# Patent

## Title
Non-uniform echo train decimation

## Abstract

Method and apparatus using at least one process to reduce a data set using a data adaptive down-sampling scheme comprising a plurality of non-uniform down-sampling factors. The method may include separating the data set into a plurality of data windows, where each of the plurality of data windows corresponds to one of the plurality of non-uniform data-sampling factors; applying the down-sampling factors, and transmitting the reduced data set from a downhole location to the surface. The data set may include an NMR echo train. The apparatus may include an NMR tool configured to acquire NMR data and at least one processor configured to perform the method.

## Background
BACKGROUND OF THE DISCLOSURE
1. Field of the Disclosure
The present disclosure relates generally to determining geological properties of subsurface formations using Nuclear Magnetic Resonance (“NMR”) methods for logging boreholes, particularly for reducing a data set using a data adaptive down-sampling scheme.
2. Description of the Related Art
A variety of techniques are currently utilized in determining the presence and estimation of quantities of hydrocarbons (oil and gas) in earth formations. These methods are designed to determine formation parameters, including among other things, the resistivity, porosity and permeability of the rock formation surrounding the borehole drilled for recovering the hydrocarbons. Typically, the tools designed to provide the desired information are used to log the borehole. Much of the logging is done after the well bores have been drilled. More recently, boreholes have been logged while drilling, which is referred to as measurement-while-drilling (MWD) or logging-while-drilling (LWD).
One commonly used technique involves utilizing Nuclear Magnetic Resonance (NMR) logging tools and methods for determining, among other things, porosity, hydrocarbon saturation and permeability of the rock formations. The NMR logging tools are utilized to excite the nuclei of the fluids in the geological formations surrounding the borehole so that certain parameters such as nuclear spin density, longitudinal relaxation time (generally referred to in the art as T1) and transverse relaxation time (generally referred to as T2) of the geological formations can be measured. From such measurements, porosity, permeability and hydrocarbon saturation are determined, which provides valuable information about the make-up of the geological formations and the amount of extractable hydrocarbons.
The NMR tools generate a static magnetic field in a region of interest surrounding the borehole. NMR is based on the fact that the nuclei of many elements have angular momentum (spin) and a magnetic moment. The nuclei have a characteristic Larmor resonant frequency related to the magnitude of the magnetic field in their locality. Over time the nuclear spins align themselves along an externally applied static magnetic field creating a macroscopic magnetization, in short: magnetization. This equilibrium situation can be disturbed by a pulse of an oscillating magnetic field, which tips the spins with resonant frequency within the bandwidth of the oscillating magnetic field away from the static field direction. The angle θ through which the spins exactly on resonance are tipped is given by the equation:

θ=γB1tp/2  (1)

where γ is the gyromagnetic ratio, B1 is the magnetic flux density amplitude of the sinusoidally oscillating field and tp is the duration of the RF pulse.

After tipping, the magnetization precesses around the static field at a particular frequency known as the Larmor frequency ω0 given by

ω0=γB0  (2)

where B0 is the static magnetic flux density. For hydrogen nuclei γ/2π=4258 Hz/Gauss, so that a static field of 235 Gauss would produce a precession frequency of 1 MHz. At the same time, the magnetization returns to the equilibrium direction (i.e., aligned with the static field) according to a characteristic recovery time known as the “spin-lattice relaxation time” or T1. T1 is controlled by the molecular environment and is typically one millisecond to several seconds in rocks.

