Relaxation time estimation in surface NMR

NMR relaxation time estimation methods and corresponding apparatus generate two or more alternating current transmit pulses with arbitrary amplitudes, time delays, and relative phases; apply a surface NMR acquisition scheme in which initial preparatory pulses, the properties of which may be fixed across a set of multiple acquisition sequence, are transmitted at the start of each acquisition sequence and are followed by one or more depth sensitive pulses, the pulse moments of which are varied across the set of multiple acquisition sequences; and apply processing techniques in which recorded NMR response data are used to estimate NMR properties and the relaxation times T1 and T2* as a function of position as well as one-dimensional and two-dimension distributions of T1 versus T2* as a function of subsurface position.

FIELD OF THE INVENTION

The field of the invention is surface Nuclear Magnetic Resonance (NMR) technologies to measure NMR properties of subsurface fluids and formations, and to use measured NMR properties to estimate other physical properties of the subsurface.

BACKGROUND

NMR systems have been in use for many years and can be used to provide imaging and/or analysis of a sample being tested. For example, U.S. Pat. No. 6,160,398, U.S. Pat. No. 7,466,128, U.S. Pat. No. 7,986,143, U.S. patent application Ser. No. 12/914,138 and U.S. patent application Ser. No. 13/104,721 describe a variety of NMR technologies, and are incorporated herein by reference. Various different types of NMR include medical NMR, often referred to as Magnetic Resonance Imaging (MRI), and surface NMR for measuring properties of earth formations. While there is some overlap in the technologies that may be applied in MRI and surface NMR, the samples being measured and the environments in which measurements are performed are different, leading to many differences in the technologies applied.

In general, surface NMR measurement involves utilizing or generating a static magnetic field within a sample volume, emitting one or more electromagnetic pulses into the sample volume, and detecting NMR responses from the sample volume. In some cases, surface NMR measurement involves emitting multiple electromagnetic pulses in rapid succession and measuring the NMR responses between the electromagnetic pulses. The measured NMR responses provide useful information about the sample volume.

Surface NMR measurements may be used to detect, for example, the abundance of hydrogen contained within an underground sample volume, and NMR relaxation times within a sample. Detected hydrogen abundance and NMR relaxation times may be used to characterize many properties of fluid-bearing formations underground, such as the porosity, total quantity of fluids, fluid composition, pore size, and permeability of the sample. Three types of relaxation times of interest are referred to in the art as T2*, T2, and T1.

There is a need in the art for better surface NMR measurement apparatus and methods. In particular, improved technologies for estimating NMR relaxation times as described herein will provide better characterization of fluid-bearing formations underground.

SUMMARY

Technologies applicable to NMR relaxation time estimation are disclosed. NMR relaxation time estimation may comprise performing surface NMR measurement methods according to this disclosure, and using resulting NMR data to estimate relaxation times and formation properties.

Some example surface NMR measurement methods may comprise generating a set or cycle of multi-pulse acquisition sequences, each multi-pulse acquisition sequence comprising a preparatory pulse, wherein said preparatory pulse may be substantially identical in each of the multi-pulse acquisition sequences in the set or cycle. The terms “set” and “cycle” are used interchangeably herein. The preparatory pulses in the pulse sequences may comprise on-resonance pulses, adiabatic pulses, and/or composite pulses.

Each multi-pulse acquisition sequence may further comprise one or more ordered subsequent pulses following the preparatory pulse. A pulse moment of an ordered subsequent pulse in at least one of the multi-pulse acquisition sequences in the set may be different from a pulse moment of a same ordered subsequent pulse in at least one other of the multi-pulse acquisition sequences in the set.

Example methods may furthermore comprise using NMR response data produced from the set of multi-pulse acquisition sequences to estimate NMR relaxation times T1, T2*, and/or T2as a function of position, and/or to estimate one, two, or other multi-dimensional distributions of T1versus T2*, or other relaxation time combinations, as a function of position.

Some example surface NMR measurement apparatus may include, inter alia, surface NMR measurement hardware such as a computer/controller, data acquisition devices, a voltage/current generator, transmit switching, signal receive electronics, and/or detection coils. The computer or other controller may be configured with surface NMR measurement control circuits or software configured to execute the surface NMR measurement techniques disclosed herein. Some example NMR measurement data processing apparatus may include a computer configured with NMR data processing software configured to process NMR data gathered according to the disclosed surface NMR measurement techniques to estimate relaxation times T1, T2*, and/or T2as a function of position, and/or to estimate one-dimensional, two-dimensional or other multi-dimensional distributions of relaxation times as a function of position as described herein.

Further aspects and variations are discussed in detail below.

DETAILED DESCRIPTION

Prior to explaining embodiments of the invention in detail, it is to be understood that the invention is not limited to the details of construction or arrangements of the components and method steps set forth in the following description or illustrated in the drawings. The invention is capable of other embodiments and of being practiced and carried out in various ways. Also, it is to be understood that the phraseology and terminology employed herein are for the purpose of the description and should not be regarded as limiting.

Technologies directed to NMR relaxation time estimation are disclosed. The attached figures illustrate, inter alia: surface NMR acquisition methods; techniques to estimate NMR relaxation times; and surface NMR apparatus. Example surface NMR acquisition methods may include generating a set of two or more multi-pulse acquisition sequences, each of the multi-pulse acquisition sequences comprising an initial preparatory pulse followed by one or more subsequent “depth sensitive” pulses. The preparatory pulses may have substantially identical properties across the set of multi-pulse acquisition sequences, while the pulse moments of the depth sensitive pulses may be varied in the set of multiple acquisition sequences. The term “pulse moment” has a standard and accepted definition in the art: pulse moment is given by the product of pulse current amplitude and pulse duration. The term “substantially identical” in the context of preparatory pulses having substantially identical properties, refers to having a difference equal to or less than 5% of the larger preparatory pulse. For example, on-resonance preparatory pulses with pulse moments of 10 Amp seconds (As) and 10.5 As would be considered “substantially identical” for the purpose of this disclosure.

Example techniques to estimate NMR relaxation times may include processing techniques for processing NMR data acquired with disclosed surface NMR acquisition methods. Acquired NMR data may be used to estimate NMR properties and relaxation times such as T1and T2* as a function of position as well as one-dimensional and two-dimensional covariance distributions of relaxation times as a function of position. Resulting estimates of the relaxation time properties of the subsurface and their spatial distribution can be used to estimate other properties of the subsurface, including pore size and permeability.

Example surface NMR apparatus may include hardware, control software and/or processing software to execute surface NMR acquisition sequences and/or NMR data processing tasks. Surface NMR apparatus may be configured to generate pulse sequences with pulse types, pulse moments, amplitudes, time delays, relative phases, or other pulse properties according to the surface NMR techniques disclosed herein. NMR data processing apparatus may be configured to use recorded NMR signals in techniques to estimate NMR relaxation times introduced above, namely, to estimate NMR properties and relaxation times as a function of position as well as one-dimensional and two-dimensional covariance distributions of relaxation times as a function of position. NMR data processing apparatus may also be configured to use resulting estimates of relaxation times of the subsurface and their spatial distribution to estimate other properties of the subsurface including pore size and permeability.

The present disclosure appreciates that not all decay times provide equivalent sensitivity to pore size and permeability. In particular T2*, which is often the most straightforward parameter to measure, is often more sensitive to inhomogeneity in the background magnetic field than to pore size or permeability. The relaxation time T2can also be significantly affected by magnetic inhomogeneity. The relaxation time which is generally least sensitive to magnetic field inhomogeneity and is most sensitive to pore size and permeability is T1; however, T1is generally a more challenging relaxation time to measure by surface NMR.

