This information is CONFIDENTIAL and must not be copied in whole or in any part, and should be filed accordingly by the addressee. It must not be shown to or discussed with anyone outside the SCHLUMBERGER organization. CMR Tool Manual Volume 1 Training Manual MH606601 Edited by Chris Morriss Houston Product Center, November 1995 The following people contributed to this manual: Bob Freedman, Bob Kleinberg, Mark Moller, Bill Vandermeer and other members of the CMR team at HPC.
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CMR Tool ManualVolume 1
Training ManualMH606601
Edited by
Chris Morriss
Houston Product Center,
November 1995
The following people contributed to this manual: Bob
Freedman, Bob Kleinberg, Mark Moller, Bill Vandermeer and
This information is CONFIDENTIAL and must not be copied in whole or in any part, and should be filed accordingly by the addressee.It must not be shown to or discussed with anyone outside the SCHLUMBERGER organization.
About this manual
This training manual is the 1st volume of the 4 volume CMR Tool Manual. Volume 2 is theWellsite Reference Manual (WRM). Volumes 3 and 4 are the Maintenance Manuals. Thecontents of each volume are shown in Table 1. To prevent needless duplication, there is verylittle overlap between the 4 volumes
The primary goals of this manual are to:
• explain the fundamentals of nuclear magnetic resonance,
• provide a general description of CMR hardware,
• establish CMR logging procedures,
• describe interpretation principles and applications.
This manual does not contain detailed operating instructions, detailed circuit diagrams ortroubleshooting procedures -- this information is available in other volumes.
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This information is CONFIDENTIAL and must not be copied in whole or in any part, and should be filed accordingly by the addressee.It must not be shown to or discussed with anyone outside the SCHLUMBERGER organization.
4. CMR Data Description and Processing Overview....................................................................38
4.4 Data redundancy and data compression..........................................................................404.5 Maximum likelihood estimation...........................................................................................42
6.4 Presentations and Formats ...............................................................................................63
6.4.1 Depth logging - Four tracks with T2-distribution...................................................63
6.4.2 Depth logging - quality control log ........................................................................ 64
6.4.3 Station Logging -- single-wait time station log display.........................................65
6.4.4 Station Logging -- multiwait time station log display.............................................666.5 Log quality control.............................................................................................................67
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1. Introduction
1.1 Hardware characteristics
The CMR Combinable Magnetic Resonance tool makes nuclear magnetic resonance (NMR)measurements that respond to the hydrogen nuclei contained in pore fluids. These measurementscontain information relating to both pore volume and pore size.
CMR hardware has been designed to overcome the limitations associated with the previous-generation NML Nuclear Magnetic Log tool. It is no longer necessary to dope the borehole withmagnetite and the CMR tool is combinable, top and bottom, with other logging tools. By usingpermanent magnets in the CMR sonde, the tool does not have to rely on the earth's magnetic fieldto make the NMR measurement. This eliminates many of the environmental corrections associatedwith the NML tool.
The CMR is a skid tool that has high vertical resolution. It must be run eccentered using abowspring, in-line eccentralizer, or powered caliper. The sonde outside diameter (OD) is 5.3 in.
Total OD with the bowspring is 6.6 in. Recommended minimum hole sizes are as follows:
With bowspring (EME-F) 7.5 in.
Withpoweredcaliper (e.g., PCD or MLT) 6.5 in.
With in-line eccentralizer (ILE-F) 6.25 in.
The CMR tool works in large boreholes, provided the bowspring or caliper device has sufficientforce to eccenter the tool. Finally, there are no mud conductivity limitations; the CMR works in bothconductive and resistive muds.
The CMR tool consists of a sonde and cartridge. A tool sketch is shown in Figure 1.1 and toolspecifications are listed in Appendix A. It is a compact tool that has a makeup length of 14.2 ftand total weight of 327 lb. Dimensions of the individual components are as follows:
Component Length (ft) Weight (lb) OD (in.)
Sonde 4.6 165 5.3
Cartridge 9.6 127 3.625
Bowspring N/A 35 6.6
A field joint is provided between the sonde and cartridge for ease of handling. The sonde and
cartridge must be operated as a set once they have been calibrated together, because sondecharacterization and master calibration data are stored in an EEPROM in the cartridge.
The CMR has through wiring to allow tools to run below it. It is a DTS compatible tool that mayalso be combined with CTS tools provided a DTA is included in the tool string. The CTS toolsmust be run below the CMR tool unless they have been modified with FTB through-wiring.
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1.2 Measurement overview
The NMR measurement is made by manipulating the hydrogen nuclei contained in fluid molecules;either water or hydrocarbon. The magnetic moment and angular momentum of hydrogen nuclei
cause them to behave like bar magnet and gyroscope combinations. The nuclei tend to align inthe magnetic fields produced by permanent magnets and radio frequency (rf) pulses. However,the alignment process is resisted by the angular momentum of the nuclei, which results in aprecessional motion analogous to the wobbling motion of a toy top spinning in the earth’s gravityfield.
Figure 1.2 shows an idealized CMR raw measurement. The received signal consists of asequence of spin-echo amplitudes that are recorded over a period of time typically in the range of0.2 to 2.0 sec. The spin-echo signal originates from hydrogen nuclei that are precessing about amagnetic field produced by magnets in the sonde. Because the hydrogen nuclei have a magneticmoment, they can induce a signal in the CMR antenna.
A
time
pm
spin echo amplitudeslitude
Figure 1.2. Idealized NMR measurement.
The spin echoes are generated by transmitting rf pulses from the same antenna used to detectthe spin echoes. Each transmitter pulse produces a spin echo, and the amplitude of the spin echois recorded by the tool. The collection of spin-echo amplitudes are referred to as a CPMG (afterCarr, Purcell, Meiboom and Gill).
CPMGs are always collected in pairs. The second set is acquired with the phase of thetransmitter pulse changed to give spin echoes of negative amplitude. The second CPMG is thensubtracted from the first CPMG to produce a “phase-alternated pair” (PAP). This procedurepreserves the signal and eliminates low-frequency electronic offsets. Further details, including afull description of the NMR phenomena, can be found in Section 2.
Two pieces of information are extracted from the spin-echo sequence: an initial signal amplitudeand the rate at which the signal amplitude dies away.
• The initial signal amplitude is proportional to the number of hydrogen nuclei in themeasurement volume that are associated with the pore fluids. Hence, the initial signalamplitude can be calibrated to give a porosity, φCMR. Because the NMR measurementresponds only to pore fluids (i.e., the hydrogen nuclei in the rock matrix do not contribute to
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the signal amplitude), φCMR is a direct measure of pore volume and is therefore obtainedwithout specifying minerology or matrix properties.
• The signal amplitude decays (i.e., dies away) exponentially with time in a manner similar tothe more familiar thermal decay time measurement. The time constant of the NMR signal decay
is called the transverse relaxation time, or more simply T2.
T2 (msec)
0.1 1.0 10.0 100.0 1000.0
T2,log
= 100 msec
φCMR
= 9.9 p.u.
Distribution
Figure 1.3. T2-distribution obtained from the spin-echo sequence shown in Figure 1.2.
In water-saturated rocks, T2 has been shown to be proportional to pore size. That is, smallpores have short T2 values, and large pores have long T2 values. At any depth in thewellbore, the rock sample probed by the CMR tool will have a distribution of pore sizes.Hence, the NMR signal decays not with a single value of T2, but rather with a distribution of
T2 values that corresponds to the distribution of pore sizes in the sample. For example,Figure 1.3 shows the T2-distribution obtained from the spin-echo sequence displayed inFigure 1.2.
The area under the T2-distribution curve is equal to the measured porosity. Hence the T2-distribution plot completely summarizes the results of the NMR measurement. It is the task of theCMR hardware and software to measure the T2-distribution of the formation at each sampleinterval in the wellbore. Details of the signal processing algorithm that computes the T2-distribution from the spin-echo amplitudes are contained in the CMR Training Manual.
Porosity and pore size information from an NMR measurement may be used to estimate bothproducible porosity and permeability.
The NMR estimate of producible porosity is referred to as the free-fluid porosity, φFF. The estimateis based on an expectation that the producible fluids reside in the large pores, whereas thebound fluids reside in the smaller pores. Hence, a T2 cutoff (i.e., a pore size cutoff) may beapplied to the T2-distribution that divides the NMR porosity into free-fluid and bound-fluidporosity (φBF), as shown in Figure 1.4.
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T2 (msec)
0.1 1.0 10.0 100.0 1000.0
small pores contain large pores contain
free fluid - φFF
Distr
ibution
bound fluid - φBF
Figure 1.4. Bound and free-fluid porosity is computed using a T2 cutoff.
An attractive feature of NMR is that the borehole measurement can be duplicated in the lab oncore samples. The correlations between NMR measurements and petrophysical properties arederived from lab measurements. For example, measurements on water-saturated core sampleshave shown that T2 cutoff values of 33 and 100 msec are appropriate for sandstones andcarbonates, respectively. These cutoff values resulted in free-fluid porosities that best matchedthe volumes of water produced from the core samples by centrifuging at 100 psi air-brine capillarypressure. Typical results for sandstone core samples are shown in Figure 1.5.
Well A
Well B
Well C
φFF
centrifugeφ
20
15
10
5
00 5 10 15 20
Figure 1.5. Comparison of NMR free-fluid porosity and volume of water centrifuged from sandstone core samples.
The NMR estimate of permeability is similarly based on an expectation that permeability willincrease with both porosity and pore size. NMR and permeability measurements on water-saturated sandstone samples have shown that permeability can be estimated by
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where KNMR is the permeability estimate, φCMR is the porosity and T2,log is the logarithmic mean T2 ofthe distribution. The logarithmic mean relaxation time of the distribution is analogous to the “centerof mass” of a body in classical mechanics (i.e., it is the T2 value at the “center of mass” of thedistribution).
The premultiplier, a, in the above Eq. 1.1 has a default value of 4. Better results can be obtainedif the premultiplier is adjusted on a per reservoir basis. A comparison of KNMR with measured brinepermeability for sandstone samples from two wells is shown in Figure 1.6.
0.01
0.01
100.00
100.00
Kbrine
Well A, a=2.8
KNMR
Well B, a=3.4
KNMR = aφNMR T2, log
4 2
Figure 1.6. Comparison of NMR permeability and measured brine permeability for sandstone samples from two wells.
The CMR tool is run in station logging mode or continuous depth logging mode. Values of φCMR,
φFF, φBF, KNMR and T2-distributions are output in both modes. Station logging is employed whengreater precision is required for the log outputs.
1.3 CMR sonde
Two magnets are located in the sonde together with an antenna and the sonde electronics. Across section of the sonde is shown in Figure 1.7. Note that the antenna section protrudes fromthe sonde body by 1 in. to minimize skid standoff in rugose hole.
The sonde electronics contain the circuitry necessary to transmit an rf magnetic field and receivethe spin-echo signal from the formation fluids. Both the transmit and receive functions use thesame antenna, which is operated in half duplex mode. The received signal (which is about 50nanovolts per porosity unit) is amplified in the sonde by a factor of about 2000 before passingthrough the sonde/cartridge head to the cartridge receiver circuits.
The antenna used to radiate the formation is housed in the antenna cradle assembly. Theassembly is an oil-filled pressure balanced environment. A small metal bellows is utilized tocompensate for changes in pressure and a replaceable plastic wear-plate covers the antenna.The antenna is essentially a half coaxial cable whose conducting surfaces are copper. Ferritematerial is placed between the inner and outer conductors to enhance the sensitivity of theantenna.
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NN
SS
CMRS-A
Replaceable Antenna Cover1.0"
Skid5.30"
4.625"
Antenna
Samarium CobaltMagnets
Channels forThru-Wires
Sonde Electronics
Figure 1.7. CMR sonde cross section.
Samarium cobalt magnets are used to produce the static magnetic field required for the NMRmeasurement. Samarium cobalt is the preferred material because it has high field strength, a highresistance to demagnetization and a Curie point of 820° C (the Curie point is the temperature atwhich permanent magnetism is destroyed). The magnets are potted inside metal cases withepoxy. The metal cases provide protection; the magnet material is brittle and will shatter onimpact.
The sonde body is made of titanium to reduce the overall weight of the tool and to provide a non-magnetic mounting for the magnets. Plows are located at both the uphole and downhole end of
the sonde to protect the magnets and antenna assembly as the tool traverses the borehole andsurface casing. They also remove soft mudcake. The plows and magnet casings are coated withtungsten carbide to provide wear resistance.
1.4 CMR cartridge
The CMR electronics cartridge contains the electronic circuits necessary to acquire and processthe spin-echo signals before being sent uphole on the telemetry channel. The cartridge containspower supplies, control circuits, telemetry interface, microprocessors, calibration circuits anddiagnostic circuits.
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2. Measurement Principles
2.1 Introduction to NMR
Nuclear magnetic resonance (NMR) refers to a physical principle -- the response of nuclei to amagnetic field. Many nuclei have a magnetic moment and therefore behave like bar magnets.They also have spin (i.e., angular momentum) that makes them behave in some respects likegyroscopes. These spinning magnetic nuclei can interact with external magnetic fields andproduce measurable signals.
There are three sources of magnetic fields during an NMR measurement:
• static magnetic fields from permanent magnets
• oscillating magnetic fields associated with radio frequency (rf) pulses
• local magnetic field fluctuations from unpaired electrons (such as those found in iron andchromium ions) and from neighboring nuclei.
NMR measurement can be made on any nuclei that have an odd number of protons and/orneutrons (e.g., H1, C13, Na23, F19 and P31). For most of these nuclei the signal is too small to bedetected with a borehole logging tool. However, hydrogen has a relatively large magneticmoment and is abundant in both water and hydrocarbon molecules found in pore fluids. By tuningthe CMR tool to the resonant frequency of hydrogen, the signal is maximized and is thereforemeasurable.
The measured quantities are signal amplitude and relaxation rates. The signal amplitude iscalibrated to give porosity. Two principal relaxation times are associated with NMRmeasurements; the longitudinal relaxation time (T1) and the transverse relaxation time (T2). Bothare described in subsequent sections. The relaxation times, either T1 or T2, are interpreted togive pore size and/or pore fluid properties.
Both T1 and T2 measurements are made on core samples using lab NMR apparatus. T1measurements usually take several minutes and are therefore not practical for a moving loggingtool. For this reason, fast T2 measurements are preferred for the CMR tool.
The CMR measurement consists of a sequence of steps: alignment, tipping, precession,dephasing, refocussing, transverse relaxation and then realignment. Each step is describedbelow. Only after all steps have been completed can the measurement be repeated; usuallyseveral seconds are required. Thus, the measurement is cyclic rather than continuous.
Terminology
For present purposes, the words "proton," "nucleus," "moment," and "spin" are all synonymsand are used interchangeably in this document. Spin is the property of nuclei or electrons that is
due to their angular momentum and results in a magnetic moment. Therefore, the term “spin” is notstrictly a synonym but is often used interchangeably by NMR practitioners.
2.1.1 Alignment: longitudinal relaxation (T1)
The first step in performing an NMR measurement is to align the magnetic moments in a staticmagnetic field. The static field is called B0 (“B zero”). Permanent magnets are well suited for
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creating a static magnetic field, although in principle electromagnets could be used. For the CMRpermanent magnets, B0 is approximately 540 Gauss, about 1000 times stronger than themagnetic field of the earth. Therefore, protons will preferentially align in the tool’s magnetic field.After the protons are aligned in the magnetic field they are said to be polarized.
The static magnetic field exerts a twisting force (i.e., torque) that tries to align the spin axis withthe magnetic field. However, when a torque is applied to a spinning object its axis movesperpendicular to the torque in a motion called precession. This motion is analogous to the motionof a toy top spinning in the earth’s gravity field, as shown in Figure 2.1.
Precessional motion
Earths gravitational field
Magnetic field, Bo
SpinningmotionProton Toy top
Spinningmotion
Figure 2.1. Hydrogen nuclei (protons) behave like spinning bar magnets. They precess about a magnetic field similarly to a
toy top spinning in the earth’s gravity field.
The precessional motion would continue indefinitely if it were not for interactions with the magneticfields of other nuclei or unpaired electrons. These interactions result in the proton losing energyand rotate it into alignment by a process that is referred to as relaxation. Again, this is similar to atoy top that gradually loses energy because of friction and eventually topples.
Analogously, polarization does not occur immediately but rather grows with a time constant calledthe longitudinal relaxation time, T1. That is,
nuclear polarization = −( )1 e-t/T1 , (2.1)
where t is the time that the nuclei are exposed to the B0 field. A typical T1 relaxation curve isshown in Figure 2.2.
For the case of hydrogen nuclei in pore fluids, polarization takes up to several seconds and canbe done while the logging tool is moving, but the nuclei must be exposed to B0 for the entiremeasurement cycle. To accomplish this, the permanent magnets on the CMR sonde areelongated in the direction of tool motion.
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0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
N u c l e a r P o l a r i z a t i o n
Bo exposure time (sec)
Nuclei Polarize Slowlyin a Magnetic Field
941110-03
T1 = 0.2 sec
1 - exp(-t/T1)
Figure 2.2. T1 relaxation curve showing the degree of alignment (polarization)with exposure time (t).
Polarization results in a net magnetization that is the vector summation of the individual magneticmoments.
2.1.2 Tipping
Once the protons are polarized they are in equilibrium (i.e., they are in a low energy state and
remain aligned unless disturbed). The second step in the measurement cycle is to tip the protonsinto the transverse plane. This is accomplished by applying an oscillating magnetic fieldperpendicular to the direction of B0 using an antenna. The oscillating magnetic field is called B1.
For effective tipping, the frequency of B1 must be
f0 = γ
π 2
B0. (2.2)
f0 is the frequency in hertz, γ is the gyromagnetic ratio of the nucleus, and B0 is the static magneticfield. γ is different for each type of nucleus. f0 is called the resonance frequency or Larmorfrequency.
For hydrogen nuclei, γ/2π = 4258 Hz/Gauss. For the CMR tool, B0 is about 540 Gauss.Therefore, B1 must have a frequency just below 2.3 MHz. It is this frequency selectivity thatmakes NMR a resonance technique.
The angle through which the protons are tipped is given by
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θ = 360 γ
π 4
B1 tP (2.3)
where θ is the tip angle in degrees, B1 is the strength of the linearly polarized oscillating field in
Gauss, and tP is the length of time the B1 field is left on. If we desire a tip angle of 90°, and if B1 is8 Gauss, then tP is 15 microseconds. (Note: Eq. 2.3 differs by a factor of 2 from other equationsfound in many NMR texts, which assume B1 is circularly polarized).
2.1.3 Precession and dephasing
After the protons (spins) are tipped 90° from the direction of B0, they immediately begin toprecess in the plane perpendicular to B0. The precession frequency is equal to the Larmorfrequency, given by Eq. 2.2.
y’
x’
z’
M
B0
Figure 2.3. Immediately after the 90 ° pulse, the spins precess in unison and the net magnetization, M , is preserved.
At first the spins precess in unison (see Figure 2.3). While doing so they generate a small
magnetic field, at frequency f0, that can be detected by the CMR antenna. Gradually, the protonslose synchronization. This is because the magnets never provide a uniform B0 field that is thesame everywhere in the formation. Since the field is slightly different at point A in the formationthan it is at point B, the protons at points A and B will precess at correspondingly differentfrequencies, according to Eq. 2.2 and as shown in Figure 2.4.
y’
x’
z’
mm
A
B
Figure 2.4. Dephasing of the spins result in a reduction of the net magnetization.
