This document discusses techniques for obtaining high-resolution estimates of total porosity, bound fluid, and free fluid volumes from NMR well logging data. It describes a processing method called "alpha processing" that uses a high-resolution measurement to refine a lower-resolution estimate. The method is applied to NMR data to provide property estimates with the maximum tool resolution of about 9 inches. Examples are given showing how the technique can identify thin laminations and determine quantitative fluid volumes in different beds.

1. - 1 -
HIGH-RESOLUTION BOUND-FLUID, FREE-FLUID AND
TOTAL POROSITY WITH FAST NMR LOGGING
N. Heaton, C. Cao Minh, R. Freedman and C. Flaum
Schlumberger
ABSTRACT
One of the most important contributions of
nuclear magnetic resonance (NMR) logs has
been the provision of quantitative estimates of
bound- and free-fluid volumes, which are
fundamental for evaluating formation
producibility. In laminated formations, it is
important that measurements are sensitive to
variations on a length scale comparable to or less
than the lamination thickness.
The vertical resolution of NMR log
measurements is defined by the antenna length,
the acquisition sequence and the logging speed.
During depth logging, each individual
measurement consists of a phase-alternated-pair
(PAP) of Carr-Purcell-Meiboom-Gill (CPMG)
sequences. Measurement schemes that combine
overlapping measurements to form PAPs provide
the best resolution, typically about 9 in., for a
tool with a 6-in. antenna. However, because of
the long polarization times that are sometimes
required, the overlapping acquisition methods
place limitations on the logging speed. For tools
having a long prepolarization magnet, non-
overlapping PAP measurements may be acquired
at logging speeds of up to 3600 ft/hr with a
minor reduction in vertical resolution. In
practice, however, the vertical resolution is often
degraded by depth-stacking, which is necessary
to improve the signal-to-noise ratio for inversion.
High-resolution processing strategies and
acquisition schemes have been developed,
applicable to standard CPMG and Enhanced
Precision Mode (EPM) data, that provide
estimates of total porosity, free-fluid and bound-
fluid volumes at the maximum tool resolution.
The methods have been evaluated on synthetic
data generated from known T2 distributions with
added random noise and on log data acquired in
a test well comprising blocks of known
lithology, thickness, porosity and permeability.
Log examples presented here show how the
processing is used to identify thin laminations
and to determine quantitative estimates of
bound-fluid and free-fluid volumes for the
constituent beds. Results are compared with
other high-resolution porosity logs and extensive
core measurements for the same well.
Combination of the new processing with EPM
acquisition and nonoverlapping measurement
schemes, implemented on a tool with a short
antenna length and long prepolarization magnet,
provides high-resolution NMR logs acquired at
fast logging speeds.
INTRODUCTION
Nuclear magnetic resonance logging tools
provide estimates of the volumes of hydrogen-
containing fluids residing within a formation.
However, the principal value of NMR logging
lies in the identification and quantification of
different fluids on the basis of their relaxation
characteristics. Notably, the separation of
porosity into bound-fluid and free-fluid
components has been fundamental for
evaluating reservoir producibility.1
In thin,
laminated formations, producibility depends not
only on the net ratio of bound-fluid to free-fluid
volumes, but also on the relative disposition of
the two fluid volumes within the different
laminae.
In principle, the measurement resolution of
NMR logging tools is limited only by the
antenna length and the sample interval employed
during logging. Whereas the antenna length is a
static feature of the tool design, the sample
interval is essentially a free parameter that must
be selected in job planning. From the point of
view of data quality, the sample interval should
be as small as possible since this optimizes the
effective signal-to-noise ratio (SNR) and
resolution of the measurement. In reality, it is
largely governed by economic considerations,
which dictate the maximum permissible logging
time and hence the minimum logging speed. For
acquisition sequences which make overlapping
measurements, the logging speed must be
reduced proportionately with sample interval.

