Glossary

Activation: Programmed command sequences that control how MRIL tools polarize formations and measure the NMR properties of those formations. Activations may contain single or multiple CPMG sequences.

This activation has been successfully used in detecting and quantifying medium-viscosity oils.

The smaller TW is chosen such that the NMR signal from the formation water is completely polarized, but the oil and/or gas signals are not. The longer TW is chosen so that most of the hydrocarbon signals are also polarized. The signal left after the subtraction of the two echo trains or the two resulting T₂ distributions contains only signal from the hydrocarbon. This method can be used to quantify oil and gas volumes.

Activation, Standard-T₂: An activation that enables the acquisition of a CPMG echo train with a TW with which formation fluids can be fully polarized and with a TE with which the diffusion effects on T₂ can be eliminated. Typical values for this activation are TE = 1.2 ms, 3 s ≤ TW ≤ 6 s, and NE = 300. This activation is mainly used for determining “effective” porosity and permeability.

Activation, Total Porosity: An activation that enables the acquisition of two CPMG echo trains with different echo spacings (TE) and different wait times (TW). One echo train is acquired with TE = 0.6 ms and TW = 20 ms (only partial polarization is achieved) and is used for quantifying the small pores, which are at least in part associated with clay-bound water. The other echo train is acquired with TE = 0.9 or 1.2 ms and with a TW that is sufficiently long so that full polarization is achieved. This echo train is used to determine effective porosity, and the summation of the two porosities (clay-bound and effective) provides total porosity information. The combination of TE and TW used to acquire the latter echo train constitutes a standard T₂ activation.

Analog-to-digital Converter: In electronics, an analog-to-digital converter (ADC, A/D, or A-to-D) is a system that converts an analog signal, such as a sound picked up by a microphone or light entering a digital camera, into a digital signal. An ADC may also provide an isolated measurement, such as an electronic device that converts an analog input voltage or current to a digital number representing the magnitude of the voltage or current.

ADC: See Analog-to-digital Converter.

Amplitude Modulated: A modulation technique used in electronic communication, most commonly for transmitting messages with a radio carrier wave. In amplitude modulation, the amplitude (signal strength) of the carrier wave is varied in proportion to that of the message signal, such as an audio signal. This technique contrasts with angle modulation, in which either the frequency of the carrier wave is varied, as in frequency modulation, or its phase, as in phase modulation.

AM: See Amplitude Modulated.

B₀: Static magnetic field generated by the NMR tool. It may also be designated as B_z. The symbols B₀ and B_z are used when referring to the scalar value of the field.

B₁: Oscillating magnetic field generated by a radio frequency (RF) resonant circuit. This field is applied in the plane perpendicular to B₀ and is used to flip the magnetization by 90° and 180°. B₁ refers to the magnitude of the field.

Bound Water: A somewhat loosely defined term that can refer either to water that is not producible or water that is not displaceable by hydrocarbons. Bound water consists of both capillary-bound water and clay-bound water.

Bulk Volume Irreducible (BVI): The fractional part of formation volume occupied by immobile, capillary-bound water.

Bulk Volume Irreducible, Cutoff (CBVI): BVI is estimated by summing the MRIL T₂ distribution up to the time T_2cutoff.

Bulk Volume Irreducible, Spectral (SBVI): BVI obtained by the MRIL spectral method. This BVI estimate is determined from a model that assigns a percent of the porosity in each spectral bin to bound water. Various models are available for use with this method.

Bulk Volume Movable (BVM): The fractional part of formation volume occupied by movable fluids, also referred to as the Free Fluid Index (FFI). It can be water, oil, gas, or a combination.

Bulk Volume Water (BVW): The fractional part of formation volume occupied by water. BVW is the product of water saturation and total porosity.

BVI: See Bulk Volume Irreducible.

BVM: See Bulk Volume Movable.

BVW: See Bulk Volume Water.

B_z: See B₀.

Carr–Purcell–Meiboom–Gill Pulse Sequence (CPMG): A pulse sequence used to measure T₂ relaxation time. The sequence begins with a 90° pulse followed by a series of 180° pulses. The first two pulses are separated by a time period τ, whereas the remaining pulses are spaced 2τ apart. Echoes occur halfway between 180° pulses at times 2τ, 4τ, …, where 2τ equals TE, the echo spacing. Decay data is collected at these echo times. This pulse sequence compensates for the effects of magnetic field inhomogeneity and gradients in the limit of no diffusion and reduces the accumulation of effects of imperfections in the 180° pulses as well.

CBVI: See Bulk Volume Irreducible, Cutoff.

CBW: See Clay-bound Water.

Clay-bound Water (CBW): Immobile structurally bound water on the surface of clay minerals. Clay surfaces are electrically charged due to ionic substitutions in the clay structure, which allow them to hold substantial amounts of ionically bound water. This water is referred to as water of adsorption or surficially bound water. Clay-bound water also includes water of capillary condensation in the micropores in clay aggregates. CBW is a function both of the surface area of the clay and the charge density on its surface. Clay consists of extremely fine particles, so it has a very high surface area. CBW contributes to the electrical conductivity of the sand but not its hydraulic conductivity. Clay-bound water cannot be displaced by hydrocarbons and will not flow. It has very short T₁ and T₂ times.

CMR™ Tool*: The Schlumberger Combinable Magnetic Resonance logging tool was introduced in 1995. The CMR tool is a pad device with a sensitive volume that extends about 1 in. in front of the pad face. This very shallow depth of investigation makes the tool very sensitive to invasion, mud cake, and borehole rugosity. The 6-in. long CMR antenna is placed on the center of a 12-in. long magnet. This arrangement provides 3 in. of magnet length to polarize protons before they are measured. The sensitive volume of the CMR tool is a 1-in. diameter, 6-in. long cylinder. The CMR tool operates in single frequency mode.

Complex Programmable Logic Device (CPLD): A programmable logic device with complexity between that of PALs and FPGAs, and architectural features of both. The main building block of the CPLD is a macrocell, which contains logic implementing disjunctive normal form expressions and more specialized logic operations.

Compressed Sensing: A signal processing technique for efficiently acquiring and reconstructing a signal, by finding solutions to underdetermined linear systems (also known as compressive sensing, compressive sampling, or sparse sampling). This is based on the principle that, through optimization, the sparsity of a signal can be exploited to recover it from far fewer samples than required by the Nyquist–Shannon sampling theorem. There are two conditions under which recovery is possible. The first one is sparsity, which requires the signal to be sparse in some domains. The second one is incoherence, which is applied through the restricted isometric property, which is sufficient for sparse signals.

CPLD: See Complex Programmable Logic Device.

CPMG: See Carr–Purcell–Meiboom–Gill Pulse Sequence.

Cycle Time: The time required to perform a CPMG measurement plus the polarization time (or wait time) before the next CPMG sequence can start.

D: See Diffusion Constant.

DDS: See Direct Digital Synthesis.

