SLB Training Manual

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.

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 training ma manual nual is the 1st volume of the 4 volume CMR Tool Manual. Volume Volume 2 iis s the Wellsite Reference Manual (WRM). (WRM) . Volumes Volumes 3 and 4 are are the Maintenance Manuals. The contents of each each volume are are shown in Table 1. To prevent needless duplication, duplication, there is very ve ry little 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 or troubleshooting procedures -- this information is available in other volumes.


Table 1. CMR Tool Manual Contents (MH606600) Vol. 1 Training Manual

Vol. 2 WRM Document

Vol. 3 Maintenance Volume

Vol. 4 Maintenance Volume

(MH606601)

(MH606602)

(TEXT) (MH606603)

(APPENDIX) (MH606604)

Document Organization




Ch 1 - Intr Introd oduc ucti tion on

Ch 1 -

Ch 2 - Measurem Measurement ent Principl Principles es Ch 3 - Hardwa Hardware re Descr Descript iptio ion n Ch 4 - Data Data Desc Descrip riptio tion n& Processing

Ch 2 -

Ch 3 -

Ch 5 - Cali Calibr brat atio ion n& Environmental Corrections Ch 6 - Operat Operating ing Proced Procedure uress

Ch 4 -

Appendix B - Safety, Handling and Transportation Appendix C - Mud Doping for Residual Oil Appendix C - Signal Processing Algorithms

Hard Hardwa ware re Desc Descri ript ptio ion n& Specifications Oper Operat atin ing g Ins Instr truc ucti tion onss (safety overview, h/w preparation, wellsite operations, wellsite troubleshooting)

Master Table of Contents Ch 1 -

Safe Safety ty,, Han Handl dlin ing g and and Transportation

Ch 2 -

Hard Hardwa ware re Desc Descri ript ptio ion n& Specifications

Ch 3 -

Deta Detail iled ed Bloc Block k Des Descr crip ipti tion on

Ch 4 -

Deta Detail iled ed Circ Circui uitt Description

Soft Softwa ware re Refe Refere renc ncee (parameters, channels, LQMS, etc)

Ch 5 -

Ch 5 -

FIT FIT & TRIM TRIM Chec Checks ks

Ch 6 -

Ch 6 -

Deta Detail iled ed Tool Tool & Acquisition Software Reference

Ch 7 - Interpreta Interpretation tion Principles Principles & Applications Appendix A - Hardware Soecifications & Ratings

Theo Theory ry of Meas Measur urem emen entt (applications, physics overview, etc)

Elec Electr tron onic ic Cali Calibr brat atio ion n Theory Disa Disass ssem embl bly y& Reassembly

Ch 7 -

RITE RITE Main Mainte tena nanc ncee

Ch 8 -

Shop Shop Trou Troubl bles eshoo hooti ting ng

Ch 9 -

Circ Circui uitt Diag Diagra ram m Lis Listi ting ng

Appendix A CMR-AA To Tool BOM, Assy Drawings & TPS. Appendix B CMRS-A So Sonde BOM, Assy Drawings & TPS. Appendix C CMRC-A Cartridge BOM, Assy Drawings & TPS. Appendix D CMR-AA Drawings Appendix E EME-F BOM, Assy Drawings & TPS. Appendix F SFT-307 BO BOM, Assy Drawings & TPS. Appendix G Reference Documents Appendix H Special Equipment Appendix I -

Wire Li Lists

Table of Contents 1. Introduction...................................................................................................................................1 1.1 Hardware characteristics.....................................................................................................1 1.2 Measurement overview......................................................................................................3 1.3 CMR sonde ........................................................................................................................6 1.4 CMR cartridge.....................................................................................................................7 2. Measurement Principles ............................................................................................................... 8 2.1 Introduction to NMR ............................................................................................................8 2.1.1 Alignment: longitudinal relaxation (T1) ....................................................................8 2.1.2 Tipping ................................................................................................................. 10 2.1.3 Precession and dephasing...................................................................................11 2.1.4 Refocussing: spin echoes....................................................................................13 2.1.5 Irreversible dephasing: transverse relaxation (T2)..............................................15 2.1.6 Realignment..........................................................................................................16 2.2 NMR relaxation mechanisms.............................................................................................17 2.2.1 Relaxation by bulk fluid processes......................................................................18 2.2.2 Surface relaxation.................................................................................................20 2.2.3 Relaxation by diffusion in magnetic field gradients...............................................22 2.2.4 Summary of relaxation processes........................................................................24 2.3 Multiexponential decay.....................................................................................................25 3. Hardware Description.................................................................................................................28 3.1 Tool concept ..................................................................................................................... 28 3.2 Operational requirements..................................................................................................30 3.3 CMR simplified block diagram...........................................................................................31 3.3.1 Sonde electronics and block description...............................................................31 3.3.2 DTS telemetry interface board..............................................................................33 3.3.3 Enhanced downhole controller board....................................................................34 3.3.4 Acquisition control/synthesizer board...................................................................34 3.3.5 Receiver board.....................................................................................................34 3.3.6 Auxiliary measurements/calibration board ............................................................34 3.3.7 Power supplies .................................................................................................... 34 3.3.8 Power up reset/RS232.........................................................................................35 3.4 CMR measurement cycle..................................................................................................35


4. CMR Data Description and Processing Overview....................................................................38 4.1 CMR spin-echo sequences..............................................................................................38 4.2 T2-distributions.................................................................................................................39 4.3 Inversion problem.............................................................................................................40 4.4 Data redundancy and data compression..........................................................................40 4.5 Maximum likelihood estimation...........................................................................................42 4.6 Measurement sensitivity limits..........................................................................................42 4.7 Standard deviations in log outputs...................................................................................43 4.8 Parameter selection...........................................................................................................43 5. Calibration and Environmental Corrections................................................................................46 5.1 Overview ......................................................................................................................... 46 5.2 Master calibration..............................................................................................................47 5.3 Electronic calibration..........................................................................................................47 5.4 Environmental corrections .................................................................................................48 6. Operating Procedures................................................................................................................49 6.1 Special procedures...........................................................................................................49 6.1.1 Tool tuning............................................................................................................49 6.1.2 Pulse sequence....................................................................................................49 6.1.3 Polarization and the polarization correction...........................................................50 6.1.4 Measurement time and logging speed..................................................................51 6.1.5 Stacking, precision and vertical resolution............................................................51 6.2 Tuning the tool to the Larmor frequency............................................................................51 6.3 MAXIS control panel ......................................................................................................... 55 6.3.1 Hardware operating parameters...........................................................................56 6.3.2 Data processing parameters ................................................................................ 58 6.3.3 Logging modes ..................................................................................................... 60 6.3.4 Diagnostic channels..............................................................................................62 6.3.5 Log outputs .......................................................................................................... 62 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.............................................66 6.5 Log quality control.............................................................................................................67 6.5.1 Operating technique.............................................................................................67 6.5.2 Response in various formations...........................................................................71 6.5.3 Borehole conditions .............................................................................................. 71 6.5.4 Repeatability........................................................................................................72


6.6 Log quality display ........................................................................................................... 73 6.7 Acquisition quality control..................................................................................................75 6.8 Environmental corrections .................................................................................................75 6.9 Master calibration..............................................................................................................75 7. Interpretation Principles and Applications .................................................................................. 76 7.1 Introduction........................................................................................................................76 7.2 Pores contain only water (or filtrate) ................................................................................. 76 7.3 Pores contain water and oil...............................................................................................79 7.4 Pores contain gas ............................................................................................................. 83 7.5 CMR applications.............................................................................................................84

Appendix A. Hardware Specifications and Ratings.......................................................................87 Appendix B. Safety, Handling and Transportation........................................................................89 Appendix C. Mud Doping Procedures for Residual Oil Determination...........................................96 Appendix D. Signal Processing Algorithms....................................................................................99


CMR Training Manual Introduction

-1-

First Edition November 1995

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 measurements contain information relating to both pore volume and pore size. CMR hardware has been designed to overcome the limitations associated with the previousgeneration NML Nuclear Magnetic Log tool. It is no longer necessary to dope the borehole with magnetite and the CMR tool is combinable, top and bottom, with other logging tools. By using permanent magnets in the CMR sonde, the tool does not have to rely on the earth's magnetic field to make the NMR measurement. This eliminates many of the environmental corrections associated with the NML tool. The CMR is a skid tool that has high vertical resolution. It must be run eccentered using a bowspring, 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) Withpoweredcaliper (e.g., PCD or MLT) With in-line eccentralizer (ILE-F)

7.5 in. 6.5 in. 6.25 in.

The CMR tool works in large boreholes, provided the bowspring or caliper device has sufficient force to eccenter the tool. Finally, there are no mud conductivity limitations; the CMR works in both conductive and resistive muds. The CMR tool consists of a sonde and cartridge. A tool sketch is shown in Figure 1.1 and tool specifications are listed in Appendix A. It is a compact tool that has a makeup length of 14.2 ft and 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 sonde characterization 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 may also be combined with CTS tools provided a DTA is included in the tool string. The CTS tools must be run below the CMR tool unless they have been modified with FTB through-wiring.



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Cartridge

Bow Spring

14.2’

Sonde

Bull Nose

Figure 1.1. CMR tool.



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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 in the 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 a precessional motion analogous to the wobbling motion of a toy top spinning in the earth’s gravity field. Figure 1.2 shows an idealized CMR raw measurement. The received signal consists of a sequence of spin-echo amplitudes that are recorded over a period of time typically in the range of 0.2 to 2.0 sec. The spin-echo signal originates from hydrogen nuclei that are precessing about a magnetic field produced by magnets in the sonde. Because the hydrogen nuclei have a magnetic moment, they can induce a signal in the CMR antenna.

A m p l i t u d e

spin echo amplitudes

time

Figure 1.2. Idealized NMR measurement. The spin echoes are generated by transmitting rf pulses from the same antenna used to detect the spin echoes. Each transmitter pulse produces a spin echo, and the amplitude of the spin echo is recorded by the tool. The collection of spin-echo amplitudes are referred to as a CPMG (after Carr, Purcell, Meiboom and Gill). CPMGs are always collected in pairs. The second set is acquired with the phase of the transmitter pulse changed to give spin echoes of negative amplitude. The second CPMG is then subtracted from the first CPMG to produce a “phase-alternated pair” (PAP). This procedure preserves the signal and eliminates low-frequency electronic offsets. Further details, including a full 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 amplitude and the rate at which the signal amplitude dies away. •

The initial signal amplitude is proportional to the number of hydrogen nuclei in the measurement volume that are associated with the pore fluids. Hence, the initial signal amplitude can be calibrated to give a porosity, φCMR. Because the NMR measurement responds 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 obtained without specifying minerology or matrix properties. •

The signal amplitude decays (i.e., dies away) exponentially with time in a manner similar to the more familiar thermal decay time measurement. The time constant of the NMR signal decay is called the transverse relaxation time, or more simply T2 . D i s t r i b u t i o n

T = 100 msec 2,log

φCMR = 9.9 p.u.

0.1

1.0

10.0

100.0

1000.0

T2 (msec)

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, small pores have short T2 values, and large pores have long T2 values. At any depth in the wellbore, 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 in Figure 1.2. The area under the T2-distribution curve is equal to the measured porosity. Hence the T2distribution plot completely summarizes the results of the NMR measurement. It is the task of the CMR hardware and software to measure the T2-distribution of the formation at each sample interval in the wellbore. Details of the signal processing algorithm that computes the T2distribution 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 both producible porosity and permeability. The NMR estimate of producible porosity is referred to as the free-fluid porosity, φFF. The estimate is based on an expectation that the producible fluids reside in the large pores, whereas the bound fluids reside in the smaller pores. Hence, a T2 cutoff (i.e., a pore size cutoff) may b e applied to the T2-distribution that divides the NMR porosity into free-fluid and bound-fluid porosity (φBF), as shown in Figure 1.4.



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D i s t r i b u t i o n


small pores contain

large pores contain

bound fluid - φ BF

free fluid - φ FF

0.1

1.0

10.0

100.0

1000.0

T2 (msec)

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 on core samples. The correlations between NMR measurements and petrophysical properties are derived from lab measurements. For example, measurements on water-saturated core samples have shown that T2 cutoff values of 33 and 100 msec are appropriate for sandstones and carbonates, respectively. These cutoff values resulted in free-fluid porosities that best matched the volumes of water produced from the core samples by centrifuging at 100 psi air-brine capillary pressure. Typical results for sandstone core samples are shown in Figure 1.5. 20 Well A Well B

15

Well C

φ FF 10 5

0 0

5

10

φ centrifuge

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 will increase with both porosity and pore size. NMR and permeability measurements on watersaturated sandstone samples have shown that permeability can be estimated by 4

2

K NMR = a (φ CMR ) (T2,log ) ,

(1.1)



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where KNMR is the permeability estimate, φCMR is the porosity and T 2,log is the logarithmic mean T2 of the distribution. The logarithmic mean relaxation time of the distribution is analogous to the “center of mass” of a body in classical mechanics (i.e., it is the T2 value at the “center of mass” of the distribution). The premultiplier, a, in the above Eq. 1.1 has a default value of 4. Better results can be obtained if the premultiplier is adjusted on a per reservoir basis. A comparison of K NMR with measured brine permeability for sandstone samples from two wells is shown in Figure 1.6. 100.00

Well A, a=2.8 Well B, a=3.4 Kbrine

4

2

KNMR = aφNMR T2, log 0.01 0.01

KNMR

100.00

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, φ FF, φBF, KNMR and T2-distributions are output in both modes. Station logging is employed when greater 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. A cross section of the sonde is shown in Figure 1.7. Note that the antenna section protrudes from the 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 receive the spin-echo signal from the formation fluids. Both the transmit and receive functions use the same antenna, which is operated in half duplex mode. The received signal (which is about 50 nanovolts per porosity unit) is amplified in the sonde by a factor of about 2000 before passing through the sonde/cartridge head to the cartridge receiver circuits. The antenna used to radiate the formation is housed in the antenna cradle assembly. The assembly is an oil-filled pressure balanced environment. A small metal bellows is utilized to compensate 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. Ferrite material is placed between the inner and outer conductors to enhance the sensitivity of the antenna.



1.0"

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Replaceable Antenna Cover Antenna Samarium Cobalt Magnets Channels for Thru-Wires

N

N

Sonde Electronics 4.625"

S

CMRS-A Skid

S

5.30"

Figure 1.7. CMR sonde cross section. Samarium cobalt magnets are used to produce the static magnetic field required for the NMR measurement. Samarium cobalt is the preferred material because it has high field strength, a high resistance to demagnetization and a Curie point of 820° C (the Curie point is the temperature at which permanent magnetism is destroyed). The magnets are potted inside metal cases with epoxy. The metal cases provide protection; the magnet material is brittle and will shatter on impact. The sonde body is made of titanium to reduce the overall weight of the tool and to provide a nonmagnetic 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 and surface casing. They also remove soft mudcake. The plows and magnet casings are coated with tungsten carbide to provide wear resistance.

1.4 CMR cartridge The CMR electronics cartridge contains the electronic circuits necessary to acquire and process the spin-echo signals before being sent uphole on the telemetry channel. The cartridge contains power supplies, control circuits, telemetry interface, microprocessors, calibration circuits and diagnostic circuits.


CMR Training Manual Measurement Principles

-8-


2. Measurement Principles 2.1 Introduction to NMR Nuclear magnetic resonance (NMR) refers to a physical principle -- the response of nuclei to a magnetic 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 like gyroscopes. These spinning magnetic nuclei can interact with external magnetic fields and produce 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 and chromium ions) and from neighboring nuclei.