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a b
c d
e f
Figure 2.5. The process of dephasing and refocussing can be compared to runners on a circular track.
The 90 ° pulse starts the race, and the runners move out together. However, their speeds vary slightly, and they slowly disperse. Eventually they are distributed uniformly around the track, as shown in (c). The 180 ° pulse is analogous to a signal from the referee that reverses the running direction (d). The fastest runners have the greatest distance to run back to the starting line. If all runners return at the same speed with which they left, they will all return to the starting line at the same time as shown in (f).
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The situation may be compared to runners on a circular track as shown in Figure 2.5. The 90°pulse starts the race, and the runners move out together. However, the speeds vary slightly,and the runners slowly disperse. Eventually they are distributed uniformly around the track, asshown in Figure 2.5 c.
When the spin directions are uniformly distributed in the transverse plane, the net magneticmoment produced by them sums to zero, and no further signal is detected by the antenna. Thesignal decay is called a "free induction decay" (FID), and it is usually exponential. The decay timeconstant is called “T2 star” (T2*). The * indicates that the decay is not a property of theformation, but of the imperfection of the measurement apparatus. An example of an FID is shownin Figure 2.9. For the CMR measurement, T2* is comparable to tP, the length of the tipping pulse(i.e., a few tens of microseconds).
After a B1 pulse, which may put hundreds of volts on the transmitting antenna, the sensitivereceiver electronics are saturated. Therefore, the free induction decay is usually lost in the deadtime of the measurement electronics. If this were the end of the story, there would be no point inattempting NMR measurements.
2.1.4 Refocussing: spin echoes
The dephasing caused by the inhomogeneity of B0 is reversible. Returning to the runner analogyshown in Figure 2.5, imagine that after the runners are dispersed around the track the refereegives a signal causing the runners to turn around and run in the opposite direction. The fastestrunners have the greatest distance to run back toward the starting line. If all runners return at thesame speed with which they left, they will all return to the starting line at the same time as shownin Figure 2.5 f.
In a similar manner, the magnetic moments can be rephased when a 180° pulse is applied at theresonance frequency f0. The 180° pulse is approximately twice as long as the 90° pulse. It doesnot reverse the direction of precession, but it does change the phase of each spin so that those
that have precessed the farthest have the farthest to return. Once the spins are back in phase,they are able to generate a signal in the antenna. That signal is called a "spin echo." The effectsof these pulses on the magnetization vector are shown in Figure 2.6, Figure 2.7 and Figure 2.8.
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y’
x’
z’
m
m
A
B
’
’
Figure 2.7. Spins begin to rephase.
y’
x’
z’
M
Figure 2.8. Spins completely rephase. Net magnetization is restored and a spin-echo signal is generated in the antenna.
Of course, the spin echo quickly disappears again. However, the technique of applying 180°pulses can be repeated over and over again. The usual procedure is to apply 180° pulses in anevenly spaced train, as close together as possible (as shown in Figure 2.9). An echo forms
midway between each pair of 180° pulses.
FID
Transmitter
Receiver
Spin Echo
TE
Spin Echo
TE
90 180 1800 00
Figure 2.9. Transmitter pulses and received spin-echo signal.
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The entire pulse sequence, a 90° pulse followed by a long series of 180° pulses, is called a"CPMG" after its inventors, Carr, Purcell, Meiboom, and Gill. The echo spacing is abbreviatedTE. For the CMR tool, the minimum TE value is 0.32 msec. Another commonly used quantity isTCP (Carr-Purcell time), which is equal to TE/2.
TETE TETETE TE
90o
180o
180o
180o
180o
180o
180o
0.2 milliseconds
Figure 2.10. CPMG spin-echo sequence from a CMR measurement.
The first six echoes of a CMR-CPMG sequence are shown in Figure 2.10. There is electronicfeed through in the first 0.2 msec. The first echo is smaller than the rest because of theinhomogeneous fields of the tool.
The CPMG pulse sequence negates the dephasing caused by the imperfection of the B0 field.However, dephasing can also be caused by molecular processes. Unlike the dephasing causedby magnet inhomogeneities, which is reversible, the dephasing resulting from molecularprocesses is irreversible.
Once irreversible dephasing occurs, the protons can no longer be completely refocussed usingthe spin-echo technique (applying 180° pulses). Thus, irreversible dephasing is monitored b ymeasuring the decaying amplitude of the spin echoes in the CPMG echo train, as shown in Figure2.11.
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Time (t)
T r a n s
v e r s e
M a g n e
t i z a t i o n
1st echo 2nd echo 3rd echo
M0
M(t) = M0 e-t/T2
Figure 2.11. Irreversible dephasing results in decreasing spin-echo amplitudes.
The amplitude of the transverse magnetization , M(t) is given by
M(t) M t T20e= − , (2.4)
where M0 is the transverse magnetization at time zero, t is time and T2 is the transverse relaxationtime constant.
.
...........
0.1 sec
A m p l i t u d e
Figure 2.12. CPMG spin-echo amplitudes measure d on a rock sample.
An example T2 decay for a rock sample is shown in Figure 2.12. Each data point is the amplitude
of a spin echo.
2.1.6 Realignment
Whenever magnetization is in phase in the transverse plane, a signal (free induction decay orspin echo) can be generated in the receiver antenna. After a time equal to several times T2, thespins completely lose phase coherence and no further refocussing is possible. The 180° pulses
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also prevent T1 processes; polarization does not occur during a CPMG. Hence, the spins arecompletely randomized at the end of the CPMG sequence.
It is not possible to start the next CPMG sequence until the spins have returned to the B0
direction, resulting in a net magnetization. Therefore, a waiting time is necessary between the end
of one CPMG and the start of the next. Once realignment has occurred, the measurement cyclecan start again.
2.2 NMR relaxation mechanisms
There are three independent relaxation mechanisms for pore fluids:
• bulk fluid mechanism
• surface relaxation mechanism
• molecular diffusion mechanism.
Each mechanism is described in a following section.
The relative importance of each mechanism depends upon the fluid type in the pores (e.g., water,oil or gas), the size of the pores, and the wettability of the rock surface. For a wide range ofconditions, the surface relaxation mechanism is dominant.
The surface and bulk relaxation mechanisms are due to magnetic interactions between the protonspins and neighboring spins. The neighboring spins can be
• other protons that are in the same molecule or in a nearby molecule
• other nuclei that have spin (this interaction is usually small)
• electron spins such as those found in paramagnetic ions (e.g., iron and chromium). Theseinteractions are usually the most important.
Longitudinal relaxation (T1) occurs when a proton can transfer energy to its surroundings via theneighboring spin; then it can relax to its lowest energy state, which is along the direction of B 0.The same transfer also contributes to transverse relaxation (T2): any spin that is aligned with B0
can no longer contribute to CPMG echoes. In the race analogy, the runner drops out of the race.
Transverse relaxation (T2) also occurs by dephasing without a transfer of energy. The merepresence of a nearby spin changes the local B0 field slightly, causing protons to precess atslightly different rates and therefore dephase. In the race analogy, the runner can be tripped b yanother runner and stumble ahead or fall behind the pack, but he stays in the race.
Longitudinal relaxation can only occur by energy transfer, but transverse relaxation can occurthrough energy transfer and dephasing. Therefore, longitudinal relaxation is always less efficientthan transverse relaxation. Consequently, T1 is always longer than T2. For bulk liquids (i.e.,
fluids measured in a large container), it is often the case that T1 and T2 are approximately equal.For nuclei in solids, T1 is usually very much longer than T2. The molecular diffusion mechanism isa pure dephasing mechanism and hence contributes only to T2. From the practical standpoint, it isworth noting that T2 is exactly represented by the spin-echo decay of the CPMG measurement;a "correction for T1" is not required.
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2.2.1 Relaxation by bulk fluid processes
The term “bulk fluid” refers to fluid in large containers (e.g., fluid in a test tube, etc.). However, thebulk fluid mechanism is always active (regardless of whether the fluid is in a large container orconfined to the pore space of a rock) and is independent of the size of the container.
NMR measurements on bulk fluids are of great interest, since T1 measurements are used toestimate several fluid properties.
For water and hydrocarbons, bulk relaxation is primarily due to fluctuating local magnetic fieldsarising from the random tumbling motion of neighboring molecules. The local fields are about 1Gauss, but the very fast molecular motions (mostly rotations of the molecules) tend to averageout the effect. The molecular motions and rotational averaging depend upon the viscosity andtemperature of the fluid; hence, T1 and T2 are both highly correlated with these variables (seeFigure 2.13, Figure 2.14, and Figure 2.15.).
For the case of water at room temperature, bulk relaxation is weak and relaxation times are long(about 3000 msec). For viscous crudes, the rotational averaging is not as effective and relaxation
times are relatively short.
3 .0
1 .0
0 .3
0 .1
0.03
T1
1.0 3.0 10 30 100 300
Viscosity (centipoises)
(sec)
Figure 2.13. Longitudinal relaxation time (T1) versus viscosity for 14 crude oils at various temperatures.
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Figure 2.14. Mean transverse relaxation time (T 2,log ) versus viscosity for bulk oil samples from the Belridge field (triangles), international oil fields and oil viscosity
standards. All samples were measured at room temperature.
Temperature and pressure effects
Temperature has a large effect on bulk relaxation rates (see Figure 2.15). Over the typicalborehole temperature range of 25° C to 175° C, relaxation times increase by about a factor of 10.
Pressure has little effect on the relaxation of water or oil. The relaxation is controlled by molecularprocesses, and on the molecular level 20,000 psi is a very modest pressure. However, pressurehas a substantial effect on relaxation of bulk gas, as shown in Figure 2.16.
0.1
1
10
0 50 100 150 200
T 1
o r T 2
( s e c o n d s )
Temperature (°C)950926-01
Water
S6 Oil
S20 Oil
Figure 2.15. Bulk relaxation of water and two oils (S6 and S20) versus temperature.
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0
2
4
6
8
10
0 3000 6000 9000 12000 15000
25 C75 C
125 C
175 C
T 1
( s e c )
Pressure (psi) 951008-01
Methane Gas
Figure 2.16. T1 versus pressure for bulk methane at 25 ° , 75 ° , 125 ° and 175 ° C.
2.2.2 Surface relaxation
In the description of NMR principles (Section 2.1), no mention was made of the unceasingmolecular motion of fluids. Brownian motion causes fluid molecules to diffuse substantialdistances during an NMR measurement. The equation for diffusion is
< x > = 6Dt , (2.5)
where < x > is the root mean square distance a molecule diffuses in time t, and D is the molecular
diffusion coefficient. For water at room temperature, D is about 2x10 -5 cm2 /sec. Thus, in onesecond (the typical length of time of an NMR measurement), a molecule can diffuse 110 microns,which is substantially greater than the pore size in many rocks.
Diffusion gives a fluid molecule ample opportunity to contact the grain surface of the rock duringthe NMR measurement. Each of these contacts provides an opportunity for surface relaxation.When fluid molecules approach grain surfaces, two things can happen. First, protons cantransfer nuclear energy to the grain surface, allowing the proton to realign with B0 and thereby
contributing to longitudinal relaxation (T1). Second, the proton can be irreversibly dephased,thereby contributing to transverse relaxation (T2). These events appear not to occur with everycollision; there is only a probability that they will occur. As suggested by Figure 2.17, whichshows the paths of two molecules in a pore, several collisions may occur before a spin isrelaxed. Nevertheless, for the case of pore fluids, the most important influence on T1 and T2 isthe interaction of fluid molecules with the surfaces of rock grains.
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Rock Grain
Light line - molecule with unrelaxed spin
Heavy line - molecule with relaxed spin
Rock Grain
Rock Grain
Figure 2.17. Relaxation at the grain surface.
Not all surfaces are equally effective in relaxing the proton spins. High-purity quartz or carbonatesurfaces are not particularly strong relaxers. Paramagnetic ions (e.g., iron, manganese, nickel andchromium) have very strong local magnetic fields. They are particularly powerful relaxers andtend to control the rate of relaxation whenever they are present. Sandstones generally have aniron content of about 1% which makes fluid proton relaxation fairly efficient. The relaxing power ofa surface is called its "relaxivity" and is denoted by the symbols ρ1 (for T1 relaxation) and ρ2 (forT2 relaxation).
The other important part of the surface relaxation mechanism is geometrical. Relaxation will berelatively slow if a small amount of surface has to relax the spins of a large volume of fluid. Thusthe relaxation rates (1/T1 and 1/T2) are the products of the intrinsic relaxivity of the surface, andthe surface to volume ratio (S/V) of the pore:
11
T1 S
SV
= ρ pore
, ( 2.6)
and
12
T2 S
S
V
=
ρ pore
. ( 2.7)
Temperature and pressure effects
The surface relaxation mechanism does not depend upon temperature or pressure. This hasbeen shown by measurements on rock samples that found no changes in relaxation times attemperatures up to 175° C and pressures up to 36,000 psi.
From a practical viewpoint, the temperature and pressure independence of surface relaxationrates considerably simplifies the interpretation of CMR measurements and strengthens theirconnection to the great body of laboratory measurements that have been made at roomtemperature and pressure.
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2.2.3 Relaxation by diffusion in magnetic field gradients
The CPMG sequence described in Section 2.1.4 removes the effect of inhomogeneous B0 fieldsfor protons that do not move during the measurement. When there are significant gradients in theB0 field, molecular diffusion can contribute to T2 relaxation (dephasing). Longitudinal relaxation
(i.e., T1) is not affected.
B0 B0 + δ B
0+ 2δ B
0+ 3δ B
0+ 4δ B
0+ 5δ
PoreA
B
C
Rock Grain
Rock GrainRock Grain
Figure 2.18. Molecular diffusion in a field gradient.
Consider a molecule located at point A during the 90° pulse that starts a CPMG sequence (seeFigure 2.18). After being tipped into the transverse plane, the proton starts precessing at f0, thelocal Larmor frequency. However, as it diffuses it encounters a slowly varying B0 and thereforeits Larmor frequency slowly changes. It is rephased by a 180° pulse at point B and continues
moving. It arrives at point C at time TE, when the spin echo is expected. Note, however, that itprecessed faster between points A and B than it did between points B and C. Because of this, itis not perfectly rephased at TE. In the meantime, other molecules are moving in other directions,each with its own precession history. Hence, refocussing of the protons at time TE is imperfect.Since molecular motions are random, the dephasing is irreversible and contributes to transverserelaxation.
For bulk liquids, T2 resulting from effect is given by
1
T2 D
D( G TE)
12
2
=
γ . (2.8)
In the above, D is the molecular diffusion coefficient, and γ is the gyromagnetic ratio of the proton.G is the gradient strength in Gauss/cm, and TE is the echo spacing defined in Figure 2.9.
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• a gradient caused by the magnet configuration (the strength of the B0 field varies by about 5Gauss over the measurement region)
• microscopic gradients induced by the applied B0 field that arise from the difference in magneticsusceptibility between rock grains and pore fluids.
The diffusion mechanism is smaller for pore fluids than bulk fluids, because molecular motions inpore fluids are restricted by grains and the nonmixing of different fluid types. The CPMGsequence minimizes the effects of diffusion, and it is not significant when the pore fluid is water oroil and the minimum CMR echo spacing of 0.32 msec is used.
The diffusion mechanism is important when gas is present, because the diffusivity of gas isseveral orders of magnitude larger than that for oil and water.
Temperature and pressure effects
The bulk diffusion coefficients of water, oil (Figure 2.19) and methane gas (Figure 2.20) increasewith temperature.
The diffusion coefficient of gas decreases with pressure (Figure 2.20).
10- 1 1
10- 1 0
10- 9
10- 8
10- 7
0 50 100 150 200
T (°C)
D
( m 2 / s )
Water
S6 Oil
S20 Oil
Diffusion Coefficient
950926-03
Figure 2.19. Diffusion coefficient for bulk water and two bulk oils versus temperature.
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0 100
1 10- 7
2 10- 7
3 10- 7
4 10- 7
5 10- 7
0 1000 2000 3000
77 F
136 F
177 F
196 F
D i f f u s i o n
C o e f f i c i e n t ( m
2 / s )
Pressure (psi)950203-01
Methane Gas
Figure 2.20. Diffusion coefficient of bulk methane gas versus pressure at 77 ° , 136 ° , 177 ° and 196 ° F.
2.2.4 Summary of relaxation processes
The relaxation processes described above act in parallel; that is, their rates add:
1T2 total
1T2 S
1T2 B
1T2 D
=
+
+
, (2.9)
where (1/T2)S is the surface relaxation, (1/T2)B is the bulk relaxation and (1/T2)D is the diffusion
relaxation.
The corresponding equation for T1 is
1
T1 total
1
T1 S
1
T1 B
=
+
. (2.10)
Note that there is no diffusion relaxation for T1, because that process is strictly a dephasingmechanism.
During CMR-T2 measurements, all three relaxation mechanisms are active. However, diffusionand bulk relaxations are often weaker than surface relaxation.
The diffusion mechanism is deliberately minimized by using a short echo spacing. When the porefluids are water and oil, diffusion effects are negligible provided the CMR tool is run with the
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minimum echo spacing of 0.32 msec. However, when the pore fluid is gas, diffusion effects areimportant and cause reduced values of T2.
Bulk relaxation is only important in the following three situations.
• The first situation occurs when water is in very large pores and therefore rarely contacts agrain surface.
• Bulk relaxation can be the dominant process when the pore fluid has a high concentration ofparamagnetic ions. For example, chromium ions in chromium lignosulfonate mud filtrates candramatically reduce the fluid relaxation time because the local field around the electron spin isso large.
• When two or more fluids occupy the pore space, bulk relaxation is important for the non-wetting fluid. For example, in a water-wet system, hydrocarbon molecules are prevented frominteracting with grain surface and therefore relax at their bulk rate.
2.3 Multiexponential decay
The transverse magnetization, M(t), in porous rocks does not decay with a single value of T2,but rather with a distribution of T2 values. The multi-exponential nature of relaxation in rocks isdue to:
• The three independent relaxation mechanisms: surface relaxation, bulk relaxation andmolecular diffusion relaxation.
• Each relaxation mechanism may be multi-exponential. This is described below for surfacerelaxation. Bulk relaxation and molecular diffusion relaxation can also be multi-exponential.
In many cases (e.g., water-saturated rocks), bulk and diffusional relaxation can be neglected.Surface relaxation is dominant and T2 is proportional to pore size. That is,
12
T2 S
S
V
=
ρ pore
. (2.11)
For a single pore, the magnetization decays exponentially, therefore, the signal amplitude as afunction of time, M(t), in a T2 measurement is given by
M(t) M expS
Vt0 2= −
ρ . (2.12)
Rocks tend to have very broad distributions of pore sizes. Each pore has its own value ofsurface-to-volume ratio. The total magnetization (being the superposition of signals from individual
pores) is therefore a summation of single exponential decays. That is,
M(t) Mi
S
Vt
i
= −
∑ exp ρ 2 =
∑M exp
- t
T2ii
. , (2.13)
where the summation is over all pores. T2i is the decay constant of the ith pore. Mi is the initialmagnetization from the ith pore and is proportional to its volume.
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The summation of the individual signal amplitudes is proportional to the porosity measured by thetool.
