Coures-Formation Evalution for petroleum Engineering -heriot watt university.pdf

Formation Evaluation
FOR
Petroleum Engineering

On September 5, 1927, a crew working for Schlumberger lowered an electric sonde
or tool down a well in Pechelbronn, Alsace, France creating the first well log.

Reservoir/Geological Model
Populate properties into simulation cells
 Stock Tank Original Oil In Place
 Productivity Index
 Recovery
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RESIDUAL
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Objectives

Aims
To understand rock properties
To understand the basic principles of the main wireline logging tools
To interpret downhole log sections
To quantify porosity, lithology, fluid saturations and permeability

WIRELINE LOGGING
Wireline logs are made using highly specialized
equipment entirely separate from that used for
drilling.
Onshore, a motorized logging truck is used which
brings its array of surface recorders, computers
and a logging drum and cable to the drill site.
Offshore, the same equipment is installed in a
small cabin left permanently on the rig.

WIRELINE LOGGING
Most logs are run while pulling the tool up from
the bottom of the hole. The cable attached to
the tool acts both as a support for the tool and
as a canal for data transmission.

WIRELINE LOGGING
The cable is wound around a motorized drum on
to which it is guided manually during logging.
The drum will pull the cable at speeds of
between 300 m/h (1000 ft/h) and 1800 m/h
(6000 ft/h), i.e. 0.3 to 1.8 km/h, depending on
the tool used. As the cable is pulled in, so the
depth of the working tool is checked.

Logging While Drilling (LWD)
Wireline logging where tool string is lowered into the well at the end of a
wireline cable after the hole is drilled.
The sensors in LWD are integrated into drill collars (DC’s) and the measurements
are made while the well is being drilled.
LWD tools provide deviation and logging options in high-angle wells.
LWD tools have to be very robust and strong to handle the torque, compression,
extension, and vibration of drilling, and certain tools (ie sonic etc) are expensive
and difficult to develop to handle this kind of treatment.

Logging While Drilling (LWD)
Advantages:
• Pre-invasion profiles and data prior to the hole washing out (or if there is a
risk of losing the hole) is obtained.
• Real time data is obtained for steering
• Data is obtained in situations where wireline acquisition is difficult (e.g. in
horizontal wells).

Measurement While Drilling (MWD)
First introduced in 1980’s to provide information on wellbore directional
surveys and other drilling related information in real-time during drilling.
Based on mud telemetry where pressure variations in the mud pulse
exercised by the tool were sensed by a computer on surface.
This technique does not allow a very high bandwidth telemetry path.

LOG DATA ACQUISITION
Wireline-logging technology is being changed by
the rapid advancements in digital
electronics and data-handling methods.
These new concepts have changed our thinking
about existing logging techniques and
remoulded our ideas about the direction of
future developments.

Basic logging measurements may contain large
amounts of information. In the past, some of this
data was not recorded because of the lack of high
data-rate sensors and electronics downhole, the
inability to transmit the data up the cable, and
inability to record it in the logging unit. Similarly,
those limitations have prevented or delayed the
introduction of some new logging measurements
and tools.

With digital telemetry, there has been a tremendous increase in the data rate that can
be handled by the logging cable.
Digital recording techniques within the logging unit provide a substantial increase in
recording capability. The use of digitised signals also facilitates the transmission of log
signals by radio, satellite, or telephone line to computing centres or base offices.

DATA TRANSMISSION
With the communications network, graphic data or log tapes can be transmitted
via satellite from the wellsite to multiple locations.
Other local transmission systems exist elsewhere in the world using telephone,
radio, and/or satellite communications. In some instances, transmission from the
wellsite is possible. In others, transmission must originate from a more permanent
communication station. With some preplanning, it is possible to transmit log data
from nearly any point in the world to another.

LOG RUNS
When a log is made it is said to be ‘run’. A log run is typically made at the end
of each drilling phase, i.e. at the end of the drilling and before casing is put in
the hole. Each specific log run is numbered, being counted from the first time
that the particular log is recorded. Run 2 of the ISF Sonic, for example, may
cover the same depth interval as a Formation Density Log Run 1. In this case it
means that over the first interval of the ISF Sonic, (i.e. Run 1), there was no
Formation Density log recorded.

Rock and fluid properties
1 Introduction
2 Rock classification system
3 Porosity
3.1 Primary Porosity
3.2 Secondary Porosity
4 Saturation
5 Permeability
5.1 Darcy's Law
5.2 Effective Permeability
5.3 Relative Permeability
6 Capillary pressure
7 Fluid properties
8 Water salinity
9 Determination of formation temperature

Porosity
Basic definitions
The capacity of the rock to contain fluids
Permeability
The ability of the fluids to flow through the rock
Saturation
The relative amounts of these fluids in the pore space
NTG
The percentage of a gross thickness of reservoir with sufficient
permeability such that it is capable of flowing hydrocarbons

ROCK CLASSIFICATION SYSTEM
This classification system is based on the following categories of rocks:
• Sandstones - SiO2;
• Limestones - CaCO3;
• Dolomite - CaCO3Mg CO3;
• NaCl, Anhydrite, Gypsum, Clay
Since the classification is on a purely chemical basis and not on a grain size basis,
silt is considered as a very small grained sandstone.
Chert is also classified as a sandstone although the crystal structure is different it
looks like sandstone on well logs.

The only apparent maverick in the system is shale,
which in reality is clay, and is classified as clay.
For general usage, there is no need to differentiate between the various clay
minerals which make up shales as long as clean shales are considered as being clay.
A few rock types have been omitted but these omissions are not considered serious.
For example, a conglomerate is nothing more than a grain size variation of
sandstone, limestones with regular, spherical grains are not classified as sandstones
but as limestone.

Limestone is calcium carbonate (CaCO3).
Since chalk results in the same response on logs as calcium carbonate, it is
classified as a limestone.
Dolomite (CaCO3Mg CO3) differs strongly from limestone on well log readings.
Physically, dolomite differs from limestone significantly in density, hardness and
other properties.
NaCl, Anhydrite, Gypsum and Clay are relatively common rocks, but differ
significantly from sandstone, limestone and dolomite.
Halite is common table salt, (NaCl) and will record as NaCl.
Anhydrite is calcium sulphate and although gypsum is calcium sulphate plus
crystalline water, the water in gypsum creates a large difference between the two
log responses.

Porosity
The capacity of the rock to contain fluids

Porosity
1- Primary Porosity
Usually related to granular, is the porosity developed by the original
sedimentation process by which the rock was created.
2- Secondary Porosity
Secondary Porosity is created by processes which occur after deposition.

Controls on Porosity
•Grain Size
•Grain Packing
•Grain Shape
•Grain Size Distribution
•Secondary Controls on Porosity

Porosity concepts in FE
Porosity reduction occurs with distribution of grain sizes so that
smaller grains fit between larger grains

Facts:
The highest porosity normally anticipated is 47.6%.
A more probable porosity is in the mid-twenties.
In reality, porosity’s greater than 40% are rare.
These may be found in surface sands that are neither compacted nor consolidate.

In general, porosities tend to be lower in deeper and older rocks.
This decrease in porosity is due primarily to:
1- overburden
2- time
3- stresses on the rock,
4- cementation.
There are many exceptions to this general trend when normal
overburden conditions do not prevail.

Shales follow very much the same porosity/depth trend as sandstones
except that porosities are normally lower in shales.
For example, in a recent mud the porosity measures about 40%.
It decreases rapidly with depth and overburden pressure until, at about 10,000ft
depth, normal porosities are less than 5%.
This is typical of Tertiary shales, with older shales being considerably more
compacted and thus lower in porosity.
Shales are essentially plastic and therefore compress more easily than sands.
These basic trends of porosity versus depth are not really noticeable in carbonates,
which tend to be pseudo-plastic and compress considerably more than sands.

Total porosity
The ratio of the entire pore space in a rock to its bulk volume.
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Effective porosity
The total porosity less the fraction of the pore space occupied by shale or clay.
Class discussions
Is this a correct assumption?

Clastics

Carbonates

Secondary Porosity :
The porosity created through alteration of rock, commonly by processes
such as dolomitization, dissolution and fracturing.

Fracture Porosity:
A type of secondary porosity produced by the tectonic fracturing of rock.
Fractures themselves typically do not have much volume, but by joining
pre_existing pores, they enhance permeability significantly.
In exceedingly rare cases, non_reservoir rocks such as granite can
become reservoir rocks if sufficient fracturing occurs!!!

A
Q 
Q= Rate of Flow, cm3/sec
Delta P= Pressure Differential, atm
A= Area, cm2
Mu= Fluid Viscosity, centipoise
L= Length, cm
K= Permeability, darcies
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Permeability

Conditions of Darcy’s Law?
1. Linear-laminar flow
2. No reaction between fluid and rock
3. One phase present at 100 percent pore-pace saturation
4. Incompressible fluid
Permeability

Effective Permeability
1) When only one fluid is present in the pores the permeability of the
formation is called the absolute permeability.
2) The effective permeability to any given fluid in a rock refers to permeability
when more than one fluid is present.
NOTE
Effective permeability is less than absolute permeability because the presence
of a second fluid reduces the effective pore diameter available for fluid flow.

Effective Permeability
NOTE:
In the case of a reservoir where only water is present, the permeability measured will
be absolute.
In the case where oil and water are present and the oil is flowing, the effective
permeability of the oil will be less than absolute permeability. This is due to the water
reducing the effective diameters of the pores through which the oil is flowing.

Relative Permeability
Relative permeability
Relative permeability curves reflect the capacity of the rock to produce given fluids
by showing the permeability of those fluids as a function of saturation.
The ratio of effective permeability of a specific fluid to absolute permeability.

Capillary pressure
Reservoir rocks are composed of many
capillaries of varying sizes. Capillary
pressure is the phenomenon by which
water or any wetting liquid is drawn up
into a capillary.
The smaller the capillary, the higher the
liquid rises.
Due to the variety of capillary diameters,
the water saturation existing within a rock
above the water table varies.