2. - 2 -
For the CMR-200* Combinable Magnetic
Resonance tool, a sample interval of 6 in. is
typically used, with logging speeds ranging from
about 200 ft/hr to 900 ft/hr depending on the
expected longitudinal relaxation times (T1) of the
formation fluids. Each sample comprises two
measurements of opposite phase which are
combined to remove electronic offsets. The
effective resolution of the resulting phase-
alternated pair (PAP) is equal to the antenna
length plus half the sample interval, which would
be 9 in. for a logging sequence with a 6-in.
sample interval. In practice, it is customary to
average several consecutive PAPs in order to
improve the SNR of the data prior to inversion.
Although desirable from the point of view of
measurement precision, this procedure degrades
vertical resolution and could mask information
concerning thin beds, resulting in inaccurate
determination of overall producibility.
Another processing method has been proposed
recently which uses high-precision quantities
based on the sum of echo amplitudes to define a
high-resolution permeability transform.2
This
approach has been shown to work well in a range
of environments but has the drawback that the
transforms themselves depend on the acquisition
parameters and may also be affected by the
properties of the formation and drilling fluids.
In this work, improvements in precision,
accuracy and efficiency of high-resolution NMR
log measurements are achieved by implementing
recent developments in three distinct aspects of
NMR logging technology. First, a new
generalized processing technique optimizes high-
resolution estimates of total porosity, bound-
fluid and free-fluid volumes. Second, Enhanced
Precision Mode (EPM) acquisition3,4
improves
precision and accuracy of bound-fluid volume
and total porosity. Finally, these techniques are
demonstrated with data acquired at fast logging
speeds using the CMR-PLUS* logging tool.4
HIGH-RESOLUTION PROCESSING
Alpha Processing. The general alpha processing
method5
can be summarized by the equation
XHR = Q ×
XLR
Q
(1)
where XHR is the desired high-resolution estimate
of some property, X, whose value at low
resolution, XLR, has been measured. The
property, Q, is measured with high resolution. Its
average value, over a depth interval comparable
to the resolution of XLR, is 〈Q〉. The statistical
error in the final estimate, XHR, depends on the
precision with which both Q and XLR can be
measured. For the method to provide reasonable
estimates of XHR, it is important that Q follows
an approximately linear relationship with X over
intervals of the order of the resolution of XLR.
Alpha processing has been successfully applied
to other measurements such as density logs,
where quantities Q and XLR derive respectively
from the short-spaced and long-spaced sensors.5
A similar approach may also be applied to NMR
data, but in this case, Q and XLR are both
obtained from measurements acquired by the
same antenna.
Adaptation of Windows Processing7
to Multi-
Level Data. In windows processing, CPMG
echo data is compressed into a reduced number
of “windows”. For each window, sensitivity
functions are computed for a range of relaxation
times that define a T2 distribution. For a specific
relaxation time T2,k the sensitivity function is
Fm,p(T2,k ) = (1− e
−WT(p) / T2, k
) e
− jTE/ T2, k
j= j1(m,p)
j2(m,p)
∑
(2)
where j1(m,p) and j2(m,p) are the first and last
echoes of the mth window for the pth wait-time,
WT(p) is the pth wait time, ξ is the T1/T2 ratio,
TE is the echo spacing, and the subindex k refers
to a specific relaxation time. For standard
processing T2 values are equally spaced on a
logarithmic scale. Typically, 30 values are used
ranging between 0.3 ms and 3000 ms. In high-
resolution processing, data from several depth
samples are inverted simultaneously using a
small number of T2,k values. These values are
determined from the T2 distribution computed
for the averaged data over the same set of depth
samples. This procedure is illustrated
schematically in Figure 1. The sensitivity
functions are the same for all depths included in
the vertical averaging. For EPM processing, a
value for ξ is determined by inversion of the
stacked data. Otherwise, an estimate is made on
the basis of the expected fluid properties.

3. - 3 -
Fitting the data. It is assumed that the echo
data acquired at each individual depth can be
well-represented by a linear combination of the
sensitivity functions, Fm,p(T2,k). If )(
~
, LI pm is the
value of the mth window for the pth wait time at
depth L, then we have
˜Im,p (L) = ak(L)Fm, p
k
∑ (T2,k ) + m,p,L , (3)
where ak(L) is the amplitude of the kth T2
component at depth L and δm,p,L is a zero-mean
random noise term. The most likely combination
of ak(L) can be determined by minimizing the
maximum likelihood function,
− ln K{ak(L)} =
˜Im,p − ak(L)Fm,p(T2,k )
k
∑
(1+ j2(m, p) − j1(m, p)) /np










2
L , m , p
∑
(4)
where np is the number of repeat PAPS acquired
for the pth wait-time. A regularization term
could also be included in equation (4). However,
reduction of the T2 distribution to a small number
of well-spaced components effectively
eliminates the need for additional regularization.
The minimization is further subject to the
constraint that the average values of the
coefficients, ak(L), over the ND depths equal
those for the stacked data, Ak,
1
ND
ak
L
∑ (L) = Ak . (5)
Equation 5 corresponds to the alpha-processing
aspect of the method and ensures that both the
total porosities and the mean logarithmic T2 of
the individual levels are consistent with those
computed for the stacked data.
Determining the high-resolution porosity,
bound-fluid and free-fluid volumes. If the
ak(L) are scaled in porosity units, the total
porosity at each depth, L, is
TCMRHR(L) = ak
k
∑ (L). (6)
Division of porosity into bound-fluid and free-
fluid components is performed by obtaining a
high-resolution estimate for the free-fluid
volume. An efficient and high-precision method
involves taking linear combinations of echo
amplitudes. If the jth echo amplitude at depth L
is W(L,j), the corresponding free-fluid volume
estimate is
FFV0(L) = U (j)W(L, j)
j
∑ (7)
where U(j) is a linear estimator function, which
is designed such that the quantity
q = U( j)e
−jTE /T2
j
∑ (8)
is approximately 0 for T2 values below the T2
cutoff and is approximately 1 for T2 values
above the T2 cutoff. In general, linear estimators
provide free fluid volumes comparable to those
obtained using tapered cutoffs in the T2 domain.8
Alpha processing may be applied to correct for
possible discrepancies between the high-
resolution linear estimates and those computed
by standard inversion. The final high-resolution
free-fluid estimate at depth L, is then
CMFFHR (L) =
NDFFV0(L)
FFV0(L' )
L'
∑