M M0 i= ∑ , (2.14)
φ K Mtool . 0= , (2.15)
where Ktool is a factor containing various calibration and environmental corrections.
In practice, each pore is not considered individually. Rather, all pores having similar surface-to-volume ratios are grouped together. Then, the sums in the equations have a manageable numberof terms; for example, 30.
For illustrative purposes, Figure 2.21 shows the NMR signal that would result from a rock samplethat has only three pore sizes, “x, y and z”. Pore size x has pore volume φX, and relaxation timeT2X, and so on.
φx
Time (t)
T2y
T2z
φx+φy+φz
φxexp(-t/T2x)
+ φyexp(-t/T2y)
+ φzexp(-t/T2z)
Time (t)
Time (t)Time (t)
T2x
φy
φz
Figure 2.21. Sketch showing the NMR signal resulting from three single exponential decays.
The goal of the CMR signal processing is to determine the underlying T2 distribution thatproduces the observed magnetization (i.e., it is a mathematical inversion problem). Figure 2.21shows the distribution for the simple case shown in Figure 2.21. The distribution is divided into aset of rectangles that have areas proportional to φX, φy and φz. The area under the distribution isproportional to the total porosity.
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φzφx
φy
T2
T2x T2y T2z
D i s t r i b u t i o n
Figure 2.21. T2 distribution for the NMR signal shown in Figure 2.21.
In general, the underlying T2 distribution is a continuous function. However, CMR spin-echo datais fit to a multi-exponential model that assumes the distribution has NS discrete relaxation times T2i
with pore volumes φi. The values of T2i are preselected and the signal processing problem is
reduced to determining the pore volume that is associated with each fixed value of T2.
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3. Hardware Description
3.1 Tool concept
NN
SS
Y (cm)
X (cm)
MAGNET
MAGNET
ANTENNA
7.5
5.0
2.5
0.0
-2.5
-5.0
-7.5
-10.0
-12.5
-7.5-5.0-2.50.02.55.07.5
B0
Field
Figure 3.1. Cross-sectional view of CMR sonde showing static magnetic field.
A cross-sectional view of the sonde is shown in Figure 3.1. There are two compound magnetsmagnetized in the same direction. The static magnetic field lines for this magnet configuration arealso shown in Figure 3.1. The static field is predominantly radial into the formation.
NN
SS
350
400450
500500550 550
7.5
5.0
2.5
0.0
-2.5
-5.0
-7.5
-10.0
-12.5
-7.5-5.0-2.50.02.55.07.5
Y (cm)
X (cm)
B0
Field
Strength
Figure 3.2. Contour plots of static magnetic field strength.
Figure 3.2 shows contour plots of the static magnetic field strength. A region of relatively uniformfield is located about 1 in. inside the formation. This region is known as the saddle point.
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• The B1 field is perpendicular to the B0 field. This condition is required for spin tipping.
• The frequency of the B1 field is set to the Larmor frequency for nuclei at the saddle point. B 0 atthe saddle point is about 540 Gauss and the corresponding Larmor frequency (f O) is slightlybelow 2.3 MHz.
• At the saddle point, the B0 field is constant over a relatively large area. This is necessary toensure an adequate measurement volume and signal strength.
In practical terms, the field is considered constant over a region in which the Larmor frequencyof the spins lies within the bandwidth of a 180o tipping pulse. This condition is equivalent to∆B = B1 / 2., where ∆B is the maximum deviation from the center field found in the resonatedregion . For the CMR tool, B1 is approximately 10 Gauss; hence, ∆B is about 5 Gauss. TheB1 field is not particularly homogeneous over the resonance region. Inhomogeneity of B1 isacceptable, as long as error-correcting pulse sequences such as the Carr-Purcell-Meiboom-Gill sequence are employed.
The sensitive region is approximately 1 in. by 1 in. (2.5 cm by 2.5 cm) and centered 1.1 in. (3
cm) from the skid. Note that the zone immediately in front of the skid does not contribute to theNMR signal. This is the “blind zone” that provides immunity against the effects of mudcake andsmall washouts. The blind zone extends 0.5 in. (1.25 cm) in front of the skid.
The antenna irradiates the sensitive region over most of its length; therefore, the sensitive regionis about 6 in. long (15.2 cm).
3.2 Operational requirements
The operational specifications of the CMR include
• a sonde no bigger than 5.3 in. (13.5 cm)
• ability to make measurements in large boreholes
• low power requirements
• a rugged metal sonde
• combinability with other tools
• no geographical limitations
• immunity to mudcake and borehole size and shape effects
• freedom from mud doping
• ease of calibration and testing.
The CMR tool has a maximum OD of 5.3 in.(13.5 cm). Because the skid is pressed against the
borehole wall with a bowspring or powered caliper, there is no upper limit on the size of theborehole that can be logged.
Since the B0 field is created by permanent magnets (rather than electromagnets) and a pulsedmeasurement technique is used, the power requirements are quite modest. Under most operatingconditions the peak sonde power is about 200 watts.
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Ensuring that the sonde survives high temperature, high pressure, abrasion, and rough handlingis vastly simplified by the all-metal construction. This is a significant departure from other boreholeNMR devices. The only nonmetallic part exposed to the environment is the antenna. This isprotected by a replaceable plastic cover. The metal sonde allows other logging tools to be run
beneath the CMR tool.There are no geographical limitations to tool operation. The CMR tool does not utilize, and is notaffected by, the earth's field which is much smaller than the field created by the permanentmagnets.
The skid was designed to limit the length of the wall-engaging section to 18 in. in order to minimizerugosity effects Where the borehole wall is substantially damaged or washed out, preventinggood contact between the face of the sonde and the formation, it is possible to pick up signal fromborehole fluid. In such cases, the tool will give erroneous results. This limitation is common to allwall-engaging logging tools. However, such zones are routinely detected by borehole caliperdevices, and data acquired in them are disregarded. Insensitivity to mudcake is assured by theblind zone. Mudcake can occasionally be as thick as 0.5 in., but rarely it exceeds that due to
modern drilling techniques.In normal operation, the sensitive region does not intrude into the borehole. This eliminates therequirement of doping the mud with particulate magnetic material such as magnetite.
The ability to calibrate and test the CMR tool in remote locations is important. Other boreholeNMR devices can not easily be tested or calibrated because of their large measurement volumes,sensitivity to the presence of metal, and common electrical noise sources. The CMR tool has arelatively small volume of investigation. This permits all calibration and test procedures to beperformed inside a small rf screened enclosure 3 ft. in length and 15 in. in diameter.
3.3 CMR simplified block diagram
A simplified block diagram is shown on Figure 3.5. The basic operational blocks are described in
the following sections.
3.3.1 Sonde electronics and block description
Antenna/tuning
The antenna is a narrow-band circuit that is tuned to the Larmor frequency for hydrogen nuclei.The Larmor frequency depends upon the strength of the magnetic fields produced by thesamarium cobalt magnets, which decreases with temperature. Hence, both the transmitting andreceiving frequency must be adjusted with wellbore temperature. The MAXIS and downholecontroller compute operating frequencies based on data received from the temperature probelocated in the sonde. Tuning is achieved by a capacitor ladder with relays to switch in
capacitance values.The antenna has a high Q, which is very desirable for reception of the weak signals from thehydrogen nuclei and which also minimizes the power requirements during transmit phase.
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Auxiliary sensors
Two additional sensors are located in the sonde: a Hall probe and temperature sensor. The Hallprobe measures the magnetic field strength midway between the magnets. The temperaturesensor is used to correct the Hall probe and to provide the temperature of the magnets. Both
temperature and Hall probe readings are used to estimate the field strength (i.e., B0) in themeasurement region, that in turn is used to set the operating frequency. The temperature readingsare also used to correct for signal attenuation with temperature (i.e., the Curie law correction).
Transmitter
The transmitter drives the antenna with high-voltage (250 volt peak) pulses of rf energy. Thepulse duration is approximately 30 microseconds and maximum current is about 2 amps. It isimportant that the transmitter frequency be at the Larmor frequency, and it is therefore adjustableover a limited range.
Q-switch
The Q-switch is used to dissipate energy stored in the antenna after a transmitter pulse, andthereby prepares the antenna for reception of the low-level spin-echo signal.
Duplexer
The duplexer is a passive coupling network that joins the antenna to the preamp. The duplexercircuit protects the preamp from damage by the very large antenna voltages during transmit. Theduplexer acts as a high impedance during the transmit pulse and as a low impedance when thespin-echo signal is received. It also acts as a broad band pass filter during receive mode.
Preamp
The preamp has multiple gain steps to achieve a voltage gain of about 2000. This amplifies the
raw antenna signal, which is in the order of hundreds of nanovolts up to a few millivolts. Theoutput of the amplifier is sent to the receiver board for further processing.
3.3.2 DTS telemetry interface board
The CMR tool uses the fast tool bus (FTB) protocol of the digital telemetry system (DTS) tocommunicate with the surface processors. The telemetry interface board provides the electronicsneeded to interface the CMR cartridge to the DTS fast tool bus. There are three main functions ofthis board:
• decode and extract commands sent to the CMR cartridge from the downlink data
• insert, encode and transmit CMR messages in the uplink data
• rebroadcast all downlink and uplink FTB data not associated with the CMR to tools aboveand below the CMR.
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3.3.3 Enhanced downhole controller board
Surface commands are received by the telemetry interface and then read and decoded by theenhanced downhole controller (EDHC). The EDHC then initializes the data acquisition andprocessing circuits accordingly.
The EDHC also reads the auxiliary channels, creates uplink messages and starts the uplinktransmission.
3.3.4 Acquisition control/synthesizer board
Timing for the data-acquisition operation is implemented on the acquisition control/synthesizerboard. Once the timing circuits are initialized on this board by the EDHC, the acquisition cyclegenerally proceeds with minimal intervention from the EDHC. The only tool control functionsduring the acquisition cycle are to set a new operating frequency (if necessary) and send a startof acquisition cycle control pulse.
The acquisition control/synthesizer board has a frequency synthesizer circuit that uses the
principle of direct digital synthesis (DDS) to compute a digital square wave of adjustablefrequency.
The acquisition control/synthesizer board also has a 64KX8 EEPROM for storing tuning controlrelay words, master calibration data, master operating frequency search data, sonde and cartridgeserial numbers and a list of modifications that have been made to the tool. Data are read to, andwritten from, the EEPROM by the EDHC using the serial link bus.
3.3.5 Receiver board
The echo signal from the sonde is routed to the receiver board where it is processed. The rawecho signal is an amplitude modulated sine wave with a frequency of about 2300 kHz. This signalis amplified and mixed down to an intermediate frequency of approximately 460 kHz and then
filtered. The resulting signal is digitized by an analog-to-digital converter and then stored in staticrandom access memory (SRAM) space. The echo samples are then read by the receiver signalprocessor and processed to extract the spin-echo amplitudes and several data quality indicators.The results are written to a triported memory module on the EDHC board.
3.3.6 Auxiliary measurements/calibration board
Several auxiliary measurements are made continuously to monitor the quality of the CMR data.These parameters are measured and transmitted to the surface every acquisition cycle. Theauxiliary measurements consist of power supply voltages, transmitter current, transmitter outputpower, sonde temperature and magnetic field strength. The EDHC reads these measurementsand includes them in the uplink message. The aux - cal board also generates test signals that areused during calibration and tool diagnostics. Calibration is performed continuously during the wait
time periods of the measurement cycle.
3.3.7 Power supplies
The CMR cartridge receives 250 Volts rms AC power from the AC main power source in the TPD.The power to the tool is carried on cable conductors 1 and 4. This AC power is used to produce
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five voltages: +/- 5 volts DC for the analog circuits, +5 volts DC for the digital circuits and +/-15volts DC. Cartridge power consumption is 30 watts.
The CMR high voltage power supply (HVPS) provides the necessary power for the generationof the high voltage rf transmitter pulses. Because large load fluctuations occur during the transmit
cycle, AC aux is used as the power source for the HVPS (rather than AC main). This power isprovided on cable conductors 2 and 10. Because of the high power requirements of thetransmitter, a duty cycle limit is imposed such that the transmitter is on for less than 3% of thetime.
3.3.8 Power up reset/RS232
On power up, the power up reset generator circuit performs a global reset of all boards in thecartridge.
As an aid in troubleshooting, the CMR cartridge has RS232 interface capabilities that interface tothe downhole controller software. The downhole controller software includes several utilities thatprovide mechanisms for testing and controlling the hardware and monitoring the data-acquisition
process.
3.4 CMR measurement cycle
The CMR measurement consists of repetitive measurement cycles that are specified by the fieldengineer by means of the MAXIS control panel. A measurement cycle consists of wait-timeintervals, during which no data are acquired, followed by acquisition periods during which thetransmitter is rapidly pulsed; each pulse produces a spin echo. The collection of spin echoes isreferred to as a CPMG.
CPMGs are always collected in pairs. The second set is acquired with the phase of thetransmitter pulse changed to give spin echoes of negative amplitude. The two sets of CPMGsare referred to as plus phase and minus phase. The CPMG pairs are eventually combined to
give "phase alternated pairs" (PAPS).
The CMR timing signals are shown on Figure 3.6 for the case where the measurement cycleconsists of two wait periods. The measurement cycle begins when the downhole controllersoftware pulses the "acquisition start" control signal. This event marks the beginning of the firstwait time. After the wait period (during which time hydrogen nuclei align with the static field) theacquisition of plus-phase echoes occurs. The procedure is then repeated for the minus-phasecycle. This is followed by further wait time/acquisition operations until all subcycles in themeasurement cycle have been completed.
A data-acquisition operation follows each wait time. This process consists of transmitting pulsesat the Larmor frequency. The first pulse is called the 90° pulse, since its function is to tip the nuclei90° into the transverse, or measurement, plane. Succeeding pulses are called 180° pulses, sincetheir function is to flip the nuclei 180°. The duration of the 90° and 180° pulses are approximately20 and 30 microseconds, respectively.
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computed from these components. There is one R value and one X value for each echo in theCPMG sequence.
To reduce both the telemetry bandwidth requirement and loading on the MAXIS system, a largeportion of the signal processing is performed in the CMR cartridge. The signal processor on the
receiver board performs the following operations:
• The first step in the processing is to compute phase-alternated pairs. R and X signals fromthe plus-phase measurement are subtracted from the corresponding R and X signals acquiredfrom the minus-phase measurement. Since the echo envelopes of the minus-phase echoesare negative with respect to those of the plus-phase echoes, the signal remains unaffected.However, any electronic offsets in the data common to both phases are removed.
• Next, the data are corrected for system gain variations using the test loop signal from thecalibration operation.
• The data is averaged with data collected from previous acquisition cycles, according to thedownhole stacking specified by the field engineer. For depth logging, up to 5 level averaging
may be selected. For station logging, the PAPs are stacked continuously for the entireduration of the station log.
• The receiver signal processor computes the phase angle between the stacked R and X data.
• The phase angles are used to compute two channels: (1) a phase coherent channel thatcontains the total signal amplitude plus noise (this is the echo amplitude channel, A(+)) and (2)a channel that contains only noise.
• The A(+) data are then compressed by summing the data over windows. The position andnumber of the windows depend on the number of echoes in the sequence. In this way thelarge number of echoes is replaced by a few window sums. For example, if there are 200echoes in the sequence the window boundaries will be at 30, 100 and 200. Echoes 2 through30 are summed and scaled; echoes 31 through 100 are summed and scaled; and echoes 101
through 200 are summed and scaled. Hence, 200 amplitudes are replaced by 3 window sums.The compressed data are used to compute T2-distributions as described in Section 4.
• The data in the noise channel are used to estimate the root mean square (RMS) noise. TheRMS noise is later used to compute the standard deviations in the CMR logs.
The results of the processing are written to the EDHC triport memory. When the data transfer iscomplete, the receiver board sends a “processing complete” interrupt to the EDHC, indicatingthere are data to transfer uphole. The processing and data transfer occur during the wait timeassociated with the next plus-phase subcycle.
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4.3 Inversion problem
The computation of T2-distributions from spin-echo sequences involves a mathematical inverseproblem. The inverse problem is the estimation of the amplitudes in the multi-exponential model(e.g., 30 components are typically used during depth logging) from the noisy spin-echo data.
NMR data from rocks can be adequately fit to a simple relaxation model involving a fewexponentials or to a stretched exponential model. These simple models are mathematically stablebut do not provide valuable information on pore size distribution and free fluid that is contained inthe T2-distributions.
The inverse problem that must be confronted in computing T2-distributions is mathematically ill-posed. It can be shown that a spin-echo sequence consisting of hundreds or thousands of spin-echo amplitudes contains only a few (e.g. 5) linearly independent pieces of information. Thereforethe problem is underdetermined; the number of unknown amplitudes (e.g. 30) far exceeds theindependent pieces of information. This results in unstable and nonunique solutions to themathematical inverse problem. The solutions are unstable because arbitrarily small changes in theinput data can lead to large changes in the estimated T2-distributions.
Tikhonov regularization method
Methods were developed during the 1960's to provide practical solutions to ill-posed inverseproblems. The regularization method imposes a criterion for selecting a smooth T2-distribution fromthe possible solutions that are consistent with the data. The smoothness criterion is consistentwith the fact that the NMR measurement kernels attenuate the high-frequency components in theunderlying T2-distributions. That is, NMR data intrinsically have low frequency content, which isthe rationale for selection of a smooth distribution. The regularization not only reduces thestatistical fluctuations on the computed T2-distributions but it also controls the standard deviationsof the logs.
4.4 Data redundancy and data compressionBecause the spin-echo sequence contains only a few independent pieces of information, theycan be compressed into a few numbers without any loss of information. Data compression isperformed downhole using a digital signal processing chip in the tool electronics cartridge.Compression reduces telemetry capacity requirements and also disk and tape storage (the spin-echo sequence can also be transmitted uphole and stored on disk if required for later processing).More importantly, data compression allows computation of T2-distributions in real time with thecomputing resources presently available at the wellsite. This would not be possible using theraw spin-echo data.
The data compression algorithm used for the CMR tool is called the window processing (WP)algorithm. The compressed data, in the WP algorithm, are sums of spin-echo amplitudes over a
small number of predetermined time intervals that are referred to as "windows. Figure 4.3 showsaveraged window sums and one-standard-deviation error bars computed from the 600 echoesshown in Figure 4.1.
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Figure 4.3. Averaged window sums for the 600 spin
echoes shown in Figure 4.1.
The averaged window sums are simply the average spin-echo amplitudes in the five windowswhose boundaries are indicated by the dashed lines in Figure 4.1. The RMS noise on theaveraged amplitude in each window is reduced, by a factor equal to the square root of the numberof echoes in the window. For example, the third window in Fig. 1 contains 100 echoes so that the2.0 p.u. of RMS noise on each spin echo is reduced to 0.2 p.u. on the averaged amplitude.
Sensitivities of window sums
The window sums exhibit varying sensitivities to the different components (T2s) in theunderlying T2-distribution that produces an observed CPMG. Figure 4.4 shows the sensitivity
curves for the five windows shown in Figure 4.1, and for an inter-echo spacing of 0.32 msec.
Figure 4.4. Sensitivity curves for window porosities computed using the window boundaries shown in Figure 4.1.
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Note that later window sums have less sensitivity to short T2 components than those from earlierwindows. In particular, only the first three window sums show much sensitivity to bound fluidbelow a 33-msec cutoff (dashed line in Figure 4.4).