DE: See Driven Equilibrium.

DEFIR: A DEFIR pulse sequence is used to measure 2D relaxation times of fluid samples. It consists of two parts: an initial DE portion, followed by a fast-inversion recovery portion. The former can achieve rapid T₁/T₂ averages in tens of milliseconds to several seconds, while the latter can determine the T₁ distribution in several seconds. The FIR pulse sequence is an application of the DE pulse sequence to conventional inversion recovery (IR). The measurement speed of T₁ is increased by about 3 times compared to saturation recovery (SR). The FIR sequence tips the magnetization vector back to the longitudinal direction after each echo acquisition. The magnetization vector is stored for the next polarization. This method saves time for repeat polarization and provides a foundation for T₁/T₂–T₁ distribution measurements with DEFIR. FIR is different from DE, which has fixed values of τ₁ and τ₂ for each scan. In FIR, the polarization time TW_FIR changes with the arrangement points, which is similar to the situation in the IR pulse sequence. Within the range allowed by the equipment, the half inter-echo spacing τ_FIR in the FIR should be as short as possible. The effect of diffusion and J-coupling will be effectively reduced while minimizing the attenuation of the magnetization vector in the transverse direction.

DEFSR: When the T₁-encoding pulse sequence is used to measure T₁–T₂, the polarization time (TW) should be arranged from 0 to 5 T₁. A set of CPMG pulse sequences is performed repeatedly with different TW, which takes much time. The T₁/T₂–T₁ distribution is obtained only by two scans with the DEFSR sequence. DEFSR consists of one DE sequence, which is immediately followed by the FSR sequence. The FSR sequence tips the magnetization vector back to the longitudinal direction after each echo acquisition; the magnetization vector is stored for the next polarization. The measurement of the T₁/T₂ distribution is obtained by the rapid measurement within dozens of milliseconds to several seconds with the DE sequence; the T₁ distribution of the fluid is obtained by the fast measurement based on the improved saturation recovery.

DIFAN: See Diffusion Analysis.

Differential Spectrum Method (DSM): An interpretation method based on dual-TW measurements. DSM relies on the T₁ contrast between water and light hydrocarbon to type and quantify light hydrocarbons. The differential spectrum is the difference between the two T₂ distributions (spectra) obtained from dual-TW measurements with identical TE. DSM interpretation is performed in the T₂ domain.

Diffusion Analysis (DIFAN): An interpretation method based on dual-TE measurements. DIFAN relies on the diffusion contrasts between water and medium-viscosity oil to type and quantify oils. The data for DIFAN are acquired through dual-TE logging with a single, long polarization time.

Diffusion Constant (D): Also known as diffusivity. D is the mean square displacement of molecules observed during a period. D varies with fluid type and temperature. For gas, D also varies with density and is therefore pressure dependent. D can be measured by NMR techniques, in particular by acquiring several CPMG echo trains with different echo spacings in a gradient magnetic field.

Diffusion Limit, Fast: The case where protons carried across a pore by diffusion to the surface layer relax at the surface layer at a rate limited by the relaxers at the surface and not by the rate at which the protons arrive at the surface. The diffusion process happens much faster than that of the fluid protons relaxing in a pore. Thus, the magnetization in the pore remains uniform, and a single T₁ or T₂ can be used to describe the magnetization polarization or decay for an individual pore. This assumption is the basis of the conversion of T₁ and T₂ distributions to pore size distributions.

Diffusion Limit, Slow: The case where protons carried across a pore by diffusion to the surface layer relax at the surface layer at a rate limited not by the relaxers at the surface but by the rate at which the protons arrive at the surface. Thus, diffusion does not homogenize the magnetization in the pore space. Multiple exponential decays are then needed to characterize the relaxation process within a single pore.

Diffusion Relaxation: A relaxation mechanism caused by molecular diffusion in a gradient field during a CPMG measurement. Molecular diffusion during a CPMG or other spin echo pulse sequence causes signal attenuation and a decrease in the apparent T₂. This attenuation can be quantified and the fluid diffusion coefficient measured if a known magnetic field gradient is applied during the pulse sequence. Diffusion only affects the T₂ measurement, not the T₁ measurement.

Diffusion, Restricted: Effect of geometrical confinement of pore walls on molecular diffusive displacement. NMR diffusion measurements estimate the diffusion constant from the attenuation caused by molecular motion over a very precise time interval. If the time interval (TE in the CPMG sequence) is large enough, molecules will encounter the pore wall or other barrier and become “restricted”. The apparent diffusion constant will then decrease.

Diffusion: The process by which molecules or other particles intermingle and migrate because of their random thermal motion.

Diffusional Coupling: The conventional interpretation of NMR measurements on fluid-saturated rocks assumes that the relaxation rate of fluid in a pore is directly related to the surface-to-volume ratio of the pore. In addition, each pore is assumed to relax independently of other pores so that the relaxation time distribution represents a signature of the distribution of pore sizes. However, such interpretation often fails if the fluid molecules in intra- (micro) and intergranular (macro) pores are diffusionally coupled with each other, which can be enhanced at high formation temperatures.

Digital Signal Processing: It is used for digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations. DSP applications include audio and speech processing, sonar, radar and other sensor array processing, spectral density estimation, statistical signal processing, digital image processing, data compression, video coding, audio coding, image compression, signal processing for telecommunications, control systems, biomedical engineering, and seismology, among others. DSP can involve linear or nonlinear operations. Nonlinear signal processing is closely related to nonlinear system identification and can be implemented in the time, frequency, and spatial–temporal domains. The application of digital computation to signal processing allows for many advantages over analog processing in many applications, such as error detection and correction in transmission as well as data compression. Digital signal processing is also fundamental to digital technology, such as digital telecommunication and wireless communications.

Direct Digital Synthesis: A method employed by frequency synthesizers used for creating arbitrary waveforms from a single, fixed-frequency reference clock. DDS is used in applications such as signal generation, local oscillators in communication systems, function generators, mixers, modulators, sound synthesizers, and as part of a digital phase-locked loop.

Direct Memory Access: A feature of computer systems that allows certain hardware subsystems to access main system memory (random-access memory) independently of the central processing unit.

DMA: See Direct Memory Access.

Driven Equilibrium CPMG: In a standard Carr–Purcell–Meiboom–Gill (CPMG) measurement, the application of the rf pulses is preceded by a recycle delay T_w that is assumed to be long compared to the longest T₁ relaxation time component (T_{1, long}) in the sample. Ideally, T_w ≥ 5T_{1, long}. This ensures that the magnetization has reached thermal equilibrium before the CPMG pulse sequence is applied. In this approach, DECPMG pulse sequence t consists of two parts: an initial Driven Equilibrium (DE) portion, followed by a CPMG echo train. In the DECPMG sequence, T_w associated with the standard CPMG sequence is replaced by a long series of rf pulses that places the spin ensemble in a driven equilibrium that is different to the thermal equilibrium. The total duration of the DE portion should be comparable to T_w to ensure the driven equilibrium is obtained.

