The quest for permeability evaluation in wireline logging

Jean-Pierre DELHOMME

Schlumberger Water Services, Le Palatin 1 - 1, cours du Triangle, 92936 La Defense Cedex - France

Note
The author is indebted to the numerous Schlumberger geologists, petrophysicists and reservoir engineers
who co-authored the articles published by Schlumberger on permeability since 1980. The present paper
borrows ideas and even sentences, sometimes cited verbatim, from the 9 papers that are listed at the
beginning of the bibliographical section. Nevertheless, rather than corporate views, this paper mainly
reflects the author’s opinion.

Abstract
For decades, a constant objective of wireline logging has been to obtain a continuous permeability log.
Except for a few attempts such as the search for an acoustic log response that could directly yield a
permeability indicator, most of the initial efforts have been directed towards deriving permeability from the
combination of porosity with some other log-derived property related to the type of pore geometry. In
sandstones, excellent results have recently been obtained with nuclear magnetic resonance (NMR) logging
that, by itself, provides information on both porosity and pore size distribution. In carbonates, the NMR
approach sometimes breaks down but the information about carbonate rock facies carried by continuous
electrical images of the borehole walls has permitted, coupled with conventional porosity logs, to generate
continuous permeability indicators in complex carbonate formations.

The challenge
Since 1856 when Henri-Philibert-Gaspard Darcy first defined fluid conductivity of a porous
material in his famous technical report known as the “Mémoire sur les fontaines publiques de la
ville de Dijon”, permeability has become one of the most studied, yet stubbornly elusive,
properties of rocks. For decades, hydrogeologists have been using pumping tests to measure
permeability in aquifers, or rather to access an average permeability-thickness value, called
transmissivity, masking permeability differences in different layers. Similarly, many well testing
techniques were developed by the petroleum industry. Well testing rapidly became an oilfield
standard because it was investigating the rock and fluid in situ, under actual reservoir flow
conditions. However, none of the well testing methods, except a rather cumbersome and lengthy
one called layer reservoir testing, are providing information about the variations of permeability
versus depth.
To achieve this goal, cores are often taken at different depths when drilling, and core samples are
analyzed under controlled laboratory conditions to measure permeability. Coring and laboratory
analyses are quite expensive procedures. Wells are therefore rarely cored continuously but, even
when they are, core permeability data can be of questionable value when only 6-inch spaced core
plugs are analyzed in heterogeneous rocks where permeability over just a few inches can vary by
five orders of magnitude. The idea thus came to try and obtain a continuous permeability profile,
using the same approach that had been successful in providing continuous profiles of porosity and
fluid saturations in the formations crossed by oil and gas, and sometimes water, wells: wireline
logging.

First methods for deriving permeability from conventional wireline logs

The first suggestion was to link conventional wireline log data, or log-derived rock properties
such as porosity, with permeability. This idea is almost as old as wireline logging itself. Over the
years, many transforms were proposed and, under certain conditions, they have been providing

1
acceptable approximations of hydraulic conductivity, i.e. of single-phase intrinsic permeability. In
the multiphase situation encountered by the oil industry, dimensionless terms called “relative
permeabilities” were added to adapt Darcy’s equation in order to describe the ability of a rock to
conduct one fluid in the presence of one or more other fluids, but no wireline logging solution has
yet been found to estimate these relative permeability values in situ, and they have always been
so far measured in laboratories on core samples.
The first formula relating intrinsic permeability with other measurable rock properties was
proposed by Kozeny (1927) and later modified by Carman (1937). This formula is commonly
written as: k = α.Φ3/S2, in which S is the grain surface area per bulk volume, Φ is the porosity
and α an empirical constant. It well describes permeability in packs of spheres of uniform size but
unfortunately breaks down in any real world formation other than unconsolidated well-sorted
sands with almost spherical grains, since not only grain size but also sorting, compaction, and
cementation affect permeability in sandstones (e.g., see
Beard and Weyl, 1973). However, for log analysts, its
greatest drawback was that the grain (or pore) surface
area could only determined on core samples.
To alleviate this problem, Wyllie and Rose (1957)
conjectured that grain surface area can be, in water-wet
formations, approximately related to the irreducible
water saturation Swirr (i.e. the amount of water in the
pore space that cannot be displaced by oil), because they
had noted that both grain surface area and Swirr increase
when grain size decreases and when sorting becomes
poorer. The advantage was that Swirr can be obtained
from logs, although sometimes with difficulty. A
consistent minimum of the bulk volume water over an
oil- or gas-bearing sandstone interval usually provides a
good Swirr estimate, but Swirr cannot be easily
determined from resistivity logs when the reservoir is
not at irreducible conditions i.e. when the hydrocarbon-
bearing zone also produces water.
Timur (1968a) based on laboratory studies of 155
sandstone cores from different US oil fields, then
proposed a slightly different relationship that was adopted Fig. 1 – Charts based on permeability
by the entire oil industry: k½ = Φ2.25 / Swirr (Fig.1). transforms proposed by Timur (top) and
By the same time, in clay-rich formations, the Archie by Wyllie and Rose (bottom).
equation, used for computing water saturation in
hydrocarbon-bearing formations from resistivity logs, started to be replaced by the so-called shaly
sand models, and some log analysts derived Swirr and k from expressions proposed by Coates and
Dumanoir (1973) for shaly sands. None of these interpretation models, however, was realistically
accounting for the effects of clay type and morphology on permeability, which sometimes was
leading to poor k estimates.
Neasham (1977) studied the impact of clay on the porosity-permeability relationship in
sandstones. From a survey of 14 very well sorted sandstones from North Sea reservoirs, with
similar textures but different types of clay morphology in the pore space, he showed that throat-
bridging clay connected across the pore space was indeed causing major reduction in
permeability, while porosity was much less affected. In other words, all the empirical correlations
based on Swirr were likely to be working well in clean mature sandstones but marginally
elsewhere.