The sensitivity curves can be understood intuitively as follows. Early echoes contain signal
contributions from all pore spaces within the rock. As time progresses, the signal from the smallpores completely decays. Therefore, later echoes contain contributions from only the large porespaces that have long T2.
The sensitivity curves show the contribution to each window sum from a unit signal amplitudewith a particular T2 relaxation time. The sensitivity to fast relaxation times, of the order of a fewmilliseconds, can be increased (e.g., the curves in Figure 4.4 shifted to the left) by using shorterearly time windows. Simulations have shown, however, that using shorter early time windowsprovides negligible practical increases in CMR porosity and is less robust in the presence ofnoise. The reason for this is that only the first few echoes contain contributions from signalshaving relaxation times shorter than a few milliseconds.
4.5 Maximum likelihood estimationThe statistical properties of the window sums are used to derive a maximum likelihood function forthese random variables. The amplitudes of the components in the multi-exponential relaxationmodel (i.e., the T2-distributions) are determined by maximizing the likelihood function subject to aconstraint that the amplitudes be non-negative. The relaxation times in the relaxation model aredetermined by user inputs (see Section 4.8) and are therefore not part of the estimation. Thismeans that, except for the positivity constraint, the estimation problem is linear.
The Tikhonov regularization method is used to select a smooth distribution that is consistent withthe raw data. Monte Carlo simulations have shown that this method results in unbiased logoutputs over the entire range of SNR. The regularization requires a parameter γ, that isautomatically computed from the input data using an algorithm that seeks to minimize the error
between the computed T2-distributions and the true underlying T2-distributions. It has beenshown that the resulting distributions are relatively insensitive to the value of γ .
The maximum likelihood function is defined in Appendix D.
4.6 Measurement sensitivity limits
The sensitivity of the NMR measurements to decay times of the order of a few milliseconds isdifficult to quantify because there is no sharp cutoff on the sensitivity response to short relaxationtimes. This can be seen from the sensitivity plots in Figure 4.4. The loss of sensitivity to shortrelaxation times is gradual and depends on the SNR of the measured data; however it is the inter-echo spacing that provides an intrinsic lower limit to the shortest relaxation times that can bemeasured. For the CMR tool, this limit is a few milliseconds. The CMR porosity reads essentially
zero porosity in hard shales and contains contributions from pores with relaxation times greaterthan a few milliseconds. The CMR porosity is therefore an effective porosity that does not includecontributions from clay-bound water. NMR laboratory measurements on core samples haveshown that clay-bound waters have relaxation times below about 3 msec.
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4.7 Standard deviations in log outputs
An important log quality control feature of the processing is the computation of the standarddeviations in all of the derived log outputs. The standard deviations can be reduced, albeit withsome loss of vertical resolution, by averaging of PAPs prior to processing the data. Thus, for a
typical CMR sandstone logging mode, a CPMG consists of a 1.3 second wait time followed b ythe acquisition of 600 spin echoes. The total time for acquisition of a single PAP is 3 seconds. Thethree-level averaging results in total CMR porosity statistical precision of less than 1.0 p.u., afree-fluid porosity precision of less than 0.5 p.u. and a capillary bound-fluid porosity precision ofabout 1.0 p.u.
Monte Carlo simulations have shown that the statistical precisions quoted above will varyslightly depending on the characteristics of the underlying T2-distributions. The porosity precisionis comparable to that obtainable with nuclear logging tools. An important difference, however, isthat the CMR porosity standard deviations are essentially independent of the SNR of themeasurements (i.e., do not depend on the porosity of the formation), whereas the precisions ofmeasurements made by nuclear logging tools are known to vary with porosity.
Unlike the CMR porosity measurements, the standard deviations in the logarithmic meanrelaxation times depend on the SNR of the measurements. Therefore, an absolute precisionspecification cannot be quoted for the estimated logarithmic mean relaxation times. The computedstandard deviations in the mean T2 are output on a quality control log.
The standard deviations in the logs are computed from a covariance matrix for each measurement.The computations require an estimate of the RMS noise. As noted earlier, the RMS noise isestimated from the data in a noise channel that is computed for each measurement. Figure 4.5shows the noise channel for the spin echoes in Figure 4.1.
Figure 4.5. Noise channel for data shown in Figure 4.1.
4.8 Parameter selection
The computation of T2-distributions and log outputs requires the selection of a set of processingparameters: (1) the number of components in the multi-exponential relaxation model (2) theminimum and maximum values of T2 in the computed T2-distribution, (3) the free-fluid cutoff, (4)
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an input T1/T2 ratio and (5) the mud filtrate relaxation time. These parameters are inputs for thecomputation of T2-distributions, relative amounts of free and bound-fluid porosity and meanrelaxation times. It is useful to briefly discuss and define the role played by each of theseparameters.
Number of components
Simulations and processing of field data have shown that the number of components hasnegligible effects on the CMR log outputs (which are integrals of the T2-distribution) provided thatat least a 10-component model is employed. Adding more components results in having morepoints on the computed T2-distributions and is necessary for displaying continuous T2-distributions. During depth logging, a 30-component model is frequently used so that T2-distributions can be displayed while logging. For station logging, a 50-component model isnormally employed.
T2min and T2max
The minimum and maximum T2 values specify the range of the T2-distribution assumed in the
relaxation model. Specification of T2min, T2max and the number of components determines therelaxation times in the model, which are chosen equally spaced on a logarithmic scale. Theminimum value of T2 is determined by the intrinsic sensitivity limit of the measurement to shortrelaxation times. The intrinsic limit for a measurement is set by the inter-echo spacing. The CMRpulse sequences, under normal conditions, have an inter-echo spacing of 0.32 msec. Thissuggests that the minimum T2 should be set in the range from 1 to 3 msec. The choice is notcritical since, for practical purposes, the log outputs are relatively insensitive to T2min. However,using 3 msec provides slightly improved porosity precision.
The value of T2max that is selected for processing is a compromise between the longestrelaxation time that can be present in the T2-distribution and the longest relaxation times that canbe resolved by the measurement. The latter is determined by the echo collection time, i.e., the
number of spin echoes in the CPMG and the inter-echo spacing. Simulations have shown thatCMR log outputs are insensitive to the value of T2max over a reasonable range of values. ForCMR depth logging with 600 or 1200 echoes, a value of 3000 msec is typically used for T2max.Re-processing of depth log data using values of T2max in the range from approximately 1500 to3500 msec should produce negligible practical changes in the logs.
During station logging, 3000 to 8000 echoes are usually collected and a value of 5000 msec forT2max is typically used. Station logs with long echo collection times are required to resolvefeatures in T2-distributions corresponding to relaxation times of the order a few seconds.Simulations and field data have shown, however, that long echo collection times are not requiredto determine accurate values of the CMR log outputs. That is, values of φCMR, φFF, φBF, and T2,log
obtained during depth logging agree with station log outputs to within the statistical uncertainty.
Free-fluid cutoff
The free-fluid cutoff is an input parameter that is used to partition φCMR into free- and bound-fluidporosity. The cutoff depends on mineralogy, and cutoffs have been determined empirically forsome sandstones and carbonates. The experimental data support a value of 30 msec insandstones and 100 msec in carbonates. The cutoff is defined so that φFF represents the porosity
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associated with relaxation times greater than or equal to the cutoff. It should be noted that thequoted cutoffs for sandstones and carbonates are not expected to be universally applicable.
T1/T2 ratios
The T1/T2 ratio is a parameter used to make a polarization correction. The correction accounts forthe incomplete polarization of the proton magnetization during the wait time that initiates a CMPG.The correction is important in rocks having T1-distributions with long relaxation times asexplained below.
The rate at which the proton magnetization approaches its equilibrium value depends on the T1-distribution of longitudinal relaxation times in the sample. If the wait time is too short, the signalassociated with the longer relaxation times will be reduced (e.g., φFF will be too low). Ideally, thewait time should be at least three times the longest relaxation time in the T1-distribution. In somelogging environments (e.g., vuggy carbonates) this would require wait times longer than 10seconds, which is clearly not practical for logging measurements.
Laboratory experiments, on a lithologically mixed suite of water-saturated rocks, have shown
that: (1) T1 and T2-distributions have approximately the same size and shape and (2) T1/T2ratios range from approximately 1 to 3 with a mean of about 1.65. The experiments wereperformed, and are valid, in the 2-MHz frequency range of the CMR tool. An inter-echo spacing of0.32 msec was used in acquiring the experimental data. At higher frequencies and for longer inter-echo spacings, the results are not necessarily valid.
Moreover, the experimental findings are valid only in the absence of molecular diffusion effects.Under normal circumstances the CMR tool response is not affected by diffusion. An exceptionoccurs in zones with unflushed gas. The relatively large gas diffusion constant can causediffusion effects that reduce the T2 of the gas. Since T1 is not affected by diffusion, enhancedT1/T2 ratios are possible.
The CMR polarization correction for single wait time logging uses an assumed input value for the
T1/T2 ratio (e.g., a value near the experimental mean of 1.65). The correction is more important forshort wait times. Using longer wait times reduces not only the magnitude of the correction but alsoany errors in log outputs that occur because the assumed ratio is not equal to the actual T1/T2ratios. Note that if the assumed T1/T2 ratio is greater than the actual ratio in the formation, then φFF
will be overestimated; the converse is also true.
T1/T2 ratios can be logged by the CMR tool using multi-wait time CPMG pulse sequences.
Mud filtrate relaxation time
The mud filtrate relaxation time is measured by the logging engineer at the wellsite prior to loggingoperations. The filtrate relaxation times in mud systems containing paramagnetic ions (e.g., Fe+++
or Cr++) can be less than 100 msec. In such environments, mud filtrate that invades the formation
can suppress the long relaxation components in the T2-distributions. If a correction is not applied,then φFF and T2,log might not be accurate. The CMR porosity is not affected by the filtrate relaxationtime; however, if a correction is not applied, then the permeability estimator based on T2,log can bepessimistic. It should be noted that, in practice, mud filtrate relaxation times of the order of 1 secare frequently encountered and the correction is negligible.
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5. Calibration and Environmental Corrections
5.1 Overview
The computation of φCMR, φFF, and φBF requires several environmental and calibration parameters.These include the master calibration constant, the formation temperature, the magnetic fieldstrength and the hydrogen index of the fluids in the zone of investigation of the measurement.
The primary calibration standard for the CMR tool is a 100 p.u. signal from a water bottle that isplaced directly on the sonde. Electronic calibration is achieved using a test loop located near theantenna. A constant amplitude signal is sent to the test loop and picked up by the antenna. Thetest loop signal is used to correct for changes in system gain that are caused by changes intemperature, operating frequency and conductivity. Signal amplitudes measured during loggingare also automatically corrected for changes in temperature and static field strength.
The calibrated and environmentally corrected porosity is given by
φ CMRDH
MC
MC
DH
O,MC
O,DH
DH
MC
AMPAMP
LOOPLOOP
BB
TEMPTEMP
1HI
=
2
, (5.1)
where:
φCMR = CMR porosity, calibrated and corrected (p.u.)
AMPDH = Raw signal amplitude (volts)
AMPMC = Amplitude of the water bottle signal (volts)
LOOPMC = Amplitude of the test loop signal during master calibration (volts)
LOOPDH = Amplitude of the test loop signal during logging (volts)
B0,MC = Static field strength during master calibration
B0,DH = Static field strength during logging (changes with the temperature of the magnets)
TEMPMC = Temperature of water during master calibration (° K)
TEMPDH = Temperature of formation during logging (° K)
HI = Hydrogen index of the fluid in the measurement region
Temperature is an important variable in both the calibration and environmental corrections. TheCMR signal amplitude varies with temperature for three reasons.
• The Curie law effect. The tendency for the hydrogen nuclei to align in the static field is
disrupted by thermal effects; hence signal amplitudes decrease with temperature. Amplitudesmeasured downhole are corrected to the temperature during the master calibration by the lastterm in Eq. 5.1:
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• The field strength of the permanent magnets decreases with temperature. A decrease in fieldstrength results in a decrease in signal amplitude.
• The electronic gain (i.e., the system gain) changes with temperature.
For the above reasons, amplitudes measured during the master calibration or downhole arealways associated with an ambient temperature and field strength.
5.2 Master calibration
Master calibrations are performed in the shop at regular intervals. The master calibration is usedto convert signal amplitudes obtained in the borehole into porosity units. During the mastercalibration, a fixture containing a water sample is placed on the tool antenna cover. The fixturewas designed so that the water completely fills the sensitive region of the measurement. Thewater is doped with Nickel Chloride (NiCl) to reduce the water T1 relaxation time to approximately50 msec. This allows the use of a short wait time and consequently a fast calibration; excellentSNR is achieved by averaging the data over a 5 minute period.
The spin-echo data are processed to determine the signal amplitude from the water solution. Thissignal amplitude (i.e., AMPMC) represents a 100 p.u. standard. During logging, the CMR porosityis simply the ratio of the signal amplitude determined downhole to the master calibration amplitude(i.e., the first term in Eq. 5.1: AMPDH /AMPMC).
The test loop signal (LOOPMC), static field strength (B0,MC) and temperature of the fluid in the bottle(TEMPMC) during calibration are stored in an EEPROM in the CMR cartridge, together with themaster calibration amplitude (AMPMC).
5.3 Electronic calibration
Electronic calibration occurs during the wait period of the measurement cycle. At this time a lowlevel (10 microvolt) signal is sent to the test loop. The signal is picked up by the antenna and
processed through the receiver circuitry.The CMR test loop is analogous to the induction test loop but with the added convenience that itcan be measured downhole. During logging, the test loop signal checks out the entire CMRsystem except for the transmitter. (Note: In test phase the loop is also used to check thetransmitter).
Changes in electronic gain occur with changes in temperature, conductivity and the operatingfrequency of the tool. During logging, a system gain correction is calculated from the loop signal(LOOPDH) and the loop signal obtained during master calibration (LOOPMC):
correction LOOP LOOPMC DH= ( ) . (5.3)
This is the second term in Eq. 5.1. The value of LOOPMC is indicative of the system gain at thetime AMPMC was determined.
The gain correction is applied downhole to both the spin-echo amplitudes and window sums. Thegain correction, which should vary slowly with depth, is also presented on the CMR qualitycontrol log.
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6. Operating Procedures
6.1 Special procedures
CMR logging involves many new concepts. These concepts, which are summarized below, mustbe understood in order to produce good quality logs.
6.1.1 Tool tuning
The tool must be operated at the Larmor frequency (i.e., the resonant frequency) for hydrogennuclei. Operation at this frequency is required to maximize the amplitude of the spin echoes andproduce a calibrated log.
The Larmor frequency (f0) depends upon the strength of the static magnetic field (B 0) generatedby the permanent magnets; that is,
f 4258.B0 0= ( 6.1)
for f0 in Hz and B0 in Gauss.
At room temperature, the static field strength in the measurement region is about 540 Gauss, andthe corresponding Larmor frequency is approximately 2300 kHz.
The strength of the static field decreases as the temperature of the samarium cobalt magnetsincrease. Because of this, the operating frequency must be periodically changed during loggingoperations. The frequency is initially determined by running the tool adjacent to a porous bed andmeasuring relative signal strengths as the operating frequency is changed. The signal amplitudepeaks at the Larmor frequency. This procedure is known as the Larmor Frequency Search Task(LFST). Once the Larmor frequency has been determined at one depth in the wellbore, theoperating frequency is automatically adjusted during logging according to temperature readings
from a sensor located in the sonde.
Further details of tool tuning are given in Section 6.2.
6.1.2 Pulse sequence
The CMR measurement cycle is defined by a set of parameters known as a pulse sequence.The pulse sequence describes the timing and manner in which the rf pulses are transmitted.
In general, a measurement cycle consists of
• A set of wait times when the transmitter is turned off. During the wait time, the hydrogen nucleialign (i.e., polarize) in the direction of the static field.
• Each wait time is followed by an acquisition period when the transmitter is rapidly pulsed toproduce the spin echoes.
The pulse sequence specifies the duration of each of the wait times, the number of times that thetransmitter is pulsed during the acquisition period (this determines the total number of spin echoesthat are collected) and the time interval between the transmitter pulses during the acquisitionperiod.
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A pulse sequence may have single or multiple wait times. Single wait times are used to measurethe T2-distribution of the formation. Multiwait time sequences are used to determine both T2-distributions and T1/T2 ratios. The T1/T2 ratio is used for a polarization correction, as describedbelow.
6.1.3 Polarization and the polarization correction
As previously stated, hydrogen nuclei align (become polarized) in the direction of the staticmagnetic field during the wait time of the measurement cycle. Because of their angular momentum,this alignment does not occur instantaneously, but rather grows with a time constant called thelongitudinal relaxation time, T1 (see the CMR Training Manual for a full description of T1).
Ideally, the wait time should be 5 to 10 sec to allow for complete polarization of the hydrogennuclei. Shorter wait times result in reduced signal, as nuclei that are not polarized do not contributeto the amplitude of the spin echoes. This in turn results in erroneously low porosity and T2values. Unfortunately, wait times of 5 to 10 sec are impractical for depth logging, because the toolwould move too far during this time interval. Because of this, shorter wait times are used in
practice and a correction is then applied for incomplete polarization.The polarization correction methodology is based on the results of lab NMR measurements oncore samples. These measurements show that T1 and T2 are closely related in rocks: both T1and T2 are proportional to pore size. Furthermore, for a large number of water saturated samples,the T1/T2 ratio was found to have a fairly narrow range -- from 1.0 to 3.0 -- and an average valueof 1.6.
For CMR measurements acquired with a single wait time, the polarization correction is determinedfrom the measured T2-distribution and an input value of the T1/T2 ratio. Both are used to estimatethe T1-distribution that in turn is used to correct the signal amplitudes. Note that a polarizationcorrection is required for the free-fluid porosity but not the bound-fluid porosity. This is becausethe bound-fluid has short T1 and therefore polarizes in a fraction of a second. During logging, free-
fluid porosity is computed both with and without the polarization correction. A free-fluidpolarization correction is then defined as
PCF FF FF,UNC=φ φ / , (6.2)
where φFF is the polarization-corrected free-fluid porosity and φFF,UNC is the uncorrected value.
Note that the polarization correction is an approximation, as the true T1/T2 ratio is often differentthan the input value. In addition, the ratio probably varies continuously with depth. For thisreason, wait times should be sufficiently long to minimize the magnitude of the correction. In orderto produce reasonably accurate logs, the correction should be less than 1.10 in zones of interest.The polarization correction, PCF, is displayed on the CMR quality control log
It is not necessary to input a T1/T2 ratio for logs acquired with multiwait times. In such cases, theT1/T2 ratio is computed directly from the signal amplitudes obtained from each of the different waittimes.
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6.1.4 Measurement time and logging speed
Compared to most other logging measurements, it takes a relatively long time to complete eachmeasurement cycle. This affects maximum logging speed since a new measurement is required foreach sample rate interval (usually 6 in.).
To understand the relationship between measurement time, sample rate and logging speed,consider the default pulse sequence for logging sandstone formations. In this case, a single waittime of 1.3 sec is used to allow for polarization of the hydrogen nuclei. Six hundred spin echoesare then measured with an interecho spacing of 0.32 msec. The acquisition time is therefore about0.2 sec and the total measurement cycle time is 1.5 sec. Hence, the total time to acquire a phasealternated pair is 3 sec. A 6 in. sample rate is used for standard vertical resolution logging. Toobtain a new PAPs during each sample interval, the cable speed must be less than 6 in./ 3 sec,i.e., 600 ft/hr.