NMR measurement can be made on any nuclei that have an odd number of protons and/or neutrons (e.g., H1, C13, Na23, F19 and P31). For most of these nuclei the signal is too small to be detected with a borehole logging tool. However, hydrogen has a relatively large magnetic moment and is abundant in both water and hydrocarbon molecules found in pore fluids. By tuning the CMR tool to the resonant frequency of hydrogen, the signal is maximized and is therefore measurable. The measured quantities are signal amplitude and relaxation rates. The signal amplitude is calibrated to give porosity. Two principal relaxation times are associated with NMR measurements; the longitudinal relaxation time (T1) and the transverse relaxation time (T2). Both are described in subsequent sections. The relaxation times, either T1 or T2, are interpreted to give pore size and/or pore fluid properties. Both T1 and T2 measurements are made on core samples using lab NMR apparatus. T1 measurements usually take several minutes and are therefore not practical for a moving logging tool. 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 described below. Only after all steps have been completed can the measurement be repeated; usually several seconds are required. Thus, the measurement is cyclic rather than continuous.

Terminology For present purposes, the words "proton," "nucleus," "moment," and "spin" are all synonyms and 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 not strictly 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 static magnetic field. The static field is called B 0 (“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 C MR permanent magnets, B 0 is approximately 540 Gauss, about 1000 times stronger than the magnetic 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 with the magnetic field. However, when a torque is applied to a spinning object its axis moves perpendicular to the torque in a motion called precession. This motion is analogous to the motion of a toy top spinning in the earth’s gravity field, as shown in Figure 2.1.

Precessional motion Magnetic field, Bo

Spinning motion

Proton

Spinning motion

Toy top

Earths gravitational field

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 magnetic fields of other nuclei or unpaired electrons. These interactions result in the proton losing energy and rotate it into alignment by a process that is referred to as relaxation. Again, this is similar to a toy top that gradually loses energy because of friction and eventually topples. Analogously, polarization does not occur immediately but rather grows with a time constant called the 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 B 0 field. A typical T1 relaxation curve is shown in Figure 2.2. For the case of hydrogen nuclei in pore fluids, polarization takes up to several seconds and can be done while the logging tool is moving, but the nuclei must be exposed to B 0 for the entire measurement cycle. To accomplish this, the permanent magnets on the CMR sonde are elongated in the direction of tool motion.



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Nuclei Polarize Slowly in a Magnetic Field 1

0.8 n o i t a z i r a l o P r a e l c u N

1 - exp(-t/T 1) 0.6

0.4

T1 = 0.2 sec

0.2

0 0

0.2

0.4

0.6

0.8

Bo exposure time (sec)

1 941110-03

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 magnetic moments.

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 protons into the transverse plane. This is accomplished by applying an oscillating magnetic field perpendicular to the direction of B 0 using an antenna. The oscillating magnetic field is called B 1. For effective tipping, the frequency of B 1 must be f0 =

 γ  B .  2π  0

(2.2)

f0 is the frequency in hertz, γ is the gyromagnetic ratio of the nucleus, and B 0 is the static magnetic field. γ is different for each type of nucleus. f 0 is called the resonance frequency or Larmor frequency. For hydrogen nuclei, γ/2π = 4258 Hz/Gauss. For the CMR tool, B 0 is about 540 Gauss. Therefore, B 1 must have a frequency just below 2.3 MHz. It is this frequency selectivity that makes NMR a resonance technique. The angle through which the protons are tipped is given by



θ = 360

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 γ  B t  4π  1 P

(2.3)

where θ is the tip angle in degrees, B 1 is the strength of the linearly polarized oscillating field in Gauss, and tP is the length of time the B 1 field is left on. If we desire a tip angle of 90°, and if B 1 is 8 Gauss, then t P is 15 microseconds. (Note: Eq. 2.3 differs by a factor of 2 from other equations found in many NMR texts, which assume B 1 is circularly polarized).

2.1.3 Precession and dephasing After the protons (spins) are tipped 90 ° from the direction of B 0, they immediately begin to precess in the plane perpendicular to B 0. The precession frequency is equal to the Larmor frequency, given by Eq. 2.2. z’

B0

y’

M x’

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 f 0, that can be detected by the CMR antenna. Gradually, the protons lose synchronization. This is because the magnets never provide a uniform B 0 field that is the same everywhere in the formation. Since the field is slightly different at point A in the formation than it is at point B, the protons at points A and B will precess at correspondingly different frequencies, according to Eq. 2.2 and as shown in Figure 2.4. z’

y’

x’

m mA

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, as shown in Figure 2.5 c. When the spin directions are uniformly distributed in the transverse plane, the net magnetic moment produced by them sums to zero, and no further signal is detected by the antenna. The signal decay is called a "free induction decay" (FID), and it is usually exponential. The decay time constant is called “T2 star” (T2*). The * indicates that the decay is not a property of the formation, but of the imperfection of the measurement apparatus. An example of an FID is shown in Figure 2.9. For the CMR measurement, T2* is comparable to t P, the length of the tipping pulse (i.e., a few tens of microseconds). After a B 1 pulse, which may put hundreds of volts on the transmitting antenna, the sensitive receiver electronics are saturated. Therefore, the free induction decay is usually lost in the dead time of the measurement electronics. If this were the end of the story, there would be no point in attempting NMR measurements.

2.1.4 Refocussing: spin echoes The dephasing caused by the inhomogeneity of B 0 is reversible. Returning to the runner analogy shown in Figure 2.5, imagine that after the runners are dispersed around the track the referee gives a signal causing the runners to turn around and run in the opposite direction. The fastest runners have the greatest distance to run back toward 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 Figure 2.5 f. In a similar manner, the magnetic moments can be rephased when a 180° pulse is applied at the resonance frequency f 0. The 180° pulse is approximately twice as long as the 90° pulse. It does not 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 effects of these pulses on the magnetization vector are shown in Figure 2.6, Figure 2.7 and Figure 2.8.

z’

mA’ m ’B m x’

m

y’

B

A

Figure 2.6. Application of 180 ° pulse.



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z’

mA’ mB’ y’ x’

Figure 2.7. Spins begin to rephase. z’

y’

M x’

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 an evenly spaced train, as close together as possible (as shown in Figure 2.9). An echo forms midway between each pair of 180° pulses. 0

0

90

0

180

180

Transmitter

FID

Spin Echo

Spin Echo

Receiver

TE

TE

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 abbreviated TE. For the CMR tool, the minimum TE value is 0.32 msec. Another commonly used quantity is TCP (Carr-Purcell time), which is equal to TE/2.

o o 90 180

TE

o 180

180

TE

TE

o

180

TE

o

o 180

o 180

TE

TE

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 electronic feed through in the first 0.2 msec. The first echo is smaller than the rest because of the inhomogeneous fields of the tool.

2.1.5 Irreversible dephasing: transverse relaxation (T2) The CPMG pulse sequence negates the dephasing caused by the imperfection of the B 0 field. However, dephasing can also be caused by molecular processes. Unlike the dephasing caused by magnet inhomogeneities, which is reversible, the dephasing resulting from molecular processes is irreversible. Once irreversible dephasing occurs, the protons can no longer be completely refocussed using the spin-echo technique (applying 180° pulses). Thus, irreversible dephasing is monitored b y measuring the decaying amplitude of the spin echoes in the CPMG echo train, as shown in Figure 2.11.



n o e i t s r a e i z v t s e n n a r g T a M

-16-


M(t) = M0 e-t/T2 M0

1st echo

2nd echo

3rd echo

Time (t)

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 0 e − t T2 ,

(2.4)

where M0 is the transverse magnetization at time zero, t is time and T2 is the transverse relaxation time constant.

e d u t i l p m A

.. . .. .. .. .

0.1 sec

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 or spin echo) can be generated in the receiver antenna. After a time equal to several times T2, the spins completely lose phase coherence and no further refocussing is possible. The 180 ° pulses



-17-


also prevent T1 processes; polarization does not occur during a CPMG. Hence, the spins are completely 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 B 0 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 cycle can 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 of conditions, the surface relaxation mechanism is dominant. The surface and bulk relaxation mechanisms are due to magnetic interactions between the proton spins 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). These interactions are usually the most important.

Longitudinal relaxation (T1) occurs when a proton can transfer energy to its surroundings via the neighboring 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 B 0 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 mere presence of a nearby spin changes the local B 0 field slightly, causing protons to precess at slightly different rates and therefore dephase. In the race analogy, the runner can be tripped b y another 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 occur through energy transfer and dephasing. Therefore, longitudinal relaxation is always less efficient than 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 is a pure dephasing mechanism and hence contributes only to T2. From the practical standpoint, it is worth noting that T2 is exactly represented by the spin-echo decay of the CPMG measurement; a "correction for T1" is not required.



-18-


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, the bulk fluid mechanism is always active (regardless of whether the fluid is in a large container or confined 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 to estimate several fluid properties. For water and hydrocarbons, bulk relaxation is primarily due to fluctuating local magnetic fields arising from the random tumbling motion of neighboring molecules. The local fields are about 1 Gauss, but the very fast molecular motions (mostly rotations of the molecules) tend to average out the effect. The molecular motions and rotational averaging depend upon the viscosity and temperature of the fluid; hence, T1 and T2 are both highly correlated with these variables (see Figure 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 T1

0 .3

(sec)

0 .1 0 . 03 1 .0

100 10 30 3 .0 Viscosity (centipoises)

300

Figure 2.13. Longitudinal relaxation time (T1) versus viscosity for 14 crude oils at various temperatures.



-19-


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 typical borehole 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 molecular processes, and on the molecular level 20,000 psi is a very modest pressure. However, pressure has a substantial effect on relaxation of bulk gas, as shown in Figure 2.16.

10 Water

) s d n o c e s (

1

2 T r o 1 T

S6 Oil S20 Oil

0.1

0

50

100

150

Temperature (°C)

200 950926-01

Figure 2.15. Bulk relaxation of water and two oils (S6 and S20) versus temperature.



-20-


Methane Gas 10

8

) c e s ( 1 T

6

4 25 C 75 C 125 C 175 C

2

0 0

3000

6000

9000

Pressure (psi)

12000 15000 951008-01

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 unceasing molecular motion of fluids. Brownian motion causes fluid molecules to diffuse substantial distances during an NMR measurement. The equation for diffusion is =

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 one second (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 during the NMR measurement. Each of these contacts provides an opportunity for surface relaxation. When fluid molecules approach grain surfaces, two things can happen. First, protons can transfer nuclear energy to the grain surface, allowing the proton to realign with B 0 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 e very collision; there is only a probability that they will occur. As suggested by Figure 2.17, which shows the paths of two molecules in a pore, several collisions may occur before a spin is relaxed. Nevertheless, for the case of pore fluids, the most important influence on T1 and T2 is the interaction of fluid molecules with the surfaces of rock grains.



-21-

Rock Grain


Rock Grain

Rock Grain Light line - molecule with unrelaxed spin Heavy line - molecule with relaxed spin

Figure 2.17. Relaxation at the grain surface. Not all surfaces are equally effective in relaxing the proton spins. High-purity quartz or carbonate surfaces are not particularly strong relaxers. Paramagnetic ions (e.g., iron, manganese, nickel and chromium) have very strong local magnetic fields. They are particularly powerful relaxers and tend to control the rate of relaxation whenever they are present. Sandstones generally have an iron content of about 1% which makes fluid proton relaxation fairly efficient. The relaxing power of a surface is called its "relaxivity" and is denoted by the symbols ρ1 (for T1 relaxation) and ρ 2 (for T2 relaxation). The other important part of the surface relaxation mechanism is geometrical. Relaxation will be relatively slow if a small amount of surface has to relax the spins of a large volume of fluid. Thus the relaxation rates (1/T1 and 1/T2) are the products of the intrinsic relaxivity of the surface, and the surface to volume ratio (S/V) of the pore: S   1  = ρ  , 1  T1 S  V   pore

( 2.6)

and S   1  = ρ  . 2  T2  S  V   pore

( 2.7)

Temperature and pressure effects The surface relaxation mechanism does not depend upon temperature or pressure. This has been shown by measurements on rock samples that found no changes in relaxation times at temperatures up to 175° C and pressures up to 36,000 psi. From a practical viewpoint, the temperature and pressure independence of surface relaxation rates considerably simplifies the interpretation of CMR measurements and strengthens their connection to the great body of laboratory measurements that have been made at room temperature and pressure.



-22-


2.2.3 Relaxation by diffusion in magnetic field gradients The CPMG sequence described in Section 2.1.4 removes the effect of inhomogeneous B 0 fields for protons that do not move during the measurement. When there are significant gradients in the B0 field, molecular diffusion can contribute to T2 relaxation (dephasing). Longitudinal relaxation (i.e., T1) is not affected.

B0

B0 + 2δ

B0 + δ

B0 + 3δ

Rock Grain

B0 + 4δ

B0 + 5δ

Rock Grain Pore

A

B

C

Rock 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 (see Figure 2.18). After being tipped into the transverse plane, the proton starts precessing at f 0, the local Larmor frequency. However, as it diffuses it encounters a slowly varying B 0 and therefore its 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 it precessed faster between points A and B than it did between points B and C. Because of this, it is 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 transverse relaxation. For bulk liquids, T2 resulting from effect is given by

 1  = D(γ G TE)   T2  D 12

2

.

(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.

The gradient, G, has two sources:



-23-


•

a gradient caused by the magnet configuration (the strength of the B 0 field varies by about 5 Gauss over the measurement region)

•

microscopic gradients induced by the applied B 0 field that arise from the difference in magnetic susceptibility between rock grains and pore fluids.

The diffusion mechanism is smaller for pore fluids than bulk fluids, because molecular motions in pore fluids are restricted by grains and the nonmixing of different fluid types. The CPMG sequence minimizes the effects of diffusion, and it is not significant when the pore fluid is water or oil 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 is several 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) increase with temperature. The diffusion coefficient of gas decreases with pressure (Figure 2.20).

Diffusion Coefficient 1 0- 7 Water -8 10 ) s / 2 1 0 m ( D

9 S6 Oil

1 0- 1 0

10

S20 Oil

-11 0

50

100

150

200

950926-03

T (°C)

Figure 2.19. Diffusion coefficient for bulk water and two bulk oils versus temperature.



-24-


Methane Gas 5 10 ) s / 4 2 m ( t n e 3 i c i f f e o C 2 n o i s u f f i 1 D

10

-7 77 F 136 F 177 F 196 F

-7

10 - 7

10 - 7

10

-7

0 0 10 0

1000

2000

Pressure (psi)

3000 950 203-0 1

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: 1 1 1  1  =   +   +   ,  T2  total  T2  S  T2  B  T2  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 1  1  =   +   .  T1 total  T1 S  T1 B

(2.10)

Note that there is no diffusion relaxation for T1, because that process is strictly a dephasing mechanism. During CMR-T2 measurements, all three relaxation mechanisms are active. However, diffusion and bulk relaxations are often weaker than surface relaxation. The diffusion mechanism is deliberately minimized by using a short echo spacing. When the pore fluids are water and oil, diffusion effects are negligible provided the CMR tool is run with the



-25-


minimum echo spacing of 0.32 msec. However, when the pore fluid is gas, diffusion effects are important 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 a grain surface.

•

Bulk relaxation can be the dominant process when the pore fluid has a high concentration of paramagnetic ions. For example, chromium ions in chromium lignosulfonate mud filtrates can dramatically reduce the fluid relaxation time because the local field around the electron spin is so large.