NET TO GROSS
NET:
Thickness of clean, permeable, hydrocarbon-containing rock in the reservoir zone.
Gross:
The thickness of rock in the reservoir zone irrespective of whether it is clean, its
permeability or its fluid saturation.
N2G:
The net to gross ratio (thickness of net rock divided by the thickness of gross rock) is
often used to represent the quality of a reservoir zone.

NET TO GROSS
Total Rock
Rock that can
store HC and
can flow
Rock that store HC
and can flow
Rock that can
contains HC
No HC
Rock that can store
HC but can’t flow
No HC
Rock that contains
no HC
Rock that can store
HC but can’t flow
No HC
GR, SP etc.
Por, K
Por, K,Sw
Gross Net Rock Net RES Net Pay

Reservoir Fluids
Reservoir fluids fall into three broad categories:
1- Aqueous solutions with dissolved salts
2- Liquid hydrocarbons
3- Gases (hydrocarbon and non-hydrocarbon).
In all cases their compositions depend upon:
1- Their source
2- History
3- Present thermodynamic conditions.

Water Saturation
Water saturation is the fraction (or percentage) of the pore volume of the
reservoir rock that is filled with water.
It is generally assumed, unless otherwise known, that the pore volume not filled
with water is filled with hydrocarbons.
Determining water and hydrocarbon saturation is one of the basic objectives of
well logging.

FLUID PROPERTIES
Hydrocarbons existing within reservoirs are combinations of compounds
such as methane, propane, butane and pentane.
In the reservoir, oil and gas are not distinguishable
as separate entities but are a system.
One way to define this system is with a pressure-
temperature (P,T) diagram which describes the
conditions of the material in the reservoir at any
given pressure or temperature.

WATER SALINITY
The waters in reservoirs in the earth vary from fresh to salt saturated
solutions. Near the surface, waters are generally very fresh with low sodium
chloride concentrations. Deeper, the waters tend to become saltier until
some maximum concentration occurs and the water often becomes fresher.
The salinity of the water is a result not only of its vertical position in the
earth, but also the age of the rocks and the physical position of the rocks
relative to surface outcrops.
At normal room temperatures, 250,000 ppm (parts per million) is a saturated
solution, while at higher temperatures the saturation point for waters is higher. For
example, at 300 degrees C, a 300,000 ppm sodium chloride solution is saturated.

FORMATION TEMPERATURE
The resistivity of aqueous solutions is a function of temperature.
The assumption that the geothermal gradient (the rate at which temperature
increases with increased depth) is linear is a good approximation.
Sometimes the maximum temperature in the borehole is less than the actual
formation temperature due to the cooling effect of circulating mud while drilling the
hole. If this is a problem, multiple runs with the maximum reading thermometer
should be made to determine a stabilised temperature.
The normal approach is
bottom hole temperature = formation temperature

Reservoir Fluids
The distribution of a particular set of reservoir fluids depends on:
Depth: The difference in the density of the fluids results in their separation over time due to gravity
(differential buoyancy).
Fluid Composition: The composition of the reservoir fluid has an extremely important control on its PVT
properties, which define the relative volumes of each fluid in a reservoir.
Reservoir Temperature: Exerts a major control on the relative volumes of each fluid in a reservoir.
Fluid Pressure: Exerts a major control on the relative volumes of each fluid in a reservoir.
Fluid Migration: Different fluids migrate in different ways depending on their density, viscosity, and the
wettability of the rock. The mode of migration helps define the distribution of the fluids in the reservoir.
Trap-Type: Clearly, the effectiveness of the hydrocarbon trap also has a control on fluid distribution (e.g.,
cap rocks may be permeable to gas but not to oil).
Rock structure: The microstructure of the rock can preferentially accept some fluids and not others
through the operation of wettability contrasts and capillary pressure. In addition, the common
heterogeneity of rock properties results in preferential fluid distributions throughout the reservoir in all
three spatial dimensions.

Summary of interpretation procedures
The objective of well logging is to determine the properties of the rocks which are
potential sources of hydrocarbons.
The logs are used to determine specifically :
• Lithology of Formation
Net to gross
• Porosity
• Fluid Content
• Saturation

The interpretation process can be summarised into the following bullet points:
• Correlate and depth match Logs
• Interpret Lithology
• Identify the permeable and non-permeable beds on the logs
• Determine and Divide the beds into zones consisting of water bearing and
hydrocarbon bearing zones
• Determine the porosity of the zones of interest
• Determine the hydrocarbon saturation of the zones of interest

CORRELATE AND DEPTH MATCH LOGS
This is necessary because the sondes are stacked upon each other in a particular
logging tool and only a certain number of sondes can be run in any particular tool.
Hence the sondes are making the measurements at different points in time as the
tool is being extracted from the well.
If the sondes were all at the same depth, at the same time, when making the
measurements then correlation would not be necessary.

The correlation of logs is usually performed on the basis of the Gamma Ray Log,
since the gamma ray log is generally run with each logging tool run in hole and
measurements made by the sondes on a particular logging tool are depth
matched automatically.
This means that all log measurements are automatically aligned with the Gamma
Ray log and therefore depth correlation of the Gamma Ray log from one logging
tool with the Gamma Ray log from another tool will ensure that all logs on both
tools are depth correlated.

INTERPRET LITHOLOGY
All exploration and appraisal wells the interpretation of the lithology will be supported by
evidence which is derived from drilled cuttings by the mudlogging engineer or wellsite
geologist and analysis of cores which have been cut and retrieved from the well.
In addition to the lithological description derived from the above, the mudlogger or
geologist will also provide an interpretation of the depth at which the formation horizons
were penetrated.
In the case of development wells the regional geology should be reasonably well defined.

INTERPRET LITHOLOGY
If the formation is made up of one mineral then a particular log
measurement may be used to identify that mineral and therefore infer the
rock type (lithology).
However, if the formation is made up of a mixture of known minerals then it
is necessary to use a combination of logs to obtain a good indication of the
mineralogical content and therefore lithology of the formation.
The composition of the rock can be inferred by crossplotting combinations
of the Density, Neutron and Acoustic log data

IDENTIFICATION OF PERMEABLE AND NON-PERMEABLE ZONES
The permeable zones on a suite of logs can be identified by referring to the
GR, SP and resistivity logs.
The Gamma Ray log is generally used as a depth reference tool and the Gamma Ray
sonde is therefore run with all logging tools.
It is however primarily used from an interpretation viewpoint to differentiate
between shales and other formation types.
Since shales generally have a very low permeability (very common caprocks) the
Gamma Ray log response can be used in a qualitative way to identify non-
permeable zones.

IDENTIFICATION OF PERMEABLE AND NON-PERMEABLE ZONES
The permeable zones on a suite of logs can be identified by referring to the
GR, SP and resistivity logs.
A comparison of the resistivity readings from the flushed zone, shallow and deep into
the reservoir will give some indication of the depth of penetration of the borehole
fluid and therefore the permeability of the formation.
We will discuss SP in the related chapter when we introduce the tool.

The resistivity logs can only be used to differentiate between hydrocarbons and water.
This is because the conductivity of gas and oil will be similar whereas the resistivity of
(salt) water and hydrocarbons will be significantly different.

When a permeable zone is penetrated by the
drillbit the drilling mud will try to penetrate
the permeable formation.
If the size of the pores in the formation are
smaller than the solids in the drilling fluid
then the solids will be trapped on the surface
of the wellbore and the fluid in the drilling
mud will pass through the solids into the
formation.

When invasion occurs, the wellbore is coated
with a thin film of solids known as the “filter
cake”.
The formation next to the wellbore is
“flushed” by the mud filtrate moving into the
formation and is therefore known as the
“flushed zone”.
The hydrocarbon saturation in the flushed
zone is a minimum and all of the formation
water is removed.

The formations deeper into the formation are
affected progressively less than the flushed
zone until at some radial depth into the
formation the fluids in the pore space are
undisturbed.
In a hydrocarbon bearing formation the hydrocarbon
saturation is reduced in the flushed zone and
increases in the transition zone until the original
saturation is reached in the undisturbed zone.

In a water bearing formation the water
saturation in the zone between the flushed
zone and the undisturbed zone would not
change but the salinity and therefore the
resistivity may.
These changes in saturation and resistivity
create resistivity profiles which can be used to
identify the water bearing and hydrocarbon
bearing formations.

When using freshwater mud:
The resistivity of the mud filtrate > formation water
Therefore in a water bearing zone the resistivity of the flushed zone is high and the
resistivity readings decrease with movement out into the undisturbed zone.
Depth

In a hydrocarbon bearing formation the resistivity of the zone behind the flushed
zone may be higher or lower than the flushed zone depending on the water
saturation and resistivity of the formation water.
When using a salt water mud the flushed zone has a lower or similar resistivity than
the undisturbed zone if the undisturbed zone contains high resistivity water. The
undisturbed zone will have higher resistivity if the formation contains hydrocarbons.
Depth

DETERMINE THE POROSITY OF THE ZONES OF INTEREST
Rock porosity is generally determined from the measurements from one,
or a combination of, the following logs:
• Acoustic log
• Density log
• Neutron log.

DETERMINATION OF SATURATION
The electrical resistivity of a formation is a very good indicator of the fluid in the
pore space of that formation.
Neither oil nor gas conducts electrical current but water does.
It is very rare however for a formation to contain no water at all and there is
generally some level of water saturation of the pore space, Sw in all formations.

Saturation Interpretation

Formation evaluation tools and analysis
1- GR
2- SP
3- Acoustic
4- Density
5- LithoDensity
6- Neutron
7- NMR
8- Resistivity

Compton scattering
is an inelastic scattering of a photon by a free charged particle, usually an electron.
Radioactivity in Nature- Gamma Ray
It results in a decrease in energy (increase in wavelength) of the photon (which may
be an X-ray or gamma ray photon).
Part of the energy of the photon is transferred to the scattering electron.