2
Better permeability transforms based on more recent wireline logging tools
In the 1980s, the information brought by the conventional logs was complemented by the first
geochemical logging tools that were using neutron-induced gamma-ray spectroscopy to measure
the abundances of elements in a formation, then transformed into mineral abundances. The basis
for obtaining permeability from those abundances was that changes in mineralogy are normally
accompanied by changes in the size, shape, and morphology of rock grains; these changes affect
the pore system geometry, which directly influences permeability. A function of mineral
abundances was substituted for the surface area term in the Kozeny-Carman relationship by
Herron (1987). This approach has been
successfully used in the US Gulf Coast. More than
anything else, it seems that, actually, the
technique was deriving a textural maturity term
from feldspar content computed from the
geochemical tool readings.
In carbonates, the traditional permeability
transforms, based on Swirr and Φ, soon appeared
to be of limited use. The reason is that, as shown
by Nurmi (1986), porosity in carbonates is often
not intergranular as in sandstones. and quite
different pore types may result from the various
diagenetic effects, such as dolomitization,
leaching, and fracturation. For a given carbonate
pore type, permeability generally increases with
porosity along a fairly consistent trend, but pore
connectivity is critical (Fig.2): for instance, non-
connected vugs contribute to porosity but very
little to permeability. Conversely, the presence of
fractures significantly increases permeability, but Fig. 2 – Porosity, pore type, and permeability in
creates little additional porosity if fractures have carbonates.
not been enlarged by dissolution.
Guided by the intuition that the Archie exponent, m, is
correlated with the pore tortuosity that also affects
permeability for a given porosity value, Watfa (1987)
observed that the presence of vugs that reduces
permeability was typically leading to high values of m
(>2), whereas the presence of fractures that increases
permeability was leading to low values of m (close to 1).
He thus assumed that permeability could be taken
proportional to Φm. This relationship at least well agrees
with the observation: vugs increase m, which lowers Φm
and thereby the k estimate; fractures decrease m, which
increases the k estimate. The proportionality constant that
Watfa said to be related to an equivalent pore radius was
fitted using core permeability data, for a given carbonate
formation, which then permitted a continuous derivation
of k, provided that m could be continuously estimated
versus depth. A method was devised that permitted
estimating m continuously. It made use of a logging tool
Fig. 3 – Comparison of “variable m” that was developed in the 1980s: the Electromagnetic
permeability and core permeability, in Propagation Tool (EPT) records a high-frequency
a Middle-East carbonate.

3
electromagnetic propagation travel time that responds to water-filled porosity but, contrary to
resistivity measurements, does it without an exponent. As a consequence, combining this log with
a resistivity log allows a continuous evaluation of m, after eliminating porosity. The method has
been successfully used in the Middle-East (Fig.3).