At the end of a θ=90° tipping pulse, spins on resonance are pointed in a common direction perpendicular to the static field, and they precess at the Larmor frequency. However, because of inhomogeneity in the static field due to the constraints on tool shape, imperfect instrumentation, or microscopic material heterogeneities, each nuclear spin precesses at a slightly different rate. Hence, after a time long compared to the precession period, but shorter than T1, the spins will no longer be precessing in phase. This de-phasing occurs with a time constant that is commonly referred to as T2*. Dephasing due to static field inhomogeneity can be recovered by generating spin echoes (see below). The remaining dephasing is characterized by the time constant T2 and is due to properties of the material.
A receiving coil is designed so that a voltage is induced by the precessing spins. Only that component of the nuclear magnetization precesses that is orthogonal to the static magnetic field. The precessing component induces a signal in the receiving coil if its orientation is appropriate. After an 180° tipping pulse (an “inversion pulse”), the spins on resonance are aligned opposite to the static field and the magnetization relaxes along the static field axis to the equilibrium direction. Hence, a signal will be generated after a 90° tipping pulse, but not after a 180° tipping pulse in a generally uniform magnetic field.
While many different methods for measuring T1 have been developed, a single standard known as the CPMG sequence (Carr-Purcell-Meiboom-Gill) for measuring T2 has evolved. In contrast to laboratory NMR magnets, well logging tools have inhomogeneous magnetic fields due to the constraints on placing the magnets within a tubular tool and the inherent “inside-out” geometry. Maxwell's divergence theorem dictates that there cannot be a region of high homogeneity outside the tool. Therefore in typical well bores, T2*<<T2, and the free induction decay becomes a measurement of the apparatus-induced inhomogeneities. To measure the true T2 in such situations, it is necessary to cancel the effect of the apparatus-induced inhomogeneities. To accomplish the same, a series of pulses is applied to repeatedly refocus the spin system, canceling the T2* effects and forming a series of spin echoes. The decay of echo amplitude is a true measure of the decay due to material properties. Furthermore it can be shown that the decay is in fact composed of a number of different decay components forming a T2 distribution. The echo decay data can be processed to reveal this distribution which is related to rock pore size distribution and other parameters of interest to the well log analyst.
Typically, data bandwidth is limited in a downhole environment. NMR echo trains may include about 1000 data points sampled uniformly over a period, such as 0.6 seconds. Data reduction techniques, including uniform decimation, that are used to meet the bandwidth limitations may result in losing critical information. The present disclosure addresses the problem of achieving reduction of data while preserving all of the critical information in an NMR echo train.
SUMMARY OF THE DISCLOSURE
In aspects, the present disclosure is related to methods and apparatuses for determining geological properties of subsurface formations using NMR methods for logging boreholes, particularly for reducing a data set using a data adaptive down-sampling scheme.
One embodiment according to the present disclosure includes a method of communicating a data set acquired in a borehole between a downhole location and a surface location, comprising: using at least one processor to reduce the data set using a data adaptive down-sampling scheme comprising a plurality of non-uniform down-sampling factors, wherein the data set is separated into a plurality of data windows, and each of the plurality of data windows corresponds to one of the plurality of non-uniform data-sampling factors; and transmitting the reduced data set from the downhole location to the surface location.
Another embodiment according to the present disclosure includes an apparatus configured to communicate a data set acquired in a borehole between a downhole location and a surface location, comprising: at least one processor configured to: reduce the data set using a data adaptive down-sampling scheme comprising a plurality of non-uniform down-sampling factors, wherein the data set is separated into a plurality of data windows, and each of the plurality of data windows corresponds to one of the plurality of non-uniform data-sampling factors; and a transmitter configured to transmit the reduced data set from the downhole location to the surface location.
Another embodiment according to the present disclosure includes a non-transitory computer-readable medium product having stored thereon instructions that, when executed by at least one processor, cause the at least one processor to perform a method, the method comprising: reducing the data set using a data adaptive down-sampling scheme comprising a plurality of non-uniform down-sampling factors, wherein the data set is separated into a plurality of data windows, and each of the plurality of data windows corresponds to one of the plurality of non-uniform data-sampling factors; and transmitting the reduced data set from the downhole location to the surface location.
Examples of the more important features of the disclosure have been summarized rather broadly in order that the detailed description thereof that follows may be better understood and in order that the contributions they represent to the art may be appreciated.



BRIEF DESCRIPTION OF THE DRAWINGS
The present disclosure is best understood with reference to the accompanying figures in which like numerals refer to like elements and in which:
FIG. 1 shows an MWD tool for use with one embodiment of the present disclosure;
FIG. 2 shows a sensor section of an MWD tool suitable for use with the present disclosure;
FIG. 3 shows an NMR sensor having multiple regions of examination;
FIG. 4 shows a flow chart of a method according to one embodiment of the present disclosure.
FIG. 5A shows a chart of an exemplary echo train from an NMR tool from one embodiment according to the present disclosure;
FIG. 5B shows a chart of a T2 distribution for the echo train of FIG. 5A;
FIG. 6A shows a chart of a reduced echo train based on the echo train of FIG. 5A;
FIG. 6B shows a chart of a T2 distribution for the reduced echo train of FIG. 6A.
FIG. 7A shows a chart of another exemplary echo train from an NMR tool from one embodiment according to the present disclosure;
FIG. 7B shows a chart of a T2 distribution for the echo train of FIG. 7A;
FIG. 8A shows a chart of a fast (short) echo train based on the echo train of FIG. 7A;
FIG. 8B shows a chart of a T2 distribution for the fast (short) echo train of FIG. 7A.
FIG. 9A shows a chart of a slow (long) echo train based on the echo train of FIG. 7A; and
FIG. 9B shows a chart of a T2 distribution for the slow (long) echo train of FIG. 7A.



