PEH:Nuclear Magnetic Resonance Applications in Petrophysics and Formation Evaluation

Publication Information

Petroleum Engineering Handbook

Larry W. Lake, Editor-in-Chief

Volume V – Reservoir Engineering and Petrophysics

Edward D. Holstein, Editor

Copyright 2007, Society of Petroleum Engineers

Chapter 3E - Nuclear Magnetic Resonance Applications in Petrophysics and Formation Evaluation

Stephen Prensky, SPE, Consultant and Jack Howard, SPE, Halliburton

Pgs. 289-355

ISBN 978-1-55563-120-8
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Nuclear magnetic resonance (NMR) has been, and continues to be, widely used in chemistry, physics, and biomedicine and, more recently, in clinical diagnosis for imaging the internal structure of the human body. The same physical principles involved in clinical imaging also apply to imaging any fluid-saturated porous media, including reservoir rocks. The petroleum industry quickly adapted this technology to petrophysical laboratory research and subsequently developed downhole logging tools for in-situ reservoir evaluation (see the next section of this chapter).

NMR logging, a subcategory of electromagnetic logging, measures the induced magnet moment of hydrogen nuclei (protons) contained within the fluid-filled pore space of porous media (reservoir rocks). Unlike conventional logging measurements (e.g., acoustic, density, neutron, and resistivity), which respond to both the rock matrix and fluid properties and are strongly dependent on mineralogy, NMR-logging measurements respond to the presence of hydrogen protons. Because these protons primarily occur in pore fluids, NMR effectively responds to the volume, composition, viscosity, and distribution of these fluids (i.e., oil, gas, and water). NMR logs provide information about the quantities of fluids present, the properties of these fluids, and the sizes of the pores containing these fluids. From this information, it is possible to infer or estimate the volume (porosity) and distribution (permeability) of the rock pore space, rock composition, type and quantity of fluid hydrocarbons, and hydrocarbon producibility (Fig. 3E.1).

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  Fig. 3E.1 – NMR logging-tool response compared to conventional logging tools. NMR porosity is independent of matrix minerals, and the total response is very sensitive to fluid properties. Differences in relaxation times and/or fluid diffusivity allow NMR data to be used to differentiate clay-bound water, capillary-bound water, movable water, gas, light oil, and viscous oils. NMR-log data also provide information concerning pore size, permeability, hydrocarbon properties, vugs, fractures, and grain size.

NMR logging provides measurements of a variety of critical rock and fluid properties in varying reservoir conditions (e.g., salinity, lithology, and texture), some of which are unavailable using conventional logging methods (Fig. 3E.1) and without requiring radioactive sources (Table 3E.1). Whether run independently as a standalone service or integrated with conventional log and core data for advanced formation and fluid analyses, NMR logging has significantly contributed to the accuracy of hydrocarbon-reservoir evaluation. During the past decade, a new generation of wireline-logging devices has been introduced into commercial service. In the past few years, logging-while-drilling (LWD) devices and downhole NMR spectrometers have also been introduced.

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  Table 3E.1

Historical Development

Within a few years after the first successful observations of NMR in 1946, and the demonstration of free-precession NMR in the earth’s magnetic field in 1948, the petroleum industry recognized the potential of NMR measurements for evaluating reservoir rocks, pore fluids, and fluid displacement (flow).

In the early 1950s, several companies—particularly California Research (Chevron), Magnolia (Mobil), Texaco, Schlumberger, and Shell—began extensive investigations to understand the NMR properties of fluids in porous media for the purpose of characterizing reservoir rocks (porosity, permeability, and fluid content). In addition to laboratory research, these investigations included proposals for logging devices and the development of well-logging methods to permit formation evaluation in situ. Although a number of patents for logging tools were issued in the 1950s, it was not until Chevron completed an experimental Earth’s field nuclear-magnetic-log (NML) logging device in 1958 that a functioning device was actually developed. Limited commercial service of these devices was introduced in 1962 by Atlas, using the Chevron centralized design, and followed in 1965 by Schlumberger, using a pad-type tool of its own design. An improved version of the Schlumberger tool was introduced in 1978. Although the potential applications for this measurement were significant, particularly in the shallow, heavy-oil fields of the San Joaquin Valley, in general, they did not live up to expectations and were not commercially successful. Tool reliability and operational limitations proved to be major obstacles: the tool was not combinable, it required high (surface) power; the signal level varied geographically and was generally very low as a result of the low-operational frequency (2 kHz); and the borehole had to be doped with powdered magnetite to suppress the proton signal from the mud. The final version of the Schlumberger NML tool—a centralized tool introduced in 1984—proved reliable and commercially successful and was in service until the advent of modern pulse-echo tools in 1994.

In 1978, the Los Alamos Natl. Laboratory developed a logging tool that employed permanent magnets and used a pulsed radio frequency (RF) (pulse-echo) NMR method. Although this particular design had serious limitations—such as a low signal-to-noise ratio (S/N) that prohibited continuous, nonstationary logging—the concept set the stage for the development of modern commercial NMR tools. This advance was soon followed by improvements in magnet and coil design that enabled continuous logging. During the 1980s, while developing a commercial logging tool, industry also carried out laboratory experiments to further understand NMR behavior in fluid-filled porous media and to develop petrophysical interpretations from these data. Ultimately, two wireline tools using different magnet and coil configurations emerged from these efforts: Numar’s mandrel device (MRIL) and Schlumberger’s skid (sometimes called "pad") design [Combinable Magnetic Resonance (CMR) tool]. Commercial logging began with these tools in 1991 and 1995, respectively. These wireline-tool designs continue to evolve (see section on Tool Design in this chapter). Recent improvements allow simultaneous acquisition of more measurements, operation in a wider range of borehole conditions, and faster logging speeds. Detailed accounts of the historical development of NMR and NMR logging are available in several published references.

In addition to improvements in wireline tools, new acquisition schemes and processing methods have improved the resolution, quality, and utility of the acquired data and enabled enhanced interpretation methods and data analysis. Concurrent with wireline improvements, LWD NMR logging services were being developed and have been introduced in the past few years. In a related development, a downhole NMR spectrometer is now available for use with a formation-testing tool for in-situ fluid analysis.

NMR Physics

Atomic nuclei spin, and this angular moment produces a magnetic moment (i.e., a weak magnetic field). The NMR technique measures the magnetic signal emitted by spinning protons (hydrogen nuclei are the protons of interest in NMR logging) as they return to their original state following stimulation by an applied magnetic field and pulsed RF energy. These signals, which are observed (measured) as parallel or perpendicular to the direction of the applied magnetic field, are expressed as time constants that are related to the decay of magnetization of the total system.

NMR devices—both laboratory spectrometers and logging tools—use strong magnets to create a static magnetic field, B₀, that aligns (polarizes) the protons in the pore fluid from their resting (random) state to the direction of the imposed magnetic field (Fig. 3E.2).

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  Fig. 3E.2 – Because of their inherent nuclear magnetism, hydrogen nuclei (left) behave as though they are tiny bar magnets aligned with the spin axes of the nuclei. In the absence of an external magnetic field, the nuclear-magnetic axes (right) are randomly aligned.

Polarization is not instantaneous—it grows with a time constant, which is called the longitudinal relaxation time, denoted as T₁. Once full polarization (magnetic equilibrium) has been achieved, the applied static magnetic field, B₀, is turned off.

The protons begin to lose energy as the imposed magnetization, M₀, decays and the protons fall out of alignment, back to their original orientation and low-energy state. The protons’ angular momentum causes them to behave like tiny gyroscopes, and the loss of energy occurs during a wobbling or axial rotation (called precession) in the direction of the applied magnetic field. M₀, also known as the bulk magnetization, provides the signals measured by NMR devices. The frequency at which the energy is emitted or is initially absorbed, f, called the Larmor or resonance frequency, is proportional to the strength of the external magnetic field, B₀, (Fig. 3E.3). The Larmor frequency is used to tune a NMR probe, permitting it to image very thin slices of a sample at different distances from the tool.

• 

  Fig. 3E.3 – In an external magnetic field, the precessional frequency (f) of a nucleus depends on the gyromagnetic (γ) of the nucleus and the strength of the external field (B₀).

An antenna detects and records the decaying magnetic field generated by the precessing nuclei. At any given time, t , the strength of this magnetic field, M_z, is proportional to the number of protons, the magnitude of B₀, and the inverse of the absolute temperature (Eq. 3E.1):

....................(3E.1)

where M_z(t) = the magnitude of magnetization at t, M₀ = the final and maximum magnetization at a given magnetic field, and t = the time that the protons are exposed to the B₀ field.

The signal recorded parallel to the direction of the applied magnetic field (z plane) is called T₁, or longitudinal (spin-lattice) relaxation. T₁ describes how quickly the protons align within the static magnetic field. The T₁ curve is an exponential curve that characterizes the rate of change of the proton magnetization (Fig. 3E.4).

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  Fig. 3E.4 - T₁ relaxation (polarization) curves indicate the degree of proton alignment, or magnetization, as a function of the time that a proton population is exposed to an external magnetic field.

T₁ is the time at which the magnetization reaches 63% of its final value, and three times T₁ is the time at which 95% polarization is achieved. Full polarization of typical reservoir-pore fluids may take several seconds. Large values of T₁ (measured in milliseconds) correspond to weak coupling between the fluid and its surrounding environment and a slow approach to magnetic equilibrium, whereas, small T₁ values represent strong coupling and a rapid approach to equilibrium. Different fluids, such as water, oil, and gas, have very different T₁ values. T₁ is directly related to pore size and viscosity.

Pulse NMR devices use precisely timed bursts (pulse sequences) of RF energy that generate an oscillating magnetic field (B₁) that tilts or "tips" the aligned protons perpendicular (x-y plane) to the direction of the applied magnetic field. The application of B₁ results in a change in energy state that causes the protons to precess in phase to one another. These changes are known as NMR.

When the B₁ field is turned off, the precessions of the protons are no longer in phase with one another, and the net magnetization decreases. In this situation, a receiver coil (antenna) that measures magnetization in the transverse direction will detect an exponential decaying signal called free-induction decay (FID); see Fig. 3E.5. NMR-logging tools use the same antenna to transmit the RF pulse (kilowatt scale) and receive the decay signal (nanovolt scale).

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  Fig. 3E.5 – After application of a 90° pulse, the proton population dephases and an FID signal can be detected.

The FID signal measured in the x-y plane is called T₂ —the transverse or spin-spin relaxation. In contrast to T₁, T₂ of hydrocarbons is much shorter (see Table 3E.2).

• 

  Table 3E.2

The primary objectives in NMR logging are measuring T₁ signal amplitude (as a function of polarization), T₂ signal amplitude and decay, and their distributions. The total signal amplitude is proportional to the total hydrogen content and is calibrated to give formation porosity independent of lithology effects. Both relaxation times can be interpreted for pore-size information and pore-fluid properties, especially viscosity.

In the laboratory, T₁ is generally measured by either of two pulse sequences: inversion recovery or saturation recovery. Inversion recovery consists of a 180° spin inversion followed by a variable recovery time and then a 90° read pulse. The magnetization vector is entirely in the longitudinal range and, thus, has a higher dynamic range than the other method. Saturation recovery uses a 90° pulse, followed by a 90° read pulse. Saturation recovery is generally considered the more robust and efficient method. Although the actual T₁ sampling sequence is very short—involving several short echoes trains, each of which requires only a few milliseconds—the total amount of time required to obtain the number of samples sufficient to define the T₁ spectrum is significantly greater.

Depending on the activation used, the computation of a T₁ spectrum requires at least 25% more, and sometimes double, the time needed for the computation of a T₂ spectrum. In NMR logging, T₁ measurement initially required either a stationary mode or very slow logging speeds. With the latest multifrequency tools, a technique used for speeding up T₁ measurements is to make simultaneous measurements of the individual steps observed during a T₁ recovery experiment in adjacent volumes; at least two such volumes are required. This technique enables T₁ acquisition in less time, thereby permitting faster logging speeds.

T₂ measurement uses the spin-echo technique, in which the protons are first tipped into the transverse (x-y) plane by a 90° RF pulse and then inverted (flipped) by a subsequent 180° RF pulse at a fixed-time interval to rephase the dephasing protons. Rephasing the protons creates a detectable signal called a spin echo (Fig. 3E.6).

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  Fig. 3E.6 – NMR spin echo: (1) to generate a spin echo, a 90° B₁ pulse is first applied; (2) after cessation of the 90° pulse, dephasing starts; (3) at τ, a 180° B₁ pulse is applied to reverse the phase angles and, thus, initiate rephrasing; (4) rephrasing proceeds; and (5) rephrasing is complete, and a measureable signal (a spin echo) is generated at 2τ.

