Pulse sequences and interpretation techniques for NMR measurements

An NMR pulse sequence and signal processing method is disclosed for measurement of fast decay response signals from materials containing a fluid state. The proposed pulse sequence and processing method are applicable in borehole NMR logging as well as measurements of attributes of man-made or natural materials. The disclosed pulse sequence comprises a series of short NMR pulse trains separated by intervals which are shorter than the time required for polarization of nuclear magnetization in bulk fluids of the fluid state. By stacking response signals to increase the signal to noise ratio, time domain data is obtained that generally corresponds to transverse decay components as short as about 0.5 ms. Various attributes of the materials being investigated can be derived in a single measurement.

FIELD OF INVENTION 
The present invention concerns nuclear magnetic resonance (NMR) pulse 
sequences used in evaluating earth formations or various porous materials 
having a fluid state. More specifically, the invention relates to NMR 
pulse sequences and methods for interpretation of NMR logging data for 
estimating earth formation properties, such as the total formation 
porosity, and/or properties of the porous materials under investigation. 
BACKGROUND OF THE INVENTION 
No single logging tool or measurement technique is presently available that 
can correctly identify properties of the rock formation, such as its 
porosity, in all circumstances. For example, bulk density measurements can 
only be used if the density of the rock matrix is known; sonic transit 
time measurements may be used if the transit times both for the rock and 
the fluids are known. A number of techniques, referred to as "crossplot 
techniques", exist that compare different measurements to estimate 
formation porosity in situ. However, none of these techniques is truly 
independent of the rock's geological make-up. 
Another approach frequently used during open-hole logging is to perform 
bulk conductivity measurements in order to identify and separate 
oil-bearing zones which have low conductivity, from water-bearing zones 
which have high conductivity. However, in practice the interpretation of 
measurement data is typically obscured by the presence of 
highly-conductive clay attached to or interspersed with sand grains. Due 
to the fact that no simple measurement exists for generating quantitative 
in situ estimates of the amount of clay and the water volume bound to the 
clay, the interpretation of in situ conductivity data is still more of an 
art than a science. 
The amount and type of clay in a formation is interesting to reservoir and 
to production engineers in its own right. For example, swelling and/or 
dislodging of certain clay particles may clog an otherwise permeable sand. 
Conventional logging tools have been often characterized in terms of their 
response to clay minerals and/or clay-bound water. In fact, most 
conventional logging measurements (such as neutron-absorption cross 
section, bulk density, natural gamma-ray radiation, spontaneous electric 
potential, sonic wave transit time, photoelectric absorption factor, etc.) 
respond in a qualitative way to the presence of clay in the formation 
being investigated, mostly because clays tend to accumulate heavy 
minerals. More information is contained in D. V. Ellis, "Well Logging For 
Earth Scientists," Elsevier 1987, chapter 19: "Clay Typing and 
Quantification from Logs," which chapter is incorporated herein by 
reference. Still, no single reliable method exists currently for 
estimating the parameters of the clay present in a formation. FIG. 1 shows 
the standard rock porosity model which provides an illustration of the 
issues discussed above. In particular, as shown in FIG. 1, the total 
porosity space is occupied by water and hydrocarbons. The volume excluded 
from what is designated in the figure as "effective porosity" is the 
clay-bound water fraction. 
It is well known that the signal measured by NMR logging tools is 
proportional to the mean density of hydrogen nuclei in the fluid that 
occupies the pore space. Pulsed NMR measurements performed downhole are 
sensitive to the amount of hydrogen atoms from liquid or gaseous 
materials, but not from solid-state rock. Therefore, in principle, NMR is 
a truly lithology-independent porosity measurement. However, with 
reference to FIG. 1, current logging tools register only part of the total 
porosity of the formation because hydrogen nuclei in the rock matrix and 
those associated with clay particles relax too rapidly to be detected and 
measured under the limited signal-to-noise (SNR) conditions available 
downhole. 
Accordingly, it is clear that the difference between a "total porosity" 
measurement (derived, for example, from a bulk density measurement, 
neutron absorption and/or sonic transit time) and the NMR-measured 
porosity can be interpreted as the amount of clay-bound water. See for 
example the disclosure in U.S. Pat. No. 5,557,200 assigned to the assignee 
of the present application, which is hereby incorporated by reference for 
all purposes. However, prior art methods require the use of separate 
techniques to measure the total porosity of a formation. In fact, 
obtaining an accurate estimate of this total porosity is still relatively 
difficult. Furthermore, an NMR measurement itself can be depressed by 
fluid effects, such as deficient hydrogen index, long polarization times 
T1, etc. 
It has been recognized in the past that specific applications of NMR 
logging can be performed with less than full recovery of magnetization. 
For example, U.S. Pat. No. 5,389,877 to Sezginer et al. describes a method 
by which a moving NMR logging tool is used to quantify the amount of 
capillary-bound fluid volume BFV. However, in the patented method the 
clay-bound volume is not recorded, nor is the log interpretation improved. 
The patent merely records a sub-set of the data required for interpreting 
an NMR log. In particular, it requires that other logging tools provide an 
estimate of total porosity of the formation. 
The method of the present invention, described in greater detail below, 
uses prior art logging tools and measurement apparatuses to obtain 
previously unavailable data relating to the composition of a geologic 
structure. In particular, a novel pulse sequence, signal processing 
technique and a method of interpretation of NMR measurements are proposed 
and used to obtain in a single experiment characteristics of the formation 
including its total porosity and clay mineral content which may then be 
used to determine additional key petrophysical parameters. In addition, 
the method of the present invention can also be used to measure properties 
of various porous materials having a fluid state. 
Additional references which provide further background information include: 
1. Ellis, D. V.: Well Logging for Earth Scientists, Elsevier, New York, 
N.Y. (1987) 305. 
2. Miller, M. N. et al.: "Spin Echo Magnetic Resonance Logging: Porosity 
and Free Fluid Index Determination," paper SPE 20561 presented at the 1990 
SPE Annual Technical Conference and Exhibition, Proceedings, 321. 