DETAILED DESCRIPTION OF THE DISCLOSURE
The volume of interest of an earth formation may be exposed to an NMR tool to generate an NMR response in the form of an NMR echo train. With a standard NMR echo train length of interest of about 1000 points sampled uniformly at 0.6 ms, an attempt of inversion may use a multiple of the echo train length in order to calculate errors and statistics (standard deviation, variance, mean, etc.). A method of data processing which uses a time domain non-uniform decimation of NMR echo trains would allow the bandwidth usage to be reduced without degrading the signal information when recovered. The NMR echo train may be divided into two or more portions (data windows). These data windows may be selected based on a transverse relaxation time distribution for protons in the volume of interest. Non-uniform decimation applied on a time-domain NMR echo train may provide for the specification of which portion(s) of the echo train are not to be down-sampled and which portion(s) of the echo train are to be down-sampled. Non-uniform decimation may be controlled so that one or more portions of the echo train that would suffer from negligible or no negative effect from the down-sampling undergo reduction, while one or more portions of the echo train that would suffer critical information loss if reduced may avoid reduction. In some embodiments, different portions of the echo train may be decimated to different degrees based on the criticality of the information stored within each portion. Non-uniform decimation may be comparable to a weighted compression of data in the time-domain. The resulting non-uniform decimated echo train data can be reconstructed at the surface without the loss of critical information.
For example, if an NMR echo train is divided into multiple portions, a first portion may not be down-sampled, since this part represents the early components in the T2 domain (clay bound water). In a second portion, down-sampling of 2 or higher may be performed. This second portion may represent the bound water in the T2 domain, and the down-sampling of the second portion is not critical to the information content. In a third portion, the down-sampling is typically higher compared to the down-sampling of the second portion. The third portion may represent the late T2 components (oil, gas) which are normally poorly resolved with limited numbers of echoes (limitation of echoes due to bandwidths limitation in the data transmission).
Non-uniform decimation allows for the collection of more information from late components with a given number of echoes and, therefore, may give a better estimation of this area in the later inversion result (T2 domain). It is notable that noise along the divided and decimated echo train remains unchanged, and, therefore, a noise calculation can be applied on this new reduced (“compressed”) echo train. In addition the data processing of this new “compressed” echo train is less complex and faster since less data needs to be handled. Thus, non-uniform decimation may be used in general data handling and is not limited to downhole applications. Illustrative embodiments of the present claimed subject matter are described in detail below.
FIG. 1 shows a schematic diagram of a drilling system 10 with a drillstring 20 carrying a drilling assembly 90 (also referred to as the bottomhole assembly, or “BHA”) conveyed in a “wellbore” or “borehole” 26 for drilling the borehole. The drilling system 10 includes a conventional derrick 11 erected on a floor 12 which supports a rotary table 14 that is rotated by a prime mover such as an electric motor (not shown) at a desired rotational speed. The drillstring 20 includes a tubing, such as a drill pipe 22 or a coiled-tubing extending downward from the surface into the borehole 26. The drillstring 20 is pushed into the borehole 26 when a drill pipe 22 is used as the tubing. For coiled-tubing applications, a tubing injector, such as an injector (not shown), however, is used to move the tubing from a source thereof, such as a reel (not shown), to the borehole 26. The drill bit 50 attached to the end of the drillstring breaks up the geological formations when it is rotated to drill the borehole 26. If a drill pipe 22 is used, the drillstring 20 is coupled to a drawworks 30 via a Kelly joint 21, swivel 28, and line 29 through a pulley 23. During drilling operations, the drawworks 30 is operated to control the weight on bit, which is an important parameter that affects the rate of penetration. The operation of the drawworks is well known in the art and is thus not described in detail herein. For the purposes of this