•

When two or more fluids occupy the pore space, bulk relaxation is important for the nonwetting fluid. For example, in a water-wet system, hydrocarbon molecules are prevented from interacting 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 is due to: •

The three independent relaxation mechanisms: surface relaxation, bulk relaxation and molecular diffusion relaxation.

•

Each relaxation mechanism may be multi-exponential. This is described below for surface relaxation. 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,

 1  = ρ  S  .  T2  S 2  V   pore

(2.11)

For a single pore, the magnetization decays exponentially, therefore, the signal amplitude as a function of time, M(t), in a T2 measurement is given by

 

 S  t .  V   

M(t) = M 0exp − ρ 2 

(2.12)

Rocks tend to have very broad distributions of pore sizes. Each pore has its own value of surface-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) =

∑

  S   M exp − ρ 2   t  i   V   

i



=

∑ M exp  T2- t    , i

.

(2.13)

i

where the summation is over all pores. T2 i is the decay constant of the ith pore. M i is the initial magnetization from the ith pore and is proportional to its volume.



-26-


The summation of the individual signal amplitudes is proportional to the porosity measured by the tool. M0

φ

=

=

∑M ,

(2.14)

i

K tool . M0 ,

(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-tovolume ratios are grouped together. Then, the sums in the equations have a manageable number of terms; for example, 30. For illustrative purposes, Figure 2.21 shows the NMR signal that would result from a rock sample that has only three pore sizes, “x, y and z”. Pore size x has pore volume φX, and relaxation time T2X, and so on.

φx

T2x Time (t)

φy

T2y Time (t)

φz

φxexp(-t/T2x) + φyexp(-t/T2y) + φzexp(-t/T2z)

φx+φy+φz

T2z Time (t)

Time (t)

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 that produces the observed magnetization (i.e., it is a mathematical inversion problem). Figure 2.21 shows the distribution for the simple case shown in Figure 2.21. The distribution is divided into a set of rectangles that have areas proportional to φX, φ y and φz. The area under the distribution is proportional to the total porosity.



-27-

n o i t u b i r t s i D


φy φx

φz T2

T2x

T2y

T2z

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 data is fit to a multi-exponential model that assumes the distribution has N S discrete relaxation times T2 i with pore volumes φi. The values of T2 i are preselected and the signal processing problem is reduced to determining the pore volume that is associated with each fixed value of T2.


CMR Training Manual Hardware Description

-28-


3. Hardware Description 3.1 Tool concept 7.5 5.0 B0 Field 2.5 0.0 X (cm) N

-2.5

N

-5.0 MAGNET S

-7.5

S

ANTENNA

-10.0 MAGNET -12.5

7.5

5.0

2.5

0.0 Y (cm)

-2.5

-5.0

-7.5

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 magnets magnetized in the same direction. The static magnetic field lines for this magnet configuration are also shown in Figure 3.1. The static field is predominantly radial into the formation. 7.5 350 400 450

B0 Field Strength

550 500

5.0 500 550 2.5 0.0

X (cm) N

-2.5

N

-5.0

S

-7.5

S

-10.0 -12.5 7.5

5.0

2.5

0.0

-2.5

-5.0

-7.5

Y (cm)

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 uniform field is located about 1 in. inside the formation. This region is known as the saddle point.



-29-


FERRITE

INNER CONDUCTOR

TUNING CAPACITORS

STEEL SHELL

OUTER CONDUCTOR

Figure 3.3. CMR antenna. The antenna used to generate the oscillating magnetic field (B 1) is located in a semicircular cavity on the face of the skid. It is shown in cross section in Figure 3.1 and in perspective in Figure 3.3. B1 field lines are shown in Figure 3.4. The antenna is 6 in. long. It is essentially a half coaxial cable whose conducting surfaces are copper. The antenna has a high Q, which is very important for the reception of weak signals from the nuclear spin system, and minimizes power requirements during transmission.

B1 Field

7.5 5.0 2.5

sensitive region

0.0

X (cm) N

-2.5

N

-5.0 -7.5 S

S

-10.0 -12.5 7.5

5.0

2.5

0.0

-2.5

-5.0

-7.5

Y (cm)

Figure 3.4. B 1 field lines. The tool is designed to resonate nuclei at the saddle point. The sensitive (or measurement) region is shown in Figure 3.4. Three necessary conditions are met in this region:



-30-


•

The B1 field is perpendicular to the B 0 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 at the saddle point is about 540 Gauss and the corresponding Larmor frequency (f O) is slightly below 2.3 MHz.

•

At the saddle point, the B 0 field is constant over a relatively large area. This is necessary to ensure an adequate measurement volume and signal strength. In practical terms, the field is considered constant over a region in which the Larmor frequency of the spins lies within the bandwidth of a 180 o tipping pulse. This condition is equivalent to ∆B = B 1 / 2., where ∆B is the maximum deviation from the center field found in the resonated region . For the CMR tool, B 1 is approximately 10 Gauss; hence, ∆B is about 5 Gauss. The B 1 field is not particularly homogeneous over the resonance region. Inhomogeneity of B 1 is acceptable, as long as error-correcting pulse sequences such as the Carr-Purcell-MeiboomGill 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 the NMR signal. This is the “blind zone” that provides immunity against the effects of mudcake and small 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 region is 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 the borehole that can be logged. Since the B 0 field is created by permanent magnets (rather than electromagnets) and a pulsed measurement technique is used, the power requirements are quite modest. Under most operating conditions the peak sonde power is about 200 watts.



-31-


Ensuring that the sonde survives high temperature, high pressure, abrasion, and rough handling is vastly simplified by the all-metal construction. This is a significant departure from other borehole NMR devices. The only nonmetallic part exposed to the environment is the antenna. This is protected 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 not affected by, the earth's field which is much smaller than the field created by the permanent magnets. The skid was designed to limit the length of the wall-engaging section to 18 in. in order to minimize rugosity effects Where the borehole wall is substantially damaged or washed out, preventing good contact between the face of the sonde and the formation, it is possible to pick up signal from borehole fluid. In such cases, the tool will give erroneous results. This limitation is common to all wall-engaging logging tools. However, such zones are routinely detected by borehole caliper devices, and data acquired in them are disregarded. Insensitivity to mudcake is assured by the blind 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 the requirement 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 borehole NMR 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 a relatively small volume of investigation. This permits all calibration and test procedures to be performed 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 the samarium cobalt magnets, which decreases with temperature. Hence, both the transmitting and receiving frequency must be adjusted with wellbore temperature. The MAXIS and downhole controller compute operating frequencies based on data received from the temperature probe located 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 the hydrogen nuclei and which also minimizes the power requirements during transmit phase.



-32-


Calibration loop Electronic calibration is accomplished using a test loop taped to the antenna. A constant amplitude signal is sent to the test loop and is picked up by the antenna and processed through the receiver chain. The test loop signal is used to correct for changes in system gain caused b y changes in temperature, operating frequency and conductivity.

Sonde Duplexor Tuning Board

Q-Switch

Antenna Test Loop

Transmitter

Preamp Bo Field and Temp Sensors

Sonde Power

Cartridge Power

High Voltage DC Power Supply +15 VDC -15 VDC

Low Voltage Power Supply

-5 VDC +5 VDC Ana

Cal Signal

+5 VDC Dig Larmor Freq Pulses Tune Word Serial Data

Acquisition Control & Synthesizer Board

Acquisition Control Signals Auxillary Measurements & Calibration Board

Larmor Freq Clock Serial Control Bus

Serial Data to Telemetry Cartridge Commands From Telemetry Cartridge

DTS Telemetry Interface

RS232 Transmit, Receive

Enhanced Downhole Controller

Receiver Board

Power Supply Voltages

Power Up Reset RS232

Figure 3.5. CMR simplified block diagram.



-33-


Auxiliary sensors Two additional sensors are located in the sonde: a Hall probe and temperature sensor. The Hall probe measures the magnetic field strength midway between the magnets. The temperature sensor 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., B 0) in the measurement region, that in turn is used to set the operating frequency. The temperature readings are 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. The pulse duration is approximately 30 microseconds and maximum current is about 2 amps. It is important that the transmitter frequency be at the Larmor frequency, and it is therefore adjustable over a limited range.

Q-switch The Q-switch is used to dissipate energy stored in the antenna after a transmitter pulse, and thereby 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 duplexer circuit protects the preamp from damage by the very large antenna voltages during transmit. The duplexer acts as a high impedance during the transmit pulse and as a low impedance when the spin-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. The output 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) to communicate with the surface processors. The telemetry interface board provides the electronics needed to interface the CMR cartridge to the DTS fast tool bus. There are three main functions of this 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 ab ov e and below the CMR.



-34-


3.3.3 Enhanced downhole controller board Surface commands are received by the telemetry interface and then read and decoded by the enhanced downhole controller (EDHC). The EDHC then initializes the data acquisition and processing circuits accordingly. The EDHC also reads the auxiliary channels, creates uplink messages and starts the uplink transmission.

3.3.4 Acquisition control/synthesizer board Timing for the data-acquisition operation is implemented on the acquisition control/synthesizer board. Once the timing circuits are initialized on this board by the EDHC, the acquisition cycle generally proceeds with minimal intervention from the EDHC. The only tool control functions during the acquisition cycle are to set a new operating frequency (if necessary) and send a start of 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 adjustable frequency. The acquisition control/synthesizer board also has a 64KX8 EEPROM for storing tuning control relay words, master calibration data, master operating frequency search data, sonde and cartridge serial numbers and a list of modifications that have been made to the tool. Data are read to, and written 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 raw echo signal is an amplitude modulated sine wave with a frequency of about 2300 kHz. This signal is 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 static random access memory (SRAM) space. The echo samples are then read by the receiver signal processor 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. The auxiliary measurements consist of power supply voltages, transmitter current, transmitter output power, sonde temperature and magnetic field strength. The EDHC reads these measurements and includes them in the uplink message. The aux - cal board also generates test signals that are used 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 +/-15 volts DC. Cartridge power consumption is 30 watts. The CMR high voltage power supply (HVPS) provides the necessary power for the generation of 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 is provided on cable conductors 2 and 10. Because of the high power requirements of the transmitter, a duty cycle limit is imposed such that the transmitter is on for less than 3% of the time.

3.3.8 Power up reset/RS232 On power up, the power up reset generator circuit performs a global reset of all boards in the cartridge. As an aid in troubleshooting, the CMR cartridge has RS232 interface capabilities that interface to the downhole controller software. The downhole controller software includes several utilities that provide 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 field engineer by means of the MAXIS control panel. A measurement cycle consists of wait-time intervals, during which no data are acquired, followed by acquisition periods during which the transmitter is rapidly pulsed; each pulse produces a spin echo. The collection of spin echoes is referred to as a CPMG. CPMGs are always collected in pairs. The second set is acquired with the phase of the transmitter pulse changed to give spin echoes of negative amplitude. The two sets of CP MGs are 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 cycle consists of two wait periods. The measurement cycle begins when the downhole controller software pulses the "acquisition start" control signal. This event marks the beginning of the first wait time. After the wait period (during which time hydrogen nuclei align with the static field) the acquisition of plus-phase echoes occurs. The procedure is then repeated for the minus-phase cycle. This is followed by further wait time/acquisition operations until all subcycles in the measurement cycle have been completed. A data-acquisition operation follows each wait time. This process consists of transmitting pulses at the Larmor frequency. The first pulse is called the 90 ° pulse, since its function is to tip the nuclei 90° into the transverse, or measurement, plane. Succeeding pulses are called 180 ° pulses, since their function is to flip the nuclei 180°. The duration of the 90° and 180° pulses are approximately 20 and 30 microseconds, respectively.



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Acquisition Start +

Acquisition Phase Wait Time Active

wait #1

90° Pulse 19.2 µs

Tipping Pulse

+

+

Tcp 160 µs

wait #1

-

wait #2

+

wait #2

-

180° Pulses 29.2 µs

2xTcp 320 µs spins spins rephase dephase

20 µs

Q Switch Enable

Start of Echo

50 µs spins in phase

Figure 3.6. CMR timing diagram. The 180° pulse rephases the nuclei, and a spin echo is received after each pulse at a time interval known as the Carr-Purcell time, Tcp. The repetition period of the 180 ° pulses is twice Tcp. Since the echoes are also separated by this amount, this time interval is also called the echo spacing, TE. The echo spacing is primarily determined by the time required for the receiver electronics to come out of saturation following the 180 ° pulse. It is desirable to have the echo spacing as short as possible, and for the CMR tool the minimum echo spacing is 320 microseconds. The transmitter energy must be dissipated before the spin echo arrives or it will swamp out the extremely small echo signal. To do this, a "Q-switch" enable signal is generated that switches a 4-ohm resistor across the antenna for approximately 20 microseconds, effectively shorting out the antenna and dissipating the energy. The spin-echo signal lasts for approximately 50 microseconds. Since the start of the signal can be predicted by the value of Tcp, the acquisition timing electronics sends a "start of echo" signal to the receiver circuits when the echo begins. The echo signal received from the sonde is an amplitude modulated sine wave at the Larmor frequency. The parameter of interest is the area under the echo envelope. To extract this information the signal must be demodulated to remove the carrier. One complication to this process is that the phase relationship of the carrier to the timing signals is unknown. Because of this, a two-channel detection system is used; that is, the in-phase (i.e., R) and quadrature (i.e., X) components of the signal are found. The magnitude of the area under the echo envelope is then



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computed from these components. There is one R value and one X value for each echo in the CPMG sequence. To reduce both the telemetry bandwidth requirement and loading on the MAXIS system, a large portion 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 from the plus-phase measurement are subtracted from the corresponding R and X signals acquired from the minus-phase measurement. Since the echo envelopes of the minus-phase echoes are 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 the calibration operation.

•

The data is averaged with data collected from previous acquisition cycles, according to the downhole 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 entire duration 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 that contains 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 and number of the windows depend on the number of echoes in the sequence. In this way the large number of echoes is replaced by a few window sums. For example, if there are 200 echoes in the sequence the window boundaries will be at 30, 100 and 200. Echoes 2 through 30 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. The RMS 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 is complete, the receiver board sends a “processing complete” interrupt to the EDHC, indicating there are data to transfer uphole. The processing and data transfer occur during the wait time associated with the next plus-phase subcycle.


CMR Training Manual Data Description and Processing Overview

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4. CMR Data Description and Processing Overview 4.1 CMR spin-echo sequences In standard depth logging modes, 600 or 1200 spin-echo amplitudes are typically recorded in each of two channels using quadrature detection. During station logging, as many as 8000 spin echoes are acquired. The two channel data are used to estimate the phase of the signal and combine the two channels into: (1) a phase coherent channel that contains the total signal amplitude plus noise (hereafter called the "signal channel" or “spin-echo sequence”) and (2) a channel that contains only noise (hereafter called the "noise channel"). The data in the signal channel are used to compute T2-distributions. The data in the noise channel are used to estimate the root-mean-square (RMS) noise. The RMS noise is used to compute the standard deviations in the CMR logs (described in Section 4.7). The signal-to-noise (SNR) of CMR measurements is substantially lower than that of data acquired by most other well logging tools. Each echo in a phase-alternated pair (PAP) contains zero mean Gaussian noise with RMS amplitude equal to approximately 3.5 p.u. During depth logging, a three-level averaging of PAPs is normally performed prior to processing the data. Three level averaging reduces the RMS noise on each spin echo to about 2.0 p.u. Therefore, the SNR of the data typically processed during depth logging ranges from 15 to about 2 in reservoir quality rocks. Unfortunately, the SNR decreases with increasing borehole and formation temperatures due to two effects. First, the tool thermal noise increases with borehole temperature. Secondly, the measured spin-echo amplitudes decrease with increasing formation temperature according to the well-known Curie law of paramagnetism.