3. Morriss, C. E. et al.: "Field Test of an Experimental Pulsed Nuclear 
Magnetism Tool," paper GGG presented at the 1993 Annual Logging Symposium 
of the Society of Professional Well Log Analysts. 
4. Chandler, R. N. et al.: "Improved Log Quality With a Dual-Frequency 
Pulsed NMR Tool," paper SPE 28365 presented at the 1994 SPE Annual 
Technical Conference and Exhibition, Proceedings, 23. 
5. Ellis, D. V.: Well Logging for Earth Scientists, Elsevier, New York, 
N.Y. (1987) 439-469. 
6. Korringa, J., Seevers, D. O. and Torrey, H. C.: "Theory of Spin Pumping 
and Relaxation in Systems With a Low Concentration of Electron Spin 
Resonance Centers," Phys. Rev. 127 (1962) 1143. 
7. Fripiat, J et al.: "Thermodynamic and Microdynamic Behavior of Water in 
Clay Suspensions and Gels," J. Colloid. Interface Sci. 89 (1982) 378. 
8. Woessner, D. E.: "An NMR Investigation Into The Range of the Surface 
Effect on the Rotation of Water Molecules," J. Magn. Reson. 39 (1980) 297. 
9. Prammer, M. G.: "NMR Pore Size Distributions and Permeability at The 
Well Site," paper SPE 28368 presented at the 1994 SPE Annual Technical 
Conference and Exhibition, Proceedings, 55. 
10. Freedman, R. and Morriss, C. E.: "Processing of Data From an NMR 
Logging Tool," paper SPE 30560 presented at the 1995 SPE Annual Technical 
Conference and Exhibition, Proceedings, 301. 
11. Prammer, M. G. et al.: "Lithology-Independent Gas Detection by 
Gradient-NMR Logging," paper SPE 30562 presented at the 1995 SPE Annual 
Technical Conference and Exhibition, Proceedings, 325. 
12. van Olphen, H. and Fripiat, J. J.: Data Handbook for Clay Minerals and 
Other Non-Metallic Minerals, Pergamon Press, New York, N.Y. (1979). 
13. Hower, J. and Mowatt, T. C.: "The Mineralogy of Illites and Mixed-Layer 
Illite Montmorillonites," The American Mineralogist, 51, (May-June 1966) 
825. 
SUMMARY OF THE INVENTION 
The present invention defines a novel pulse sequence, logging technique and 
a signal processing scheme that employ existing NMR instruments or logging 
tools to directly quantify the amount of bound water in the materials 
under investigation, or clay-bound water in the formation. The method of 
the present invention is characterized by the rapid accumulation of only 
those NMR signal components which are typical for clay-bound water and 
have very fast T1 and/or T2 relaxation times. The signal-to-noise ratio 
can typically be enhanced by a factor of seven or more, compared to the 
standard NMR measurement. 
The signal processing scheme extracts very fast decaying components from 
the high-SNR measurement and combines the measurement of these components 
with the standard NMR measurement to completely characterize the 
distribution (or compartmentalization) of the various components of the 
total porosity in the rock under investigation. 
Finally, in accordance with the present invention one can improve the 
resistivity interpretation model based on the use of parallel conduction 
paths for clay-bound water and non-clay-bound water. Specifically, having 
obtained each fluid volume from the NMR measurement separately simplifies 
the log interpretation and provides more accurate estimates of all 
parameters of interest. Additional properties of materials under 
investigation can be obtained by combining the measurements in accordance 
with the present invention with external measurements, as known in the 
art. 
In a particular embodiment of the present invention, a nuclear magnetic 
resonance (NMR) method is disclosed for measuring an indication of 
attributes of materials containing a fluid state, the method comprising 
the steps of: 
(a) applying in a pre-determined sequence at least two short NMR pulse 
trains, each pulse train comprising at least one pulse and resulting in at 
least one response signal from said materials, the interval T.sub.s 
between any two short pulse trains being less than the time required for 
polarization of substantially all nuclear magnetization in bulk fluids of 
the fluid state contained in said materials; and 
(b) stacking NMR response signals from said at least two short NMR pulse 
trains to obtain time domain data indicative of fast decay components of 
the fluid state contained in said materials. 
In an separate embodiment of the present invention an NMR borehole logging 
method is disclosed for measuring an indication of petrophysical 
attributes of an earth formation, the method comprising the steps of: 
(a) applying in a pre-determined sequence at least two short NMR pulse 
trains, each pulse train comprising at least one pulse and resulting in at 
least one response signal from said earth formation, the interval T.sub.s 
between any two short pulse trains being less than the time required for 
polarization of substantially all nuclear magnetization in any bulk fluid 
contained in said earth formation; and 
(b) stacking NMR response signals from said at least two short NMR pulse 
trains to obtain time domain data indicative of fast decay components of a 
fluid state contained in said earth formation.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
There are two versions of modern pulse-NMR logging tools in use today: the 
centralized MRIL.RTM. tool made by NUMAR Corporation, and the side-wall 
CMR tool made by Schlumberger. The MRIL.RTM. tool is described, for 
example, in U.S. Pat. No. 4,710,713 to Taicher et al. and in various other 
publications including: "Spin Echo Magnetic Resonance Logging: Porosity 
and Free Fluid Index Determination," by Miller, Paltiel, Millen, Granot 
and Bouton, SPE 20561, 65th Annual Technical Conference of the SPE, New 
Orleans, La., Sept. 23-26, 1990; "Improved Log Quality With a 
Dual-Frequency Pulsed NMR Tool," by Chandler, Drack, Miller and Prammer, 
SPE 28365, 69th Annual Technical Conference of the SPE, New Orleans, La., 
Sept. 25-28, 1994). Details of the structure and the use of the MRIL.RTM. 
tool are also discussed in U.S. Pat. Nos. 4,717,876; 4,717,877; 4,717,878; 
5,212,447, 5,280,243, 5,309,098, and 5,412,312, all of which are commonly 
owned by the assignee of the present invention. 