In practice, a sequence of pulses is used to generate a series of spin echoes (echo train) in which echo amplitude decreases exponentially with the time constant, T₂. A variety of multiple-echo pulse sequences have been developed for different purposes. In well logging and petrophysical studies, the most widely used is the Carr-Meiboom-Purcell-Gill (CMPG) sequence. A polarization period is followed by a 90° tip pulse, which in turn is followed by a series of alternating RF pulses and measurements of echo amplitudes detected by the logging-tool antenna. Successive 180° pulses are applied at a fixed-time interval (echo spacing, T_E), and the echoes are recorded between the pulses (Fig. 3E.7). By recording an echo train, T₂ can be calculated from the decay in the height (amplitude) of successive echoes using Eq. 3E.2:

....................(3E.2)

where M_x(t) = the amplitude of the transverse magnetization (i.e., the amplitude of the spin-echo train) at time t, and M_0x = the magnitude of the transverse magnetization when t = 0 (i.e., the time at which the 90° pulse stops).

• 

  Fig. 3E.7 – The CPMG pulse sequence is used in NMR logging to generate a spin-echo train; a 90° B₁ pulse is followed by a sequence of 180° B₁ pulses. Spin echoes of decreasing amplitude follow the 180° B₁ pulses.

A single T₂-pulse sequence may involve several hundred or thousand echoes. Only the amplitude (peak) of each spin echo is measured and stored. A series of echo trains is recorded and the signals stacked to improve S/N, especially at shorter relaxation times.

When recording multiple CMPG sequences, the time period between spin-echo recovery and the next 90° CMPG excitation—during which the protons are repolarized by the static magnetic field—is called the wait time, T_W (Fig. 3E.8). Each CMPG sequence may use a different wait time, echo spacing, and number of echoes. An additional advantage of the CMPG sequence is that a small echo spacing, T_E, in the CMPG sequence can minimize the diffusion effect on T₂. CMPG measurement sets are always collected in phase-alternate pairs (PAP) to preserve the signal and to eliminate low-frequency electronic offsets. In general, pulse NMR offers better methods to measure relaxation times and quantify liquid displacement in rock.

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  Fig. 3E.8 – CPMG pulse sequences (top) and alternating polarization (T₁-relaxation) curves and spin-echo train acquisition (bottom).

In-Gradient Diffusion

FID is caused by inhomogeneities in the magnetic field that are primarily caused by the existence of magnetic-field gradients. Gradients in the magnetic field occur, in part, because of the distance from the magnet to the sensitive (measurement) volume. For a given geometry, the gradient is inversely related to magnetic-field strength. Compared to laboratory and clinical NMR devices, NMR-logging tools produce a relatively weak and inhomogeneous static magnetic field. In the case of reservoir rocks, differences between the magnetic properties of the rock matrix and pore fluids may also contribute to a magnetic-field gradient. T₂, but not T₁, is affected by this phenomenon, which is called diffusion. In the presence of high magnetic-field gradients, diffusion effects make T₂ interpretation difficult. However, because the gradients produced by NMR-logging tools are relatively constant, they can be accounted for in T₂ interpretation. In fact, the existence of these field gradients has actually proved beneficial in NMR logging. Magnetic resonance imaging (MRI) is the process by which NMR measurements are obtained in a gradient magnetic field.

NMR Petrophysics

Laboratory Studies

Extensive laboratory studies on NMR behavior and on the properties of fluid-saturated porous media have been conducted since the inception of NMR and throughout the development of NMR-logging tools. The results from these investigations have provided the petrophysical foundation for understanding the logging measurements and for developing interpretation models and applications.

Low-field, bench-top pulse-NMR spectrometers were developed concurrently with logging tools so that wellbore measurements could be duplicated on core samples in the laboratory. These instruments operate and record data in the same manner as NMR-logging tools. Because NMR analysis is nondestructive, NMR and conventional capillary-pressure measurements can be performed on the same samples, in both the saturated and partially saturated states. Low-field spectrometers provide the ability to make repeatable measurements of rock- and fluid-NMR properties. This ability, in turn, permitted correlation and calibration of laboratory and field measurements and also permitted direct transfer of interpretation models developed in the laboratory to logging data. Where core is unavailable for NMR-log calibration, new technology and methods now allow NMR petrophysical measurements on drill cuttings.

Laboratory NMR studies are routinely conducted for the following purposes:

• Verifying formation porosity.
• Evaluating textural effects, such as microporosity, on NMR-log response.
• Determining formation-specific models that enhance the accuracy of determining bulk-volume-irreducible (BVI) water, free-fluid index (FFI), and, ultimately, permeability.
• Developing models to identify and quantify hydrocarbons, including residual oil.
• Developing models to predict changes in pore size (facies).

Much of this work is summarized in Kenyon, Murphy, Woessner, and Dunn et al. The most recent laboratory studies have suggested that some established NMR core-log relationships should be further investigated to better account for data scatter. A related area of study not dealt with here is NMR imaging of fluid flow in core.

As in NMR logging, data quality is critical. To achieve the desired objectives, laboratory NMR studies should include a preplanning phase similar to that used in logging. (See the Job Planning section of this chapter).

Petrophysical Properties

The basic petrophysical parameters of porosity, permeability, and producibility can be determined from either T₁ or T₂ echo-decay data. Until low-field spectrometers were developed, T₁ was the preferred acquisition method in the laboratory, where time is not a concern. Because T₁ measurement requires more time than T₂, T₂ became the primary acquisition mode in pulse-NMR logging because it allowed logging at speeds that were commercially viable. Fortunately, there is a correlation between T₁ and T₂; and T₁ can be estimated from T₂ data by extrapolating the T₂ decay-obtained-polarization pulses of different lengths (i.e., using different values of T_W; see Fig. 3E.9).

• 

  Fig. 3E.9 – T₁ measurement can be determined from a series of multiple wait-time T₂ measurements. The peak amplitudes from T₂ the measurements trace the outline of the curve (dotted).

Modern logging tools are capable of operating in either T₁- or T₂-acquisition modes. The logging mode is dictated by operational factors and job objectives and may, in fact, switch back and forth, as needed. (See further discussion in the LWD Tool section of this chapter.)

NMR Properties of Fluids

T₁ relaxation occurs when the precessing proton system transfers energy to its surroundings. T₂ relaxation occurs through a similar transfer in energy and also through dephasing. Consequently, transverse relaxation, T₂, is always faster than longitudinal relaxation, T₁. The emphasis of the proton NMR techniques used in formation evaluation is on the NMR fluid response from the pore fluids where T₂ ≤ T₁. The NMR response in solids (i.e., the non-shale/clay component of the rock matrix) is very short compared to the pore-fluid signal, and is generally not measured by laboratory or logging devices.

NMR relaxation of fluids depends on whether the fluid is measured in bulk form as a wetting-pore fluid within a rock matrix or in a gradient magnetic field. Bulk relaxation is the intrinsic relaxation property of a fluid that is controlled by viscosity, chemical composition, temperature, and pressure: T_2bulk≅T_1bulk. Fluids contained within pores have different relaxation characteristics, namely those of surface relaxation.

Surface relaxation occurs at the fluid-solid interface between a wetting-pore fluid and the rock-pore walls (Fig. 3E.10) and is different from the relaxation in either the solid or the fluid, individually. Surface relaxation dramatically decreases both T₂ and T₁ and is the dominant component contributing to T₂. When a nonwetting fluid (e.g., oil) is also present in rock pores, the nonwetting fluid may continue to relax at its bulk-relaxation rate.

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  Fig. 3E.10 – Schematic illustrating surface relaxation.

Surface relaxation is expressed by the following equations (Eqs. 3E.3 and 3E.4):

....................(3E.3)

and

....................(3E.4)

where ρ₂ = T₂ surface relaxivity (i.e., T₂ relaxing strength of the grain surfaces); ρ₁ = T₁ surface relaxivity (i.e., T₁ relaxing strength of the grain surfaces); and (S/V) pore=ratio of pore surface to fluid volume.

Surface relaxivity varies with mineralogy; and, for simple pore shapes (S is the surface area of a pore and V is the volume of the same pore), S/V is a measure of pore size. In a brine-wet rock, T₂ in smaller pores will be less than T₂ in large pores; consequently, identical pore water in different rocks can have a wide range of relaxation times because of variations in surface relaxivity. Laboratory studies have demonstrated that in water-wet rocks, the surface and volume ratio (S/V) is also a measure of permeability.

Fluids controlled by surface relaxation exhibit T₂ values that are not dependent on temperature and pressure. For this reason, laboratory NMR measurements made at room conditions are commonly used to calibrate formulas used to estimate petrophysical parameters such as permeability and bound water.

Diffusion-induced relaxation occurs when a significant gradient exists in the static magnetic field. Molecular diffusion in this gradient causes additional dephasing that contributes to increased T₂ relaxation. In addition to the magnetic-field gradient, diffusion is also controlled by inter-echo spacing and fluid diffusivity, viscosity, molecular composition, temperature, and pressure.

Bulk-fluid processes and surface relaxation affect both T₁ and T₂, while diffusion only affects T₂ relaxation. All three processes are independent and act in parallel according to the following equations (Eqs. 3E.5 and 3E.6):

....................(3E.5)

and

....................(3E.6)

The relative importance of the three diffusion-relaxation mechanisms depends on the fluid type in the pores (e.g., water, oil, or gas), the sizes of the pores, the strength of the surface relaxation, and the wettability of the rock surface (see Table 3E.3).

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  Table 3E.3

T₂ Decay

Eq. 3E.2 states that the T₂ decay associated with a single pore size in water-saturated rocks is proportional to the pore size. In fact, because reservoir rocks typically comprise a distribution of pore sizes and frequently contain more than one fluid type, a CMPG T₂ spin-echo train actually consists of a distribution of T₂ decays, rather than a single T₂ decay. In these cases, the exponential decay is described by Kenyon et al. as follows:

....................(3E.7)

where M(t) = measured magnetization at t; M_i(0) = initial magnetization from the ith component of relaxation; and T_2i = decay constant of the ith component of transverse relaxation. The summation is over the entire sample (i.e., all pores and all different types of fluid).

Fig. 3E.11 illustrates the multiexponential decay character of a porous medium containing pores of different sizes and a single wetting phase. Surface relaxation dominates when a short inter-echo spacing is used and the formation is only brine saturated. Under this condition, T₂ is directly proportional to pore size. When all pores are assumed to have similar geometric shape, the largest pores (see Fig. 3E.11, left column) have the lowest S/V and, thus, the longest T₂. Medium-size pores have smaller S/V, yielding shorter T₂ values. The smallest pores have the highest S/V and the shortest T₂ values.

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  Fig. 3E.11 – A 100% water-saturated pore (upper left) has a single T₂ value (upper center) that depends on pore size and, thus, its spin-echo train exhibits a single exponential decay (upper right) that also depends on pore size. Multiple pores at 100% water saturation (bottom left) have multiple T₂ values (bottom center) that depend on the pore sizes and, thus, their composite spin-echo train exhibits multiexponential decay (bottom right) that also depends on the pore sizes.

Eq. 3E.7 can also be expressed as follows:

....................(3E.8)

where (S/V)_t is the surface-to-volume ratio of the ith pore. When t = 0, the following is true:

....................(3E.9)

If the measured magnetization for 100% bulk water, M_100%(0), is known, then M(0) and M_0i can be calibrated to porosity by the following equation:

....................(3E.10)

where ϕ = calibrated porosity of the formation, ϕ_i = calibrated porosity associated with all pores of the ith pore size (also known as the incremental porosity). Therefore, the T₂ distribution (in the form of the amplitudes, M_0i, associated with the time constants, T_2i, is calibrated to the porosity distribution (i.e., the individual pores ϕ_i with the associated time constants T_2i).

If the rock is water-wet and the pores are partially saturated (i.e., the pores contain oil and/or gas in addition to water), then the total signal comprises contributions from each component in the following equation:

....................(3E.11)

where M_oil = magnetization produced by oil protons in the pores, M_gas = magnetization produced by gas protons in the pores, T_2oil = T₂ of oil measured with a CMPG sequence, and T_2gas = T₂ of gas measured with a CMPG sequence.

In a brine-saturated rock, the T₂ decay spectrum represents a pore-size distribution. However, when nonwetting fluids (e.g., oil or gas) are present, the T₂ spectrum includes a bulk response from the nonwetting fluid, in addition to the pore-size response. Pores containing the nonwetting fluid either appear in the spectrum at a decay time that is faster than is normally associated with the pores, or do not appear at all if the surface layer is too thin. This behavior affects the appearance of the T₂ spectrum and associated T₂ distribution but not the total signal amplitude (i.e., porosity).