Driven Equilibrium: The DE portion consists of repeated [excite-echo-store] units that transfer the magnetization from the longitudinal direction to the transverse plane for a duration τ₂ and then restore it to the longitudinal direction for a duration τ₁. This is achieved by an initial 90 pulse followed by two 180 refocusing pulses and a second 90 pulse centered on the second echo. This cycle is repeated p times in each scan until the magnetization reaches a dynamic or driven equilibrium M_de. Ideally, the durations τ₁ and τ₂ are much shorter than the longitudinal and transverse relaxation times T₁ and T₂. This condition is referred to as the fast pulsing regime.

DSM: See Differential Spectrum Method.

DSP: See Digital Signal Processing.

D–T₂: An adjoint density distribution for diffusion and T₂ relaxation, which is obtained by D–T₂ pulse sequence. The initial part can be considered a diffusion editing sequence. During the diffusion editing period, pulsed field gradient or static field gradient can be applied to perform diffusion editing to capture diffusion information. Then, a series of 180 refocusing pulses are performed to obtain T₂ relaxation information. The adjoint D–T₂ distribution can be obtained by performing 2D Laplace Transform.

Duplexer: The duplexer is an electronic device that allows bi-directional (duplex) communication over a single path. In NMR antenna communications systems, it isolates the receiver from the transmitter while permitting them to share a common antenna.

Earth’s Field NMR: Nuclear magnetic resonance (NMR) in the geomagnetic field is conventionally referred to as Earth’s field NMR (EFNMR). EFNMR is a special case of low-field NMR. In the Earth’s magnetic field, the hydrogen resonates at audio frequencies of around 2 kHz and generates very weak signals, which need more detection sensitivity to be improved.

Echo Spacing (TE): In a CPMG sequence, the time between 180° pulses. This time is identical to the time between adjacent echoes.

EDM: See Enhanced Diffusion Method.

Enhanced Diffusion Method (EDM): An interpretation method based on diffusion contrasts between different fluids. Enhancement of the diffusion effect during echo data acquisition allows water and oil to be separated on a T₂ distribution generated from data acquired with a selected long TE. For typing medium-viscosity oils, EDM uses CPMG measurements acquired through standard T₂ logging with a long TE. For quantifying fluids, EDM needs data acquired through dual-TW logging with a long TE or through dual-TE logging with a long TW.

FFI: See Free Fluid Index.

FID: See Free Induction Decay.

FIR: See DEFIR.

Free Fluid Index (FFI): The fractional part of formation volume occupied by fluids that are free to flow. A distinction must be made between fluids that can be displaced by capillary forces, and fluids that will be produced at a given saturation. In MRIL logging, FFI is the BVM estimate obtained by summing the T₂ distribution over T₂ values greater than or equal to T_2cutoff.

FSR: See DEFSR.

Free Induction Decay (FID): The FID is the transient NMR signal resulting from the stimulation of the nuclei at the Larmor frequency, usually after a single RF pulse. The characteristic time constant for a FID signal decay is called T*. T* is always significantly shorter than T₂.

FMR: Focused Magnetic Resonance tool developed by Weatherford, is a new pad-type wireline NMR tool and commercialized in 2018.

Field Programmable Gate Array: It is an integrated circuit designed to be configured by a customer or a designer after manufacturing—hence the term “field programmable”. FPGAs contain an array of programmable logic blocks, and a hierarchy of “reconfigurable interconnects” allowing blocks to be “wired together”, like many logic gates that can be inter-wired in different configurations. Logic blocks can be configured to perform complex combinational functions, or merely simple logic gates like AND and XOR.

FPGA: See Field Programmable Gate Array.

FIFO: First Input, First Output. In computing and systems theory, FIFO is a method for organizing the manipulation of a data structure (often, specifically a data buffer) where the oldest (first) entry, or “head” of the queue, is processed first.

For the proton, γ = 42.58 MHz T⁻¹.

G: The strength of the gradient magnetic field seen by the NMR measurement.

Gain: Represents the relative voltage gain of the system: both the antenna gain and electronics gain. Because the electronics gain is quite stable, the gain is sensitive to antenna loading, Q. At the beginning of each pulse sequence, a measured low-level signal is sent from a test antenna (known as the B1 loop) to the main antenna, and the received signal is processed just as echoes would be processed. The received signal is then measured and compared to the original input signal. This provides the gain. The gain is used to compensate for signal losses due to Q loading effects of the borehole and due to system drift.

Gauss: Unit of magnetic field strength. 10 000 gauss = 1 tesla. The earth’s magnetic field strength is approximately 0.5 gauss.

Gradient Coil: A set of coils employed to produce pulsed field gradients to perform spatial encoding, such as phase-encoding and frequency-encoding, which is widely used in medical MRI.

Gradient Magnetic Field: A magnetic field whose strength varies with position. The MRIL tool generates a gradient magnetic field that varies in the radial direction. Within the small sensitive volume of the MRIL tool, this gradient can be regarded as linear and is usually expressed in gauss cm⁻¹ or Hz mm⁻¹.

Gradient: Amount and direction of the rate of change in space of some quantity, such as magnetic field strength.

Gyromagnetic Ratio (γ): Ratio of the magnetic moment to the angular momentum of a particle. A measure of the strength of the nuclear magnetism. It is a constant for a given type of nucleus.

Hydrogen Index (HI): The ratio of the number of hydrogen atoms per unit volume of a material to the number hydrogen atoms per unit volume of pure water at equal temperature and pressure. The HI of gas is a function of temperature and pressure.

HI: See Hydrogen Index.

Inversion Recovery: A pulse sequence employed to measure T₁ relaxation time. The sequence is “180°-t_i 90°-Acquisition-TW,” where i = 1 … N. The first 180° pulse inverts the magnetization 180° relative to the static magnetic field. After a specific wait time (t, the inversion time), a 90° pulse rotates the magnetization into the transverse plane, and the degree of recovery of the initial magnetization is measured. After a wait time TW to return to full polarization, the sequence is repeated. To produce sufficient data for measurement of T₁, this sequence must be repeated many times with different t_i and thus is very time-consuming.

IR: See Inversion Recovery.

Halbach Magnet: A Halbach array is a special arrangement of permanent magnets that augments the magnetic field on one side of the array while canceling the field to near zero on the other side. This magnet configuration was proposed by Physicist Klaus Halbach.

k-Space: In MRI physics, k-space is the 2D or 3D Fourier transform of the MR image measured. Its complex values are sampled during an MR measurement, in a premeditated scheme controlled by a pulse sequence, i.e. an accurately timed sequence of radiofrequency and gradient pulses. In practice, k-space often refers to the temporary image space, usually a matrix, in which data from digitized MR signals are stored during data acquisition. When k-space is full (at the end of the scan) the data are mathematically processed to produce a final image. Thus k-space holds raw data before reconstruction.