Correlation of permeability with acoustic logging measurements

During the late 1970s, Lebreton has advocated for some years that a permeability index may be
derived from a ratio of the absolute peak values of the three first half-cycles of the acoustic
waveform recorded by a sonic logging tool. There was no convincing explanation why this ratio
and permeability should be related. Improved acoustic coupling into fractures may have been
causing the observation reported by Lebreton et al. (1978) since, right at a fracture, there is far
better coupling between the borehole and the formation than elsewhere. Anyway, this triggered,
in the 1980s and early 1990s, several attempts to correlate permeability with the Stoneley wave
data recorded by sonic logging tools, such as the DSI (Dipole Shear Sonic Imager) tool.
The DSI tool generates low-frequency tube waves –called Stoneley waves– that propagate up and
down the borehole with a special monopole transmitter operating at frequencies of 600 Hz to 5
KHz. While these waves preserve most of their energy in the borehole, some energy is attenuated
in front of permeable formations as the wave pressure pushes fluid from the borehole into the
formation, similar to a quick small-scale pressure test. In so doing, this technique gains direct
entry to permeability by physically moving fluid through the formation. The velocity of the wave
is slowed down by an amount that can be related to the ratio of formation permeability to fluid
velocity (Winkler et al., 1989). In the absence of mudcake, and knowing the acoustic velocity of
the borehole fluid, the permeability can be estimated.
A preferred method, based on energy and not velocity
attenuation, establishes permeability from Stoneley
waves without needing any further information (Cassel
et al., 1994). Furthermore, rather than to measure direct
Stoneley energy transmission between sonic tool
transmitter and receiver, it measures the attenuation
seen between two adjacent receivers, thus narrowing
the field of investigation to the distance between these
near and far receivers i.e. about 15 cm, which provides
higher resolution. Excellent agreement has been
observed in Middle-East carbonates between core
measurements and such permeability indicators (Fig.4).
However, it may be difficult to get quantitative
permeability estimates in the presence of mudcake that
interferes with the wave’s ability to move fluid into the
formation. Fig. 4 – Comparison of core measurements
It remains that Stoneley wave interpretation has been and permeability indexes from Stoneley
instrumental in fractured formations. The way fractures waves, in a Middle-East carbonate.
affect Stoneley waves is different than for
compressional and shear waves: acoustic energy is not lost through mode conversions but as a
result of moving the fluid into the fracture, and Stoneley attenuation is therefore quite
independent of the fracture dipping angle and mostly a function of fracture permeability. Stoneley
waves have thus proven to be an excellent fracture indicator (e.g., see Hornby et al., 1987) in tight
formations where finding open fractures is equivalent to finding permeable zones.
Whereas all approaches based on Swirr were geared to oilfield conditions and hydrogeologists
could not utilize them, the techniques based on geochemical, electromagnetic propagation, and
sonic logging could very well be used in water wells. The same holds true for the techniques that
are going to be described hereafter.

4
Nuclear magnetic resonance logging: a new way to estimate permeability
Magnetic resonance imaging instruments are commonly used as diagnostic tools in medicine
today, but nuclear magnetic resonance (NMR) is also extensively used by the oil industry in
wireline logging, as part of its quest for permeability. The physics and interpretation of NMR logs
will now be thoroughly reviewed, starting from the earlier NMR tools, so as to provide the reader
with explanations about a technique that, unfortunately, is still often not very well understood. In
a nutshell, NMR logging gives unprecedented information about both porosity and pore size
distribution that is used to successfully derive continuous permeability logs, notably in
siliciclastic formations.

A brief history of early NMR logging techniques

The physical principle called nuclear magnetic resonance refers to the response of atom nuclei to
externally applied magnetic fields. Many atom nuclei have a magnetic moment, i.e. behave like
tiny spinning magnets. These spinning nuclei can interact with a magnetic field, producing
detectable signals. For most elements, nevertheless, the measured signals are weak, but hydrogen
--that is abundant in both water and hydrocarbons contained in the pore space of rocks-- has a
relatively large magnetic moment. As far back as 1946, NMR signals from hydrogen atom nuclei
(i.e. protons) were observed by Purcell and Bloch. Oil industry interest followed right away, with
several patents for NMR logging tools filed in the 1950s. The first NMR logging tool was
developed by Brown and Gamson (1960) of Chevron Research and the first log was run in 1960.
Schlumberger ran two versions of this tool, under license from Chevron, and later developed a
tool commercialized at the end of the 1970s.
The principle of the early NMR tools was the following: the protons spinning in the formation are
initially aligned to the Earth's magnetic field; the logging tool has a horizontally-mounted coil
that transmits an oscillating magnetic field perpendicular, or transverse, to the direction of the
Earth's magnetic field which tips the protons 90°, and then turns it off; the tipped protons
immediately start to wobble or precess about the Earth's magnetic field, --just as a child's
spinning top precesses in the Earth’s gravitational field, its spinning axis describing a cone-- at a
frequency called the Larmor frequency, and they gradually relax back towards the Earth's
magnetic field; the precessing protons create a small magnetic field, oscillating at the Larmor
frequency, which is detected by the same tool coil. At first all the protons precess in unison but,
as the protons precess about the static field, they gradually lose synchronization, mainly due to
irreversible molecular interactions. This causes the magnetic field in the transverse plane, and
hence the detected signal, to decay.
The quantities measured were NMR signal amplitude and decay. Because the voltage level in the
tool coil was reduced by several orders of magnitude in going from transmitting to receiving
mode, there was a delay before the induced signal could be measured, and amplitude had to be
extrapolated back to time zero. But continuing research into the interpretation of these
measurements produced some outstanding contributions. The obtained signal amplitude was
found to indicate free-fluid porosity. Timur (1968b) developed the concept of free-fluid index
(FFI) that he related to Swirr ( Swirr = 1 – FFI / Φ ) and he proposed a method to estimate
permeability using NMR in 1968. However, the decay of the NMR signal during each
measurement cycle, called the (transverse) relaxation time or T2, generated the most excitement
among the petrophysical community. Relaxation time was found to depend on pore size, larger
pores that contain the most readily producible fluids allowing longer relaxation times. Seevers
(1965) developed a first relationship between relaxation time and permeability of sandstones. A
relationship between pore size, fluid and matrix properties was then presented by Loren and
Robinson (1969).
However, with these early NMR logging tools, the volume of investigation could not be
controlled and, to prevent the tool from reading borehole fluid, drilling mud had to be treated with