Compton scattering
Radioactivity in Nature- Gamma Ray
A gamma ray of energy E" transfers a portion of its energy to an electron e".
This results in a gamma ray of reduced energy E' leaving the site of collision at an angle,
with respect to the direction of the incident gamma ray.
The displaced electron is shown by e'.

What it does for us?
Estimate shale content
Estimate bed boundaries, stratigraphic correlations
Perforating depth control
Identify mineral deposits of potash, uranium, and coal
Monitor movement of injected radioactive material
GR

UNIT API
However, this results in extremely unwieldy values. Conventionally, the gamma ray log is
reported in pseudo-units called API units.
The API unit is defined empirically by calibration to a reference well at the University of
Houston. This reference well is an artificial one that is composed of large blocks of rock of
accurately known radioactivity ranging from very low radioactivity to very large radioactivity.
The API unit is 1/200th of the difference between the highest activity formation in the
reference well, and the lowest.

GR- Uses of the Total Gamma Ray Log
Every well may have as many as 5 independent sets of gamma ray log data. Why?
I. Determination of Lithology
II. Determination of Shale Content
III. Depth Matching
The high vertical resolution of the gamma ray log makes it extremely useful for
depth matching and fine scale correlation.
The first three applications are by far the most important.

GR- Determination of Shale Content
In most reservoirs the lithologies are quite simple, being cycles of sandstones and
shales or carbonates and shales.
Once the main lithologies have been identified, the gamma ray log values can be
used to calculate the shaliness or shale volume Vsh of the rock.
This is important as a threshold value of shale volume is often used to help
discriminate between reservoir and non-reservoir rock.

Shale volume is calculated in the following way:
- First the gamma ray index IGR is calculated from the gamma ray log data using the
relationship
min
max
min
log
GR
GR
GR
GR
IGR
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


However, to be correct the value of IGR should be entered into the chart from which
the corresponding value of Vsh may be read.

Spectral Gamma Ray (SGR)Tools
Physical Principle
Most of the gamma ray radiation in the earth originates from the decay of
three
radioactive isotopes:
potassium 40 (K40), with a half-life of 1.3 x 109 years;
uranium 238 (U238), with a half-life of 4.4 x 109 years; and
thorium 232 (Th232), with a half-life of 1.4 x 1010 years.

FOR
Reservoir Evaluation and Management
Petroleum Geoscience

Formation evaluation tools and analysis
1- Radioactivity
GR, Vsh and NTG
2- Resistivity
Saturation
3- Acoustic
Porosity, geology, seismic
4- Density
Total porosity, gas-bearing, evaporates, ...
5- Neutron
Porosity, Lithology, gas-bearing, …
6- LithoDensity
Lithology, Heavy Minerals and Inter-Well Correlation, fractures
7- ... SP, NMR, PLT, FMI, LWD , VSP, ...

Acoustic
The sonic or acoustic log measures
the travel time of an elastic wave
through the formation. This
information can also be used to
derive the velocity of elastic waves
through the formation.

Acoustic
When the sound energy arrives at the receiver, having passed through the rock, it
does so at different times in the form of different types of wave. This is because the
different types of wave travel with different velocities in the rock or take different
pathways to the receiver.

Acoustic tools
The transmitter fires at t = 0.
It is not shown in the figure because it is masked
from the received information by switching the
receiver off for the short duration during which
the pulse is transmitted. This is done to ensure
that the received information is not too
complicated, and to protect the sensitive
receiver from the high amplitude pulse.

Acoustic
The bulk modulus, K is the extent to which a material can withstand isotropic squeezing
Imagine an amount of material subjected to an isotropic pressure P1. Now let the
isotropic pressure increase to a pressure P2. The material will compress from its initial
volume v1 to a new smaller volume v2. The bulk modulus is then given by;
  1
1
2
1
1
2
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/ v
v
P
v
v
v
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P
K
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Acoustic
The shear modulus, m is the extent to which a material can withstand shearing.
Imagine an amount of material subjected to a isotropic pressure P1. Now apply a
shear stress (non-isotropic pressure) Ps to one side of the sample. The material will
shear to the new shape, and its overall length will increase from its initial length l1
to a new larger length l2. The bulk modulus is then given by;

 s
s P
l
l
P



1
2

Acoustic tools
Borehole Compensated Sonic (BHC) Tool
This tool compensates automatically for problems
with tool misalignment and the varying size of the
hole (to some extent) that were encountered with
the dual receiver tools.
It has two transmitters and four receivers,
arranged in two dual receiver sets, but with one
set inverted (i.e., in the opposite direction).

Acoustic tools
Sometimes the first arrival, although
strong enough to trigger the
receiver nearer the transmitter, may
be too weak by the time it reaches
the far receiver to trigger it.

Acoustic tools
Instead, the far receiver may be triggered by a different, later arrival in the sonic
wave train, and the travel time measured on this pulse cycle will then be too large
and not representative of the true compressional wave velocity in the formation.
When this occurs, the sonic curve shows a very abrupt and large excursion towards
a higher t value. This is known as "cycle skipping".
Such skipping is more likely to occur when the signal is strongly attenuated by
unconsolidated formations, formation fractures, gas saturation, aerated muds, or
rugose or enlarged borehole sections.

Acoustic tools
Long-spaced Sonic (LSS) Tools
LSS sonic tools, with transmitter-receiver spacings of 8 ft and 10 ft or 10ft and 12ft,
measure the interval transit time of the formation better than the usual BHC sonic
tool. This tool is more likely to yield a measurement free from the effects of
formation alteration, relaxation damage (from the drilling process), and enlarged
borehole.

Acoustic tools
Array Sonic Tools
The tool provides all of the measurements provided by
the BHC and LSS logs and, in addition, provides several
other features. The tool contains two broadband (5 to 18
kHz) piezoelectric transmitters spaced 2 ft apart. Two
piezoelectric receivers are located 3 ft and 5 ft from the
upper transmitter. These receivers have a dual role. In
open hole, they are used in conjunction with the two
transmitters to make standard short-spaced 3ft - 5ft and
5ft -7ft depth-derived, borehole-compensated t logs. In
cased wells, they are used to make standard 3ft cement
bond logs (CBL) and 5-ft Variable Density* logs (VDL).

Sonic log
Porosity Determination
1. The Wyllie Time Average Equation
2. Empirical Equation
3. Core porosity
4. Secondary and Fracture Porosity
5. The Effect of Shale, hydrocarbon and prsessure

Sonic log
Porosity Determination
The sonic log is commonly used to calculate the porosity of formations, however
the values from the FDC and CNL logs are superior.
It is useful in the following ways:
 As a quality check on the FDC and CNL log determinations.
 As a robust method in boreholes of variable size (since the sonic log is relatively
insensitive to caving and wash-outs etc.).
 To calculate secondary porosity in carbonates.
 To calculate fracture porosity.

Sonic log
The Wyllie Time Average Equation
“the time average equation“.
ma
f
ma
s
t
t
t
t







log


Sonic log
A list of input values to these equations for common lithologies and fluids is given
in the Table.
The Wyllie Time Average Equation

Sonic log
Calibration against Core
Occasionally, there is good core coverage in a well,
so core porosities are available. If this is the case,
it is useful to calibrate the sonic log against the
core porosity. A cross-plot of core porosity against
the transit time at the same depth should produce
a straight line that can be extrapolated to the x-
axis to give a value for the local matrix transit
time dtma.

Sonic log
Porosity from Empirical Equation
Long-standing problems with using the time-average equation, coupled with
numerous comparisons of sonic transit time versus porosity, led to the
development of an empirical transit time-to-porosity transform. The transform is
empirical, being based entirely on comparisons of sonic transit time and an
independent porosity measurement.

Sonic log
Secondary and Fracture Porosity
  S
D
N 


 
 ,
2
By contrast, the density and neutron logs record the total porosity.
The sonic log is sensitive only to the primary intergranular porosity.
The difference between the two measurements, therefore, can be used to calculate a
value for the secondary porosity, whether it be isolated vugs in carbonates or
fractures. This is called the secondary porosity index (SPI or fie2), and is defined:

Sonic log
The Effect of Shale on the Sonic Derived Porosity
If any shale laminae exist within the sandstone, the apparent sonic porosity
values are usually increased by an amount proportional to the bulk volume
fraction of laminae. The t readings are increased because tsh is generally
greater than t ma of the sandstone matrix.
The following formula is used to correct for shaliness.

Sonic log
The Effect of Gas on the Sonic Derived Porosity
Generally, consolidated and compacted sandstones have porosities from 15 to
25%. In such formations, the response of the sonic log seems to be relatively
independent of the exact contents of the pores: water, oil, gas, or even
disseminated shale. However, in some higher porosity sandstones (30% or
greater) that have very low water saturation (high hydrocarbon saturation) and
very shallow invasion, the t values may be somewhat greater than those in the
same formations when water saturated.

Sonic log
Overpressure
Formations having abnormally high fluid pressures
are often overlain by overpressured shales, which
have an excess of pore water. Sonic transit time is
greater in these shales than in normally compacted
shales. Thus, a sonic log may be used to predict the
possibility of over-pressure.
An overpressured zone distinguished from sonic log data.

Compton scattering
is an inelastic scattering of a photon by a free charged particle, usually an electron.
It results in a decrease in energy (increase in wavelength) of the photon (which may
be an X-ray or gamma ray photon).
Part of the energy of the photon is transferred to the scattering electron.
DENSITY LOGGING TOOLS

Compton scattering
A gamma ray of energy E" transfers a portion of its energy to an electron e".
This results in a gamma ray of reduced energy E' leaving the site of collision at an angle,
with respect to the direction of the incident gamma ray.
The displaced electron is shown by e'.
DENSITY LOGGING TOOLS

THE FORMATION DENSITY LOG
Density logs are primarily used as porosity logs. Other uses include:
A. Identification of minerals in evaporite deposits,
B. Detection of gas,
C. Determination of hydrocarbon density,
D. Evaluation of shaly sands and complex lithologies,
E. Determination of oil-shale yield,
F. Calculation of overburden pressure
G. Rock mechanical properties

THE FORMATION DENSITY LOG
FDC Log Presentation.

