical travel time of
the Stoneley wave
where ∆ts is the travel time of shear wave
In permeable rocks, permeability can be estimated
from the observed Stoneley travel time by
K=f(ISt,a,b), where Ist=∆tSt(meas)/∆tSt(calc) is the
Stoneley-index, a and b are regional constants
depending on lithology, porosity and formation fluid
2
mf
2
s
b
mf
d)
(calculate
St Δt
Δt
ρ
ρ
Δt 

Bala
(2010)
Haldorsen et al. (2006)

Monopole sources cannot excite refracted shear
waves in slow formations (velocity of mud is higher)
Dipole sondes contain two dipole sources oriented
orthogonally along the tool X and Y axes and a
receiver array
Flexural wave is a dispersive (guided) wave generated
by the dipole transmitters, the particle motion of
which is perpendicular to the direction of wave
propagation. Radially asymmetric compressional wave
in the borehole causes pressure increase in one
direction, and pressure decrease in the opposite
direction (like a wave traveling along a rope fixed at
one end). In low frequency boundary case its slowness
is equal to that of the shear wave
Shear wave splitting - in azimuthally anisotropic rocks
the shear wave splits into two orthogonally polarized
flexural wave components that propagate with
different velocities (i.e. fast and slow shear waves)
In the crossline signal the contribution of the two
shear waves depends on the directional angle of
anisotropy (Θ)
© Baker Hughes

Source of anisotropy is the spatial
alignment of mineral grains, layers,
fractures, faults, tectonic stress. They cause
wave velocity to vary with direction
Shear waves propagate faster in
polarization direction parallel to fractures
than perpendicular to them (see figure in
case of fractures parallel to borehole wall)
Steps of S wave data processing are
filtering, cross correlation of full waveform
trace signals, rotation, velocity analysis of
in-line data, directional correction
Magnitude of shear wave anisotropy is
characterized by the relative difference
between the travel times of fast and slow
shear waves
(DTSSLOW-DTSFAST)/AVGDTS
Badri et al. (2000)

Regional and local stress fields
(horizontal and vertical or overburden
stress components)
Natural or drilling induced fractures
(e.g. breakout is formed in the direction
of minimum horizontal stress, and so
increases the diameter of the borehole)
Azimuth of the fast shear wave
propagation is parallel to the direction
of maximal horizontal stress, and that
of the slow shear wave is parallel to the
direction of minimal horizontal stress
Design of hydraulic fracture treatments
to improve oil or gas well performance
Hydraulic fracture will usually penetrate
the formation in a plane normal to
minimum stress, or parallel to the plane
of maximum stress. Any stress
anisotropy (tectonic stress) will cause
the fracture to be other than vertical
© Baker Atlas (2001)

©Schlumberger
Well-logging methods Combination of porosity logs

Applicable to a more accurate estimation
of porosity and identification of lithology
Measured quantities are plotted in one
coordinate system (crossplot), the points
corresponding the data pairs fit on
characteristic lithological lines (line
between the matrix and fluid points) or in
their neighbourhood, the indicated values
on the lithological lines show the porosity
value of a clean (water saturated) rock
Porosity is marked by the perpendicular
lines falling on the plotted point and the
lithological lines corresponding to the given
mineral combination
N−ρb crossplot gives an estimate to
porosity independent of lithology (with
2% estimation error), but regarding the
lithology it provides ambiguous solution
Detection of shale and gas, differentiation
between dry and wet shales
Sand line Dolomite line
Porosity (%)
Limestone line
© MOL Group

M-N plot is based on the
combination of three porosity logs
M, N are calculated as lithological
parameters depending on lithology
and independent of porosity, they
are the gradients of acoustic,
density and neutron density
crossplots
Discrete points show the different
mineral types (for salty and fresh
muds), dashed lines indicate the
practical range of porosity
©Schlumberger
f
b
N
N,f
f
b
f
ρ
ρ
Φ
Φ
N
ρ
ρ
Δt
Δt
0.003
M