5
a magnetite sIurry before logging, in order to reduce the borehole signal to below measurement
threshold. This time consuming treatment was not very popular with drillers and hindered the
acceptance of NMR logging. The 1970s and 1980s saw continuation of this work on NMR
logging by many oil companies or oilfied service companies (e.g., see Kenyon et al., 1986), in
parallel with laboratory NMR techniques developed to characterize core samples. To make the
logging technique more widely acceptable meant a radical design change to use permanent
magnets instead of the Earth's magnetic field for aligning protons, and to profit from advances in
pulsed NMR technology commonly used in the laboratory.

The more recent generations of NMR logging tools

The use of powerful permanent magnets, applied to the formation as the logging tool moves up
the borehole, permits that the position of the measurement volume can be controlled by tool
design, thus eliminating the need for borehole mud doping. The use of a pulse sequence helps
compensate for some reversible dephasing effects caused by the inhomogeneity of the static
magnetic field. When this field is not perfectly homogeneous, the protons precess at slightly
different Larmor frequencies, causing a decay that is not a property of the formation. The protons
can be rephased when pulses that tip them 180° are transmitted. Pulses are applied repeatedly in
an evenly spaced train. Each time the protons rephase, they generate a signal, called a spin echo.
This configuration was proposed by Jackson (1980 & 1984) who filed his patent in 1978 and the
first experimental pulsed logging tools were eventually developed in the late 1980s. The MRIL
(Magnetic Resonance Imager) tool built in 1990 by NUMAR --now a subsidiary of Halliburton--
was the first commercial pulsed NMR tool. It incorporates a long permanent magnet to create a
static lateral field in the formation. The tool is run centralized in the borehole, and the
measurement volume consists of a thin concentric cylindrical shell with a length of 61 cm along
hole and a depth of investigation varying with the borehole diameter (about 7.5 cm for a 10 in. or
25 cm hole).
A side-looking configuration invented by Schlumberger (Kleinberg et al., 1992) was the basis for
the CMR (Combinable Magnetic Resonance) tool commercialized in 1995. It is run pressed
against the borehole wall by a bowspring. A short directional antenna sandwiched between a pair
of permanent magnets focuses the measurement on a zone located 2.8 cm inside the formation,
with a length along hole of only 15 cm providing high vertical resolution.
By design, the area between the CMR tool skid and the measurement volume does not contribute
to the NMR signal. This provides immunity to the effects of mudcake and hole rugosity. The two
permanent magnets generate a focused static magnetic field which is about 1000 times stronger
than the Earth's magnetic field, i.e. of about 550 gauss in the measurement region. The
measurement sequence starts with a wait time of about 1.3 sec to allow for complete polarization
of the hydrogen protons in the formation along the length of the skid. Then the antenna typically
transmits a train of several hundred magnetic pulses into the formation. The entire pulse
sequence, a 90° pulse of 4 gauss switched on for 16 µsec oscillating at the Larmor frequency
followed by a long series of 180° pulses, is called a CPMG sequence after its inventors: Carr, and
Purcell (1954) and Melboom and Gill (1958). The antenna also acts as a receiver and records
each spin echo amplitude. The Larmor frequency for hydrogen nuclei in a field of 550 gauss is
about 2.3 MHz. The echo spacing is 320 µsec for the CMR tool. T2 distribution is derived from
the decaying spin echo curve.
In the latest Schlumberger tool, the MRX (Magnetic Resonance eXpert) tool, the number of
echoes and their spacing are programmable, among other novel features, so as to adapt to
conditions where it is needed to measure long T2 values (e.g., see Freedman, 2006).

