AU2367199A - Dual-wait time nmr processing for determining apparent T1/T2 ratios, total porosity and bound fluid porosity - Google Patents

Description

AUSTRALIA

Patents Act 1990 COMPLETE SPECIFICATION STANDARD PATENT Applicant(s): SCHLUMBERGER TECHNOLOGY, B.V.

Invention Title: DUAL-WAIT TIME NMR PROCESSING FOR DETERMINING APPARENT Ti/T 2 RATIOS, TOTAL POROSITY AND BOUND FLUID POROSITY.

a a a a a a The following statement is a full description of this invention, including the best method of performing it known to me/us: oo 1 3508/004 DUAL-WAIT TIME NMR PROCESSING FOR DETERMINING APPARENT Ti/T 2

RATIOS,

TOTAL POROSITY AND BOUND FLUID POROSITY This application claims the benefit of United States provisional application 60/085,035 filed May 11, 1998.

Background of the Invention This invention is concerned with evaluating subsurface formations surrounding earth boreholes.

SMore particularly, it is concerned with obtaining accurate T 2 distributions, apparent Ti/T 2 ratios, total porosity, and bound fluid porosity from nuclear magnetic resonance measurements collected using dualwait time methods.

The economic value of a formation containing hydrocarbons generally depends on the amount of oil or gas contained in a unit volume of a subsurface reservoir, which, among other things, is a function of its porosity and its hydrocarbon saturation. Nuclear Magnetic Resonance (NMR) well logging provides a means So" by which various parameters may be obtained to determine the economic value or "quality" of a 2 formation surrounding a given wellbore. The parameters include such factors as the total NMR porosity (Pr), free fluid porosity and bound fluid porosity These parameters are used to determine the amount and type of hydrocarbons present within the formation, as well as provide an indication as to the difficulty of extracting those hydrocarbons from the formation. It is therefore important that such factors are determined accurately so a reliable assessment can be made regarding the commercial viability of a specific well site.

NMR logging is based on the fact that the nuclei of many elements have angular momentum (hereinafter, "spin") and a magnetic moment. Nuclear spins align themselves along an externally applied static magnetic field which provides a known initial starting point or a thermal equilibrium condition.

This equilibrium is disturbed by a pulse of an oscillating magnetic field, which tips the spins away 20 from the static field direction. The degree to which S. the spins are tipped is dependent upon the magnitude of the oscillating magnetic field.

After tipping, two things occur simultaneously. First, the spins precess around the static field at the Larmor frequency (o yBo), where B, is the strength of the static field and y is the gyromagnetic ratio, a nuclear constant. Second, the spins return to the equilibrium condition according to a decay time which is known as the "spin-lattice relaxation time" or T 1 T, is controlled by the molecular environment and is typically ten to one thousand milliseconds for water in rocks. Also 3 associated with the spin of molecular nuclei is a second relaxation time which is known as "spin-spin relaxation time" or T 2 At the end of a ninety degree tipping pulse, all the spins are pointed in a common direction perpendicular to the static field and they precess at the Larmor frequency. However, small inhomogeneities in the static field due to imperfect instrumentation or microscopic material heterogeneities cause each of the nuclear spins to precess at a slightly different rate. Therefore, after some time, the spins will not precess in unison, that is, they will dephase. When dephasing is due to static field inhomogeneity of the apparatus, the dephasing time is called T 2 When the dephasing is due to properties of the material, the dephasing time is called T 2

T

2 can be as long as several seconds in an unconfined low viscosity liquid such as water, and as short as ten microseconds in a solid. Liquids confined in the pores of rocks present an intermediate case 20 where T 2 is in the range from approximately 0.1 to hundreds of milliseconds, depending on various factors, such as the number of pores, the pore size, and fluid viscosity.

A well known method for measuring T 2 is called 25 the Carr-Purcell-Meiboom-Gill ("CPMG") sequencing method. In solids, where T 2 is very short, T 2 can be determined from the decay of a detected signal after a ninety degree pulse. However, for liquids where T 2

T

2 the free induction decay becomes a measurement of 30 the apparatus-induced inhomogeneities. To measure the true T 2 in such liquids, it is necessary to cancel the effect of the apparatus-induced inhomogeneities.

4 This cancellation is achieved by applying a sequence of RF (radio frequency) magnetic pulses. The first pulse is a ninety degree pulse that causes the nuclear spins to start precessing. After the spins have begun precessing, a one hundred eighty degree pulse is applied to keep the spins in the measurement plane and to cause the spins which are dispersing in the transverse plane to precess in the reverse direction, thereby refocusing the spins. By repeatedly reversing and refocusing the spins using one hundred eighty degree pulses, a series of "spin-echoes" occur.

The succession of one hundred eighty degree pulses, after the initial ninety degree pulse, is the Carr- Purcell sequence which measures the irreversible dephasing T 2 due to material properties.

Meiboom and Gill devised a modification to the Carr-Purcell pulse sequence such that after the spins are tipped by ninety degrees and start to dephase, the carrier of the one hundred eighty degree 20 pulses is shifted relative to the carrier of the ninety degree pulse. Consequently, any error that occurs during an even pulse of the CPMG sequence is canceled out by an opposing error in the odd pulse. The CPMG sequences may be further improved by using phase alternated pairs (PAPS) of CPMGs to eliminate baseline shifts. Phase alternated pairs of CPMGs differ by shifting the ninety degree pulses by one hundred eighty coo. degrees. A detailed explanation of NMR principles and pulse sequences is described in Freedman U.S. Pat. No.