× CMFF
(9)
where CMFF is the free-fluid estimate
computed for the averaged data. Computation of
high-resolution bound-fluid volumes is now
straightforward,
BFVHR(L) = TCMRHR(L) − CMFFHR(L) .
(10)
High-resolution estimates for the logarithmic
mean T2 (T2LM), SDR permeability (KSDR) and
Timur-Coates permeability (KTIM) can also be
derived :

4. - 4 -
ln[T2LMHR(L)] =
ak
k
∑ (L)ln[T2,k ]
ak
k
∑ (L)
(11)
c
HR
b
HRHR
LLMT
LTCMRaLKSDR
)](2[
)]([)(
↔
=
(12)
[ ]
'
'
)(
)(
)(')(
c
HR
HR
b
HRHR
LBFV
LCMFF
LTCMRaLKTIM
↔
=
(13)
In these expressions, the parameters a, b, c, a’, b’
and c’ are adjustable parameters. Ideally, these
should be calibrated for each well or region from
which NMR data is acquired. Typical values are
a = 104
mD, a’ = 4 mD/ms2
, b = b’ = 4 and c =
c’ = 2.
Errors in the High-Resolution Estimates. The
overall standard deviation for the high-resolution
porosity is estimated according to
22
)()()( += TCMRHRTCMR (14)
where__TCMR is the standard deviation of TCMR
computed for the averaged data and ____is the
standard deviation due to errors associated
entirely with the high-resolution processing. In
practice it is found that ____increases as the
fraction of short T2 components in the T2
distribution increases. The extent to which
precision is affected by these fast-relaxing
components depends on the noise level of the
echo data. From the analysis of synthetic data
generated with a broad range of different T2
distributions and noise levels, an empirical
expression has been obtained,
−+√
↵

= −
3
/30
2 )2)(5.1(2
4
1 E
SEE T (15)
where T2S is the shortest T2 in the reduced T2
distribution and E is the standard deviation of
the noise per echo. Equations (14) and (15) were
designed to provide error estimates for data
acquired with at least 600 echoes and echo
spacings of 200 µs, which are typical for CMR*
acquisition. The standard deviation in the high-
resolution bound fluid volume is obtained from
equations 15 and 16 with _TCMR replaced by _BFV.
Precision of CMFFHR is governed essentially by
the statistical errors in the linear estimate, FFV0.
The standard deviation of the high-resolution
free-fluid estimate is then
(CMFFHR) ≈ (FFV0)
= (L(n))
2
n
∑ E .
(16)
For typical log data, σ(CMFFHR) generally falls
in the range from 0.2 pu to 0.5 pu, indicating that
the free fluid volume can be determined with
both good precision and high resolution.
Determination of Single CPMG Estimates
from PAP data. The processing described above
provides estimates at each sampling point. The
absolute resolution of each of these estimates is
determined by the total length of formation
which contributes to the original data at that
depth. For PAP data, this is equal to the antenna
length plus the distance moved between
successive CPMG measurements. If
nonoverlapping measurements are made, the
resolution is twice the antenna length. However,
if sequential PAPS are acquired, consecutive
echo trains are not independent. In fact, each
PAP has one CPMG measurement in common
with the preceeding PAP and another CPMG
measrement in common with the following PAP.
Using this simple relationship, it is possible to
obtain porosity estimates associated with the
individual CPMG echo data. The vertical
resolution of the resulting estimates is just one
antenna length.
Consider the general case of a series of
measurements, <xL>, made at depths, L, which
are averaged sequentially to provide output data,
<XL>. The individual measurements comprise a
signal component, xL, and a random zero-mean
noise component, δL. The combined PAP
measurement <XL> can be expressed as
XL = (x
L−1
+
L−1
+ xL + L )/ 2. (17)
If we now make an initial guess, 0
~x , for x0, an
estimate for x1 can easily be computed,

5. - 5 -
x1 = 2 X1 − ˜x0 = x0 − ˜x0 + x1 + 0 + 1.
(18)
Using this estimate for x1, a similar estimate for
x2 can now be obtained
x2 = 2 X2 − ˜x1 = ˜x0 − x0 + x2 − 0 + 2 .
(19)
The general result for depth L is
= LLxL
Lx
L
XLx ++∆−=−− 0)1(12 ,
(20)
where ∆0 is an error associated with the initial
estimate for x0,
0000
~ −−=∆ xx . (21)
This alternating error term can be filtered to give
corrected estimates for the quantities of interest,
xL. The result is conveniently expressed in vector
notation
x' = x −
x . K
N