Data Fit-Inversion

The raw data recorded by an NMR device are a series of spin-echo amplitudes (echo train) as a function of time, usually at fixed time increments (bins). These NMR measurements are statistical, and stacking is required to improve the precision of the log outputs. The precision depends on formation-fluid properties, activation (acquisition) type, and the number of pulses stacked. The data are mathematically inverted (mapped) by use of a best-fit curve to produce a distribution of T₂ values as a function of relaxation time (Figs. 3E.12 and 3E.13). Initially, biexponential-fitting algorithms were used; however, T₂ decay in fluid-saturated rocks is multiexponential, because of this, multiexponential models were developed and are commonly used for inverting the data. The inverse solution (T₂ distribution) is a function of both the measured echo data and the chosen smoothness (regularization) for the inversion. However, because regularization is controlled in part by the S/N, the fit that is actually used is not unique; that is, there can be a number of differently shaped T₂ distributions that fit the original echo-decay curve. In general, the area under the T₂-distribution curve (porosity) and the general location in time of the high-porosity bins are robust; however, caution is advised when interpreting the fine details of the distribution. Because the spin echoes are measured over a very short time, an NMR tool travels no more than a few inches along the wellbore while recording the spin-echo train; thus, the recorded spin-echo data can be displayed on a log as a function of depth.

• 

  Fig. 3E.12 – Spin-echo-decay train. The amplitudes of the spin echoes are recorded over time. A best fit line is applied to the data before inversion. In this example, the raw spin-echo measurements recorded at T_E = 1 ms are shown together with a data-fitting curve (solid).

• 

  Fig. 3E.13 - T₂ distribution. Mathematical inversion is used to convert the spin-echo-decay data to a T₂ distribution. This distribution is the most likely distribution of T₂ values that produce the echo train. With proper calibration, the area under the T₂-distribution curve is equal to the porosity. When the rock is water-saturated, this distribution will correlate with pore-size distribution. The presence of hydrocarbons will affect the T₂ distribution depending on the hydrocarbon type, viscosity, and saturation.

T₂ Distribution

The mathematical statement (Eq. 3E.10 and Eq. 3E.11) that T₂ distribution observed in water-saturated rock represents the pore-size distribution and porosity of the rock has been confirmed using mercury-injection capillary pressure (MICP) methods (see Figs. 3E.14 and 3E.15).

NMR responds to pore-body size, and MICP responds to pore-throat size. In clastic rocks in which there is a good correlation between pore-body and pore-throat size, there is often good qualitative agreement between NMR and MICP data, as Figs. 3E.14 and 3E.15 illustrate. The NMR porosity, reflected in the T₂ distribution, is a spectrum comprising rock matrix and fluid components (see Fig. 3E.16).

• 

  Fig. 3E.14 – The correlation between MICP and T₂ distribution in water-saturated sandstones.

• 

  Fig. 3E.15 – The correlation between MICP and T₂ distribution in water-saturated carbonates.

• 

  Fig. 3E.16 – NMR-porosity model. These figures illustrate the distribution of pore size and pore fluids used in NMR logging. The suggested NMR mnemonics are Halliburton’s. Because NMR tools respond to the invaded zone, a mud-filtrate component is added between movable water and oil. NMR-logging tools are sensitive to fluids but not to matrix materials and dry clay. NMR porosity is affected by HI, T_W, and T_E.

Although matrix minerals and dry clay may contain hydrogen atoms in the form of hydroxyl groups, the T₁ relaxation times of these nuclei are too long to be polarized by a moving NMR-logging tool, and their T₂ relaxation times are too short to be recorded. The fluid component is subdivided into bound and free subcomponents. The hydrogen nuclei of clay-bound water are adsorbed on the surfaces of clay grains. These hydrogen protons can be polarized by NMR-logging tools and recorded when a sufficiently short T_E is used. Similarly, hydrogen protons in capillary-bound water and movable fluids (e.g., free water, mud filtrates, oil, and gas), are polarized and recorded by NMR-logging tools with appropriate values for T_E and T_W.

The porosity and pore-size information from NMR measurements can be used to estimate producible porosity (i.e., the movable fluids) and permeability and for hydrocarbon identification (see the Applications section of this chapter).

Logging Tools

Compared to laboratory or clinical NMR, the dimensions of a typical borehole and the nature of continuous logging impose severe constraints on the physics, equipment, and operation of NMR-logging tools. Unlike laboratory devices, logging measures an external sample by use of a weaker magnetic field while in motion relative to the sample.

NML Tool

The NML tool—the first generation of NMR logging (1960–1994)—was an Earth’s field device that measured the free-induction decay in the Earth’s magnetic field. Proton polarization (alignment) was achieved using a magnetic field produced by a coil energized with a strong direct current. Each experiment required several seconds to allow complete polarization. The power was turned off, and the same coil was used to receive the free-induction signal.

There were a number of problems inherent in this technology. NML devices measured the proton signal in the borehole fluid as well as in the surrounding formation. Magnetite powder was circulated into the mud system to cancel the borehole hydrogen signal thereby preventing it from overwhelming the formation signal. This was a time-consuming process. The low intensity of the Earth’s magnetic field (0.5 gauss) resulted in a low S/N. The NML had a large dead time (i.e., time between the cessation of the static magnetic field and the first measurement), approximately 20 ms; pore fluids with relaxation times less than the dead time were not measurable. The initial signal amplitude had to be extrapolated backwards from the subsequent free-induction decay data. The NML could not distinguish between oil and water or measure total porosity; however, the dead time was close to the T₂ cutoff established for irreducible water saturation. The NML could detect movable fluids and provided a measurement called the Free Fluid Index (FFI). An expanded discussion of the NML technology can be found in Brown and Neuman and Brown.

Pulse NMR

Unlike conventional magnetic resonance imaging (MRI) devices in which the sample is placed inside the stationary coil, a borehole-logging device investigates a sample (rock volume) that is outside the device itself while moving along the borehole. This setup has been called the "inside-out" NMR problem because the geometry of the magnets and coils is inverse to that used in laboratory-NMR spectrometers. To obtain useful measurements, a logging tool must generate a large, radially symmetric static magnetic field and also a high-frequency oscillating magnetic field. Each must be capable of penetrating one or more inches into the formation surrounding the borehole. The diameter of a typical well limits the size of the permanent magnets that can be used and, therefore, the strength of the magnetic field that can be generated by a logging device. In comparison with laboratory-NMR and clinical-NMR devices, which may operate at 10 MHz and the static magnetic fields of which are commonly in the range 1 to 2 Tesla (high field), modern logging tools and laboratory spectrometers designed for petroleum investigations are considered low-field devices. They operate at or below 2 MHz and generate relatively weak (< 200 gauss) and inhomogeneous magnetic fields (i.e., gradients up to 20 gauss/cm). By comparison, the NML operating frequency was only 2 kHz, and the Earth’s magnetic field is only 0.5 gauss. These factors limit borehole investigation to protons (hydrogen) and the use of relaxation data only. Chemical shifts (widely used in the biological field) are not observable. Furthermore, to compensate for the lower S/N that results from low-field intensity, logging tools must acquire more echoes and/or stack data to improve S/N. As mentioned previously, with the introduction of pulse-echo tools, T₂ became the primary acquisition mode because it permitted faster logging—a major factor in high-cost wells.

This new design provides a number of operational advantages over the NML:

• Using permanent magnets rather than electromagnets reduces the surface-power requirement.
• Focusing the sensitive region of the magnetic field at some distance into the formation eliminates the requirement for suppressing the mud signal.
• Using an RF pulse from a coil tuned to the Larmor frequency ensures that only nuclei in the sensitive region are in resonance.
• Controlling the pulse duration means shorter dead times that, in turn, allow a better estimate of initial decay amplitude (porosity) measurement for short T₂ components (bound-fluid evaluation).
• Enabling more sophisticated pulse sequences allows for measurement of additional rock and fluid properties.

One initially unwanted product of this design is the creation of gradients in the static magnetic field that causes molecular diffusion. The strength of the magnetic field gradient, G, is controlled by tool design and configuration (i.e., tool size and tool frequency); by environmental conditions such as formation temperature; and by internal gradients induced by the applied field, B₀. Subsequent characterization of these gradients has enabled the in-gradient diffusion to be used for hydrocarbon typing.

Wireline-Tool Designs

From the beginning, a debate in NMR logging has been whether to use a centralized or eccentered tool design. There are two different wireline designs in current commercial service: (1) the Numar (now a part of Halliburton) magnetic resonance imaging tool (MRIL), a centralized mandrel device; and (2) the Schlumberger CMR tool and the Baker Atlas MREX eccentered devices, both of which require contact with the borehole wall. The general designs of both the MRIL (mandrel-type) and CMR (pad-type) have evolved over the past decade with the addition of new capabilities and faster logging speeds, made possible by improved electronics and improved data acquisition and processing. Computalog is field testing a prototype mandrel device: the Nuclear Magnetic Resonance Tool (NMRT) developed by NPF Karotazh.

A centralized NMR-logging tool like the MRIL must be longer than a pad device, simply to contain magnets of sufficient strength to project the required magnetic field, through the borehole and into the formation. This factor results in a greater sensitivity to borehole salinity than a pad device, which can exclude the mud from its measurement. The MRIL design generates relatively thin (1 to 2 mm) sensitive volumes, but the reduced S/N that accompanies these volumes is compensated by the vertical size of the sensitive area. It also generates a relatively high magnetic gradient. In contrast, a contact device, such as the CMR, can use smaller magnets and electronics, which provide higher vertical resolution but a shallower depth of investigation (DOI) and greater sensitivity to borehole rugosity. In addition to the standard permanent magnets, some designs now include "prepolarization" magnets, which are added to ensure full polarization at typical logging speeds.

The latest wireline NMR-logging tools operate simultaneously in several RF frequencies to measure (image) multiple sample volumes. In the presence of a gradient magnetic field, pulses with different frequencies will cause protons in different (and parallel) regions of space (i.e., measurement or sensitive volumes) to resonate. Cycling through several frequencies excites protons in different cylindrical volumes, allowing measurements to be made more quickly. If the frequencies of multifrequency measurements are very close together, then the sensitive volumes are very close together; and, for practical purposes, the rocks sampled can be considered to be the same. This principle is the same as that used for slice selection in medical MRI imaging. These tools acquire multiple echo trains using different values of T_W, T_E, and variable magnetic gradients (G) in a single logging pass. The time between measurements made at multiple frequencies can be as little as the time of an echo train, and the time between measurements made at a single frequency is essentially the time needed to repolarize (T_W). The thickness of these sensitive volumes may be as small as 1 mm. Furthermore, recent advances in tool design now permit cost-effective T₁ acquisition. Table 3E.4 summarizes the capabilities, advantages, and disadvantages of T₁ and T₂ acquisition. These differences influenced the designs of the LWD tools discussed in the next section. Multifrequency operation provides measurements at multiple DOIs (typically 1 to 4 in.). This allows invasion effects to be accounted for in the data interpretation, thus enabling determination of near-wellbore fluid saturation and oil properties at high resolution.

• 

  Table 3E.4

LWD Tools

The latest entries into NMR logging are LWD tools. The development of LWD-NMR is ongoing and significant changes in hardware design, as well as significant changes and improvements in data acquisition and processing, can be expected in the next few years. The general benefits of LWD have been discussed elsewhere—in particular, NMR-LWD offers a nonradioactive alternative for porosity measurement, an NMR alternative to wireline in high-risk and high-cost wells, and enables high-resolution fluid analysis in thin beds and laminated reservoirs.

By definition, logging tools operating in the drilling environment are built into drill collars and are, therefore, mandrel devices. In contrast to wireline tools, they must be capable of making measurements when the drillstring is stationary, sliding or rotating, centered or eccentered.

LWD-tool measurements are either omnidirectional or azimuthal, depending on tool design. The incorporation of magnetometers allows binning of the data into azimuthal sectors. Omnidirectional measurements can be generated from azimuthal data, but not the reverse. Although current LWD-NMR services provide only omnidirectional data, patents have been issued for tools with azimuthal capability.

A major concern introduced with the advent of LWD-NMR is the effect of drillstring lateral motion on the basic NMR measurement. NMR measurements are not instantaneous, they involve both polarization and decay, time-dependent components. Lateral movement of a wireline tool or LWD drillstring shifts the polarization volume and the sensitive-measurement area, relative to one another, and these shifts may result in incomplete polarization or incomplete measurement of the decay. Low-velocity motion affects only the decay, but high-speed motion can also affect the initial decay amplitude.

The currently available LWD tools offer different solutions to this concern. While both tool designs can operate in either T₁ or T₂ acquisition mode and both incorporate accelerometers and magnetometers for detecting lateral motion for quality control of the NMR measurements, they differ in their choice of primary measurement mode. Operational factors, such as the slower logging speed (i.e., rate of penetration in drilling), compared with typical wireline logging, also affect the choice of measurement mode.

The NMR acquisition sequences are programmable and interchangeable with those used in wireline tools. Switching between these acquisition modes is accomplished by a variety of methods, including elapsed time, counting measurements, and differentiating between drilling and nondrilling conditions. T₁-mode records echo amplitudes as a function of time. Data output consists of porosity, free-fluid, and bound-water volumes, and can provide a quick-look permeability estimate. T₂-mode is a multifrequency mode that records multiple wait-time CMPG spin-echo amplitudes and is capable of using all wireline-pulse sequences. T₂-mode output includes porosity, free fluid, clay- and capillary-bound water, and differences in the multiple wait-time data are used for hydrocarbon indication.