Larmor Equation:f = γB₀∕2π. This equation states that the frequency of precession, f, of the nuclear magnetic moment in a magnetic field is proportional to the strength of the magnetic field, B₀, and the gyromagnetic ratio, γ.

Larmor Frequency: The frequency at which the nuclear spins precess about the static magnetic field, or the frequency at which magnetic resonance can be excited. This frequency is determined by the Larmor equation.

Logging While Drilling (LWD): A technique of conveying well logging tools into the well borehole downhole as part of the bottom hole assembly.

M: Net magnetization vector. See Magnetization.

M₀: Equilibrium value of the net magnetization vector directed along the static magnetic field.

Magnetization, Longitudinal (M_z): Component of the net magnetization vector along the static magnetic field B₀ (or B_z).

Magnetic Moment: A measure of the magnetic properties of an object or particle (the proton for example) that causes the object or particle to align with the static magnetic field.

Magnetic Resonance (MR): Magnetic resonance describes a group of phenomena more general than NMR. It also includes nuclear quadruple resonance (NQR) and electron paramagnetic resonance (EPR). Because the term nuclear is often related to radioactivity, the term MR is used to avoid this connotation. (NMR means nuclear magnetic resonance, i.e., the term nuclear refers to the magnetic resonance of an atomic nucleus.)

Magnetic Resonance Imaging Logging (MRIL): The name for the specific NMR logging tool developed by NUMAR Corporation in the mid-1980s. The MRIL tool uses a permanent gradient magnetic field and an orthogonal RF magnetic field (for generating CPMG pulse sequences) to select concentric cylindrical shell volumes for NMR measurements.

Magnetic Resonance Imaging (MRI): Refers to imaging with NMR techniques. Most MRI machines use a pulsed gradient magnetic field that permits one to localize the NMR signals in space. MRI is used on core samples and in core flooding or flow mechanism studies.

Magnetic Susceptibility (χ): The measure of the ability of a substance to become magnetized. Differences in magnetic susceptibility of the pore fluids and the matrix cause internal field gradients.

Magnetization (M): A macroscopic vector quantity resulting from the alignment of the nuclear magnetic moment with the static magnetic field. This vector projected into the plane perpendicular to the static magnetic field is known as transverse magnetization. It is this quantity that is observed by NMR.

MagTrak: A LWD NMR tool produced by Baker Hughes, which can offer industry-standard, T₂-based, real-time magnetic resonance data that locates and identifies producible fluids even under the most difficult drilling conditions, such as high inclination and high-risk wells.

MAP: A software program developed by NUMAR for inverting echo-train data to a T₂ distribution. The inversion algorithm used in MAP is based on Singular Value Decomposition (SVD).

MCBW: CBW estimate obtained by summing the T₂ distribution obtained from partially polarized CPMG echo trains acquired with a TE = 0.6 ms and TW = 20 ms.

MPHI: The porosity estimate obtained by summing the T₂ distribution over T₂ values greater than or equal to 4 ms and less than or equal to the highest T₂ value in the distribution, e.g., 1024 ms. MPHI is often referred to as the effective porosity.

MR: See Magnetic Resonance.

MRI: See Magnetic Resonance Imaging.

MRIAN: See MRIL Analysis.

MRIL: See Magnetic Resonance Imaging Logging.

MRIL Analysis (MRIAN): An interpretation method that incorporates deep resistivity data, MRIL standard T₂ logging measurements, and the dual water model. MRIAN determines water-filled porosity in the virgin zone, which can be compared with the flushed-zone results provided by MRIL stand-alone analysis techniques, such as TDA, EDM, and DIFAN.

MRIL B₀Radial Dependence: The static magnetic field B₀ of the MRIL tool is a gradient field, whose strength B₀ decreases as the distance from the tool axis increases. The radial dependence is B₀ ∝ r⁻², where r is the distance from the axis of the tool.

MRIL B₀Temperature Dependence: The static magnetic field B₀ of the MRIL tool is generated by a permanent magnet. The temperature dependence of the strength of B₀ arises from the fact that the magnetization of the permanent magnet is temperature-dependent. The mean field approximation gives T⁻¹ temperature dependence in the temperature regime, typical of borehole conditions, where T is the absolute temperature.

MRIL B₁Temperature Correction: The B₁ 90° pulse is determined during the MRIL shop calibration done at room temperature. Because of the difference between room temperature and downhole temperature, the energy of the B₁ pulse needed for 90° tipping downhole will be different from the energy determined at the shop; therefore, a temperature correction for B₁ is needed.

MRIL Borehole Washout Effect: An MRIL log will show the effect of serious borehole washouts when the sensitive volume intersects the borehole. An increase in MPHI and BVI will be seen in the log response. The MRIL tool responds to water-based mud as bound formation fluid because of the large quantity of dispersed clays and the associated water of hydration. Oil-based mud exhibits short relaxation times because of the large quantities of emulsifiers used to control water.

Washouts may be affecting an MRIL log if

• A comparison of caliper measurements with the depth of investigation for the appropriate downhole temperature indicates that the borehole is intersecting the sensitive volume of the tool.

• An abnormally large BVI is observed.

• An increase in MPHI corresponds to an increase in the caliper and MBVI = MPHI.

MRIL-C Tool: NUMAR’s second-generation MRIL tool, introduced in 1994.This tool is capable of performing multiple experiments simultaneously (e.g., the MRIL-C has dual-frequency capability, and the MRIL-C+ has triple-frequency capability). The MRIL-C/TP tool, which was introduced by NUMAR in 1996, provides an estimate of total porosity as well as effective porosity. The C/TP tool is able to measure total porosity because the tool can use a reduced TE (0.6 ms). Furthermore, because the tool experiences reduced ringing, the first echo contains valuable information. Because MRIL-C tools operate in either dual- or triple-frequency mode, successive measurements at different frequencies can follow one another more quickly. Each MRIL frequency excites a signal from different physical locations and thus it is not necessary to wait for repolarization to occur in one location before making a measurement in another location. Alternating between frequencies allows more measurements to be made in a given time, thus permitting logging speed to be increased without reducing S/N, or permitting S/N to be increased without reducing logging speed.

MRIL Depth of Investigation: The depth at which the MRIL tool provides information. Because the Larmor frequency is a function of B₀ and B₀ is radially dependent, the Larmor frequency is also radially dependent and thus defines the depth of investigation of the MRIL tool. Furthermore, because B₀ is also temperature-dependent, it follows that the Larmor frequency and thus the depth of investigation are also temperature-dependent when a fixed B₁ frequency is used, which is always the case. As the temperature of the magnet increases, B₀ decreases, and the depth of investigation decreases accordingly (e.g., a depth of investigation of about 16 in. at 25 °C decreases to about 14 in. at 150 °C). The variation of depth of investigation with temperature for MRIL tools is discussed and displayed in NUMAR literature and charts.