Figure 4.1. Typical spin-echo sequence for depth logging. Dashed line are window boundaries. A typical spin-echo sequence with 600 echoes is shown in Figure 4.1. The solid line in the figure represents the signal decay in the absence of noise. The SNR of the data shown in this example is in the midrange of that typically acquired during CMR depth logging operations.



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4.2 T2-distributions The decay of spin-echo sequences in porous rocks are properly described by continuous T2distributions. The multi-exponential nature of NMR relaxation in rocks is a result of the pore size distribution. That is, under some plausible assumptions, it can be shown that the T2-decay rate of NMR signals from fluids in an individual pore is proportional to its surface-to-volume ratio. The total NMR signal (being the superposition of signals from a distribution of individual pores) is therefore a summation of single exponential decays. The sum of the amplitudes of the individual decays is proportional to the total porosity measured by the tool. T2-distributions are displayed by plotting the amplitudes versus their associated relaxation times on a logarithmic scale. The computed T2-distributions are the primary result of the processing and are used to compute logs of CMR porosities (φCMR), free-fluid porosities (φFF), capillary bound fluid porosities (φBF) and logarithmic mean relaxation times (T 2,log).

Figure 4.2. Typical T2-distribution for a clean sand. A T2-distribution typical of a clean sandstone formation is shown in Figure 4.2. The total porosity is proportional to the area under the T2-distribution. The free-fluid porosity is proportional to the shaded area having T2 relaxation times greater than 33 msec. The 33 msec is an empirically determined cutoff that is frequently used in sandstones to partition the distribution into bound and free-fluid porosities. The logarithmic mean relaxation time for the distribution is 44 msec. The logarithmic mean relaxation time of a distribution is analogous to the "center of mass" of a body in classical mechanics. The logarithm of the mean relaxation time is computed by averaging the logarithms of the relaxation times in the distribution each weighted by its signal amplitude. The logarithmic mean relaxation times are used in the estimation of permeability in sandstone formations.



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4.3 Inversion problem The computation of T2-distributions from spin-echo sequences involves a mathematical inverse problem. 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 few exponentials or to a stretched exponential model. These simple models are mathematically stable but do not provide valuable information on pore size distribution and free fluid that is contained in the T2-distributions. The inverse problem that must be confronted in computing T2-distributions is mathematically illposed. It can be shown that a spin-echo sequence consisting of hundreds or thousands of spinecho amplitudes contains only a few (e.g. 5) linearly independent pieces of information. Therefore the problem is underdetermined; the number of unknown amplitudes (e.g. 30) far exceeds the independent pieces of information. This results in unstable and nonunique solutions to the mathematical inverse problem. The solutions are unstable because arbitrarily small changes in the input 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 inverse problems. The regularization method imposes a criterion for selecting a smooth T2-distribution from the possible solutions that are consistent with the data. The smoothness criterion is consistent with the fact that the NMR measurement kernels attenuate the high-frequency components in the underlying T2-distributions. That is, NMR data intrinsically have low frequency content, which is the rationale for selection of a smooth distribution. The regularization not only reduces the statistical fluctuations on the computed T2-distributions but it also controls the standard deviations of the logs.

4.4 Data redundancy and data compression Because the spin-echo sequence contains only a few independent pieces of information, they can be compressed into a few numbers without any loss of information. Data compression is performed downhole using a digital signal processing chip in the tool electronics cartridge. Compression reduces telemetry capacity requirements and also disk and tape storage (the spinecho 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 the computing resources presently available at the wellsite. This would not be possible using the raw 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 sh ows averaged window sums and one-standard-deviation error bars computed from the 600 echoes shown 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 windows whose boundaries are indicated by the dashed lines in Figure 4.1. The RMS noise on the averaged amplitude in each window is reduced, by a factor equal to the square root of the number of echoes in the window. For example, the third window in Fig. 1 contains 100 echoes so that the 2.0 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 the underlying 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 earlier windows. In particular, only the first three window sums show much sensitivity to bound fluid below 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 small pores completely decays. Therefore, later echoes contain contributions from only the large pore spaces that have long T2. The sensitivity curves show the contribution to each window sum from a unit signal amplitude with a particular T2 relaxation time. The sensitivity to fast relaxation times, of the order of a few milliseconds, can be increased (e.g., the curves in Figure 4.4 shifted to the left) by using shorter early time windows. Simulations have shown, however, that using shorter early time windows provides negligible practical increases in CMR porosity and is less robust in the presence of noise. The reason for this is that only the first few echoes contain contributions from signals having relaxation times shorter than a few milliseconds.

4.5 Maximum likelihood estimation The statistical properties of the window sums are used to derive a maximum likelihood function for these random variables. The amplitudes of the components in the multi-exponential relaxation model (i.e., the T2-distributions) are determined by maximizing the likelihood function subject to a constraint that the amplitudes be non-negative. The relaxation times in the relaxation model are determined by user inputs (see Section 4.8) and are therefore not part of the estimation. This means 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 with the raw data. Monte Carlo simulations have shown that this method results in unbiased log outputs over the entire range of SNR. The regularization requires a parameter γ, that is automatically 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 been shown 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 is difficult to quantify because there is no sharp cutoff on the sensitivity response to short relaxation times. This can be seen from the sensitivity plots in Figure 4.4. The loss of sensitivity to short relaxation times is gradual and depends on the SNR of the measured data; however it is the interecho spacing that provides an intrinsic lower limit to the shortest relaxation times that can be measured. 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 greater than a few milliseconds. The CMR porosity is therefore an effective porosity that does not include contributions from clay-bound water. NMR laboratory measurements on core samples have shown 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 standard deviations in all of the derived log outputs. The standard deviations can be reduced, albeit with some 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 y the acquisition of 600 spin echoes. The total time for acquisition of a single PAP is 3 seconds. The three-level averaging results in total CMR porosity statistical precision of less than 1.0 p.u., a free-fluid porosity precision of less than 0.5 p.u. and a capillary bound-fluid porosity precision of about 1.0 p.u. Monte Carlo simulations have shown that the statistical precisions quoted above will vary slightly depending on the characteristics of the underlying T2-distributions. The porosity precision is comparable to that obtainable with nuclear logging tools. An important difference, however, is that the CMR porosity standard deviations are essentially independent of the SNR of the measurements (i.e., do not depend on the porosity of the formation), whereas the precisions of measurements made by nuclear logging tools are known to vary with porosity. Unlike the CMR porosity measurements, the standard deviations in the logarithmic mean relaxation times depend on the SNR of the measurements. Therefore, an absolute precision specification cannot be quoted for the estimated logarithmic mean relaxation times. The computed standard 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 is estimated from the data in a noise channel that is computed for each measurement. Figure 4.5 shows 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 processing parameters: (1) the number of components in the multi-exponential relaxation model (2) the minimum 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 the computation of T2-distributions, relative amounts of free and bound-fluid porosity and mean relaxation times. It is useful to briefly discuss and define the role played by each of these parameters.

Number of components Simulations and processing of field data have shown that the number of components has negligible effects on the CMR log outputs (which are integrals of the T2-distribution) provided that at least a 10-component model is employed. Adding more components results in having more points on the computed T2-distributions and is necessary for displaying continuous T2distributions. During depth logging, a 30-component model is frequently used so that T2distributions can be displayed while logging. For station logging, a 50-component model is normally 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 the relaxation times in the model, which are chosen equally spaced on a logarithmic scale. The minimum value of T2 is determined by the intrinsic sensitivity limit of the measurement to short relaxation times. The intrinsic limit for a measurement is set by the inter-echo spacing. The CMR pulse sequences, under normal conditions, have an inter-echo spacing of 0.32 msec. This suggests that the minimum T2 should be set in the range from 1 to 3 msec. The choice is not critical 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 longest relaxation time that can be present in the T2-distribution and the longest relaxation times that can be 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 that CMR log outputs are insensitive to the value of T2max over a reasonable range of values. For CMR 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 to 3500 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 for T2max is typically used. Station logs with long echo collection times are required to resolve features 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 required to determine accurate values of the CMR log outputs. That is, values of φCMR, φ FF , 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-fluid porosity. The cutoff depends on mineralogy, and cutoffs have been determined empirically for some sandstones and carbonates. The experimental data support a value of 30 msec in sandstones 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 the quoted 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 for the 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 as explained below. The rate at which the proton magnetization approaches its equilibrium value depends on the T1distribution of longitudinal relaxation times in the sample. If the wait time is too short, the signal associated with the longer relaxation times will be reduced (e.g., φFF will be too low). Ideally, the wait time should be at least three times the longest relaxation time in the T1-distribution. In some logging environments (e.g., vuggy carbonates) this would require wait times longer than 10 seconds, 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/T2 ratios range from approximately 1 to 3 with a mean of about 1.65. The experiments were performed, and are valid, in the 2-MHz frequency range of the CMR tool. An inter-echo spacing of 0.32 msec was used in acquiring the experimental data. At higher frequencies and for longer interecho 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 exception occurs in zones with unflushed gas. The relatively large gas diffusion constant can cause diffusion effects that reduce the T2 of the gas. Since T1 is not affected by diffusion, enhanced T1/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 for short wait times. Using longer wait times reduces not only the magnitude of the correction but also any errors in log outputs that occur because the assumed ratio is not equal to the actual T1/T2 ratios. Note that if the assumed T1/T2 ratio is greater than the actual ratio in the formation, then φ FF 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 logging operations. 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 relaxation time; however, if a correction is not applied, then the permeability estimator based on T 2,log can be pessimistic. It should be noted that, in practice, mud filtrate relaxation times of the order of 1 sec are frequently encountered and the correction is negligible.


CMR Training Manual Calibration and Environmental Corrections

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5. Calibration and Environmental Corrections 5.1 Overview The computation of φCMR, φ FF, and φBF requires several environmental and calibration parameters. These include the master calibration constant, the formation temperature, the magnetic field strength 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 is placed directly on the sonde. Electronic calibration is achieved using a test loop located near the antenna. A constant amplitude signal is sent to the test loop and picked up by the antenna. The test loop signal is used to correct for changes in system gain that are caused by changes in temperature, operating frequency and conductivity. Signal amplitudes measured during logging are also automatically corrected for changes in temperature and static field strength. The calibrated and environmentally corrected porosity is given by

φ CMR

2  AMP   LOOP   BO,MC   TEMP   1  MC DH DH   =        ,  AMP B TEMP  MC   LOOPDH   O,DH   MC   HI 

(5.1)

where: φCMR

= CMR porosity, calibrated and corrected (p.u.)

AMPDH

= Raw signal amplitude (volts)

AMPMC

= Amplitude of the water bottle signal (volts)

LOOP MC

= 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. The CMR 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. Amplitudes measured downhole are corrected to the temperature during the master calibration by the last term in Eq. 5.1:    TEMPDH  .  TEMP  

(5.2)

MC



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•

The field strength of the permanent magnets decreases with temperature. A decrease in field strength 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 are always 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 used to convert signal amplitudes obtained in the borehole into porosity units. During the master calibration, a fixture containing a water sample is placed on the tool antenna cover. The fixture was designed so that the water completely fills the sensitive region of the measurement. The water is doped with Nickel Chloride (NiCl) to reduce the water T1 relaxation time to approximately 50 msec. This allows the use of a short wait time and consequently a fast calibration; excellent SNR 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. This signal amplitude (i.e., AMPMC) represents a 100 p.u. standard. During logging, the CMR porosity is simply the ratio of the signal amplitude determined downhole to the master calibration amplitude (i.e., the first term in Eq. 5.1: AMP DH /AMPMC). The test loop signal (LOOP MC), static field strength (B 0,MC) and temperature of the fluid in the bottle (TEMPMC) during calibration are stored in an EEPROM in the CMR cartridge, together with the master calibration amplitude (AMP MC).

5.3 Electronic calibration Electronic calibration occurs during the wait period of the measurement cycle. At this time a low level (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 it can be measured downhole. During logging, the test loop signal checks out the entire CMR system except for the transmitter. (Note: In test phase the loop is also used to check the transmitter). Changes in electronic gain occur with changes in temperature, conductivity and the operating frequency of the tool. During logging, a system gain correction is calculated from the loop signal (LOOPDH) and the loop signal obtained during master calibration (LOOP MC): correction = (LOOPMC LOOPDH ) .

(5.3)

This is the second term in Eq. 5.1. The value of LOOP MC is indicative of the system gain at the time AMPMC was determined. The gain correction is applied downhole to both the spin-echo amplitudes and window sums. The gain correction, which should vary slowly with depth, is also presented on the CMR quality control log.



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5.4 Environmental corrections The signal amplitudes measured during logging are automatically corrected for changes in temperature and static field strength, as per Eq. 5.1. Formation temperature is obtained from the sonde temperature sensor. The determination of the static field strength during logging is described in Section 6. Corrections for hydrogen index may also be optionally applied.

Temperature correction Signal amplitudes measured in boreholes must be corrected for the Curie law effect that causes a reduction in signal amplitude with temperature. The formation temperature is used in the correction together with the master calibration temperature (i.e., the temperature that corresponds to the 100 p.u. signal). The formation temperature is approximated by a temperature sensor located in the CMR sonde.

Magnetic field strength The amplitude of the measurement is proportional to the square of the magnetic field strength in the zone of investigation. The field strength changes with tool temperature and, therefore, a correction is applied to account for the fact that the master calibration is performed at a different field strength. In practice, other effects besides temperature can cause changes in the magnitude of the static field. Iron scrapings from the drilling process can adhere to the tool magnets and perturb the static field. The CMR tool has a special pulse sequence for measuring the static field strength downhole that is used immediately prior to logging. During logging, the field strength is estimated from a Hall probe and temperature sensor located in the sonde and the correction is automatically applied.

Hydrogen index The hydrogen index of the fluid in the measurement zone is an input parameter used by the processing. It is used to correct for the fact that the tool master calibration is performed using a water sample with a hydrogen index of 1. The software computes the hydrogen index of formation fluids from: •

the salinity of the mud filtrate

•

formation pressure (estimated by the mud column hydrostatic pressure that is computed from an input value of mud weight and the true vertical depth)

•

formation temperature (estimated from the sonde temperature readings).

The hydrogen correction is an option in the MAXIS software. The correction assumes that formation fluids are mud filtrate and is therefore an approximation. However, it is an important correction in saline muds. For example, if the mud filtrate has a hydrogen index of 0.95, φCMR will be 5% too low if the correction is not applied. In zones with unflushed hydrocarbons, the hydrogen index of the composite fluids is generally unknown. It depends on many variables including the fluid saturations, formation pressure, oil properties, and gas types (methane, propane, etc.).


CMR Training Manual Operating Procedures

-49-


6. Operating Procedures 6.1 Special procedures CMR logging involves many new concepts. These concepts, which are summarized below, must be 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 hydrogen nuclei. Operation at this frequency is required to maximize the amplitude of the spin echoes and produce a calibrated log. The Larmor frequency (f 0) depends upon the strength of the static magnetic field (B 0) generated by the permanent magnets; that is, f

0

= 4258.B 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, and the corresponding Larmor frequency is approximately 2300 kHz. The strength of the static field decreases as the temperature of the samarium cobalt magnets increase. Because of this, the operating frequency must be periodically changed during logging operations. The frequency is initially determined by running the tool adjacent to a porous bed and measuring relative signal strengths as the operating frequency is changed. The signal amplitude peaks 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, the operating 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 nuclei align (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 to produce the spin echoes.

The pulse sequence specifies the duration of each of the wait times, the number of times that the transmitter is pulsed during the acquisition period (this determines the total number of spin echoes that are collected) and the time interval between the transmitter pulses during the acquisition period.