 K
(22)
where x' contains the corrected values, x has
elements Lx , and K is a vector with elements kL
= (-1)L
. Equation (22) provides final estimates
that are independent of 0
~x .
For large N, the statistical error in the final
estimates, Lx' derives primarily from the
uncertainty, δL, in the Lth measurement. The
standard deviation of δL is √2 σ, where σ is the
standard deviation of the noise associated with
the averaged measurement, <XL>. A systematic
error, corresponding to the alternating
component of the true values, xL , is introduced
as a result of equation (22). However, in real
formations, porosity fluctuations are highly
irregular and the error produced by removal of a
high-frequency periodic component should be
relatively small. The magnitude of the error
decreases with increasing N.
The method is applicable to raw echo data or any
other quantity which is a linear function of the
echo amplitudes. It may also be applied to
quantities which are approximately linear
functions of the echo amplitudes, such as the
porosity, bound-fluid and free-fluid volume
estimates derived from the processing of PAP
echo data.
The validity of the method has been tested using
simulated data. T2 distributions and echo trains
were generated at regular intervals of 6 in. Each
T2 distribution comprises a bound-fluid peak,
with T2 values ranging from 0.3 ms to 20 ms and
a free-fluid peak with T2 values between 70 ms
and 700 ms. The ratio of the peak amplitudes
varies between 0.1 and 10 with a periodicity of
15 in, defining a lamination thickness of about
7.5 in. Random zero-mean noise of 3.5 pu per
echo was added to each echo train. Succcessive
echo trains were averaged sequentially to mimic
PAP data with an effective vertical resolution of
12 in. Porosity, bound-fluid and free-fluid
estimates were obtained for this averaged data at
each depth by standard inversion. These logs
were then subject to the resolution enhancement
scheme outlined above.
The results are shown in Figure 2. Bound-fluid,
free-fluid and total porosity estimates are shown
in Tracks 1, 2 and 3 respectively. There is a
pronounced enhancement in resolution for the
single-level free-fluid and bound-fluid estimates
(blue curves) relative to the PAP estimates
(green curves). The total porosity curves vary
more slowly. Observe that no significant artifacts
are introduced into the single-level total porosity
estimate. For free-fluid and bound-fluid
volumes, single-level estimates provide a much
better description of the input formation values
(shown as red curves) than do the original
estimates for the PAP data. Note that the single-
level quantities were derived entirely from the
PAP data without any other input.
LOG EXAMPLES
Synthetic Data – A depth-log simulator has been
used to evaluate the high-resolution processing
method. The simulator generates an echo-decay
corresponding to a predetermined T2 distribution
at each depth together with a noise component.
Every T2 distribution is defined by two log-
normal peaks whose amplitudes and log mean T2
values vary sinusoidally with depth. Periodicities
are input for the total porosity, the ratio of the
peak intensities and their log mean T2 values.
Figure 4 shows the results of a depth-log
simulation over 40 ft with a sampling interval of