©Halliburton
Apparent values of matrix parameters are
plotted on the crossplot
where ΦN,D and ΦN,S are porosities
estimated from neutron vs. density and
neutron vs. acoustic crossplots, respectively
Diagram allows the estimation of mineral
composition; one mineral (point), two
minerals (line), three minerals (triangle)
Distance of the plotted points from the tip
of the triangle is inversely proportional to
the quantity of the given mineral
Estimation of porosity is not possible
S
N,
f
S
N,
ma
D
N,
f
D
N,
b
ma
Φ
1
Δt
Φ
Δt
Δt
Φ
1
ρ
Φ
ρ
ρ







©Halliburton Protons (hydrogen nuclei) of the pore fluid are polarized with
strong stationary magnetic field then a radio frequency pulse
train is generated by an antenna
Time constant of the polarization process is the polarization
time T1 (for pore water 1−500 ms, for oil 3000−4000 ms and
for gas 4000−5000 ms)
Between two pulses, after turning off the magnetic field, the
magnetic moments of the protons precess around the
direction of the original magnetic field. Because of the spatial
dependence and inhomogeneity of the magnetic field the
protons are not in phase, therefore the measured 2.2 kHz
decaying signal quickly decays
A set of signals at Larmour frequency is induced in the
receiver coil as the effect of radio frequency excitation
(pulsing). Response of the repeated (pulsing) magnetic field is
the spin-echo sequence called echo-train
Initial amplitude of the envelope of the measured signal
sequence is proportional to the number of protons in the
formation (the measurement is sensitive to hydrogen index)
Well-logging methods NMR logging

Coates et al. (1999)

Relaxation time T2 is the time constant of
the relaxation process showing exponential
decay (for pore water 1−500 ms, for oil
300−1000 ms and for gas 30−60 ms)
T2 relaxation time depends on pore size
and pore fluid type. When the water (or
bound water) occupies a small pore space,
small T2 times are measured and vice versa
Protons of the matrix and bound water of
shale (and capillaries) have small T2 times
(n100 s), but free pore fluids have high T2
times (n100 ms)
Hydrocarbons stretch the distribution of T2
values depending on hydrocarbon type,
viscosity and its amount
During the measurement a T2 time
constant sequence is measured at a given
depth, which frequency (occurrence)
distribution is displayed on a well log
Asquith and Krygowski (2004)

NMR measurement is practically lithology independent, it is sensitive
only to pore fluids (at some inches of investigation depth)
Determination of effective porosity and bound water saturation of
water and hydrocarbon reservoirs
More accurate determination of secondary porosity compared to
procedures based on conventional well logs (this fact has been
confirmed by core measurements)
Determination of permeability of hydrocarbon reservoirs
Identification of hydrocarbon type
Determination of pore-size (or grain-size) distribution
Determination of the quantity of moveable fluids
Detection of gas based on density-porosity vs. NMR porosity
crossplot

Effect of rock matrix and irreducible water can be eliminated, if the
measurement starts with a 25−30 ms time-delay compared to the beginning of
the precession, in this case, the initial amplitude of measured signal is
proportional to the amount of free fluid
Free Fluid Index (FFI) is the volume of fluids, which chemically or electrically
are not bound to shale or matrix and move freely in the pore space
Measured signal originates from the flushed zone
In the knowledge of porosity the irreducible water saturation is calculated
With known porosity and irreducible water saturation the absolute
permeability can be calculated by e.g. using Timur’s equation
   
irr
w,
irr
w,
irr
hc,
x0 S
1
S
S
S
FFI 









FFI
1
S irr
w,

Initial amplitude of single echoes
carries information on porosity
From each T2 relaxation time of the
echo train a porosity (ΦNMR) value
can be estimated by using inverse
modeling
Area under the curve of frequency
distribution of T2 relaxation times
gives an estimate to porosity
(when Sw=1)
Based on the density distribution
function, the pore-size distribution
can be obtained
T2 cut-off is the value at where the
bound and moveable fluids are
distinguished (23−33 ms is the
default value used in sands, it is
usually higher in carbonates)
Coates et al. (1999)

Permeability increases with effective porosity and pore size. Conventional
methods determine a matrix permeability, which underestimate the
permeability of mixed porosity rocks (e.g. fractured hydrocarbon reservoirs)
Coates model depends on a T2
cutoff
T2-average model is independent
on a T2 cutoff
where is the geometric mean of
T2 values, C and a are lithology
dependent constants
Asquith and Krygowski (2004)
2
4
NMR
NMR
BVI
FFI
C
Φ
k 