The Halliburton tool (MRI-LWD) uses T₁ as its preferred acquisition mode. Halliburton considers T₁ more robust for determining porosity and free-fluid volume. The anticipated maximum rates of penetration for LWD—1 to 3 ft/min—allow T₁ acquisition. T₁ is motion tolerant compared with T₂. A sequence of interleaved measurements made at different recovery times is used to construct the T₁ relaxation decay (buildup). As long as the sensitive volume (shell) is contained within the much larger volume reached by the saturation pulse, the measurement is valid. During post-processing, drilling and nondrilling periods are identified, and the invalid T₁ data recorded during drilling are discarded.

Schlumberger’s tool (ProVision LWD-NMR) uses T₂ for its primary measurement. While both companies agree that T₁ is motion tolerant, Schlumberger considers T₁ to be less robust for estimating porosity, bound-fluid, and free-fluid volumes because of the poor S/N resulting from the longer time require for equivalent-quality T₁ measurements. A reduced S/N impacts data quality (e.g., statistical repeatability and vertical resolution), logging speed, and, ultimately, the results. T₂ measurement also enables rapid calibration and correlation with the large body of wireline-NMR data. The multiple wait-time acquisition includes a fully polarizing (3 to 12 seconds), a partially polarizing (normally 0.6 to 1 seconds), and a very fast wait time (typically 0.08 seconds). Porosity and bound-fluid volume are calculated for both the long- and the medium-wait-time measurements, and significant differences between the long-wait-time and medium-wait-time porosity provide real-time hydrocarbon indication. When necessary, logs are corrected for incomplete polarization of the hydrogen nuclei, and T₁ distributions are estimated from the measured T₂ relaxation.

Baker Atlas is presently field testing a new LWD device (MagTrak) that operates in T₂ acquisition mode and has a vertical resolution of less than 3 in. This tool design achieves a motion-tolerant T₂ measurement through a combination of a very-low gradient magnetic field, circuitry that permits a T_E as low as 0.6 ms, and the use of special stabilizers.

Downhole NMR Spectrometer

Contamination of hydrocarbon reservoirs by oil-based mud (OBM) and synthetic oil-base mud (SOBM) is a significant problem for accurate reservoir and fluid analysis in wells in which OBMs are used, especially offshore. Direct knowledge or an estimate of the OBM’s NMR characteristics is required to distinguish it from connate oil in fluid samples obtained by formation testers. Acquisition of T₁, T₂, and D₀ (the self-diffusion coefficient) permits evaluation of connate oil, oil viscosity, and gas/oil ratio. Furthermore, in costly drilling environments, real-time acquisition of NMR properties permits immediate, rather than delayed, fluid evaluation. Information on NMR fluid properties is also valuable for the interpretation of NMR wireline and LWD logs.

The recently introduced downhole NMR spectrometer, incorporated into a formation-testing tool, can obtain NMR measurements of OBM contamination directly, on live samples at in-situ conditions. As the testing tool pumps fluid from the reservoir into the borehole or sample chamber, the spectrometer—using a measurement time of 30 seconds—measures the hydrogen index (HI), T₁, T₂, and diffusion. The T₁ measurement is made while flowing; T₂ and diffusion are static measurements. The T₁ distribution is important in differentiating between highly refined OBM filtrates and native oil. The T₁ characteristics of these common filtrates are measured and cataloged so that the data from oil-based filtrates can be distinguished from native hydrocarbons.

Log-Presentation

NMR-log data are presented in a variety of formats designed to emphasize specific aspects of the data and thus enable rapid visual interpretation of movable and immovable fluids, porosity, and permeability. Data interpretation is further enhanced when additional log and core information are also included in the log presentation.

The T₂ distribution is typically displayed in waveform presentation, image (variable-density log, VDL) format, and bin-distribution plot. Each T₂ format represents the distribution of the porosity over T₂ values, and hence, over the pore sizes (Figs. 3E.17 and 3E.18).

• 

  Fig. 3E.17 – Log presentation illustrating some of the formats used to present T₂ distributions: Track 1, a plot of the cumulative amplitudes from the binned T₂-distribution; Track 2, shallow, medium, and deep resistivity log curves; Track 3, a color VDL image of the binned T₂ distribution; Track 4, a waveform presentation of the same information. The displayed T₂ distribution typically corresponds to binned amplitudes for exponential decays that may range from 0.5 to 1,024 ms. Logging data are much noisier than laboratory data, and the T₂ distribution shown on well logs is comparatively coarse.

• 

  Fig. 3E.18 – Integrated NMR-log evaluation. This log presentation includes GR, caliper, and SP (Track 1), resistivity data (Track 2), NMR T₂ distribution (Track 3), DSM-analysis results (Track 4), TDA analysis results (Track 5), and NMR-resistivity integrated analysis results (MRIAN, Track 6).

NMR Applications

NMR-log data can be analyzed independently or in combination with conventional-log and core data. As an independent logging service, NMR can provide porosity, permeability index, and complete information on fluid type and saturation of the flushed zone. Some data-interpretation methods operate in the echo-decay time domain, while others operate in the T₂-relaxation domain.

Porosity Determination with NMR

The initial amplitude of the spin-echo train is proportional to the number of hydrogen nuclei associated with the fluids in the pores within the sensitive volume. This amplitude is calibrated in porosity units (see Eq. 3E.10). The accuracy of this amplitude measurement depends on three factors: first, a sufficiently long polarization time, T_W, is needed to achieve complete polarization of the hydrogen nuclei in the fluids; second, a sufficiently short inter-echo spacing, T_E, is needed to record the decays for fluids associated with clay pores and other pores of similar size—if either T_W is too short or T_E too long, NMR porosity will be underestimated; third, the number of hydrogen nuclei in the fluid should equal the number in an equivalent volume of water (i.e., HI = 1); if the HI of any of the pore fluids is significantly less than 1, a correction to porosity is necessary.

Porosity was one of the earliest NMR measurements and is still an important one. Assuming that the logging tool is properly calibrated and functioning normally (see discussion of Quality Control in this chapter), interpretation of the porosity measurement depends on several other factors, including vintage of the logging tool, whether hydrocarbons are present, and fluid type.

There are two major contrasts between NMR porosity and conventional density and neutron-nuclear-porosity logs. First, NMR porosity does not depend on the mineralogy of the matrix, except in cases in which the formation contains significant amounts of ferromagnetic or paramagnetic materials, and in most cases, it is considered a lithology-independent measurement. Second, NMR porosity is not sensitive to either borehole or mudcake and does not require corrections because the measurement zone (i.e., sensitive volume) is focused within the formation, beyond the borehole wall and these influences. The accuracy and precision of NMR-derived porosity has been confirmed through comparisons with core porosity obtained using conventional laboratory measurement methods (Fig. 3E.19).

• 

  Fig. 3E.19 – Comparison of core- and log-NMR porosity. In this clean sandstone example, there is good agreement between porosity derived from laboratory-NMR measurements and porosity derived from conventional core analysis. NMR-porosity values typically fall within ±1 p.u. of the measured core-porosity values. Here, NMR-laboratory data were measured at T_E = 0.5 ms and T_E = 1.2 ms.

Influence of Tool Version on the Porosity Measurement. The original NML tool had such a large dead time (e.g., minimum echo spacing, T_E) that it could not measure clay- and capillary-bound fluids; thus, it was only capable of measuring free-fluid porosity, which is now called NMR effective porosity (MPHI). The minimum T_E used in the early versions of pulse-NMR tools was still relatively large, and those tools still could not see all the clay-bound fluids. With improvements in logging technology, most NMR logs recorded after 1997 are considered "total-porosity" logs. Current logging tools use a minimum T_E of 0.3 ms in continuous mode and a T_E as small as 0.1 ms in stationary mode.

In clean, water-filled formations, MPHI should approximately equal neutron-density crossplot porosity. In shaly sands, MPHI should approximately equal density porosity, calculated with the correct grain density; however, the MPHI may not equal effective porosity because of the effects of HI and long T₁ components (Eq. 3E.12):

....................(3E.12)

where MPHI is measured by the NMR tool; ϕ_e is effective porosity of the formation; HI is related to the amount of fluid in the effective porosity system; T_W is polarization time used during logging; and T₁ is longitudinal relaxation time of the fluid in the effective porosity system. Older NMR logs may indicate very low porosity in shales.

MPHI is almost always less than NMR total porosity (MSIG):

....................(3E.13)

where MSIG is measured by NMR total-porosity logging, and clay-bound-water porosity (MCBW) is measured by the NMR tool with partial-polarization acquisition. In very clean formations, however, NMR MCBW is virtually zero, and then MPHI equals MSIG (see Fig. 3E.16).

NMR total porosity may approximate density or neutron-density porosity. The reported clay-bound volume should not be considered absolute because the boundary between clay- and capillary-bound porosity components can vary with clay type and distribution. Whenever possible, the relationship of clay type and volume should be confirmed through core analysis and comparison with other log data.

Porosity-Logging Modes. Several modes of porosity logging are currently in use: standard T₂ mode, short T_W (e.g., bound-fluid logging), intermediate T_W (e.g., polarization correction and the "clean, wet formation" method), and long T_W, or multiple-wait-time acquisition (e.g., total-porosity logging).

Total-porosity-logging mode provides data to determine porosity, permeability, and productivity (mobile fluids). Total-porosity acquisition is a multiple-wait-time acquisition that acquires two echo trains to obtain the total porosity. One echo-train acquisition uses a long T_E (e.g., 0.9 or 1.2 ms) and a long T_W (3 to 8 seconds) to achieve complete polarization. This echo train provides the effective porosity. The second echo-train acquisition uses a short T_E (0.2 to 0.6 ms) and a short T_W (20 ms) that is only long enough to achieve complete polarization of the fluids in the small pores (i.e., clay-bound porosity). Although the long T_W acquisition may achieve full polarization in gas zones, the porosity may still require HI correction. The short T_W echo trains are stacked to improve S/N. Total porosity is obtained by combining the two separate T₂ distributions, usually at 4 ms. The standard T₂ acquisition is used in situations in which there is little to no diffusion or T₁ contrast. The benefits of standard T₂ acquisition are increased logging speed without degradation of data quality; or superior data quality at normal logging speeds.

In bound-fluid logging mode, T_W is kept relatively short, ranging from 0.3 to 1.0 seconds. The benefit of using a short T_W is faster logging speeds while determining the clay- and capillary-bound fluid volumes. The drawback is underpolarization of the free-fluid volume.

When this logging mode is used, the free-fluid volume is computed from other log data (e.g., density, neutron-density crossplot, or acoustic). In polarization mode (CMR tool), a correction to the free-fluid volume is made using the observed relationship of T₁ to T₂, on the basis of the T₂ acquired while logging. The magnitude of the polarization correction must be monitored because, in addition to porosity, the T₁/T₂ ratio is also influenced by changes in the types of formation and pore fluid. This method generally works well in clastics, but in conditions of high T₁ and T₂, such as in carbonates or light oil, the correction may actually introduce additional error.

Another mode of operation is to find a clean, wet formation and perform a sweep of different wait times (T_W) ranging from 2 to 5 seconds to determine the one needed for full polarization. Because oil and gas may have very long T₁ values or require an HI correction, the use of intermediate T_W methods does not guarantee that the NMR porosity will be fully reported.

Optimization of the acquisition is critical to accurate NMR measurements and interpretation (see the Job Planning section of this chapter). The effect of incorrect acquisition parameters on the T₂ distribution is illustrated in Fig. 3E.20. In this figure, the sequence of graphs shows the effects of T_E, T_W, pulsing time (T_P), and S/N on the measured NMR characteristics of a core sample:

• A: Initial acquisition results show an apparent unimodal distribution.
• B: Increasing the T_P shows that this sample is, in fact, bimodal. There is a significant change in the T₂ distribution, but little to no change in the cumulative porosity.
• C: Decreasing the echo spacing (T_E) reveals fast components in this sample that were previously masked by a T_E that is too long. There is a significant change in the cumulative porosity with a characteristic shift of the fastest components in the distribution to shorter T₂ values.
• D: Increasing the wait time (T_W) has significantly increased cumulative porosity. After correction for a T_W that is too short, there is a characteristic shift in the slow T₂ components to longer T₂ values.
• E: Increasing the S/N results in sharper resolution of the two major components. Although the definition of each component in the T₂ distribution improves, little change is noted in the cumulative porosity.
• F: The final result, in which all acquisition parameters have been optimized (red), is compared with the initial result (blue).

BVI Determination. Determining the BVI of water in a formation is one of the earliest and most widely used applications of NMR logging. BVI refers to the immovable or bound water in a formation. BVI is a function of both the capillary-pressure curve for the rock and the height above free water (Fig. 3E.21).

• 

  Fig. 3E.20 – Dependence of T₂ distribution on NMR-acquisition parameters. In all figures, blue represents previous results, red represents new results, solid lines represent incremental T₂ (read on the left axis), and dashed lines represent cumulative T₂ vs. T₂ relaxation time (read on the right axis).