The Schlumberger CMR tool is described, for example, in U.S. Pat. Nos. 
5,055,787 and 5,055,788 to Kleinberg et al. and further in "Novel NMR 
Apparatus for Investigating an External Sample," by Kleinberg, Sezginer 
and Griffin, J. Magn. Reson. 97, 466-485, 1992. 
The content of the above patents and publications is hereby expressly 
incorporated by reference. It should be understood that the present 
invention is equally applicable to both hardware configurations discussed 
above, as well as to generic instruments for measuring NMR signals. 
With reference to the attached drawings, FIG. 2 shows a standard pulse 
sequence typically employed by NMR logging tools, such as the Numar 
MRIL.RTM. and the Schlumberger CMR tools. As shown in FIG. 2, a wait time 
interval (T.sub.w) of approximately 0.5-10 sec is used first to allow for 
polarization of the formation by the tool's static magnetic field. Then, a 
Carr-Purcell-Meiboom-Gill (CPMG) pulse-echo train is executed, consisting 
of an excitation pulse (A) and an alternating sequence of refocusing 
pulses (B). Following each pair of excitation pulse and a refocusing 
pulse, acquisition window (C) is applied next. Complex data from such a 
pair of echo trains are co-added on an echo-by-echo basis to remove 
certain artifacts and to enhance the NMR signal, as known in the art. More 
pairs may be added to enhance the signal-to-noise ratio. The echo train, 
consisting of a superposition of exponentially decaying signals is then 
submitted to a processing scheme which calculates the underlying decay 
modes of the received NMR echo signal. 
Specifically, a processing method (Prammer's method) for calculating the 
underlying decay modes of the NMR signal is described in U.S. Pat. No. 
5,517,115 to the present inventor. The content of this patent is hereby 
expressly incorporated by reference for all purposes. As discussed in the 
patent, if such a measurement is repeated many times while the tool is 
held stationary, it is possible to identify the portion of the clay-bound 
water in the signal. 
NMR RESPONSE OF CLAY-BOUND WATER 
As discussed above with reference to the rock porosity model in FIG. 1, 
conventional hydrogen-NMR responds well to hydrogen in fluids and very 
poorly or not at all to hydrogen in solids. Thus, downhole NMR logging is 
only concerned with the fluid-filled porosity of the rock space. The rate 
of signal decay is a strong function of the local surface-to-volume ratio 
in the pore space. Both T.sub.1 (longitudinal) and T.sub.2 (transversal) 
relaxation times, which are on the order of a few seconds in fresh water, 
can be reduced by several orders of magnitude once the liquid is 
introduced into the pore space and is in contact with the grain surfaces. 
The effect has been explained in physical terms by the theory of surface 
relaxation. The first generation of NMR logging tools was limited to an 
intrinsic "dead time" of 20 ms, corresponding to a T.sub.2 cutoff time of 
about 30 ms, which in many shaly sand formations separates irreducible 
from movable fluids. Today's commercial pulsed-NMR tools also quantify the 
capillary-bound ("irreducible") regime in the T.sub.2 range of 4-30 ms. 
Clay-bound water, however, has much faster T.sub.2 times due to the 
enormous specific surface area of clays (up to 800 m.sup.2 /g). Details on 
specific surface areas and NMR measurements on smectites and kaolinites 
can be found in Fripiat et al. D. E. Woessner has studied longitudinal 
relaxation times (T.sub.1) at 8 and 25 MHz in aqueous solutions of 
hectorite. He found a perfectly linear relationship between the relaxation 
rate (1/T.sub.1) and the amount of dry clay per water volume. The 
plausible explanation for these data is the combination of two factors: 
(1) a short-range dipole-dipole surface relaxation effect that does not 
extend more than 1-2 layers of water molecules from the solid surface, and 
(2) fast exchange between this mono-molecular surface water layer and the 
clay-associated water volume due to thermal diffusion. 
In order to more closely resemble the downhole measurement, laboratory NMR 
experiments were performed at 1 MHz to determine transverse relaxation 
times T.sub.2. Representative samples of montmorillonite (a smectite), 
illite, kaolinite and chlorite were obtained from the Source Clay Minerals 
Repository of the Clay Mineral Society, located at the University of 
Missouri. Table 3 summarizes the sample clay types and their properties. 
The samples were prepared by adding 0%, 12.5%, 25% and 50% by weight of 
synthetic sea-water brine, mixing the paste and pressing the mixture at 
2500 psi. NMR amplitudes and T.sub.2 distributions of the sealed samples 
were measured in a commercially available core analyzer, operating at 1 
MHz, a temperature of 25.degree. C., and at echo spacings (T.sub.e) of 0.3 
ms and 0.5 ms. The water content was determined by weighing each sample 
before and after overnight vacuum-drying at 103.degree. C. The results are 
listed in Table 4. 
Except for the montmorillonite sample SWy-2, no clay sample had an NMR 
signal without having water added to it. SWy-2 absorbs 7% water by weight 
under normal indoor humidity conditions. At this concentration, the bound 
water relaxes extremely fast with poor visibility at the 0.5 ms echo 
spacing. As more brine is added, T.sub.2 increases up to 1 ms, while all 
absorbed water becomes NMR-visible. The latter fact is consistent with the 
"fast exchange" hypothesis borne out of Woessner's data. The clay-bound 
water in the other clay samples is always fully visible at T.sub.e =0.5 
ms. As expected, T.sub.2 increases linearly with the amount of water 
absorbed. The illite sample could not absorb more than 15.8% brine, the 
kaolinite was limited to 20.0% and the chlorite to 7.5%. Selected T.sub.1 
measurements were performed, yielding ratios of T.sub.1 /T.sub.2 between 
1.5 and 2 as indicated in Table 4. 