In some embodiments, methods according to this disclosure may constrain the mathematical estimation of T1to yield more accurate values of the T1relaxation time. Methods according to this disclosure may incorporate information pertaining to the covariance of T1with other relaxation times, which can be used to improve the precision and interpretation of relaxation time estimates.

FIG. 1illustrates an example acquisition sequence for a laboratory saturation recovery experiment. The sequence illustrated inFIG. 1comprises two transmit operations101and103, shown on the “transmit” line, wherein transmit operation101is followed by a receive operation102, and transmit operation103is followed by a receive operation104, shown on the “receive” line. The transmit pulses101and103are separated by a delay time referred to as τd,j. A longitudinal magnetization of a sample to which transmitted pulses are applied is illustrated underneath the receive line.FIG. 1furthermore includes an example saturation recovery curve can be generated by repeating the illustrated sequence of transmit and receive operations while varying the delay times τd,jbetween each jth pulse sequence.

In a laboratory NMR measurement, the characterization of decay times for a sample volume may be generally straightforward, providing for high precision and accuracy. An example laboratory NMR measurement begins by placing a sample of known volume containing a hydrogen-bearing fluid in a static magnetic field. At equilibrium with the static magnetic field, the hydrogen nuclei produce a net nuclear spin magnetization that is aligned parallel to the direction of the background magnetic field (along the “longitudinal” or z axis).

A coil or antennae may then be used to apply an oscillating magnetic field transmit pulse to the sample, for example in the first transmit operation101. The applied oscillating magnetic field is referred to as B1and in the case of an on-resonance pulse may be tuned to the Larmor frequency of the hydrogen nuclei, referred to as f0. The application of B1causes the spins to rotate an angle α, which is proportional to the pulse moment q of the transmit operation. For an on-resonance pulse transmitted at frequency f0, q is given by the product of the B1field amplitude within the sample and the duration of the B1magnetic field produced by the transmit pulse.

After the transmit pulse101is extinguished, the component of the magnetization in the sample that was rotated into the so-called “transverse plane” (perpendicular to the longitudinal axis), precesses about the longitudinal axis generating a detectable NMR signal that resonates at the Larmor frequency. The NMR signal may be detected and observed in the first receive operation102. The NMR signal following a transmit pulse is referred to as the Free-Induction Decay (FID) signal. The FID signal decays over time as magnetization in the transverse plane simultaneously loses coherence and recovers to equilibrium alignment along the longitudinal axis.

The effective transverse relaxation time T2* describes the characteristic decay time of coherent magnetization in the transverse plan and can be observed directly as the decay time of the FID signal. The transverse relaxation time T2describes the characteristic decay time of coherence magnetization in the transverse plane with elimination or mitigation of static de-phasing in an inhomogeneous field. The longitudinal relaxation time T1describes the characteristic time required for the magnetization to recover to equilibrium along the longitudinal axis. Because the state of the longitudinal magnetization is not directly indicated by the decay FID signal, a multi-pulse measurement sequence may be used to quantify T1.

The so-called “saturation recovery” method is illustrated inFIG. 1. The “saturation recovery” method starts with the system at equilibrium, with magnetization of a sample aligned along the longitudinal axis (Mz=M0) prior to the application of an initial “saturation” pulse, e.g., the first transmit operation101illustrated inFIG. 1. In the laboratory, the value of q for the saturation pulse may be set such that the B1magnetic field produced by the saturation pulse induces a α=90 degree flip of the magnetization across the entire sample volume; thus magnetization of the sample is rotated into the transverse plane, and there remains substantially zero longitudinal magnetization immediately after the saturation pulse (Mz=0).

Following the saturation pulse, an FID signal may be observed at the first receive operation102, and the longitudinal magnetization of the sample may begin to recover along the longitudinal axis with characteristic recovery time specified as T1.

After a finite delay time τd, a subsequent 90 degree pulse may be applied, e.g., the transmit operation103. This subsequent pulse acts to rotate the magnetization of the sample which has recovered along the longitudinal axis back into the transverse plane. A subsequent FID signal may be observed in a subsequent receive operation104. The observed magnitude of the subsequent FID signal may substantially exactly reflect the magnitude of the longitudinal magnetization Mz(τd) that had recovered to equilibrium prior to application of the subsequent pulse.

By repeating this sequence using a range of delay times, and recording the values of Mz(τd), a saturation recovery curve can be generated that reflects the recovery of the longitudinal magnetization as a function of delay time. For example the sequence may be repeated M times where the value of the delay time τd,jis varied in each jth-indexed sequence. An example saturation recovery curve is illustrated at the bottom ofFIG. 1. Fitting the curve with an exponential or multi-exponential function (e.g., by Laplace inversion) may provide an estimate of the T1relaxation time or T1relaxation time distribution. While methods such as illustrated inFIG. 1may work in the laboratory, the real-world circumstances of surface NMR measurement in the field makes it more difficult to estimate relaxation times, and in particular to estimate T1, outside the laboratory.

FIG. 2depicts an example surface NMR measurement apparatus according to this disclosure. The example surface NMR measurement apparatus200may include a computer210, function generators211,212, AC voltage/current generator(s)230, transmit switch(es)240, NMR sensor(s)250, receive switch(es)260, preamplifier(s)270, and Analog to Digital (AD) converter(s)220. The NMR sensor(s)250are illustrated as an induction coil. Computer210comprises measurement control module(s)201and data processing module(s)202. The NMR sensor(s)250may be positioned over a ground surface280, and a subsurface fluid281is shown under the ground surface280. An arrow representing an example direction of Earth's magnetic field282is also shown.

InFIG. 2, the computer210may be coupled to function generators211,212by connections213and214, respectively. The computer210may also be coupled to AC voltage/current generator(s)230by connection215, to transmit switch(es)240by connection216, to receive switch(es)260by connection217, and to AD converter(s)220by connection222. Furthermore, function generators211,212may be coupled to AC voltage/current generator(s)230by connections231and232, respectively. AC voltage/current generator(s)230may be coupled to transmit switch(es)240by connections233and234. Transmit switch(es)240may be coupled to both ends241and242of the induction coil implementing NMR sensor(s)250. The ends of the induction coil(s)241and242may be coupled to receive switch(es)260by connections261and262, respectively. Receive switch(es)260may be coupled to preamplifier(s)270by connections271and272. Preamplifier(s)270may be coupled to AD converter(s)220by connection221.

In general, with regard toFIG. 2, measurement control module(s)201may be configured to perform NMR measurements according to this disclosure by appropriately controlling the various other illustrated components of the surface NMR measurement apparatus200. For example, the various components may be operated to produce current pulses on the NMR sensor(s)250, to thereby create NMR excitation pulses. Properties of transmitted pulses, delay times between pulses, and any other aspects of pulse sequences may be adjusted to produce sets of multi-pulse acquisition sequences according to this disclosure. The computer210may be configured to produce a pulse by selecting a pulse phase, pulse moment, and/or other pulse properties, and activating the AC voltage/current generator(s)230. The computer210may also be configured to establish appropriate delay times between pulses in multi-pulse acquisition sequences. The computer210may be configured to select a pulse phase for example by activating a function generator211or212corresponding to a desired pulse phase, so that the selected function generator211or212provides an input pulse phase to the AC voltage/current generator(s)230, which may then be amplified by the AC voltage/current generator(s)230to produce a corresponding pulse on the NMR Sensor(s)250. The computer210may also optionally be configured to close one or more transmit switch(es)240when activating the AC voltage/current generator(s)230, and open the transmit switch(es)240after activating the AC voltage/current generator(s)230.