Faster logging speeds can be achieved if the wait time is shortened. In some formations thiswould lead to large polarization corrections and an unacceptable decrease in the accuracy of thelog, as described in Section 6.1.3.
6.1.5 Stacking, precision and vertical resolution
NMR is a statistical measurement analogous to the nuclear count rate-type measurements.Stacking of data by vertical averaging is required to obtain logs with acceptable precision (i.e.,acceptable repeatability). Three-level averaging is the default for depth logging. Under mostcircumstances, this will result in φCMR logs with a precision of less than 1 p.u., φFF logs with aprecision of less than 0.5 p.u., and φBF logs with a precision of about 1.0 p.u. Unlike nuclearlogging measurements, CMR precision does not change with porosity.
The precision of the log can be improved by increasing the vertical averaging; however, thisresults in a decrease in vertical resolution. For example, consider the case above where the cycletime and logging speed are adjusted to give a new sample every 6 in. Three-level averaging
results in a log that is averaged over 18 in. of formation, and 5 level averaging results in a log thatis averaged over 30 in. of formation. CMR logs that are averaged over 5 levels have similarvertical resolution to Litho-Density logs.
The precision of NMR measurements depends upon temperature. An increase in temperatureresults in an increase in the noise in the data and a reduction in signal strength. When loggingdeep hot wells, it may be preferable to increase the amount of averaging to ensure goodprecision.
6.2 Tuning the tool to the Larmor frequency
The Larmor frequency (f0) is the frequency at which the hydrogen nuclei precess in the transverse(i.e., measurement) plane. It is therefore the frequency of the received signal.
The tool must be operated at the Larmor frequency. The Larmor frequency changes withtemperature and as magnetic debris accumulates on the magnets; hence, the operating frequencymust be periodically adjusted while logging. Operation at frequencies higher or lower than theLarmor frequency result in low signal amplitudes and therefore erroneously low porosity values.
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The Larmor frequency is sometimes called the resonant frequency and when the tool is operatedat this frequency it is said to be “on resonance” or “tuned” to the Larmor frequency. Tuning thetool involves the following:
• Tuning the antenna to resonate at the Larmor frequency to detect the weak NMR signal. This
is accomplished by changing the capacitance connected to the antenna. The amount ofcapacitance is specified by the tuning relay control word (abbreviated to “tune word” in thefollowing).
• Operating the transmitter at the Larmor frequency. The transmitter pulse produces an rfmagnetic field that tips the hydrogen nuclei away from the static field direction. Efficient tippingoccurs only if the pulses are at the Larmor frequency.
The Larmor frequency is given by
f0 0B=
γ
π 2, (6.3)
where B0 is the static field strength in the measurement region, and γ is the gyromagnetic ratio ofthe resonated nucleus.
For hydrogen nuclei, γ / 2π = 4258 Hz/Gauss. Hence the Larmor frequency is determined entirelyby B0 For the CMR tool, B0 is nominally 540 Gauss at room temperature. This corresponds to aLarmor frequency just below 2300 kHz.
B0 decreases with temperature. The samarium cobalt magnets in the CMR sonde have atemperature coefficient of about 1 Gauss/ 5O C. This corresponds to a change in Larmorfrequency of 0.85 Khz/ O C. Therefore, the tool operating frequency must be adjusted according tothe ambient temperature of the magnets.
B0 is also affected by metal debris that is scavenged by the magnets. The metal debris usually
accumulates on the magnets during the descent through the surface casing. Obviously, theamount of metal debris varies by well, and for this reason the Larmor frequency must bedetermined in situ, as described below.
A
Frequency - kHz
1400
1200
1000
800
600
400
200
0
2240 2260 2280 2300 2320 2340 2360 2380
Sonde Characterization Curve
mplitu
de
Figure 6.1. Signal amplitude versus operating frequency.
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The Larmor frequency is determined by measuring signal amplitudes as the operating frequencyof the tool is changed. Figure 6.1, known as the sonde characterization plot, shows thecharacteristic curve for these types of measurements. The data was generated in the lab frommeasurements performed on a water bottle sample. The Larmor frequency is the frequency at
which the maximum signal amplitude occurs. For this example, it is 2310 kHz, which correspondsto a B0 of 542 Gauss.
The same general principle applies to determining the Larmor frequency downhole with oneimportant exception; it took several hours to collect the data shown in Figure 6.1. Measurementswere taken at 240 different frequencies and several hundred readings were averaged at eachfrequency to obtain high precision. Obviously, this amount of time is not available during logging.Therefore, measurements are made at only 7 frequencies. The results are compared to the sondecharacterization data to determine the Larmor frequency. This method takes advantage of the factthat the sonde characterization and downhole measurements are identical except for a shift infrequency and amplitude.
The semi automatic procedure for tuning the tool downhole has been semi-automated and is
known as the Larmor Frequency Search Task (LFST). The procedure consists of the followingsteps:
1. The tool must be tuned in a porous interval. In thick zones, the tool can be moved s lowlywhile it is tuned. In thin porous zones, it is preferable to tune the tool while stationary (unlessthere is danger of sticking). The interval that has the highest porosity should be selectedsince the time taken to complete the LFST decreases with porosity. A minimum porosity of 10p.u. is generally required to complete the task within 3 min.
2. An initial estimate of the Larmor frequency is computed based on the reading from thetemperature sensor in the sonde. This estimate will be close to the true Larmor frequency if thetool has not accumulated large amounts of metal debris on the magnets. The initial estimate isdenoted as FI.
Tune Word
2500
2000
1500
500
0
40 50 70
1000
60 80 90 100 110 120 130 140
Test Loop Amplitude vs Tune Word
Amplitude
Figure 6.2. Test loop signal amplitude versus tuning relay control word.
3. The capacitance connected to the antenna is then adjusted (by changing the tune words) tomake the antenna resonate at FI. The capacitance required depends on both wellboretemperature and pressure and cannot be predicted accurately from surface measurements.
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Therefore, the correct value is determined in situ using an automatic procedure known as thetune word search task (TWST). During this procedure, the calibration signal is sent to the testloop at frequency FI, and received signal amplitudes are recorded for selected tune words, asshown in Figure 6.2. The signal amplitude peaks at the correct tune word. It should be noted
that it is necessary to establish the correct tune word for one only operating frequency underwellbore conditions. As the operating frequency is subsequently changed (during the LFST orduring depth logging) the appropriate tune word is selected from a look-up table stored in anEEPROM in the cartridge. The Larmor frequency is then determined by measuring signalamplitudes for 7 values of transmitter frequency centered around F I. The signal amplitudes arefit to the sonde characterization data and the Larmor frequency interpolated from the fit; it is thefrequency at the maximum amplitude. This results of this procedure are shown in Figure 6.3.
Figure 6.3. Signal amplitude versus operating frequency at wellbore temperature.
The LFST determines the operating frequency for one depth interval (i.e., one temperature) in thewell. During logging the operating frequency is automatically adjusted in 1 kHz steps according toestimates of B0 made from the sonde temperature sensor. This corresponds to a temperaturechange of approximately 1.2O C [2.1O F].
B0 is also estimated from a Hall probe that measures the magnetic field strength inside the sonde.The Hall probe reading can be extrapolated to give the field strength in the sensitive region (i.e.,B0). Accumulation of metal debris on the sonde affects the Hall probe estimate of B 0 but not thetemperature estimate. During logging, the difference between the two estimates is calculated. If
the difference exceeds 1 Gauss, the LFST must be performed to accurately determine B0.
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6.3 MAXIS control panel
A control panel has been implemented in order to simplify logging operations. The control panelallows setting of parameters that control both the acquisition and processing of CMR data. The
value of these parameters depend upon mineralogy and whether the tool is in depth logging orstation logging mode. The panel also displays various diagnostic channels from the tool andcomputed outputs that indicate log quality. The control panel is shown in Figure 6.4.
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Parameter values entered into the control panel are transferred to the local parameter buffer whenthe Apply button is selected. The knowledge base is also updated at this time. If the Resetbutton is selected, parameter values in the control panel are overwritten by values in the localparameter buffer.
For ease of operation, several default logging modes are available with preset parameter values.These modes are designed to assist personnel who are unfamiliar with the tool operation andcover the majority of logging environments encountered in the field. When one of the defaultmodes is selected, most of the parameters cannot be changed. Therefore, selection of one of thedefault modes results in a standard final product. A logging mode is selected via the Mode button.When the button is activated, a pull-down menu appears that lists the available logging modes.Several of the modes are described in Section 6.3.3.
An expert logging mode is also provided. In this mode all the parameters may be changed tovalues that are within certain limits. This allows a set of parameters to be customized to suit aparticular environment. The ability to customize parameter sets adds complexity to the systembut is considered worthwhile because it can lead to better quality logs and/or faster logging
speeds in some environments. Parameters that are entered manually in expert mode can besaved by selecting the File button. The parameters are then saved to a file in the current disksubdirectory by activating SAVE in the submenu. The parameters may be retrieved later b yselecting the RESTORE option. The File button is active only when expert mode is selected.
CMR signal processing may be switched on or off using the control panel. The purpose of thisswitch is to set the CMR log outputs to absent values when the logging speed is too high forreliable outputs. This occurs when the CMR tool is run in combination and the logging speed isincreased between zones of interest.
A description of the parameters in the control panel follows.
6.3.1 Hardware operating parameters
# of wait times. This specifies the number of different wait times in a pulse sequence. Thisparameter has an upper limit of 8 and is editable only in expert mode.
Echo Spacing. This is the time interval between successive echoes and is also the time intervalbetween successive transmitter pulses. This parameter must be greater than 0.32 msec and issubject to a duty cycle constraint. The default value is 0.32 msec and it is editable only in expertmode.
Set Pulse Sequence. This specifies the duration of each of the wait times in the pulsesequence, the number of echoes collected after each of the wait times, and the number of timeseach wait time is repeated within the measurement cycle. Editing is allowed only in expert mode,and values are subject to duty cycle constraints. An example of the dialogue window associatedwith this button is shown in Figure 6.5.
Send Echoes (yes/no). If set to yes, the spin-echo sequence is sent uphole together with thewindow sums. The default is yes.
Spin echoes are considered raw data and may be requested by clients who wish to process thedata using their own signal processing code. The spin-echo sequences are phase alternated,corrected for system gain changes and stacked according to the value of Downhole Stacking.
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Auto Frequency (yes/no). If set to yes, the tool operating frequency is periodically changedaccording to the sonde temperature. The default is yes.
Auto Cal (yes/no). If set to yes, the calibration signal from the test loop is measured and appliedto correct for system gain changes. This option is used to disable the auto calibration in the event
that the calibration circuit is broken. The default is yes.
CMRT SEQUENCES
Wait Time Order Wait Time (s) Number of Echoes Repitition
1 15.0 8000 1
2 8.0 5000 1
3 3.0 1800 1
4 1.3 600 2
5 .3 300 3
Apply Cancel
Figure 6.5. MAXIS set pulse sequence window.
Sample interval. This is the sample rate in inches for depth logging. It is generally set to 6 in. forstandard resolution logging or 3 in. for high vertical resolution logging.
Update interval. The time interval (in sec) for updating station log outputs on the control panel.The default is 30 sec.
Max log speed. This is calculated by the system from the input pulse sequence and samplerate interval.
For a single-wait time sequence, the maximum logging speed allows sufficient time for one PAP tobe acquired during the sample rate interval.
For a multiwait time sequence, the maximum logging speed allows sufficient time for all PAPsassociated with one subsequence (including repeats) to be acquired during the sample rate
interval.
Downhole Stacking (cont, 1, 2, 3, 4, 5). This determines the number of PAPs that are stackeddownhole prior to computing the window sums. The default for depth logging is 3. During stationlogging, when the PAPs are stacked continuously, downhole stacking is set to cont.
For depth logging, stacking must be performed either downhole or uphole (i.e., downhole stackingshould be set to 1 if uphole stacking is used).
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6.3.2 Data processing parameters
6.3.2.1 Signal processing parameters
The signal processing software determines amplitudes on the T2-distribution (e.g., the P i‘s, in
Figure 6.6) at preselected values of T2. These amplitudes output in an array called AMP_DIST.A curve is fit through the computed points to give the appearance of a continuous curve. Thepreselected T2 values are equally spaced on a logarithmic scale and between values of T2 minand T2 max.
The number of preselected T2 values is referred to as the number of components in thedistribution.
T2 MinT2 Max
Pi
Figure 6.6 Points on the distribution are computed at preselected values of T2.
The processing parameters are described below:
T2 min. This is the minimum value of T2 for the computed T2-distribution. T2 min can be edited inexpert mode only.
T2 max. This is the maximum value of T2 for the computed T2-distribution. T2 max can be editedin expert mode only.
# of components. This parameter defines the number of components in the T2-distribution andis set to 30 and 50 for depth and station logging, respectively. This parameter can be changedonly in expert mode .
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Uphole Stacking. This parameter defines the number of consecutive samples that are averageduphole. The default is 1 and the maximum value is 30. This parameter can be changed only inexpert mode.
For depth logging, stacking must be performed either downhole or uphole (i.e., downhole stacking
should be set to 1 if uphole stacking is used). It is preferable to utilize downhole stacking.However, due to hardware limitations, a maximum of 5 level stacking can be performed downhole.Uphole stacking is utilized if more than 5 level stacking is required.
Regularization (auto/manual). This sets the amount of regularization (or smoothing) that isapplied to the computed T2-distributions. Regularization is required to produce repeatable logoutputs from the inherently noisy raw data. The amount of regularization is determined by theinput value of gamma. High values of gamma improve the precision of the log outputs but mayintroduce small bias errors and also give smooth T2-distributions that lack detail.
The default setting for this switch is auto. When auto is selected, values of gamma are determinedfrom the signal-to-noise ratio of the data and details of the T2-distribution.
Manual regularization can be selected only in expert mode. When manual is selected, a secondwindow appears that allow values of regularization to be set for each wait time.
6.3.2.2 Interpretation and environmental correction parameters
T2 cutoff. This is the value of T2 that separates bound and free-fluid porosities. It is set to 30msec for sandstones and 100 msec for carbonates. It can be edited in any mode.
Permeability. This button allows the selection of a permeability model (SDR or Timur/Coates).After a model is selected, a second menu appears for setting the model coefficients andexponents.
T1/T2. This parameter is used for the polarization correction that is applied to single-wait timedata. The default is 1.5.
T2 mud filt. The T2 of the mud filtrate can be measured at the wellsite and its value used tocorrect the T2-distributions. The default value is 50,000 msec, and it can be changed only inexpert mode. The T2 of the filtrate is also recorded on the log heading.
Hydrogen Index (auto/manu). A hydrogen index correction may be optionally applied to theCMR porosity and free-fluid porosity based on salinity, temperature and pressure.
If auto is selected, a second menu appears for inputting mud type (oil or water), mud filtratesalinity, formation water salinity, mud weight and deviation. For water muds, it is assumed that theformation is completely flushed and the mud filtrate salinity is used. For oil-base muds, it isassumed that there is no invasion and the formation water salinity is used for the correction.
Formation pressure is assumed to be equal to the hydrostatic pressure that is computed from the
tool depth, mud weight and well deviation. The formation temperature is approximated by thesonde temperature.
Values of hydrogen index may be entered directly if manu is selected. The default setting is manucombined with a hydrogen index equal to 1.0. This parameter is editable in any mode.
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6.3.3 Logging modes
Default parameter values for several of the modes are described below and also summarized inTable 1.
6.3.3.1 Depth logging modes• Sandstone depth log. The wait time is set to 1.3 sec. Six hundred echoes are then collected
with an echo spacing of 0.32 msec. Total time to acquire 1 PAP is approximately 3 sec.
The sample rate may be set by the user. The default value is 6 in. The maximum loggingspeed for this combination of sample rate and pulse sequence is 600 ft/hr.
Carbonate depth log. The wait time is set to 2.6 sec. Twelve hundred echoes are thencollected with an echo spacing of 0.32 msec. Total time to acquire 1 PAPs is approximately 6sec.
The sample rate may be set by the user. The default value is 6 in. The maximum loggingspeed for this combination of sample rate and logging speed is 300 ft/hr.
• Expert depth log. Default parameters are the same as for the sandstone depth log mode. Allparameters are editable but are subject to constraints.
6.3.3.2 Station logging modes
During station logging, PAPs are continuously stacked as they are accumulated to improve thesignal-to-noise ratio. New log outputs are periodically computed from the stacked data anddisplayed on the control panel. The station log is terminated when a signal-to-noise ratio of atleast 20 has been attained.
• Sandstone station log. The wait time is set to 3 sec. Three thousand echoes are thencollected with an echo spacing of 0.32 msec. Total time to acquire 1 PAP is approximately 8
sec.• Carbonate station log. The wait time is set to 6 sec. Five thousand echoes are then collected
with an echo spacing of 0.32 msec. Total time to acquire 1 PAP is approximately 15 sec.
• Expert station log. Default parameters are the same as for the sandstone station log mode. Allparameters are editable but subject to constraints.
• Sandstone multiwait time station log. This pulse sequence consists of the following 3 sub-sequences:
1. a wait time of 0.18 sec followed by the acquisition of 300 echoes.
2. a wait time of 0.38 sec followed by the acquisition of 600 echoes.
3. a wait time of 1.2 sec followed by the acquisition of 1800 echoes.• Calibration bottle. This mode is used for the monthly master calibration or for logging the
calibration bottle as a prejob check. The wait time is set to 0.5 sec. Three hundred echoes arethen collected with an echo spacing of 0.32 msec. Total time to acquire 1 PAP isapproximately 0.6 sec.
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6.3.4 Diagnostic channels
The following diagnostic channels are displayed on the control panel. If a signal is outside of thespecified range, the background color on the display changes from green to red.
Noise level. The root mean square (RMS) noise, in porosity units, is estimated for eachsubsequence in the measurement cycle. Therefore, up to 8 values are available depending onthe pulse sequence selected. For multiwait time sequences, the display shows the RMS noise forthe first sub-sequence.
Note that the RMS noise is calculated from the PAPs after stacking. The RMS noise is alsodisplayed on the quality control log.
Signal/noise. This is the signal-to-noise ratio of the stacked PAPs.
Frequency. This is the tool operating frequency in MHz.
Temperature. This is the temperature reading from the sensor located in the CMR sonde. It isused to estimate B0 and for the Curie law correction.
∆B. This is the difference between the temperature estimate of B0 and the Hall probe estimate. If∆B exceeds 1 Gauss (0.1 mtesla), a Larmor frequency search task must be performed toaccurately measure B0.
Voltages. The transmitter peak voltage, regulated and unregulated high voltages are displayed.
6.3.5 Log outputs
Values of CMR porosity, free-fluid porosity, logarithmic mean T2 and signal-to-noise ratio are alsodisplayed on the control panel.
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6.4 Presentations and Formats
6.4 .1 Depth logging - Four tracks with T2-distribution
Bound Fluid Volume (BFV)
(V/V)0 0.3
CMR Free Fluid (CMFF)
(V/V)0.3 0
CMR Porosity (CMRP)
(V/V)0.3 0
Gamma Ray (GR)
(GAPI)0 150
Permeability - CMR (KCMR)
(MD)0.1 1000
T2 Distribution (LC03)
(MS)3 3000
Tension (TENS)
(LBF)10000 0
T2 LOG Mean (T2LM)
(MS)0.1 1000
Bound Fluid Perm
4700
Figure 6.7. CMR four-track presentation with T2-distribution.