The "fast exchange" hypothesis predicts a linear relationship between 
relaxation rate and the surface-to-volume ratio: 
##EQU1## 
The laboratory measurements allow one to estimate values for the surface 
relaxivity .rho..sub.2 from specific surface areas (Table 3) and from the 
water-to-dry ratios (Table 4). As shown in Table 4, the computed values 
are almost constant (0.8-1 .mu.m/s), except for the chlorite sample, which 
is probably compromised by an overestimated specific surface area. 
Apparently, clay mineralogy has little influence on the T.sub.2 values, 
but rather the surface-to-volume ratio is the dominant factor. 
Furthermore, these values for surface relaxivity are substantially smaller 
than those reported in the literature for sandstones (of the order of 5-20 
.mu.m/s). Fortunately for a downhole measurement, the low surface 
relaxivities of clays imply a range of T.sub.2 values that can be measured 
with the current MRIL logging tool technology. 
The cation exchange capacity (CEC, Table 3) of clays is fundamental to the 
conversion of bulk resistivity measurements into water saturation and 
hence hydrocarbon saturation estimates. The number of available exchange 
sites is proportional to a clay's specific surface ratio, and therefore 
the observed T.sub.2 can be turned into an indicator of CEC: T.sub.2 
components greater than 3 ms indicate little or no CEC; the range 1-2 ms 
is associated with illite-type CEC's, and T.sub.2 's less than 1 ms 
indicate smectites with high CEC values. 
A field study was conducted at Shell's Stribling #1 test well near Johnson 
City, Tex., to confirm the laboratory T.sub.2 data and to prove the 
concept of a downhole clay-bound water measurement. The well was drilled 
and cored in 1964 and is open-hole from casting at 305 ft to total depth 
at 1268 ft. Its geological composition is well characterized, consisting 
of shaly sands and shales below 1100 ft. The heavy and variable clay 
contents made this well very suitable for the present study. Illite as the 
dominant clay mineral in these formations. 
An MRIL engineering test tool was used to acquire station logs in the 
various shaly sandstone sections. FIGS. 2 and 3 show representative data 
collected at a station opposite a formation with about 50% bioturbated 
shale. Carr-Purcell-Meiboom-Gill echo trains with 1000 data points and an 
echo-to-echo spacing of 0.51 ms were acquired and averaged for 15 minutes 
in order to increase the signal-to-noise ratio, i.e. the precision of the 
measurement. The very fast initial decay visible in FIG. 2 has a time 
constant of 1 ms and is due to clay-bound water. 
FIG. 3 illustrates the accumulated result of 300 actual measurements from 
NUMAR's MRIL.RTM. tool, each measurement consisting of about 1000 echoes 
with an echo-to-echo spacing of 510 microseconds. 
FIG. 4 illustrates the result of applying Prammer's processing method to 
the data shown in FIG. 3. Each peak in this "relaxation spectrum" shown in 
FIG. 4 corresponds to a major relaxation mode of the underlying signal. In 
particular, from left to right one can identify three peaks: (a) 
clay-bound water, (b) capillary bound water and (c) movable water. In 
accordance with the Prammer's processing method the integrated areas under 
the peaks are proportional to the individual water volumes. In the example 
illustrated in FIG. 4, the amount of clay-bound water volume is 4.8%; 
capillary-bound water volume is 4.9%; and movable water volume is 1.8% of 
the total volume. 
FIG. 4 also illustrates the customary T2 "cutoff" values which, in this 
example are 3 ms for the clay vs. non-clay boundary and 30 ms for 
non-movable vs. movable water. While these cutoff values are not 
universally applicable, they are fairly standard in the logging industry 
for use in oil reservoirs in shaly sandstone foundations. 
In the stationary example illustrated in FIG. 4 it took about 15 minutes to 
accumulate the stationary data. In a moving tool, of course, much less 
time is available for accumulation. Therefore, given that the achievable 
signal-to-noise ratio is limited by basic physical parameters and the tool 
construction, less information can be extracted from the log data. In 
particular, T.sub.2 information below 3 ms becomes very unreliable and 
"regularization" schemes must be applied to suppress very fast relaxation 
modes in the data. 
The present invention consists of three parts: development of a novel pulse 
sequence, data processing and measurement interpretation. 
The novel pulse sequence in accordance with a preferred embodiment of the 
present invention is shown in FIG. 5. The first part of the sequence is 
identical to the one shown in FIG. 2. As shown in FIG. 5, immediately 
following the regular CPMG train is issued a series of short echo trains 
characterized by short wait intervals (T.sub.s). Preferably, about 0.5-10 
seconds are required for the long wait period T.sub.w, followed by a 
standard CPMG pulse-echo train of several 100 ms duration, followed by a 
short wait time T.sub.s having about 10-100 ms duration. The short wait 
time T.sub.s is followed next by a CPMG train having about 1-100 echoes, 
which is followed by another short wait time, and so forth. In a specific 
example, 16 echoes can be used. Typically, for every long pulse train, 
between about 10 to 100 short echo trains are used. The sequence of short 
pulse trains is phase-cycled, i.e., alternate trains use phase-reversed 
refocusing pulses. All echoes from the short trains are co-added to yield 
several final short recovery data points. In a specific example using 16 
echoes, corresponding number of short recovery data points are generated. 
Results from a field test of the novel pulse sequence shown in FIG. 5 are 
illustrated in a specific example in FIG. 6. In this example, standard 
echo data and short-recovery data were acquired on separate passes, but at 
the same logging speed (5 ft/min) and over the same depth interval. In an 
alternative embodiment of the present invention both measurements can be 
performed simultaneously resulting in obvious advantages in terms of 
speeding up the measurement process. Track 1 in FIG. 6 presents the first 
three echoes from the standard echo train. The echo-to-echo spacing used 
in this example was 1.2 ms. The effect of thermal noise in this experiment 
is clearly seen from fact that later echoes are sometimes higher than 
earlier ones which would not be the case with noiseless data. 