Density Operation
All the newer tools have two detectors to
help compensate for the mudcake
problem.
The newer two detector tools are called
compensated formation density logs, an
example of which is Schlumberger’s FDC
(Formation Density Compensated) tool.

Density tools
Calibration
Corrections also need to be made if the borehole is larger than 10 inches in
diameter.

Density log
Determination of Porosity
The porosity (fie) of a formation can be obtained from the bulk density if the
mean density of the rock matrix and that of the fluids it contains are known.
The bulk density rhob of a formation can be written as a linear contribution of
the density of the rock matrix rhoma and the fluid density rhof , with each
present is proportions (1- fie) and fie, respectively :

Density log
  f
ma
b 


 

 1
When solved for porosity, we get
f
ma
b
ma








rhob = the bulk density of the formation
rhoma = the density of the rock matrix
rhof = the density of the fluids occupying the porosity
f ie= the porosity of the rock.

Density log
The value of the matrix density taken depends upon the lithology of the interval under
question. For sandstones, the density of quartz is 2.65 g/cm3, and for limestones, the
density of calcite is 2.71 g/cm3. Clay minerals have varied grain densities. Often core
data is used to provide accurate matrix densities for particular intervals.

Density log
The Effect of Fluid Density.
The porosity may also be in error if the fluid density is misjudged.
The fluid existing in the zone of the rock measured by the formation density tool is
usually mud filtrate.
The density of these fresh and salt waters is approximately 1.0 g/cm3 and 1.1 g/cm3,
respectively. However, these vary with temperature and composition, so accurate
values for the actual reservoir formation water at the relevant reservoir temperatures
should be used wherever possible.

Repeat Formation Tester (RFT)
Objectives:
(1) measurement of formation fluid pressure at a number of depths, permitting the
estimation of fluid pressure gradients, initial reservoir pressure and fluid contacts.
(2) sampling of reservoir fluids at selected depths, to confirm the reservoir contents
indicated from petrophysics and from (1) above.
(3) collection of PVT samples of the reservoir fluid to determine composition
and yield data for the preliminary design of processing facilities.
(4) indications of formation permeability.

Modular Dynamics Formation Tester (MDT)
Objectives:
(1) measurement of formation fluid pressure at a number of depths, significant
improvements through Combined Quartz Gauge (CQG) and sampling capabilities
(efficient fluid contacts determination).
(2) Condensates and critical fluids at the sandface sampling can be done fast
(3) Lateral hydraulic continuity (recently done in ME)
(4) Ability to to control a multitude of tool functions from the surface
...

Density log
The Effect of Gas
If residual hydrocarbons exist in the region investigated
by the FDC tool, their presence may affect the log
readings. The effect of oil may not be noticeable
because the average fluid density, ρf (from ρo and ρmf )
will probably still be close to unity. If there is appreciable
residual gas saturation, its effect will be to lower the ρa.
Figure shows the corrections that must be added to the
recorded ρa values to obtain true ρb values when low-
pressure gas or air (ρg approx. = 0) occupies the pores.

Density log
The Effect of Shale
Interpretation of the density log can be affected by shale or clay in the formations.
Although the properties of shales vary with the formation and locality, typical
densities for shale beds and laminar shale streaks are of the order of 2.2 to 2.65
g/cm3. Shale densities tend to be lower at shallow depths where compacting
forces are not as great. Dispersed clay or shale disseminated in the pore spaces
may have a somewhat lower density than the interbedded shales. The following
relation exists to correct for shaliness.

Density log
The Effect of Shale
This corrected value of density may then be used in Eq.
f
ma
b
ma








 
sh
sh
sh
b
bclean
V
V



1
.




Density log
Calibration with Core Porosities

Density log
Identification of Lithology

Density log
EFFECT OF PRESSURE ON POROSITY DETERMINATION
The bulk density of shale increases with compaction, and
in areas where the sediments are relatively young the
increase of shale density with depth is apparent on the
logs.
However, departure from this trend is observed in over-
pressured zones; shale density decreases with increasing
depth.

Density log
EFFECT OF PRESSURE ON POROSITY DETERMINATION
This decrease often appears in shales as much as
several hundred feet above high-pressure permeable
sands. A high-density zone (the sealing barrier) usually
lies at the top of this interval of decreased density.
Density logs run at intervals during the drilling of a
well can be used to predict abnormally pressured
zones so that precautions can be taken to eliminate
possible hazards.

Litho Density Tool
The Litho-Density Log is an improved and expanded version of the FDC log. In
addition to the bulk density measurement, the tool also measures the photoelectric
absorption index of the formation, Pe. via Photoelectric Effect.
When the photon, in the course of a collision with an electron, transfers all its energy to
the electron in the form of kinetic energy, the electron is ejected from its atom and the
photon disappears.

Litho Density Tool
Compton Scattering and Photo-Electric Absorption

Factors Influencing the PEF Log
Litho Density Tool

Litho Density Tool
Uses of the Litho-Density Log
Determination of Lithology

Litho Density Tool
Uses of the Litho-Density Log
Determination of Lithology
Matrix identification in a multi-mineral system using the PEF and density log
data for a formation saturated with a fluid of density equal to 1.0 g/cm3.

Neutron tools
Neutron logs are used principally for delineation of porous
formations and determination of porosity. They respond
primarily to the amount of hydrogen in the formation.
Thus, in clean formations whose pores are filled with water
or oil, the neutron log reflects the amount of liquid filled
porosity.
The scattering reactions occur most efficiently with
hydrogen atoms.

Neutron tools
Neutron Emission




 n
C
He
Be
1
0
12
6
4
2
9
4

Neutron tools
Neutron Absorption
significant absorbing
1- Hydrogen
2- Chlorine



 H
n
H 2
1
1
0
1
1



 Cl
n
Cl 37
17
1
0
36
17

Neutron tools
Hydrogen Index
 
 

i
H
H
i
i
H
H
mass
H
A
n
A
n
A
n
C
AH = the atomic mass of hydrogen atoms in the material
Ai = the atomic mass of non-hydrogen element i
nH = the number of hydrogen atoms in a molecule of the material
ni = the number of non-hydrogen atoms of element i in a molecule of the material

Neutron tools
Hydrogen Index
Hydrogen index calculations for some reservoir minerals and fluids.

Neutron tools
There are three main types of neutron tool:
• The Gamma Ray/Neutron Tool (GNT)
• The Sidewall Neutron Porosity Tool (SNP)
• The Compensated Neutron Log (CNL)

Neutron tools
Gamma Ray/Neutron Tool (GNT)
This tool has a neutron source and a single detector that is sensitive to high energy
capture gamma rays and thermal neutrons and is non-directional.
The tool can be run in either open or cased holes, and in both cases is run centered.
Because the tool is centered, the detected neutrons and gamma rays have to travel
through both mudcake and drilling mud.
1-A 3-3/8 inches diameter tool is used in open holes,
2- A 1-11/16 or 2 inch diameter tool is used in cased holes.
The source to detector spacing varies between tool manufacturers, but is in the
range 15.5 to 19.5 inches.

Neutron tools
Sidewall Neutron Porosity Tool (SNP)
This tool is designed for use in open holes only. The tool has a source and a single
detector with a 16 inch spacing, which are mounted on a skid that is pressed against
the borehole wall.
Often this will be the same carrier that holds the formation density source and detector.
Because the tool is pressed against the borehole wall, the drilling mud does not affect
the measurement, and the attenuation due to the mudcake is reduced.

Neutron tools
Sidewall Neutron Porosity Tool (SNP)
However rough holes can cause misalignment of the either the source of the detector
with the borehole wall, and hence give erroneous readings.
The detector is sensitive to epithermal neutrons. These neutrons are not yet slow
enough to take part in absorption reactions with hydrogen and chlorine.
Hence, the SNP tool readings are unaffected by the presence of chlorine in high salinity
muds and formation fluids.

Neutron tools
Compensated Neutron Log (CNL)
This tool is designed to be sensitive to thermal neutrons, and is therefore affected by
the chlorine effect. It has two detectors situated 15in and 25in from the source.
The detector further from the source is larger to ensure that adequate count rates
are observed.
The critical measurement for this tool is the difference in the thermal neutron
population, which results from neutron capture and neutron scattering.

Neutron tools
The tool readings are presented in limestone porosity units in the same way as the
sidewall neutron porosity tool.
The CNL tool has a very strong source of neutrons to ensure that the measured
count rates are sufficiently high to obviate any significant errors associated with
statistical fluctuations in the count rate despite the longer source-detector spacing
for this tool compared to the GNT and SNP tools.

Neutron tools
The stronger source permits a deeper
depth of investigation as well as allowing
the tool to operate in cased holes.
The CNL tool is run eccentred in the hole by
an arm which presses the tool against the
side of the borehole. This means that the
tool is insensitive to the type of mud in the
hole, but implies that the readings are only
for one portion of the borehole wall.