30 5,291,137 (hereinafter the "Freedman patent") which is hereby incorporated by reference.

1 5 The CPMG pulse sequence for a phase alternated pair can be written in the form: CPMG' xI -(echo)j) 1,2 j. (1) For purposes of the present discussion, the important parameter in the above equation describing the CPMG pulse sequence is the wait time that precedes each set of RF pulses that produce the spin-echoes. A wait time W is required after each set of RF pulses so that the nuclear polarization which produces the spin-echo signals can approach its thermal equilibrium value (in the magnetic field Bo, which may be produced by a permanent magnet in an NMR logging tool).

The use of multi-wait time CPMG pulse sequences to improve recovery of the short relaxation time portion of a T 2 distribution is not a new idea and was first recognized by Freedman and Morriss and disclosed in U.S. Patent 5,486,762 (hereinafter "Freedman-Morriss"). The multi-wait time method implemented by Freedman-Morriss attempted to recover a 20 more accurate porosity by combining data from singlewait time CPMG measurements. This method utilized three somewhat different wait times to increase the polarization of the formations excited by CPMG pulses in an effort to increase the amplitude of the resulting spin-echo signals. The objective of the this method was to recover the long relaxation times in a T 2 distribution and to obtain Ti information without having to fully polarize the surrounding formation. The accuracy improvement on the short T 2 relaxation times was secondary and it does not provide the improved was secondary and it does not provide the improved 6 precision achievable with dual-wait time methods.

Moreover, the Freedman-Morriss method did not provide a robust and improved porosity for depth logging where the signal-to-noise ratio (SNR) of the measurements can be low.

Sezginer and Straley disclose a method in U.S. Patent 5,389,877 for improving the SNR of the bound-fluid porosity measurement by using a quick succession of short CPMG sequences with short recovery times. This method is only concerned with the short T 2 relaxation times and does not provide both bound-fluid and total NMR porosity.

Prammer, PCT patent application WO 97/341 discloses a method of using the short-wait time data from the Numar MRIL tool to compute a T 2 distribution for very short relaxation times, less than about 3 msec and greater than about 0.5 ms. The long-wait time data from the MRIL tool is used to compute a T 2 distribution for the long relaxation times those greater than 20 3 msec). These two separate T 2 distributions are joined to produce a total T 2 distribution. One problem with this method is that it can lead to artifacts on the total T 2 distribution obtained from the concatenation of the two separate distributions. These artifacts can 25 include spurious peaks and erroneous amplitudes that can lead to incorrect estimation of total NMR porosity from the T 2 distributions.

Dunn et al. disclose a method for combining NMR data collected at somewhat different wait times in o 30 a paper entitled "A Method For Inverting NMR Data Sets With Different Signal To Noise Ratios" SPWLA 39th Annual Logging Symposium May 26-29, 1998. However,

I

7 this method assumes a known Ti/T 2 ratio and therefore may suffer from distortion of the T 2 amplitude distributions which can result in an incorrect total porosity measurement.

In view of the foregoing, it would be desirable to provide methods for determining total NMR porosity and bound-fluid porosity with greater precision.

It would also be desirable to provide methods to for determining total NMR porosity and bound-fluid porosity self-consistently from dual-wait time data.

It would be further desirable to provide methods for determining total NMR porosity which are not sensitive to the underlying T, distribution of the formation being logged.

It would be additionally desirable to provide methods for determining apparent T 1

/T

2 values calculated from dual-wait time NMR data received from that formation.

SUMMARY OF THE INVENTION Accordingly, it is a primary object of the present invention to provide new methods for acquiring and processing NMR data for determining total NMR porosity and bound-fluid porosity with greater 25 precision.

It is another object of the present invention to provide new methods for determining total NMR porosity and bound-fluid porosity self-consistently from dual-wait time data.

i 30 It is another object of the present invention "to provide new methods for determining total NMR 8 porosity which are not sensitive to the underlying T: distribution of the formation being logged.

It is another object of the present invention to provide methods for determining total NMR porosity and bound-fluid porosity of a formation by using an apparent TI/T 2 value calculated from dual-wait time NMR data received from that formation rather than assuming a value.

It is a further object of the present invention to provide new methods for determining total NMR porosity in response to spin-echo pulse sequences received by an NMR well logging tool when the tool: (1) is traversing a wellbore and providing a static magnetic field, waiting a first period of time W,, sufficient to substantially polarize all the fluid in the formations traversed by the wellbore pulsing the formation with a set RF pulses, collecting a first set of the spin-echo pulse sequences, waiting a second period of time W, which is different than the S" 20 first period of time Wi, pulsing the formation with 6* another set of RF pulses, collecting a second set of the spin echo pulse sequences, and optionally repeating steps for a user-defined number of times to collect additional sets of second wait time 25 spin-echo data.

It is a further object of the present invention to provide a new method for determining bound-fluid porosity in response to spin-echo pulse sequences received by an NMR well logging tool when the tool: is traversing a wellbore proving a static magnetic field, waiting a first period of time W 1 sufficient to substantially polarize all the bound

L

9 fluid in a traversed formation pulsing the formation with a set RF pulses, collecting a first set of the spin-echo pulse sequences, waiting a second period of time W, which is different than the first period of time W1, pulsing the formation with another set of RF pulses, collecting a second set of the spin echo pulse sequences, and optionally repeating steps for a user-defined number of times to collect additional sets of second wait time spin-echo data.