  2
2
4
NMR
NMR T
Φ
a
k 
2
T

Asquith
and
Gibson
(1982)
Well-logging methods Resistivity logging

©Schlumberger
B is a surface electrode and A,
M, N electrodes are mounted on
the sonde. Electric current flows
into the formation through the
electrode pair A-B, voltage is
measured on the electrode pair
M-N, apparent resistivity Ra is
derived in units of ohmm
Lateral sonde - distance M-N is
small in comparison with
distance A-0 (0 denotes the
midpoint of distance M-N, the
spacing of the sonde is distance
A-0
Normal sonde - distance of
electrode N is minimum 10−20
times the distance A-M (spacing
of the sonde)

Measuring current of conventional
specific resistivity sondes are led by
highly conductive (high salinity)
muds or low resistivity adjacent
beds, thus an unfocused direct
current field is formed
Conventional resistivity logs do not
characterize the formation, which
causes problems especially in the
interpretation of thin and high
resistivity layers
Solution is the application of logging
tools evolving focused current field
called laterolog sondes

Focusing (guard) electrodes A1 and A2
force the current of the measuring
electrode A0 into the formation, the
monitoring electrodes M1 and M’1 and M2
and M’2 are short-circuited in pairs (they
are on same potential), the potential
difference proportional to the resistivity of
the rock is observed between one of the
monitoring electrodes and an electrode
placed at the surface. Focusing is possible
on different scales and sondes with
different investigation depths are available
Dual (DLL) laterolog tool operates with
two different spacings and frequency
(35Hz−20kHz) simultaneously (i.e. deep
and shallow penetration: LLd and LLs)
Applicable in salty muds (Rmf<3Rw) and
formations with high Rt. It cannot be
applied in oil-based muds (no electric
coupling between the tool and formation)
and air-drillings (no invasion)
©Schlumberger

Serra (1984)
Microlog is a pad type sonde pressed
to the borehole wall, three electrodes
with 1−1 inch distances (conventional
resistivity logging)
Micronormal mode (A0-M2) measures
Rx0 with average penetration of 3−4
inches (invaded zone). Microinverse
mode (M1-M2) measures Rmc with 1−2
inches penetration (mud cake)
Positive separation of resistivity curves
(Rnorm>Rinv) refers to the presence of
mud cake and permeable formation.
No separation or negative separation
indicates an impermeable bed
Applied primarily as a mud cake
indicator, its drawback is its sensitivity
to hole size, microlog should be
corrected for mud cake

Microlaterolog (RMLL) utilizes a focused current
field, which provides a reliable value of Rx0 in
case of small and medium mud cake thicknesses,
the measured signal originates primarily from
the flushed zone, investigation depth is 10 cm
Spherically Focused Microresistivity Log (RSFL)
uses a spherical current field (by not too deep
investigation depth), it is more focused than
RMLL tool and less sensitive to mud cake, DLL
sonde is usually equipped with it to make a
measurement of Rx0
Proximity log (RPL) is composed of a metal
sonde pad and electrodes separated by
insulating beds, electrode A0 contacts with the
borehole on a great surface for smaller power
fluctuation. Tool provides accurate Rx0 also at
thick mud cakes; resistivity Rt may influence the
reading in case of small invasion depth

Method assumes a step
resistivity profile (Rx0, Rt)
Tornado diagram is used to
determine Rx0, Rt and di from
dual laterolog (RLLD, RLLS) and
microresistivity data (e.g. RMFSL)
Corrected true resistivity of the
formation
Resistivity of invaded zone
©Schlumberger
LLD
LLD
t
(corr)
t )R
/R
(R
R 
)
/R
(R
R
R
x0
t
(korr.)
t
x0 