Neutron tools
Uses of the Neutron Log

Neutron tools
EFFECT OF SHALE
Also, the neutron tool measures water of crystallisation.
For example, nonporous gypsum (CaSO4 + 2H2O) has a large apparent porosity
because of its significant hydrogen content.
sh
sh
Nsh
N
clean
N
V
V



1
.
_



To correct for shaliness, use the relation:

Neutron tools
EFFECT OF CARBONATES ON POROSITY DETERMINATION
In carbonates having intergranular porosity the time average formula still applies,
but, sometimes, pore structure and pore size distribution are quite different from
that of sandstones. There is often some secondary porosity consisting of vugs and/
or fractures with much larger dimensions than the pores of the primary porosity.
In vuggy formations, the velocity of sound seems to depend mostly on the primary
intergranular porosity, and the porosity derived from the sonic reading through the
time-average formula (φSV) will tend to be too low by an amount approaching the
secondary porosity. Thus, if the total porosity (φt) of a formation exhibiting primary
and secondary porosity (φ2) is available (from a neutron and/or density log, for
example, the amount of secondary porosity can be estimated:

1
2
Volume of Shale
5. Form the menu bar click
on Log-> Shale volume->
Neutron Density
6. The Vshale input dialogue
box pops up
- Select the well (s), the
family and click the Neu
and Density buttons to
activate both curves
- Click create to activate the
work flow manager
Density-Neutron
ɸ Neu – ɸ Den
____________________
ɸNeushale – ɸDenshale
Vshale =
5
6
26

Neutron tools
Determination of volume of the shale
from Density Neutron Crossplot
The separation between neutron and density porosity is a
common method for calculating shale volume.
It is accurate only when the shaly sand contains pure quartz
plus clay minerals.

Neutron tools
Most sandstones are not pure quartz. When other minerals
are present, some of the separation is due to these minerals.
Micas, siderite, ankerite, and volcanic rock fragments are
common in many sandstones. All are heavier than quartz,
causing the excess separation by reducing density porosity
and increasing neutron porosity.

Neutron tools
Density log in porosity units follows the classical form:
(water term) PHID = PHIe * Sxo * PHIDw
(hydrocarbon term) + PHIe * (1 - Sxo) * PHIDh
(shale term) + Vsh * PHIDsh
(matrix term) + (1 - Vsh - PHIe) * Sum (Vi * PHIDi)
PHIDh = log reading in 100% hydrocarbon
PHIDi = log reading in 100% of the ith component of matrix rock
PHID = log reading
PHIDsh = log reading in 100% shale
PHIDw = log reading in 100% water
PHIe = effective porosity (fractional)
Sxo = water saturation in invaded zone (fractional)
Vi = volume of ith component of matrix rock
Vsh = volume of shale (fractional)

Neutron tools
Neutron log in porosity units follows the classical form:
(water term) PHIN = PHIe * Sxo * PHINw
(hydrocarbon term) + PHIe * (1 - Sxo) * PHINh
(shale term) + Vsh * PHINsh
(matrix term) + (1 - Vsh - PHIe) * Sum (Vi * PHINi)
PHINh = log reading in 100% hydrocarbon
PHINi = log reading in 100% of the ith component of matrix rock
PHIN = log reading
PHINsh = log reading in 100% shale
PHINw = log reading in 100% water
PHIe = effective porosity (fractional)
Sxo = water saturation in invaded zone (fractional)
Vi = volume of ith component of matrix rock
Vsh = volume of shale (fractional)

Neutron tools
The following assumptions are made:
PHIDw = PHIDh = PHINw = PHINh = 1.0,
PHIDi = PHINi = 0.0. Sxo = 1.0
Then by subtracting the two equations and solving for Vsh,
we get:
Vshxnd = (PHIN - PHID) / (PHINSH - PHIDSH)

ELECTRICAL LOGGING
P.A. Dickey 1942

ELECTRICAL LOGGING
 
I
V
r
I
V
V
r
R M
A 


 
 4
4
Old Electrical Logs

ELECTRICAL LOGGING
The Basic Laterologs LL3
The LL3 also uses currents from bucking electrodes to
focus the measuring currentinto a horizontal sheet
penetrating into the formation. Symmetrically
placed on either side of the central A0 electrode are
two very long (about 5-ft) electrodes, A1 and A2, which
are shorted to each other. A current, io, flows from the
A0 electrode, whose potential is fixed. From A1 and A2
flows a bucking current, which is automatically adjusted
to maintain A1 and A2 at the potential of Ao.

ELECTRICAL LOGGING
The LL7 device comprises a centre electrode, A0, and
three pairs of electrodes: M1and M2; M’1 and M’2; and
A1 and A2. The electrodes of each pair are symmetrically
located with respect to A0 and are electrically connected
to each other by short-circuiting wire. A constant
current, io, is emitted from A0. Through bucking
electrodes, A1 and A2 , an adjustable current is emitted.

ELECTRICAL LOGGING
The bucking current intensity is adjusted automatically
so that the two pairs of monitoring electrodes, M1
and M2 and M’1 and M’2, are brought to the same
potential. The potential drop is measured between
one of the monitoring electrodes and an electrode at
the surface (i.e., at infinity). With a constant io current,
this potential varies directly with the formation
resistivity.

ELECTRICAL LOGGING
The shallow-investigation LL8 measurement is recorded with small electrodes on
the dual induction-laterolog sonde. The device is similar in principle to the LL7
tool except for its shorter spacings. The thickness of the i0 current sheet is 14 in.,
and the distance between the two bucking electrodes is somewhat less than 40 in.
The current-return electrode is located a relatively short distance from A0. With this
configuration, the LL8 device gives sharp vertical detail, and the readings are more
influenced by the borehole and the invaded zone than those of the LL7 and LL3 tools.

ELECTRICAL LOGGING
The Dual Laterolog

ELECTRICAL LOGGING
The Spherically Focussed Log
MSFL: Micro Spherically Focused Log

ELECTRICAL LOGGING
Induction Logs
Environmental Factors on Induction Logging Tools
Invasion
The invaded and flushed zone signals become more important when invasion
diameter (di) increases and the resistivity contrast between invaded and virgin
zones increases. For the old tools, service companies provide charts allowing the
determination of di and Rt when Rxo was known. The invasion affect becomes
significant when the resistivity of the formation is higher than that of the invaded
zone.

ELECTRICAL LOGGING
Induction Logs
Annulus
In highly permeable oil bearing formations with low water saturation and high oil
mobility, it is possible for an annulus of high formation water saturation to form
between the invaded and virgin zones. The outcome of this results in an
erroneously low Rt. Necessary corrections provided by the service companies
should be applied to compensate for this effect.

ELECTRICAL LOGGING
Induction Logs
Skin Effect
For very conductive formations, secondary currents (also called eddy currents) are
produced within the formation. These currents create a negative electromotive
force (emf) which opposes the original magnetic field produced by the transmitter
coil in the induction logging tool. When present near the vicinity of the tool, these
secondary currents tend the electromagnetic field to penetrate deeper into the
formation. Modern tools have auto corrections applied.

ELECTRICAL LOGGING
Induction Logs
Bed Thickness and Adjacent Beds
Service companies provide charts to correct for bed thickness (if it is smaller than
the vertical resolution of the tool) and for shoulder bed resistivities. If the bed is
very thin and conductive, correction becomes necessary because the measured
resistivity in that zone will read too low.

ELECTRICAL LOGGING
Log Presentation

ELECTRICAL LOGGING
Uses of Electrical Logs
Recognition of Hydrocarbon Zones
Calculation of Water Saturation
Textures and Facies Recognition
Correlation
Lithology Recognition

RESISTIVITY
r
E
I


L
A
I
E
R


A
L
E
I
R
C



1

RESISTIVITY
Material Resistivity
Oil
Gas
Formation Water
Water based mud filtrate
Oil based mud filtrate
Matrix Material
HIGH
LOW
LOW
HIGH
HIGH
HIGH

RESISTIVITY
Uninvaded Formations
we can say that the resistivity of the formation Rt depends upon
1) Porosity
2) water saturation Sw,
3) the resistivity of the formation water Rw.
This resistivity is called the true resistivity of the formation.
It is the resistivity of the formation in the uninvaded zone, where the rock contains
some saturation of oil So, gas Sg, and water Sw, and where So+Sg+Sw=1.

RESISTIVITY
Formation Factor (Archie’s First Law)
w
o FR
R 
m
F 

m = the cementation index/factor/exponent (no units).
w
m
o R
R 


RESISTIVITY
Formation Factor (Archie’s First Law)
There are a range of equations used in the oil industry to calculate the formation factor
1- The Humble Formula.
This is applied to clean sandstones with a sucrosic texture.
2- The Soft Formation Formula.
3- The Low Porosity Carbonate Formula. Valid for low porosity clean carbonates with
no fracturing.
15
.
2
62
.
0 

 
F
2
81
.
0 

 
F
m
F 


019
.
0
87
.
1 

m

RESISTIVITY
Partial Water Saturation
Archie’s Second Law!
n
w
S
I 

where:
Sw = the fractional water saturation of the rock
I = the resistivity index
n = the saturation exponent.
o
t IR
R 

RESISTIVITY-Saturation
Combining Archie’s Laws
o
t IR
R  w
o FR
R  n
w
S
I 

m
F 

w
m
n
w
t R
S
R 

 
But we are interested in Sw
n
t
o
n
t
w
n
t
m
w
w
R
R
R
F
R
R
R
S 





n
t
o
n
t
w
n
t
m
w
w
R
R
R
F
R
R
R
S 





True Formation Resistivity Rt
 Since drilling mud invasion affects a significant portion of the formation around the borehole, it is
important to evaluate the invasion profile and, if necessary, perform the necessary corrections.
 The determination of Rt can be a problem in case of thin beds. It is a good practice to make sure that the
resistivity devices in use have the resolution that we need.
 If there are clays present in the formation, the bound water in clays can act as a conductor and this can
decrease the Rt value.
 Also the overburden pressure at insitu downhole can cause a significant increase in Rt.

SW calculation
Humble Equation Procedure
Step 1: Determine porosity from acoustic, density or Neutron log.
Step 2: Determine F from Humble Formula
Step 3: Determine Rt from deep reading
corrected for borehole, bed thickness and invasion.
Step 4: Determine Rw
Step 5: Determine Sw from the Archie Equation

SW calculation
SW-1 chart
n
t
o
n
t
w
n
t
m
w
w
R
R
R
F
R
R
R
S =
=
=
−
φ

SW calculation
Sw-1 for flushed zone water saturation:
1) The Rxo reading is inserted on the Rt leg of the
nomograph
2) Rmf value is inserted in the Rw leg.