disclosure, it is necessary to know the axial velocity (rate of penetration or ROP) of the bottomhole assembly. Depth information and ROP may be communicated downhole from a surface location. Alternatively, the method disclosed in U.S. Pat. No. 6,769,497 to Dubinsky et al. having the same assignee as the present application and the contents of which are incorporated herein by reference may be used. The method of Dubinsky uses axial accelerometers to determine the ROP. During drilling operations, a suitable drilling fluid 31 from a mud pit (source) 32 is circulated under pressure through a channel in the drillstring 20 by a mud pump 34. The drilling fluid passes from the mud pump 34 into the drillstring 20 via a desurger (not shown), fluid line 38 and Kelly joint 21. The drilling fluid 31 is discharged at the borehole bottom 51 through an opening in the drill bit 50. The drilling fluid 31 circulates uphole through the annular space 27 between the drillstring 20 and the borehole 26 and returns to the mud pit 32 via a return line 35. The drilling fluid acts to lubricate the drill bit 50 and to carry borehole cutting or chips away from the drill bit 50. A sensor S1 typically placed in the line 38 provides information about the fluid flow rate. A surface torque sensor S2 and a sensor S3 associated with the drillstring 20 respectively provide information about the torque and rotational speed of the drillstring. Additionally, a sensor (not shown) associated with line 29 is used to provide the hook load of the drillstring 20.
In one embodiment of the disclosure, the drill bit 50 is rotated by only rotating the drill pipe 22. In another embodiment of the disclosure, a downhole motor 55 (mud motor) is disposed in the drilling assembly 90 to rotate the drill bit 50 and the drill pipe 22 is rotated usually to supplement the rotational power, if required, and to effect changes in the drilling direction.
In an exemplary embodiment of FIG. 1, the mud motor 55 is coupled to the drill bit 50 via a drive shaft (not shown) disposed in a bearing assembly 57. The mud motor rotates the drill bit 50 when the drilling fluid 31 passes through the mud motor 55 under pressure. The bearing assembly 57 supports the radial and axial forces of the drill bit. A stabilizer 58 coupled to the bearing assembly 57 acts as a centralizer for the lowermost portion of the mud motor assembly.
In one embodiment of the disclosure, a drilling sensor module 59 is placed near the drill bit 50. The drilling sensor module contains sensors, circuitry and processing software and algorithms relating to the dynamic drilling parameters. Such parameters typically include bit bounce, stick-slip of the drilling assembly, backward rotation, torque, shocks, borehole and annulus pressure, acceleration measurements and other measurements of the drill bit condition. A suitable telemetry or communication sub 72 using, for example, two-way telemetry, is also provided as illustrated in the drilling assembly 90. The drilling sensor module processes the sensor information and transmits it to the surface control unit 40 via the telemetry system 72.
The communication sub 72, a power unit 78 and an MWD tool 79 are all connected in tandem with the drillstring 20. Flex subs, for example, are used in connecting the MWD tool 79 in the drilling assembly 90. Such subs and tools form the bottom hole drilling assembly 90 between the drillstring 20 and the drill bit 50. The drilling assembly 90 makes various measurements including the pulsed nuclear magnetic resonance measurements while the borehole 26 is being drilled. The communication sub 72 obtains the signals and measurements and transfers the signals, using two-way telemetry, for example, to be processed on the surface. Alternatively, the signals can be processed using a downhole processor in the drilling assembly 90.
The surface control unit or processor 40 also receives signals from other downhole sensors and devices and signals from sensors S1-S3 and other sensors used in the system 10 and processes such signals according to programmed instructions provided to the surface control unit 40. The surface control unit 40 displays desired drilling parameters and other information on a display/monitor 42 utilized by an operator to control the drilling operations. The surface control unit 40 typically includes a computer or a microprocessor-based processing system, memory for storing programs or models and data, a recorder for recording data, and other peripherals. The control unit 40 is typically adapted to activate alarms 44 when certain unsafe or undesirable operating conditions occur.