High frequency (20 kHz) alternating current
with constant intensity is lead into the
transmitter coil. EM field of the current
induces high frequency (concentric with the
axis of sonde) eddy (Foucault) currents in
the formation, which are proportional to
the conductivity of the rock. EM field of the
Foucault currents induces voltage in the
receiver coil, which is proportional to the
electric conductivity (mS/m) of the rock
Resistivity is directly plotted on the well log
in units of ohmm
Induction measurements are distorted by
the skin-effect (i.e. measured signal and the
depth of investigation decreases especially
in highly conductive rocks), borehole effect,
adjacent beds (smaller Rt is measured
especially at high Rt/Rs), effect of invasion
(great invasion depth and small Rx0)
©Schlumberger

In case of multi-coil sondes the signals
of receiver coils are summed up to
minimize the effect of borehole,
shoulder beds and invasion
Array induction tool was developed to
measure with several coils at different
frequencies simultaneously (i.e. shallow,
medium and deep penetration)
Applicable in freshwater or electrically
non-conductive (oil-based or air-drilling)
muds (Rmf>3Rw), and formations with
small and medium Rt
Not used in salty muds and in (thin)
layers with resistivity higher than 100
ohmm
Hunka et al. (1990)

Ellis and Singer
(2007)
Geometric factor (G) describes the portion of the
measured signal by a sonde, which originates
from the volume of the given geometry (assuming
homogeneous medium)
A cylindrically symmetric zone characterized by
geometric factor Gn (as a weight) and conductivity
Cn contributes to the measured conductivity Ca
with the product GnCn. In the mud, in the invaded
zone, in the uninvaded zone and in the shoulder
beds equation Gn=1 fulfils
Geometric factor vs. invasion depth diagram gives
that what portion of the observed information
originates from the invaded and the uninvaded
zone at the investigation depth corresponding to
the diameter of the invaded zone
In case of step resistivity profile the corrected
resistivity
0.75
90
Invaded
zone
(75% info)
Uninvaded
Zone
(25% info)
t
x0
x0
x0
(corr)
IL R
G
1
R
G
R
1 



Determination of the invasion profile and true resistivity by
sondes using different depths of investigation
Determination of porosity
Determination of water saturation
Identification and separation of water and hydrocarbon reservoirs
Detection of changes in grain sizes
Borehole imaging based on microresistivity measurements e.g. by
using Formation MicroScanner (FMS) tool
Permeability estimation in shallow aquifers (Csókás method)
Water prospecting involves conventional resistivity tools, while
focused sondes are used in hydrocarbon exploration

Rider (2000)
Conductive invasion
Rmf < Rw

Shale (Rsh)
Hydrocarbon reservoir and/or
porosity decrease
Aquifer
Shale
Hydrocarbon reservoir and/or
porosity decrease
Ellis
and
Singer
(2007)
Resistive invasion
Rmf > Rw

Archie’s formula can be applied to the flushed zone
Water saturation of clean formations in the flushed zone
Porosity of hydrocarbon reservoirs derived from resistivity logs
Porosity of aquifers derived from resistivity logs (Sx0=1, a  1, mn2)
mf
x0
w
0 FR
R
FR
R 


n
res.)
(hc
x0
mf
n
res.)
(hc
x0
(aquifer)
x0
x0
R
FR
R
R
S 

m
res.)
(hc
x0
mf
n
x0
R
n
res.)
(hc
x0
mf
m
x0
R
R
S
a
Φ
R
R
Φ
a
S 


x0
mf
R
R
R
Φ 

In the knowledge of Rx0 and Rt, the Archie’s formulae derive (saturation
exponent n=2)
Empirical relation between the water saturations of invaded and uninvaded
zones (α=0.2−0.5)
Hydrocarbon exponent α=1/5 is generally used for giving an estimate to water
saturation
Ratio Rmf/Rw can be calculated from the SP log, Rx0 and Rt can be estimated
from Tornado charts
w
mf
t
x0
x0
w
R
/
R
R
/
R
S
S

α
w
x0 S
S 
8
/
5
w
mf
t
x0
w
R
/
R
R
/
R
S 









Clay minerals have an excess
negative charge, which attracts the
cations from the free pore water
Cations surrounded by a hydrate
envelope are adsorbed on the clay
particles. Further off the surface of
the mineral grains a diffuse layer
develops the thickness of which is
inversely proportional to salinity
Depending on the salt content of
pore water, cations of the diffuse
layer can be removed by applying
an electrical field
Surplus conductivity originating
from the excess charge contributes
to the total conductivity of rock
Gonçalvès and Rousseau-Gueutin
(2008)