It is a further object of the present invention to provide a means by which the collected spin-echo data may be used determine an apparent value of the true TI/T 2 ratio, and a new set of spectral amplitudes {ak}.

In accordance with these and other objects of the present invention, a dual-wait time NMR processing method is described which provides a more accurate measurement of total NMR porosity and bound-fluid 0***b S* 20 porosity than is possible with single-wait time Se* methods. The invention may be used in conjuncti'on with a conventional NMR logging tool that includes a permanent magnet which produces a static magnetic field

B

0 As the logging tool traverses a borehole, the 25 magnetic moment vectors in surrounding the formations tend to become polarized tend to align themselves in the direction of the magnetic field).

The NMR tool waits for a first period of time (WJ) to elapse, and energizes the formation with a series of RF pulses and collects a first set of spin-echo signals.

After this set of spin-echo signals is acquired, the polarization of the formation is close to 10 zero. The NMR logging tool waits for a second period of time (W 3 to elapse, being different than to partially re-polarize the molecules. Then the formation is re-energized with another set of RF pulses and a second set of spin-echo pulses is collected.

This step may be optionally repeated for a user-defined number of times to collect multiple sets of W, or "short-wait time data" for every set of W 1 or "long-wait time data." The short-wait time data may then be averaged to improve the SNR of that data. Increasing the number of sets of short-wait time data collected and averaged reduces the T 2 sensitivity threshold the shortest detectable T 2 of the NMR logging tool.

Once the spin-echo pulse sequences are collected, they may be processed according to the teachings of the Freedman patent, the signal plus noise spin-echo amplitudes, Aj' and are computed and the window sums Im,m+i, are generated. A signal processing system then constructs the maximum likelihood function of equation 7 which is a function of the variable (the apparent Ti/T 2 ratio of the examined formation) and the set of variables {ak} representing the T 2 -distribution of the formation. This equation allows the self-consistent combination of the short-wait time data having a higher SNR with long-wait time data having a lower SNR to provide high accuracy results. The maximum likelihood function is minimized with respect to the aforementioned variables which provides a set of spectral amplitudes {ak} and an 30 apparent TI/T 2 ratio for the examined formation. This information may then be used to determine certain properties of the logged formation, such as the total 11 and bound-fluid porosity, free-fluid porosity, permeability, and pore size distribution.

Brief Description of the Drawings The above and other objects of the present invention will be apparent upon consideration of the following detailed description taken in conjunction with the accompanying drawings, in which like reference characters refer to like parts throughout.

FIG. 1 is an illustration of a conventional NMR logging system that may be used in conjunction with the present invention.

FIG. 2 illustrates a typical spin-echo signal plus noise amplitude Aj spectrum that may be obtained from a given subsurface formation when excited with an RF pulse sequence.

FIG. 3 shows a comparison of the true and computed total and free-fluid porosities (track 1) as well as a comparison of the true and computed T 2 distributions (track 2) from a Monte Carlo simulation 20 using a single-wait time processing method.

FIG. 4 shows a comparison of the true and computed total and free-fluid porosities (track 1) as well as the total and free fluid porosity standard deviations (track 2) for the single-wait time 25 simulation shown in FIG. 3.

FIG. 5 is a plot of a Ti/T 2 ratio versus T 2 used to generate synthetic data for the dual-wait time simulations.

FIG. 6 is a plot of the T 1 and T 2 30 distributions used to generate synthetic data at a simulated depth of 3975.5 feet.

:simulated depth of 3975.5 feet.

12 FIG. 7 shows a comparison of the true and computed total and free-fluid porosities (track 1) as well as a comparison of the true and computed T 2 distributions (track 2) from a Monte Carlo simulation using a dual-wait time processing method.

FIG. 8 shows a comparison of the true and computed total and free-fluid porosities (track 1) as well as the total and free fluid porosity standard deviations (track 2) for the dual-wait time simulation shown in FIG. 7.

FIG. 9a is a plot of the first thirty longwait time spin-echo pulses acquired for one realization of random noise.

FIG. 9b is a plot of the first thirty shortwait time spin-echo pulses acquired for one realization of random noise.

FIG. 10 is a graphical representation of the dual-wait time processing of the present invention being applied to a bi-exponential T 2 distribution.

20 FIG. 11 is a graph which illustrates the signal computed from the estimated bi-exponential T.

distribution in FIG. 10 and the input signal for the long-wait time data.

FIG. 12 is a graph which illustrates the signal computed from the estimated bi-exponential T 2 distribution in FIG. 10 and the input signal for the short-wait time data.

Background The dual-wait time data acquisition and 06: 30 processing methods of the present invention are based on an extension of the "windows processing" method 13 disclosed in the Freedman patent. Some key concepts of the Freedman patent along with some NMR basics are introduced here to facilitate comprehension of the invention. However, it will be understood that this introduction is not meant to be all-inclusive, and the Freedman patent should be consulted if more detail is desired.

FIG. 1 illustrates a conventional NMR logging system 10 which includes a NMR logging tool 2 adapted to be disposed in borehole 3, and a processing system 4 located at the surface of borehole 3 and electrically connected to NMR logging tool 2 for processing signals received from the logging tool.

In operation, NMR logging tool 2 traverses borehole 3 in close proximity to the surrounding formations and applies a static magnetic field B• (not shown). At selected times, an oscillating magnetic field B 1 in the form of CPMG pulses similar to those described by equation 1 are applied to a particular 20 portion of the earth formations surrounding borehole 3.