SW calculation
Flushed Zone in Humble Equation Procedure
Step 3: Determine Rxo from shallow resistivity log
Step 4: Determine Rmf

SW calculation
RESISTIVITY VS POROSITY CROSSPLOTS
n
t
m
w
w
R
R
S
−
=
φ
m=n=2 and a=1
t
w
w
R
R
S =
.
ϕ
t
w
w
R
S
R 1
=
ϕ

SW calculation
Assumptions:
1- 100% water-saturated formation, Sw = 1
2- Rt = Ro
If Ro for water-saturated formations is plotted on an inverse square-root scale
versus porosity, all points should ….
fall on a straight line given by
o
w
R
R
=
ϕ
t
w
w
R
S
R 1
=
ϕ

SW calculation
Furthermore, the points corresponding to any other constant value of Sw
will also fall on a straight line, since in Equation
the coefficient,√Rw/Sw, is constant for constant values of Rw and Sw.
t
w
w
R
S
R 1
=
ϕ

Several points plotted over an interval in which
formation-water resistivity is constant
Assuming that at least some of the points are from
100% water bearing formations,
the line for Sw = 1 is drawn from the pivot point
(porosity= 0, Rt = ∞)through the most north-
westerly plotted points.

The slope of this line defines the value of Rw.
For porosity = 10%,
Ro = 6.5 ohm.m.
For this formation, the most appropriate F - porosity
relation is
Thus, for porosity = 10%, F = 100.
Since Rw = Ro/F, Rw = 6.5/100 = 0.065 ohm.m
2
1
ϕ
=
F

For other Sw values, Rt and Ro are related by the
equation
For Sw = 50%, 1/Sw2= 4, and Rt = 4Ro.
This relation establishes the line for Sw = 50%.
2
w
o
t
S
R
R =

RESISTIVITY
The Hingle Plot
If the matrix composition remains
constant over the formations under
investigation,
the basic measurement from the sonic,
density, or neutron logs can be plotted
directly versus Rt with similar results.

RESISTIVITY
The Hingle Plot
This is possible because of the linear
relationship between porosity and bulk
density, sonic transit time or neutron
hydrogen index response.

RESISTIVITY
The Hingle Plot
The transit time has been plotted against the
induction resistivity for several levels.
The north-westerly points define the 100%
water saturation line.
The transit time value at the point where this
line intersects the horizontal line of infinite
resistivity is the matrix transit time, tma.

RESISTIVITY
The Hingle Plot
tma is found to be approximately 47.5
ms/ft, corresponding to a matrix velocity of
21,000 ft/sec.
A vertical line drawn through F = 100 (or φ
= 10) intersects the water line at Ro = 5
ohm-m; accordingly, Rw (= Ro/F) is 0.05
ohm-m.

RESISTIVITY
Resistivity vs Porosity Crossplot Procedure
Step 1: Determine f for a number of zones from porosity
acoustic, density or Neutron log.
Step 2: Determine the resistivity Rt of the zones from a deep
reading resistivity log
Step 3: Plot the values of f (on a linear scale) versus Rt (on an
inverse square root scale).

RESISTIVITY
Step 4: Draw a line through the average points in the
northwest part of the plot. If water zones are present in
the zone this line represents the water (or 100% Sw)
line.
The values of Rt along this line represent the resistivity
of the water-saturated formations, Ro. The extrapolation
of this line to zero conductivity defines the matrix travel
time.

RESISTIVITY
Step 5: Check the matrix value derived in Step 4 against
the value of matrix travel time derived from other
sources. This is a good check for errors in the 100%Sw
line.

RESISTIVITY
Step 6: For other Sw values, Rt and Ro are related by the
equation Rt = Ro/Sw
2. For Sw = 50%, 1/Sw
2 = 4, and Rt = 4 Ro.
This relation stablishes the line for Sw = 50%. Calculate the
relationship between Rt and Ro for various values of Sw
from the equation. Plot the values of Ro for Sw = 10%,
20%, 30% and 50%, using the above relationship, for a set
of porosities.

RESISTIVITY
Step 7: Determine Sw in the zones of interest, from the
position of the plotted points in relation plot saturation
lines.

Water Bearing Rock
 Total Resistivity (Ro) of water
bearing formation is controlled
by:
a) Resistivity of the water (Rw)
b) The amount of water present
expressed as Porosity (ɸ)
c) The shape of the water filling
the pores given as m,
cementation
Therefore
Ro = Rw x ɸ-m equation 1
Archie first equation
Hydrocarbon Bearing Rock
 Total Resistivity (Rt) is now affected
by the presence of HC. So in addition
to the parameters in equation 1
Total resistivity is dependent on:
d) Saturation of water Sw (fraction of ɸ
bearing water)
e) The geometry of the water coating
the grains n (saturation exponent)
Therefore
Ro = Rw x ɸ-m x Sw-n equation 2
Archie second equation
SATURATION
22

23
m= cementation exponent
From core analysis or
assume
sandstone m=1.8
carbonate m=2.0
Rt=True formation resistivity (Ωm)
Un-invaded Zone
(Deep Resistivity Log)
n= Saturation exponent
assume n=m
Rw=formation water resistivity (Ωm)
Produced water analysis
or
calculated in the water leg using Pickett plot
Sw= Water saturation
ɸ= Porosity
Density/Neutron Log
m
w
t
n
R
R
Sw φ
=
−
ARCHIE EQUATION (Clean Sand Model)
Mr Gustavus E. Archie
SATURATION

Rw from Logs
 Estimated from a water bearing
interval Based on first Archie
equation
Ro = Rw x ɸ-m
 Determine Ro from deep
resistivity Log (LLD)
 Determine porosity from
logs(density)
 If possible estimate m from core
else assume value
1
Por(frac)
0.1
1.0
10
Rt
(
Ωm
)
Rw
Slope = m
SATURATION
PICKETT PLOT
24

SELF POTENTIAL (SP)
The spontaneous potential log (SP) measures
the natural or spontaneous potential difference
(sometimes called self-potential) that exists
between
the borehole
and
the surface
in the absence of any artificially applied current.
NOTE: A conductive mud is required

SELF POTENTIAL (SP)
SP is generated by the diffusion of ions
through two solutions of different
salinities
separated by a
shale membrane and a liquid-junction
membrane.
Schematic of potential and current in and around a permeable bed

SELF POTENTIAL (SP)
The SP log has four main uses:
The detection of permeable beds.
The determination of Rw.
The indication of the shaliness of a formation.
Correlation.

SELF POTENTIAL (SP)
There are three requirements for the existence of an SP current:
• A conductive borehole fluid (e.g., a water based mud).
• A sandwich of a porous and permeable bed between low porosity and
impermeable formations.
• A difference in salinity between the borehole fluid and the formation fluid,
which are the mud filtrate and the formation fluid in most cases.
Note, however, that in some special cases an SP current can be set-up when there
is no difference in salinity, but where a difference in fluid pressures occurs.

SELF POTENTIAL (SP)
1- Electrochemical Components
2- Electrokinetic Components
The origin of the spontaneous potential has two different components.

SELF POTENTIAL (SP)
Electrochemical Components
Consider a permeable formation with thick shale beds above and below.
Assume that the two electrolytes (mud filtrate and interstitial formation
water) contain sodium chloride (NaCl) only. Because of the layered clay
structure and the charges on the layers, shales are permeable to the Na+
cations but impervious to the Cl- anions.

SELF POTENTIAL (SP)
Electrochemical Components
Only the Na+ cations (positive charges) are able to move through the shale
from the more concentrated to the less concentrated NaCl solution. This
movement of charged ions is an electric current, and the force causing them
to move constitutes a potential across the shale called membrane potential.

SP-Electrochemical Components
Another component of the electrochemical potential is produced at the edge of
the invaded zone, where the mud filtrate and formation water are in direct
contact. Here Na+ and Cl ions can diffuse (move) from either solution to the other.
Since Cl- ions have a greater mobility than Na+ ions, the net result of this ion
diffusion is a flow of negative charges (Cl- ions) from the more concentrated to the
less concentrated solution.

SP-Electrochemical Components
This is equivalent to a conventional current flow in the opposite direction,
indicated by the straight Arrow A in the upper half of Figure. The current flowing
across the junction between solutions of different salinity is produced by an
electromagnetic force (emf) called liquid-junction potential. The magnitude of the
liquid-junction potential is only about one-fifth the membrane potential.

SP- Electrokinetic Components
An electrokinetic potential, Ek (also known as streaming potential or
electrofiltration potential) is produced when an electrolyte flows through
a permeable, non-metallic, porous medium. The magnitude of the
electrokinetic potential is determined by several factors, among which are
the differential pressure producing the flow and the resistivity of the
electrolyte.

In the borehole, an electrokinetic emf, Ekmc, is produced by the flow of mud filtrate
through the mudcake deposited on the borehole wall opposite permeable formations.
In practice, little or no electrokinetic emf is actually generated across the permeable
formation itself. This is because practically all the differential pressure between the
borehole and undisturbed virgin formation is expended across the less permeable
mudcake.

Any remaining differential pressure across the formation is normally not
great enough to produce any appreciable electrokinetic emf.
An electrokinetic emf, Eksh, may, however, be produced across the shale, since it may
have sufficient permeability to permit a tiny amount of filtration flow from the mud.

Each of these electrokinetic emf’s contributes to a more negative SP reading
opposite the permeable bed and opposite the shale, respectively. The net
contribution to the SP deflection (measured from the shale line) is, therefore, the
difference between the contributions of the mudcake and the shale electrokinetic
effects.

In practice, these electrokinetic emf’s are similar in magnitude, and the net
electrokinetic contribution to the SP deflection is therefore usually small,
normally regarded as negligible. This is particularly true if the formation water is
rather saline (resistivity less than 0.1 ohm-m) and the differential pressure has a
normal value of only a few hundred psi or less.