• 

  Fig. 3E.21 – Correlating NMR T_2cutoff to capillary pressure: (a) grains are shown in gray, capillary-bound water (BVI) in light blue, and free fluids in a gradient tone blue/red; (b) capillary pressure curve (black dots) defines capillary pressure (P_c) in which water saturation becomes irreducible (S_wirr); (c) a single-porosity cutoff value on the T₂ distribution, corresponding to this pressure.

In practice, BVI serves as an indicator of, and is used for, estimating producibility and permeability. There are two methods currently used for BVI determination. One is the cutoff-BVI (CBVI) model, which is based on a fixed-T₂ value (T_2cutoff) that divides BVI and FFI. The second is the spectral BVI (SBVI) model, which assumes the coexistence of free and bound fluids in any pore described by the T₂ distribution at water saturation (S_w) = 100%. This coexistence is expressed through a weighting factor that defines the fraction of bound water associated with each pore size. The SBVI method is used primarily for quantifying movable water and, secondarily, for estimating permeability.

CBVI (Cutoff) Model. The T₂ signal from the rock matrix is actually so rapid that even modern logging tools cannot detect it. Consequently, the recorded T₂ distribution represents only the porosity occupied by movable (FFI) water and immovable BVI and clay-bound-water (CBW) components. Assuming that the mobility of reservoir fluids is primarily controlled by pore size (i.e., the producible fluids reside in large pores and the immobile, or bound, fluids reside in small pores), a fixed-T₂ value can relate directly to a pore size at or below which fluids will not move. This value (T_2cutoff) is used to divide the T₂ distribution into movable (i.e., producible or free fluids and FFI) and immovable (i.e., bound-fluid, BVI, and CBVI) components (Fig. 3E.22). T_2cutoff is a variable that differs from one formation to another and is influenced by a variety of factors including capillary pressure, lithology, grain size, compaction, and pore characteristics.

• 

  Fig. 3E.22 – Illustration of the T_2cutoff used in the CBVI model to divide NMR porosity into movable and immovable components.

In practical use, T_2cutoff is either determined in the laboratory or a default value is assumed. If time and expense permit, accurate T_2cutoff values can be defined by comparing the T₂ distributions obtained on fully and partially water-saturated core samples taken from the logged interval (Fig. 3E.23).

• 

  Fig. 3E.23 – Determination of T_2cutoff from core measurements. NMR measurements on fully saturated (S_W = 100%) core samples at irreducible saturation (S_wirr) can be used to establish a T_2cutoff for use in CBVI model. The T₂ distributions are displayed as incremental porosity and cumulative porosity. The cumulative curves are used to determine T_2cutoff.

In the absence of laboratory data, lithology-dependent default values are used for T_2cutoff. Default T_2cutoff values are based on local field experience or common practice; for example, typical values used in the Gulf of Mexico are 33 ms for clastics (sandstones) and 92 or 100 ms for carbonates. When using a default value, remember that, in fact, the T_2cutoff can actually vary within a single lithology because the capillary pressure at which irreducible water saturation (S_wirr) is achieved varies between the actual rocks. In addition, T_2cutoff is also influenced by pore-wall chemistry, the presence of minor paramagnetic or ferromagnetic components, texture, and pore-throat to pore-body ratios. The use of an incorrect value for T_2cutoff may result in underestimation of recoverable reserves or in bypassing a pay zone.

SBVI (Spectral) Model. The SBVI model was developed to address the limitations of the CBVI model in some rocks, particularly in very-well-sorted rocks in which there is a very narrow range of grain and pore sizes. In these rocks, the NMR echo-decay can typically be fit by a single-exponential decay that produces a sharp peak in the T₂ distribution. When a fixed cutoff is used for determining BVI, it may result in significant error because of the presence of immovable water contained in microporosity associated with pore irregularities. This microporosity component is apparent at S_wirr, but not at S_w = 100% (Fig. 3E.24).

• 

  Fig. 3E.24 – BVI associated with microporosity in a coarse-grained rock having a narrow range in pore sizes. The T₂ distribution at S_w=100% exhibits a single sharp peak (upper). The T₂ distribution at S_w<100% exhibits two peaks (lower). One appears below the T_2cutoff value, the result of the irreducible water on the pore surfaces. The other appears above the T_2cutoff and represents the oil in the pore fluid. The T₂ value of the second peak is close to the T₂ of bulk oil. This same effect is seen in a North Sea chalk.

A weighting function defines the fraction of bound water in each pore size that is present in the T₂ distribution at S_w = 100% (Fig. 3E.25). Several methods have been proposed for obtaining the weighting function.

• 

  Fig. 3E.25 – SBVI model. For a given T₂, the SBVI-weighting factor provides the fractional volume of irreducible fluids in the pores whose size is associated with that T₂. The model shown is a step function and is commonly used to describe the weighting factors.

In general, the SBVI method is superior to the CBVI method for determining BVI in rocks in which S_w = 100%. The presence of hydrocarbons (i.e., S_w < 100%), however, introduces complications to the SBVI method. To overcome the limitations of both methods for determining BVI, the recommended practice is to compute two bound-water values—one from the cutoff (CBVI) and one from the spectral (SBVI) method—and take the larger of the two.

Permeability Estimation

The ability to estimate formation permeability is one of the earliest benefits of NMR logging and remains the most important application. Laboratory studies demonstrate that pore-water relaxation time is inversely related to the S/V ratio of the pore space (Fig. 3E.26). The NMR estimate of permeability is based on theoretical and core-based models that show that permeability increases with increasing porosity and pore size (S/V).

• 

  Fig. 3E.26 – Variation in T₂ decay with permeability. This plot illustrates the difference between echo trains obtained from formations with similar porosity but different pore sizes. In terms of T₂ distribution, this difference is expressed in different FFI/BVI ratios. The permeabilities were computed using the Timur-Coates model.

The measurement of formation permeability, in general, is greatly influenced by the method used, the limitations of each, and the scale at which the measurements are made. As stated previously, MICP curves obtained on core samples correlate to pore-throat size, while NMR measures pore-body size.

NMR logging does not provide direct and continuous measurement of permeability; rather, a formation-permeability estimate, or index, is calculated from the spectral-porosity measurements using permeability models that are based on a combination of empirical and theoretical relationships. Several permeability models have been developed, and two are in common use: the free-fluid (Timur-Coates or Coates) model and the mean-T₂ [the Schlumberger-Doll-Research (SDR)] model. The free-fluid model can be applied to water-saturated and hydrocarbon-saturated reservoirs, and the mean-T₂ model can be applied to water-saturated reservoirs. These permeability models assume that a good correlation exists between porosity, pore-body and pore-throat size, and pore connectivity. This assumption is generally valid in clastic (e.g., sand/shale) sequences, but in carbonates or other lithologies, model-derived permeabilities may not be reliable.

Typically, a permeability model is calibrated over a particular zone of interest and verified, wherever possible, by core or well/formation test data. Once this is done, the NMR log can provide a robust continuous-permeability estimate within the zone of interest.

Both models treat permeability as an exponential function of porosity, ϕ⁴, and include a parameter to account for the fact that NMR measures pore-body size, not pore-throat size (Fig. 3E.27). In the Coates model, the pore-size parameter enters implicitly through T_2cutoff, which determines the ratio of FFI to BVI. In the SDR model, the size parameter enters through the geometrical mean of the relaxation spectra, T_2gm. In water-saturated rocks, both models provide similar and good results; however, when hydrocarbons are present, the SDR model fails because T_2gm is no longer controlled exclusively by pore size.

• 

  Fig. 3E.27 – NMR-permeability models. The free-fluid permeability, Coates, model (top) uses the MFFI/MBVI ratio to describe the changes in the S/V ratio. The SDR permeability model (bottom) uses an average T₂ value to describe changes in S/V.

Free-Fluid (Timur-Coates or Coates) Model. In the simplest form of the free-fluid model, permeability, k_Coates, is expressed as follows (Eq. 3E.14):

....................(3E.14)

where ϕ is MSIG, MBVI is obtained through the CBVI or SBVI method, MFFI is the difference between MSIG and MBVI (assuming that there is no clay-bound water, see Fig. 3E.16), and C is a formation-dependent variable. The free-fluid model is very flexible and has been calibrated using core data for successful use in different formations.

To calibrate the model to core, Eq. 3E.14 is solved in the form of a straight line, y = mx + b:

....................(3E.15)

Assuming b = 0 in the equation (3E.15), core permeability is substituted for k. The slope of the line, m (i.e., C value in Eq. 3E.15), is determined using a least-squares regression (Fig. 3E.28).

• 

  Fig. 3E.28 – Crossplot of core and NMR data used for determining the Coates permeability constant, C. Assuming b = 0 in Eq. 3E.15, core permeability is substituted for k, and the slope of the line, m, is the C value in Eq. 3E.14.

Despite the flexibility of this model there are formation conditions that limit the effectiveness of the model and may require a correction (Table 3E.5). The presence of hydrocarbons (i.e., oil, oil filtrate, or gas) in the BVI component may result in an overestimate of BVI by either the CBVI or SBVI methods, leading to an underestimate of permeability. An HI correction can be applied when gas is present. The very short T₂ values associated with heavy oil may be counted in the BVI component and result in an underestimate of permeability.

• 

  Table 3E.5

Mean-T₂[Schlumberger-Doll-Research (SDR)] Model. Using the SDR model, permeability is expressed as

....................(3E.16)

where ϕ is NMR effective porosity (MPHI), T_2gm is the geometric mean of the T₂ distribution, and C is a formation-dependent variable. The SDR model works very well in water-saturated zones. In the presence of oil or oil filtrates, the mean T₂ is skewed toward the T_2bulk, because of the effects of partial polarization, leading to an overestimate of permeability. In unflushed gas zones, mean-T₂ values are too low relative to the flushed-gas zone; and permeability is underestimated. Because hydrocarbon effects on T_2gm are not correctable, the SDR model fails in hydrocarbon-bearing formations. The Coates and SDR models represent matrix permeability and, therefore, are not applicable to estimation of permeability in fractured formations.

Other Comments on NMR-Based Permeability Estimation. Table 3E.5 compares the Coates and SDR models under different reservoir conditions, and it may be advisable to use both methods in an effort to constrain values for permeability.

There are a number of benefits in having available NMR-derived permeability and BVI. This information enables more-accurate quantification of reservoir heterogeneity and improves estimation of reserves and ultimate recovery. Other applications include optimizing the locations of perforations, well spacing, tailoring completions to maximize recovery rates and efficiencies, and improving primary and secondary recovery design schemes.

Hydrocarbon (Fluid) Typing

The NMR T₂-porosity relationship in which T₂ is a function of pore size (i.e., S/V ratio, see Eq. 3E.8) holds for water-saturated rocks. The presence of hydrocarbons in water-wet rocks alters the T₂ distribution, thus affecting the porosity interpretation. Despite the variability in the NMR properties of fluids, the locations of signals from different types of fluids in the T₂ distribution can often be predicted or, if measured data are available, identified (Fig. 3E.29).

• 

  Fig. 3E.29 – NMR-oil typing. The position and spread of the oil component in the T₂ distribution depends on oil viscosity and formation wettability. Oil typing is easiest in water-wet formations because of the moderate breadth and distinct positions of the different oil components in the T₂ distribution. Oil typing is most difficult in mixed-wet formations because the oil and water components are broad and overlap one another.

Hydrocarbon typing and prediction of fluid properties by NMR logs is predicated on reliable laboratory correlations between NMR measurements (i.e., relaxation times and diffusion) and fluid properties [e.g., specific gravity, viscosity, and gas/oil ratio (GOR)]. Early studies were limited to investigations at ambient conditions; however, using the standard correlations derived from these studies may result in seriously underestimating viscosity. More-recent studies have expanded these correlations to oils and mud filtrates at reservoir conditions.

NMR logging uses specialized CMPG pulse-acquisition sequences to exploit these differences in pore-fluid NMR properties to achieve specific objectives. The CMPG parameters—wait time (T_W), echo spacing (T_E), the number of echoes (N_E), and the number of sequence repetitions—are selected to take advantage of the wide variation in NMR fluid properties (Fig. 3E.30) for estimating total porosity and for hydrocarbon typing. Table 3E.2 illustrates the range of NMR-related properties of fluids for Gulf of Mexico sandstones, for example. Table 3E.6 lists variations in CMPG pulse sequences for different objectives using time-domain analysis (TDA) and Enhanced Diffusion Method (EDM). The multifrequency tools now in service permit the simultaneous acquisition of multiple measurements on the same rock volume using different acquisition sequences during the same logging run. The general approach is to log in a mode that allows gathering the full spectrum of data. Specialized applications, including some direct fluid-identification methods, involve customized-acquisition sequences that require slower logging and acquisition of more echoes.