After the CPMG pulses are applied, NMR logging tool 2 waits for a predetermined period of time W before applying another CPMG pulse sequence. During that time, a receiving antenna in NMR tool 2 (not shown) •25 measures the voltages induced by the precession of the magnetic moments of individual protons in the volumes of the traversed formation which generate a plurality **of spin-echo voltage pulses representative of their magnetic moments. This process is repeated as NMR i 30 logging tool 2 traverses borehole 3 so that a series of spin-echo measurements representing the traversed formations is obtained.

14 NMR logging tool 2 may contain digital and/or analog circuitry (not shown) for processing the received voltage pulses by integrating each of the spin-echo voltage pulses over a time interval, there being a total of J time intervals, each time interval being centered about a time tj j*TE, where j= 1, 2, J, and TE equal to the echo spacing. The integrated signals are be recorded as-inphase (R amplitudes and quadrature or out of phase (X amplitudes.

Signal processing system 4 may then estimate a signal phase theta from the J spin-echo R and X amplitudes associated with the spin-echo receiver voltage pulses using the following equation:

J

e atan2 I (2) S* where atan2 is the four-quadrant arctangent function.

Next, the in-phase amplitudes, quadrature (X amplitudes, and the estimated signal phase e associated with the spin-echo receiver voltages may be combined to 20 produce a signal plus noise amplitude Aj using equation 3.

Ai Rjcose Xsin (3) Each set of CPMG pulses applied to a subsurface i formation produces multiple spin-echo signals which in turn results in multiple signal plus noise amplitudes ~~i 15 A i FIG. 2 illustrates a typical distribution spectrum of spin-echo signal plus noise amplitudes Aj"' which may be generated by a given subsurface formation excited by a CPMG pulse sequence. The A,' spectrum shown in FIG. 2 may be partitioned into multiple "windows" m. The individual amplitudes within a given window m may be summed to produce a representative window sum Im,m+1 for each window m using equation 4.

N +1 I AI.) m, m.l j .Pm (4) Because each Aj' spectrum is typically partitioned into N, windows, multiple window sums Im,m+ are computed for each Aj spectrum. In addition to producing the signal plus noise amplitudes Aj', a set of amplitudes 15 Aj' may also be produced from the spin-echo pulses using equation Aj-' R sinb X.cos6 These Aj' amplitudes may be used for estimating an RMS noise, which is defined to be the square root of 4 (psi), where 4 is the noise power. The RMS noise value may be used to compute the dimensionless parameter y (gamma) Detailed Description of the Preferred Embodiments Dual-wait time NMR processing methods are presented that provide a more accurate determination of 16total NMR porosity and bound-fluid porosity than is possible with single-wait time logging. The increased precision and reduced T 2 sensitivity limit provided by dual-wait time data is approximately equivalent to a factor of two increase in the hardware SNR.

The method of the present invention may employ both short-wait time and long-wait time (W 1 RF pulse sequences that are applied to substantially the same subsurface formation to obtain a series of spin-echo measurements. Multiple short-wait time RF sequences are typically applied for each application of a long-wait time RF sequence. The short-wait time RF sequences produce a relatively small number of spinecho pulses which are signals from formations with very short T 2 relaxation times formations with small pores and clay bound water). Multiple short-wait time sequences are obtained so that they may be averaged to improve the SNR of the data.

In contrast, the long-wait time RF sequences 20 provide a relatively large number of spin-echo pulses which represent a spectrum of T 2 relaxation times short, medium, and long T 2 relaxation times) that may exist in a given formation. This invention teaches a way to self-consistently combine short-wait time RF 25 data having an improved SNR with long-wait time data having a lower SNR to produce a more accurate total NMR porosity and bound-fluid porosity than is possible with single-wait time logging.

The dual-wait time data acquisition method of 30 the present invention may be used in conjunction with I ~conventional NMR logging system 10 shown in FIG. I.

However, it will be understood that any other 17 conveyance method and/or data transmission means may be used if desired logging while drilling, and NMR logging tool 2 need not be directly electrically connected to a controller or particular signal processing device).

In operation, NMR logging tool 2 traverses borehole 3 at a user-defined speed and constantly applies a static magnetic field Bo to the surrounding formations. A first period of time, W, a longwait time) is allowed to elapse to polarize the molecules in given formation before a first set of RF pulses a set CPMG pulses) is applied. When the RF pulses energize the formation, a first set of spinecho pulses is received by NMR logging tool 2. After the pulses are received, the net polarization of the molecules in the excited formation is close to zero. A second wait-time W, a short-wait time which is different from WI) is allowed to elapse so that magnetic field B, can partially re-polarize the formation. Once 20 WS elapses, a second set of RF pulses is immediately applied to the formation and a second set of spin-echo pulses is collected by NMR logging tool 2.

Acquisition of the short-wait time spin-echo pulses ("short-wait time data") may be repeated a user- 25 defined number of times for each acquisition of long- 9* wait time spin-echo pulses ("long-wait time data").

For example, ten such short-wait time data sets may be obtained for each acquisition of a long-wait time data 9 set. NMR logging tool 2 and/or signal processing 30 system 4 may average the multiple short-wait time data sets to improve the SNR of that data. This is desirable because the short-wait time data provides 18 information about formations with short T 2 relaxation times formations with small pores and clay bound water) that are difficult to recover because only a few of the acquired spin-echo pulses contain information about these formations. Furthermore, the quality of short-wait time data can be obscured by varying environmental factors encountered during a logging run.