MRIL-Prime Tool: NUMAR’s latest generation of MRIL tool, introduced in 1998. This tool is capable of performing multiple experiments at up to nine frequencies. By alternating between nine frequencies, measurements can be made at a much higher rate. The MRIL-Prime provides measurements of clay-bound water, effective porosity, capillary-bound water, and hydrocarbon typing in just one pass. Besides saving time, acquiring all the data in one pass eliminates depth-shift errors. The MRIL-Prime tool has additional pre-polarization magnets placed above and below the antenna that allow for full polarization of the fluids. This pre-polarization design can provide 12 s of polarization at logging speeds as high as 24 ft min⁻¹. Furthermore, the capability of the tool to fully polarize fluids at high logging speeds and obtain a full T₂ distribution without any corrections makes the logging results much less sensitive to certain job-design parameters. Planning logging jobs for earlier tools required some knowledge of the time needed to polarize fluids. The MRIL-Prime tool can simply handle the longest polarization times without reducing logging speed. Thus, this tool can be run much like standard triple-combo tools—just run the tool to the bottom of the hole and log up without special passes in the hole and without having to subsequently assemble data from different passes. This is why the MRIL-Prime tool is the first NMR device that can realistically be considered a “primary formation evaluation” logging tool.

MRIL-WD™ Tool: One of the serials of MRIL tools proposed and commercialized by Halliburton, which is used for Logging While Drilling. This tool can provide partial porosities and permeability for petrophysical analysis and allow pre-defined T₁ cutoffs to enable rock quality assessment. The usage of T₁ measurement for MRIL-WD is very important because of the impacts of lateral vibration or axial motion effects. T₁ relaxation times are insensitive to those motion effects.

MRIL Sensitive Volume Thickness: The thickness of the zone for which the MRIL tool provides information. The thickness of the sensitive volume for the MRIL tool is approximately 1 mm and is a function of the gradient strength of the B₀ field and the frequency band of the B₁ field.

MR Scanner Tool: One of the wireline NMR tools created by Schlumberger, which can make simultaneous multifrequency measurements at multiple depths of investigation. The pad-type design is unbiased by formation water salinity. The tool has a main 18-in. long antenna, and two high-resolution 6-in. antennas. The main antenna operates at multiple frequencies and is intended primarily for fluid characterization applications. The high-resolution antennas operate at a single frequency at shallower shells to quickly capture the short relaxation component like bound water, etc.

Mercury Injection Capillary Pressure: The most direct and effective way to evaluate reservoir pore structure is the mercury injection experiment. Mercury injection capillary pressure curves are obtained through mercury injection experimental analysis of cores to evaluate reservoir pore structure. It is often compared with or can be replaced by NMR T₂ or T₁ distribution at certain conditions, such as fast diffusion limit.

MICP: See Mercury Injection Capillary Pressure.

MREX tool: It is a multifrequency, multiple field gradient, side-looking NMR logging tool. The multifrequency operation allows the continuous acquisition of data without the blank period for polarization recovery; multiple gradients are essential for any diffusion-based hydrocarbon typing; and the side-looking concept reduces the borehole loading effect for salt-saturated wells as well as avoids contamination of borehole signals from large-diameter well bores.

MRIL-XML™: A new generation wireline NMR tool developed by Halliburton, aiming at providing excellent bed resolution and evaluating a reservoir’s full range of pore sizes from micro to macro. Industry-leading pore size characterization for micropores is achieved by a very fast inter-echo spacing, down to 0.3 ms.

MSIG: Porosity estimate obtained by combining data from dual-TE logging with TE = 0.6 and 1.2 ms. MSIG should agree well with the total porosity measured on cores. MSIG = MCBW + MPHI.

Mud Doping: The practice of adding magnetite to the drilling mud. With the now-obsolete NML tool, doping was essential to kill the borehole signal. However, doping the mud with a paramagnetic substance to change the NMR properties of invading mud filtrate may still be desirable. For instance, if the invaded zone is flushed with paramagnetic ions, then the bulk relaxation time of the brine is shortened, and water signals are killed. Thus, only oil signals remain, and residual oil saturation can be determined through NMR measurements. MnCl₂, has recently been shown to be a cost-effective doping agent for this application.

M_x: See Transverse Magnetization.

M_z: See Longitudinal Magnetization.

NE: Number of echoes in a CPMG echo train.

NML™ Tool: The Nuclear Magnetic Logging tool, an obsolete NMR logging tool that utilized the earth’s magnetic field. The NML tool measured the precession of hydrogen protons in the earth’s magnetic field after the alignment of protons with a superimposed magnetic field. The sensitive volume of the NML was not a thin cylindrical shell, but a full cylinder centered around the tool; therefore, the measurement contained borehole signals. Operation of the NML required special doping of the borehole fluids to eliminate the signal from the protons in the borehole.

NMR: See Nuclear Magnetic Resonance.

Nuclear Magnetic Resonance (NMR): NMR, as a physical phenomenon, is the absorption or emission of electromagnetic energy by nuclei in a static magnetic field, after excitation by a stable RF magnetic field. NMR, as an investigative tool, is a method that uses the NMR phenomenon to observe the static and dynamic aspects of nuclear magnetism. The method requires a static magnetic field to orient nuclear magnetic moments, and an orthogonal oscillating field (at RF frequencies) to excite the nuclear magnetic moments. The frequency of the oscillating field must satisfy the Larmor resonance condition. NMR can be used to detect molecular structures and probe molecular interactions. It is a major chemical spectroscopic technique with many applications, including probing properties of fluids in porous media. Despite the term nuclear, NMR does not involve radioactivity.

Numerically Controlled Oscillator: It is a digital signal generator which creates a synchronous (i.e. clocked), discrete-time, discrete-valued representation of a waveform, usually sinusoidal. NCOs are often used in conjunction with a digital-to-analog converter (DAC) at the output to create a direct digital synthesizer (DDS).

NCO: See Numerically Controlled Oscillator.

Oil-based Mud Filtrate: Oil-based mud, also known as oil-based drilling fluid. It consists of oil, water, organic clay and an oil-soluble chemical treatment agent. Oil-based mud is resistant to high temperatures and salt and calcium erosion, which is conducive to well stability and has good lubrication and less damage to oil and gas layers. It is widely used in all kinds of drilling platforms.

OBM Filtrate: See Oil-based Mud Filtrate.

PAP: See Phase Alternate Pairs.

Paramagnetic Materials: Materials with a small but positive magnetic susceptibility. The addition of a small amount of paramagnetic material to a substance may greatly reduce the relaxation times of the substance. Most paramagnetic substances possess an unpaired electron and include atoms or ions of transition elements (e.g., manganese and vanadium) or rare earth elements. Oxygen (O₂) is also paramagnetic and contributes to the relaxation of water. Paramagnetic substances are used as contrast agents in medical MR imaging and to dope the borehole fluids in some applications of NMR logging. Copper sulfate (CuSO₄) is used to dope the water in a calibration tank to reduce water relaxation times, thereby significantly reducing MRIL calibration time.