In shaly formations, the shale content should also be taken account in
water saturation estimation
Archie’s formula should be
modified by adding a term of
excess conductivity of clay
Term X can be approximated in
different empirical ways
X
FR
S
R
1
C
S
F
C
C
w
n
w
t
excess
n
w
w
t





De Witte’s dispersed shale model - free water and clay particles dispersed
in the pore space conduct an electric current like a mixture of electrolytes
where porosity Φ includes the pore volume of free water, hydrocarbons,
and dispersed shale, water saturation S is the fraction of intermatrix
porosity occupied by formation-water and dispersed-shale mixture, q is the
pore volume occupied by dispersed shale, Sw=(S-q)/(1-q) is water
saturation in the fraction of true effective porosity
By combining the above equations, water saturation is calculated







 


w
sh
2
t R
q
S
R
q
a
S
Φ
R
1
   



















 




sh
w
sh
2
sh
w
sh
t
w
2
w
R
2
R
R
q
R
2
R
R
q
R
R
a
q
1
1
S

Laminated shaly sand model - resistivities of sand and shale are connected in
parallel
where Rsh and Rsd are the resistivities of shale and clean sand laminae,
respectively, Vlam is the bulk volume fraction of shale
Formation porosity  is calculated from the resistivity of clean sand laminae
Rsd and its porosity sd
Resistivity response equation connecting Rt and Sw
sh
lam
sd
lam
t R
V
R
V
1
R
1



 
lam
sd
2
w
w
2
sd
2
w
w
sd
sd V
1
Φ
Φ
S
R
Φ
a
S
R
F
R 




 
 













sh
lam
t
2
w
lam
w
sh
lam
w
lam
2
w
2
t R
V
R
1
Φ
aR
V
-
1
S
R
V
aR
V
-
1
S
Φ
R
1

Schlumberger’s (total) shale model - a quadratic response function was developed
based upon laboratory investigations and field experience, which is independent of the
type and distribution of shale
where Vsh is the total volume of shale, Rsh is the resistivity of a near-by shale layer, the
second term of the left side is the excess conductivity of shale
Poupon and Leveaux (Indonesia) model - empirical equations are used for water
saturation estimation both in the flushed and uninvaded zones of hydrocarbon
reservoirs
  sh
w
sh
sh
w
2
w
2
t R
S
V
V
1
aR
S
Φ
R
1



 
   
 
   n
x0
mf
m
sh
V
0.5
1
sh
x0
n
w
w
m
sh
V
0.5
1
sh
t
S
aR
Φ
R
V
R
1
S
aR
Φ
R
V
R
1
sh
sh























Exchangeable cations in the electrochemical double layer can be displaced by other
cations of the free pore water and those of adsorbed on neighboring clay particles. Cation
exchange capacity (CEC) measures the quantity of cations (in units of mmole/g) that a
clay mineral can accommodate on its negatively charged surface, which is often expressed
in terms of its contribution per unit pore volume (Qv in mekv/cm3). CEC is proportional to
the specific surface area of the clay
Waxman-Smith model - term XQv, but the measurement of CEC causes inconvenience in
the analysis of well logs. Dual water model - conductivity response function for insulating
rock matrix
where Cwe is equivalent conductivity, Vw and Vwb are the bulk volumes of formation and
bound water, respectively, Φt is total porosity, Swt is total water saturation including
bound and free water. Effective porosity and water saturation of clean formation
 











 w
wb
wt
wb
w
n
wt
m
t
wb
w
wb
wb
w
w
n
wt
m
t
we
n
wt
m
t
t C
C
S
S
C
a
S
Φ
V
V
C
V
C
V
a
S
Φ
C
a
S
Φ
C
 