• 

  Fig. 3E.30 – Typical NMR properties for pore fluids. Differences in these properties between fluids are exploited by methods that use specific acquisition sequences for hydrocarbon typing buy use of T₁ or diffusion-weighting mechanisms.

• 

  Table 3E.6

Determination of the appropriate interpretation method is largely based on the estimated viscosity of the anticipated hydrocarbons (see Fig. 3E.31). These methods will be explained in the following paragraphs.

• 

  Fig. 3E.31 – Graph indicating the current viscosity limits for NMR-interpretation techniques. The resistivity-density technique is limited to gas reservoirs, and the SSM method has been effectively replaced by the newer DSM method. The y-axis is the relaxation time.

Selection of the appropriate acquisition sequence and the choice of acquisition parameters depend on the logging objectives and are part of prejob planning. This process considers several factors regarding the anticipated rock and pore-fluid properties. For example, for characterizing large pores (clastics), clean formations, carbonates, and light oil—all of which are associated with long-T₂ values—a large number of echoes should be acquired, and a longT_W should be used. However, more echoes and longer T_W may require reduced logging speeds. In contrast, characterization of small pores (i.e., low permeability), shaly formations, low porosity, and BVI determination involves the short T₂ component of the NMR-porosity spectrum and often it can be accomplished using fewer echoes and shorter T_W, which may allow normal logging speeds.

Fluid-typing methods fall into two broad categories depending on the NMR properties that are being exploited: (1) T₁-weighting mechanisms take advantage of differences in fluid T₁ values, and (2) diffusion-weighted mechanisms make use of the diffusion-constant differences between oil and water. There are two general types, or sets, of CMPG acquisitions that are associated with each mechanism: dual T_W and dual T_E. These two sets cover the range of major fluid-typing objectives; some interpretation techniques can use one or the other, or both. Each serves specific purposes and is optimized to provide data for specialized analysis programs. In general terms, each consists of at least two echo-train acquisitions in which one or more parameters are varied. The total, or the difference between the echo-train signals, provides an estimate or indicator of porosity, light hydrocarbons, or oil (Fig. 3E.32).

• 

  Fig. 3E.32 – CPMG acquisition types used for hydrocarbon typing: (a) a T₁-weighted method is used to differentiate hydrocarbons from water, and (b) a diffusivity-weighted method is used to differentiate viscous oil from water or to differentiate gas from liquids.

Advanced hydrocarbon-typing objectives can involve customized-acquisition sequences that are run at reduced logging speeds or even in stationary mode.

T₁-Weighted Mechanism (Dual-T_W Acquisition). The dual-T_W acquisition method is used primarily to identify and quantify light hydrocarbons (gas and light oil) by separating them from the water signal through T₁ weighting. The dual-T_W acquisition can also provide the standard-T₂ acquisition dataset for determination of spectral NMR porosity, permeability, and productivity (mobile fluids). The T_E is kept the same in both echo-train acquisitions (0.9 or 1.2 ms), and a short T_W (1 second) and long T_W (8 seconds) are used. The water signal is contained in both acquisitions, but because of the light hydrocarbons (which have long T₁ values), the signal is suppressed in the acquisition using the short T_W. Thus, the presence of a signal in the difference of the measurements (differential spectrum) is considered a strong indicator of gas or light oils (Fig. 3E.33).

• 

  Fig. 3E.33 – Methods using T₁-weighting for hydrocarbon typing: (a) in TDA, T₂ echo-train subtraction takes place in the time domain, and (b) in the differential-spectrum method (DSM), T₂ echo-train subtraction takes place in the T₂ domain.

Fluid volumes can be quantified by integrating the difference into T₂ spectra and correcting for the polarization difference between long and short wait times. Fluid typing and quantification are performed through the differential-spectrum (DSM) method and the TDA method. Two conditions must be met to ensure successful DSM interpretation: T₁ contrast between the hydrocarbon and brine phases (i.e., a water-wet formation containing light hydrocarbons), and T₂ contrast between the gas and oil phases. DSM assumes that the hydrocarbon phases relax uniexponentially. DSM is commonly used for: (1) hydrocarbon typing in shaly sands, where the the neutron-density crossover may be suppressed because of the high amount of clay minerals in the rock to confirm the presence of light oil in fine-grained rock, and (2) for gas detection in the presence of OBM invasion. Ideally, DSM can be used to compensate for the hydrocarbon effects on NMR measurements and thereby enable correction of NMR total porosity and NMR effective porosity; however, because of S/N requirements, TDA is the preferred technique for correcting NMR logs.

In contrast to the DSM approach, the TDA technique works directly with the echo-decay data (i.e., in the time domain rather than the T₂ domain; see Fig. 3E.34). The measured long- and short-wait-time decay trains are subtracted into an echo difference that indicates the presence of a long-T₂ component (usually a hydrocarbon). By working in the time domain, when the T₂ inversion is performed, only the hydrocarbon T₂ component will be present.

• 

  Fig. 3E.34 – Example of TDA. Track 1 shows the pore volumes for gas(red), OBM filtrate and/or native oil (green), movable water (dark blue), and capillary-bound water (light blue) obtained from TDA quantitative analysis using an MRIL data set. Tracks 2 and 3 show the T₂ and T₁ values, respectively, of gas and light oil calculated through TDA. The lower part of Track 2 shows the oil/water and gas/oil contacts, while the upper part of the track indicates the presence of gas and oil.

TDA—an outgrowth of the DSM technique—is based on the fact that different fluids have different rates of polarization (i.e., different T₁ relaxation times). TDA provides the following results:

• Fluid types in the flushed zone.
• Corrected NMR porosity in gas reservoirs.
• Corrected NMR porosity in light oils.
• Complete fluid-saturation analysis in the flushed zone, using only NMR data.

The TDA technique is a more robust method than DSM, in part because it provides better corrections for underpolarized hydrogen and HI effects (Figs. 3E.34 and 3E.35).

• 

  Fig. 3E.35 – Log examples showing the results of DSM and TDA analysis. Light hydrocarbons can be identified through the subtraction of echo trains obtained at two polarization times. Track 4 displays the differential spectrum obtained from the subtraction of the two separate T₂ distributions derived from echo trains acquired with short- (T_WL) times, T_WS = 1 second and T_WL = 8 seconds. The water signals in each completely cancel, while hydrocarbon signals only partially cancel and remain when the two T₂ distributions are subtracted from one another. Track 5 displays the TDA results. TDA is performed in time domain (as opposed to T₂ domain), and can quantify up to three phases (gas, light oil, and water; gas and water; or light oil and water).

Several factors inherent in the dual-T_W acquisition require reduced logging speeds: to achieve full polarization (long T_W) in one acquisition channel, to acquire the small signal amplitudes associated with the short T_W values in another other channel, and to meet the requirement for acceptable S/N levels. A new triple-wait-time method addresses these issues and also allows T₁ acquisition.

Diffusion-Weighted Mechanism (Dual-T_E Acquisition). NMR-logging tools generate relatively large field gradients, which are a function of the operating frequency and tool type. If the pore fluids have high diffusivity constants (D₀), these large gradients may cause diffusion to become the dominant T₂-relaxation mechanism, even at a reasonably short interecho time. The T₂ contrast between the liquid and gas phases can then be exploited for hydrocarbon typing.

The identification of viscous oil in water-wet rock using T₁-weighting mechanisms (dual-T_W acquisition) is very difficult because there is little T₁ contrast between water and viscous oil. However, a significant difference in the diffusion characteristics of water and viscous oil is used to create a T₂ contrast that separates the two NMR signals, thereby permitting identification. The inter-echo spacing, T_E, is chosen long enough that the water and oil signals are fully separated in the T₂-domain (i.e., water is at lower T₂ than oil; see Fig. 3E.36).

• 

  Fig. 3E.36 – EDM example. The existence of a signal on the T₂ distribution longer than the T_2DW indicates the presence of oil in the formation. In this log display, the T₂ distributions from T_E = 1.2, 3.6, and 4.8 ms are shown in Tracks 3, 4, and 5, respectively. In the EDM results, in Track 4 and 5, a significant signal to the right of the T_2DW line indicates obvious oil zones. Also note the increased definition and separation in the fluid signal that occurs in Track 5 because of the increased T_E. This observation is used to recognize pay in EDM-log displays.

Diffusion-weighting techniques, such as shifted-spectrum method (SSM), enhanced-diffusion method (EDM), and diffusion analysis (DIFAN), use the dual-T_E acquisition to create this T₂ contrast. T_E is chosen such that diffusion, rather than surface relaxation, is the dominant relaxation mechanism, and thus, the upper limit of T₂ for pore water is T₂ diffusion, designated T_DW. The dual-T_E acquisition set uses long T_W and T_E values, typically 0.9 or 1.2 ms and 3.6 or 4.8 ms, respectively. In this acquisition, the fluid with the larger diffusion constant (water) has a spectrum shifted more to earlier times than the fluid with the smaller diffusion constant (viscous oil). The presence in the spectra of a minimally shifted portion identifies high-viscosity oil in the formation (see the lower portion of Fig. 3E.37). These techniques are primarily used for identifying the presence of viscous oil. They are also used in carbonates in which a reduced surface relaxation (compared to clastics) may also result in a reduced T₁ contrast.

• 

  Fig. 3E.37 – SSM application in gas (upper) and oil (lower) reservoirs.

SSM. This method was the first developed using the diffusion-weighted mechanism and was originally developed for use in gas reservoirs as a qualitative technique (see the upper portion of Fig. 3E.37). However, because of signal-processing difficulties and slower logging speeds, this method was effectively replaced by the EDM.

EDM. This method is the later variation of SSM. Depending on oil-NMR properties and the job objective, EDM data processing can be done in either the T₂ domain or time domain. If the EDM objective is to discriminate pay from nonpay, then a single CMPG measurement with long T_W (for full polarization) and long T_E (for diffusion enhancement) is sufficient; thus, standard-T₂ logging with a long T_E can be used. If the EDM objective is to quantify fluids in a pay zone, then dual-T_E logging will be required. The short-T_E measurements will provide correct MPHI and BVI. If the T₂ contrast over the zone of interest is not expected to be large enough to separate the T₂ values of water and oil, then dual-T_W logging with a single, long T_E may be required to obtain data for TDA processing.

One caveat for users of the EDM: the flushed-zone saturation (S_xo) obtained from EDM may not reflect the true volume of residual hydrocarbons in the flushed zone if the faster portion of the hydrocarbon’s T₂ spectrum gets fully polarized by both wait-time measurements. A correction to S_xo can be applied if the full-hydrocarbon T₁ spectrum can be determined by other means, such as laboratory measurements.

DIFAN. DIFAN is an empirical model used for quantitative-diffusion analysis. This method uses a dual-T_E acquisition and is useful for typing and quantifying oils with viscosities ranging between 0.5 to 35 cp at reservoir conditions (i.e., temperature ≥ 200°F and pressure ≥ 2,000 psi). It is not recommended for light oils and condensates because the D 0 contrast between hydrocarbons and water is too small.

Neither EDM nor DIFAN is recommended for use in high-viscosity oil (heavy oil) because the difference between the T₂ values of dead oil and irreducible water is too small. The DIFAN model generates two T₂ distributions using the two echo trains generated from dual-T_E logging.

Echo Ratio Method. An apparent diffusion coefficient, calculated from the ratio of long and short T_E echo-train data (time domain), serves as a qualitative gas indicator. This method is accurate and provides a direct measurement of gas volume, but requires high HI values for good results.

The dual-T_W and dual-T_E techniques described above only provide T₂ distributions and are considered one-dimensional methods. Oil-saturation determination using these methods may be difficult or even impossible because differential diffusion-weighted methods assume that NMR water and hydrocarbon signals can be cleanly separated by subtracting the acquisitions made at different T_E values. In practice, however, partial—or even total—overlap is common.

To avoid these problems, new multifluid-forward models were developed to take advantage of the full suite of data obtained using the latest multifrequency logging tools. These models perform a simultaneous inversion of the NMR fluid properties obtained in multiple parameter-domain dimensions (e.g., T₁, T₂, and D₀). These methods make use of the enhanced T₂ relaxation in a magnetic-field gradient (i.e., incorporate measurement of the diffusion coefficient, D₀) and the large contrast between diffusion coefficients of oil and water. In effect, they are simultaneously combining both T₁- and diffusion-weighted processing techniques, and thus, provide more accurate and robust results. In addition to porosity and permeability information, the output data from these inversion models are plotted as two-dimensional plots (e.g., D-T₂ plot) in which the oil and water signals are clearly separated. Recent two-dimensional NMR techniques include diffusion editing, diffusion mapping, and relaxation-diffusion 2D.

Multidimensional (2D and 3D) NMR analysis greatly increases the accuracy of fluid typing and saturation determination. These methods are particularly useful for identifying highly diffusive fluids (e.g., gas, condensate, and light oil) and for identifying wettability alteration caused by OBM-filtrate invasion or chemical surfactants used in enhanced recovery operations. This information is essential for reservoir simulation, development, and production.