Adjusting the number of short-wait time data sets averaged provides a means by which the user can adapt the SNR of the collected data to meet specified accuracy requirements. For example, if NMR logging tool 2 is traversing a somewhat noisy subsurface formation, the SNR of the short-wait time data may be increased to improve data quality.

The dual-wait time techniques described above can be configured for different types of logging operations. For example, assume total porosity and bound-fluid porosity are desired from a particular logging run. Both W, and W, may be assigned certain wait-time values in order to efficiently obtain this information. For example, W, may be assigned a relatively long wait-time value which is sufficient to ensure that the fluid in a traversed formation is substantially polarized by magnetic field Bo 25 about 95% of the fluid is polarized). By assigning such a value, NMR logging tool 2 will acquire long-wait time data that reflects the spectrum of T 2 relaxation times associated with the traversed formation. This information may then be used to calculate total NMR porosity.

On the other hand, W, may be assigned a short-wait time value such that only clay-bound water ri 19 and fluid contained in small- pores are substantially polarized by magnetic field B 0 By using such a short Ws value, NMR logging tool 2 may quickly acquire multiple sets of short-wait time data that reflect only the short T 2 relaxation times of the traversed formation. As mentioned above, these data sets may then be averaged to increase the SNR, thus improving short-wait time data precision. Both the long and short wait-time data may then be combined in accordance with equation 7 (which is discussed in detail below) to calculate the apparent Ti/T 2 ratio and the set of spectral amplitudes {ak} of the traversed formation.

Total porosity and bound-fluid porosity may then be computed from this information.

Although total porosity and bound-fluid porosity may be obtained using only long-wait time data, acquiring data in a dual-wait time mode provides a significant SNR benefit which translates into improved logging speeds and/or improved vertical resolution for total porosity measurements. For example, assume NMR logging tool 2 in a single-wait time mode and can acquire a set of long-wait time data 1.5 seconds. In dual-wait time mode, NMR logging tool 2 may also acquire one long-wait time data set

S**

25 seconds) and, for example, ten short wait-time data 9** sets with a 20 msec recovery time and an echo spacing of 0.2 msec (a total 0.26 seconds). Thus, one dualwait time data sequence requires 1.76 seconds to acquire compared to 1.5 seconds for a single-wait time 30 data sequence.

However, the precision benefit realized by dual-wait time processing methods is approximately j__(j(Xiiijl *j ;j _ld 20 equal to a factor two improvement over a single-wait method. (This shown by comparison of the standard deviation curves 110 and 112 in FIGS. 5 and 9 which are discussed in more detail in the MONTE CARLO ANALYSIS section.) To achieve the same SNR using single-wait time logging, four single-wait time measurements requiring 1.5 seconds each would have to be collected compared to 1.76 seconds for a dual-walt time data set.

Consequently, the gain in logging speed for a specified vertical resolution may be expressed as the ratio of six to 1.76 seconds or a factor of 3.4.

Another type of logging run which may be performed using dual-wait time techniques is one in which only bound-fluid porosity data is obtained. In this case, W, may be assigned a wait-time value which is long enough to ensure that the bound-fluid in formations traversed by NMR logging tool 2 is substantially polarized. A user-defined number of short-wait time data sets may be collected with W, 20 retaining the short wait-time value previously described. The acquired long-wait time data will reflect the T 2 relaxation times of the bound-fluid in the traversed formation and thus may be used to calculate bound-fluid porosity. When the long-wait 25 time data and short-wait time data are combined in accordance with equation 7, bound-fluid porosity may be computed that realizes the same factor of two benefit *over single-wait time processing as described above.

It will be understood by one of ordinary :30 skill in the art that the dual-wait time concept of the present invention may be extended to encompass RF pulse sequences that include multiple-wait times more 21 than two). For example, in certain environments dualwait time data may not provide sufficient sensitivity to accurately estimate the apparent T 1

/T

2 ratio. In this case, a user-defined number of intermediate wait times WI (each of which may or may not collect and average a user-defined number of data sets) may be inserted between Ws and W, to "customize" the pulse sequence and thus increase the sensitivity of NMR logging tool 2 to suit a particular formation.

Moreover, the user may adjust the duration of one or both of the wait-times W, and WI) to change the sensitivity range of NMR logging tool 2. This provides the logging operator with the flexibility to adjust the logging profile so that virtually any formation may be accurately logged.

Once spin-echo data is obtained using the above-described acquisition techniques, it may be processed according to the teachings of the Freedman patent as explained in the BACKGROUND section. That 20 is, signal plus noise amplitudes A/ and Aj' may be calculated and windows sums Im may be generated (note that the m-th window sum notation has been changed from the Im,m+ term used in the Freedman patent to simply I).

Next, this information may be further processed in 25 accordance with the present invention by computing the T distributions by minimizing the maximum likelihood functional shown below in equation 7 2 1 N I fa ,J 2 y n 1^ 1 2 y 2 :1 (7) p=l m=1 2T u2 2T k 1 pp m,p P 22 where the T 2 distribution is described by the set of N, amplitudes and is the "window sum" data for the m-th window and wait time Wp. The amplitude a, is the amplitude of the signal that decays with relaxation time T 2 This is the product of the portion of the pore volume that contains protons which decay with time constant T 2 ,k and the proton density of those spins relative to water hydrogen index). The outer summation over the index p is a sum over wait times two wait times for a dual-wait time sequence), the inner summation over the index m is a sum over the Nw(p) windows for each CPMG with wait time Wp. The functional is the expectation value of m,p and is defined by equation 8, N

W

I akF (Tk) (1-exp(- (8) k=1 72,k where, for each wait time p, Fm,p( 2 is a set of Nx N(Jp) sensitivity functions, and are defined by equation 9.