A suitable device for use of the present disclosure is disclosed in U.S. Pat. No. 6,215,304 to Slade, the contents of which are fully incorporated herein by reference. It should be noted that the device taught by Slade is for exemplary purposes only, and the method of the present disclosure may be used with many other NMR logging devices, and may be used for wireline as well as MWD applications.
It should be noted that underbalanced drilling is commonly carried out using a coiled tubing instead of a drillstring. Hence the disclosure of the BHA being conveyed on a drillstring is not to be construed as a limitation. For the purposes of the present disclosure, the term “drilling tubular” is intended to include both a drillstring as well as coiled tubing.
Referring now to FIG. 2, the tool has a drill bit 107 at one end, a sensor section 102 behind the drill head, and electronics 101. The sensor section 102 comprises a magnetic field generating assembly for generating a Bo magnetic field (which is substantially time invariant over the duration of a measurement), and an RF system for transmitting and receiving RF magnetic pulses and echoes. The magnetic field generating assembly comprises a pair of axially spaced main magnets 103, 104 having opposed pole orientations (i.e. with like magnetic poles facing each other), and three ferrite members 109, 110 axially arranged between the magnets 103, 104. The ferrite members are made of “soft” ferrite which can be distinguished over “hard” ferrite by the shape of the BH curve which affects both intrinsic coercivity (Hj the intersection with the H axis) and initial permeability (μi, the gradient of the BH curve in the unmagnetized case). Soft ferrite μi values typically range from 10 to 10000 whereas hard ferrite has μi, of about 1. Therefore the soft ferrite has large initial permeability (typically greater than 10, preferably greater than 1000). The RF system comprises a set of RF transmit antenna and RF receive antenna coil windings 105 arranged as a central “field forming” solenoid group 113 and a pair of outer “coupling control” solenoid groups 114.
The tool has a mud pipe 160 with a clear central bore 106 and a number of exit apertures 161-164 to carry drilling mud to the bit 107, and the main body of the tool is provided by a drill collar 108. Drilling mud is pumped down the mud pipe 160 by a pump 121 returning around the tool and the entire tool is rotated by a drive 120. Coiled tubing or a drillstring may be used for coupling the drive to the downhole assembly.
The drill collar 108 provides a recess 170 for RF transmit antenna and RF receive antenna coil windings 105. Gaps in the pockets between the soft ferrite members are filled with non-conducting material 131, 135 (e.g: ceramic or high temperature plastic) and the RF coils 113, 114 are then wound over the soft ferrite members 109, 110. The soft ferrites 109, 110 and RF coil assembly 113, 114 are pressure impregnated with suitable high temperature, low viscosity epoxy resin (not shown) to harden the system against the effects of vibration, seal against drilling fluid at well pressure, and reduce the possibility of magnetoacoustic oscillations. The RF coils 113, 114 are then covered with wear plates 111 typically ceramic or other durable non-conducting material to protect them from the rock chippings flowing upwards past the tool in the borehole mud.
Because of the opposed magnet configuration, the device of Slade has an axisymmetric magnetic field and region of investigation 112 that is unaffected by tool rotation. Use of the ferrite results in a region of investigation that is close to the borehole. This is not a major problem on a MWD tool (except for special situations discussed below that are the focus of this disclosure) because there is little invasion of the formation by borehole drilling fluids prior to the logging. The region of investigation is within a shell with a radial thickness of about 20 mm and an axial length of about 50 mm. The gradient within the region of investigation is less than 2.7 G/cm. It is to be noted that these values are for the Slade device and, as noted above, the method of the present disclosure may also be used with other suitable NMR devices. This field gradient of less than 2.7 G/cm may be considered to be a “near zero” field gradient for the purposes of the present disclosure as discussed below.
Two magnetic fields may be used to conduct a typical NMR measurement: a static magnetic field B0 and an alternating magnetic field B1 having a component orthogonal to B0. Pulsed NMR is used in which the alternating field B1 is applied into the sample as a sequence of bursts (usually called pulses):