The shading between the CMR porosity and the CMR free-fluid curves indicates the bound-fluidvolume. The bound-fluid volume is also presented as a separate curve with porosity increasingto the right. T2-distributions are displayed in track 4 together with the T2 cutoff (solid blue line).
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6.4.2 Depth logging - quality control log
CMR System Gain (CMR_GAIN)
(----)0 1
CMR Temperature (CMR_TEMP)
(DEGF)75 125
Standard Deviation of CMR Porosity
(CMRP_SIG)
(V/V)0.1 0
Standard Deviation of Free Fluid
(CMFF_SIG)
(V/V)0.1 0
Delta B0 (DELTA_B0)
(MTES)-0.5 0.5
Operating Frequency (FREQ_OP)
(KHZ)2260 2310
Gamma Ray (GR)
(GAPI)0 150
Computed GAMMA (GAMMA[0])
(----)0 10
Polarization Correction (POLC[0])
(----)0 10
RMS Noise (RMS_NOISE[0])
(V)5 0
Signal Phase (SPHASE[0])
(DEG)-180 180
Tension (TENS)
(LBF)10000 0
4700
Figure 6.8. Log quality control presentation format.
Track 1 contains the correlation curves and the polarization correction (see Section 6.1.3 for adescription of the polarization correction).
Track 2 contains information relating to the tool operation: signal phase, system gain (this is theinverse of the electronic gain correction described in Section 5.3), sonde temperature, operatingfrequency, ∆B (this is the difference between B0 estimated from the Hall probe and B0 estimatedfrom the sonde temperature, as described in Section 6.2).
Track 3 contains information relating to the precision of the output logs: CMR porosity standarddeviation, free-fluid porosity standard deviation, RMS noise, and the value of regularization(Gamma) used to process the data.
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6.4.3 Station Logging -- single-wait time station log display
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6.4.4 Station Logging -- multiwait time station log display
Figure 6.10. CMR multiwait time station log report.
Three wait times are used for this station log; 1.2, 0.36 and 0.18 sec. T2-distributions arecomputed for each wait time assuming a T1/T2 ratio of 1.0. These distributions are used tocalculate the true T1/T2 ratio (in this case, 2.187). An updated distribution is then computed usingthe true T1/T2 ratio.
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6.5 Log quality control
6.5.1 Operating technique
Tool positioning
The CMR tool must be run eccentered using a bowspring, in-line eccentralizer or a poweredcaliper device. Note: the LDT caliper does not eccenter the CMR tool.
Skid contact with the formation is essential. Knuckle joints must be used when the CMR tool isrun with tools that have standoffs or centralizers (e.g., AIT-H). Tool turners are required indeviated wells. Short-axis orientation hardware is recommended in oval holes.
The CMR skid extends 1 in. beyond the sonde body. When the CMR tool is combined witheccentered tools (e.g. APS or CNT), knuckle joints must be used to prevent undesirablestandoff.
Pulse sequenceSelect the appropriate pulse sequence according to mineralogy. In almost all situations, one ofthe standard modes (carbonate or sandstone) is appropriate.
Maximum logging speeds
The CMR requires slow logging speed (typically 300 to 600 ft/hr). Verify that the winch canoperate at the required speed.
Maximum logging speeds are calculated by the MAXIS based on the pulse sequence and samplerate. The maximum logging speed ensures that a new measurement is acquired during eachsample interval.
Do not exceed the maximum logging speed. If exceeded, there is a possibility that a newmeasurement will not be acquired during a sample interval. When this occurs, log values from theprevious sample frame are written into the current sample frame. This results in “stair stepping”on the log.
Sample rate
• CMR standard resolution logs have a 6 in. sample rate.
• CMR high vertical resolution logs have a 3 in. sample rate.
• When long wait times are used, the sample rate may be increased to 9 in. to increase loggingspeed, provided that the resulting vertical resolution (about 30 in., for 3 level averaging) isacceptable.
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Tool tuning
Correct tool tuning (tune word and Larmor frequency search tasks) is the single most importanttask for running a valid log.
• The tool must be tuned a minimum of three times; (1) immediately before the repeat pass, (2)immediately before the main pass, and (3) at the completion of logging. Display the TWSTand LFST reports on the CMR log print.
• The tool should be tuned adjacent to an interval that has the highest porosity. Ideally, this isthe same interval that will be logged with the CMR.
• Best results are obtained when the tool is moved slowly (up and/or down) during the LFST.The tool should be alongside the porous zones for the duration of the LFST (about 2 min.).If the zone is thin, and there is no danger of tool sticking, the tool can be tuned whilestationary.
• It is desirable (but not essential) that the CMR temperature stabilize before tuning the tool.
Monitor the tool temperature displayed on the control panel. Temperature stabilization takesat least 10 minutes, so it is good practice to first run a depth tie in pass, etc.
Tool temperature usually lags borehole temperature when
◊ the tool is initially at the bottom of the well,
◊ when several intervals are logged that are separated by more than several thousand ft.,and the tool is moved quickly between the intervals.
In these situations, perform an initial tune word search and Larmor frequency search task.Repeat the LFST until the Larmor frequency from two consecutive searches differ by lessthan 3 kHz. This is usually accomplished with 2 or 3 attempts.
• Examples of acceptable and unacceptable LFST results are shown on Figure 6.11, Figure6.12, Figure 6.13 and Figure 6.14. Problems occur in low porosity, in shales and when theinput center frequency is too high or too low.
The LFST must be repeated if there is any doubt about the validity of the result. The tool isconsidered to be adequately tuned when two consecutive LFST results (i.e., “The foundoperating frequency (kHz)”, on the LFST report) agree to within 3 kHz.
• The tool must be retuned if delta B (displayed on the control panel) exceeds 0.1 mtesla (1gauss) during logging.
Pay close attention to delta B when logging wells that have long casing strings. The CMRtends to pick up large amounts of metal debris in these wells.
This information is CONFIDENTIAL and must not be copied in whole or in any part, and should be filed accordingly by the addressee. Itmust not be shown to or discussed with anyone outside the SCHLUMBERGER organization.
This information is CONFIDENTIAL and must not be copied in whole or in any part, and should be filed accordingly by the addressee. Itmust not be shown to or discussed with anyone outside the SCHLUMBERGER organization.
6.5.4 Repeatability
A typical repeat analysis is shown in Figure 6.15. Note that the free-fluid porosity repeatability issuperior to that of the CMR porosity. Also note that the repeatability of logarithmic mean T2
deteriorates with decreasing porosity.
The following conditions degrade repeatability.
• A change in tool orientation between the repeat and main pass, especially in vuggycarbonates. The CMR has a small azimuthal coverage.
• Irregular tool motion, as encountered in “sticky” and rugose boreholes.
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6.6 Log quality display
An example log quality display for the CMR tool is shown in Figure 6.16.
CMR System Gain (CMR_GAIN)
(----)0 1
CMR Temperature (CMR_TEMP)
(DEGF)75 125
Standard Deviation of CMR Porosity
(CMRP_SIG)
(V/V)0.1 0
Standard Deviation of Free Fluid
(CMFF_SIG)
(V/V)0.1 0
Delta B0 (DELTA_B0)
(MTES)-0.5 0.5
Operating Frequency (FREQ_OP)(KHZ)2260 2310
Gamma Ray (GR)
(GAPI)0 150
Computed GAMMA (GAMMA[0])
(----)0 10
Polarization Correction (POLC[0])
(----)0 10
RMS Noise (RMS_NOISE[0])(V)5 0
Signal Phase (SPHASE[0])
(DEG)-180 180
Tension (TENS)
(LBF)10000 0
4700
Figure 6.16. CMR log quality display.
Ensure that the log quality control outputs have the following values.
• The polarization correction depends on wait time. If the correction exceeds 1.10 in zones ofinterest, relog the zone using a longer wait time.
• Gamma and signal phase depend on porosity.
◊ Gamma should be low in high porosity intervals (~ 1). High values (>10) are normal in lowporosity intervals (i.e., shale).
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◊ Signal phase should be relatively constant (+/-10°) in high porosity intervals. Signalphase may be erratic in low porosity (e.g., less than 5 p.u.); this is not symptomatic of atool problem.
◊ When the signal phase is 180°, the curve will jump from the right hand to left hand edge of
the track because (-)180° is equal to (+)180°. This is not symptomatic of a tool problem.
• RMS noise and standard deviation depend on temperature and the amount of stacking. Thefollowing values are for 3 level stacking.
◊ RMS noise should be comparable to the values shown on Figure 6.17.
◊ At 25° C, CMR porosity and free -fluid porosity standard deviations are less than 1.25and 0.5 p.u, respectively.
Both standard deviations increase with temperature. At 175° C, CMR porosity and free -fluid porosity standard deviations are about 3.0 and 1.5 p.u, respectively.
The RMS noise and standard deviations can be decreased by increasing the stacking. Five-
level averaging is recommended for temperatures greater than 140° C.
0
1
2
3
4
20 60 100 140 180
Temperature - °C
R M S N o i s e - V o l t s
Figure 6.17. Plot of RMS noise versus temperature.
• System gain and operating frequency depend on temperature.
◊ System gain varies with temperature and mud conductivity.
System gain is close to 1 in low temperature wells that have fresh muds.
System gain is lower (~ 0.5) in hot wells that have conductive mud. In these wells,system gain typically spikes very low (~ 0.3) in washouts.
◊ Operating frequency changes in 1 kHz steps for each 1.2° C change in temperature.
This information is CONFIDENTIAL and must not be copied in whole or in any part, and should be filed accordingly by the addressee. Itmust not be shown to or discussed with anyone outside the SCHLUMBERGER organization.
7. Interpretation Principles and Applications
7.1 Introduction
CMR interpretation principles are based on the results of lab NMR measurements. The ability toduplicate CMR measurements in the lab is very useful, because it allows a direct comparisonbetween NMR and other core measurements (e.g., porosity, producible porosity andpermeability) for the same sample of rock.
CMR measurements and lab NMR measurements differ in one important respect: NMR porosityfrom lab spectrometers is approximately equal to core porosity and is therefore considered to betotal porosity. On the other hand, the CMR measurement is relatively insensitive to the smallestpores that have fast T2. Because of this, CMR porosity is often less than total porosity. Fieldexperience shows that CMR porosity is equal to total porosity in clean formations but has asignificantly lower value in shaly formations. Apparently, the clay-bound water volume is notincluded (or is at least underestimated) in CMR porosity as indicated in Figure 7.1. Consequently,the total bound-fluid porosity can only be obtained by subtracting the free-fluid porosity from atotal porosity estimate (e.g., nuclear log porosity).
clay
bound
water
capillary
bound
water
producible
water
φtotal
φFF
φCMR
Figure 7.1. In shaly rocks, φ CMR is less than total porosity.
The correlations between NMR measurements and pore size, permeability and producibleporosity were established for core samples that were completely saturated with water. Becauseof the shallow depth of investigation of the CMR tool (about 1 in.), the tool measures a region thatis substantially flushed with mud filtrate and correlations developed for water-saturated rocks aregenerally applicable. In intervals that have poor flushing, the CMR log may have a significanthydrocarbon effect. This can be used to advantage as described in the following sections.
7.2 Pores contain only water (or filtrate)
Theoretical studies of the NMR phenomena predict that T2 in water-saturated rocks is closelyrelated to pore size. Specifically,
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where ρ2 is the surface relaxivity, S is the surface area of a pore and V is the volume of the pore.
T2B is the bulk relaxation of the pore fluid. For water, T2B is approximately 3500 msec and the lastterm in Eq. 7.1 can be neglected. For mud filtrate, T2B may be short (i.e., less than 200 msecs) ifthe filtrate contains paramagnetic ions. In this case, the measured T2 must be corrected for bulk
relaxation. That is,
1
T2
1
T2
1
T2
S
VC B
= −
= ρ 2 , (7.2)
where T2C is the corrected T2.
Since S / V has the dimensions of inverse length, T2 can be rescaled into a pore size (i.e., small
pores have short T2 values and large pores have long T2 values).
Lab NMR measurements confirm that T2 is proportional to pore size; T2-distributions obtained onwater-saturated samples are highly correlated with pore size distributions obtained from othertechniques, such as mercury injection (e.g., see Figure 7.2), or by image analysis on thinsections.
0.1 1.0 10 100 1000 10000
.01 .1 1 10 100
mercury injectionthroat diameter (microns)
T2 (msec)
Figure 7.2. Comparison of T2-distributions (solid line) with throat diameters determined by mercury injection (dashed line) for four shaly sandstone samples.
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The surface relaxivity, ρ2, in Eq. 7.1 is a measure of the rock surface's ability to promote NMR
relaxation. The surface relaxation is primarily due to magnetic field interactions between hydrogennuclei and paramagnetic ions (e.g., iron and manganese) at the rock grain surface. The surfacerelaxation cannot be measured directly; its value is inferred by comparing T2-distributions to pore
size distributions. These comparisons indicate that surface relaxation is reasonably constant inmost sandstones (about 10 microns/sec). The surface relaxivity in carbonates is three timesweaker than for sandstones (about 3 microns/sec).
The NMR estimate of producible porosity is based on an expectation that the producible fluidsreside in large pores, whereas bound-fluids (e.g., capillary-bound and clay-bound waters) residein small pores; hence, a T2 cutoff may be established that divides the total porosity into bound-fluid and free-fluid porosity (see Section 1.1). The T2 cutoff was determined by measuring thevolume of fluids produced by spinning core samples in a centrifuge. Cutoff values of 33 and 100msec for sandstones and carbonates, respectively, result in the best agreement between free-fluid porosity and centrifuged water volume. The different cutoffs for sandstones and carbonatesreflect their difference in surface relaxivities.
Under reservoir conditions, the capillary-bound water volume depends upon the capillarypressure as well as the pore size distribution of the rock. The capillary pressure varies with fluiddensities and height above the water table. The T2 cutoffs quoted above are appropriate for a100 psi air-brine capillary pressure. T2 values should be adjusted if the reservoir capillarypressure is significantly different from 100 psi. The new cutoff can be estimated by multiplying thecutoff by the ratio (100/capillary pressure). For example, for a capillary pressure of 50 psi in asandstone reservoir, the appropriate cutoff would be 66 msec.
The CMR permeability estimate is based on an expectation that permeability increases with bothporosity and pore size. NMR and brine permeability measurements on core samples haveresulted in several empirical correlations. The following permeability models are included in theMAXIS and Geoframe software:
K a TCMR 2,log CMRb1 c1= ( ) ( )1 φ , (7.3)
and
K aCMR 2FF
BFCMR
c2
b2
= ( )
( )104φ
φ φ . (7.4)
In the above, relaxation time is in milliseconds and porosity is in decimal units. The default valuesfor the multiplicative factors and exponents are: a1=4, a2=1, b1=2, b2=2, c1=4, c2=4. The two
models represented by Eqs. 7.3 and 7.4 are referred to as the SDR and Timur/Coates models,respectively.
It should be noted that both producible porosity and permeability are expected to increase withpore throat diameter, whereas NMR responds to pore body diameter. Fortunately, thethroat/body ratio is approximately constant for most sandstones. However, some variations canbe expected in vuggy carbonates, which results in poorer correlations.
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7.3 Pores contain water and oil
When two or more fluids occupy the pore space of the rock, the surface relaxation mechanism isonly effective for the fluid that is in contact with the grain surface. The nonwetting fluid relaxes atits bulk rate.
T2-distributions for water-wet rocks are a superposition of two T2-distributions: (1) a distributionoriginating from the water that depends on the S/V distribution of the water, and (2) a distributionoriginating from the oil that depends on the bulk relaxation of the oil. For example, Figure 7.3shows T2-distributions for a rock sample completely saturated with water, and the rock samplesaturated with both water and Soltrol. The T2-distribution for bulk Soltrol is also shown. Whenthe pores contain both water and Soltrol, the distribution is bimodal with a short T2 water peakand a long T2 Soltrol peak. This assignment is based on the observation that the short T2 peakis similar to the distribution obtained on the water-saturated rock, and the long T2 peak is close tothe T2 of bulk Soltrol. These measurements indicate that Soltrol is not wetting the rock surface.
Figure 7.3. T2-distributions for a core sample 100% saturated with water (dash),bulk Soltrol (dotted), and the core sample with 28% Soltrol and 72% water (line).
Soltrol is a refined oil that has a narrow T2-distribution. In contrast, unrefined oils have broad T2-distributions that span several decades as a result of the mixture of hydrocarbon types within
each crude (see Figure 7.4). Crude oil T2-distributions frequently consist of a long T2 peakoriginating from the most mobile hydrogen nuclei and a tail to shorter relaxation times from nucleiwith more restricted motions. As the hydrogen chain length increases, viscosity increases, andrelaxation times shorten.
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Figure 7.4. T2-distributions for 31 bulk oil samples from the Belridge field,California. The distributions are plotted in order of increasing viscosity, from top left to bottom right. Sample number, logarithmic mean T2 (msec) and viscosity (centipoise) are shown for each sample.
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Oil with higher viscosity is predominantly in the bound-fluid range unless it is extremely viscousand has T2 shorter than 2 or 3 msec, which is below the detection threshold of the CMR tool. Inthis case the oil volume is not included in the CMR porosity.
Viscosity (cp)
1
10
100
1000
1 10 100 1000 10000
T2,log
(msec)
Figure 7.7. Logarithmic mean T2 (T 2,log ) of bulk oil is inversely proportional to viscosity.
A summary of the pore fluid types included in the CMR porosity measurement is shown in Figure7.8.
crude oil
visc >1000 cp
clay
bound
water
producible
water
φtotal
φFF
φCMR
capillary
boundwater
crude oil
visc 40 to
1000 cp
crude oil
visc <
40 cp
Figure 7.8. Summary of pore fluid types included in φ CMR
and φ FF (when a T2 cutoff of 33 msec is used).
When large volumes of oil are present in the flushed zone, permeability estimation using the SDRequation is unreliable. If the oil is low to medium viscosity (such that the free-fluid and bound-fluidporosities are unaffected), the Timur/Coates equation is expected to give reasonable results.
The CMR T2-distributions can be used to identify oil zones when the oil and water signals arewell separated (e.g., the situation shown in Figure 7.5). The T2 peak associated with the oilsignal can be used to estimate the oil viscosity. When light oil is present in shaly sands, T2-
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distributions typically extend to longer times than those for 100% water-saturated rocks. This hasproved valuable for finding oil zones where conventional interpretation methods are unreliable. Atthe other extreme, very heavy oil and bitumen can be identified by CMR porosity readings thatare much lower than nuclear porosity logs (cautionary note: this also occurs in shaly rocks and
gas zones).
7.4 Pores contain gas
When gas is present, the CMR porosity reads low as a result of two effects:
• The CMR tool is calibrated to read correctly for pore fluids that have a hydrogen index of 1.0(similar to the neutron tool). The hydrogen index of gas is significantly less than 1.0.
For CMR logs run with long wait times, the signal amplitude from the gas is equal to thevolume of gas times the hydrogen index of the gas.