Track 2 in FIG. 6 illustrates the first three echoes resulting from 
co-adding 50 short-recovery measurements in place of a single standard 
measurement. The echo-to-echo spacing in this experiment was 0.51 ms. The 
signal-to-noise ratio for the short-recovery measurements was improved by 
a factor of .sqroot.(50).apprxeq.7 over the standard log. Notably, the 
echo amplitudes in track 2 are depressed compared with those in track 1, 
because they are associated with fast T.sub.1 recovery. Tracks 3 and 4 
present two more logging passes over the same depth interval, and are 
equivalent to tracks 1 and 2, respectively. 
In accordance with a preferred embodiment of the present invention the 
signals obtained above are processed using a method illustrated in FIG. 7 
and summarized as follows: 
(A) The standard CPMG data obtained in block 10 is subjected in block 20 to 
the T.sub.2 inversion procedure outlined in U.S. Pat. No. 5,517,115, using 
a pre-specified model of principal T.sub.2 relaxation components. For 
example, the numerical sequence: 4, 8, 16, 32, 64, 128, 256, 512, 1024, 
2048 ms can be used in a specific embodiment. Block 50 in FIG. 7 indicates 
the T.sub.2 relaxation spectrum obtained on output of block 20. The sum of 
all detected modes obtained in block 60 is designated as the effective, or 
standard NMR porosity. The T.sub.2 relaxation spectrum in block 50 is used 
to differentiate capillary-bound water from movable fluids (water or 
hydrocarbons). 
(B) The accumulated fast-T.sub.s short echo trains in block 30 are 
subjected in block 40 to T.sub.2 inversion using another pre-specified set 
of relaxation components. In the specific embodiment illustrated in FIG. 
7, the sequence: 0.5, 1, 2, 4, 8, 2048 ms, of relaxation components was 
used. In this example, amplitudes found to relax with 4, 8 or 2048 ms are 
discarded as being incompletely polarized. On the other hand, the 
amplitudes associated with 0.5, 1 and 2 ms relaxation times represent the 
fast relaxation spectrum (block 50) and are next summed in block 70 to 
yield what is (tentatively) equated to "clay-bound porosity." 
As shown in FIG. 7, a complete T2 distribution can be assembled in block 50 
from concatenated responses in blocks 20 and 40. In the specific example 
shown, the T.sub.2 comprises the 0.5, 1, 2, 4, 8, 16, 32, 64, 128, 256, 
512, 1024 and 2048 ms relaxation modes. The sum of all these responses is 
taken in block 80 as a measure of the total formation porosity. In 
accepting this measure it is assumed that the rock is completely filled 
with liquids of hydrogen indices equal to the one of water. Tables 1 and 2 
provide a complete listing of the stationary and logging measurement 
parameters, respectively. 
The processing scheme described above with reference to FIG. 7 is an 
illustration of a preferred embodiment of the present invention, in which 
the porosity measurements are obtained on the basis of the T.sub.2 
relaxation spectrum approach. In an alternative embodiment of the present 
invention, equivalent processing can be done in the time domain. Briefly 
stated, in this alternative embodiment the "standard" NMR echo data is 
used to obtain a rough estimate of the time dependency of the early data 
points. Next, the high-signal-to-noise, high-quality data points from 
short echo trains are used to refine this estimate and to draw an accurate 
relaxation curve, interpolated back to time zero. The resulting composite 
relaxation curve can then be submitted to T.sub.2 inversion to produce a 
unified T.sub.2 distribution. 
The signal processing method of the present invention allows to determine, 
in a single measurement experiment, both the total porosity of the 
formation, and the clay bound porosity which parameters can next be used 
to obtain additional petrophysical parameters of interest. 
MODEL INTERPRETATION 
There exist many models for interpreting resistivity measurements in shaly 
sand formations. Most of these methods incorporate a model of parallel 
conduction paths for electrical current flowing through water with 
conductivity C.sub.w and through clay-bound water with conductivity Ccw. 
The C.sub.w parameter can be deduced from log responses in 
100%-water-filled formations or can be measured on produced water samples. 
Parameter Ccw is frequently modeled is a simple function of temperature 
using, for example, the formula 
EQU C.sub.cw =0.000216*(T.sub.f +504.4)*(T.sub.f -16.7) 
where Tf is the formation temperature. 
Further inputs required in the measurement interpretations are the water 
saturation associated with C.sub.w (S.sub.w) and the water saturation 
associated with C.sub.cw (S.sub.wb). See, for example the discussion in 
U.S. Pat. No. 5,557,200 assigned to the assignee of the present 
application, the content of which is expressly incorporated by reference 
for all purposes. Both parameters S.sub.w and S.sub.wb can be obtained 
from NMR measurements using the novel pulse sequence and the signal 
processing method of the present invention. 
In particular, as indicated above, the area under the T.sub.2 distribution 
gives the total volume available for fluid accumulation. The "fast" end of 
the T.sub.2 distribution is mostly associated with clay-bound water; the 
partial "fast T.sub.2 " area divided by the total area yields the 
parameter Swb. Similarly, the water saturation S.sub.w can be extracted 
from the "slow T.sub.2 " area of a T.sub.2 distribution. The proposed 
method of interpretation represents a significant improvement over the 
published prior art, in which saturation parameters had to be estimated 
from separate and often inaccurate measurements. 
TIME-DOMAIN ANALYSIS OF COMPOSITE ECHO TRAINS 
Another preferred embodiment of the present invention involves the use of 
composite echo trains in which the two separate processing branches of the 
algorithm illustrated in FIG. 7 are optimized individually. More 
specifically, consider pairs of echo trains as shown in FIGS. 8A and 8B: 
(1) FIG. 8A illustrates a regular set of echoes from a CPMG sequence with a 
wait time T.sub.w such that 
EQU T.sub.w .gtoreq.3.times.max(T.sub.1), 
where max (T.sub.1) denotes the highest expected T.sub.1 time of the 
fluid(s). 