Surface NMR measurement apparatus200may also be configured to receive and record NMR signal data received via the NMR sensor(s)250. Surface NMR measurement apparatus200may be configured to receive and record NMR signal data after one or more excitation pulses. In some embodiments, the computer210may be configured to close the receive switch(es)260after a pulse. The preamplifier(s)270amplify NMR signals received via induction coil(s)250. The AD converter(s)220convert the received and amplified signals to digital NMR signal data, e.g. by sampling received NMR signals at a desired sampling rate, and the computer210or other device equipped with storage media may be configured to store the resulting digital NMR signal data.

In some embodiments, the NMR data processing module202may be configured to process NMR measurement data, generated by operation of the measurement control module201and the various other components of surface NMR measurement apparatus200. NMR data processing module202may be configured to estimate NMR relaxation times as disclosed herein, e.g., by estimating NMR relaxation times202A and/or estimating one- or multi-dimensional covariance distributions of NMR relaxation times202B, as further described in connection withFIG. 7andFIG. 8. It will be appreciated that while the computer210may be configured to include NMR data processing module202, in some embodiments NMR measurements and NMR data processing may be performed separately, e.g., by first performing measurements with system200, then processing acquired NMR data at a later time and/or with a different computing device comprising NMR data processing module202, or by a human operator.

It will be appreciated that surface NMR measurement apparatus may be configured differently than illustrated inFIG. 2in some embodiments. To recite just a few of the many possible configuration options, computer210may be programmed with software that controls the generation of pulse sequences and the acquisition of NMR data. A set of data acquisition devices may comprise devices configured generate the control signals for the pulse sequences, such as function generators211,212, and AD converter(s)220that receive, convert and/or record NMR signals. The AC voltage/current generator(s)230may be configured to generate one or more current pulses in the induction coil(s)250in a transmit mode, to induce a coherent precession of NMR spins in a sample volume. Optional transmit switch(es)240may be configured to isolate transmitter noise from the receive circuitry during a receive mode. NMR sensor(s)250may be arranged other than as induction coils, and may be configured in a variety of ways as described herein or as known or as may be developed in the art. Optional receive switch(es)260may be configured to isolate the receive preamplifier(s)270from the potentially large voltage on the NMR sensor(s)250during transmit mode. Optional preamplifier(s)270may be configured to amplify the detected NMR signals prior to digitization by the AD converter(s)220. The optional transmit switch(es)240and receive switch(es)260may comprise active devices such as relays, and/or passive devices such as diodes. Optional tuning capacitors, not shown inFIG. 2, may be used in the transmit mode to increase the transmitted current in the induction coil(s)250, and/or in receive mode to increase the amplitude of the NMR signal voltage across the terminals of the induction coil(s)250.

In some embodiments, NMR sensor(s)250may comprise an array of coils comprising one or more transmit coils, one or more receive coils, and/or one or more combination transmit and receive coils. For example, NMR sensor(s)250may comprise one transmit coil and multiple receive coils. NMR sensor(s)250may comprise one combination transmit and receive coil, and multiple receive coils. NMR sensor(s)250may comprise multiple combination transmit and receive coils. These and other multicoil arrangements may be configured in some embodiments as will be appreciated. Multicoil arrangements may be useful for localization of fluids in structure280, as described for example in U.S. Pat. No. 2,466,128, entitled “Multicoil Data Acquisition and Processing Methods,” issued Dec. 16, 2008, which is incorporated by reference herein.

Any combination of hardware and software that enables the acquisition and processing of NMR signals is suitable to implement embodiments of this disclosure. An architecture to implement the disclosed methods could comprise, for example, elements illustrated inFIG. 2, such as an AC voltage and current generator230, a digital control system implemented at least in part by computer210, a transmit switching circuit including transmit switch(es)240, a receive switching circuit including receive switch(es)260, a multi-channel receive circuit including, e.g., a plurality of induction coils in NMR sensor(s)250, preamplifier(s)270, a digital acquisition system including AD converter(s)220, a digital storage device which may be implemented within computer210or other digital storage device, and a digital computer210. The switching circuits may transition a system such as200between a transmit-mode, when the coil(s)250are connected to the transmit circuit, and receive-mode when the coil(s)250are connected to the receive circuit.

In general, NMR measurements may be collected by transmitting one or more pulses of alternating current through NMR sensor(s)250. The alternating current may be tuned to the Larmor frequency of hydrogen nuclei, for example, and may generate a magnetic field in a subsurface fluid281alternating at the Larmor frequency. The alternating magnetic field radiates into the subsurface fluid281and modifies the nuclear magnetization state of hydrogen atoms present in subsurface fluid281. The transmitted alternating magnetic field perturbs the magnetization from equilibrium alignment in a static magnetic field, so that some component of the nuclear magnetization rotates into the transverse “xy” plane. Once rotated from equilibrium, the magnetization relaxes over time back to the equilibrium state over time, decaying from the transverse plane and re-growing along the longitudinal axis. The rotation of the magnetization by the transmitted pulse(s) and subsequent relaxation to equilibrium are described by the phenomenological Bloch equations. The evolution of the magnetization under the Bloch equations depends on several variables including the amplitude of the transmitted field, the duration and timing of the transmitted field, the phase of the transmitted field, the longitudinal relaxation time T1, FID relaxation rate T2*, and/or the spin-spin relaxation time T2of the hydrogen nuclei under investigation. These aspects of NMR measurement may be used in determining the various NMR properties described herein.

In surface NMR measurement of subsurface fluids, the Earth's magnetic field282may be utilized as the static background field and the B1field may be generated by transmitting current through one or more wire loops250laid out on the ground surface. Commonly an on-resonance excitation pulse is used (i.e., transmitted at the Larmor frequency f0). The resulting excitation and precession of the nuclear magnetization in subsurface fluids281induces a voltage on the same coil250or additional coils, and the coil voltage may be recorded at computer210as the received NMR signal.

In contrast to laboratory measurements, for which the B1field is uniform over the investigated volume, for surface NMR measurements in the field the B1magnetic field varies over the subsurface volume (i.e. the B1magnetic field is always stronger closer to the coil). As a result, there may be a distribution of the B1magnetic field amplitude and thus, for an on-resonance pulse, a distribution of tip angles within the subsurface following the transmitted pulse. Fluids located at a particular position in the subsurface exhibit a maximum amplitude response if the tip angle at that position is close to 90 degrees or 270 degrees and a minimum amplitude response if the tip angle at that position is close to 0 degrees or 180 degrees. By increasing or decreasing the product q of current I on the coil250during the transmitting pulse and the transmitting pulse duration tp, the distribution of tip angles α as a function of subsurface position may be varied as well as the sensitivity of the measurement to fluids at varying depths. The product q may be referred to as the pulse moment. The maximum excitation depth is a function of q: as the pulse moment is increased, the maximum excitation depth is also increased. We use the term “maximum excitation depth” of a pulse to refer to the depth below which tip angle rotations resulting from the pulse are substantially less than 30 degrees, e.g., anywhere from 0 degrees to 15 degrees. It will be appreciated that any tip angle may be selected for the purpose of measuring maximum excitation depth. A mathematical inversion of the recorded data measured for different values of q may be used to estimate the variation in NMR parameters as a function of depth.

In an example single-pulse NMR FID measurement scheme, a single acquisition sequence may comprise transmitting one on-resonance pulse with finite duration tpand a current I on a surface loop and then recording the subsequent NMR FID signal as one or more voltage measurements. A complete data set may comprise a collection of N single acquisition sequences, where the value of q is varied between each ith acquisition sequence. The magnitude of I may be varied, and the duration of the pulse, tp, may also be varied to vary q. Identical single acquisition sequences may be repeated to increase the signal-to-noise ratio.