• Gas has long T1 values, ranging from 3 to 7 sec (depending on formation temperature andpressure). Conversely, T2 for gas is short because of diffusional relaxation. As a result
T1/T2 ratios are very high - typically much higher than the input ratio used for the polarizationcorrection. Therefore, logs run with typical wait times (1 to 3 sec.) are not adequatelycorrected for incomplete polarization.
Gas is a strongly nonwetting fluid. For this reason, gas is unlikely to be in the small pore spaces
of the rock. Therefore, a gas effect is expected for both φCMR and φFF, but not for φBF. Pore fluids
included in the CMR log outputs are shown in Figure 7.9, when both gas and water are present.
clay capillaryboundwater
ga sboundwater
φCMR
φtotal
φFF
produciblewater
Figure 7.9. Summary of pore fluid types included in φ CMR
and φ FF when gas and water are present.
Because of the gas effect on φCMR , φFF and mean T2, permeability can only be estimated usingthe Timur/Coates model and by incorporating other log data. For example,
K a2
BF
c2
b2
= ( )
( )104
φ
φ
φ , (7.5)
where φ is a gas-corrected porosity (e.g., crossplot or ELAN effective porosity).
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7.5 CMR applications
The CMR measurement has broad applications since effective porosity, producible porosity,bound-fluid porosity and permeability estimates are required for all producing formations. In
addition, CMR logs have good vertical resolution with 9 in. beds fully resolved at slow loggingspeeds.
CMR porosity applications
• Total porosity independent of mineralogy
In clean, liquid-filled formations, φCMR is a measure of total porosity that is obtained withoutspecifying mineralogy.
• Effective porosity in shaly formations
In shaly formations, φCMR is less than total porosity because contributions from the smallestpore sizes are not included in the measurement. Although the pore size limit is not exactly
defined, field experience suggests that the clay-bound water is not included in φCMR. Therefore,φCMR is approximately equal to effective porosity. Furthermore, the volume of clay water canbe estimated by subtracting φCMR from a total porosity measurement (from nuclear logs, forexample).
• Gas zone identification
φCMR reads low in gas zones - much lower than Litho-Density porosity. The CMR gas effectindicator is especially useful in shaly reservoirs as the neutron and density logs do notalways “cross over” in these formations.
• Sourceless porosity
φCMR is obtained without using a radioactive source.
T2 applications
• Pore size distributions
In water-saturated rocks, pore size distributions are estimated from T2-distributions. Thedistributions are used to determine bound-fluid and free-fluid porosity. In carbonates, vuggyporosity is identified by long components (~ 1000 msec) in the distribution.
• Permeability estimation
Logarithmic mean T2 is used in the SDR model to estimate permeability.
• Oil volume and viscosity
In partially oil-saturated rocks that are predominately water wet, oil volume and viscosity canbe estimated from the T2-distribution provided the oil and water signals are separated. Oilvolume is obtained by integrating the area under the oil signal. Oil viscosity is estimated fromthe T2 peak of the oil signal.
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Free-fluid porosity applications
• Producible porosity
φFF is a producible porosity estimate.
• Permeability estimation
φFF is used (together with φCMR and φBF) in the Timur/Coates model to estimate permeability.
• Reserve estimation
In nonheavy oil reservoirs that produce without a water cut, the volume of oil is equal to φFF.The CMR tool is shallow reading, so the free-fluid porosity is actually a mixture of oil and mudfiltrate. However, the volume of mud filtrate is equal to the volume of flushed oil, as shown inFigure 7.10.
clay
boundwater
capillary
boundwater
clay
boundwater
capillary
boundwater
crude oil
(visc < 40cp)
mud
filtrate
crude oil
(visc < 40cp)
Invaded
Zone
Invaded
Zone
Non
φFF
φFF
Figure 7.10. Free-fluid porosity in the invaded and noninvaded zones,for an interval that does not contain producible water.
• Water-cut prediction
For reservoirs that contain producible water, φFF is greater than the oil volume from a water
saturation calculation. Figure 7.11 shows that producible water can be predicted even thoughthe CMR tool measures the invaded zone, as the free-fluid porosity is numerically equal inboth the invaded and noninvaded zone.
clay
bound
water
capillary
bound
water
clay
bound
water
capillary
bound
water
crude oil
(visc < 40cp)
mud
filtrate
crude oil
(visc < 40cp)Invaded
Zone
Invaded
Zone
Nonproducible
water
Water Vol Oil Vol
φFF
φFF
Figure 7.11. Pore fluid types in a nonheavy oil reservoir that contains producible water.
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• Steam flood efficiency in heavy oil reservoirs
In heavy oil reservoirs, φFF is equal to the producible water volume (Figure 7.12). Intervalswith high producible water respond poorly to steam flooding, since the steam tends to migrateaway from the wellbore and localized heating, required to decrease the oil viscosity, is not
achieved.
clay
b o u n d
w a t e r
capil lary
b o u n d
w a t e r
m u d
f i l t r a t e (visc > 40 cp)
crude oil
(visc > 40 cp)
crude oilcapil lary
b o u n d
w a t e r
clay
b o u n d
w a t e rw a t e r
producible
Invaded
Zone
InvadedZone
No n
FF
FF
Figure 7.12. In a heavy oil reservoir, the free-fluid porosity is equal to the producible water volume.
• Remaining oil volume estimation.
φFF is used to estimate remaining oil volume for reservoirs that have been waterflooded andare now under consideration for tertiary recovery schemes. This technique involves addingmanganese EDTA to the mud system, thus reducing the T2 of the mud filtrate below thethreshold value for computing the free-fluid porosity. It is assumed that the oil volume in theinvaded zone is equal to the oil volume in the noninvaded zone (i.e., the filtrate flushingefficiency is comparable to the water flood efficiency). In this case the residual oil volume (i.e.,
the remaining oil volume) is equal to the free-fluid porosity (Figure 7.13).
clay
bound
water
capillary
bound
water
mud filtrate
with EDTA (visc < 40 cp)
remaining oil
(visc < 40 cp)
remaining oil
water
producible
Invaded
Zone
InvadedZone
No n
φFF
capillary
bound
water
clay
bound
water
Figure 7.13. φ FF estimates the remaining oil volume after the mud filtrate signal is eliminated by adding manganese EDTA to the drilling fluids.
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87
A. CMR Hardware Specifications and Ratings
Equipment associated with the CMR tool is described in Table 1. CMR physical specificationsare listed in Table 2. Tool performance and operating specifications are listed in Table 3. Tool
shipping data are listed in Table 4.
Component Temp(°F)
Pressure(kpsi)
Hole Size (in.)Min Max
Diameter(in.)
Weight(lbm)
Length(in.)
CMR-AA 350 20 * * 5.3 292 169.9
EME-F 350 20 7.785 21 6.6 35 0
ILE-D 350 20 6.5 13 3.625 118.5 96.0
AH-178 350 20 - 3.625 22 11.9
AH-190 350 20 - 3.625 22 11.9
ILE-F 350 20 6.5 13 3.625 118.5 96.0* depends on choice of EME or ILE
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88
Performance Ratings:
Logging Speed STD: 600 ft/hr in sandstone mode; 300 ft/hr in carbonate mode
HIRS: 200 ft/hr in sandstone mode; 100 ft/hr in carbonate mode
Depth of Investigation 0.5 in. Blind Zone (2.5% point)
1.0 in. Radial 50% point (most often quoted D.O.I.)1.5 in. Radial 95% point
Vertical Resolution 6 in. measurement aperature;
9 in. vertical resolution, HIRS logging with 3-level averaging
18 in. vertical resolution, STD logging with 3-level averaging
φCMR 1.0 pu @ 25°C, 3 level averaging
φFF 0.5 pu @ 25°C, 3 level averaging
Nominal Raw S/N 25 - 27 db
Pulse-to-Echo Spacing 160 µs
Operating Ratings:
Temperature -25°C to 175°C
Pressure 20 kpsi
Mud Type & Salinity Unlimited
Telemetry & Power Requirements:
Telemetry DTS (500 kbits/s)
Telemetry Bandwidth 1.6 kbits/s (min.: Sandstone depth log without raw echoes)
14.0 kbits/s (max.: Carbonate depth log with raw echoes)
Power 30 watts (AC MAIN); 75 watts (AC AUX)
Table 3. CMR-A performance and operating specifications.
Cartridge (CMRC-A) Sonde (CMRS-A)
Shipping Length
(including thread protectors)
11.05 ft (132.54 in.) 6.02 ft (72.23 in.)
Shipping Weight
(including thread protectors)
213 lbs. 140 lbs.
Restrictions for all AirShipments
None CMRS sonde must be shipped in theCMRS Shipping Box (H549555). Boxis 6.6 ft long and weighs 135 lbs.
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89
B. Safety, Handling and Transportation
Be aware of electrical and mechanical sources of hazards in the tool.
Electrical hazards
• The cartridge and sonde upper head pins contain voltages sufficient to shock personnel.Upper head pins #1 and #4 contain the 250 VAC power for the tool.
• Securely ground all equipment during test and repair. Suitable ground jumpers (with a clip ateach end) can be made from the materials shown in Table 1-1.
Table 0-1 Ground Clip Jumper Components
Quantity Part Num-ber
Description
2 B-09100 Battery Clip
Asrequired
H-031716 #11-1 Flexible wire
12 Inches E-019888 Shrinkable tubing
2 E-08630 25 Amp Solder Lug
Sonde power is delivered to the upper head of the tool string on cable wires 2, 3, 5, 6 witharmor return. This is the standard sonde power path and the use of armor return makes it dou-bly important that the tool body be adequately and independently grounded with a jumper.This is because, if for some reason, the armor return path became open while sonde powerwas on, the tool housing would rise to the sonde head voltage. Within the telemetry cartridgethe power on cable wires 2, 3, 5, 6 are joined and passed to the tools on head pin 2 and re-
turned on pin 10. Sonde head voltage can vary between 200 and 350 Vrms depending onthe length of the cable.
Mechanical hazards
• The bellows used in the Antenna Cradle Assembly of the CMRS-A sonde can easily bepunctured when cleaning this area of the sonde. Be very careful if using a screw driver orpunch to remove any mud that may be caked in this area.
• The Antenna Cradle Assembly of the sonde is pressure balanced and is therefore filled withoil. The oil may be under pressure so be very careful when removing the filler plugs from theassembly.
• DO NOT place the CMRS-A sonde next to a tool that uses sodium iodide crystals or photo-multiplier tubes. The strong magnetic field may permanently damage the tool.
• The accelerometers, inclinometers and magnetometers in the dipmeter tools (MEST, FMS,GPIT, OBDT, HDM) may become magnetized if transported too close to the permanent mag-nets in the CMRS sonde.
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90
Danger to personnel
• Never work alone on a tool when it is powered up.
• Stand on a dry floor or a rubber mat when possible.
• Avoid touching the tool when it is powered up. If touching the tool is necessary, do not touch
more than one part of the tool at a time.
• Follow proper lifting procedures when handling the tool.
• Nickel Chloride crystals are used to make the liquid solution for topping off the “CalibrationFixture.” Be very careful when mixing the NiCl crystals with distilled water. The NiCl materialis irritating to the skin, eyes and mucous membranes. It is also harmful if swallowed. Whenstoring the Nickel Chloride, the three labels shown in Figure 3 should be affixed to the con-tainer.
In addition to the standard electrical hazards of high voltage (250 VAC cartridge power and 200-600 VDC in the sonde power system), the CMRS contains two extremely powerful magnets thatrequire special handling. The primary areas of danger from the high static magnetic fields are:
• Pacemakers
The high magnetic fields surrounding the sensor could conceivably interfere with the sensitiveelectronics used in some devices.
• Flying objects
Magnetically permeable items (most commonly used metal instruments), such as spannerwrenches, spring to life when the tool is brought near. A finger or hand between the waywardspanner and the magnet could be severely injured.
Also, if the magnet is being carried from one place in the shop to another and you walk tooclose to a metal object, i.e., file cabinet, your hand could be pulled up against the cabinet.
• Loose magnets• The magnets themselves can become ambulant during removal or installation (a rare occur-
rence). The biggest danger occurs if the magnets come close to each other, as they will pivotand snap together with alarming speed. This could cause severe injury if a hand or fingerwere pinched by the magnets. SFTs may be required.
Keep loose magnets at least three feet apart.
• Navigation
If the tool or magnets are transported in a carrier that uses compasses as navigational aids,special shielded carry cases that meet government guidelines are be required.
Danger to equipment• Be sure that all power to the tool is off before uncoupling the CMRC-A from the telemetry
cartridge, CMRS-A sonde, or any test cable.
• Extreme care should be taken when removing any multi-layer ceramic modules and pin gridarrays of the DHC and the CMRC-A. Pull the circuit evenly and slowly out of its socket using
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91
special tools such as E047413 (Advanced Interconnections Universal Push-off Blade TypeExtraction Tool)
• Follow the SMC (Surface Mounted Component) maintenance procedures as documented inthe maintenance manual.
• When soldering, respect the following recommendations:
◊ Use a low voltage (24V output) soldering iron.
◊ Use a solder sucker to clean up IC leads.
• Do not energize the cartridge with any sub-chassis removed from the cartridge or sonde.
• Because of the large quantity of electronic components mounted on the circuit boards and thechassis of the CMRC-A cartridge and the CMRS-A sonde, it is best to turn the cartridgepower OFF before attaching any test equipment to the terminals. This will reduce the possi-bility of short-circuits. When in doubt, solder-tack a short length of wire to the terminal beforeattaching the test equipment.
• Do not scratch the protective coating on the quartz windows of the programmable compo-
nents, such as EPROM, EPLD and PAL.
• The Antenna Cradle Assembly oil level must be checked prior to every job. If the assemblybecomes low on oil, the Antenna could be damaged.
CAUTION
Use only DC-111 on O-Rings. All other grease that has graphite, teflon or other filler should never be used.
These other fillers will allow water to seep under the O-Ring.
Other hazards
The static magnetic field created by the magnets can cause damage to:
• Analog watches;Do not wear your watch when working on the sonde as the magnetic field created by themagnets is large enough to ruin a watch.
• Magnetic data tapes or disks;
The magnetic field created by the magnets is strong enough to wipe data tapes or disksclean.
• Credit cards;
The magnetic strips used on credit cards and ATM cards can be erased by the magnetic fieldcreated by the magnets.
Special Shipping InstructionsThe current International Air Transport Association's (IATA) “Dangerous Goods Regulations”document defines a magnetized material as any material, when packed for air transport, that has amagnetic field strength of 0.159A/m (0.002 gauss) or more at a distance of 2.1 m (7 ft) from anypoint on the surface of the assembled package.
This regulation also governs the loading of magnetized materials in aircraft. This includes;
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92
1. Magnetized material must not be loaded in such a position that it will have a significant effecton the direct-reading magnetic compasses or on the master compass detector units.
2. The minimum stowage distance of the magnetized materials from the aircraft compasses orcompass detector units will depend upon the intensity of the magnetized materials fieldstrength and varies from 1.5 m (5 ft) for those materials which just meet the threshold level of
the magnetized material definition (see “1” above), to 4.6 m (15 ft) for materials which pos-sess the maximum field strength permitted;
a. 0.418 A/m (0.00525 gauss) at 15 ft. or,
b. produces a magnetic compass deflection of 2 degrees or less at 15 ft.,
• multiple packages may produce a cumulative effect.
1. For carriage by aircraft, any package that has a magnetic field of more than 0.418 A/m(0.00525 gauss) at 15 ft. or, produces a magnetic compass deflection of more than 2 degreesat 15 ft. from any surface of the package, is considered “Forbidden” and must not be shippedby air freight. It must be shipped by ground transportation.
NOTE
Some pressure housing used on tools are made of material that may become magnetizedafter running in a well.
A shipping container, CMRS Shipping Box, (H549555) has been designed which complies withIATA requirements. All “air” shipments must use this container.
IMPORTANT
Do Not discard this shipping container. It is reusable.
The magnetic shield located inside the CMRS Shipping Box is made of iron and could causecompass deviation even though it does not emit a magnetic field and it does meet all IATA re-
quirements.
When shipping the sonde by helicopter, if the shipping box is too large to be placed in thehelicopter then the magnetic shield should be removed from the box and placed directly over themagnets on the sonde.
The label shown in Figure 1 must be placed on the shipping box (or on the magnetic shield ifbeing shipped by helicopter) in several places so that it is clearly visible from all directions. Inaddition, a “Dangerous Goods Manifest” must be completed and provided to the courier. Anexample of the manifest is shown in Figure 2.
Surface shipment does not require any special container as there are no special handling require-ments for magnetic material by D.O.T.
The latest information on shipping dangerous goods related to magnetics is found in IATA“Dangerous Goods Regulations”. Each district that will be shipping tools by air freight (includinghelicopter) should have a set of the regulations available. The regulations are revised and re-issued annually. There are several places from which the regulations may be obtained. Two arelisted below:
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93
Labelmaster - Telephone 1-800-621-5808.
Figure 1. Label that must be applied to the shipping container when magnetic material is being shipped by air freight. The minimum size
of the label is 110 cm X 120 cm.
In summary, the shipping instructions include:
1. Sonde must be shipped in CMRS shipping container.
2. Magnetic labels must be placed on the shipping container.
3. A Dangerous Goods Manifest must accompany the shipment.
As can be seen in Figure 2, the manifest must include:
◊ Proper Shipping Name which is “Magnetized Material”.
This information is CONFIDENTIAL and must not be copied in whole or in any part, and should be filed accordingly by the addressee.It must not be shown to or discussed with anyone outside the SCHLUMBERGER organization.
This information is CONFIDENTIAL and must not be copied in whole or in any part, and should be filed accordingly by the addressee.It must not be shown to or discussed with anyone outside the SCHLUMBERGER organization.
This information is CONFIDENTIAL and must not be copied in whole or in any part, and should be filed accordingly by the addressee.It must not be shown to or discussed with anyone outside the SCHLUMBERGER organization.
C. Mud Doping Procedures forResidual Oil Determination
General procedures
• Manganese can be added to the drilling mud to shorten the T2 of the filtrate and separate thefiltrate and oil signals. When the signals are separated, the volume of oil can be quanitified byapplying a cutoff to the T2-distribution.
**** Note: use MANGANESE, not magnesium ****
• Manganese EDTA is preferred for shaly sandstones and bentonitic drilling muds. Manganesechloride (MnCl2) is cheaper, but the manganese exchanges with other ions (usually sodium)on clay surfaces. See Paper Q, 1995 SPWLA Symposium, Paris.
• Manganese additives can change the mud properties. It is important to test a sample of mudbefore adding it to the entire mud system.
• The required manganese concentration is partly determined by the crude oil T2-distribution at
formation temperature. The oil may have significant signal amplitude at low T2.
The T2-distribution can be measured on a sample, or estimated from the oil viscosity and b yusing the crude oil distributions shown in Section 7.
The oil T2-distribution is also important for determing the wait times for logging, which shouldbe sufficiently long for complete polarization. Station logging is used when long wait times arerequired and to improve the precision of the CMR measurement.
• A sample calculation for determining the concentration of manganese is shown below.
The concentration depends on formation temperature and whether manganese EDTA or man-ganese chloride is used.
• The T2 of a doped filtrate sample can be measured with the CMR tool. Also, compare theamplitude of the filtrate signal to the amplitude of the calibration bottle signal (the manganesemay shorten the filtrate T2 below the sensitivity of the CMR). The flitrate sample must besufficiently large to fill the CMR sensitive volume (use a plastic bottle similar in size to themaster calibration bottle).