(2) FIG. 8B illustrates a set of echoes, which is heavily overlapped to 
give a very high signal-to-noise ratio, obtained by stacking short echo 
trains with a wait time T.sub.PR such that 
EQU T.sub.PR &lt;&lt;3.times.max(T.sub.1). 
In accordance with a preferred embodiment of the method of the present 
invention, data obtained as shown in FIGS. 8A and 8B is combined such 
that: 
(1) the information about the long signal decays is retained; and 
(2) the SNR improvement from the stacked echo train is optimally utilized. 
In particular, the regular echo set can be expressed mathematically as 
EQU S.sub.R (t)=.intg.A(T.sub.2).sub.e.sup.-t/T.sbsp.2 
d(T.sub.2)+N(0,.sigma..sub.R) (2) 
where A(T.sub.2) is a T.sub.2 distribution, and N is a normal noise 
distribution with zero mean and a standard deviation .sigma..sub.R. The 
initial amplitude (time=0) corresponds to full polarization. 
The stacked echo set illustrated in FIG. 8B can be expressed mathematically 
as 
##EQU2## 
where A(T.sub.2) is the same T.sub.2 distribution, T.sub.PR is the partial 
recovery time, T.sub.1 (T.sub.2) is the T.sub.1 distribution associated 
with the T.sub.2 distribution, and NA is the number of averages used to 
obtain the data stack. Due to the short repeat time, the initial amplitude 
does not correspond to full magnetization. 
The stacked echo trains span an experiment time T.sub.s. Next, in 
accordance with the method of the present invention, the time-average over 
the data is formed as follows: 
##EQU3## 
Similarly, the time average A.sub.R for the regular data set is calculated 
over the same time interval T.sub.s using the expression: 
##EQU4## 
The difference D between amplitudes is expressed as 
EQU D=A.sub.R -A.sub.S, (6) 
and added to S.sub.S (t) to obtain: 
EQU S.sub.S *(t)=S.sub.S (t)+D, (7) 
as shown in FIG. 9. 
Finally, echo trains S.sub.R and S.sub.S * are combined in a composite 
train S.sub.C illustrated in FIG. 9B, according to the definition: 
##EQU5## 
The composite echo train S.sub.C has the high signal-to-noise ratio 
necessary to extract fast decaying components, and also retains 
information about the slowly decaying and slowly polarizing components. 
A composite T.sub.2 distribution can be calculated from the composite train 
S.sub.C by means of the inversion method disclosed in U.S. Pat. No. 
5,517,115 to Prammer. 
SHALE VOLUME AND NET-TO-GROSS CALCULATION 
Consider an earth formation consisting of laminations of shale and sand, as 
shown in FIG. 10. Note that the thickness of an individual sand or shale 
layer may range from approximately 1 mm to many meters and may not always 
be resolved by the aperture (range of integration) of the NMR instrument. 
As shown in the art, hydrocarbon fluids can only migrate to and accumulate 
in the sand layers. In the following description, the following 
definitions are used: 
.o slashed..sub.T --total porosity; integrated over the measuring device's 
vertical aperture 
.o slashed..sub.shale --shale porosity; integrated 
.o slashed..sub.sand --sand porosity. 
The net-to-gross N/G ratio is given by 
EQU N/G=.o slashed..sub.sand /.o slashed..sub.T. (9A) 
The ratio N/G is currently estimated by visual inspection of core samples 
or by logging with electrical "micro-imaging" devices that send electrical 
current through multiple electrodes into the formation. Another way to 
estimate N/G is from natural radioactivity, because shales tend to be more 
radioactive than sands. 
However, using the method of the present invention, the N/G ratio can be 
estimated directly as follows. A typical T.sub.2 spectrum is shown in FIG. 
11. For many clay minerals (illites, smectites), water occupying the shale 
porosity relaxes with NMR relaxation times less than about 3 ms. 
Therefore, the part of the T.sub.2 spectrum below approximately 3 ms can 
be identified as shale porosity .o slashed..sub.shale ; the rest is 
identified as sand porosity .o slashed..sub.sand. The capacity of a 
reservoir to hold hydrocarbons is proportional to the sand portion of the 
total porosity. Equation 9A above can be rewritten as: 
##EQU6## 
ESTIMATION OF CLAY AND SHALE VOLUME 
Reference is made to "Measurements of Clay-Bound Water and Total Porosity 
by Magnetic Resonance Logging" by Prammer et al., The Log Analyst, 
November/December 1996 pp. 61-69. As shown in this paper, an earth 
formation can consist of the following components: 
1) rock matrix (e.g. Quartz) 
2) clay minerals, 
3) water bound to clay minerals, 
4) capillary-bound fluid, 
5) unbound fluids. 
The component (3) corresponds to shale porosity .phi..sub.shale, whereas 
component (4) is the sand porosity .phi..sub.sand. 
By estimating .o slashed..sub.shale from the T.sub.2 spectrum, as discussed 
above, and by noting the dominant T.sub.2 relaxation time of the 
clay-bound water, an estimate of the clay mineral component type can be 
obtained from Table 4. 
Furthermore, having identified the clay type, by assuring an average water 
weight-to-dry clay weight ratio, an estimate of the dry clay weight can be 
obtained. Again, refer to Table 4, columns 2 and 5. 
ESTIMATION OF RESERVOIR PRESSURE 
In highly laminated reservoirs, as illustrated in a diagram form in FIG. 
10, the clay mineral type is fairly uniform. In this case, the relative 
water content and the average pore size in the shale is dominated by the 
pressure compacting a shale lamination. The more pressure, the smaller the 
pore sizes become, resulting in a decrease in T.sub.2. By following the 
trend in shale T.sub.2 's vertically, a pressure profile can be obtained, 
indicative of high or low pressure differentials. 
FIELD TEST RESULTS 
Field testing to verify the use of the method of the present invention was 
performed at Amoco's test site CTF-DM #21A in the Catoosa field in Rogers 
County, Oklahoma. The well was drilled in 1993 to a total depth of 1774 
ft. It is open-hole from casing at 162 ft to TD and contains fresh gel 
mud. Geologically, the well shows sequences of shales, shaly sandstones, 
limestones and dolomites. 