Residual Oil (S_xo) Calculation

Estimation of residual-oil saturation is one of the oldest applications of NMR logging. Unlike resistivity-log analysis, NMR analysis does not rely on formation-water salinity to obtain water saturation. This feature provides NMR logging with a distinct advantage over conventional resistivity analysis in mixed or unknown salinity conditions—an advantage that can be extremely useful in waterflood or steamflood projects for evaluating residual-oil saturation after the flood or to look for bypassed oil. Initially, NMR evaluation of residual-oil saturation required use of a dopant (e.g., Mn-EDTA and MnCl₂) to flush the invaded zone with paramagnetic ions to shorten the bulk relaxation time of the brine. This process enabled separation of the oil and water signals, leading to direct measurement of S_xo. With the combination of modern multifrequency NMR tools and new methods of analysis, such as EDM and TDA, the use of borehole dopant is no longer necessary. Standalone NMR interpretation is possible in OBM, but in water-base-mud (WBM), it is possible only when S_wirr is known.

Viscosity Evaluation

In water-wet rocks, the NMR-relaxation spectrum is controlled by viscosity; relaxation is directly related to viscosity, η, by Eq. 3E.17:

....................(3E.17)

For oil and water, the diffusion constant, D₀, can be approximated by Eq. 3E.18:

....................(3E.18)

where A = 2.5 for water, A = 1.3 for oil, and T_K is temperature in K.

NMR properties of gas can be obtained from published charts that relate viscosity to (1) the center of the relaxation curve, (2) to an American Petroleum Inst. (API) standard value, or (3) from published formulas. These published sources assume that methane is the dominant component of the gas. In the absence of laboratory data at in-situ conditions, reservoir NMR properties can be estimated by use of Eq. 3E.17. One note of caution: Eqs. 3E.17 and 3E.18 are based on "dead oil" measurements. As mentioned earlier, the relaxation-time dependence on viscosity/temperature of live crude oil may differ significantly from correlations based on hydrocarbon liquids at ambient conditions.

Anisotropy and Geomechanics

NMR T₁ and T₂ relaxometry and derived permeability can be used to determine the Biot elastic constant, which is used for estimating pressures that are critical to sand control, hydraulic fracturing, wellbore stability, and determination of formation stress.

Low-Permeability (Tight) Sandstones

Field experience indicates that invasion or imbibition in tight sands is very shallow. Depending on borehole size, the diameter of invasion, and fluid properties, a mandrel tool may have sufficient DOI to measure beyond the flushed zone. A combined interpretation using both T₁ and T₂ can provide positive identification of fluids in these reservoirs. In addition, in these tight formations, in which formation testers typically may not obtain a fluid sample within a reasonable time period, NMR fluid characterization can separate hydrocarbon from oil filtrate and other pore fluids.

Heavy Oil, Tar Sands, and Tar Mats

The early acquisition of reliable viscosity information is essential to efficient development of heavy-oil reservoirs. NMR logs offer a viable alternative to downhole fluid sampling for determining viscosity information in heavy-oil reservoirs. The presence of tar mats in a reservoir, commonly near the bottom of the oil column, may form vertical permeability barriers and, thereby, isolate the oil leg from the water-drive aquifer. NMR logs, in conjunction with conventional logs, can provide accurate identification of tar-mat levels and viscosity estimation, from empirical relationships. (See the Job Planning section of this chapter.)

Carbonates and Comples Lithologies

NMR-log evaluation is relatively routine in what might be termed "conventional reservoirs," namely those of homogenous lithology and uniform pore sizes, typically sandstone and chalk reservoirs. In contrast, log evaluation of complex and heterogeneous reservoirs, with complex pore geometries, is not straightforward. These reservoirs include, in particular, the highly important Middle East carbonates, as well as other reservoirs comprised of mixed lithologies and mineralogies, or both, in which wettability may also vary. In these reservoirs, there is likely no simple relationship between petrophysical properties and porosity. Instead of a dependence on the volume of pore space, they are dependent on the typically heterogeneous pore distribution, pore types, pore connectivity, and grain sizes. This fundamental difference between siliciclastic and carbonate rocks (primarily the result of diagenetic processes) limits the applicability of routine NMR methods, especially permeability evaluation. Improving NMR evaluation of carbonates has proved challenging and is the subject of a number of recent studies and proposed techniques. (See the Job Planning section of this chapter.)

Pseudocapillary-Pressure Curves

As discussed in the Petrophysics section, establishing a correlation between NMR T₂ distribution and MICP is fundamental to NMR interpretation and the computation of S_w. Once such correlations are established for a particular reservoir or field, pseudocapillary-pressure curves can be generated directly from the NMR-log relaxation-time distributions.

Productibility

Accurate determination of BVI enables evaluation of reservoir-fluid (e.g., gas, oil, and water) contacts, production characteristics (producibilty), and the determination of net and recoverable reserves. Furthermore, NMR-derived permeability can be used to generate idealized flow profiles across a completion interval. These profiles provide a diagnostic tool for identifying nonflowing portions of the zone and the need for remedial work.

Combined NMR Applications

NMR tools have shallow depths of investigation and provide results only for the invaded zone. NMR-log data can be integrated with core data and conventional log data (i.e., neutron, density, acoustic, and resistivity) in post-acquisition processing to provide improved determinations of reservoir rock properties, hydrocarbon storage capacity, and reservoir productivity in a variety of environments including gas-bearing and low-resistivity reservoirs. Interpretation models that include NMR data can provide more reliable results than those using only conventional logs.

The combination of NMR and deep-resistivity data provides a complete analysis of the fluids in the uninvaded zone. Resistivity measurements alone cannot distinguish between capillary-bound and movable water, but they do represent deep investigations of fluid saturation. Furthermore, resistivity-based methods are often inadequate or unreliable in reservoirs in which salinity and lithology vary. The addition of NMR-derived BVI and CBW from the flushed or invaded zone can significantly enhance the estimation of resistivity-based fluid saturation, both in clastics and carbonates. The addition of NMR data allows the identification and evaluation of water-free production in low-resistivity formations (Fig. 3E.38).

• 

  Fig. 3E.38 – Integrated-NMR-resistivity shaly sand analysis. Whereas resistivity logs (Track 2) read very low values and indicate that the zone below XX200 is water wet, NMR measurements show that BVI (Track 4, gray) increases with depth. However, T₂ measurements (Tracks 3 and 4) suggested the presence of hydrocarbon, which testing confirmed in what turned out to be a water-free zone.

The combination of conventional deep-resistivity data with NMR-derived CBW, BVI, FFI, and MPHI can greatly enhance petrophysical estimations of effective pore volume, water cut, and permeability. It is the preferred technique for identifying low-resistivity pay zones. Fig. 3E.38 presents the results of Halliburton’s MRI analysis (MRIAN) service in a turbidite sequence. The sand below XX200 depth has an average resistivity of approximately 0.5 ohm-m (Track 2) and average neutron-density porosity of approximately 38% (Track 4). A quick look, or preliminary analysis, using only the conventional data presented in Tracks 1, 2, and 4, would label this a wet zone. MRIL-NMR data are also presented in Track 1 (T₂-distribution bin data), Track 2 [NMR-derived permeability (Coates)], and Track 3 (VDL presentation of T₂ distribution). The MRIAN results, BVI, and FFI are presented in Track 4. BVI gradually increases with depth, suggesting that the sand is fining downward (i.e., as sand grains become finer, the volume of capillary-bound water that they hold increases). Comparison of the BVI with the resistivity profile (Track 2) shows that the resistivity decreases where the bound water increases. The MRIAN analysis clearly shows that the zone does not contain any movable water and will produce only oil. The interval below XX200 was tested and produced oil with no water.

The combination of NMR fluid identification with resistivity-derived saturation provides a better understanding of hydrocarbon movement in gas monitoring, as seen in the following field example (Fig. 3E.39).

• 

  Fig. 3E.39 – Integrated-NMR and resistivity analysis.

NMR and LWD logs were run in a deviated Middle East light-oil carbonate reservoir to monitor gas injection. NMR logs were well suited for gas monitoring by use of the TDA technique and were not affected by formation-water salinity. NMR gas-corrected porosity was in close agreement with core porosity; conventional log-porosity was low because of salinity effects. Combined interpretation of water-saturation analyses from tools with different depths of investigation identified the movable fluid present in the reservoir as WBM filtrate. Track 1 contains T₂ bin data and conventional SP and gamma ray curves; Track 2 shows NMR-permeability derived from the standard Coates model and LWD resistivity; Track 3 contains a T₂ distribution in a variable-density format; Track 4 contains T₂ distributions of data acquired with long T_W and short T_W; Track 5 is the differential spectrum; Track 6 contains TDA results; and Track 7 contains MRIAN results.

NMR Acoustic/Density Combination

Because NMR tools are affected by the lower HI in gas-bearing reservoirs, a moving tool may not fully polarize the gas, which has a long T₁. Conventional acoustic and density logs are not influenced by these factors and, when used jointly with NMR logs, they can provide robust porosity evaluation. The basic assumptions of these techniques are that the reference porosity is measured correctly (e.g., appropriate matrix density is used) and that the NMR T_W is long enough to recover the water but not all of the gas. If the T_W is too short, a false gas signal may be seen. One way to check whether the T_W is appropriate is to log with a longer wait time (e.g., T_W = 2 seconds rather than 1 second) and look for a significant difference in porosity (i.e., the porosity may be slightly higher because of increased polarization of the gas).

NMR-Log Quality Control

Quality control (QC) procedures are especially important during the creation of integrated computed products and to ensure optimal NMR data acquisition. NMR tools have calibration standards and real-time QC indicators. Standard techniques include examination and verification of service company calibrations and QC curves, and calibrations and examination of the repeatability of the computed porosities. Processed results should agree with other data from logs, core, and/or formation test results. NMR QC includes a series of prejob and post-job checks and calibrations.

Prejob Calibration and Quality Checks During Logging

Several prejob QC steps are necessary to ensure reliable results. These steps are described in this section.

Frequency Check. The amplitude of the NMR measurement is proportional to the square of the magnetic field strength in the measurement region. To attain maximum signal strength, the tool must operate at the correct frequency. Because temperature affects magnetic field strength, a frequency sweep is recorded before the calibration and logging run and is repeated downhole to account for changes in temperature. The CMR tool includes sensors that monitor temperature and changes in the magnetic field strength and adjusts frequency automatically to changes in sonde temperature. The accumulation of metal drilling debris on the magnets can adversely affect the NMR measurements, and the tool may require occasional retuning. The MRIL-gradient field creates a self-correcting effect, and the tool rarely requires retuning after the initial downhole tuning. Drifting off frequency may present itself as a loss of porosity (CMR) or loss of precision (MRIL). Field calibration should be included on the log.

Statistical Calibration. A statistical calibration to 100% porosity (water) should be made at the shop and/or wellsite before and after every logging job for all combinations of T_E frequency and for expected quality factor (Q level); calibration should be done at the shop at least monthly. Primary calibration involves either a flask of fluid (for the CMR tool) or a water tank (for the MRIL tool).

HI. NMR-tool calibration uses water where HI = 1. However, when the HI of the formation pore fluids is expected to be less than one, the NMR-porosity readings will be proportionally lower, and correction is necessary. An NMR tool’s processing software will, therefore, compute a correction based on the salinity of the mud filtrate and on the maximum formation pressure and temperature. In general, a mud-filtrate relaxation time of < 200 ms may suppress the long T₂ components in a T₂ distribution. A specific HI value may be used when residual hydrocarbons or OBM filtrates are present.

System Gain. CMR and MRIL tools monitor and calibrate in real time for downhole changes in system gain. A gain measurement is made as a part of each pulse sequence. Gain indicates the amount of loading applied to the NMR tool’s transmitter circuit by borehole fluid and formation resistivity. Gain is affected by changes in temperature, mud conductivity, and borehole size. Because gain is frequency dependent, the operating frequency of a tool should be set to achieve maximum gain. Abrupt changes or spikes in gain should not be present. For a particular MRIL tool, the gain value determines the appropriate acquisition power (Q) level.

System Noise (Ringing). Noise contamination of the spin-echo signal, known as ringing, may be a remnant of the RF pulsing process. Noise can interfere with the echo trains and, when present, is usually evident in the NMR porosity readings, either as poor repeatability or lack of agreement with other tools. Both tools (CMR tool and MRIL tool) monitor ringing.

χ. χ is a measure of the quality of fit between the calculated decay curve and the recorded echo amplitudes. Problems with the echo data are likely to be reflected in the χ curve. In general, the value of χ should be less than two but may average slightly higher in certain situations. Spikes in χ may correlate with spikes in porosity and usually indicate tool problems, even if χ remains lower than two. χ serves as is a primary MRIL log-quality indicator and is monitored while logging.