Permeability, Absolute: A measure of the ability of a rock to conduct a fluid or gas through its interconnected pores when the pores are 100% saturated with that fluid. Measured in darcies or millidarcies (md).

Permeability, Effective: The capability of a rock to conduct a fluid in the presence of another fluid, immiscible with the first, is called its effective permeability to that fluid. Effective permeability not only depends on the permeability of the rock itself but also on the relative amounts of the different fluids in the pores.

Permeability, Relative: The ratio between the effective permeability to a given fluid at a partial saturation and the permeability at 100% saturation. Relative permeability is the ratio of the amount of a specific fluid that will flow at a given saturation, in the presence of other fluids, to the amount that would flow at a saturation of 100%, other factors remaining the same.

Phase Alternate Pairs (PAP): A method of acquiring two echo trains that are 180° out of phase. The change in the echo-train phase is accomplished by changing the phase of the initial 90° pulse in the CPMG sequence by 180°. The effect of this change is to reverse the sign of the echo data. In processing, the two echo trains are subtracted to eliminate the effects of ringing and baseline offset.

Polarization Time (TW): See Wait Time.

When two or three fluid phases are present, however, the non-wetting phases occupy the larger pores while the wetting phase occupies the smaller pores because of the capillary effect. In addition, the relaxation rate of non-wetting fluids is smaller than that of wetting fluids because the T₂ of non-wetting fluid does not include the surface term. Both the capillary and surface effect result in shorter T₂ for wetting-phase fluids compared to the T₂ for the same fluid types in bulk. Much less change is expected for the non-wetting fluid T₂. Thus, different fluid phases can be identified by carefully analyzing the T₂ distribution or by using relaxation-weighting techniques (such as dual-TW and dual-TE) for multiphase saturation cases.

PFG: See Pulse Field Gradient.

PCA: See Principle Component Analysis.

PFG-SE: See Pulsed Field Gradient and Spin Echo.

PFG-STE: See Pulsed Field Gradient Stimulated Echo.

Phase-sensitive detector: It is used to detect the phase between two signals. Envelope detection has two problems: first, the demodulation process is based on the half-wave or full-wave rectification of the AM signal, so it is impossible to identify the phase of the modulated signal from the output of the detector; second, the envelope detection circuit itself does not have the ability to distinguish signals with different carrier frequencies. In order to make the detection circuit have the ability to discriminate signal phase and frequency, and improve the anti-interference ability, it is necessary to use the phase-sensitive detection circuit.

Porosity, Effective: A somewhat arbitrary term sometimes used to refer to the fractional part of formation volume occupied by connected porosity and excluding the volume of water associated with clay. In NMR logging, the term has usually been associated with porosity that decays with T₂ greater than 4 ms. Effective porosity often refers to the interconnected pore volume occupied by movable fluids, excluding isolated pores and pore volume occupied by adsorbed water. Effective porosity contains fluid that may be immovable at a given saturation or capillary pressure. For shaly sands, effective porosity is the fractional volume of a formation occupied by only fluids that are not clay bound and whose hydrogen indexes are 1.

Porosity, Total: The total pore volume occupied by fluids in a rock. Includes isolated non-connected pores and volume occupied by adsorbed, immobile fluids. For a shaly sand formation, total porosity is the fractional part of the formation volume occupied by both clay-bound and non-clay-bound fluids.

Preamplifier: A preamplifier, also known as a preamp, is an electronic amplifier that converts a weak electrical signal into an output signal strong enough to be noise-tolerant and strong enough for further processing. Without this, the final signal would be noisy or distorted. They are typically used to amplify signals from analog sensors. Because of this, the preamplifier is often placed close to the sensor to reduce the effects of noise and interference.

Precession: The motion of the axis of a spinning body so as to trace out a cone. It is caused by the application of a torque tending to change the direction of the rotation axis. The precession of the proton spin axis about the B₀ field axis occurs at the Larmor frequency.

Principal Component Analysis: Principal component analysis (PCA) is a useful statistical method that has found applications in many fields, of which, compression is an important one. PCA can effectively find out the most contributive elements and structures in the huge amount of data and eliminate those who contribute little or even are redundant, therefore simplifying the data and revealing the simple structure hidden in the complex data sets without losing much information. PCA is mathematically defined as an orthogonal linear transformation that transforms the data to a new coordinate system such that the greatest variance by some projection of the data comes to lie on the first coordinate (called the first principal component), the second greatest variance on the second coordinate, and so on. In this new coordinate system, instead of all the variables in the original sample, only the spatial coordinates corresponding to the characteristic values of the maximal linearly independent subset of the original sample are needed.

Proton Density: The concentration of mobile hydrogen atoms per unit volume. NMR data can be corrected for hydrogen density changes by dividing the apparent NMR porosity by the appropriate hydrogen index.

Proton: A positively charged elementary particle that provides the charge in an atomic nucleus. A hydrogen nucleus contains one proton. The symbol ¹H is used to designate the hydrogen nucleus.

Pro-VISION: A LWD NMR tool developed by Schlumberger.

PSDs: See Phase-sensitive detector.

Pulsed Field Gradient: A pulsed field gradient is a short, timed pulse with spatial-dependent field intensity. Any gradient is identified by four characteristics: axis, strength, shape and duration. Pulsed field gradient (PFG) techniques are key to magnetic resonance imaging, spatially selective spectroscopy and studies of diffusion via diffusion-ordered nuclear magnetic resonance spectroscopy. PFG techniques are widely used as an alternative to phase cycling in modern NMR spectroscopy.

Pulse Shaping: The amplitude, shape, and width of RF pulses define the frequency selectivity of an NMR measurement (see also Hard Pulse and Soft Pulse). Soft pulses are shaped to improve their frequency selectivity as well as other parameters. How shaping brings about these improvements can be easily understood by taking the Fourier transform of RF pulses. A hard pulse is rectangular in shape and excites a wide range of frequencies far from the main lobe. Thus, the frequency selectivity of a hard pulse is poor. A soft pulse has a greater spread in the time domain but excites a narrow, uniform range of frequencies. Thus, the frequency selectivity of a soft pulse is good.

Pulse, 180°: An RF pulse designed to rotate the net magnetization vector 180° in the rotating frame of reference. Ideally, the amplitude of a 180° pulse multiplied by its duration is twice the amplitude of a 90° pulse multiplied by its duration. Each 180° pulse in the CPMG sequence creates an echo.

Pulse, 90°: An RF pulse designed to rotate the net magnetization vector 90° from its initial direction in the rotating frame of reference. If the spins are initially aligned with the static magnetic field, this pulse produces transverse magnetization and free induction decay (FID).