The NMR voltage V(t,q) measured in the coil as a function of time and q can be expressed in a forward model as the product of the spatial distribution of water content and T2* decay behavior at each subsurface location r, and a kernel K(r,q) that represents underlying NMR physics, parameters of the coil geometry, parameters of the transmitted pulse, and other known parameters. A mathematical spatial inversion of the data collected by such a single-pulse scheme, using the aforementioned model, yields the estimated NMR response from each subsurface volume element, reflecting the total longitudinal magnetization existing prior to the pulse (proportional to water content) and the T2* decay behavior of the fluid associated with this longitudinal magnetization. The resulting estimates of water content and T2* decay behavior as a function of subsurface position can be used to estimate other properties of the subsurface formation, including pore size and permeability. However, the FID relaxation time T2* may be less sensitive to pore size and permeability than the relaxation time T1.

FIG. 3illustrates an example NMR acquisition sequence for NMR Pseudo Saturation Recovery (PSR). PSR may provide an approach to measuring T1by NMR which attempts to reproduce the saturation recovery experiment, described above for the case of laboratory conditions.FIG. 3illustrates a set of multi-pulse acquisition sequences including acquisition i300and acquisition i+1310. Acquisition i300may be performed first, and acquisition i+1310may be performed next. Each acquisition sequence comprises transmit operations illustrated on a transmit line and receive operations illustrated on a receive line.

In acquisition i300, a transmit operation301is followed by a receive operation302, there is a delay time τdbetween transmit operations, and a subsequent transmit operation303is followed by a subsequent receive operation304. Transmit operations301and303have a pulse moment qi.

In acquisition i+1310, transmit operation311is followed by receive operation312, there is a delay time τdbetween the transmit operations, and a subsequent transmit operation313is followed by a subsequent receive operation314. Transmit operations311and313have a pulse moment qi+1. FID signals FID1are received in receive operations302and312, and FID signals FID2are received in receive operations304and314. FID1and FID2may be different in the different receive operations302,312,304, and314.

In a basic PSR measurement scheme, a single acquisition sequence may comprise transmitting two on-resonance transmit pulses, such as301and303, separated by an adjustable delay time τd. In each single acquisition, the two transmit pulses may have substantially the same q-value. The FID signal following the subsequent transmit pulse (“FID2”) may be recorded; the FID following the first pulse (“FID1”) may also be recorded. An individual delay time data set may comprise of N single acquisition sequences wherein the value of q for the two transmit pulses is varied between each ith acquisition in the set and the value of τdremains fixed. A complete PSR dataset may comprise M multiple individual delay time datasets between which the value of τdis varied between each jth-indexed acquisition.

While the PSR dataset V(t, q, τd) may be sensitive to the T1recovery, the PSR dataset V(t, q, τd) may be inadequate to quantify the spatial variation in T1behavior in the subsurface. This is in part because the kernel that describes the PSR voltage signal in a forward model is a function of T1; thus, the mathematical inversion is non-linear and poorly conditioned. In light of this complication, the following simplifying assumptions might be made: (i) within the subsurface volume contributing to the signal, the preparatory pulse is assumed to produce substantially a 90 degree tip angle and zero longitudinal magnetization; (ii) the signal following the subsequent pulse only reflects the magnitude of the longitudinal magnetization the recovers during the delay time. As such, the PSR experiment may be approximated as an ideal saturation recovery experiment. However, this approach may have limited validity and certain drawbacks described below.

In fact, the above listed simplifying assumptions are generally at least partially invalid for the PSR dataset because both on-resonance pulses in each double-pulse sequence actually produce a range of tip angles within the subsurface. For volumes in which the tip angle is far from 90 degrees, a residual portion of the magnetization will be left along the longitudinal axis following the first pulses, and the longitudinal component will be non-zero. This residual magnetization will be excited by the subsequent pulses into the transverse plane; thus, such volumes where the tip angle is far from 90 degrees will contribute to the signal following the subsequent pulses that is associated with magnetization that has undergone T1recovery. As a result, the use and interpretation of PSR data can lead to errors in estimated values of T1.

In addition to a need for improved determinations of T1, NMR measurements may be improved by methodology for utilizing sensitivity of the measurement to the covariance of the T1and T2* relaxation times in a geologic formation. Covariance of different NMR relaxation times can be exploited to improve the characterization of subsurface formations. For example, dense sampling of one relaxation time can be used to improve the resolution of a subsequent relaxation time. Further, the two-dimensional relaxation time distribution derived from a two-dimensional inversion of relaxation times can provide more detailed information about the properties of the subsurface formation and fluid contained therein. For surface NMR, T1and T2* may show significant covariance and this covariance may be exploited to provide additional constraint for the data inversion and more detailed characterization of the geologic formation. Thus in some embodiments, methodologies may use theoretically bounded covariance of T1and T2* to constrain and provide improved estimation of relaxation time magnitudes. For example, it is known that T2* is never longer than T1, and this may be used (among other theoretically established covariance properties) to constrain estimation of T1. In some embodiments, estimated covariance of T1and T2* can be used to provide more detailed characterization of a geological formation than T1or T2* alone.

The methods described in connection withFIG. 1andFIG. 3use on-resonance pulses and do not take advantage other pulse types or pulse sequence properties, described below, that may be useful for surface NMR measurements. Other pulse types and pulse sequences included in the present disclosure are illustrated inFIGS. 4A, 4B, and 4C,FIGS. 5A, 5B, and 5C, andFIG. 6.

FIG. 4Aillustrates properties of an on-resonance pulse.FIG. 4Billustrates properties of a composite pulse.FIG. 4Cillustrates properties of an adiabatic pulse. In an on-resonance pulse as illustrated inFIG. 4A, the current amplitude I(t), phase φ(t), and frequency f(t), may be held constant over the duration of the pulse. In a composite pulse as illustrated inFIG. 4B, the phase and/or the amplitude of the pulse may be changed between two or more discrete intervals of the pulse, e.g., from a value of I0to a value of I1and from a value of φ0to a value of φ1. In an adiabatic pulse as illustrated inFIG. 4C, the amplitude of the pulse and/or the frequency of the pulse may be varied continuously over the duration of the pulse. For example, I(t) may be varied from 0 to a maximum value of Imaxas the frequency is varied from an off-resonance value of foffto the on-resonance Larmor frequency f0.

By selecting appropriate functions for I(t), φ(t), and f(t), composite and adiabatic pulses can produce tip angles in subsurface volumes underneath NMR surface coils that may be substantially uniform over a wider range of B1field strength, and thus may be substantially more uniform over a wider range of distances from the surface coil, than may be achieved using standard on-resonance pulses. For example, composite and adiabatic pulses can be designed to produce tip angles that are close to 90 degrees over a wide range of depths (e.g. adiabatic half-passage) or 180 degrees over a wide range of depths (e.g. adiabatic full-passage).

While on-resonance pulses may be distinguished from other on-resonance pulses by differences in pulse moment, composite and adiabatic pulses do not have a single pulse moment value. That said, “effective” pulse moment values may be calculated to distinguish composite pulses from other composite pulses, and adiabatic pulses from other adiabatic pulses. Another way to distinguish on-resonance, composite, and adiabatic pulses is by maximum excitation depth. The maximum excitation depth of an on-resonance pulse, a composite pulse or and adiabatic pulse is generally a function of I(t), φ(t), and f(t) for the pulse. The maximum excitation depth of a composite pulse or and adiabatic pulse is also generally less than the maximum excitation depth of an on-resonance pulse with an equivalent value off ∫I(t) dt. This disclosure may therefore refer to differences in maximum excitation depth or to differences in pulse moment to distinguish between pulses in some circumstances.