6. - 6 -
6 in. Porosity varies between 2 pu and 25 pu
with a periodicity of 1 ft. The T2 values range
between 10 ms and 600 ms. This simulation is
intended to represent clean formations with
varying grain sizes interspersed with low-
porosity streaks. Each echo train contained 1200
echoes with an echo spacing of 200 µs. A zero-
mean gaussian random noise component with a
standard deviation of 3.5 pu was added to the
echo trains at each depth. Input T2 distributions
are shown in Track 5. Track 4 shows the
distributions computed using TCMR processing
with five-level averaging, corresponding to a
vertical resolution of 30 in. It is immediately
evident from inspection of the T2 distributions
that most of the information concerning the
fluctuations in porosity is lost as a result of the
vertical averaging. This fact is emphatically
demonstrated by the total porosity curve
(TCMR) for five-level stacked data presented in
track one, which shows significantly reduced
fluctuations. The high-resolution total porosity
(TCMR_HR) shown in Track two, provides a
much better representation of the true porosity.
For comparison purposes, Track three shows the
TCMR curve computed for the same data
without stacking. This also provides a reasonable
representation of the sharp porosity fluctuations,
although deviations from the true porosity are
more pronounced than in the case of the
TCMR_HR curve.
Note that the differences in precision and
accuracy between TCMR and TCMR_HR shown
in Figure 4 result from the fact that the TCMR
processing used in the simulations was not
optimized for single-level data. The TCMR
processing can be adapted to also process single-
level data and provide essentially the same
results as TCMR_HR. The adaptation for
processing lower S/N data requires increasing
the regularization so that the T2 sensitivity limit7
will be slightly degraded. The advantage is that
high-resolution T2 distributions are also
computed.
Figure 5 presents the results of a second
simulation that was designed to mimic sand-
shale laminations. In this case, the total porosity
varies relatively slowly with depth but the
bound-fluid and free-fluid volumes, represented
by short T2 and long T2 peaks respectively,
fluctuate sharply with a periodicity of 12 in. The
bound fluid T2 values range from 0.3 ms to 20
ms. Free fluid T2 values fall between 70 ms and
700 ms. Note that the five-level averaged TCMR
curve in Track 1 follows the true porosity quite
faithfully, except at the peak maxima and
minima, where some effects of averaging are
detectable. In contrast, the corresponding free-
fluid estimate (green curve) does not capture the
dramatic fluctuations present in this formation
(orange curve). Outputs of the high-resolution
processing are displayed in Track 2. Although
some minor deviations are introduced in the
high-resolution curve, it nevertheless provides a
resaonable representation of the true porosity.
The high-resolution free-fluid estimate shows
excellent agreement with the input free-fluid
volume. Track 3 presents the results of standard
processing of the same data without any vertical
averaging. Note that the TCMR curve shows
somewhat larger deviations from the true
porosity than the high-resolution processing
provides. The free-fluid volume follows the
input free-fluid very accurately.
The rms total error in the porosity estimates are
listed below for the two synthetic logs.
Simulation 1 refers to the clean formation with
short length scale porosity fluctuations shown in
Figure 4. Simulation 2 refers to the sand-shale
laminations presented in Figure 5.
Simulation 1 Simulation 2
σ (TCMR-5) / pu 6.5 1.1
σ (TCMR-1) / pu 1.5 2.4
σ(TCMR_HR) / pu 0.9 1.7
σ (CMFF-5) / pu 4.1 4.0
σ (CMFF-1) / pu 1.4 0.5
The precision of the high-resolution porosity is
comparable to that which would normally result
from three-level averaging in the case of the
clean formation simulation and two-level
stacking in the case of the sand-shale simulation.
CMR-200*, Australia – This well was drilled
though some thinly bedded sand-shale sequences
and had extensive coring. Figure 6 shows a
comparison of high-resolution porosities and
Timur-Coates permeabilities with core data.
Neutron and density porosity logs are presented
in Track 1. The standard five-level-averaged
TCMR porosity curve is compared with core
porosity in Track 2. Observe that the core
porosity displays dramatic fluctuations
particularly in the lower section of this interval.
These variations, which extend to almost 20 pu
over less than 1 ft in some cases, are not apparent
in the standard density porosity or the five-level

7. - 7 -
averaged TCMR curves. The high-resolution
porosity, plotted in Track 3, captures the sharp
porosity fluctuations more accurately. Track
four compares the five-level averaged data and
high-resolution Timur-Coates permeability
estimates with core permeability. Note the high
permeability point at about 77 ft. which is
detected by the high-resolution permeability
estimate but does not appear in the five-level
averaged permeability log.
Figure 7 compares the results of two independent
passes over the same interval. Track 1 shows the
neutron and density porosity as presented in
Figure 6. Tracks 2 and 3 respectively show the
five-level averaged TCMR and high-resolution
TCMR_HR curves for the two passes. The five-
level averaged free-fluid volume, CMFF, and
high-resolution estimate, CMFF_HR, for the two
passes are compared in Tracks 4 and 5. Because
of a relatively high salinity (90,000 ppm) and
temperature (100 o
C) the rms noise per echo was
approximately 4.0 pu for these logs. Despite this
comparatively high noise level, CMFF_HR
displays excellent repeatability. The standard
deviation in CMFF_HR is just 0.4 pu. Average
standard deviations for TCMR and TCMR_HR
over this section are 1.5 pu and 2.5 pu
respectively. It is important to recognize that
although there is some penalty in precision when
using high-resolution processing relative to
vertical averaging, absolute accuracy may be
improved significantly. This is demonstrated
clearly in Figures 6 and 7. In particular, the high-
resolution porosity estimates show much better
agreement with core porosity values than does
the five-level averaged porosity, despite some
loss of precision.
CMR-PLUS*, Engineering Test Well, Houston
The example shown in Figure 8 was acquired
using the CMR-PLUS* tool in the engineering
test well in Houston, which is made up of
artificial formations made of blocks of known,
thickness, lithology, porosity and permeability.
The logs shown were obtained at a logging speed
of 1800 ft per hour using EPM acquisition. Two
passes were made using the same parameters.
Total porosity, free-fluid and bound-fluid logs
for the two passes are plotted in tracks 1, 2 and 3
respectively. In track 1, the block porosities are
also shown. All three logs show excellent
repeatability and match the block porosities over
the entire well. Note, in particular, that the 1-ft
thick beds above 30 ft are identified clearly by
the high-resolution logs. This example
demonstrates that high-resolution porosity,
bound-fluid and free-fluid logs can be obtained
with good precision and accuracy at relatively
fast logging speeds.
CMR-PLUS*, Canada This well contains heavy
oil and gas in a shaly sand with some fine
laminations. It was logged at 1200 ft/hr using the
CMR-PLUS* with EPM acquisition. The logs
are presented in Figure 9. Tracks 1 to 3 compare
the standard bound-fluid, free-fluid and total
porosity logs, processed using five-level
averaging, with the corresponding high-
resolution curves. Neutron density logs are
presented in Track 4. Track 5 shows the deep
and shallow resisitivity logs. Over the section
from 90 ft to 100ft, the CMR high-resolution
curves are relatively featureless and overlay the
averaged logs. In contrast, from 100 ft to 120 ft,
the CMFF_HR and BFV_HR curves show
increased activity due to the fine laminations that
are apparent in the FMI image. Note that the
BFV_HR and CMFF_HR logs largely
compensate each other so that the total porosity
log alone provides little indication of the
laminations. The fluctuations in free-fluid and
bound-fluid correlate well with the laminations
in the FMI. Below 120 ft. the formation contains
hydrocarbon, as evidenced by the increased
resistivity. A substantial part of the hydrocarbon
signal is not detected by the CMR tool, because
of the very short relaxation times which result
from the high viscosity of the oil.
CONCLUSIONS
A new high-resolution processing strategy for
NMR logs provides estimates for total porosity,
bound-fluid and free-fluid volumes at the
maximum tool resolution. Combining the
processing method with EPM acquisition and
nonoverlapping measurement schemes, it is
possible to obtain reliable porosity, bound-fluid
and free-fluid volumes with good precision and
high resolution. The high-resolution quantities
are extremely useful for the identification and
characterization of thin beds and estimating
producibility in laminated formations.
ACKNOWLEDGEMENTS