Important electrokinetic effects may also be seen in very low-permeability
formations (less than a few millidarcies) in which an appreciable part of the
pressure differential is applied across the formation itself. If formation permeability
is so low that little or no mudcake is formed, most of the pressure differential
between the formation pore pressure and hydrostatic head of the mud column is
applied to the formation.

If the formation water is brackish, if the mud is resistive, and if the formation is
clean and has some porosity, the electrokinetic effect may be quite large,
sometimes exceeding - 200 mV.

SELF POTENTIAL (SP)
Uses of the Spontaneous Potential Log
The main uses of this log are:
 The detection of permeable beds.
 The determination of Rw.
 The indication of the shaliness of a formation.
 Correlation

SELF POTENTIAL (SP)
Calculation of Rw
This is one of two quantitative use of the SP log. However, it is extremely useful
when no formation water samples or water-bearing sands are available to
otherwise obtain Rw from during an analysis for OOIP.
There are three methods which will be described here.
1- The Quick-Look Method
2- The Single Chart Method
3- The Smits Method

Saturation
Original Humble formula F = 0.62 / phi2.15
Humble Equation Procedure for Sw:
Step 3: Determine Rt from deep reading resistivity (induction or laterolog) log
corrected for borehole, bed thickness and invasion.
Step 4: Determine Rw

Saturation
RW from the SP Log
In a clean formation, the static SP (SSP) curve value is
Weq
mfeq
R
R
k
SSP log
−
=
where,
K = temperature-dependent constant = 61 + 0.133 T degrees F
T = Formation Temperature, degrees F
Rmfeq = Resistivity of Mud Filtrate
Rweq = Equivalent Formation Water Resistivity

Saturation
RW from the SP Log
In a clean formation, the static SP (SSP) curve value is
Weq
mfeq
R
R
k
SSP log
−
=
Knowing the formation temperature, the static SP value recorded opposite a
porous,
Permeable
nonshaly formation
can be transformed into the resistivity ratio Rmfe/ Rwe

Saturation
RW from the SP Log
Procedure:
Step 1: Identify a permeable, water bearing zone near to the hydrocarbon bearing
zone of interest
Step 2: Determine the formation temperature at the zone of interest
The formation temperature can be found from either:
• Direct measurement (if the zone is at total depth and maximum temperature
reading is used)
or
• The bottom hole temperature, total depth and average surface temperature
and Chart Gen-6.

Saturation
RW from the SP Log
Step 3: Correct the Rmf resistivity values for the formation temperature found in Step 2.
The value of Rmf can be found on the log heading.
For predominantly NaCl muds:
1- if Rmf at 75 °F is greater than 0.1 ohm-m, use Rmfe = 0.85. Rmf at formation temperature;
2- if Rmf at 75 °F is less than 0.1 ohm-m use the NaCl (solid) curves of Chart SP-2 to derive a
value of Rmfe value corrected to formation temperature from Chart Gen-9.
For freshwater gypsum muds, the dashed lines of Chart SP-2 are used to convert Rmf to Rmfe.

Saturation
RW from the SP Log
Step 4: Draw the shale base line on the SP Log
The shale base line in fresh mud environments
will generally be the line established
by the maximum SP deflections to the right.

Saturation
Step 5: Mark out the bed boundaries on the SP
Log
The bed boundaries on the SP Log are the
inflection points on the curve.
The inflection point (or maximum slope) on the
curve occurs due to maximum current flow in
the wellbore at the boundary.
RW from the SP Log

Saturation
Step 6: Read the maximum SP value for the
permeable zone of interest
The SP value is the millivolt reading indicated
on the log, from the shale base line to
the maximum deflection on the SP in the
permeable bed.
RW from the SP Log

Saturation
RW from the SP Log
Step 7: Correct the SP value in Step 6 for thickness and resistivity effects
Chart SP-4 is a generalised correction chart for the SP. It corrects for bed thickness
and resistivity effects on the SP amplitude.
Notice on Chart SP-4 that low resistivity, thick beds require little to no correction.

Saturation
Step 8: Determine the mudfiltrate to apparent formation water resistivity ratio,
Rmfe/Rwe
Chart SP-1 relates the corrected SP deflection, formation temperature and the ratio
of the resistivity of the mud filtrate to apparent formation water resistivity for a
sodium chloride solution (Rwe). Determine Rmfe/Rwe from this chart
RW from the SP Log

n
t
o
n
t
w
n
t
m
w
w
R
R
R
F
R
R
R
S =
=
=
−
φ

Neutron log- excavation effect
A decrease in the neutron log apparent porosity reading below that expected on
the basis of the hydrogen indices of the formation component.
Excavation effect results from the presence of a second formation fluid with a
hydrogen index lower than that of the water. Thus, for example, in the presence of
gas saturation

EFFECT OF HYDROCARBONS ON POROSITY DETERMINATION
Neutron Log
A neutron and density log combination provides a more accurate porosity and a value of
minimum gas saturation. (Hydrocarbon effect will be discussed further in Chapter 6 in the
Cross plotting Section.)
H0 = 1.28 rhoo .
Hydrogen Index of Oils

Another set of equations can be used to estimate the hydrogen index
of hydrocarbon fluids:
For very light hydrocarbons ( ρh < 0.25),
Hh~2.2 ρh
For heavy hydrocarbons (ρh > 0.25),
Hh ~ ρh + 0.3
Another proposal suggests the equation
When this additional rock matrix is
“excavated” and replaced with gas,
the formation has a smaller
neutron-slowing characteristic.
The calculated difference in the
neutron log readings has been
termed the excavation effect.
If this effect is ignored, too-high
values of flushed-zone gas
saturation and too-low values of
porosity are given.

where ΔφNex, φ, and SwH are in fractional units.
For sandstone the coefficient, K, is 1
for limestone it is about 1.046,
and for dolomite it is about 1.173.
Note that the second term of this equation is rather small and
can often be disregarded.

NUCLEAR MAGNETIC RESONANCE (NMR) TOOL
The tool makes use of the gyromagnetic property of
protons (e.g. hydrogen nuclei) which behave like
magnets rotating around themselves.
Since hydrogen nuclei are abundantly present in pore
spaces in the composition of water or hydrocarbons,
they align themselves along the direction of the applied
magnetic field by the NMR tool.
Once the magnetic field is removed the protons relax to
a stable alignment.

From this, the NMR tool derives the following two
signals which are then used for NMR interpretation.
T1 – Longitudinal Relaxation Time
T2 – Transverse Relaxation Time

A number of NMR tools have been introduced in the logging industry. A
few of them include
1- Combinable Magnetic Resonance (CMR) by Schlumberger.
2- MRIL by Halliburton
3- Magnetic Resonance Explorer (MREX) by Baker Hughes
4- Magnetic Resonance Scanner (MR-Scanner) which is Schlumberger’s
new generation wireline NMR logging tool.

Their main use is:
1- The determination of total porosity (occupied by water or hydrocarbons)
2-Bound fluid porosity
3- Permeability (qualitative insight)
4- Viscosity.
The downside of these tools are for them being expensive, having considerably
lower logging speeds.

In the laboratory, the NMR tool is used in Special Core Analysis for pore
characterisation.
There is one advantage over traditional mercury injection methods for pore size
distribution in that it doesn’t use mercury which can be hazardous in the
laboratory.
More recent studies consider the role of NMR in studies of fluid (viscosity, heavy
oils) and rock:fluid properties (wettability).

Lithology and Porosity in complex formations
The measurements of the neutron, density, and sonic logs depends on:
1- Porosity
2- Formation Lithology
3- The fluid in the pores
4- In some instances, on the geometry of the pore structure.

Chart CP-1c
NEUTRON-DENSITY CROSSPLOTS

Chart CP-7
Poor porosity and
reservoir rock (sandstone,
limestone, dolomite)
resolution.
But they are quite useful
for determining some
evaporite minerals.
SONIC-DENSITY CROSSPLOT

Chart CP-2b
Weighted average (Wyllie)
observed (Raymer, Hunt, and Gardner)
SONIC-NEUTRON CROSSPLOTS
Resolution between
sandstone, limestone, and
dolomite lithologies is good,
and errors in choosing the
lithology pair will have only a
small effect on the porosity
value found

DENSITY-PHOTOELECTRIC CROSS SECTION CROSS PLOTS

NGS CROSSPLOTS
Some minerals have characteristic concentrations of thorium, uranium, and potassium.

M-N PLOT
Combine the data of all three porosity logs to provide the lithology-dependent quantities.
M: the slopes of the individual lithology lines on the sonic-density crossplot charts
N: the slopes of the individual lithology lines on the density-neutron crossplot charts.
100
/
)
(
f
b
f t
t
M
ρ
ρ −
−
=
f
b
N
Nf
N
ρ
ρ
φ
φ
−
−
=
For fresh mud tf = 189μs/ft ρf = 1g/cc, and φNf = 1
So, they are essentially independent of porosity, and a crossplot provides lithology
identification
The multiplier 1/100 is used to make the M
values compatible for easy scaling.