TW−TP−τ1−(RP−τ2−echo−τ2)n 

wherein TW is a (long) wait time of usually several times the spin lattice relaxation time, TP is a tipping pulse for tipping the nuclear spins at an angle substantially equal to ninety degrees to cause precession thereof, τ1, τ2 are waiting times, RP is a refocusing pulse for tipping the nuclear spins greater than 90° and n is the number of echoes to be acquired in one sequence. The duration of the events between the echoes is called the interecho time TE. The echoes manifest themselves as rotating macroscopic magnetizations and can be detected with a receiver coil. The induced voltages/currents in this coil are the desired NMR signals. In order to obtain NMR signals and refocus them correctly, it is important to adhere to NMR resonance conditions, i.e. B0 and B1 amplitudes as well as pulse phases and shapes need to be chosen correctly as known to people familiar with the art of NMR. An exemplary optimized echo sequence called ORPS is discussed, for example, in Hawkes '013. In the ORPS sequence, the tipping pulse is typically 90°, but the refocusing pulses are less than 180°. This is in contrast to the CPMG sequence in which the refocusing pulses are 180° pulses.

Generally, the geometry of the NMR measurement device gives rise to a volume in the earth formation where the B0 field has the correct strength to fulfill a resonance condition and in which an RF field can be presented with a substantial strength and orientation to reorient nuclear spins within the volume. This volume is often referred to as the sensitive volume. For a tool in motion, as the tool moves axially, the volume containing those protons excited by the excitation pulse (first pulse of the echo sequence) moves away from the sensitive volume. Hence, the number of spins available to contribute to the subsequent NMR signal is reduced with each subsequent echo. As a consequence, those echoes obtained later in an echo sequence with axial tool motion appear small compared to those echoes obtained later in an echo sequence acquired with no tool motion. “Later echoes” does not mean that only the last echoes of a sequence are affected. In fact, the loss of signal starts right at the beginning of a sequence and develops over time in a unique pattern. This phenomenon is called outflow.
In general, NMR echo sequences are repeated several times for the purpose of increasing the final signal-to-noise ratio. Even without concern over signal-to-noise ratio, an echo sequence is usually repeated at least once in order to form a phase-alternated pair (PAP) for the purpose of removing offset and ringing effects.
At the end of a sequence obtained with axial tool motion, the magnetization of the sensitive volume is substantially zero. A wait time TW during which re-magnetization of the formation occurs is used as part of the sequence of pulses. Choosing a wait time of at least 5 times the longest T1 of the formation ensures that the formation is fully magnetized (>99% magnetization) immediately prior to the excitation pulse of the ensuing sequence. However, shorter wait times are often chosen in order to achieve a higher NMR data rate, leading to an improved axial resolution or signal-to-noise ratio. The drawback of shortening TW is that the formation may not be fully magnetized immediately prior to the ensuing sequence. As a consequence, the total porosity that is measured in a tool having axial motion can be too low, and the measured T2-distribution is generally distorted, mainly for the longer T2 components.
Similar considerations are present in the radial direction due to radial fluid flow into the borehole. A result of the radial inflow of fluid is an outflow of polarized nuclei from the region of examination, as for the case of vertical tool movement discussed above. By reducing the field gradient, the “outflow effect” can be reduced. In the present disclosure, the tool is designed in such a way as to maintain close to a zero static field gradient in the radial direction, thus minimizing radial motion effects in the NMR signal. In addition to the outflow effect, motion causes a distortion of the phases of the NMR signals, which also reduces the amplitude of the received NMR signal. The phase distortion can be reduced by reducing the static magnetic field gradient but also by reducing the interecho time TE.
A similar solution can be used for a different problem, that of making NMR measurements in small boreholes. A BHA designed for use in a small borehole is limited to a small magnet size, so that a normal tool would have a small region of investigation. With small sensitive regions it is difficult to achieve a sufficient signal to noise ratio, which is required to have a high accuracy of the measurement combined with a good vertical resolution. In addition to or instead of expanding the radial extent of the zone of near zero field gradient, one embodiment of the disclosure combines multiple resonance areas to one big sensitive region, where the measurement is carried out. This combination can be done by designing one common antenna covering all areas.
FIG. 3 shows an exemplary logging tool 301. Three magnets 303 are shown. Adjacent magnets have like poles facing each other so as to define two regions of examination 309a, 309b. Antennas 307 are used for generating the RF pulses and measuring the spin echo signals. The electronics module 305 that includes a processor is used for processing the signals received by the antennas. In the configuration shown, the signals from the two antennas are summed, so that effectively, signals from a region of examination that is a combination of 309a and 309b are obtained. This increases the signal to noise ratio, but also reduces the vertical resolution of the NMR measurements. For the purposes of the present disclosure, the BHA may be considered to be a “carrier” and the magnet assembly produces a static magnetic field in one or more regions of examination. The static field gradient in the region of examination is nearly zero, so that during the length of the pulse sequence given by eqn. (1), the “outflow” effect is small and signals are obtained from nuclear spins that have been polarized. Another factor to be considered is that the outflow during the time TE should also be small, so that the spin echo signals are without phase distortion.