S*I j*TE Fm 2 E exp(- (9) SJ m(P) T2,k 20 Rm(p) and Rm are the left and right endpoints, respectively, of the m-th window and TE is the echo spacing. The parameter in equation 8 is determined by minimization of equation 7 with respect to and The set of N, relaxation times {T 2 are the relaxation times of the amplitudes {ak} describing the 23

T

2 distribution which can be selected to be equally spaced on a logarithmic scale that spans the expected range of T 2 relaxation times from 0.1 to 5000 msec) in rocks. Equations 7-9 above describe a model in which is the apparent TI/T 2 ratio that is assumed constant for all parts of a given excited specimen.

The value of is not presupposed but instead it is derived from the data. Although subsurface formations saturated with mixed fluids do not have a single Ti/T 2 ratio, it can be proved by computer simulations that this model is sufficient to accurately estimate total porosity and T 2 distributions. The joint estimation of the parameter and the set of spectral amplitudes {ak} using both the short and long-wait time CPMG data provides a self-consistent fit to both data sets. This eliminates the sensitivity to the underlying Ti distribution that occurs if an assumed fixed value of the parameter is used.

In the summation over the index m in 20 equation 8, 'p is the variance of the noise per echo in the stacked CPMG data and 42p is the number of echoes in window m acquired with wait time Wp. The summation over the index k in equation 7 is a regularization term that selects a smooth and minimum error solution to the under-determined and ill-conditioned inversion problem.

The regularization smoothing parameters yp are estimated from the data.

In operation, NMR logging tool 2 may acquire and process data as follows. First, a set of long-wait 30 time data representing a particular formation is collected. Next, a series of short-wait time data sets ten) are collected for substantially the same _Fi~ 24 formation, and those data sets are averaged to improve the SNR. The long-wait time data is then combined with the averaged short-wait time data using equation 7 to produce the apparent T 1

/T

2 ratio S and a set of spectral amplitudes {ak} which represent the T 2 distribution of the examined formation. This information may be recorded on an output log so that it may be correlated with particular depth as shown in FIGS. 4 and 8.

If desired, however, the acquired data may be further averaged (stacked) to additionally improve the SNR. For example, as NMR logging tool 2 traverses a formation it may collect five dual-wait time data sets five long-wait time data sets and 49 short-wait time data sets. The long-wait time data is averaged together and the short-wait time data is averaged together before being combined in equation 7. This practice produces more precise results but decreases the vertical resolution of the output data. An example of data obtained using a dual-wait time method with five level stacking in shown in FIG. 8.

Monte Carlo Analysis The improvements of dual-wait processing methods over single-wait time processing can be demonstrated by Monte Carlo simulations that use synthetic T 2 distributions to generate short and longwait time CPMG echo trains having realistic noise per echo based on the dual-wait time acquisition sequence and known measurement noise of the CMR-200 tool. The thirty model T 2 distributions used for the simulations 30 are the same ones used in the publication by Freedman, et al. SPWLA Transactions, Paper 0, 1997.

I

25 First, FIGS. 3 and 4 illustrating the results of Monte Carlo simulations performed using single-wait time processing and data acquisition are reviewed. The thirty model T 2 distributions used in the simulations are represented by solid lines 114 in track 2 (righthand side) of FIG. 3. The thirty T 2 distributions are normalized to have a total porosity of 20 p.u.(porosity units) as indicated by the solid vertical line 104 on the left-hand side of track 1. This simulation was performed using the pulse sequence parameters indicated in FIG. 3 W=30 seconds, J=5000, TE=0.2 ms, noise per echo=2.2 and The CPMG echo trains for the single-wait time simulation were generated using a wait time of thirty seconds and an assumed single T,/T 2 ratio equal to one. The latter assumption means that the T, and T 2 distributions are identical. This ensures that all the protons in the volume of interest are fully polarized at the expiration of the thirty second wait time.

20 Therefore, the porosity deficit between the computed total porosity in FIG. 3 broken line 103) and the true total porosity represented by solid line 104 (20 is due to missed porosity from the short T 2 relaxation times. A noise per echo of 2.2 p.u.

25 for each phase-alternated-pair (PAP) of CPMG echo trains were used in the simulations. The noise level and echo spacing are appropriate for a Schlumberger CMR-200 tool in a low salinity and low temperature environment. The simulations were done with five level 30 PAP stacking to further reduce the noise. The computed and true free-fluid porosity logs (line 101 and line 102, respectively) and the computed T 2 distributions are 26 also shown in FIG. 3. The recovery of all of the freefluid demonstrates that the thirty second wait-time fully polarizes the longest relaxation times in the T, distribution. The undetected porosity in the T 2 distributions is shown as the difference between line 103 and line 104 near the top and bottom of track 1 (lefthand side) in FIG. 3. This results from the distributions containing several p.u. of porosity with

T

2 relaxation times below approximately 0.3 msec which is the T 2 sensitivity limit or the minimum detectable T 2 for single-wait time logging under these conditions.

Track 2 of FIG. 4 shows the standard deviations in the computed total porosity (line 110) and the computed free-fluid porosity (line 111) determined from the single wait-time simulations. The mean and maximum values of the standard deviations in the estimated total porosity for the thirty T 2 distributions are 0.68 p.u. and 1.1 respectively, for the single-wait time simulation.