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A pulse sequence may have single or multiple wait times. Single wait times are used to measure the T2-distribution of the formation. Multiwait time sequences are used to determine both T2distributions and T1/T2 ratios. The T1/T2 ratio is used for a polarization correction, as described below.

6.1.3 Polarization and the polarization correction As previously stated, hydrogen nuclei align (become polarized) in the direction of the static magnetic 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 the longitudinal 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 hydrogen nuclei. Shorter wait times result in reduced signal, as nuclei that are not polarized do not contribute to the amplitude of the spin echoes. This in turn results in erroneously low porosity and T2 values. Unfortunately, wait times of 5 to 10 sec are impractical for depth logging, because the tool would 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 on core samples. These measurements show that T1 and T2 are closely related in rocks: both T1 and 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 value of 1.6. For CMR measurements acquired with a single wait time, the polarization correction is determined from the measured T2-distribution and an input value of the T1/T2 ratio. Both are used to estimate the T1-distribution that in turn is used to correct the signal amplitudes. Note that a polarization correction is required for the free-fluid porosity but not the bound-fluid porosity. This is because the bound-fluid has short T1 and therefore polarizes in a fraction of a second. During logging, freefluid porosity is computed both with and without the polarization correction. A free-fluid polarization correction is then defined as PCF =φFF / φ FF,UNC ,

(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 different than the input value. In addition, the ratio probably varies continuously with depth. For this reason, wait times should be sufficiently long to minimize the magnitude of the correction. In order to produce reasonably accurate logs, the correction should be less than 1.10 in zones of interest. The polarization correction, PC F, 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, the T1/T2 ratio is computed directly from the signal amplitudes obtained from each of the different wait times.



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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 each measurement cycle. This affects maximum logging speed since a new measurement is required for each 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 wait time of 1.3 sec is used to allow for polarization of the hydrogen nuclei. Six hundred spin echoes are then measured with an interecho spacing of 0.32 msec. The acquisition time is therefore about 0.2 sec and the total measurement cycle time is 1.5 sec. Hence, the total time to acquire a phase alternated pair is 3 sec. A 6 in. sample rate is used for standard vertical resolution logging. To obtain 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 this would lead to large polarization corrections and an unacceptable decrease in the accuracy of the log, 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 most circumstances, this will result in φCMR logs with a precision of less than 1 p.u., φ FF logs with a precision of less than 0.5 p.u., and φBF logs with a precision of about 1.0 p.u. Unlike nuclear logging measurements, CMR precision does not change with porosity. The precision of the log can be improved by increasing the vertical averaging; however, this results in a decrease in vertical resolution. For example, consider the case above where the cycle time 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 that is averaged over 30 in. of formation. CMR logs that are averaged over 5 levels have similar vertical resolution to Litho-Density logs. The precision of NMR measurements depends upon temperature. An increase in temperature results in an increase in the noise in the data and a reduction in signal strength. When logging deep hot wells, it may be preferable to increase the amount of averaging to ensure good precision.

6.2 Tuning the tool to the Larmor frequency The Larmor frequency (f 0) 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 with temperature and as magnetic debris accumulates on the magnets; hence, the operating frequency must be periodically adjusted while logging. Operation at frequencies higher or lower than the Larmor 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 operated at this frequency it is said to be “on resonance” or “tuned” to the Larmor frequency. Tuning the tool 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 of capacitance is specified by the tuning relay control word (abbreviated to “tune word” in the following).

•

Operating the transmitter at the Larmor frequency. The transmitter pulse produces an rf magnetic field that tips the hydrogen nuclei away from the static field direction. Efficient tipping occurs only if the pulses are at the Larmor frequency.

The Larmor frequency is given by

f0 = 

γ  B ,  2π  0

(6.3)

where B0 is the static field strength in the measurement region, and γ is the gyromagnetic ratio of the resonated nucleus. For hydrogen nuclei, γ / 2π = 4258 Hz/Gauss. Hence the Larmor frequency is determined entirely by B0 For the CMR tool, B 0 is nominally 540 Gauss at room temperature. This corresponds to a Larmor frequency just below 2300 kHz. B0 decreases with temperature. The samarium cobalt magnets in the CMR sonde have a temperature coefficient of about 1 Gauss/ 5 O C. This corresponds to a change in Larmor frequency of 0.85 Khz/ O C. Therefore, the tool operating frequency must be adjusted according to the 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, the amount of metal debris varies by well, and for this reason the Larmor frequency must b e determined in situ, as described below. Sonde Characterization Curve 1400

A m p l i t u d e

1200 1000 800 600 400 200

0 2240

2260

2280

2300

2320

2340

2360

2380

Frequency - kHz

Figure 6.1. Signal amplitude versus operating frequency.



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The Larmor frequency is determined by measuring signal amplitudes as the operating frequency of the tool is changed. Figure 6.1, known as the sonde characterization plot, shows the characteristic curve for these types of measurements. The data was generated in the lab from measurements 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 corresponds to a B0 of 542 Gauss. The same general principle applies to determining the Larmor frequency downhole with one important exception; it took several hours to collect the data shown in Figure 6.1. Measurements were taken at 240 different frequencies and several hundred readings were averaged at each frequency 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 sonde characterization data to determine the Larmor frequency. This method takes advantage of the fact that the sonde characterization and downhole measurements are identical except for a shift in frequency 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 following steps: 1. The tool must be tuned in a porous interval. In thick zones, the tool can be moved s lowly while it is tuned. In thin porous zones, it is preferable to tune the tool while stationary (unless there is danger of sticking). The interval that has the highest porosity should be selected since the time taken to complete the LFST decreases with porosity. A minimum porosity of 10 p.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 the temperature sensor in the sonde. This estimate will be close to the true Larmor frequency if the tool has not accumulated large amounts of metal debris on the magnets. The initial estimate is denoted as FI. Test Loop Amplitude vs Tune Word 2500

A m p l i t u d e

2000 1500 1000 500 0 40

50

60

70

80

90

100

110

120

130

140

Tune Word

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) to make the antenna resonate at F I. The capacitance required depends on both wellbore temperature 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 the tune word search task (TWST). During this procedure, the calibration signal is sent to the test loop at frequency FI, and received signal amplitudes are recorded for selected tune words, as shown 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 under wellbore conditions. As the operating frequency is subsequently changed (during the LFST or during depth logging) the appropriate tune word is selected from a look-up table stored in an EEPROM in the cartridge. The Larmor frequency is then determined by measuring signal amplitudes for 7 values of transmitter frequency centered around F I. The signal amplitudes are fit to the sonde characterization data and the Larmor frequency interpolated from the fit; it is the frequency at the maximum amplitude. This results of this procedure are shown in Figure 6.3.

Larmor Frequency Search Task 120

A m p l i t u d e

- Amplitudes measured downhole

100 80

Sonde characterization curve

60 40 f = 2425 kHz 0

20 0 2300 2320 2340 2360

.

2380

2400 2420 2440 2460

2480 2500

Operating Frequency

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 the well. During logging the operating frequency is automatically adjusted in 1 kHz steps according to estimates of B 0 made from the sonde temperature sensor. This corresponds to a temperature change of approximately 1.2 O 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 the temperature 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 B 0.



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6.3 MAXIS control panel A control panel has been implemented in order to simplify logging operations. The control panel allows 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 or station logging mode. The panel also displays various diagnostic channels from the tool and computed outputs that indicate log quality. The control panel is shown in Figure 6.4. CMRT Control Panel File

Mode

Current Mode: Pulse Parameters # of wait times Echo spacing (us)

1 320.00

Auto-cal

Sample interval (in) 6.00 Update interval (sec) 30.00 Max Log speed (ft/h) 600.00 Uphole Processing Parameters

Downhole Parameters

Auto Frequency

Sandstone Depth Log Logging Parameters

Set Pulse Sequence. . . .

Send Echoes

CMR*

No Yes Yes

Downhole stacking

Apply Reset

Signal Process On

Regularization

Auto

T1/T2

1.50

T2 min (ms)

1.00

T2 max (ms)

1500.00

T2 cutoff (ms)

33.00

T2 mud filt. (ms)

3000.00

# of components

30

Uphole stacking

1

Hydrogen index

Manu

Permeability model

SDR

Frequency (KHz)

2300.00

Monitored Signals Regulated HV (v)

247.60

Unregulated HV (v) 285.05 Noise (pu)

0.012

Delta B (mtes)

0.03

Temperature (degC)

25.31

Xmitter peak volt (v)

10.26

System gain

1.00

Monitored Data Channels CMR porosity (pu) 23.00 FF porosity (pu)

19.60

Log Mean T2

215.00

Signal / Noise

11.00

Figure 6.4. MAXIS control panel.



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Parameter values entered into the control panel are transferred to the local parameter buffer when the Apply button is selected. The knowledge base is also updated at this time. If the Reset button is selected, parameter values in the control panel are overwritten by values in the local parameter 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 and cover the majority of logging environments encountered in the field. When one of the default modes is selected, most of the parameters cannot be changed. Therefore, selection of one of the default 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 to values that are within certain limits. This allows a set of parameters to be customized to suit a particular environment. The ability to customize parameter sets adds complexity to the system but 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 be saved by selecting the File button. The parameters are then saved to a file in the current disk subdirectory by activating SAVE in the submenu. The parameters may be retrieved later b y selecting 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 this switch is to set the CMR log outputs to absent values when the logging speed is too high for reliable outputs. This occurs when the CMR tool is run in combination and the logging speed is increased 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. This parameter 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 interval between successive transmitter pulses. This parameter must be greater than 0.32 msec and is subject to a duty cycle constraint. The default value is 0.32 msec and it is editable only in expert mode. Set Pulse Sequence. This specifies the duration of each of the wait times in the pulse sequence, the number of echoes collected after each of the wait times, and the number of times each 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 associated with 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 the window sums. The default is yes. Spin echoes are considered raw data and may be requested by clients who wish to process the data 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 changed according 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 applied to 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)

Apply

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

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. for standard 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 sample rate interval. For a single-wait time sequence, the maximum logging speed allows sufficient time for one PAP to be acquired during the sample rate interval. For a multiwait time sequence, the maximum logging speed allows sufficient time for all PAPs associated 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 stacked downhole prior to computing the window sums. The default for depth logging is 3. During station logging, 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 stacking should 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. The preselected T2 values are equally spaced on a logarithmic scale and between values of T2 min and T2 max. The number of preselected T2 values is referred to as the number of components in the distribution.

Pi T2 Min

T2 Max

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 in expert mode only. T2 max. This is the maximum value of T2 for the computed T2-distribution. T2 max can be edited in expert mode only. # of components. This parameter defines the number of components in the T2-distribution and is set to 30 and 50 for depth and station logging, respectively. This parameter can be changed only in expert mode .



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Uphole Stacking. This parameter defines the number of consecutive samples that are averaged uphole. The default is 1 and the maximum value is 30. This parameter can be changed only in expert 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 is applied to the computed T2-distributions. Regularization is required to produce repeatable log outputs from the inherently noisy raw data. The amount of regularization is determined by the input value of gamma. High values of gamma improve the precision of the log outputs but may introduce 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 determined from 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 second window 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 30 msec 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 and exponents. T1/T2. This parameter is used for the polarization correction that is applied to single-wait time data. The default is 1.5. T2 mud filt. The T2 of the mud filtrate can be measured at the wellsite and its value used to correct the T2-distributions. The default value is 50,000 msec, and it can be changed only in expert 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 the CMR 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 filtrate salinity, formation water salinity, mud weight and deviation. For water muds, it is assumed that the formation is completely flushed and the mud filtrate salinity is used. For oil-base muds, it is assumed 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 the sonde temperature. Values of hydrogen index may be entered directly if manu is selected. The default setting is manu combined 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 in Table 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 logging speed 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 then collected with an echo spacing of 0.32 msec. Total time to acquire 1 PAPs is approximately 6 sec. The sample rate may be set by the user. The default value is 6 in. The maximum logging speed 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. All parameters 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 the signal-to-noise ratio. New log outputs are periodically computed from the stacked data and displayed on the control panel. The station log is terminated when a signal-to-noise ratio of at least 20 has been attained. •

Sandstone station log. The wait time is set to 3 sec. Three thousand echoes are then collected 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. All parameters are editable but subject to constraints.

•

Sandstone multiwait time station log. This pulse sequence consists of the following 3 subsequences:

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 are then collected with an echo spacing of 0.32 msec. Total time to acquire 1 PAP is approximately 0.6 sec.


CMR Training Manual Operating Procedures •

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Mud sample. This mode is used to determine T2 for a mud or mud filtrate sample at the well site. The wait time is set to 5 sec. Three thousand echoes are then collected with an echo spacing of 0.32 msec. Total time to acquire 1 PAP is approximately 12 sec.

# of Wait Times Depth logging Sandstone 1 Carbonate 1 Expert up to 8 Station logging Sandstone Carbonate Sandstone MWT

Carbonate MWT

Expert

1 3

3

up to 8

Wait Time (sec)

# of Echoes

T2 min

T2 max

T2 cut

1.3

600

3

3000

33

2.6

1200

3

3000

100

up to 8000 3.0

3000

1

3000

33

6.0

5000

1

5000

100

1.20

1800

1

3000

33

0.38

600

0.18 2.0

300 3000

1

3000

100

1.0

1800

0.65

1200 up to 8000

Notes: •Default echo spacing is 0.32 msec for all modes. •Default number of components is 30 for depth logging and 60 for station logging. •Allowed number of echoes is 200, 300, 600, 1200, 1800, 3000, 5000, 8000 •A duty cycle limit applies for all modes; the wait time must be roughly twice the time during which echoes are acquired.

Table 1. CMR logging modes.



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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 the specified 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 each subsequence in the measurement cycle. Therefore, up to 8 values are available depending on the pulse sequence selected. For multiwait time sequences, the display shows the RMS noise for the first sub-sequence. Note that the RMS noise is calculated from the PAPs after stacking. The RMS noise is also displayed 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 is used to estimate B 0 and for the Curie law correction. ∆B. This is the difference between the temperature estimate of B 0 and the Hall probe estimate. If ∆B exceeds 1 Gauss (0.1 mtesla), a Larmor frequency search task must be performed to accurately measure B 0.

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 also displayed on the control panel.