M-N PLOT
M= 0.79 and N= 0.55
The combination selected
would depend on the
geological probability of its
occurrence in the formation

M-N PLOT, controlling factors
1- Secondary porosity
2- Shaliness
3- Gas-filled porosity

M-N PLOT

M-N PLOT
Rhob= 2.65
PhiN= 18%
Dt=65
lithology?
100
/
)
(
f
b
f t
t
M
ρ
ρ −
−
=
f
b
N
Nf
N
ρ
ρ
φ
φ
−
−
=

M-N PLOT
Rhob= 2.25
PhiN= 10%
Dt=87
formation?
100
/
)
(
f
b
f t
t
M
ρ
ρ −
−
=
f
b
N
Nf
N
ρ
ρ
φ
φ
−
−
=

MID PLOT (Matrix Identification Plot)
Useful to indicate lithology, gas, and secondary porosity.
Data required:
1- Apparent total porosity, φta, must be determined using the appropriate neutron-
density (Chart CP-1a or CP-1b depending upon whether it is fresh or salt water), and
empirical (red curves) neutronsonic crossplots (Charts CP-2a or CP-2b ).
2- Next, an apparent matrix transit time, tmaa and an apparent grain density, ρmaa,
are calculated:

𝜌𝜌𝑚𝑚𝑚𝑚𝑚𝑚 =
𝜌𝜌𝑏𝑏−𝜑𝜑𝑡𝑡𝑡𝑡𝜌𝜌𝑓𝑓
1−𝜑𝜑𝑡𝑡𝑡𝑡
𝑡𝑡𝑚𝑚𝑚𝑚𝑚𝑚 =
𝑡𝑡−𝜑𝜑𝑡𝑡𝑡𝑡𝑡𝑡𝑓𝑓
𝑡𝑡𝑚𝑚𝑚𝑚𝑚𝑚 = 𝑡𝑡 −
𝜑𝜑𝑡𝑡𝑡𝑡𝑡𝑡
𝐶𝐶
Field-observed
Time Avrage

𝜌𝜌𝑚𝑚𝑚𝑚𝑚𝑚 =
𝜌𝜌𝑏𝑏−𝜑𝜑𝑡𝑡𝑡𝑡𝜌𝜌𝑓𝑓
𝑡𝑡𝑚𝑚𝑚𝑚𝑚𝑚 =
𝑡𝑡−𝜑𝜑𝑡𝑡𝑡𝑡𝑡𝑡𝑓𝑓
𝑡𝑡𝑚𝑚𝑚𝑚𝑚𝑚 = 𝑡𝑡 −
𝜑𝜑𝑡𝑡𝑡𝑡𝑡𝑡
𝐶𝐶
where,
ρb is bulk density from density log,
t is interval transit time from sonic log,
ρf is pore fluid density,
tf is pore fluid transit time,
φta is apparent total porosity,
c is a constant (c approx. = 0.67)

Tip
The apparent total porosity is not necessarily the same in the equations.
For use in the tmaa equations, it is the value obtained from the neutron-sonic
crossplots (Charts CP-2a or CP-2b).
For use in the ρmaa equation, it is the value obtained from the neutron-density
crossplot (Charts CP-1a or CP-1b).

1- identify the rock mineralogy by its proximity to
the labelled points
2- Mineral mixtures would plot at locations between
the corresponding pure mineral points.
3- The presence of gas shifts the plotted points to
the north-east

4- Secondary porosity shifts points in the direction
of decreased tmaa
5- For the SNP log, shales tend to plot in the region
to the right of anhydrite on the MID plot.
6- For the CNL log, shales tend to plot in the region
above the anhydrite point.

Another crossplot technique for identifying lithology uses data from the Litho-Density log.
It crossplots the apparent matrix grain density, ρmaa, and the apparent matrix
volumetric cross section, Umaa (in barns per cubic centimetre).
𝑈𝑈𝑚𝑚𝑚𝑚𝑎𝑎 =
𝑃𝑃𝑒𝑒𝜌𝜌𝑒𝑒−𝜑𝜑𝑡𝑡𝑡𝑡𝑈𝑈𝑓𝑓
Pe= photoelectric absorption cross section index,
Ρe= electron density ,
φτa = apparent total porosity.

EFFECT OF SHALINESS, SECONDARY POROSITY AND HYDROCARBONS ON
SONIC
DENSITY
NUETRON CROSSPLOTS

Effect of Shaliness on Crossplots
Shaliness produces a shift of the crossplot point in the direction of a so-called shale point
on the chart.
The shale point is found by crossplotting the measured values (ρsh, φNsh, tsh) observed in the
neighbouring shale beds.

Generally, the shale point is in the south-
east quadrant of neutron-density and
sonic-density crossplot, and in the lower
centre of the density-photoelectric cross
section crossplot.

These shale values, however, may only
approximate the parameters of the shaly
material within the permeable beds.

Effect of Secondary Porosity on Crossplots
Sonic logs respond differently to secondary porosity than the neutron and density logs.
They largely ignore vuggy porosity and fractures and respond primarily to
intergranular porosity; neutron and density tools respond to the total porosity.
Because the sonic wave finds a faster path around them.

Effect of Secondary Porosity on Crossplots
Thus, on crossplots involving the sonic log, secondary porosity displaces the points
from the correct lithology line and indicates something less than the total porosity
The neutron-density crossplots yield the total porosity.

Effect of Hydrocarbons on Crossplots
Gas or light hydrocarbons cause the
apparent porosity from the density log
to increase (bulk density to decrease)
and porosity from the neutron log to
decrease.

On a neutron-density crossplot this
results in a shift (from the liquid-filled
point of the same porosity) upward and
to the left, almost parallel to the
isoporosity lines.

If a gas correction is not made, the
porosity read directly from the crossplot
chart may be slightly too low. However,
the lithology indication from the chart can
be quite erroneous.

Arrow B-A illustrates the correction for
this hydrocarbon shift. Log Point B is for a
clean limestone containing gas of density
0.1 g/cm3.
Corrected Point A falls near the limestone
line, and porosity can be read directly.

The hydrocarbon shift (Δρb)h and (ΔφN)h
are given by:
(Δρb)h = - AφShr Hydrocarbon shift (Δρb)h
And
(ΔφN)h = - BφShr - ΔφNex, Hydrocarbon shift (ΔφN)h
where ΔφNex is excavation effect

Example:
For oil-bearing formations
A = (1.19 - 0.16 Pmf) ρmf - 1.19 ρh - 0.032
And
𝐵𝐵 = 1 −
𝜌𝜌ℎ + 0.3
𝜌𝜌𝑚𝑚𝑚𝑚 1 − 𝑃𝑃𝑚𝑚𝑚𝑚
Pmf = filtrate salinity in ppm NaCl.

Example:
For gas-bearing formations
A = (1.19 - 0.16 Pmf) ρmf - 1.33ρh
And
𝐵𝐵 = 1 −
2.2 𝜌𝜌ℎ
𝜌𝜌𝑚𝑚𝑚𝑚 1 − 𝑃𝑃𝑚𝑚𝑚𝑚

Shr = residual hydrocarbon saturation,
ρh = hydrocarbon density in g/cc ,
ρmf = mud filtrate density in g/cc
Pmf = filtrate salinity in ppm NaCl.

FOR
Reservoir Evaluation and Management
Petroleum Geoscience

Water Bearing Rock
 Total Resistivity (Ro) of water
bearing formation is controlled
by:
a) Resistivity of the water (Rw)
b) The amount of water present
expressed as Porosity (ɸ)
c) The shape of the water filling
the pores given as m,
cementation
Therefore
Ro = Rw x ɸ-m equation 1
Archie first equation
Hydrocarbon Bearing Rock
 Total Resistivity (Rt) is now affected
by the presence of HC. So in addition
to the parameters in equation 1
Total resistivity is dependent on:
d) Saturation of water Sw (fraction of ɸ
bearing water)
e) The geometry of the water coating
the grains n (saturation exponent)
Therefore
Ro = Rw x ɸ-m x Sw-n equation 2
Archie second equation
SATURATION
3

4
m= cementation exponent
assume
sandstone m=1.8
carbonate m=2.0
Rt=True formation resistivity (m)
Un-invaded Zone
(Deep Resistivity Log)
n= Saturation exponent
assume n=m
Rw=formation water resistivity (m)
Produced water analysis
or
calculated in the water leg using Pickett plot
Sw= Water saturation
ɸ= Porosity
Density/Neutron Log
m
w
t
n
R
R
Sw 


ARCHIE EQUATION (Clean Sand Model)
Mr Gustavus E. Archie
SATURATION

Rw from Logs
 Estimated from a water bearing
interval Based on first Archie
equation
Ro = Rw x ɸ-m
 Determine Ro from deep
resistivity Log (LLD)
 Determine porosity from
logs(density)
 If possible estimate m from core
else assume value
1
Por(frac)
0.1
1.0
10
Rt
(
Ωm
)
Rw
Slope = m
SATURATION
PICKETT PLOT
5

MICRORESISTIVITY VS POROSITY CROSSPLOTS
A resistivity-porosity plot can also be made using
the values from a shallow-investigation resistivity
log, such as the microlaterolog or MicroSFL log.
If MSFL~ Rxo then a line through points of mud
filtrate-saturated formations (Sxo = 1) should have
a slope related to Rmf.

Both the deep induction reading and the
microlaterolog at the same levels are plotted in a
series of water-bearing formations, porosity from a
neutron-density crossplot.
Two trends Sw=1 and Sxo=1.
There are some points not in these trends can be
divided into two groups

1- Points whose microlaterolog readings fall on the
Sxo = 1 line but whose deep induction log readings
fall below the Sw = 1 line (Points 2, 9, 10)
These are probably the result of either:
a) deep invasion
b) adjacent-bed effect in which RID is greater than
Rt.

2- Points whose induction log readings fall on the
Sw = 1 line but whose microlaterolog points fall
above the Sxo = 1 line are possibly due to:
shallow invasion in which RMLL is lower than Rxo.

Rwa Comparison
If water saturation is assumed to be 100%, the Archie water saturation equation reduces to
𝑅𝑤𝑎 = 𝑅𝑡/F ~ RID/F
Rwa=Rw in the water leg
Rwa>Rw in the hc leg
We can drive
𝑆𝑤 = 𝑅𝑤
𝑅𝑤𝑎
The Rwa technique is useful for
1- identifying potential hydrocarbonbearing zones
2- obtaining Rw values.

Coures-Formation Evalution for petroleum Engineering -heriot watt university.pdf

Coures-Formation Evalution for petroleum Engineering -heriot watt university.pdf

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