Pulse, Hard: A term used to describe a high-power, short-duration RF pulse used in NMR pulse sequences. In contrast, soft pulses are usually low-power, long-duration RF pulses. Hard pulses are usually rectangular shaped in the time domain and excite wide frequency bands often extending beyond the desired resonance frequency. Hard pulses generally make good use of available RF power but exhibit poor frequency selectivity. Because of the narrower pulse widths, hard pulses are more suitable for pulse sequences that require short echo spacing (TE). See Pulse Shaping for frequency selectivity.

Pulse, Soft: Low-power, long-duration RF pulses used in NMR measurements. Soft pulses in the time domain are rectangular pulses in the frequency domain. In medical MRI applications, a soft 90° pulse typically has a width of a few milliseconds. Although soft pulses need not conform to a particular shape, they usually have crafted pulse envelopes, e.g., truncated Sinc pulses (bell-shaped envelopes), to improve frequency selectivity. See Pulse Shaping for frequency selectivity.

Q-Switch: A technique which is used for decreasing the dead time of the RF coil. Downhole NMR activations normally require large power to excite formation. Residual energy will oscillate in the RF coil resulting in longer dead times of the NMR system. It is not beneficial for the detection of fluids with short relaxation times because of longer inter-echo spacing related to dead times. The Q-switch technique will accelerate the energy oscillated in the RF system and shorten the inter-echo spacing.

Radial Profiling: If mud filtrate invasion has happened, the formation will consist of a flushed zone, an invaded zone, and an undisturbed zone. Invasion frequently causes fluid saturations to vary over the first few inches of formation away from the wellbore in wells drilled with oil-based or water-based mud. For resistivity logs, shallow, medium and deep resistivity logging can be implemented for solving this issue. The state-of-the-art nuclear magnetic resonance logging tools acquire data in thin shells at distinct redial depths of investigation (DOI) so that a radial profile will be obtained to efficiently describe the saturation variation due to the filtrate invasion.

Radio Frequency (RF): Electromagnetic radiation at a frequency in the same general range as that used for radio transmissions. The Larmor frequency for 1H is typically in this range. For an MRIL tool, the Larmor frequency is in the range of 580 to 750 KHz.

Regularization: The process which is used to stabilize the inversion from the measured NMR echo decay to the T₂ spectra. There are many methods in use, of which MAP is one. They all result in smoothed spectra, which vary depending on the method and amount of regularization. The need to use regularization means that there is no unique NMR spectrum or pore distribution. In most cases, the major features of the spectra are independent of the method of regularization.

Relaxation Time: A time constant associated with the return of nuclear spins to their equilibrium positions after excitation. Several relaxation times are defined in NMR measurements. Each is related to different molecular interaction mechanisms. The most frequently measured relaxation times are T₁ and T₂. For bulk water, T₁ and T₂ are approximately 3 s. The relaxation times of water in rocks are much smaller and are generally less than 300 ms.

Relaxation Time, Bulk Fluid: The relaxation produced by the interaction of the fluid with itself. For most cases of interest T₁ and T₂ are equal. For gas, however, because the diffusivity of gas is much higher than that of liquids, the apparent T₂ of gas measured by the CPMG technique in a gradient magnetic field can be much smaller than T₁.

Relaxation Time, Longitudinal (T₁): Longitudinal, or spin-lattice, relaxation time. This time constant characterizes the alignment of spins with the external static magnetic field.

Relaxation Time, Transverse (T₂): Transverse, or spin–spin, relaxation time. This time constant characterizes the loss of phase coherence that occurs among spins oriented at an angle to the main magnetic field and that is due to interactions between spins. T₂ never exceeds T₁. Both T₂ and T₁ have been successfully related to petrophysical properties of interest, such as pore size, surface-to-volume ratio, formation permeability, and capillary pressure.

Residual Oil: Oil remaining in the reservoir rock after the flushing or invasion process, or at the end of a specific recovery process or escape process.

Resonance: Vibration in a mechanical or electrical system caused by a periodic stimulus, with the stimulus having a frequency at or close to the natural frequency of the system.

RF: See Radio Frequency.

Ringing: The oscillatory response of a magnet to the application of high-energy RF pulses. When the MRIL RF antenna is energized with high-energy RF pulses, the MRIL magnet resonates or “rings”. The MRIL magnet acts like a piezoelectric crystal, generating an acoustic oscillating voltage that interferes with the formation signal. Ringing is frequency-dependent, and each magnet has a different ringing window (typically 20 to 40 kHz wide) where the ringing effect is smaller than at other frequencies. The ideal operating frequency is one that is located in the middle of a broad ringing window.

Rotating Frame of Reference: A frame of reference, which rotates around the axis of the static magnetic field (B₀) at a frequency equal to that of the applied RF magnetic field (B₁).

Running Average: This represents the total number of individual experiments (i.e., complete echo trains) needed to produce a high signal-to-noise. Because the PAPs technique is used during a CPMG measurement, the Running Averaging is at least two.

RA: See Running Average.

Relaxometry: Relaxometry refers to the study and/or measurement of relaxation variables in Nuclear Magnetic Resonance and Magnetic Resonance Imaging. In NMR, nuclear magnetic moments are used to measure specific physical and chemical properties of materials.

Ringing: The downhole NMR tool’s magnet is a highly magnetic, ceramic material. When an oscillating electric current flows through the antenna surrounding the magnet, an electromechanical effect, called ringing, occurs in the tool.

S/N: See Signal-to-noise Ratio.

Saturation Recovery: A pulse sequence is a commonly used method to extract T₁ relaxation time. It is often constructed as follows: firstly, a 90° RF pulse will modify the equilibrium magnetization of the spin population to be rotated by 90°, and then, a free evolution period (evolution time period, in which magnetization is under recovery) is permitted to relax, and finally, a detection pulse is applied to detect the signal recovery degree compared to its equilibrium value M0.

SBVI: See Spectral Bulk Volume Irreducible.

SG: See Static Field Gradient.

SG-SE: See Static Field Gradient and Spin Echo.

SG-STE: See Static Field Gradient and Simulated Echo.

Shifted Spectrum Method (SSM): An interpretation method based on dual-TE measurements with identical TW. The SSM relies on the diffusivity contrast between fluids with different diffusivity to type viscous hydrocarbons. The shifted spectrum refers to the observation of the T₂ distribution shifted to smaller T₂ values when TE is increased. Gases have much higher diffusivity than oil or water, and are more sensitive to echo spacing (TE) changes. Heavy oils have very low diffusivity, and are least sensitive to TE changes. The SSM is performed in the T₂ domain and uses the difference in the shift between fluids of different diffusivity to identify fluids.

Signal Averaging: A method of improving signal-to-noise ratio by averaging echo trains.

Signal-to-noise Ratio (S/N): The ratio of signal amplitude to noise amplitude. Signal refers to the desired part of a detected signal; noise refers to the remainder of the detected signal and includes random noise. S/N is a measure of data quality. The S/N of NMR measurements can be improved by averaging several echo trains, by sampling larger volumes, or by increasing the strength of the B₀ magnetic field. If the noise is random (statistical) noise only, then averaging n measurements improves S/N by n^1∕2.