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6.4 Presentations and Formats 6 .4 .1

Depth logging - Four tracks with T2-distribution

4700

0

10000

Gamma Ray (GR) (GAPI) Tension (TENS) (LBF)

150 0

Bound Fluid Volume (BFV) Permeability - CMR (KCMR) (V/V) 0.3 0.1 (MD) 1000 3

0 0.3

CMR Free Fluid (CMFF) (V/V)

0 0.1

Bound Fluid CMR Porosity (CMRP) 0.3 (V/V)

T2 Distribution (LC03) (MS) 3000

T2 LOG Mean (T2LM) (MS) 1000 Perm

0

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-fluid volume. The bound-fluid volume is also presented as a separate curve with porosity increasing to 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 4700

Gamma Ray (GR) (GAPI)

0

0

Polarization Correction (POLC[0]) (----)

10000

Tension (TENS) (LBF)

150

10

0

0

CMR System Gain (CMR_GAIN) (----)

1

75

CMR Temperature (CMR_TEMP) (DEGF)

125

-0.5

Delta B0 (DELTA_B0) (MTES)

Standard Deviation of CMR Porosity (CMRP_SIG) 0.1 (V/V)

0

Standard Deviation of Free Fluid (CMFF_SIG) 0.1 (V/V)

0

Computed GAMMA (GAMMA[0]) (----)

10

0.5 0

Operating Frequency (FREQ_OP) 2260 (KHZ) 2310 5

-180

Signal Phase (SPHASE[0]) (DEG)

RMS Noise (RMS_NOISE[0]) (V)

0

180

Figure 6.8. Log quality control presentation format. Track 1 contains the correlation curves and the polarization correction (see Section 6.1.3 for a description of the polarization correction). Track 2 contains information relating to the tool operation: signal phase, system gain (this is the inverse of the electronic gain correction described in Section 5.3), sonde temperature, operating frequency, ∆B (this is the difference between B 0 estimated from the Hall probe and B 0 estimated from the sonde temperature, as described in Section 6.2). Track 3 contains information relating to the precision of the output logs: CMR porosity standard deviation, 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

CMR STATION LOG REPORT

DEPTH(Ft): 33.533

PARAMETER SUMMARY Mode: Sandstone-station log Echo spacing(us):

320.000

Wait times(sec):

(3.000 )

Number of echoes:

(3000 )

Repetition:

(1 )

Regularization:

Auto

T2 min(msec): 1.000

T2 max(msec): 3000.000

T2 cutoff(msec): 33.000

T1/T2: 1.500

Update int.(sec): 8.0

MEASURED DATA C MR P or os it y(V /V ): 0 .1 92

F re e F lu id (V /V ): 0 . 160

L og M ea n T 2(m se c) : 1 20 .4 32

C om pu ted T 1/ T2 : N/ A

P er mea bi li ty (m d): 7 8. 34 5

T em pe ra tu re (d eg c) : 26 .0 65

Signal/Noise: (36.111 )

T2 cutoff

0.7

0.6

0.5

0.4 Amplitude 0.3

0.2

0.1

0 1

10

100

1000

10000

T2(ms)

Figure 6.9. CMR single-wait time station log report. CMR log outputs are displayed on the station log report, together with the measurement cycle and processing parameter values. A quality control log, similar to that shown for depth logging, is also available for station logging.



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6.4.4 Station Logging -- multiwait time station log display

CMR STATION LOG REPORT

DEPTH(Ft): 32.325

PARAMETER SUMMARY Mode: Expert-station log Echo spacing(us):

320.000

Wait times(sec):

(1.200 0.380 0.180 )

Number of echoes:

(1800 600 300 )

Repetition:

(1 3 5 )

Regularization:

Auto

T2 min(msec): 1.000

T2 max(msec): 3000.000

T2 cutoff(msec): 33.000

T1/T2: 1.000

Update int.(sec): 13.0

MEASURED DATA C MR P or os it y( V/V ): 0 . 16 2

F re e Fl uid (V /V ): 0 .1 50

L og M ea n T 2( ms ec ): 2 3 5. 82 1

Computed T1/T2: 2.187

Permeability(md): 154.542

Temperature(degc): 26.588

Signal/Noise: (30.250 34.463 32.781 )

T2 cutoff

0.4

Updated 0.35

Wait time 1 Wait time 2

0.3

Wait time 3

0.25 Amplitude 0.2 0.15 0.1 0.05 0 1

10

100

1000

10000

T2(ms)

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 are computed for each wait time assuming a T1/T2 ratio of 1.0. These distributions are used to calculate the true T1/T2 ratio (in this case, 2.187). An updated distribution is then computed using the 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 powered caliper 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 is run with tools that have standoffs or centralizers (e.g., AIT-H). Tool turners are required in deviated 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 with eccentered tools (e.g. APS or CNT), knuckle joints must be used to prevent undesirable standoff.

Pulse sequence Select the appropriate pulse sequence according to mineralogy. In almost all situations, one of the 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 can operate at the required speed. Maximum logging speeds are calculated by the MAXIS based on the pulse sequence and sample rate. The maximum logging speed ensures that a new measurement is acquired during each sample interval. Do not exceed the maximum logging speed. If exceeded, there is a possibility that a new measurement will not be acquired during a sample interval. When this occurs, log values from the previous 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 logging speed, provided that the resulting vertical resolution (about 30 in., for 3 level averaging) is acceptable.



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Tool tuning Correct tool tuning (tune word and Larmor frequency search tasks) is the single most important task 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 TWST and LFST reports on the CMR log print.

•

The tool should be tuned adjacent to an interval that has the highest porosity. Ideally, this is the 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 while stationary.

•

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 takes at 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 less than 3 kHz. This is usually accomplished with 2 or 3 attempts. •

Examples of acceptable and unacceptable LFST results are shown on Figure 6.11, Figure 6.12, Figure 6.13 and Figure 6.14. Problems occur in low porosity, in shales and when the input 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 is considered to be adequately tuned when two consecutive LFST results (i.e., “The found operating 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 (1 gauss) during logging. Pay close attention to delta B when logging wells that have long casing strings. The CMR tends to pick up large amounts of metal debris in these wells.



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2

t n e m e r u s a e M d e l a c S

5 . 1

1

5 . 0

0

2100 2125

2150

2175

2200

2225

2250

2275

2300

2325

2350

2375 2400

Frequency (kHz)

Figure 6.11. LFST result under ideal conditions; 100 p.u. signal source in the lab.

2


5 . 1

1

5 . 0

0

2100 2125

2150

2175

2200

2225

2250

2275

2300

2325

2350

2375 2400

Frequency (kHz)

Figure 6.12. LFST result under borehole conditions. This result is borderline acceptable and should be repeated..



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2


5 . 1

1

5 . 0

0

2100 2125

2150

2175

2200

2225

2250

2275

2300

2325

2350

2375 2400

Frequency (kHz)

Figure 6.13. Input center frequency too high. Redo the LFST.

2


5 . 1

1

5 . 0

0

2100 2125

2150

2175

2200

2225

2250

2275

2300

2325

2350

2375 2400

Frequency (kHz)

Figure 6.14. Input center frequency too low. Redo the LFST.



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6.5.2 Response in various formations •

Clean formations The CMR porosity is comparable to neutron and density porosities in clean sandstones and carbonates.

•

Shaly formations The CMR porosity is an effective porosity; and is therefore lower than neutron and density porosities in shaly formations. Free-fluid porosity is usually much lower than CMR porosity in shaly formations.

•

Gas zones In gas zones, the CMR porosity is much lower than density porosity, and usually slightly lower than neutron porosity. The CMR response in gas zones depends on invasion and the hydrogen index of the gas.

•

Shales In shales, CMR porosity is low (often close to zero p.u.) and free-fluid porosity is typically zero p.u.

•

Heavy oil zones CMR porosity does not include the volume of heavy oil (or bitumen). The CMR porosity is much lower than neutron and density porosities when heavy oil is present.

6.5.3 Borehole conditions •

Washouts CMR porosity spikes high in washouts and intervals where the skid is not in good contact with the formation.

•

Mudcake CMR readings are unreliable when mudcake thickness exceeds 0.5 in.



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6.5.4 Repeatability A typical repeat analysis is shown in Figure 6.15. Note that the free-fluid porosity repeatability is superior 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 vuggy carbonates. The CMR has a small azimuthal coverage.

•

Irregular tool motion, as encountered in “sticky” and rugose boreholes.

•

Poor skid contact .

•

High formation temperature.

8100

0


100

1

Permeability - CMR (KCMR) (MD) 1000 0.3

CMR Porosity (CMRP) (V/V)

0

0

GR_REP Curve (GR_REP) (GAPI)

100

1

KCMR_REP Curve (KCMR_REP) (MD) 1000 0.3

CMR Free Fluid (CMFF) (V/V)

0

0

1

TENS_REP Curve (TENS_REP) 10000 (LBF) 0

1

10000


T2 LOG Mean (T2LM) (MS)

1000 0.3

CMRP_REP Curve (CMRP_REP) (V/V) 0

T2LM_REP Curve (T2LM_REP) CMFF_REP Curve (CMFF_REP) (MS) 1000 0.3 (V/V) 0

Figure 6.15. CMR repeat analysis.



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6.6 Log quality display An example log quality display for the CMR tool is shown in Figure 6.16.

4700

0


150

Polarization Correction (POLC[0]) 0 (----)

10000


10

0

0

CMR System Gain (CMR_GAIN) (----)

CMR Temperature (CMR_TEMP) 75 (DEGF) Delta B0 (DELTA_B0) (MTES)

-0.5

1

Standard Deviation of CMR Porosity (CMRP_SIG) 0.1 (V/V)

Standard Deviation of Free Fluid (CMFF_SIG) 125 0.1 (V/V)

0.5 0

Operating Frequency (FREQ_OP) 2260 (KHZ) 2310 5

-180

Signal Phase (SPHASE[0]) (DEG)

Computed GAMMA (GAMMA[0]) (----) RMS Noise (RMS_NOISE[0]) (V)

0

0

10

0

180

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 of interest, 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 low porosity intervals (i.e., shale).



•

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◊

Signal phase should be relatively constant (+/-10 °) in high porosity intervals. Signal phase may be erratic in low porosity (e.g., less than 5 p.u.); this is not symptomatic of a tool 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. The following 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 1.25 and 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. Fivelevel averaging is recommended for temperatures greater than 140° C. 4

3

s t l o V e s 2 i o N S M R 1

0 20

60

100

140

180

Temperature - C °

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.



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6.7 Acquisition quality control While acquisition is running, monitor the following signals in the IO monitor. •

DHC_ERR (DHC error). Background color should be green.

•

DSP_ERR (DSP error). Background color should be green.

•

STATE_ERR (state error). Background color should be green, except while the tool operating mode is changing.

•

VOLT_ERR. (Voltage error). Background color should be green.

•

HPB0 (Hall probe B). Should be between 51 and 56 mtesla when the tool is in open hole.

•

NUM_MSG (number of messages). Should be incrementing, except while the tool operating mode is changing.

•

CMR_TEMP (temperature). Should correspond with expected values.

6.8 Environmental corrections Corrections for hydrogen index and mud filtrate T2 can be applied at the wellsite. If required, it is recommended that the corrections be applied in playback phase. Both the playback and real time logs should be presented. The mud filtrate correction is usually not applied unless the filtrate T2 is less than 200 msec. An additional sample should be measured if the T2 is less than 200 msec. Record the filtrate T2 in the remarks section of the log heading.

6.9 Master calibration Master calibrations must be less than one month old.


CMR Training Manual Interpretation Principles and Applications

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7. Interpretation Principles and Applications 7.1 Introduction CMR interpretation principles are based on the results of lab NMR measurements. The ability to duplicate CMR measurements in the lab is very useful, because it allows a direct comparison between NMR and other core measurements (e.g., porosity, producible porosity and permeability) for the same sample of rock. CMR measurements and lab NMR measurements differ in one important respect: NMR porosity from lab spectrometers is approximately equal to core porosity and is therefore considered to be total porosity. On the other hand, the CMR measurement is relatively insensitive to the smallest pores that have fast T2. Because of this, CMR porosity is often less than total porosity. Field experience shows that CMR porosity is equal to total porosity in clean formations but has a significantly lower value in shaly formations. Apparently, the clay-bound water volume is not included (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 a total porosity estimate (e.g., nuclear log porosity).

φtotal clay bound water

capillary bound water

producible water

φCMR

φFF

Figure 7.1. In shaly rocks, φ CMR is less than total porosity. The correlations between NMR measurements and pore size, permeability and producible porosity were established for core samples that were completely saturated with water. Because of the shallow depth of investigation of the CMR tool (about 1 in.), the tool measures a region that is substantially flushed with mud filtrate and correlations developed for water-saturated rocks are generally applicable. In intervals that have poor flushing, the CMR log may have a significant hydrocarbon 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 closely related to pore size. Specifically, 1 T2

= ρ 2

S V

+

1 , T2B

(7.1)



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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, T2 B is approximately 3500 msec and the last term in Eq. 7.1 can be neglected. For mud filtrate, T2 B may be short (i.e., less than 200 msecs) if the filtrate contains paramagnetic ions. In this case, the measured T2 must be corrected for bulk relaxation. That is, 1 T2 C

 1 1  S = − = ρ 2 ,  V  T2 T2B 

(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 on water-saturated samples are highly correlated with pore size distributions obtained from other techniques, such as mercury injection (e.g., see Figure 7.2), or by image analysis on thin sections.

mercury injection throat diameter (microns) .1

.01

0.1

1.0

1

10

10

100

1000

100

10000

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 hydrogen nuclei and paramagnetic ions (e.g., iron and manganese) at the rock grain surface. The surface relaxation 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 in most sandstones (about 10 microns/sec). The surface relaxivity in carbonates is three times weaker than for sandstones (about 3 microns/sec). The NMR estimate of producible porosity is based on an expectation that the producible fluids reside in large pores, whereas bound-fluids (e.g., capillary-bound and clay-bound waters) reside in small pores; hence, a T2 cutoff may be established that divides the total porosity into boundfluid and free-fluid porosity (see Section 1.1). The T2 cutoff was determined by measuring the volume of fluids produced by spinning core samples in a centrifuge. Cutoff values of 33 and 100 msec for sandstones and carbonates, respectively, result in the best agreement between freefluid porosity and centrifuged water volume. The different cutoffs for sandstones and carbonates reflect their difference in surface relaxivities. Under reservoir conditions, the capillary-bound water volume depends upon the capillary pressure as well as the pore size distribution of the rock. The capillary pressure varies with fluid densities and height above the water table. The T2 cutoffs quoted above are appropriate for a 100 psi air-brine capillary pressure. T2 values should be adjusted if the reservoir capillary pressure is significantly different from 100 psi. The new cutoff can be estimated by multiplying the cutoff by the ratio (100/capillary pressure). For example, for a capillary pressure of 50 psi in a sandstone reservoir, the appropriate cutoff would be 66 msec. The CMR permeability estimate is based on an expectation that permeability increases with both porosity and pore size. NMR and brine permeability measurements on core samples have resulted in several empirical correlations. The following permeability models are included in the MAXIS and Geoframe software: K CMR

b1

= a1(T2,log ) (φ CMR )c1,

(7.3)

and b2

 φ  c2 4 K CMR = a2 (10 )  FF  (φ CMR ) .  φ BF  

(7.4)

In the above, relaxation time is in milliseconds and porosity is in decimal units. The default values for 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 with pore throat diameter, whereas NMR responds to pore body diameter. Fortunately, the throat/body ratio is approximately constant for most sandstones. However, some variations can be 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 is only effective for the fluid that is in contact with the grain surface. The nonwetting fluid relaxes at its bulk rate. T2-distributions for water-wet rocks are a superposition of two T2-distributions: (1) a distribution originating from the water that depends on the S/V distribution of the water, and (2) a distribution originating from the oil that depends on the bulk relaxation of the oil. For example, Figure 7.3 shows T2-distributions for a rock sample completely saturated with water, and the rock sample saturated with both water and Soltrol. The T2-distribution for bulk Soltrol is also shown. When the pores contain both water and Soltrol, the distribution is bimodal with a short T2 water peak and a long T2 Soltrol peak. This assignment is based on the observation that the short T2 peak is similar to the distribution obtained on the water-saturated rock, and the long T2 peak is close to the 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 T2distributions 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 peak originating from the most mobile hydrogen nuclei and a tail to shorter relaxation times from nuclei with more restricted motions. As the hydrogen chain length increases, viscosity increases, and relaxation 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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Figure 7.5 shows a T2-distribution for a rock sample that contains both water and 27 ° API crude oil. The distribution is distinctly bimodal with peaks at 10 and 150 msec. Figure 7.5 also show s the T2-distribution for the sample after it has been soaked in deuterium oxide (D 2O). During the soaking process, the D 2O diffuses into the sample and reduces the concentration of H 2O to a negligible level. D 2O does not contribute an NMR signal at the operating frequency of the lab spectrometer; therefore, the T2-distribution after soaking is entirely from the in-situ oil. The distribution is essentially identical to the bulk crude T2-distribution indicating that the oil is not contacting the grain surfaces. The signal amplitude from the in-situ oil (i.e., the area under the distribution) is proportional to the volume of oil in the sample. Similar plots are shown in Figure 7.6 for a similar rock sample (sample B) that contains 16° API crude.