8. - 8 -
ABOUT THE AUTHORS
Dr. Nicholas Heaton received his PhD in
chemistry from the University of Southampton in
1987. He worked in NMR research at the
University of California at San Diego and the
University of Stuttgart. In 1998 he joined
Schlumberger Sugar Land Technology Center as
NMR interpretation-development products
specialist.
Chanh Cao Minh is the CMR section manager at
the Sugar Land Technology Center. His
biographical sketch can be found in Paper II of
the 1998 SPWLA Annual Meeting Transactions.
Dr. Bob Freedman is the Engineering Advisor in
the Magnetic Resonance Department at the
Schlumberger Product Center in Sugar Land,
Texas. He was a member of the engineering team
that built the first CMR tool. Bob has made
many contributions to Schlumberger technology.
Some of his contributions to magnetic resonance
logging include the invention and
implementation of the CMR Window Processing
algorithm, the CMR Enhanced Precision Mode
processing and acquisition scheme, the Density-
Magnetic Resonance method for evaluation of
gas-bearing reservoirs and the downhole data
compression algorithm used in the CMR tools.
Recently Bob developed a new NMR fluid
characterization method. He has a Ph.D. in
physics from the Univ. of California at San
Diego. Following graduate school Bob was
hired as a Post-Doctoral Fellow in condensed
matter physics at the Xerox Palo Alto Research
Center. After the fellowship, Bob became a
member of the research staff in the physics
department at the Univ. of Chicago. He later
worked in Shell Oil operations and research for
five years. He joined Schlumberger almost 15
years ago after working for five years as an
independent petroleum consultant.
Charles Flaum obtained his B.Sc. degree at
McGill University in Montreal in 1970 and a
Ph.D. in Nuclear Physics at the University of
Rochester in 1975. After two years as a
postdoctoral fellow at Brookhaven National
Laboratories, he joined Schlumberger as a field
engineer in 1977. Since then his career has
moved him through various assignments in the
field, engineering and research. He now manages
the NMR research effort at Schlumberger–Doll
Ridgefield Research center.
REFERENCES
Coates, G. and Denoo, S., “The Producibility
Answer Product”, The Technical Review,
Schlumberger, June 1981
Sezginer, A., Cao Minh, C., Heaton, N., Herron,
M. Freedman, R. and Van Dort, G. “An NMR
High-Resolution Permeability Indicator”,
Transactions of the SPWLA Annual Logging
Symposium, June 1999
Freedman, R. “Dual-Wait Time Processing for
More Accurate Total and Bound-Fluid Porosity”,
U.S. Patent Application 156417, 1998
McKeon, D., Cao Minh, C., Freedman, R.,
Harris, R., Willis, D., Davies, D., Gubelin, G.,
Oldigs, R., and Hurlimann, M., “An Improved
NMR Tool for Faster Logging”, Transactions of
the SPWLA Annual Logging Symposium, June
1999
Flaum, C., Galford, J. and Ducket, S., “Method
for Determining Formation Characteristics with
Enhanced Vertical Resolution”, U.S. Patent
4,794,792
Freedman, R., “Processing Method and
Apparatus for Processing Spin Echo IN-Pahse
and Quadrature Amplitudes from a Pulsed
Nuclear Magnetism Tool and Producing New
Output Data to be Recorded on an Output
Record” , U.S. Patent 5,292,137
Freedman, R., Boyd, A., Gubelin, G., McKeon,
D., Morriss, C.E. and Flaum, C., “Measurement
of Total NMR Porosity Adds New Value to
NMR Logging”, Transactions of the SPWLA
Annual Logging Symposium, June 1997
Kleinberg, R.L. and Boyd, A., “Tapered Cutoffs
for Magnetic Resonance Bound Water Voume”,
SPE Paper 38737, 1998