The difference between the MRIL effective porosity .PHI..sub.MRE and MRIL 
total porosity .PHI..sub.MRT is illustrated in FIG. 12. Shown is the log 
over a 100 ft shaly section as follows: Track 1: gamma ray in API units 
(0-150); tracks 2 and 3: porosities on a scale of 0 to 0.3. Density 
porosity is shown light solid, neutron porosity is dashed. There is almost 
no effective porosity and .PHI..sub.MRE (center track, bold solid) shows 
little development. On the other hand, .PHI..sub.MRT (right track, solid) 
agrees well with density porosity. All MRIL data was acquired in a single 
pass using the acquisition sequence shown in FIG. 5. 
The second log example (FIG. 13) illustrates the advantages of the 
lithology-independence of .PHI..sub.MRT, obtained in accordance with the 
present invention. In a water-filled or oil-filled formation of unknown 
lithology, the matrix density can be estimated as follows: Using the total 
MRIL porosity (in decimal units; .PHI..sub.MRT is shown in track 3 as bold 
line) as the porosity term in the bulk density response, 
EQU .rho..sub.b =.phi..sub.MRT .rho..sub.f1 +(1-.phi..sub.MRT).rho..sub.ma,(10) 
and setting .rho..sub.f1 =1.0 g/cm.sup.3 for water, an apparent matrix 
density .rho..sub.app can be computed: 
##EQU7## 
The result of this calculation is shown in FIG. 13. At X623 ft, an abrupt 
change in lithology exists from an apparent matrix density of .about.2.68 
g/cm.sup.3 to .about.2.85 g/cm.sup.3. From core analysis, it is known that 
the sandstone above X623 consists mostly of quartz (2.657 g/cm.sup.3) and 
that the limestone/dolomite mix below X623 is mostly dolomite (2.85 
g/cm.sup.3). Track 3 shows density porosites for .rho.=2.65 g/cm.sup.3 
(dashed line), and for .rho.=2.85 g/cm.sup.3 (solid line), to be in 
excellent agreement with the MRIL porosity .PHI..sub.MRT (bold solid 
line). In mixed or unknown and gas-free formations, the NMR measurement 
can provide a stand-alone porosity answer that is independent of core 
analysis, and/or crossplot techniques that rely on different tool 
responses. 
FIG. 14 illustrates the behavior of the very fast relaxation components 
computed in accordance with the present invention in various lithologies. 
Track 1 is the spectral gamma ray in API units 1-150, and track 3 contains 
porosites on a scale of 0 to 0.3. Density porosity calibrated for a 
sandstone matrix (.rho.=2.65 g/cm.sup.3) is shown dashed; effective MRIL 
porosity is light solid; total MRIL porosity is shown in bold solid. 
Evidently, the density log is affected by hole rugosity in several places, 
whereas the MRIL is not (for example, at X295, X322, X334, X402, X431 and 
X52). In track 2, the difference .PHI..sub.MRT -.PHI..sub.MRE is broken 
down into the fastest three T.sub.2 relaxation components. The individual 
bands in track 2 indicate the individual intensities of the relaxation 
modes: 2 ms (left, black), 1 ms (center, white) and 0.5 ms (right, black). 
The sandstone sections (X340-X390 and X418-X595) show good agreement 
between the density log and .PHI..sub.MRT. In the very clean section from 
X555 to X595, no clay-bound signal is detected (track 2), and full 
agreement exists between density porosity, .PHI..sub.MRE and 
.PHI..sub.MRT. In the shaly sections (high gamma ray readings) a 
characteristic clay-bound water signal develops with a T.sub.2 of 1-2 ms. 
Density porosity and .PHI..sub.MRT continue to agree, while effective 
porosity is considerably reduced and at places vanishes. Differences 
between density porosity and total MRIL porosity, where MRIL porosity is 
higher than density porosity, are indicative of lithologies with matrix 
densities greater than 2.65 g/cm.sup.3. This is the case in the top shale 
(above X281), where recomputing the density response yields an apparent 
matrix density close to 2.80 g/cm.sup.3. The clay-bound signal has a clear 
signature of 1-2 ms. Below the shale section, in the interval X281-X330, 
layers of limestone and shale are interspersed. For example, the limestone 
at X310 is identified by high effective porosity and an undercall in 
sandstone density porosity. The 1-2 ms T.sub.2 signature is missing in 
this section, replaced by a very fast decay below 1 ms, which could be due 
to microporosity in the limestone or due to interbedded, dense shale 
thinner than the logging tools' resolution limits. 
OTHER APPLICATIONS 
The novel pulse sequence and processing method was described above with 
reference to NMR logging. However, the sequence and method are equally 
applicable in various other situations, including NMR measurements of 
porous materials. For example, U.S. Pat. No. 5,672,968, one of the 
co-inventors of which is the inventor of the present application, 
describes analysis of cement-based materials using NMR measurements. The 
content of this application is herewith expressly incorporated for all 
purposes. 
As shown in the U.S. Pat. No. 5,672,968, concrete which is used for 
construction can be analyzed to determine its structural properties, such 
as strength, potential for shrinkage and others in the final cured 
concrete. As the concrete is a mixture of various materials and includes a 
water portion, the method of the present invention can be used to 
determine various attributes of the materials, such as the curing 
properties of the various cement mixtures. 
It should be clear to those skilled in the art that the pulse sequence and 
the method of the present invention can also be used in measuring 
properties of samples of porous materials in a laboratory setting, as well 
as in situ logging-type including logging/measuring while drilling 
(LWD/MWD) measurements, as described in detail above. 