Sample A

27o API crude

Figure 7.5. Top, T2-distributions for a core (sample A) containing water and 27 ° API crude (line), and deuterium oxide and 27 ° API crude (dotted). Bottom, T2-distribution for the bulk crude.

Sample B

16o API crude

Figure 7.6. Top, T2-distributions for a core (sample B) containing water and 16 ° API crude (line), and deuterium oxide and 16 ° API crude (dotted). Bottom, T2-distribution for the bulk crude. The above examples illustrate that both the T2-distribution and the logarithmic mean T2 are affected by the presence of oil in the invaded zone. The free-fluid and bound-fluid porosities may also be affected, depending on the viscosity of the oil. A plot of logarithmic mean T2 versus viscosity is shown in Figure 7.7. Light and medium crudes with viscosity less than 40 centipoise have mean T2 greater than 33 msec. The T2-distributions for these oils are predominately in the free-fluid porosity range. However, they may also have significant amplitudes below 33 msec.



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Oil with higher viscosity is predominantly in the bound-fluid range unless it is extremely viscous and has T2 shorter than 2 or 3 msec, msec, which is below b elow the detection threshold of the CMR tool. In this case the oil volume is not included in the CMR porosity.

1000

100

T 2,log (msec) 10

1

1

10

100

1000

10000

Viscosity (cp) Figure 7.7. Logarithmic mean T2 (T 2,log 2,log ) of bulk oil is inversely proportional to viscosity. A summary of the pore fluid types included in the CMR porosity measurement measurement is shown s hown in Figure Figure 7.8.

φtotal crude oil visc > 1000 cp

clay bound water


crude oil visc 40 to 1000 cp

φCMR

crude oil visc < 40 cp

producible water

φFF

Figure 7.8. Summary of pore fluid types included in φ CMR CMR and φ FF (when a T2 cutoff of 33 msec is used). FF When large volumes of oil are present in the flushed zone, permeability estimation using the SDR equation is unreliable. If the oil is low to medium viscosity (such that the free-fluid and bound-fluid bound-flu id porosities 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 are well separated (e.g., the situation shown in Figure 7.5). The T2 peak associated with the oil signal can be used to estimate the oil viscosity. visco sity. When light oil oil is present pre sent in shaly sands, sand s, T2T 2-



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distributions distributions typically extend to longer times than those for 100% water-saturated water-saturated rocks. This has proved valuable for finding oil zones where conventional interpretation methods are unreliable. At the other extreme, extrem e, very heavy oil and bitumen can be identified identified by CMR porosity poro sity readings that are much much lower than nuclear nuclear porosity porosi ty logs (cautionary (cautiona ry note: this also occurs in shaly s haly 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 h ave a hydrogen hyd rogen index of o f 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 the volume of gas times the hydrogen index of the gas.

•

Gas has long T1 values, ranging from 3 to 7 sec (depending on formation temperature and pressure pres sure). ). Conversely, Conver sely, T2 for 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 u sed for the polarization correcti correction. on. Therefore, logs run with typical typ ical wait times (1 to 3 sec.) are not adequately adequat ely corrected 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 effect is expected expecte d 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.

φtotal clay bound water


producible water

ga s

φFF φCMR Figure 7.9. Summary of pore fluid types included in φ CMR CMR and φ FF when gas and water are present. Because of the gas effect on φCMR , φFF and mean mean T2, permeability permeab ility can only be b e estimated using the Timur/Coates model and by incorporating other log data. For example,

 φ  b2  (φ ) c2 , K = a2 (10 4 )   φ BF   

( 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 lo gs have good vertical resolution with 9 in. beds fully resolve re solved d at slow slo w logging speeds.

CMR porosity applications •

Total porosity independent of mineralogy In clean, liquid-filled formations, φCMR is a measure of total porosity that is obtained without specifying mineralogy.

•

Effective porosity in shaly formations In shaly formations, φCMR is less than total porosity because contributions from the smallest pore 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 approximatel appro ximately y equal to effective porosity po rosity.. Furtherm Furthermore, ore, the volume of clay water wate r can be estimated by subtracting φCMR from a total porosi por osity ty measurement (from nuclear logs, logs , for for example).

•

Gas zone identification φCMR reads low in gas zones - much lower than Litho-Density porosity. The CMR gas effect indicator is especially useful in shaly reservoirs as the neutron and density logs do not always “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. The distributions are used to determine bound-fluid and free-fluid porosity. In carbonates, vuggy porosity 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 that are predominately water wet, oil volume and viscos vi scosity ity can be estimated from the T2-distribution provided the oil and water signals are separated. Oil volume is obtained by integrating the area under the oil signal. Oil Oi l viscosit visc osity y is estimated from from the T2 peak of the oil signal.



-85-


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 mud filtrate. However, the volume of mud filtrate is equal to the volume of flushed oil, as shown in Figure 7.10. clay bound water


mud filtrate

crude oil (visc < 40cp)

Invaded Zone

φFF clay bound water



Non Invaded Zone

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 though the CMR tool measures the invaded zone, as the free-fluid porosity is numerically equal in both the invaded and noninvaded zone. clay bound water


mud filtrate


Invaded Zone

φFF Water Vol clay bound water


Oil Vol producible water


Non Invaded Zone

φFF Figure 7.11. Pore fluid types in a nonheavy oil reservoir that contains producible water.


CMR Training Manual Interpretation Principles and Applications •

-86-


Steam flood efficiency in heavy oil reservoirs In heavy oil reservoirs, φFF is equal to the producible water volume (Figure 7.12). Intervals with high producible water respond poorly to steam flooding, since the steam tends to migrate away from the wellbore and localized heating, required to decrease the oil viscosity, is not achieved. clay capillary bound bound water water

mud filtrate

crude oil (visc > 40 cp)

Invaded Zone

FF clay bound

capillary bound

water

water

producible water

crude oil (visc > 40 cp)

No n Invaded Zone

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 and are now under consideration for tertiary recovery schemes. This technique involves adding manganese EDTA to the mud system, thus reducing the T2 of the mud filtrate below the threshold value for computing the free-fluid porosity. It is assumed that the oil volume in the invaded zone is equal to the oil volume in the noninvaded zone (i.e., the filtrate flushing efficiency 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

capillary bound

water

water

mud filtrate

remaining oil

with EDTA

(visc < 40 cp)

Invaded Zone

φ FF clay bound

capillary bound

water

water

producible

water

remaining oil

(visc < 40 cp)

No n Invaded Zone

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. Procedures for doping the mud are in Appendix C.


CMR Training Manual Hardware Characteristics and Ratings

87


A. CMR Hardware Specifications and Ratings Equipment associated with the CMR tool is described in Table 1. CMR physical specifications are 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

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

3.625

118.5

96.0

*

6.5

13

13

* depends on choice of EME or ILE Table 1. Equipment information.

Physical Description:

CMR-A with EME-F

CMR-A with ILE-D

CMR-A with ILE-F

Configuration (bto-t)

CMR

... AH191 / ILE-D / AH178 / CMR ...

... ILE-F / CMR ...

Make-Up Length

14.16 ft

24.14ft

22.16 ft

Tool Measure Point from bottom of string

20.59 in.

140.4 in.

116.6 in.

Weight

327 lbs.

454.5 lbs.

410.5 lbs.

6.6 in.

5.3 in.

5.3 in.

Maximum Diameter Hole Size Recommendation s:

min. max.

7.785 in. 21.0 in.

Fishing Strength

100,000 lbs.

min. 6.3 in. max. 10.0 in.

min. max.

6.3 in. 10.0 in.

100,000 lbs.

100,000 lbs.

Table 2. CMR-A physical specifications.


87

CMR Training Manual Hardware Characteristics and Ratings

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

φ FF

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 14.0 kbits/s

Power

30 watts (AC MAIN); 75 watts (AC AUX)

(min.: Sandstone depth log without raw echoes) (max.: Carbonate depth log with raw echoes)

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.

None

CMRS sonde must be shipped in the CMRS Shipping Box (H549555). Box is 6.6 ft long and weighs 135 lbs.

Restrictions for all Air Shipments

Table 4. CMR-A shipping data.


88

CMR Training Manual Safety, Handling and Transportation

-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 at each end) can be made from the materials shown in Table 1-1.

Table 0-1 Ground Clip Jumper Components Quantity

Part Number

Description

2

B-09100

Battery Clip

As required

H-031716

#11-1 Flexible wire

12 Inches

E-019888

Shrinkable tubing

E-08630

25 Amp Solder Lug

2

Sonde power is delivered to the upper head of the tool string on cable wires 2, 3, 5, 6 with armor return. This is the standard sonde power path and the use of armor return makes it doubly 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 power was on, the tool housing would rise to the sonde head voltage. Within the telemetry cartridge the power on cable wires 2, 3, 5, 6 are joined and passed to the tools on head pin 2 and returned on pin 10. Sonde head voltage can vary between 200 and 350 Vrms depending on the length of the cable.

Mechanical hazards •

The bellows used in the Antenna Cradle Assembly of the CMRS-A sonde can easily be punctured when cleaning this area of the sonde. Be very careful if using a screw driver or punch 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 with oil. The oil may be under pressure so be very careful when removing the filler plugs from the assembly.

•

DO NOT place the CMRS-A sonde next to a tool that uses sodium iodide crystals or photomultiplier 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 magnets in the CMRS sonde.


89


-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 “Calibration Fixture.” Be very careful when mixing the NiCl crystals with distilled water. The NiCl material is irritating to the skin, eyes and mucous membranes. It is also harmful if swallowed. When storing the Nickel Chloride, the three labels shown in Figure 3 should be affixed to the container.

In addition to the standard electrical hazards of high voltage (250 VAC cartridge power and 200600 VDC in the sonde power system), the CMRS contains two extremely powerful magnets that require 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 sensitive electronics used in some devices.

•

Flying objects Magnetically permeable items (most commonly used metal instruments), such as spanner wrenches, spring to life when the tool is brought near. A finger or hand between the waywa rd spanner 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 too close 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 occurrence). The biggest danger occurs if the magnets come close to each other, as they will pi vot and snap together with alarming speed. This could cause severe injury if a hand or finger were 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 grid arrays of the DHC and the CMRC-A. Pull the circuit evenly and slowly out of its socket using


90


-91-


special tools such as E047413 (Advanced Interconnections Universal Push-off Blade Type Extraction Tool) •

Follow the SMC (Surface Mounted Component) maintenance procedures as documented in the 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 the chassis of the CMRC-A cartridge and the CMRS-A sonde, it is best to turn the cartridge power OFF before attaching any test equipment to the terminals. This will reduce the possibility of short-circuits. When in doubt, solder-tack a short length of wire to the terminal before attaching the test equipment.

•

Do not scratch the protective coating on the quartz windows of the programmable components, such as EPROM, EPLD and PAL.

•

The Antenna Cradle Assembly oil level must be checked prior to every job. If the assembly becomes 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 the magnets 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 disks clean.

•

Credit cards; The magnetic strips used on credit cards and ATM cards can be erased by the magnetic field created by the magnets.

Special Shipping Instructions The 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 a magnetic field strength of 0.159A/m (0.002 gauss) or more at a distance of 2.1 m (7 ft) from any point on the surface of the assembled package. This regulation also governs the loading of magnetized materials in aircraft. This includes; 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.

91


-92-


1. Magnetized material must not be loaded in such a position that it will have a significant effect on 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 or compass detector units will depend upon the intensity of the magnetized materials field strength 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 possess 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 degrees at 15 ft. from any surface of the package, is considered “Forbidden” and must not be shipped by air freight. It must be shipped by ground transportation.

NOTE Some pressure housing used on tools are made of material that may become magnetized after running in a well. A shipping container, CMRS Shipping Box, (H549555) has been designed which complies with IATA 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 cause compass deviation even though it does not emit a magnetic field and it does meet all IATA requirements. When shipping the sonde by helicopter, if the shipping box is too large to be placed in the helicopter then the magnetic shield should be removed from the box and placed directly over the magnets on the sonde. The label shown in Figure 1 must be placed on the shipping box (or on the magnetic shield if being shipped by helicopter) in several places so that it is clearly visible from all directions. In addition, a “Dangerous Goods Manifest” must be completed and provided to the courier. An example of the manifest is shown in Figure 2. Surface shipment does not require any special container as there are no special handling requirements 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 (including helicopter) should have a set of the regulations available. The regulations are revised and reissued annually. There are several places from which the regulations may be obtained. Two are listed below: Lab Safety Supply - Telephone 1-800-356-0783 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.

92


-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

◊

Class or Division

◊

UN or ID No. which is “UN2807”

◊

Packing Inst. which is “902”

which is “Magnetized Material”.

which is “9”


93


-94-


Figure 2. Dangerous goods manifest example.


94


-95-


Figure 3. Nickel chloride labels.


95

CMR Training Manual Mud Doping Procedures

-96-


C. Mud Doping Procedures for Residual Oil Determination General procedures •

Manganese can be added to the drilling mud to shorten the T2 of the filtrate and separate the filtrate and oil signals. When the signals are separated, the volume of oil can be quanitified by applying a cutoff to the T2-distribution. **** Note: use MANGANESE, not magnesium ****

•

Manganese EDTA is preferred for shaly sandstones and bentonitic drilling muds. Manganese chloride (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 mud before 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 y using the crude oil distributions shown in Section 7. The oil T2-distribution is also important for determing the wait times for logging, which should be sufficiently long for complete polarization. Station logging is used when long wait times are required 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 manganese chloride is used.

•

The T2 of a doped filtrate sample can be measured with the CMR tool. Also, compare the amplitude of the filtrate signal to the amplitude of the calibration bottle signal (the manganese may shorten the filtrate T2 below the sensitivity of the CMR). The flitrate sample must be sufficiently large to fill the CMR sensitive volume (use a plastic bottle similar in size to the master calibration bottle).

•

The initial spurt loss is responsible for the majority of filtrate invasion. Diffusion is too slow for effective invasion. It is necessary to add the manganese solution prior to drilling the zone of interest. A reasonable overbalance is required (~ 100 psi). On the other hand, a large overbalance (> 500 psi) can cause viscous stripping which results in misleadingly low values of oil volume.

•

Consult with the client to determine optimum mud properties and drilling procedures. Logging for residual oil determination requires careful pre job planning.



-97-


Example calculation The following example calculation determines the amount of manganese EDTA required to shorten the fitrate T2 to 10 msec, at a temperature of100 ° C. •

Figure C.1. shows T2 versus temperature, for various manganese concentrations.

100 0.01 moles/liter

) c e s m (

0.02

10

2 T

0.05

0.1 moles/liter

1 0

50

100 T (C)

150 951030-02

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 10 msec.

•

Managnese is available in the form of MnCl 2.4H2O. Note the four waters of hydration, which must be accounted for when weighing the solid. MnCl2.4H2O <=> 198 grams/mole

•

EDTA is available as Na 2.EDTA.2H2O. Na2.EDTA.2H2O <=> 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 MnCl2.4H 2O and 22 grams of Na 2.EDTA.2H 2O (this includes a 20% excess).

•

1 barrel is equal to 159 liters, for each barrel of mud add: 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.