9. - 9 -
Fig. 1. Vertical stacking of echo trains and inversion to obtain T2 distribution for averaged data. An equivalentT2 distribution is
formed with a reduced number number of T2 bins of approximately equal amplitude. The total porosity and logarithmic mean T2
value of the reduced distribution are identical to those for the original distribution.
ΦΦ
Fig. 2. Comparison of single-level (6 in. resolution) and PAP averaged (12 in. resolution) porosity estimates for simulated logs
representing thin sand-shale laminations. Bound-fluid, free-fluid and total porosity estimates are shown in Tracks 1, 2 and 3
respectively. There is a pronounced enhancement in resolution for the single-level free-fluid and bound-fluid estimates (blue curves)
relative to the PAP estimates (green curves). Observe that no significant artifacts are introduced into the single-level total porosity
estimate, which varies slowly with depth. For free-fluid and bound-fluid volumes, single-level estimates provide a much better
description of the input formation values (shown as red curves) than do the original PAP data. Note that the single level quantities
were derived entirely from the PAP data without any other input.

10. - 9 -
T2 Distribution
(5-LEV)
0.3 3000
(ms)
TCMR (5-LEV)
0.3 0
Porosity
CMFF (5-LEV)
Free Fluid
0.3 0
0.3 0
0.3 0
0.3 0
TCMR (1-LEV)
0.3 0
0
0
TCMR_HR
Porosity
CMFF_HR
Free Fluid
0.3 0
0.3 0
0.3 0
Porosity
CMFF(1-LEV)
Free Fluid
0.3
0.3
0.3 0
T2 Distribution
(Input)
0.3 3000
(ms)
10
20
30
MD
(ft)
Fig. 4. Depth-log simulation with a
sample interval of 6 in. where the
porosity varies between 2 pu and 25 pu
with a periodicity of 1 ft and T2 values
range between 10 ms and 600 ms. This
simulation is intended to represent
clean formations with varying grain
sizes interspersed with low porosity
streaks. Each echo train contained 1200
echoes, an echo spacing of 200 µs and a
zero-mean gaussian random noise
component with a standard deviation of
3.5 pu per echo. Input T2 distributions
are shown in Track 5. Track 4 shows
the distributions computed using
standard processing with five-level
averaging. The high-resolution total
porosity (TCMR_HR) shown in Track
2, clearly provides a much better
representation of the true porosity than
the five-level averaged TCMR curve
shown in Track 1. The TCMR curve
computed without stacking, shown in
Track 3, also provides a reasonable
representation of the sharp porosity
fluctuations, although deviations from
the true porosity are more pronounced
than in the case of TCMR_HR.
Fig. 5. Depth-log simulation designed
to mimic sand-shale laminations. the
total porosity varies gradually with
depth but the bound-fluid and free-fluid
volumes, represented by the short T2
and long T2 peaks respectively,
fluctuate sharply with a periodicity of
12 in. The five-level average computed
T2 distriubutions and input T2
distributions are shown in Tracks 4 and
5. The five-level average TCMR curve
in Track 1, follows the true porosity
quite faithfully, except at the peak
maxima and minima, where some
effects of averaging are detectable. In
contrast, the corresponding free-fluid
estimate does not capture the dramatic
fluctuations present in this formation.
Outputs of the high-resolution
processing are displayed in Track 2.
The TCMR_HR curve provides a
reasonable representation of the true
porosity. The high-resolution free-fluid
estimate shows excellent agreement
with the input free-fluid volume. Track
3 presents the results of standard
processing of the same data without any
vertical averaging. Note that the TCMR
curve shows somewhat larger
deviations from the true porosity than
provided by the high-resolution
processing. The free-fluid volume
follows the input free-fluid very
accurately.
T2 Distribution
(5-LEV)
0.3 3000(ms)
TCMR (5-LEV)
0.3 0
Porosity
0.3 0
0.3 0
TCMR (1-LEV)
0.3 0
0
TCMR_HR
Porosity
0.3 0
Porosity
0.3
T2 Distribution
(input)
0.3 (ms)
10
20
30
MD
(ft)