Improved Pulse Sequences

FIGS. 5A, 5B, and 5Cillustrate example surface NMR acquisitions in “crush recovery” sequences.FIGS. 5A, 5B, and 5Cillustrate a class of acquisition sequences, which differ from the PSR acquisition sequence shown inFIG. 3. Unlike the PSR sequence for which the preparatory pulse changes between each ith acquisition, for the sequences shown inFIGS. 5A, 5B, and 5C, the initial “preparatory” pulse may be substantially identical between each ith acquisition, and the second or other subsequent “depth profiling” pulse may be changed between each ith acquisition. Thus, the maximum excitation depth of the preparatory pulse may be substantially identical for the set of N measurements with varied q2.

FIG. 5Aillustrates a NMR acquisition comprising a set of two multi-pulse acquisition sequences for simplicity of explanation, understanding that sets may comprise any number of multi-pulse acquisition sequences. The multi-pulse acquisition sequences are referred to as acquisition i500and Acquisition i+1510. Each sequence comprises transmit operations and receive operations.

During a transmit operation501of acquisition i500, an on-resonance preparatory pulse with pulse moment q1is transmitted. The transmit operation501is followed by a receive operation502in which NMR signals FID1are received. During a subsequent transmit operation503of acquisition i500, an on-resonance depth profiling pulse with pulse moment q2,iis transmitted. The subsequent transmit operation503is followed by a subsequent receive operation504in which NMR signals FID2are received.

Acquisition i+1510may be performed after acquisition i500. As with acquisition i, during a transmit operation511of acquisition i+1510, an on-resonance preparatory pulse with pulse moment q1may be transmitted. The transmit operation511may be followed by a receive operation512in which NMR signals FID1are received. During a subsequent transmit operation513of acquisition i+1510, an on-resonance depth profiling pulse with pulse moment q2,i+1is transmitted. The subsequent transmit operation513may be followed by a subsequent receive operation514in which NMR signals FID2are received.

InFIG. 5A, the pulse moment q1of the on-resonance preparatory pulses501and511(or the maximum excitation depth of the on-resonance preparatory pulses) may be substantially identical in acquisition i500and acquisition i+1510. The pulse moments q2,iand q2,i+1of the depth profiling pulses503and513, however, may be substantially different. While any difference between depth profiling pulses503and513may be usefully applied depending on the circumstances, some embodiments may comprise differences ranging between 0.5×, in which the largest depth profiling pulse is 50% larger than the smallest depth profiling pulse, and 10,000×, in which the largest depth profiling pulse is 10,000 times larger than the smallest depth profiling pulse. The term “substantially different” in the context of difference between pulse moments of depth profiling pulses refers to any difference equal to or greater than 0.5×, in which the largest depth profiling pulse is 50% larger than the smallest depth profiling pulse. Difference between depth profiling pulses503and513in the general range of about 500×, in which the largest depth profiling pulse is about 500 times larger than the smallest depth profiling pulse may prove useful in many embodiments. It should be understood that in embodiments comprising many acquisitions, there may be small differences between the depth profiling pulses of some acquisitions and larger differences between the depth profiling pulses of other acquisitions.

Furthermore, inFIG. 5A, the pulse moment q1of the on-resonance preparatory pulses501and511, and thus the maximum excitation depth of pulses501and511, may be substantively different from the pulse moments q2,iand q2,i+1of the depth profiling pulses503and513. When the pulse moment q1of preparatory pulses501and511is substantively greater than the pulse moments q2,iand q2,i+1of the depth profiling pulses503and513, the maximum excitation depth of preparatory pulses501and511may be greater than the maximum excitation depths of depth profiling pulses503and513.

For the purpose of this disclosure, the term “substantively different” in the context of differences between pulse moments (or maximum excitation depths) of preparatory pulses and pulse moments (or maximum excitation depths) of depth profiling pulses refers to any difference equal to or greater than 25% of the smaller pulse moment or smaller maximum excitation depth. In some embodiments, differences between pulse moments (or maximum excitation depths) of preparatory pulses and pulse moments (or maximum excitation depths) of depth profiling pulses may be equal to or greater than 50% of the smaller pulse moment or smaller maximum excitation depth. It is noted that using a single DC power supply the transmission of a long pulse or long pulse sequence may decrease energy stored on the power supply such that the bus voltage decreases as energy is dissipated in the pulses, and the resulting pulses show a decreased amplitude (and therefore, decreased pulse moment) as the energy is dissipated. Such decreases in pulse moment associated only with pulse transmission and dissipation of power supply energy do not comprise a substantive difference in pulse moment as the term is understood herein.

FIG. 5Billustrates a NMR acquisition in which the initial preparatory pulses are composite pulses, and as inFIG. 5A, described above, the preparatory pulses remain substantially identical between each ith acquisition, while the subsequent (depth profiling) on-resonance pulses may be changed between each ith acquisition.FIG. 5Bmay generally be understood with reference toFIG. 5A, above.FIG. 5Bcomprises an acquisition i520and an acquisition i+1530, wherein acquisition i520comprises transmit operations521and523and receive operations522and524, and wherein acquisition i+1530comprises transmit operations531and533and receive operations532and534. In contrast withFIG. 5A, however, preparatory pulses521and531comprise composite, rather than on-resonance pulses, which affects received NMR signals FID1and FID2in each receive operation522,524,532, and534.

The composite preparatory pulses521and531may be designed with appropriate values of I(t), φ(t), and f(t) so that the maximum excitation depth of the preparatory pulses521and531may be greater than or equal to the maximum excitation depth of the subsequent pulses523and533. In some embodiments, the maximum excitation depth of the composite preparatory pulses521and531may be substantively different from the maximum excitation depths of the depth profiling pulses523and533. Preparatory pulses521and531may also differ qualitatively from depth profiling pulses523and533in some embodiments, e.g., when the preparatory pulses523and533comprise composite pulses (with varied f(t) and I(t)) and the subsequent pulses523and533comprise resonance pulses (f(t)=f0).

FIG. 5Cillustrates a NMR acquisition in which the initial preparatory pulses are adiabatic pulses, and as inFIG. 5A, described above, the preparatory pulses remain substantially identical between each ith acquisition, while the subsequent (depth profiling) on-resonance pulses may be changed between each ith acquisition.FIG. 5Cmay generally be understood with reference toFIG. 5A, above.FIG. 5Ccomprises an acquisition i540and an acquisition i+1550, wherein acquisition i540comprises transmit operations541and543and receive operations542and544, and wherein acquisition i+1550comprises transmit operations551and553and receive operations552and554. In contrast withFIG. 5A, however, preparatory pulses541and551comprise adiabatic, rather than on-resonance pulses, which affects received NMR signals FID1and FID2in each receive operation542,544,552, and554.

The adiabatic preparatory pulses541and551may be designed with appropriate values of I(t), φ(t), and f(t) so that the maximum excitation depth of the preparatory pulses541and551may be always greater than or equal to the maximum excitation depths of the subsequent pulses543and553. In some embodiments, the maximum excitation depth of the adiabatic preparatory pulses541and551may be substantively different from the maximum excitation depths of the depth profiling pulses543and553. Preparatory pulses541and551may also differ qualitatively from depth profiling pulses543and553in some embodiments, e.g., when the preparatory pulses543and553comprise composite pulses (with varied f(t) and I(t)) and the subsequent pulses543and553comprise on-resonance pulses (f(t)=f0).

In some embodiments, at least one multi-pulse acquisition sequence in a set of multi-pulse acquisition sequences according toFIG. 5A, 5B, or5C may include a substantive difference between an initial preparatory pulse and a subsequent depth profiling pulse in the sequence. Also, in some embodiments, at least one of, and up to all of, the subsequent depth profiling pulses in an individual multi-pulse acquisition sequence (within a set of multi-pulse acquisition sequences) may comprise a substantive difference between the preparatory and subsequent pulses.