NOMENCLATURE 
.PHI..sub.MRE magnetic resonance effective porosity 
.PHI..sub.MRT magnetic resonance total porosity 
.rho..sub.b bulk density 
.rho..sub.app apparent matrix density 
.rho..sub.f1 fluid density 
.rho..sub.ma matrix density 
N.sub.e number of echoes in a single echo train 
T.sub.1 magnetic resonance longitudinal relaxation time 
T.sub.2 magnetic resonance transversal relaxation time 
T.sub.e echo-to-echo sampling time 
T.sub.pr partial recovery time 
T.sub.w wait time 
Although the present invention has been described in connection with a 
preferred embodiment, it is not intended to be limited to the specific 
form set forth herein, but is intended to cover such modifications, 
alternatives, and equivalents as can be reasonably included within the 
spirit and scope of the invention as defined by the following claims. 
TABLE 1 
______________________________________ 
STATIONARY MEASUREMENTS 
Echo 
Data set 
Depth Spacings 
Recovery Times 
Comments 
______________________________________ 
S1120SF 1120 1.2 + 0.51 
3000 ms standard 
S1120TRX 
1120 0.51 3000 + 10 + 20 + 50 
special 
fast recovery 
S1122TRX 
1122 1.2 + 0.51 
3000 standard 
S1122XXX 
1122 0.51 3000 + 10 + 20 + 50 
special 
fast recovery 
S11124SF 
1124 1.2 + 0.51 
3000 standard 
S1124TRX 
1124 0.51 3000 + 10 + 20 + 50 
special 
fast recovery 
S1131SF 1131 1.2 + 0.51 
3000 standard 
S1131TRX 
1131 0.51 3000 + 10 + 20 + 50 
special 
fast recovery 
S1150SF 1150 1.2 + 0.51 
3000 standard 
S1150TRX 
1150 0.51 3000 + 10 + 20 + 50 
special 
fast recovery 
S1157SF 1157 1.2 + 0.51 
3000 standard 
S1157TRX 
1157 0.51 3000 + 10 + 20 + 50 
special 
fast 
______________________________________ 
recovery 
TABLE 2 
______________________________________ 
LOGGING MEASUREMENTS 
Echo 
Data set 
Spacing Recovery Times 
Comments 
______________________________________ 
T1MAGM 1.2 ms T.sub.w = 3000 ms 
standard log 
T1MAGR 1.2 T.sub.w = 3000 
same as T1MAGM 
T2MAGM 0.6 T.sub.w = 3000 
standard log 
T2MAGR 0.6 T.sub.w = 3000 
same as T1MAGM 
T3MAGM 0.51 T.sub.w = 3000 
standard log 
T3MAGR 0.51 T.sub.w = 3000 
same as T1MAGM 
T9M 0.51 T.sub.w = 3000, T.sub.3 = 10 
51 bursts of 16 echoes each 
T9R 0.51 T.sub.w = 3000, T.sub.3 = 10 
same as T9M 
T10M 0.51 T.sub.w = 3000, T.sub.3 = 50 
51 bursts of 16 echoes each 
T10R 0.51 T.sub.w = 3000, T.sub.3 = 50 
same as T10M 
T20M 0.51 T.sub.w = 3000, T.sub.3 = 50 
51 bursts of 16 echoes each 
T21M 0.51 T.sub.w = 3000, T.sub.3 = 100 
51 bursts of 16 echoes each 
______________________________________ 
TABLE 3 
______________________________________ 
CLAY TYPES AND PROPERTIES OF SAMPLES 
Total CEC 
Surface Area 
(meq/ 
Clay Types 
Clay ID 
(m.sup.2 /g) 
100 g) 
Remarks 
______________________________________ 
mont- SWy-2 760 (theoretical.sup.a) 
76b 
morillonite 
616 (measured.sup.a) 
illite 1Mt-1 93 (measured.sup.a) 
15.sup.c 
&lt;10% smectite 
layers 
kaolinite 
KGa-1b 18 (measured.sup.a) 
2.sup.b 
chlorite 
CCa-2 40 (estimated.sup.d) 
n/a sample contains 
large amount of iron 
______________________________________ 
All samples were obtained from the Clay Mineral Society, Source Clay 
Minerals Repository, Univ. of Missouri, Columbia, MO. 
.sup.a) Unpublished data, courtesy of D. Mardon (eGME adsorption 
measurements). 
.sup.b) van Olphen and Fripiat, 1979..sup.12 
.sup.c) Hower and Mowatt, 1966..sup.13 
.sup.d) Ellis, 1987..sup.5 
TABLE 4 
__________________________________________________________________________ 
RESULTS OF LABORATORY T.sub.2 MEASUREMENTS 
T.sub.2 of clay- 
Apparent .rho..sub.2 
Water Weight 
NMR Visibility 
bound water at 
surface 
per dry clay 
at Te = 0.5 ms 
Te - 0.5 ms 
relaxivity 
Clay ID 
weight (%) 
(ms) (ms) (.mu.m/s) 
Remarks 
__________________________________________________________________________ 
SWy-2 
7.0 20 -- -- T.sub.2 &lt; 0.2 ms 
18.9 90 0.3 1 
31.1 100 0.5 1 
54.4 100 1 0.9 T.sub.1 = 1.5 ms 
1Mt-1 
8.8 90 1 0.9 
15.8 100 2 0.8 
KGa-1b 
11.7 100 8 0.8 
17.4 100 12 0.8 
20.0 100 16 0.7 T.sub.1 = 30 ms 
CCa-2 
7.5 100 5 0.4 .rho..sub.2 may be too 
low due to over 
estimated surface 
area 
__________________________________________________________________________ 
Measurements were made at 1 MHz and at 25.degree. C. on the clay samples 
listed in Table 1. Samples were saturated with different amounts of brine 
pressed at 2500 psi and sealed. Water weight was determined from weight 
loss by overnight drying in a vacuum chamber at 103.degree. C. NMR 
visibility is the ratio of calibrated NMR amplitude (in ml of water) per 
ml of water content determined from weight loss. Apparent transversal 
surface relaxivities .rho..sub.2 were calculated from specific surface 
areas # (Table 1), the waterto-dry weight ratios and from T.sub.2 's.