• The initial spurt loss is responsible for the majority of filtrate invasion. Diffusion is too slow foreffective invasion. It is necessary to add the manganese solution prior to drilling the zone ofinterest. A reasonable overbalance is required (~ 100 psi). On the other hand, a large over-balance (> 500 psi) can cause viscous stripping which results in misleadingly low values ofoil volume.
• Consult with the client to determine optimum mud properties and drilling procedures. Logging
for residual oil determination requires careful pre job planning.
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Example calculation
The following example calculation determines the amount of manganese EDTA required to shortenthe fitrate T2 to 10 msec, at a temperature of100° C.
• Figure C.1. shows T2 versus temperature, for various manganese concentrations.
1
1 0
1 0 0
0 5 0 1 0 0 1 5 0
T 2
( m s e c )
T (C)
0.1 moles/liter
0.01 moles/liter
0.02
951030-02
0.05
Figure.1. Filtrate T2 versus temperature for various manganese concentrations. (Chart is for manganese EDTA solutions.
See Figure.2. for manganese chloride solutions).
• At 100° C, a manganese concentration of 0.05 moles per liter of mud is required for a T2 of 10msec.
• Managnese is available in the form of MnCl2.4H2O. Note the four waters of hydration, whichmust be accounted for when weighing the solid.
MnCl2.4H2O <=> 198 grams/mole
• EDTA is available as Na2.EDTA.2H2O.
Na2
.EDTA.2H2
O <=> 374 grams/mole
Note: A 20% excess of EDTA is required to prevent precipitation of 2Mn.EDTA.
• For each liter of mud add:
10 grams of MnCl2.4H2O and 22 grams of Na2.EDTA.2H2O (this includes a 20% excess).
• 1 barrel is equal to 159 liters, for each barrel of mud add:
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1.6 kg of MnCl2.4H2O and 3.5 kg of Na2.EDTA.2H2O (this includes a 20% excess).
• Figure C.2. shows T2 versus temperature, for various manganese concentrations. Use thischart if manganese chloride is added to the mud.
24
28
20
16
10 20 30 40 50
Temperature (C)
T 2 ( m s e c )
0.00104 moles/liter
0.00077 moles/liter
Figure 2. Filtrate T2 versus temperature for various manganese concentrations. (Chart is for manganese chloride solutions.
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99
D. CMR Signal Processing Algorithms
CMR Spin Echo Pulse Sequence
A very brief discussion of the pulse sequenceused by the CMR is given here. Other sections of thisdocument should be referred to for more detail.
The CMR tool makes pulsed NMRmeasurements at frequencies close to 2 MHz by usingthe Carr-Purcell-Meiboom-Gill (CPMG) pulse sequenceto produce wave forms consisting of hundreds tothousands of spin echoes. At the end of each CPMG,the proton magnetization is practically zero. Therefore,each CPMG must be initiated by a wait time. Duringthe wait time, the magnetization is allowed to recover
towards its equilibrium value in the magnetic fieldproduced by a permanent magnet in the tool. Followingthe wait period, which for depth logging is typicallyabout a second, a 90-degree radio frequency pulse isapplied. This pulse rotates the magnetization vector intothe plane transverse to the direction of the magneticfield. Following the initial 90-degree pulse, a sequenceof evenly spaced 180-degree pulses is applied at oddmultiples of the Carr-Purcell time ( t cp), e.g., at the
times, t cp , 3t cp ,L , (2 J −1)t cp . A set of J spin echoes
at times, 2t cp , 4t cp ,L , J × 2t cp , is produced. The echo
spacing, 2t cp , for the CMR tool is nominally set at
320 µ sec.
The basic unit of measurement is a phasealternated pair (PAP) of CPMG wave forms. A PAPwave form is computed from two successive CPMGs.The two CPMGs have identical pulse sequences exceptthat the phases of the initial 90-degree radio frequencypulses are shifted with respect to each other by 180degrees. Subtraction of the two CPMGs results in aPAP spin-echo wave form. This procedure removesbaseline shifts and antenna ringing effects that can beproduced by the 180-degree pulses.
The Signal Processing Problem
The decay of the envelope of a CPMG
spin-echo sequence in a rock can be characterized by an
intrinsic T 2-distribution, P(T 2 ), of single exponential
decays. This distribution accounts for the proton spin
relaxation produced by spin-spin interactions with
magnetic impurities on the rock pore surfaces. Under
some plausible assumptions, the decay time distribution
of a rock can be shown to be isomorphic to its pore size
distribution. Inasmuch as all of the CMR log quantities
of interest are computed from this distribution, theestimation of P(T 2 ) in the presence of random noise
defines the signal processing problem. Since the decay
times in rocks can span several decades, it is also useful
to define the logarithmic distribution, Pa (logT 2 ) ,
which is used to display the T 2-distributions on a
logarithmic scale. The two distributions are related
mathematically by
P(T 2 ) =cPa (log T 2 )
T 2, (1)
where c = (ln10)−1 . One of the challenges of the signal
processing is that the signal-to-noise ratios (SNR)during logging are frequently less than one.
Formulation of the Problem
The raw CMR spin-echo signals are acquiredby a phase sensitive detector (PSD) in two channels.The acquired signals are 90 degrees out of phase withone another, but the signal phase with respect to areference signal in the tool is unknown. Apreprocessing algorithm estimates the signal phase and
then transforms the raw data into "in-phase," ˜ A j(+ ) , and
"quadrature," ˜ A j(− ) ,
channels. The transformed quadrature
channel, which contains only tool electronic noise, isused to estimate the tool rms noise on a single echo foreach wave form that is processed.
The T 2 decay time distribution, P(T 2 ), obeys
a Fredholm integral equation of the first kind. That is,the signal processing problem requires solution of theintegral equation,
˜ A j(+ )
= dT 2 P(T 2 ) f (W ,T 1a )exp(− j∆T 2a
)
T min
T max
∫ + N j (2)
for j = 1,2,L , J , where ˜ A j(+ ) are signal-plus-noise
CPMG spin-echo amplitudes of the j − th echo. The
function, f (W , T 1a ) = (1− exp( −W T 1a
)) , is a polarization
correction. It accounts for the incomplete recovery of the magnetization during the wait period ( W ) that
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100
precedes each CPMG sequence. In Eq.2, the inter echospacing is denoted by ∆ . The additive thermal noise( N j ) is zero mean uncorrelated Gaussian with known
statistical properties (i.e., < N j > = 0 and
< N j N k > = ψ δ j ,k where ψ is the rms noise on a
single echo. Angular brackets are used here to denotestatistical averages. At room temperature ψ ≈ 5 p.u.
for an echo on a single PAP. In practice, the noise isreduced by stacking (averaging) PAP wave forms. The
rms noise can be reduced, ideally, by a factor N r if
N r PAP wave forms are averaged. The vertical
resolution of the log is determined by threeinterdependent factors. These are: (1) the totalmeasurement time to acquire a PAP wave form, (2) thenumber of PAP wave forms that are averaged for eachset of new log outputs, and (3) the logging speed.
The contribution of the mud filtrate to theobserved relaxation can be accounted for by a wellsitemeasurement of the filtrate relaxation time (T mf ) and
by defining apparent relaxation times, e.g.,
(T 1a )−1 = (ξ T 2 )−1 + (T mf )−1,
(T 2a )−1 = (T 2 )−1 + (T mf ).−1
(3)
In Eq. 3, we have made use of an empirically basedrelationship, i.e., T 1 = ξ T 2 , that relates the intrinsic
T 1 and T 2-distributions in a rock sample for
measurements made in the 2 MHz frequency range.Laboratory experiments were conducted at SDR to study
the parameter, ξ , that represents the T 1 / T 2 ratio. Theratios were found to vary from sample to sample in therange from roughly 1 to 3. The experimental data baseconsisted of 105 samples from a wide range of lithologies which includes carbonates, sandstones,diatomites and shales.
The simplest CMR pulse sequence consists of repetitions of PAP spin-echo wave forms each beinginitiated by a single wait time (W). The spin echo dataobtained from single wait time pulse sequences does notcontain any information about the T 1 / T 2 ratios of the
rock formations being logged. During single wait time
logging anassumed
nominal value of the ratio is, bynecessity, used by the signal processing. For example, anominal value, ξ 0 ≈ 1.5, has been used in sandstones.
It has been shown that using single pulse waittime logging involves an uncontrolled approximation.The root of the problem is the variability of trueT 1 / T 2 ratios ( ξ ) in rocks. The uncontrolled
approximation is the use of assumed ratios in the signal
processing that are not equal to the true ratios. Thisassumption can lead to significant accuracy errors in theCMR log outputs in some logging environments. Theproblem is amplified in high porosity rocks with longT 1 relaxation times (many carbonates). In rocks with
short decay times (many shaly sands) single wait time
depth logs are accurate and multi-wait time logging isnot necessary. The accuracy problem can be eliminatedby using multiple wait time CPMG pulse sequences. Ina later section, multiple wait time pulse sequences arebriefly discussed.
Discretization of the Signal, WindowSums and Maximum Likelihood Estimation
The next step is to discretize the integral inEq. 2 by replacing the integral by a summation,
˜ A j
(+) = al
f l
l=1
N s
∑ exp(−j∆
T 2a,l) + N j , (4)
where it is assumed that the signal has N s spectral
amplitudes al
with intrinsic relaxation times T 2,l
which are equally spaced on a logarithmic scale in theclosed interval (T min,T max ). Note that solution of the
multi-exponential model is numerically feasible becausethe relaxation times are fixed. It follows from thediscretization that al ≡ P(T 2, l )δ
l, where δ
lis the width
of an integration trapezoid centered about T 2,l. Thus,
estimation of the decay time distribution is reduced to
determination of the spectral amplitudes ( al) in Eq.4.The J individual spin-echoes in a PAP wave
form are highly redundant. For example, in depthlogging mode where each PAP normally consists of 600 or 1200 echoes, the marginal independence of theindividual echoes is exploited to reduce the J spinechoes to N w = 5 "window sums." The window sums
are obtained by summing the ˜ A j(+ ) over
non-overlapping windows. It has been shownmathematically, that the window sums contain the sameinformation as the original data. The window sums havedifferent sensitivities to the decay times in thespectrum. For example, the window sum obtained from
the first window is sensitive to all the spectralcomponents whereas the window sum computed fromthe last window is sensitive only to the slowly decayingcomponents. An attractive feature of this data reductionscheme is its simplicity. Also processing of thewindow sums instead of the original J spin echoesreduces the processing time by a factor proportional to
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101
Unbiased estimates of the spectral amplitudesare obtained by minimizing the negative logarithm of the maximum likelihood function for the window sums.Specifically, the maximum likelihood estimates areobtained by minimizing
− ln L =( ˜ I m − I m{a
l})2
2ψ [ N m +1 − N m + δ m,1]m=1
N w
∑ +γ
2ψ al
2
l=1
N s
∑ , (5)
with respect to al
subject to a positivity constraint
(i.e., al
≥ 0). In Eq.5, the ˜ I m are the window sums,
which are random variables whose expectation values,
I m {a
l} , are linear functions of the spectral amplitudes.
The quantities N m and N m +1 are the echo numbers of
the left and right endpoints of the m − th window andδ m,1 is the familiar Kronecker delta function. The last
term suppresses noise artifacts in the solutions. Theparameter γ is called a regularization parameter.
It has been shown that minimization of Eq.5 isequivalent to an expansion of the T 2 -distribution in
terms of the non-null space eigenfunctions of a highlyrank deficient linear operator that can be obtained bydifferentiation of Eq.5. The eigenfunction analysis alsoshows: (1) why only a few window sums are requiredfor the estimation of P(T 2 ) and (2) why the estimated
distributions depend only slightly on the exact positionschosen for the window boundaries. A nice feature of theprocessing is that the logs have negligible dependence
on the regularization parameter for a relatively widerange of values of γ . A mathematical algorithm is
used to compute, based on the input log data, optimalvalues ( γ opt ) of the regularization parameters. The
optimal values depend inversely on the SNR and alsoon the details of the intrinsic T 2 -distributions. As a
general rule, for a given SNR, distributions with shortdecay times will have larger optimal values thansimilarly shaped distributions with longer decay times.
Computation of the Logs
In depth logging mode, the primary loggedquantities are estimates of the total NMR porosity,φ nmr , free fluid porosity, φ f (T c ) , and logarithmic mean
relaxation time, T 2,log . A continuous T 2 -distribution is
displayed, along with T 2,log on the field logs.
In station logging mode, data with a higherSNR are obtained by stacking, and as a result, moreaccurate logarithmic T 2 -distributions can be computed.
It is these distributions that are related to rock pore sizedistributions.
The primary log quantities are expressed asintegrals over the distribution functions, e.g.,
φ nmr = K tool dT 2T min
T max
∫ P(T 2 ) ≡ K tool al
l=1
N s
∑ , (6)
where K tool is a factor containing various calibration
and environmental corrections such as the Curie lawtemperature dependence of the signal. The free fluidporosity φ f (T
c ) is obtained from the integral in Eq.6
by replacing the lower limit of integration by anempirically determined cutoff T c which partitions φ nmr
into free and bound fluid porosities,
φ bf (T c ) = φ nmr − φ f (T c ) .
The logarithmic mean relaxation time is
defined by T 2,log = 10m , where m is the mean logarithm
of the logarithmic T 2 -distribution and is defined by
m =
d (log T 2 ) Pa (logT 2 )logT 2log T min
log T max
∫
d (logT 2 )Pa (logT 2 )
log T min
log T max
∫ =
allogT 2, l
l=1
N s
∑
al
l=1
N s
∑.(7)
Computation of the Standard DeviationsIn the Logs
The standard deviations in the logs due torandom noise fluctuations provide a measure of logrepeatability and confidence in the log values. Logs of the standard deviations are computed for each of theprimary logged quantities and displayed for the porosity
estimates. The standard deviations are computed from anexact covariance matrix for the multi-exponentialmodel. For example, the variance in the estimated totalporosity is by definition
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102
where a "hat" is used to denote that φ nmr is an estimate
of the true porosity defined in Eq.6. In terms of thecovariance matrix,
C l,k , one finds that,
σ 2 (φ nmr ) = (K tool )2 C l,k
l=1
N s
∑k =1
N s
∑ , (9)
where by definition, C l,k = < δ a
lδ ak > . Here
δ a
l= a
l− < a
l> are the deviations, produced by noise
fluctuations, of the spectral amplitudes from theirexpectation values. An exact expression for C l ,k can be
calculated because of the linearity of themulti-exponential model. The covariance matrix isproportional to the rms noise on a single echo in themeasurement which, as discussed above, is computedfor each measurement. The expressions for the variances
in φ f (T c ) and φ bf (T c ) are identical to those in Eq.9
except for obvious changes in the summation limits.
Multi-Wait Time CPMG Logging
As noted earlier, the use of single wait timepulse CPMG sequences and an assumed value ( ξ 0) of
the T 1 / T 2 ratio in the signal processing algorithm
involves an uncontrolled approximation. It can producesignificant accuracy errors in the log outputs. The rootof the problem is the variability of the T 1 / T 2 ratios in
reservoir rocks. The accuracy errors are amplified inhigh porosity rocks that have long T 1 components.
Although, the errors can be lessened by using longerwait times it has been shown that this strategy isinefficient and leads to reduced logging speeds.
Consider a multi-wait time pulse sequencewith wait times W p where p = 1,2,L , N wt . Studies
have shown that, N wt = 3 , provides good results from
multi-wait time pulse sequences. The CMR signalprocessing algorithm for multi-wait time pulsesequences is an addition to the window processing
algorithm described above. The CMR log outputs φ nmr ,
φ f (T c ), φ bf (T c ) , etc. for multi-array pulse sequences
are arrays instead of scalars. For example, there are N wt
output values of φ nmr , i.e., one for each wait time, etc.
Additionally, each output array contains one newupdated log output which is computed simultaneouslywith an estimate of the true T 1 / T 2 ratio. The updated
log outputs are more accurate because they are derivedusing the estimated true T 1 / T 2 ratio instead of the
assumed ratio ( ξ 0 ).
The updated log outputs and true T 1 / T 2 ratio
estimates ( ξ ) are computed by minimization of a cost
function,
C (ξ v ,{av,l}) = al, p −
av,l f l(W p ,ξ v )
f l(W p ,ξ 0 )
l=1
N s
∑ p=1
N wt
∑2
. (10)
The apparent spectral amplitudes ( al, p )
determined for each single wait time in the multi-waittime pulse sequence assume the role of the "data" in Eq.(10). The cost function is a function of a variable, ξ v ,
which represents the T 1 / T 2 ratio. It is also a functional
of a distribution of variables, {av,l}, which represent
the intrinsic T 2-distribution. Note that the intrinsic
distribution is a physical property of the rock and,
therefore, is independent of the wait times. Theestimates of the true T 1 / T 2 ratios and true spectral
amplitudes are obtained by minimization of the cost
function. That is, let ξ v∗ and {av,l
∗ } be the feasible
values for which the cost function attains its globalminimum. Then the true T 1 / T 2 ratio estimates are
given by, ξ = ξ v∗ . Likewise, the estimated T 2-
distributions are given by, {al} = {av,l
∗ }. The updated
log outputs are computed from the estimated T 2-
distributions. A flowchart of the signal processingalgorithm for processing multi-wait time pulsesequences is shown in Fig. 1.
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103
Compute Std. Devs.In Porosity LogsFor Each Wait Time
Sonde PSD
EstimateSignal Phases
Compute
A(+)
A( - )Estimate
Rms NoiseA
(+)A
( - )
θp
∧
~
R j ,p~X j ,p
p
~~~
Compute Window Sums~
~
Minimize- ln L
p
a
Compute LogOutputs For Each
Compute Signal
Color MapsDistributions For
Record Logs
Construct And
al
∧{ }
γ opt,p
~
R j ,p
~X j ,p θp
∧
j ,p j ,p
j ,p
j ,p
Im, p
l,p
N
wt
> 1 ?No
Construct Cost Function
And Perform Minimization
Yes
ξ∧
Compute Updated Logs
Flowchart For Multi-Wait Time Logging
Compute
Wait Time
Compute Std. Dev.In Logarithmic Mean T2For Each Wait Time
Figure 1. Signal processing flowchart for multi wait time logging.
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104
Nomenclature
This section defines the symbols used in this note.
˜ A j(+ ) = "in-phase" amplitude of j-th spin echo
signal computed from raw two
channel data. Used to computewindow sums.
˜ A j(− ) = "quadrature" amplitude of j-th spin
echo signal computed from raw twochannel data. Used to estimate rmsnoise.
al(al) = true spectral amplitude (estimate) of
l− th component in multi-exponential model.
{a
l} = set of true spectral amplitudes referred
to as the T 2-distribution.
al, p = apparent spectral amplitude estimates
for wait time W p computed with
assumed T 1 / T 2 ratio ( ξ 0).
av,l = variable spectral amplitude in cost
function (see Eq. (10)).
av,l
∗ = value of av,l for which the cost
function in Eq. (10) attains its globalminimum.
C l,k = covariance matrix used to compute thestandard deviations in the logs.
C (ξ v ,{av,l}) = cost function which is minimized to
estimate true T 1
/ T 2
ratios and
updated log outputs from multi-waittime pulse sequence log data.