20 The dual-wait time Monte Carlo simulation results disclosed herein used the same thirty model T 2 distribution used for the single-wait time simulation but do not assume a single TI/T 2 ratio. The T 1

/T

2 ratio was varied arbitrarily as a function of T 2 for each of 25 the input T 2 distributions used in the dual wait-time simulation. A plot of T,/T 2 ratio versus T 2 is shown in FIG. 5. The same TI/T 2 ratio versus T 2 was assumed for each of the thirty model T 2 distributions. Using any one of the thirty model T 2 distributions and the 30 relationship in FIG. 5, the corresponding

T,

distribution can be constructed. For example, in FIG. 3, the T, distribution corresponding to the 27 distribution at a simulated "depth" 3975.5 track 2, the 12-th T 2 distribution from the top) is shown in FIG. 6.

FIG. 7 shows the results of a dual-wait time simulation which was performed with Wl long-wait time value equal to 5 seconds and W2 shortwait time value equal to .02 seconds. During this simulation, ten short-time data sets were collected for each long-wait time data set. The J1 and J2 values represent the number echoes acquired for the long and short-wait times respectively. N1 and N2 indicate the stacking level used (5 level stacking) Comparison of FIG. 7 with the results of the single wait-time simulation in FIG. 3 shows that the dual-wait time simulation provides improved recovery of the very short relaxation times in the T 2 distributions near the top and bottom of FIG. 7 compare line 103 in FIG. 3 with line 108). Moreover, there are no a..

2 artifacts produced by the dual- wait time processing 20 algorithm of equation 7. The long wait-time used in this simulation was not sufficient to fully polarize the long T, relaxation times as evidenced by the deviation of line 106 from line 107 near the bottom of S-track 1 in FIG. 7, which represents an under-estimation 25 of free-fluid porosity. However, the accuracy of this value may be improved by increasing the polarization time Wi).

~FIG. 8 shows the standard deviations in the computed total porosity (line 112) and the computed a. a Sa. 30 free-fluid porosity (line 113) determined from the dual await-time simulations. The mean and maximum of the standard deviations in the estimated total porosity for 28 the thirty T 2 distributions are 0.33 p.u. and 0.51 p.u., respectively.

Comparison of FIGS. 4 and 8 show that the precision of total porosity for the dual-wait time processing compared to the single-wait time is roughly a factor of two or better. To achieve the same improved precision and accuracy using single-wait time acquisition and processing would require approximately a factor of two improvement in SNR. The gain in SNR has very important consequences and leads to significantly improved logging speed and/or vertical resolution for total porosity measurements.

To illustrate the benefits of the dual-wait time method, consider the standard sandstone logging mode for the Schlumberger CMR-200 tool. For singlewait time logging the total acquisition time in sandstone mode for one CPMG is typically 1.5 sec. For the dual-wait time mode, the total acquisition time is the sum of the long-wait time sequence 1.5 sec) and the time to acquire, for example, ten short-wait time pulses trains. For a short-wait time pulse with a 20 msec recovery time and an echo spacing of 0.2 msec it takes 0.26 sec to acquire ten short-wait time CPMG pulses with thirty echoes per pulse. Thus, one total dual-wait time sequence requires 1.76 seconds compared to 1.5 seconds for the single-wait time sequence, however, to achieve the same SNR using single-wait time logging requires four times as many measurements as with dual-wait time logging. Thus, the gain in logging speed for a specified vertical resolution is the ratio of six to 1.76 seconds or a factor of 3.4.

29 Conversely, a dual-wait time sequence logging at 600 ft/hour with a seven inch sampling of PAP CPMG sequences would have a thirty-five inch vertical resolution after five level vertical stacking. For a single-wait time sequence acquired at 600 ft/hour'with the same SNR, twenty level vertical averaging of six inch samples would be required giving a vertical resolution of 120 inches. Note the ratio of the vertical resolutions is the factor 3.4.

The first thirty spin-echo pulses for one realization of the random noise for the short and longwait time sequences is shown in FIGS. 9a and 9b for the

T

2 distribution at depth 3975.5. Note the reduced noise per echo on the short-wait time data in FIG. 9b.

Another example of dual-wait time processing is shown in FIG. 10. The dual-wait time processing is applied to a bi-exponential T 2 distribution having components at 23.7 and 237 msec. The T, of the component at 23.7 msec is 28 msec corresponding to a T 1

/T

2 ratio of 1.2. The T, of the component at 237 msec is 664 msec corresponding to a T 1

/T

2 ratio of 2.8. This illustrates p that the sample does not have a single value of Ti/T 2 The algorithm of equation 7 returned an apparent Ti/T 2 ratio, 5 1.44. Despite equation 7 supposing a single 25 TI/T 2 ratio, the estimation of total porosity and/or the

T

2 distribution is not hindered.

The solid lines in FIGS. 11 and 12 show for a single Monte Carlo trial, the computed spin-echo signals from the estimated T 2 distribution in Fig. 30 and the input signals (denoted by circles) for the long and short-wait time CPMG data, respectively. Note the ij~l~_;bi_ 30 excellent fit for both the short and long-wait time data.

It will be understood that the foregoing is only illustrative of the principles of the invention, and that various modifications can be made by those skilled in the art without departing from the scope and spirit of the invention.

In the claims which follow and in the preceding description of the invention, except where the context requires otherwise due to express language or necessary implication, the word "comprising" is used in the sense of "including", i.e. the features specified may be associated with further features in various embodiments of the invention.