A deeper insight into the interpretation of NMR logs

Molecules in fluids are in constant Brownian motion. Besides the relaxation by molecular
diffusion in magnetic field gradients that the CPMG pulse sequence is compensating for, there

6
exist two main NMR relaxation mechanisms, i.e. bulk fluid relaxation and grain surface
relaxation. Both mechanisms result from molecular interactions and create the irreversible
dephasing that can be observed by means of the decaying amplitude of spin echoes. The bulk
relaxation is caused by the magnetic interactions between neighboring precessing protons in the
fluid itself, while the grain surface relaxation is caused by the probability for a precessing proton
moving about pore space of colliding with a grain surface.
Bulk fluid relaxation can often be neglected but can be important when water is in very large
pores, which may be the case in vuggy carbonates, and when, therefore, hydrogen protons rarely
contact a surface. Water in a test tube has a long T2 relaxation time of 3700 msec at 40°C, a value
that may be approached in a rock with very large vugs. Bulk relaxation also matters when non-
movable hydrocarbon is present in the measurement region: the nonwetting phase does not
contact the pore surface, and so it cannot be relaxed by the surface relaxation mechanism; in
addition, increasing fluid viscosity shortens bulk relaxation times.
Grain surface relaxation is, by far, the most important process affecting relaxation times. Because
of complex atomic-level electromagnetic field interactions at the grain surface, there is a high
probability -characterized by a parameter called the surface relaxivity, ρ2- that the proton in the
fluid will relax when it encounters a grain surface. For a given grain type, e.g. in sandstones, the
speed of relaxation depends on how frequently protons can collide with the surface, and this
depends on the surface-to-volume ratio (s/v) and thereby on pore size. For example, relaxation
times for a sandstone typically range from 10 msec for small pores to 500 msec for large pores.
Collisions are less frequent in large pores that have a small s/v and relaxation times are, therefore,
relatively long. Conversely, small pores have a large s/v and short relaxation times.
For a single pore, nuclear spin magnetization decays exponentially, and the signal amplitude
decays with time constant T2 = (ρ2.(s/v))-1. Rocks have a distribution of pore sizes, each with its
own value of s/v. The NMR signal is the sum of the signals coming from all the pores located in
the measurement volume. The initial NMR signal amplitude is thus proportional to porosity; its
overall decay is the sum of the individual decays, which reflects pore size distribution. Separating
out ranges of T2 values by a mathematical inversion process produces the T2 distribution curve.
The area under the curve represents the porosity and the curve shape the distribution of pore
sizes. This inversion process normally requires stacking, in order to improve the signal-to-noise
ratio, which slightly degrades the vertical resolution.

From NMR-derived porosity and pore size distribution to permeability

Traditionally, the total porosity seen in formations
is subdivided into three components: free-fluid
porosity, capillary-bound water, and clay-bound
water. NMR free-fluid porosity is determined by
applying a cutoff, of generally 33 msec for
sandstones, to the T2 distribution curve. The area
underneath the curve above the cutoff gives free-
fluid porosity (Fig.5). As NMR tool technology
has improved over the last decade with shorter
echo spacing (today, for example, the CMR-200
and CMR-Plus tools can measure T2 down to the
0.3-msec range), the fast decaying clay-bound
water signal with T2 values below 3 msec can also
now be measured and distinguished from
capillary-bound water.
NMR permeability is derived from empirical Fig. 5 – T2 distributions for two sandstones with
same porosity but different permeabilities and
relationships that were developed from brine pore sizes (the yellow area corresponds to free-fluid
permeability measurements and NMR porosity).

7
measurements concurrently made in the laboratory on hundreds of different core samples. The
two widely applied permeability transforms are the Timur-Coates and the Schlumberger-Doll
Research (SDR) equations. While the Timur-Coates transform contains the total porosity and the
ratio of the free-fluid volume to the bound-fluid volume, the SDR transform is based on the NMR
porosity and the logarithmic mean of T2 : kNMR = C (ΦNMR)4 (T2, log)2 where kNMR is the estimated
permeability, ΦNMR is CMR total
porosity, T2,log is the logarithmic
mean of the T2 distribution, and C is
a constant depending upon the
formation, e.g. 4 for sandstones and
0.1 for carbonates.
In Fig.6, CMR porosity shows a
good match with core porosity
measurements and, after fine-tuning
of constant C, CMR permeability
overlays core permeability points
over the whole interval. Notably,
over the zone with little porosity
variation and where permeability
varies from 0.07 md to 10 md, CMR
permeability values compares well
to that of core measurements. The
value of C used for this well was
Fig. 6 – Comparison of CMR porosity and CMR permeability with applied to subsequent CMR logs in
core measurements. the same formation, enabling the oil
company to reduce coring costs.
It has also been observed that the sum of all spin-echo amplitudes is proportional to the product
of porosity and average T2, and correlates well with permeability. This alternative yields better
results in high noise environments and can be interpreted without stacking, which leads to a new
NMR permeability indicator (Sezginer, 1999) with higher vertical resolution (typically 20 cm).