wb
wb
wt
w
wb
t
eff
S
1
S
S
S
and
S
1
Φ
Φ






EM wave propagation in high frequencies (25
MHz−1.1 GHz) is specified by the dielectric
properties of rocks
Electric polarization induced by electric field E
(V/m)
where  is dielectric constant (As/Vm), D is the
vector of electric induction (As/m2)
EPT sonde measures both the propagation time
of EM wave tpm (ns/m) and attenuation of that
Am (dB/m) between two receivers at a
penetration of 3-15 cm. The former is specified
by phase shift, while the latter is given by
amplitude contraction
Polar compounds (e.g. water) have high
dielectric constants, molecules are orientated by
EM wave, rock matrix and hydrocarbons being
non-polar compounds have small dielectric
constant, EM wave is less attenuated by them
Propagation velocity of EM waves in rocks is
inversely proportional to the dielectric constant
E
D ε

©Schlumberger
Well-logging methods Special logging techniques

Rock/Fluid * tp (ns/m)
Sandstone 4.65 7.2
Dolomite 6.8 8.7
Limestone 7.5−9.2 9.1−10.2
Anhydrite 6.35 8.4
Gypsum 4.16 6.8
Halite 5.6−6.35 7.9−8.4
Shale 5−25 7.45−16.6
Freshwater (250C) 78.3 29.5
Oil 2−2.4 4.7−5.2
Gas 3.3 6.0
*Dielectric constant relative to air

Because of the small transmitter-receiver spacing, spherical wave approximation is used,
therefore the raw attenuation data should be corrected for spherical spreading
Energy loss is the greatest in highly conductive rocks (e.g. brine, shale, bound water), the
(lossy) propagation time (tpm) measured by the EPT sonde is recalculated to loss-free time
(tp)
EPT response function used in clean reservoirs
Water saturation of the flushed zone in the knowledge of EPT times of rock constituents
Method allows for an optimal use of porosity estimation in aquifers, the advantage of
which is its insensitivity to salinity. Water and oil-bearing reservoirs can be separated more
easily compared to conventional resistivity tools
3604
A
t
t m
2
pm
p 

 
    ma
p,
t
hc
p,
x0
mf
p,
x0
t
p t
Φ
1
t
S
1
t
S
Φ
t 




   
 
hc
p,
mf
p,
t
hc
p,
ma
p,
t
ma
p,
p
x0
t
t
Φ
t
t
Φ
t
t
S






Measurement configuration Velocity (or absorption) tomography



v
dl
t

CBIL sonde Acoustic amplitude and traveltime image logs

©
Halliburton
Caliper tool provides a continuous measurement
of borehole size in the units of inch or cm
Arms are used for centralization and pushing the
sonde to the borehole wall. Each arm is connected
to a potentiometer, which causes the resistance to
change as the diameter of the borehole changes,
creating a varying electrical signal that represents
the changing shape of the borehole
Applications are separation of permeable and
impermeable beds (i.e. detection of cavern and
mud cake), the thickness of mud cake
where dn and d are the nominal (drill-bit) and
measured diameters, respectively; detection of
fractures and vugs; determination of borehole
volume and amount of mud filtrate invasion;
estimation of cement volume required in casing
operations
 /2
d
d
h n
mc 


Testing the condition of cased boreholes
- CBL and VDL logs - determination of the quality of cement bound, strength and fracturing
- CBIL log - analysis of the casing (indicating damage of casing, fractures), designation of places of
perforations
- CCL (Casing Collar Locator) log - determination of the locations of casing joints
- Gamma-gamma log - check of the gravel
Production well logging (PWL) methods
- GR log - determination of relative depth and lithology
- Time-lapse neutron-neutron and neutron-gamma measurements - studying the change in water and
hydrocarbon saturation during exploitation, indication of the displacement of gas-fluid phase
boundary
- BATS (Borehole Audio Tracer Survey) logs - locating the gas infiltration, detection of gas flow-through
(at several frequencies)
- Special gamma-gamma measurement – measurement of fluid density in the well
- Spinner and advanced flowmeters - flow velocity, flow rate and fluid composition
- Special logging tools - pressure, temperature, differential temperature (determination of geothermal
gradient, determination of the place of inflow in the well, flow behind casing, location of injection in
an injection well)
- Resistivity measurements - conductive tools are not feasible, induction measurements can be made
in plastic casing (e.g. water exploration)