It is to be noted that the example given in FIG. 3 is directed towards the problem of obtaining an adequate signal in a small borehole. Basically the same design with a single region of examination can be used to address the problem of fluid inflow by selecting the combination of field gradient, and echo train length to satisfy the outflow condition.
In an alternate embodiment of the disclosure, using two independent antennas, the spin echo signals from region of examination 309a and region of examination 309b are stored separately in the electronics module. Depth determinations may be conveniently made by having synchronized clocks downhole and uphole and measuring the length of the drill string at the surface. When drilling has progressed so that the measurements made in one region of examination 309b are at the same depth as those made earlier in the other region of examination 309a, then the data corresponding to the same depth may be combined. This method of summing data from the same depth increases the signal to noise ratio without reducing the vertical resolution.
FIG. 4 shows a flow chart of a method 400 according to one embodiment of the present disclosure. In step 410, the logging tool 301 may be used to acquire NMR LWD data set from a volume of interest of the earth formation. In step 420, the data set may be separated into a plurality of portions (data windows). The data windows may be selected based one or more characteristics of the data, such as, but not limited to, the transverse relaxation time distribution of protons in the volume of interest. In step 430, the data set may be reduced by applying a data adaptive down-sampling scheme to the data windows. The data adaptive down-sampling scheme may include two or more different down-sampling factors. At least one of the down-sampling factors may be applied to each of the plurality of data windows. In step 440, the reduced data set may be transmitted from downhole to a surface location. While the above example uses an NMR data set, any type of data set may be used with embodiments of the present disclosure. While the above example shows downhole to surface communication in step 440, embodiments of this disclosure are not limited to downhole to surface communication or bandwidth limited environments.
FIG. 5A shows an exemplary acquired echo train from downhole of length 1000 points. Curve 500 represents the echo train. The first data window 510 covers the range of 0.6 ms to 42 ms. The second data window 520 covers the range of 42.6 ms to 180 ms. The third data window 530 covers the range of 180.6 ms to 360 ms. The fourth data window 540 covers the range of 360.6 ms to 600 ms. FIG. 5B shows the T2 distribution 550 of the echo train from FIG. 5A.
FIG. 6A shows the echo train of FIG. 5A after down-sampling has been applied. The reduced echo train is represented by curve 600. The first data window 510 has been not been down-sampled (down-sampling factor of 1). The second data window 520 has been down-sampled by 2 (sampling at 1.2 ms). The third data window 530 has been down-sampled by 3 (sampling at 1.8 ms). The fourth data window 540 has been down-sampled by 5 (sampling at 3.0 ms). FIG. 6B shows the T2 distribution 650 of FIG. 6A. It may be noted that while the reduced echo train 600 includes 365 points, down from 1000 points in echo train 500, the information has been preserved, as shown by the T2 distributions 550 and 650.
FIG. 7A shows another exemplary echo train of length 1000 points. Curve 700 represents the echo train and includes fast (short) and slow (long) T2 decay. Curve 710 represents the echo train with noise added, as would be typical in a downhole environment. Curve 720 represents the echo train after decimation. Curve 730 represents a recovered echo train based on the decimation curve 720. Curve 740 represents a recovered echo train after T2 distribution. FIG. 7B shows the T2 distributions for the echo trains from FIG. 7B. Curve 750 represents the T2 distribution of curve 700. Curve 760 represents the T2 distribution of curve 710. Curve 770 represents the T2 distribution of curve 720. As will be shown in FIGS. 8A, 8B, 9A, and 9B, the recovered decimation curves closely follow the echo train with noise (simulating real conditions) over the entire sampled period.
FIG. 8A shows the fast (short) T2 decay of the echo trains in FIG. 7A. Curve 800 represents the fast (short) echo train. Curve 810 represents the fast (short) echo train with noise added, as would be typical in a downhole environment. Curve 820 represents the fast (short) echo train after decimation. Curve 830 represents a recovered fast (short) echo train based on the decimation curve 820. Curve 840 represents a recovered fast (short) echo train after T2 distribution. FIG. 8B shows the T2 distributions for the echo trains from FIG. 8B. Curve 850 represents the T2 distribution of curve 800. Curve 860 represents the T2 distribution of curve 810. Curve 870 represents the T2 distribution of curve 820.
FIG. 9A shows the slow (long) T2 decay of the echo trains in FIG. 7A. Curve 900 represents the slow (long) echo train. Curve 910 represents the slow (long) echo train with noise added, as would be typical in a downhole environment. Curve 920 represents the slow (long) echo train after decimation. Curve 930 represents a recovered slow (long) echo train based on the decimation curve 920. Curve 940 represents a recovered slow (long) echo train after T2 distribution. FIG. 9B shows the T2 distributions for the echo trains from FIG. 9B. Curve 950 represents the T2 distribution of curve 900. Curve 960 represents the T2 distribution of curve 910. Curve 970 represents the T2 distribution of curve 920.
In addition to the reduction in data points, the number of matrix manipulations performed downhole is reduced. For example, when inverting a non-square matrix this will require the following operations to be executed:

    Let X(n×m) matrix, computing the partial inverse of X is as follows:

Pinv(X)=(XTX)−1*XT 

    The inversion will require O(m3) XTX will require O(n2m) and the last multiplication would require O(m2n).
    If m=30 and n=1000 that will translate to:

30×30×30+1000×1000×30+30×30×1000=30,927,000 instructions,

then replacing 1000 by 365 may result in a reduction of time in performing this operation:

30×30×30+365×365×30+30×30×365=4,352,250 instructions (about 86% reduction)



In some embodiments, processing time may also be reduced by compressing the signal by using the PCA technique where comp1×5=s1×1000*Loads1000×5 and similarly compNew1×5=s1×365*LoadsNew365×5.
The disclosure has been described with reference to a NMR device that is part of a BHA conveyed on a drillstring. The disclosure is equally applicable for NMR devices conveyed on coiled tubing. The processing described herein may be done using a downhole processor and the results stored on a suitable memory downhole or telemetered to the surface. Alternatively, the data may be stored on a downhole memory and processed when the BHA is tripped out of the borehole. With improved telemetry capability, it should be possible to telemeter the NMR measurements to a surface location and do the processing there.
The results of the processing may be used to estimate, using known methods, properties of interest such as a T2 distribution, volumetrics, permeability, bound volume irreducible, effective porosity, bound water, clay-bound water, total porosity, pore size distribution, and other rock and fluid properties that are based on NMR data. These are all used in reservoir evaluation and development.
The processing of the data may be conveniently done on a processor. The processor executes a method using instructions stored on a suitable non-transitory computer-readable medium product. The non-transitory computer-readable medium product may include a ROM, an EPROM, an EAROM, a flash memory, and/or an optical disk.
While the foregoing disclosure is directed to the specific embodiments of the disclosure, various modifications will be apparent to those skilled in the art. It is intended that all such variations within the scope and spirit of the appended claims be embraced by the foregoing disclosure.

## Claims

1. A method of communicating a data set acquired in a borehole between a downhole location and a surface location, comprising:
using at least one processor to reduce the data set using a data adaptive down-sampling scheme comprising a plurality of non-uniform down-sampling factors, wherein the data set is separated into a plurality of data windows, and each of the plurality of data windows corresponds to one of the plurality of non-uniform data-sampling factors; and
transmitting the reduced data set from the downhole location to the surface location.

2. The method of claim 1, wherein the data set includes nuclear magnetic resonance echo train data.

3. The method of claim 1, further comprising:
acquiring the data set in the borehole.

4. The method of claim 1, wherein each of the plurality of down-sampling factors has a value of at least 2.

5. The method of claim 1, further comprising:
separating the data set into the plurality of data windows.

6. The method of claim 1, wherein the plurality of data windows are mutually exclusive.

7. The method of claim 1, wherein the plurality of data windows is selected based on a distribution characteristic of the data set.

8. The method of claim 1, wherein the plurality of data windows is selected based on a transverse relaxation time distribution for protons.

9. The method of claim 1, wherein the selection of the plurality of data windows includes a number of data windows in the plurality of data windows and a range for each of the data windows.

10. An apparatus configured to communicate a data set acquired in a borehole between a downhole location and a surface location, comprising:
at least one processor configured to:
reduce the data set using a data adaptive down-sampling scheme comprising a plurality of non-uniform down-sampling factors, wherein the data set is separated into a plurality of data windows, and each of the plurality of data windows corresponds to one of the plurality of non-uniform data-sampling factors; and

a transmitter configured to transmit the reduced data set from the downhole location to the surface location.

11. The apparatus of claim 10, wherein the data set includes nuclear magnetic resonance (NMR) echo train data.

12. The apparatus of claim 11, further comprising:
an NMR tool configured to acquire the NMR echo train data in the borehole.

13. The apparatus of claim 10, wherein each of the plurality of down-sampling factors has a value of at least 2.

14. The apparatus of claim 10, the at least one process further configured to:
separate the data set into the plurality of data windows.

15. The apparatus of claim 10, wherein the plurality of data windows are mutually exclusive.

16. The apparatus of claim 10, wherein the plurality of data windows is selected based on a distribution characteristic of the data set.

17. The apparatus of claim 10, wherein the plurality of data windows is selected based on a transverse relaxation time distribution for protons.

18. The apparatus of claim 10, wherein the selection of the plurality of data windows includes a number of data windows in the plurality of data windows and a range for each of the data windows.

19. A non-transitory computer-readable medium product having stored thereon instructions that, when executed by at least one processor, cause the at least one processor to perform a method, the method comprising:
reducing the data set using a data adaptive down-sampling scheme comprising a plurality of non-uniform down-sampling factors, wherein the data set is separated into a plurality of data windows, and each of the plurality of data windows corresponds to one of the plurality of non-uniform data-sampling factors; and
transmitting the reduced data set from the downhole location to the surface location.

20. The non-transitory computer-readable medium product of claim 19 further comprising at least one of: (i) a ROM, (ii) an EPROM, (iii) an EEPROM, (iv) a flash memory, and (v) an optical disk.