Some specific interpretation issues related to NMR logs in carbonates

The interpretation model assuming that, in water-saturated reservoir rocks, the T2 and pore-size
distributions are directly related well explains why NMR T2 curves are successfully used to
characterize sandstones containing mixed pore-size distributions. However, there is some concern
within the oil industry that NMR does not work as well in carbonate reservoirs. First, NMR
responses in carbonates differ from those in sandstones: all pore surfaces are not equally effective
in relaxing hydrogen nuclei and carbonates are about three times less efficient in relaxing the
nuclear magnetism than sandstones. For carbonates, relaxation times therefore tend to be three
times longer and a 100 msec cutoff was proposed for free-fluid porosity. This cutoff value has
often to be locally adapted. For instance, in the Thamama formations of Abu Dhabi, permeable
grainstones could be distinguished from lower permeability packstones and mudstones with a 225
msec cutoff. But, while carbonate formations contain mixed pore-size distributions, e.g.,
intergranular porosity and vugs, NMR logging data in these formations nevertheless frequently
yield unimodal T2 distributions, which often results in inconsistent T2 cutoff values to distinguish
bound and free fluids, and leads to unreliable permeability predictions.
Developments in NMR research (Ramakhrisna, 1999) have now explained why the conventional
approach breaks down in grain-supported carbonates which have dual pore systems. The
breakdown is due to diffusion of spinning protons between the micro- and macropores. If the
surface relaxivity is small enough, protons originally in the micropores can diffuse into the
macropores before their nuclear spins relax; the decay of these spins then proceeds much more

8
slowly. Conversely, spinning protons originally in the macropores can penetrate into the
micropores where they encounter more surface interactions, speeding up their decay. Diffusion
therefore causes the area under the short T2 peak -the porosity fraction associated with
micropores- to decrease; at the same time, the position of the higher T2 peak shifts towards
shorter times. Acting together, these two effects
tend to merge the two peaks and produce a
unimodal T2 distribution that bears little
resemblance to the bimodal distribution one would
expect from a dual-porosity system.
In chalk formations with a single pore system,
NMR logging performs very well, as
demonstrated by an example from the Ekofisk
formation in the North Sea (Fig.7). While it is
widely believed that chalk formations are
homogeneous, borehole electrical images have
revealed thin laminations. In the image, light
yellow indicates electrically resistive low-porosity
chalk and dark brown more conductive higher
porosity chalk. While the standard CMR
permeability transform show little evidence of
Fig. 7 – Comparison of CMRPlus high-resolution
these laminations, the high-resolution permeability
permeability with FMI borehole electrical images indicator log shows permeability variations that are
consistent with the laminations seen in the images.

Borehole image analysis: a way to access permeability through rock facies typing
In carbonates with complex pore structure and sometimes difficult NMR interpretation, a saving
grace for permeability logging (Akbar et al., 1995 & 2000) has been the development, in the late
1980s, of high-resolution borehole imaging tools, such as the FMI (Fullbore formation Micro
Imager) tool which provides a picture of most of the
borehole wall with 192 small current-emitting electrodes
mounted on four pads and four flaps pressed against the
formation. As the tool is pulled up the hole, a
measurement is made every 2.5 mm and the small
electrodes also have an effective horizontal spacing of
2.5 mm. Borehole orientation, tool azimuthal orientation,
and borehole diameter are all recorded, allowing the 3-
dimensional positioning of every measurement.
Small scale conductivity variations in the electrical
images (Fig.8) permit to identify the presence of macro
or vuggy porosity in carbonates and to recognize the
facies …and permeability in carbonates is predominantly
a function of the facies (or rock type).
While pores in clastic rocks are located between grains
and uniformly distributed throughout the rock, in
carbonates the diagenesis can significantly modify pore Fig. 8 – Mottled fabric of a Middle-East
space and permeability because those rocks are highly carbonate rock shown by a FMI image
susceptible to dissolution: grains can be dissolved to form (dark = pores, light = grains and matrix).
new pore space, shells can be dissolved creating moldic
porosity, dissolution along fractures or cracks can create large vugs or even caves; depositional
bedding is rarely preserved; also, whereas clastic diagenesis normally does not involve a change