Claims (22)

1. A method for logging a wellbore comprising: applying a static magnetic field in to a subsurface formation penetrated by said wellbore; waiting a first period of time after said placing step to polarize said subsurface formation; exciting said polarized subsurface formation with a set of pulses from an oscillating magnetic field; acquiring a first set of spin-echo pulses from said subsurface formation; waiting a second period of time after said acquiring step, said second time period being different than said first time period so that said static magnetic can field can at least partially P. re-polarize said subsurface formation; again exciting said polarized subsurface formation with another set pulses from said S oscillating magnetic field; and acquiring a second set of spin-echo pulses from the formation.

2. The method of claim 1 further comprising: repeating steps for a user- defined number of times to obtain a plurality of said second set spin-echo pulses; averaging said plurality of second set spin-echo pulses; and 32 transmitting said first set of spin- echo pulses from step and said average from step to a signal processing system.

3. The method of claim 1 further comprising: waiting a sufficient period of time in said first waiting step such that fluid contained in said subsurface formation is substantially polarized.

4. The method of claim 1 further comprising: waiting a sufficient period of time in said second waiting step such that clay bound water and fluid contained in small pores in said subsurface formation is substantially polarized. The method of claim 1 wherein said exciting step is characterized by the use of CPMG pulse sequences. 9

6. The method of claim 1 wherein said again exciting step is characterized by the use of CPMG pulse sequences.

7. The method of claim 1 further comprising: repeating steps for a user- defined number of times wherein said first waiting period is varied to one or more user-defined waiting times such that additional sets of spin-echo pulses are 33 received from said subsurface formation to increase sensitivity to T 2 distributions of said formations.

8. The method-of claim..7 further comprising: selecting said user-defined wait times to be shorter in duration than said first waiting period and longer in duration than said second waiting period.

9. The method of claim 7 wherein step is repeated for a user-defined number of times for one or more of said user-defined wait times. The method of claim 9 further comprising: averaging the additional sets of spin- echo pulses obtained which have equal user-defined wait •times to improve the signal-to-noise ratio of the spin echo pulses. C.

11. The method of claim 1 further comprising altering duration of said first waiting step to modify T 2 sensitivity range. C*

12. The method of claim 1 further comprising altering duration of said second waiting step to modify T 2 sensitivity range. S.

13. The method of claim 1 further comprising generating an apparent TI/T 2 ratio and a set of spectral amplitudes in response to sets of spin- 34 echo pulses received from step using said signal processing system.

14. The method of claim 13, wherein said generating step comprises: constructing a maximum likelihood function which self-consistently combines said sets of spin-echo pulses; and minimizing a negative logarithm of said maximum likelihood function to produce said apparent T,/T 2 ratio and said set of spectral amplitudes {ak}. A method for logging a wellbore to obtain bound fluid porosity information comprising: applying a static magnetic field to a subsurface formation penetrated by said wellbore; waiting a first period of time after said placing step so that said static magnetic field substantially polarizes bound fluid contained in said subsurface formation; exciting said polarized subsurface formation with a set of pulses from an oscillating magnetic field; acquiring a first set of spin-echo pulses from said subsurface formation; waiting a second period of time after said acquiring step, said second time period being different than said first time period so that said static magnetic can field can at least partially u mre-polarize said subsurface formation; 4 35 again exciting said polarized subsurface formation with another set of pulses from said oscillating magnetic field; and acquiring a second set of spin-echo pulses from the formation.

16. The method of claim 15 further comprising: repeating steps for a user defined number of times to obtain a plurality of said second set spin-echo pulses; averaging said plurality of second set spin-echo pulses; and transmitting said first set of spin- echo pulses from step and said average from step to a signal processing system.

17. The method of claim 15 further comprising waiting a sufficient period of time in said second waiting step such that clay bound water and fluid contained in small pores in said subsurface formation is substantially polarized.

18. The method of claim 15 wherein said exciting step is characterized by the use of CPMG pulse sequences.

19. The method of claim 15 wherein said again exciting step is characterized by the use of CPMG pulse sequences. 36 The method of claim 15 further comprising: repeating steps for a user- defined number of times wherein said first waiting period is varied to one or more user-defined waiting times such that additional sets of spin-echo pulses are received from said subsurface formation to increase sensitivity to T 2 distributions of said formations.

21. The method of claim 20 further comprising: selecting said user-defined wait times to be shorter in duration than said first waiting period and longer in duration than said second waiting period.

22. The method of claim 20 wherein step is repeated for a user-defined number of times for one or more of said user-defined wait times.

23. The method of claim 22 further S: comprising: averaging the additional sets of spin- echo pulses obtained which have equal user-defined wait times to improve the signal-to-noise ratio of the spin echo pulses.

24. The method of claim 15 further comprising altering duration of said first waiting step to modify a T 2 sensitivity range. 37 The method of claim 15 further comprising altering duration of said second waiting step to modify a T 2 sensitivity range.

26. The method of claim 15 further comprising generating an apparent T/T 2 ratio and a set of spectral amplitudes {ak in response to sets of spin- echo pulses received from step using said signal processing system.

27. The method of claim 15, wherein said generating step comprises: constructing a maximum likelihood function which self-consistently combines said sets of spin-echo pulses; and minimizing a negative logarithm of said maximum likelihood function to produce said apparent T 1 /T 2 ratio and said set of spectral amplitudes {ak}. Dated this 12th day of April 1999 SCHLUMBERGER TECHNOLOGY, B.V. By their Patent Attorneys GRIFFITH HACK Fellows Institute of Patent and Trade Mark Attorneys of Australia