-98-


1.6 kg of MnCl 2.4H2O and 3.5 kg of Na 2.EDTA.2H2O (this includes a 20% excess). •

Figure C.2. shows T2 versus temperature, for various manganese concentrations. Use this chart if manganese chloride is added to the mud.

28 0.00077 moles/liter ) c e s m ( 2 T

24

20 0.00104 moles/liter

16 10

20

30

40

50

Temperature (C)

Figure 2. Filtrate T2 versus temperature for various manganese concentrations. (Chart is for manganese chloride solutions. See Figure1. for manganese EDTA solutions).


CMR Training Manual Signal Processing Algorithms.


-99-

D. CMR Signal Processing Algorithms CMR Spin Echo Pulse Sequence A very brief discussion of the pulse sequence used by the CMR is given here. Other sections of this document should be referred to for more detail.

The CMR tool makes pulsed NMR measurements at frequencies close to 2 MHz by using the Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence to produce wave forms consisting of hundreds to thousands 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. During the wait time, the magnetization is allowed to recover towards its equilibrium value in the magnetic field produced by a permanent magnet in the tool. Following the wait period, which for depth logging is typically about a second, a 90-degree radio frequency pulse is applied. This pulse rotates the magnetization vector into the plane transverse to the direction of the magnetic field. Following the initial 90-degree pulse, a sequence of evenly spaced 180-degree pulses is applied at odd multiples 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, 2 t cp , 4t cp , L , J × 2 t cp , is produced. The echo spacing, 2 t cp , for the CMR tool is nominally set at 320 µ sec.

The basic unit of measurement is a phase alternated pair (PAP) of CPMG wave forms. A PAP wave form is computed from two successive CPMGs. The two CPMGs have identical pulse sequences except that the phases of the initial 90-degree radio frequency pulses are shifted with respect to each other by 180 degrees. Subtraction of the two CPMGs results in a PAP spin-echo wave form. This procedure removes baseline shifts and antenna ringing effects that can be produced by the 180-degree pulses.

The Signal Processing Problem

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, the estimation 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 (log T 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 acquired by a phase sensitive detector (PSD) in two channels. The acquired signals are 90 degrees out of phase with one another, but the signal phase with respect to a reference signal in the tool is unknown. A preprocessing algorithm estimates the signal phase and then transforms the raw data into "in-phase," A˜ j( + ) , and "quadrature," A˜ ( − ) , channels. The transformed quadrature j

channel, which contains only tool electronic noise, is used to estimate the tool rms noise on a single echo for each 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 the integral equation, ˜ (+) = A j

T max

∫

dT 2 P( T 2 ) f ( W , T 1a )exp( −

T min

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

for j

= 1,2,L

j∆ ) T 2 a

+ N j

(2)

˜ ( + ) are signal-plus-noise , J , where A j

CPMG spin-echo amplitudes of the j − th echo. The function, f ( W , T 1a ) = (1 − exp( T − W )) , is a polarization 1a

correction. It accounts for the incomplete recovery of the magnetization during the wait period ( W ) that

This information is CONFIDENTIAL and must not be copied in99 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.


precedes each CPMG sequence. In Eq.2 , the inter echo spacing is denoted by ∆ . The additive thermal noise ( N j ) is zero mean uncorrelated Gaussian with known statistical

properties

< N j N k > = ψ δ j , k

(i.e.,

where

< N j > = 0


-100-

and

ψ is the rms noise on a

single echo. Angular brackets are used here to denote statistical averages. At room temperature ψ ≈ 5 p.u. for an echo on a single PAP. In practice, the noise is reduced by stacking (averaging) PAP wave forms. The rms noise can be reduced, ideally, by a factor N r if

processing that are not equal to the true ratios. This assumption can lead to significant accuracy errors in the CMR log outputs in some logging environments. The problem is amplified in high porosity rocks with long T 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 is not necessary. The accuracy problem can be eliminated by using multiple wait time CPMG pulse sequences. In a later section, multiple wait time pulse sequences are briefly discussed.

N r PAP wave forms are averaged. The vertical resolution of the log is determined by three interdependent factors. These are: (1) the total measurement time to acquire a PAP wave form, (2) the number of PAP wave forms that are averaged for each set of new log outputs, and (3) the logging speed.

Discretization of the Signal, Window Sums and Maximum Likelihood Estimation

The contribution of the mud filtrate to the observed relaxation can be accounted for by a wellsite measurement of the filtrate relaxation time ( T mf ) and

˜ ( +) A j

by defining apparent relaxation times, e.g., ( T 1a ) −1

= ( ξ T 2 )−1 +

( T 2 a ) −1

=

( T mf ) −1 ,

( T 2 ) −1 + ( T mf ).−1

The next step is to discretize the integral in Eq. 2 by replacing the integral by a summation, N s

= ∑a =1

l

l

f l exp( −

j∆ ) T 2 a , l

+

N j ,

(4)

where it is assumed that the signal has N s spectral amplitudes al with intrinsic relaxation times T 2, l (3)

In Eq. 3, we have made use of an empirically based relationship, 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. The ratios were found to vary from sample to sample in the range from roughly 1 to 3. The experimental data base consisted 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 being initiated by a single wait time (W). The spin echo data obtained from single wait time pulse sequences does not contain any information about the T 1 / T 2 ratios of the rock formations being logged. During single wait time logging an assumed nominal value of the ratio is, by necessity, used by the signal processing. For example, a nominal value, ξ 0 ≈ 1. 5, has been used in sandstones. It has been shown that using single pulse wait time logging involves an uncontrolled approximation. The root of the problem is the variability of true T 1 / T 2 ratios ( ξ ) in rocks. The uncontrolled approximation is the use of assumed ratios in the signal

which are equally spaced on a logarithmic scale in the closed interval ( T min, T max ) . Note that solution of the multi-exponential model is numerically feasible because the relaxation times are fixed. It follows from the discretization that al ≡ P( T 2, l )δ l, where δ l is 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 depth logging mode where each PAP normally consists of 600 or 1200 echoes, the marginal independence of the individual echoes is exploited to reduce the J spin echoes to N w = 5 "window sums." The window sums ˜ (+) are obtained by summing the over A j

non-overlapping windows. It has been shown mathematically, that the window sums contain the same information as the original data. The window sums have different sensitivities to the decay times in the spectrum. For example, the window sum obtained from the first window is sensitive to all the spectral components whereas the window sum computed from the last window is sensitive only to the slowly decaying components. An attractive feature of this data reduction scheme is its simplicity. Also processing of the window sums instead of the original J spin echoes reduces the processing time by a factor proportional to N w • J −1 .


100


Unbiased estimates of the spectral amplitudes are obtained by minimizing the negative logarithm of the maximum likelihood function for the window sums. Specifically, the maximum likelihood estimates are obtained by minimizing N w

− ln L

( I ˜m

− I m {a })2 γ = + 2 ψ [ N m +1 − N m + δ m ,1 ] 2 ψ m =1

∑

l


-101-

It is these distributions that are related to rock pore size distributions.

The primary log quantities are expressed as integrals over the distribution functions, e.g.,

N s

∑

al2 , (5)

=1

l

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 } , 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 and δ m ,1 is the familiar Kronecker delta function. The last l

term suppresses noise artifacts in the solutions. The parameter γ is called a regularization parameter. It has been shown that minimization of Eq. 5 is equivalent to an expansion of the T 2 -distribution in terms of the non-null space eigenfunctions of a highly rank deficient linear operator that can be obtained by differentiation of Eq.5. The eigenfunction analysis also shows: (1) why only a few window sums are required for the estimation of P( T 2 ) and (2) why the estimated distributions depend only slightly on the exact positions chosen for the window boundaries. A nice feature of the processing is that the logs have negligible dependence on the regularization parameter for a relatively wide range of values of γ . A mathematical algorithm is used to compute, based on the input log data, optimal values ( γ opt ) of the regularization parameters. The optimal values depend inversely on the SNR and also on the details of the intrinsic T 2 -distributions. As a general rule, for a given SNR, distributions with short decay times will have larger optimal values than similarly shaped distributions with longer decay times.

Computation of the Logs In depth logging mode, the primary logged quantities 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

T max

φ nmr

= K tool

N s

∫ dT P(T ) ≡ K ∑ 2

2

tool

al ,

(6)

=1

l

T min

where K tool is a factor containing various calibration and environmental corrections such as the Curie law temperature dependence of the signal. The free fluid porosity φ f ( T c ) is obtained from the integral in Eq.6 by replacing the lower limit of integration by an empirically 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 = 10 m , where m is the mean logarithm of the logarithmic T 2 -distribution and is defined by log T max

∫

d (log T 2 ) Pa (log T 2 )log T 2

m

=

N s

∑ a log T = ∑a

2, l

l

=1

log T min log T max

l

∫ d (log T )P (log T ) 2

a

2

log T min

N s

.(7)

l

=1

l

Computation of the Standard Deviations In the Logs The standard deviations in the logs due to random noise fluctuations provide a measure of log repeatability and confidence in the log values. Logs of the standard deviations are computed for each of the primary logged quantities and displayed for the porosity estimates. The standard deviations are computed from an exact covariance matrix for the multi-exponential model. For example, the variance in the estimated total porosity is by definition

displayed, along with T 2,log on the field logs. In station logging mode, data with a higher SNR are obtained by stacking, and as a result, more accurate logarithmic T 2 -distributions can be computed.

ˆ ) = σ 2 ( φ nmr

< ( φ ˆ nmr )2 > − ( < φ ˆ nmr > )2 ,

(8)


101


ˆ where a "hat" is used to denote that φ nmr is an estimate of the true porosity defined in Eq.6. In terms of the covariance matrix, C l, k , one finds that,

ˆ ) σ ( φ nmr 2

N s

= ( K tool )

2

where

by

l, k

definition,

The updated log outputs and true T 1 / T 2 ratio ˆ ) are computed by minimization of a cost estimates ( ξ function,

N s

∑ ∑ C k =1


-102-

,

(9) C ( ξ v ,{av , l})

=1

l

C l, k =

< δ aˆ

l

δ aˆ k

>.

calculated because of the linearity of the multi-exponential model. The covariance matrix is proportional to the rms noise on a single echo in the measurement which, as discussed above, is computed for each measurement. The expressions for the variances ˆ ( T ) and φ ˆ ( T ) are identical to those in Eq.9 in φ f c bf c except for obvious changes in the summation limits.

Multi-Wait Time CPMG Logging As noted earlier, the use of single wait time pulse 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 produce significant accuracy errors in the log outputs. The root of the problem is the variability of the T 1 / T 2 ratios in reservoir rocks. The accuracy errors are amplified in high porosity rocks that have long T 1 components. Although, the errors can be lessened by using longer wait times it has been shown that this strategy is inefficient and leads to reduced logging speeds.

=

∑∑

p =1

Here

δ aˆ l = aˆ l − < aˆ l > are the deviations, produced by noise fluctuations, of the spectral amplitudes from their expectation values. An exact expression for C l , k can be

2

 av , f ( W p , ξ v )  ˆ − a  , p  f ( W p , ξ 0 )  =1 

N wt N s

The

l

l

. (10)

l

l

apparent

l

spectral

amplitudes

( aˆ l, p )

determined for each single wait time in the multi-wait time 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. The estimates 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 global minimum. Then the true T 1 / T 2 ratio estimates are ˆ = ξ ∗ . Likewise, the estimated T given by, ξ v

2

distributions are given by, {aˆ l} = {av∗, l}. The updated log outputs are computed from the estimated T 2 distributions. A flowchart of the signal processing algorithm for processing multi-wait time pulse sequences is shown in Fig. 1.

Consider a multi-wait time pulse sequence with 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 signal processing algorithm for multi-wait time pulse sequences is an addition to the window processing ˆ algorithm described above. The CMR log outputs φ nmr , ˆ ( T ) , φ ˆ ( T ) , etc. for multi-array pulse sequences φ f c bf c

are arrays instead of scalars. For example, there are N wt ˆ output values of φ nmr , i.e., one for each wait time, etc. Additionally, each output array contains one new updated log output which is computed simultaneously with an estimate of the true T 1 / T 2 ratio. The updated log outputs are more accurate because they are derived using the estimated true T 1 / T 2 ratio instead of the assumed ratio ( ξ 0 ).


102



-103-

Flowchart For Multi-Wait Time Logging

~

Sonde

PSD

~

Estimate

R j , p X j , p

Signal Phases ∧

θp ~

~

∧

R j , p X j , p θp Compute Estimate Rms Noise

~

~( - )

A

A

(+)

~

j , p

j , p

(-)

A j , p ~

A

(+)

j , p

p

Compute Window Sums ~

I

Compute Std. Devs. In Porosity Logs For Each Wait Time

Compute γ opt,p

m, p

Construct And Minimize - ln Lp

Compute Std. Dev. In Logarithmic Mean T2 For Each Wait Time

^ a l,p No

Compute Signal Distributions For Color Maps

Compute Log Outputs For Each Wait Time

N

wt

>1 ?

Yes

Construct Cost Function And Perform Minimization ∧

∧

{a } l

ξ

Compute Updated Logs Record Logs

Figure 1. Signal processing flowchart for multi wait time logging.


103


Nomenclature This section defines the symbols used in this note. ˜ ( + ) = "in-phase" amplitude of j-th spin echo A j signal computed from raw two channel data. Used to compute window sums. ˜ (−) = A j

al ( aˆ l) =

"quadrature" amplitude of j-th spin echo signal computed from raw two channel data. Used to estimate rms noise.

aˆ l, p =

N j =

random noise on the j-th spin-echo in a CPMG wave form.

N m ( N m +1 ) =

left (right) echo number of m-th window.

N r =

number of PAPs in a stack of spin-echo wave forms.

N w =

number of windows used to reduce original redundant data.

N wt =

number of wait times in a multi-wait time pulse sequence.

true spectral amplitude (estimate) of − th component in multiexponential model.

P( T 2 ) =

T 2 decay time distribution.

Pa (log T 2 ) =

set of true spectral amplitudes referred to as the T 2 -distribution.

logarithmic T 2 decay time distribution.

˜ = R j

apparent spectral amplitude estimates for wait time W p computed with

measured raw spin-echo amplitudes in channel 1.

t cp =

Carr-Purcell time equal to one-half of inter-echo spacing.

T c =

T 2 cutoff separating bound and freefluid porosity.

T 2 =

intrinsic spin-spin relaxation time of rock (a continuous variable).

l

{al} =


-104-

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 global minimum.

C l , k =

covariance matrix used to compute the standard 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-wait time pulse sequence log data. f l =

I ˜m = I m {al} =

J = K tool = m =

N s =

T 2 a =

apparent spin-spin relaxation time of rock including relaxation of mud filtrate.

T 2, l =

intrinsic spin-spin relaxation time of l-th spectral component.

T 2,log = T 1a =

polarization function used to correct l− th spectral amplitude for insufficient wait time.

T min ( T max ) =

amplitude of m-th window sum.

T mf =

expectation value of m-th window sum.

W =

logarithmic mean relaxation time. apparent longitudinal relaxation time of rock including relaxation of mud filtrate. minimum (maximum) assumed T 2 . nmr relaxation time of mud filtrate. wait time preceding each CPMG in a single wait time pulse sequence.

number of echoes in a CPMG wave form.

W p =

the p-th wait time in a multi-wait time pulse sequence.

tool constant used to convert from measurement units to porosity.

˜ = X j

measured raw spin-echo amplitudes in channel 2.

mean logarithm of the logarithmic T 2 -distribution.

γ ( γ opt ) = regularization parameter (optimal value) computed by the signal processing algorithm.

number of spectral components in the multi-exponential model.

∆ = inter echo spacing equal to 320 µ sec for the CMR tool.


104

SLB Training Manual

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