Spin Echo: After spins are excited by an RF pulse, the spins experience FID because of B₀ inhomogeneities. Spin isochromats, which are groups of spins precessing at exactly the same Larmor frequency, lose phase coherence during FID. However, during this decay, the isochromats do not experience many spin–spin interactions and still retain phase memory. If a second pulse (180°) is applied at time τ after the first RF pulse, the spin isochromats will re-phase in the same amount of time τ. A macroscopic signal (the spin echo) then occurs at precisely TE = 2τ. Even if the second pulse is not a 180° pulse, a spin echo can still be observed, but this echo will be of smaller amplitude. A third pulse will repeat the process.

Spin: Intrinsic angular momentum of an elementary particle or system of particles, such as a nucleus. Spin is responsible for the magnetic moment of the particle or system.

SR: See Saturation Recovery.

Static Field Gradient: For most downhole NMR tools, the static magnetic field is static field gradient-based due to the configuration design of the permanent magnet.

Stimulated Echo: The echo formed after magnetization evolves first in the x–y plane, then in the z direction, and again in the x–y plane. A stimulated echo is observed after a three-pulse sequence. Because of B₁ inhomogeneities, stimulated echoes occur during CPMG sequences used on logging tools at the same times as regular echoes and must be compensated for through calibration.

Surface Relaxivity (ρ): A measure of the capability of a surface to cause protons to relax, i.e., lose orientation or phase coherence. This quantity depends on the strength of fluid-matrix interactions. It also varies with the wettability of the rock surface. Surface relaxation strength ρ falls in the range of approximately 0.003 to 0.03 cm s⁻¹ for clastics. ρ is smaller for carbonates.

SVD: Singular Value Decomposition method, is normally used in the data compressing during NMR data processing.

T₁: See Longitudinal Relaxation Time.

T₁–T₂: The T₁–T₂ adjoint density distribution, which can be obtained by a T₁–T₂ pulse sequence. It is defined with the combination of IR (or SR) and CPMG pulse sequences. Variable lengths of τ₁ is the T₁ editing period, which should be changed several times to edit T₁ information. The following CPMG sequence is used to acquire T₂. The acquired NMR signals are related to the function of T₁ and T₂ which can be obtained independently by using a two-dimensional Laplace transform.

T₁–D–T₂: The T₁–D–T₂ adjoint density distribution, which can be obtained by a T₁–D–T₂ pulse sequence. It is defined with the combination of IR (or SR), Diffusion Editing and CPMG pulse sequences. The initial window I to edit T₁ is achieved by an inversion recovery sequence or saturation recovery sequence. In window II, the diffusion sensitivity is achieved by a direct echo sequence where the echo spacing τ₂ are varied. Here the constant gradient is implemented (pulsed field gradient can also be used), while this part can also be achieved by the pulse field gradient or the stimulated echo. In window III, the echo spacing T_E of the standard CPMG sequence should be set short enough to make the decay times independent of diffusion and to obtain the original T₂.

T₂: See Transverse Relaxation Time.

$T2*$: Time constant characterizing the loss of phase coherence that occurs among spins oriented at an angle to the main magnetic field and that is due to a combination of magnetic field inhomogeneity and magnetic interaction. $T2∗$ is always much shorter than T₂. In the limit of no diffusion, loss of coherence produced by field inhomogeneity can be reversed by the application of 180° pulses, which results in the formation of spin echoes.

T_2cutoff: A value of T₂ that is empirically related to the capillary properties of the wetting fluid in a rock. It is used to differentiate different pore sizes and quantify the amount of bound water. Typically, porosity associated with T₂ values less than approximately 33 milliseconds (T_2cutoff = 33 ms) are summed to obtain BVI for clastics and, similarly, T_2cutoff of approximately 90 ms for carbonates. Note that these values are empirical and may be rock-specific.

T_2S: Time constant that describes the contribution of surface relaxivity to the transverse relaxation time of fluid in a rock. When a single wetting fluid fills the pores, T_2S dominates the relaxation process. Thus, T₂ is proportional to (S/V) of a pore, where S/V is the surface-to-volume ratio. If a spherical pore is assumed, T₂ is proportional to the pore radius.

TDA: See Time Domain Analysis.

TE: See Echo Spacing.

Time Domain Analysis (TDA): An alternate method to the differential spectrum method for processing dual-TW echo trains. The interpretation is performed in the time domain rather than in the T₂ domain. The key features of the TDA are the subtraction of the two echo trains from one another, and the processing of the echo differences in the time domain using predicted or measured oil, gas, and water relaxation times and hydrogen index values. In the DSM, the dual-TW echo trains are first inverted into T₂ spectra and subtracted from one another. The interpretation is done in T₂ spectrum domain. The effect of T₂ spectrum broadening because of noise and regularization smears the partial porosities into adjacent bins, and the subtracted spectrum may contain negative amplitudes that are obviously incorrect. The TDA method has fewer problems with the noise-induced T₂ spectrum broadening, and because fewer free parameters need to be determined, the solution is more stable. However, subtracting echoes reduces S/N.

Transverse Magnetization (M_x): Component of the net magnetization vector at right angles to the static magnetic field.

TW: See Wait Time.

Tesla: A unit of magnetic strength, 1 tesla = 10 000 gauss = 1000 mT.

TC: See Cycle Time.

Viscosity: Resistance of a fluid to flow. Viscosity is due to internal friction caused by molecular cohesion in the fluid. The diffusion constant D is inversely proportional to viscosity.

Vertical Resolution: The minimum formation thickness that can be quantitatively analyzed by logging data.

VR: See Vertical Resolution.

Wait Time (TW): The time between the last CPMG 180° pulse and the first CPMG pulse of the next experiment at the same frequency. This time is the time during which magnetic polarization or T₁ recovery takes place. It is also known as polarization time.

Water-wet: A solid surface is water-wet when the adhesive attraction of water molecules for the solid substance is greater than the attraction between water molecules, i.e., adhesive force > cohesive force. The angle of contact of a water droplet on a water-wet solid surface will be less than 90° (measured inside the water phase). A mobile non-wetting oil phase would advance over the adhesive layer of water. Only water has a surface relaxation mechanism in a water-wet formation.

Wettability: The capability of a solid surface to be wetted when in contact with a liquid. A liquid wets a solid surface when the surface tension of the liquid is reduced so that the liquid spreads over the surface. Only the wetting fluid in a rock pore has a surface relaxation mechanism. Therefore, wettability affects the NMR properties of fluids in reservoir rocks.

γ

See Gyromagnetic Ratio.

ρ

See Surface Relaxivity.

χ

See Magnetic Susceptibility.

η

See Viscosity.

ϕ

Porosity.