11. - 9 -
Fig. 6. Comparison of high-
resolution porosities and Timur-
Coates permeabilities with core
data. Standard neutron and
density porosity logs are
presented in Track 1. The five-
level-averaged TCMR porosity
curve is compared with core
porosity in Track 2. High-
resolution porosity, TCMR_HR ,
is compared with core porosity
in Track 3. Note that TCMR_HR
captures the sharp porosity
fluctuations, which are missed
by the TCMR log. Tracks 4 and
5 compare core permeability
with the five-level averaged
permeability, KTIM, and the
corresponding high-resolution
log, KTIM_HR. Note the high
permeability point at about 77 ft.
which is identified by a peak in
the high-resolution permeability
estimate but does not appear in
the five-level average
permeability log.
80
90
110
100
120
10000.1 1000
T2 Distribution
0.3 3000(ms)
NPHIMD
(ft)
GR DPHI
0.3 0
TCMR(5-LEV)
CPOR
0.3 0
CPOR CKH CKH
TCMR_HR KTIM(5-LEV)
0.1 1000
KTIM_HR
0.3 0 10000.1
0.3 0 0.3 0 0.3 0 0.1
Fig. 7. Comparison of the results
of two independent passes over
the same interval. Track 1 shows
the neutron and density
porosities. Tracks 2 and 3
respectively show the five-level-
average TCMR and high-
resolution TCMR_HR curves for
the two passes. The five-level
average free-fluid volume,
CMFF, and high-resolution
estimate, CMFF_HR, for the two
passes are compared in Tracks 4
and 5. Despite comparatively
high noise level of ~ 4.0 pu per
echo, CMFF_HR displays
excellent repeatability. The
standard deviation for
CMFF_HR is 04 pu for the two
passes. Corresponding standard
deviations for TCMR and
TCMR_HR over this section are
1.5 pu and 2.5 pu respectively.
Although there is some penalty
in precision when using high-
reslution processing relative to
vertical averaging, overall
accuracy may be improved
significantly.
80
90
110
100
120
T2 Distribution
0.3 3000(ms)
NPHIMD
(ft)
GR DPHI
0.3 0
0.3 0
TCMR(1) TCMR_HR(1) CMFF(1) CMFF_HR(1)
0.3 0 0.3 0 0.3 0 0.3 0
TCMR(2) TCMR_HR(2) CMFF(2) CMFF_HR(2)
0.3 0 0.3 0 0.3 0 0.3 0

12. - 9 -
Limestone 3’
Marble 1’
Berea 1’
Dolomite 1’
Limestone 3’
Berea 3’
Marble 3’
Chalk 3’
Dolomite 1’
Nugget 1.5’
30
40
TCMR_HR(1) CMFF_HR(1) BFV_HR(1)
0.3 0 0.3 0 0.3 0
TCMR_HR(2) CMFF_HR(2) BFV_HR(2)
0.3 0 0.3 0 0.3
0
0.3 3000T2 (ms)
T2 Distribution
Fig. 8. Logs acquired using the CMR-PLUS* tool in the engineering test well in Houston, which is made up of artificial formations made of
blocks of known, thickness, lithology, porosity and permeability. The logs shown were obtained at a logging speed of 1800 ft per hour using
EPM acquisition. Two passes were made using the same parameters. Total porosity, free-fluid and bound-fluid logs for the two passes are
plotted in Tracks 1, 2 and 3 respectively. In Track 1, the block porosities are also shown. All three logs show excellent repeatability and
match the block porosities over the entire well. Note, in particular, that the 1 ft thick beds above 30 ft are identified clearly by the high-
resolution logs. This example demonstrates that high-resolution porosity, bound fluid and free fluid logs can be obtained with good precision
and accuracy at relatively fast logging speeds.

13. - 9 -
Fig. 9. Results from Canadian well, logged at 1200 ft/hr using the CMR-PLUS* with EPM acquisition. Tracks 1 to 3 compare the standard
bound-fluid, free-fluid and total porosity logs, processed using five level averaging, with the corresponding high-resolution curves. Neutron
density logs are presented in Track 4. Track 5 shows the deep and shallow resisitivity logs. Over the section from 90 ft to 100ft, the CMR
high-resolution curves are relatively featureless and overlay the averaged logs. In contrast, from 100 ft to 120 ft, the CMFF_HR and
BFV_HR curves show increased activity due to the fine laminations that are apparent in the FMI image. Note that the BFV_HR and
CMFF_HR logs largely compensate each other so that the total porosity log alone provides little indication of the laminations. The
fluctuations in free-fluid and bound-fluid correlate well with the laminations in the FMI. Below 120 ft. the formation contains hydrocarbon,
as evidenced by the increased resitivity. A substantial part of the hydrocarbon signal is not detected by the CMR tool, because of the very
short relaxation times which result from the high viscosity of the oil.
DPHI
0.4 0
NPHI
0.4 0
TCMR
0.4 0
T2 Distribution
0.3 3000(ms)
MD
TCMR_HR
AHT90
0.4 0 0.2 2000
0.4 0
CMFF_HR
CMFF
0.4 0
0.4 0
BFV_HR
BFV
RXO8
0.2 2000
FMI
CMFF_HR
0.3 0
BFV_HR
0.3 00.4
(ft)
110
120
100
90
0
GR