FIG. 5A, 5B, or5C each illustrate a set of acquisitions comprising two acquisitions, wherein each acquisition comprises two transmit pulses and two receive operations. It will be appreciated that sets may comprise additional acquisitions, and that acquisitions may comprise additional pulses. The illustrated depth profiling subsequent pulses may comprise one or more ordered subsequent pulses following the preparatory pulses, each ordered subsequent pulse having a pulse moment or maximum excitation depth, and wherein a pulse moment or maximum excitation depth of an ordered subsequent pulse in at least one of the acquisition sequences in a set may be substantially different from a pulse moment of the same ordered subsequent pulse in at least one other of the acquisition sequences in the set. For example, if an acquisition comprises three subsequent pulses including a first, a second, and a third ordered subsequent pulse, the first, second or third subsequent pulse may be substantially different from a same ordered first, second or third subsequent pulse in at least one other of the acquisition sequences in the set.

In some embodiments, acquisition schemes disclosed herein may be referred to as “Crush Recovery” (CR) sequences. In a CR acquisition scheme, an individual acquisition sequence may comprise transmitting two pulses separated by an adjustable delay time τd. The FID signal following the subsequent pulse (“FID2”) may be recorded; the FID following the preparatory pulse (“FID1) may also be recorded. A single delay time CR data set may be comprised of N individual acquisition sequences wherein I(t) and f(t) for the initial preparatory pulses are fixed, the pulse moments q2for the subsequent pulses are varied between individual acquisitions with index i, and the delay time τdremains fixed. A complete CR dataset may be comprised of M multiple individual delay time datasets of index j between which the value of τdis varied. A complete CR dataset for a particular fixed preparatory pulse may comprise a multitude of FID2signals recorded as a function of time for varying values of q2and τd. It will be appreciated that apparatus according toFIG. 2may be configured to gather such data sets, and methods may be performed comprising sequences of pulse transmit and receive operations effective to gather such data sets. Such methods may include, inter alia, the use of on-resonance, composite, or adiabatic preparatory pulses, the use of substantially identical preparatory pulses with different subsequent pulses, and/or subsequent pulses with maximum excitation depths that may be substantively smaller than the maximum excitation depth of the preparatory pulses.

In the preceding CR embodiment, the preparatory pulse may be referred to as the “crush” pulse and the subsequent pulse may be referred to as the “depth-profiling” pulse. A purpose of the crush pulse is to negate, substantially mitigate, or invert signals present in the subsequent FID that are associated with the subsurface longitudinal magnetization state existing prior to application of the crush pulse. A purpose of the depth-profiling pulse is to detect, with sensitivity as a function of depth, the component of the longitudinal that has recovered during the delay time.

In the case of an on-resonance crush pulse, the crush pulse may typically have a substantively higher pulse moment and greater maximum excitation depth than the subsequent pulse. Thus, this preparatory pulse induces large tip angles within the same subsurface volumes where the subsequent depth-profiling pulse induces significant amplitude tip angles. Specifically, within volumes sampled by the subsequent pulse, the crush pulse creates large tip angles that may include multiple complete rotations (i.e. rotations greater than 360 degrees). Thus the orientation of the magnetization immediately after the pulse may show a high degree of spatial variability ranging from 0 to 360 degrees over a small spatial scale. Because the subsurface tip angles produced by the application of the preparatory pulse are poorly correlated spatially within the shallower volumes sampled by the subsequent pulse, the initial longitudinal magnetization is effectively crushed and contributes little coherent energy to the subsequent FID signal excited by the subsequent pulse. As a result, the magnetization state prior to the application of the subsequent pulse primarily reflects the component of the longitudinal magnetization that has been subject to T1recovery prior to application of the subsequent pulse.

In the case of an adiabatic or composite crush pulse, values of I(t), φ(t), and f(t) may be selected such that the pulse produces tip angle near 90 degrees so as to minimize the longitudinal magnetization over a wider range of depths than an on-resonance pulse. Because the crush pulse has also a greater investigation depth than the on-resonance depth-profiling pulse, the crush pulse minimizes the longitudinal magnetization over the same range of depths where the depth-profiling pulse induces spatially coherent and significant amplitude tip angles. Thus, the initial longitudinal magnetization is effectively crushed and contributes little coherent energy to the subsequent FID signal excited by the subsequent pulse. As a result, the magnetization state prior to the application of the subsequent pulse primarily reflects the component of the longitudinal magnetization that has been subject to T1recovery prior to application of the subsequent pulse. In other embodiments, values of I(t), φ(t), and f(t) may be selected such that the pulse produces tip angles near 180 degrees so as to invert the longitudinal magnetization over the range of depths where the depth-profile pulse produces spatially coherent and significant amplitude tip angles.

Varying the value of q2for the subsequent depth-profiling pulse between single acquisitions provides sensitivity to the recovered magnetization as a function of depth and spatial location. Varying the value of τdbetween single delay time acquisitions provides sensitivity to the T1recovery process over time. In some embodiments, a complete CR dataset can be acquired for more than one value of q1. In other embodiments, identical acquisitions may be repeated and combined to improve the signal to noise ratio.

To implement the acquisition sequences described herein, NMR measurement methods and apparatus according to this disclosure may arbitrarily and independently control the pulse moment q of transmitted pulses. In some embodiments, the value of q may be varied by changing the duration of two pulses independently (i.e., the value of q2can be made smaller than the value of q1by shortening the duration of the subsequent pulse). Changing the duration of the pulse, however, changes the effective bandwidth. Thus, in some embodiments, the value of q may instead be changed by varying the current I(t) passed through the surface coil (i.e., the value of q2can be made smaller than the value of q1by reducing the current passed through the coil for the subsequent pulse). Alternatively, both the pulse duration and current can be varied together to control the effective value of q. Methods and apparatus according to this disclosure may also be useful to dynamically change the value of I(t) and/or pulse durations to implement effective adiabatic or composite pulses.

To implement the acquisition sequences described herein, NMR measurement methods and apparatus according to this disclosure may arbitrarily and independently control the current amplitude I(t) of the transmitted pulses. A number of embodiments may be effective to control the current that is passed through the surface coil for each pulse independently; such embodiments may also allow the amplitude of a single pulse to be dynamically varied. In some embodiments, the pulse current may be supplied by switching voltage from one or more DC power supplies with a fixed bus voltage. In such embodiments, two or more separate supplies with different and independent bus voltages can used to supplying driving voltage for the two different pulses, thus producing pulses with different amounts of current. Alternatively if there is a single DC power supply, the duty cycle of the AC (Larmor frequency) switched current from the DC supply can be varied between pulses or dynamically during a single pulse to decrease or increase the total rms current for the pulses.

In some embodiments, the current between pulses may be controlled or changed dynamically during a single pulse, by adjusting the impedance of the transmitting device and/or the transmitting coil or coils, between the two pulses. In such embodiments the impedance of the transmitter and/or the coil may be adjusted by adding or subtracting resistive or reactive electronics in the transmitter-coil circuit.

In some embodiments, the current between pulses may be controlled or changed dynamically during a single pulse, by adjusting the difference between the resonant frequency of the coil and the frequency of the driving voltage. As the difference between the driving voltage frequency and the coil resonant frequency increase, the current on the coil will decrease. This approach may be particularly useful for controlling the functions I(t) and f(t) for an adiabatic pulse, where it is often required that the amplitude of I(t) be small when the offset between f(t) and the Larmor frequency f0is large.