9
in mineralogy, in carbonates a diagenetic process i.e. the replacement of calcium carbonate by
magnesium carbonate, called dolomitization, can significantly improve the permeability.
A trend in FMI interpretation in the early 1990s has been towards automated quantitative image
analysis (Delhomme, 1992), and an innovative method for characterizing rock type and
permeability was later developed. First
the textural variations in the borehole
electrical images are captured: the types,
sizes, and densities of both conductive
and resistive features are determined,
conductive paths between large
conductive features (usually cracks or
fractures connecting large vugs) are
identified.
This information about the internal
organization of the rock is summarized
as “textural” logs that are then combined
with conventional logs such as gamma
ray, neutron, and density providing
information about porosity and
lithology. This is achieved by means of
an artificial neural network (ANN)
software that produces a continuous
identification of the rock types
(carbonate facies).
Once the rock type is identified, a
porosity-permeability transform could
be specified, at each depth, to estimate
permeability, as suggested in Fig.2.
However, it has been found simpler, and
more efficient, to use the ANN software
for producing directly a continuous
quantitative permeability estimate.
The ANNs for both rock type and
permeability determination are trained
on cored intervals, from the same well
or from a nearby well.
This approach has proved to be so
powerful that it has been successfully
retrofitted to be applied to old wells
where only high-resolution dipmeter
(e.g. SHDT) data, and not images, had
been acquired. Fig. 9 displays results
obtained in that way from an Abu Dhabi
well. Photographs in the composite plot
show blown-up pictures of 3 distinct
rock types. Note the more precise log-
Figure 9 – Rock type zonation and continuous permeability derived rock type zonation, and the good
indicator derives from high-resolution dipmeter data combined agreement of log-derived permeability
with conventional porosity and lithology logs. estimates with core permeability data.

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What about permeability anisotropy ?
In the past years, reservoir engineers have increasingly paid attention to permeability anisotropy.
With more and more highly deviated and horizontal wells in the oil and gas fields, vertical
permeability may be the most important reservoir parameter because it affects production -the
larger the vertical anisotropy, the higher the productivity index-, injection performance, or gas
and water coning. Vertical permeability is routinely determined from cores, but the problem with
anisotropy is that it varies with scale: permeability barriers anticipated from core plug data may
have, or lack, lateral extension and influence, or not, the flow patterns at a larger scale. Vertical
interference testing with the Modular formation Dynamics Tester (MDT) tool (Pop, 1993) is more
a wireline-conveyed technique than a true logging one, but it provides this type of information.
Horizontal anisotropy is also a major concern in oil and gas fields. A horizontal well drilled
normal to the direction of larger horizontal permeability will be a much better producer, or
injector, than one drilled parallel to it. Wireline logging measurements in a pilot vertical well
provides valuable information for horizontal well design. Shear sonic logging may, for instance,
be used to identify the maximum and minimum stress directions that usually coincide with the
maximum and minimum horizontal permeability directions: natural (micro)fractures aligned with
the maximum stress direction open up in the direction normal to it, but stress anisotropy may also
cause minor permeability anisotropies in the absence of fractures, by distorting the pore space.
Hydrogeologists may soon be facing the same situation than reservoir engineers if horizontal
wells start to be drilled for aquifer storage and recovery or to mitigate saltwater intrusion in
coastal aquifers.

References

Articles published in the Oilfield Review and other Schlumberger reviews since 1980:

- Akbar M. et al., 1995, “Classic Interpretation Problems: Evaluating Carbonates”, Oilfield Review,
vol.7, no.1, pp.38-57.
- Akbar M. et al., 2000, “A Snapshot of Carbonate Reservoir Evaluation”, Oilfield Review, vol.12, no.4,
pp.20-41.
- Allen D. et al., 1988, “Probing for Permeability: An Introduction to Measurements”, The Technical
Review, vol.36, no.1, pp.6-20.
- Allen D. et al., 2000, “Trends in NMR Logging”, Oilfield Review, vol.12, no.3, pp.2-19.
- Ayan C. et al., 1994, “Measuring Permeability Anisotropy: The Latest Approach”, Oilfield Review,
vol.6, no.4, pp.24-35.
- Kenyon W. et al., 1994, “Nuclear Magnetic Resonance Imaging: Technology for the 21st Century”,
Oilfield Review, vol.7, no.3, pp.19-33.
- Mathieu G. et al., 1985, “Applying Sonic Data: Fracture Detection”, The Technical Review, vol.33,
no.1, pp.69-79.
- Nurmi R., 1984, “Permeability in Sandstones”, The Technical Review, vol.32, no.1, pp.4-10.
- Nurmi R., 1986, “Carbonate Close Up”, Middle East Well Evaluation Review, No.1, pp.22-35.

Other articles on permeability and logging:

- Beard D.C. and P.K. Weyl, 1973, “Influence of Texture on Porosity and Permeability of
Unconsolidated Sands”, AAPG Bulletin, vol.57, pp.349-369.
- Brown R.J.S. and B.W. Gamson, 1960, “Nuclear Magnetism Logging”, Journal of Petroleum
Technology, vol.12, pp.199-207.
- Carman P.C., 1937, Fluid Flow Through Granular Beds”, Transactions of the Institution of Chemical
Engineers, vol.15, pp.150-166.