Asquith and Krygowski (2004) Szabó et al. (2013)
Larionov model
(young rocks)
Larionov model
(old rocks)
Inverse modelling
Linear approximation
based on GR index
Well-logging methods Interpretation of well logs

  
 
 
 
 
BN
BM
RW
BA
DENSD]
THSD
DENSH
THSH
DENMF
THMF
[
DEN
1
DENSD]
USD
DENSH
USH
DENMF
UMF
[
DEN
1
DENSD]
KSD
DENSH
KSH
DENMF
KMF
[
DEN
1
ATSD
ATSH
ATCH)
)
-
(1
ATMF
(
CNSD
CNSH
BC
1
BCOR
CNMF
GRSD
DENSD
GRSD
DENSH
GRSH
DEN
1
DENSD
DENSH
BETA
DENMF
ALFA
1
1.07
DENMF
SW
POR
RD
VSD
VSH
SX0
POR
TH
VSD
VSH
SX0
POR
U
VSD
VSH
SX0
POR
K
VSD
VSH
SX0
SX0
POR
AT
VSD
VSH
SX0
POR
CN
VSD
VSH
GR
VSD
VSH
SX0
POR
DEN


































































DEN effective density
GR natural gamma-ray intensity
CN neutron porosity
AT acoustic travel time
K potassium
U uranium
TH thorium
RD resistivity (uninvaded zone)
POR effective porosity
SX0,SW water saturation
VSH shale volume
VSD quartz (sand) volume
MF - mud filtrate CH - hydrocarbon
SH - shale SD - sand W - pore water
BA, BM, BN - textural constants
Petrophysical parameters
Zone parameters
Calculated well logs

Well logs serve as input data, petrophysical
parameters represent the model that should
be estimated, the relation between the data
and model are given by response functions
applicable to predict synthetic well logs
Inversion unknowns are petrophysical
(reservoir) parameters
A set of local joint inversion procedures are
solved to estimate the model parameters
Slightly overdetermined inverse problem
solved by the weighted least squares method
(weigh coefficients are data variances),
prediction errors should be normalized
because of the different magnitudes of data
Layer thicknesses are normally determined
manually or by cluster analysis (they are not
in the local response functions)
Interval inversion approach for improving
overdetermination rate and estimation
accuracy, estimation of layer thicknesses and
zone parameters varying slowly in the
processed interval
©Gearhart

Applied to solve an overdetermined inverse problem (N>M)
Objective function to be minimized
Weighting matrix
Solution of the inverse problem (∂E/∂m=0) is the estimated model vector
  )
m
(
)
d
(
T
1
)
d
(
T
)
est
(
d
W
G
G
W
G
m

 

   
min
d
d
E
2
N
1
k k
c
k
m
k











 



























2
RD
2
RS
2
U
2
K
2
GR
(d)
σ
0
0
0
0
0
σ
0
0
0
0
0
σ
0
0
0
0
0
σ
0
0
0
0
0
σ
W












Data types have different magnitudes and dimensional units
Consider the normalized deviation between the k-th field and calculated data
It is favorable to use normalization also in the model space
Let us shorten the above expression with new symbols ( )
It leads to the weighted least squares solution of the inverse problem

















M
1
j
j
m
j
k
)
o
(
k
)
o
(
k
)
o
(
k
)
m
(
k
)
o
(
k
k
k m
m
g
d
1
d
d
d
d
e
f
o

















M
1
j
)
o
(
j
j
m
j
k
)
o
(
k
)
o
(
j
)
o
(
k
)
o
(
k
)
m
(
k
m
m
m
g
d
m
d
d
d
f
o

o
m
j
k
)
o
(
k
)
o
(
j
ki
)
o
(
j
j
j
)
o
(
k
)
o
(
k
)
m
(
k
k
m
g
d
m
G
m
m
x
d
d
d
y
















y
W
G
x
G
W
G
min
f
W
f
E
x
G
y
f
T
T
T 











m
m
m 0







Input well logs
Result of cluster analysis

Evaluation of shale volume and hydraulic conductivity by factor analysis of hydrogeophysical well logs
Szabó et al. (2015)

Well-logging-methods_new................

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