In some embodiments, the effective pulse moment between two pulses may be controlled by transmitting on two different coils. In this embodiment the large pulse moment of the preparatory pulse is achieved by transmitting on a coil with low impedance and/or a larger number of turns, and the smaller pulse moment of the subsequent pulse is achieved by transmitting on a coil with higher impedance and/or smaller number of turns.

In some embodiments, the effective pulse moment difference between the preparatory and subsequent pulses may be controlled by using separate transmitters to generate the preparatory and subsequent pulses.

Disclosed methods to dynamically control and vary the amplitude of a signal pulse or to control and vary the relative amplitude of at least two pulses in a multi-pulse sequence may be useful in the field of geophysical surface NMR for measurements different from those described above. For example, some acquisitions may use a single adiabatic pulse where I(t) is dynamically varied. A single adiabatic pulse may be selected to provide excitation of fluids in the subsurface over a wider range of depths than an on-resonance pulse and thus improved signal detection. As another example, a spin-echo pulse sequence may be acquired in which a preparatory excitation pulse has half the amplitude of a subsequent refocusing pulse, so that the subsequent pulse provides twice the effective tip angle as the preparatory pulse. It may be preferable to achieve a double of tip angle by adjusting the relative amplitude of the excitation and refocusing pulses; instead adjusting their relative duration would change the effective bandwidth of the two pulses.

In some embodiments, the phase of the transmitted pulses may be controlled in order to eliminate particular signal artifacts that are undesired. Specifically for embodiments of the CR acquisition scheme, signal artifacts that are not associated with the FID2signal that are generated by the subsequent depth-profiling pulse may be eliminated. These artifacts can potentially include NMR or non-NMR signals that share phase coherence with the transmitted pulses. Specifically, for the CR sequence, artifacts associated with residual transverse magnetization from the preparatory pulse and non-NMR artifacts associated with the subsequent pulse may be effectively cancelled. A phase cycling strategy can be implemented to mitigate such artifacts.

In some embodiments of phase cycling for the CR sequence, acquisitions in which the phase of the pulses are varied, but all other parameters are kept identical may be repeated and combined to improve signal to noise and to suppress artifacts. To achieve artifact suppression by phase cycling for a single CR acquisition, two identical acquisitions may be acquired, referred to as A and B. The phase of the preparatory pulse in both sequences may be fixed between acquisition A and B; the subsequent pulse may have a value of φ2in acquisition A and a value of φ2+180° in acquisition B. Data for the two acquisitions may then be linearly combined by subtracting the data for acquisition B from the data for acquisition A. The result is that undesired artifacts that have constant phase between both acquisitions are cancelled, including (i) NMR signals representing residual transverse magnetization from the preparatory pulse and (ii) non-NMR signals that are associated with the hardware artifacts after the subsequent pulse. NMR signals that have a 180° phase shift between the acquisitions are preserved, specifically the component of the FID2signal associated with recovered longitudinal magnetization.

Some embodiments may use more than two pulses to allow detection of NMR spin echo signals used to further estimate the T2relaxation time, and its covariance with T1and T2*, as a function of subsurface position. In one such embodiment, that may be termed “crush-recovery spin-echo” (CRSE), a set of multi-pulse acquisition sequences may comprise a collection of multi-pulse acquisition sequences, wherein at least three pulses are used in each multi-pulse acquisition sequence. The preparatory crushing pulse may be on-resonance, adiabatic, or composite and at least two on-resonance subsequent pulses may have values of q2, q3, where the value of q3is 0.75 to 2.5 times the value of q2. A second pulse may be referred to as the “depth sensitive pulse” and a third pulse may be referred to as the “refocusing pulse”. The delay time between the preparatory and second pulse may be called τd1, and the delay time between the second and third pulse may be called τd2. In at least one of the multi-pulse acquisition sequences in the set, the properties of the crushing pulse are constant, the value of τd1is constant, and maximum excitation depth of the second pulse is substantively less than that of the preparatory pulse. In such an embodiment, the preparatory pulse may act to crush the magnetization within a range of subsurface depths where later pulses provide sensitivity to NMR FID and spin echo signals. Spin echo signals may be observed following the third (refocusing) pulse.

FIG. 6illustrates a NMR acquisition in which additional refocusing pulses may be transmitted in an acquisition sequence and a train of spin echo signals may be recorded between the refocusing pulses. Such an embodiment may be referred to as a Crush-Recovery Carr-Purcell-Meiboom-Gill (CRCPMG) sequence.FIG. 6may generally be understood with reference toFIG. 5A, above. FIG. comprises an acquisition i600and an acquisition i+1610, wherein acquisition i600comprises transmit operations601and603, as well as refocusing pulses605, and receive operations602and604, as well as receive operations for spin echo signals606. Acquisition i+1610comprises transmit operations611and613, as well as refocusing pulses analogous to refocusing pulses605in acquisition i, and receive operations612and614, as well as receive operations for spin echo signals as illustrated. InFIG. 6, the preparatory pulses601and611and depth profiling pulses603and613may be according to any ofFIG. 5A, 5B, or5C.

In embodiments according toFIG. 6, the refocusing pulses605in a single acquisition such as acquisition i600may have similar pulse moments q3. The time delays between each refocusing pulse τd2may be similar for the single acquisition and between acquisitions, with varied values of q2and q3between acquisitions, that is, varied pulse moments for depth profiling pulses603and613, and varied pulse moments for refocusing pulses605and the refocusing pulses of acquisition i+1610. In some embodiments, the time delay between a depth profiling pulse603and a first refocusing pulse605may be approximately 0.5*τd2. A complete CRCPMG dataset may comprise multiple acquisitions between which the value of q2, q3, τd1, and τd2are varied.

Processing of Surface NMR Signals

Various processing approaches can be used to process data acquired following the above embodiments to estimate the spatial variation in fluid content and relaxation times in the subsurface. The below outlined approaches to estimate fluid content, T2*, and T1in the subsurface are made possible because of two unique characteristics of the aforementioned CR acquisition scheme: (i) the initial longitudinal magnetization is effectively crushed prior to application of the subsequent pulse, and (ii) the initial conditions prior to application of the depth-sampling pulse are consistent across any set of single acquisitions for which the properties of the preparatory pulse and τdare fixed. As a result, it is possible to use a standard NMR mathematical inversion kernel described in prior art to isolate the signal associated with the recovered longitudinal magnetization as a function of depth.

In some embodiments, a complete CR dataset can be processed in several stages, as shown inFIG. 7andFIG. 8.FIG. 7andFIG. 8represent operations which may be performed in accordance with example methods, processing operations and/or functional modules which may be implemented in a computing device, and instructions which may be recorded on a computer readable medium.

Referring toFIG. 7, the complete CR dataset701may comprise a collection of voltage signals V(t, τd, q2), such as702,703, and any other voltage signals, with M values of τd. The CR dataset701may be separated into M single delay-time datasets V(t, τd=τd,j, q2)702,703, etc. A mathematical spatial inversion may be performed for each jth dataset at blocks704,705, etc., to derive scaled position or depth-separated signal S(t, τd=τd,j, z=zk) represented by data items706,707, etc., for each depth layer zkin the subsurface. Here the S(t, τd=ττd,j, z=zk) signals708represents the FID2response associated with the component of the longitudinal magnetization that has recovered by T1over a delay time of τd,jat a depth interval zk. The S(t, τd,j, z) signals708may also be scaled during the inversion so that they reflect the volumetric water content at each depth. The mathematical inversion may alternatively operate in two or three spatial dimensions to estimate the scaled signals as a function of the location of finite volume elements.