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- Carr H.Y. and E.M. Purcell, 1954, “Effects of Diffusion on Free Precession in Nuclear Magnetic
Resonance Experiments”, Physical Review, vol.94, no.3, pp.630-638.
- Cassel B. et al., 1994, “Permeability Prediction Based on Anelastic Attenuation Using Dipole Shear
and Low Frequency Monopole Sources in a Carbonate Reservoir in Saudi Arabia”, paper presented at
the GEO-94 Middle-East Geosciences Conference, Bahrain.
- Coates G.R. and J.L. Dumanoir, 1973, “A New Approach to Improved Log-Derived Permeability”,
Transactions of the SPWLA 14th Annual Logging Symposium, Lafayette, USA, paper R.
- Delhomme J.P., 1992, “A Quantitative Characterization of Formation Heterogeneities Based on
Borehole Image Analysis”, Transactions of the SPWLA 33rd Annual Logging Symposium, Oklahoma
City, USA, paper T.
- Freedman R., 2006, “Advances in NMR Logging”, paper SPE 89177.
- Herron M.M., 1987, “Estimating the Intrinsic Permeability of Clastic Sediments from Geochemical
Data”, Transactions of the SPWLA 28th Annual Logging Symposium, London, UK, paper HH.
- Hornby B.E. et al., 1987, “Fracture Evaluation from the Borehole Stoneley Wave”, Expanded abstracts
of the SEG 57th Annual International Meeting, New Orleans, USA, pp.688-691.
- Jackson J.A., 1984, “Nuclear Magnetic Resonance Well Logging”, The Log Analyst, vol.25, p.16-30.
- Jackson J.A. and R.K. Cooper, 1980, “Magnetic Resonance Apparatus”, US Patent #4,350,995.
- Kenyon W.E. et al., 1986, “Compact and Consistent Representation of Rock NMR Data for
Permeability Estimation”, paper SPE 15643.
- Kleinberg R.L. et al., 1992, “Novel NMR Apparatus for Investigating an External Sample”, Journal of
Magnetic Resonance, vol.97, no.3, pp.466-485.
- Lebreton F. et al., 1978, “Logging Tests in Porous Medium to Evaluate the Influence of their
Permeability on Acoustic Waveforms”, Transactions of the SPWLA 19th Annual Logging Symposium,
El Paso, USA, paper Q.
- Loren J.D. and J.D. Robinson, 1969, “Relations between Pore Size, Fluid and Matrix Properties, and
NML Measurements”, paper SPE 2529.
- Meiboom S. and D. Gill, 1958, “Modified Spin-Echo Method for Measuring Nuclear Relaxation
Times”, The Review of Physical Instruments, vol.29, no.8, pp.688-691.
- Neasham J.W., 1977, “The Morphology of Dispersed Clay in Sandstone Reservoirs and its Effects on
Sandstone Shaliness, Pore Space, and Fluid Flow Properties”, paper SPE 6858.
- Pop J.J. et al., 1993, “Vertical Interference Testing with a Wireline-Conveyed Straddle-Packer Tool”,
paper SPE 26481.
- Ramakhrisna T.S. et al., 1999, “Forward Models for Nuclear Magnetic Resonance in Carbonate
Rocks”, The Log Analyst, vol.40, no.4, pp.260-270.
- Seevers D.O., 1966, “A Nuclear Magnetic Method for Determining the Permeability of Sandstones”,
Transactions of the SPWLA 7th Annual Logging Symposium, Tulsa, USA, paper ???.
- Sezginer A. et al., 1999, “An NMR High-Resolution Permeability Indicator”, Transactions of the
SPWLA 40th Annual Logging Symposium, Oslo, Norway, paper NNN.
- Timur A., 1968, “An Investigation of Permeability, Porosity, and Residual Water Saturation
Relationships”, Transactions of the SPWLA 9th Annual Logging Symposium, New Orleans, USA,
paper J.
- Timur A., 1968, “Effective Porosity and Permeability of Sandstones Investigated Through Nuclear
Magnetic Resonance Principles”, Transactions of the SPWLA 9th Annual Logging Symposium, New
Orleans, USA, paper K.
- Watfa M. and F.Z. Youssef, 1987, “An Improved Technique for Estimating Permeability in
Carbonates”, paper SPE 15732.
- Wyllie M.R.J. and W.D. Rose, 1950, “Some Theoretical Considerations Related to the Quantitative
Evaluation of the Physical Characteristics of Reservoir Rocks from Electrical Log Data”, Petroleum
Transactions of AIME, vol.189, pp.105-118.
- Winkler K.W. et al., 1989, “Permeability and Borehole Stoneley Waves: Comparison Between
Experiment and Theory”, Geophysics, vol.54, pp.66-75.

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