In some embodiments, the aforementioned mathematical spatial inversion may follow a linear inversion using a standard forward modeling kernel K(r,q) where r is a subsurface position (or K(z,q) in 1D) which is used for standard NMR single-pulse FID measurements. It should be noted that the use of the standard kernel is possible at least in part because the initial conditions prior to the application of the subsequent pulse are identical for all acquisition sequences where q1and τdare fixed. Attempting to use the same approach to invert data acquired using a PSR sequence may produce erroneous results because the initial conditions prior to the application of the subsequent pulse may vary as the q-value of the subsequent pulse varies (because the q-value of the preparatory pulse also changes). Other signal conditioning processes including the application of noise cancellation or phase compensation may be applied at any stage before or during the spatial inversion step.

In some embodiments, a spatial inversion of a CRSE or CRCPMG dataset may follow a similar procedure as was outlined above for the CR dataset, wherein the forward model kernel for the FID signal is replaced by a forward model kernel for a spin-echo signal. The output of such a mathematical inversion may be spin echo signals S(z, t, τd1, τd2) estimated as a function of depth.

Returning to the CR dataset, given the spatially inverted FID2signals for a given depth S(t, τd) there are various approaches that can be used to estimate the relaxation times, multi-exponential distributions of relaxation times, and the covariance of the relaxation times. Various embodiments for estimating T2* and T1from a crush recovery dataset are illustrated in a schematic flow chart inFIG. 8.

In some embodiments, the S(t, τd=τd,j) signal801for each jth delay time at each depth may be processed using a 1-dimensional Laplace inversion802to determine a T2* distribution. Each T2* distribution is then subdivided into bins such as803and804, classifying short T2*803or long T2*804signals according to a specified cut-off value of T2*. For each delay time, the integrated amplitude of the signal is calculated for the short T2* bin SA(τd) and the long T2* bin SB(τd). The resulting SA(τd) and SB(τd) curves may be processed separately using a single-exponential fit or Laplace inversion in blocks805and806to determine the fluid volume and T1characteristics of NMR signals having short T2* values807separately from the fluid volume and T1characteristics of NMR signals having long T2* values808. Alternatively, the T2* distributions can be separated into more than two bins (e.g. three bins to independently classify signals with short, intermediate, and long T2* decay times, or any arbitrary number of subdivided bins).

In some embodiments, a finite number of decay time bins equal to or smaller than the total number of delay time datasets may be specified, and the S(t, τd) signals for which τdis within each specified bin range may be combined by linear averaging. For example a signal SC(t) may be computed by averaging signals with a given range of short τdat block811and a subsequent signal SD(t) may be computed by averaging the signals with a given range of long delay times at block812. The resulting SC(τd) and SD(τd) curves may then be processed separately using a single-exponential fit or Laplace inversion at blocks813,814to determine the fluid volume and T2* characteristics of NMR signals having short T1values815separately from the fluid volume and T2* characteristics of NMR signals having long T1816. Alternatively, the S(t, τd) signals may be divided into any number of bins less than the total number of delay times acquired in the complete dataset.

In some embodiments, the S(t, τd) signals can be processed to simultaneously estimate the a two-dimensional distribution of T2* versus T1. Generally, the S(t, τd) can be represented by the following function assuming a multi-exponential relaxation behavior:

In some embodiments, a two-dimensional Laplace inversion of the S(t, τd) can be used at block821to estimate the two-dimensional distribution and covariance of T2* and T1at a given depth, shown at block822. An advantage of such embodiments is that it is possible to impose constraints on the covariance of T2* and T1. For example a constraint can be exercised that the value of T1must be greater than the value of T2*, as is known to be required by NMR physics. Further, it is possible to specify a bound on the value of T1, the value of T2*, or on the ratio of T1to T2*, which can improve the stability of the inversion. Specifying bounds in the manner also enables dense sampling and precision of the T2* decay process (set by the dense data sampling rate of the NMR voltage recording) to improve that the temporal resolution of the T1decay process, which is sparsely sampled in time (given a finite number of τdvalues).

In some embodiments, data may be acquired using a CRCPMG sequence and used to estimate the two-dimensional covariance distribution of T1and T2. In such an embodiment the spatially inverted data S(t, τd1) for a fixed value of τd2may first be analyzed to determine the amplitude of each spin echo signal Sechorecorded at the center time t between refocusing pulses and for each value of τd1in the full set of acquisitions. A two-dimensional Laplace inversion of the resulting dataset Secho(t, τd1) may then be used to estimate the two-dimensional distribution and covariance of T2and T1at a given depth. The decay time TDassociated with diffusion of the fluid is a function of the delay time between refocusing pulses (τd2). Thus if acquisitions with varied values of τd2are included in the set, the resulting dataset Secho(t, τd1, τd2,) may be used with a three-dimensional Laplace inversion to determine a three-dimensional covariance distribution of T1T2and TD. T1, T2*, T2, TD, and their spatial distribution in the subsurface derived by the above methods may be used to estimate other properties, including fluid, geologic, hydrogeologic, mineralogic, or biogeologic properties. For example T1and T2can be highly sensitive to fluid viscosity, pore size, permeability, and surface mineralogy and so can be used to estimate these properties. Also TD, T2*, and the ratio of T2*:T1or T2:T1may be sensitive to the magnetic properties of the formation and diffusion coefficient of the fluid.

In some embodiments, surface NMR apparatus and subsurface characterization techniques provided herein may be applied to image NMR properties at positions in the subsurface. In some embodiments, NMR apparatus and subsurface characterization techniques provided herein may be applied to image and estimate NMR relaxation times at positions in the subsurface, which can be related to subsurface properties of interest, including pore size and permeability. In some embodiments, NMR apparatus and subsurface characterization techniques provided herein may be applied to estimate relaxation times and to provide improved estimation and imaging of the T1relaxation at positions in the subsurface. In some embodiments, NMR apparatus and subsurface characterization techniques provided herein may be applied to provide improved estimation and imaging of the covariance of more than one relaxation time at positions in the subsurface. In some embodiments, NMR apparatus and subsurface characterization techniques provided herein may be applied to provide estimation of more than one relaxation time and their covariance as a function of depth from surface NMR measurements.

Those skilled in the art will recognize that it is common within the art to describe devices and/or processes in the fashion set forth herein, and thereafter use engineering practices to integrate such described devices and/or processes into data processing systems. That is, at least a portion of the devices and/or processes described herein can be integrated into a data processing system via a reasonable amount of experimentation. Those having skill in the art will recognize that a typical data processing system generally includes one or more of a system unit housing, a video display device, a memory such as volatile and non-volatile memory, processors such as microprocessors and digital signal processors, computational entities such as operating systems, drivers, graphical user interfaces, and applications programs, one or more interaction devices, such as a touch pad or screen, and/or control systems including feedback loops and control motors (e.g., feedback for sensing position and/or velocity; control motors for moving and/or adjusting components and/or quantities). A typical data processing system may be implemented utilizing any suitable commercially available components, such as those typically found in data computing/communication and/or network computing/communication systems. The herein described subject matter sometimes illustrates different components contained within, or connected with, different other components. It is to be understood that such depicted architectures are merely exemplary, and that in fact many other architectures can be implemented which achieve the same functionality. In a conceptual sense, any arrangement of components to achieve the same functionality is effectively “associated” such that the desired functionality is achieved. Hence, any two components herein combined to achieve a particular functionality can be seen as “associated with” each other such that the desired functionality is achieved, irrespective of architectures or intermediate components. Likewise, any two components so associated can also be viewed as being “operably connected”, or “operably coupled”, to each other to achieve the desired functionality, and any two components capable of being so associated can also be viewed as being “operably couplable”, to each other to achieve the desired functionality. Specific examples of operably couplable include but are not limited to physically couplable, physically interacting, wirelessly interacting, and/or logically interacting components.

While various embodiments have been disclosed herein, other aspects and embodiments will be apparent to those skilled in art.