Correction for RF-Tipping Pulse. The strength of the CMPG RF pulse (B₁) that produces proton tipping and rephasing is measured as part of every pulse sequence and requires correction for changes in borehole temperature. If the pulse angles are either < 90° or > 90°, the magnetization will be undertipped or overtipped, respectively. The measured amplitude will, thus, be too small, and porosity will be underestimated. The B₁ curve should be relatively constant but should show some variation with changes in borehole and formation conductivity. B₁ will decrease across conductive washouts and conductive formations. Changes in the B₁ values should track changes in total conductivity and vary together in the same direction as gain. The need for excessive correction (i.e., > 5% of the optimum shop-peak value) may indicate a tool problem and can result in undertipping or overtipping of the protons, a reduced S/N ratio, and a loss of precision in determining porosity. Sudden changes in the B₁ correction curve may also indicate a tool problem.

γ. Regularization methods are used to select a smooth T₂ distribution that is consistent with the spin-echo sequence. These methods require a parameter γ that is automatically computed from the raw echo data. Values of γ are dependent on the S/N ratio and the shape of the underlying T₂ distribution. In high-S/N environments (i.e., medium-to-high-porosity formations), typically γ < 5; in low-S/N environments (i.e., tight sands and shales), γ > 10.

Repeatability. Whenever possible, a repeat pass should be recorded with parameters identical to those used in the main pass. These parameters include T_W, N_E, and T_E, as well as computation parameters such as the echoes selected for processing, and for T_2cutoff. The generally accepted goal for porosity is a standard deviation of 1 porosity unit (p.u.). Repeatability of BVI is usually > 1 p.u., and repeatability of FFI is usually >> 1 p.u.

If repeatability is a concern, decreasing logging speed or increasing the degree of echo data stacking during logging in post-job processing can improve S/N ratio and repeatability. Typically, fluid-typing applications using dual-T_W or dual-T_E methods are more sensitive to data repeatability than a standard NMR log acquired for porosity, bound fluid, and permeability.

A given data set should agree with similar data acquired by other logs, formation tests, and/or core analysis.

Environmental Corrections. NMR logs are similar to neutron logs in that they respond to the hydrogen volume present in a sample. Because the hydrogen volume changes with temperature and pressure, NMR logs require environmental corrections for temperature and pressure similar to those applied to neutron logs. Also, the magnitude of NMR resonance (and S/N ratio) varies inversely with temperature. NMR-logging tools include a temperature sensor to acquire the data needed for this correction. At high temperatures, data stacking can be increased or logging speeds reduced to compensate for a lower S/N ratio.

Porosity Check. NMR porosity can serve as an important diagnostic of data quality. High porosity readings may result from washouts (e.g., borehole fluid in the sensed volume), tool problems, improper environmental corrections or calibration issues, loss of pad contact (for the CMR tool), tool eccentering, or borehole ellipticity (for the MRIL tool). Low porosity readings may result from insufficient wait time, light-hydrocarbon effects, the presence of heavy oil, improper frequency tuning, and/or calibration error.

Post-Logging Quality Check

NMR-log responses should be checked against conventional logs when they are available (see the Applications section of this chapter).

NMR-Log Job Planning

In some complex reservoirs, low-resistivity/low-contrast pay, low-porosity/low-permeability, and medium-to-heavy oil, NMR-log data—independently or in combination with other log data—provide the best and/or only means of accurate formation and fluid evaluation. Because NMR-log data acquisition is complex, job preplanning is essential to ensure optimal selection of acquisition parameters that will result in reliable and accurate data and in the maximum information possible in any given reservoir and logging environment. A clear understanding of the logging job objectives is necessary for optimizing the NMR acquisition parameters to best achieve these objectives. This process must take place before the actual logging.

Typical preplanning consists of three steps:

• Define the need for NMR measurements.
• Collect all available borehole (e.g., diameter, mud, salinity, and temperature) and reservoir (e.g., formation and fluid properties) information needed to assess the expected NMR responses in the zone of interest, and understand what can and cannot be resolved with NMR.
• Select the appropriate tool (on the basis of operational considerations, borehole size, and condition) and acquisition type (i.e., determining the appropriate acquisition parameters, data resolution, and logging speed) that will provide maximum answers for a given job.

Although the actual in-situ reservoir characteristics may be unknown, estimates of the anticipated fluid properties, based on available information such as reports for nearby wells or fields, are used to define and optimize an acquisition sequence that will provide the data needed to meet the job objectives.

In addition to job objectives, determination of the appropriate NMR-acquisition parameters is also influenced by operational considerations and the anticipated in-situ reservoir properties (Fig. 3E.40). The most critical factors follow.

• 

  Fig. 3E.40 – Reservoir and operational factors influencing the choice of CMPG acquisition.

Lithology

Although reservoir lithology generally plays a minor role in NMR-data acquisition, it does play a significant role in data analysis and interpretation. Aspects of reservoir lithology that influence reservoir T₂ values include the following.

Carbonates. Different T_2cutoff values are required because surface relaxivity in carbonates is weaker than in sandstones, resulting in slower relaxation rates (longer T₂). Longer T₁ in carbonates than in sandstones may require longer T_W during acquisition. (See the Application section of this chapter.)

Isolated Pores. The presence of relatively isolated pores (e.g., vugs) will not affect NMR porosity, but it will cause the standard permeability equations (Coates and SDR) to overestimate permeability. (See the Permeability section of this chapter.)

Ferromagnetic and Paramagnetic Minerals. The presence of these minerals may enhance surface relaxation significantly, shifting the T₂ spectrum to very short relaxation times. Depending on the amount of paramagnetic material, relaxation may become too fast to be detected, and the NMR measurement will underestimate porosity. In these cases, standard cutoff values do not apply.

Heavy Oil and Tar Sands. Intervals containing these types of hydrocarbons have very fast relaxation components and may not be detected using conventional acquisition methods. Special methods have been developed for detection and accurate evaluation of these reservoirs. (See the Applications section of this chapter.)

Wettability

Wettability can have a significant impact on NMR-log response. The use of NMR for determination of wettability has been extensively studied both in laboratory and in the field. In general, petrophysical-NMR studies and NMR-logging applications assume reservoir rocks are water wet; however, because mixed-wettability reservoirs do exist (e.g., some carbonates, black shales, and heavy-oil reservoirs), this assumption may lead to incorrect reserve estimates and to unexpected dynamic behavior during waterflood. When a pore is water wet, oil relaxes at its bulk rate. In mixed-wettability reservoirs, the oil and water each relax through a combination of bulk relaxation and surface interaction and depend on the ratio of water-wet surface area to water volume and oil-wet surface area to oil volume. The oil relaxation spectra will be shifted from bulk relaxation into the irreducible-water part, resulting in complex spectra that are difficult to interpret. Nevertheless, these shifts provide qualitative wettability indicators that allow NMR logs to provide an early indication of reservoir wetting behavior.

The invasion of OBM or SOBM can alter formation wettability and is a significant concern in NMR logging, which typically measures fluid and formation properties in the flushed zone. Invasion by these muds can alter strongly water-wet sandstones and carbonates to intermediate-wet or oil-wet rocks. In water-wet reservoirs that have undergone OBM or SOBM invasion, the T_2cutoff model may significantly underestimate S_wirr because wettability alteration changes the water and oil relaxation-time distributions. The magnitude of underestimation depends on the type of OBM surfactants, their concentration in the flushing fluid, and the flushing volume. Controlling the volume of OBM invasion and the concentration of OBM surfactants should minimize the effects of OBM invasion on estimation of S_wirr.

Borehole Rugosity

NMR-logging tools have relatively shallow DOIs. Pad-type tools (e.g., the CMR tool) are run eccentered and require good contact with the borehole wall for accurate measurements. Measurements made by pad-type tools can be significantly affected by severe borehole rugosity and washouts, resulting in overestimation of porosity.

Mandrel devices are run centered, and DOI can range from 1 to 4 in., depending on borehole size. The sensitive area is normally beyond minor borehole rugosity. When borehole conditions result in an elliptical borehole (e.g., breakouts or erosion) or otherwise inhibit or prevent centralization (e.g., in highly deviated or horizontal boreholes), contact tools may be a better choice if pad alignment and contact with the borehole wall can be maintained.

Mud Type

The quality of NMR data acquired in OBM is generally superior to that acquired in WBM. The conductivity of OBM is lower; lower conductivity reduces loading effects on the transmitter/receiver system, resulting in higher S/N ratio. This issue is of greater concern for mandrel tools (e.g., MRIL tool) because, in conductive muds, the power of the RF pulse is reduced as the pulse is transmitted across the borehole. The use of fluid-excluding sleeves can minimize this problem.

Signal dissipation in conductive mud is not a serious concern for pad-type tools (CMR) that maintain contact with the borehole wall. Because NMR tools read the flushed zone, OBM filtrate invasion produces an additional hydrocarbon signal that may significantly complicate log interpretation. Careful prejob planning can reduce interference of the OBM-filtrate signal and the response from the native fluids. The relatively long T₁ relaxation times and diffusivity of OBM make it difficult to differentiate its signal using the shifted-spectrum or differential-spectrum approaches.

Metal Debris

Metal drilling debris in the borehole fluid may affect NMR-measurement quality by distorting and altering the logging tool’s magnetic field. The pad-type tool is more susceptible to field distortion. Metal debris should be removed from the mud, either through the use of the prepolarizing magnets (included in the latest tool designs) or by using magnets at the shale shaker. A new wireline tool uses an autotuning feature to correct the operating frequency for changes in the static magnetic field caused by metallic debris in the borehole.

Logging Speed and Running Average

The logging speed of an NMR tool is influenced by a number of factors, primarily by tool type (e.g., centered or eccentered, number of operating frequencies, or length of antenna), logging objectives (e.g., acquisition type—T_W, T_E, or N_E—sequence repetitions and vertical resolution), and borehole properties (e.g., diameter and mud resistivity). S/N ratio is primarily controlled by borehole size and mud resistivity. As S/N ratio decreases, the running average (RA) needed to maintain a specified error in porosity increases. The general practice is to require a porosity standard deviation of ≤ 1 p.u. The value of RA and the antenna aperture (i.e., length), combined with the logging speed, determines the vertical resolution. Even so, there is always a complex tradeoff in logging speed, accuracy (e.g., S/N ratio or N_E), and job objectives. High accuracy and precision require reduced logging speeds. A method for increasing the overall logging speed is to reduce the vertical resolution in zones of secondary or no interest and also to reduce the vertical resolution in homogeneous intervals.

Vertical Resolution

The vertical resolution of NMR-logging tools is primarily a function of antenna length (i.e., tool design) and logging speed. The maximum vertical resolution, usually obtained when the tool is at rest (e.g., in stationary mode), is the length of the antenna. During continuous logging, vertical resolution decreases at a rate proportional to logging speed. Contact-logging tools, in general, use smaller sensors and antennae and, thus, have better vertical resolution than centered tools. The contact-NMR tool (i.e., the CMR tool) has a resolution advantage when bed thickness is in the range between 0.5 and 5 ft. Outside of this range, both designs deliver similar results. Prejob planning includes selecting a logging speed to obtain the optimum resolution.

Post-job data reprocessing to enhance bed resolution may result in a loss of repeatability. Vertical resolution can also be improved by optimizing the NMR signal through the removal of signal noise during data processing.

Summary

This chapter has outlined the fundamental properties that are measured by NMR tools and has reviewed the use of these measurements to discern various characteristics of the reservoir rock including its fluid contents. Whether used as a standalone service or in combination with other logs and core data, NMR logs can provide an improved understanding of reservoir petrophysics and producibility. However, NMR logs are the most complex logging service introduced to date and require extensive prejob planning to ensure optimal acquisition of the appropriate data needed to achieve the desired objectives. Review of the references cited in this chapter indicates the rapid pace of advancement in NMR logging research, development, and applications. Users of NMR logging, including engineers, log analysts, petrophysicists, and geologists, should anticipate new developments in this discipline, as reported by SPE, the Soc. of Petrophysicists and Well Log Analysts (SPWLA), and other publications noted in the references.

NMR-Tool Mnemonics

Table 3E.7 presents a cross reference of logging-tool output-data mnemonics for the different service companies currently offering NMR-logging services.

• 

  Table 3E.7

Nomenclature

A	=	pore-fluid-specific value used to approximate the diffusion constant
a	=	constant in the mean-T2 and viscosity relationship
B0	=	static magnetic field, gauss
B1	=	amplitude of the oscillating magnetic field perpendicular to B0, gauss
C	=	coefficient in the Coates permeability model
D0	=	molecular diffusion coefficient, gauss/cm
f	=	Larmor (precessional) frequency, Hz
G	=	field-strength gradient, gauss/cm
k	=	permeability, darcy
kCoates	=	permeability derived using the Timur-Coates model, darcy
kSDR	=	permeability derived using the mean-T2 model, darcy
M	=	magnetization, gauss/cm3
M0	=	macroscopic magnetization, gauss/cm3
M0i	=	magnitude of the initial magnetization from the ith component, gauss/cm3
M0x	=	magnitude of the transverse magnetization at t = 0, gauss/cm3
M100%	=	magnitude of the magnetization for 100% bulk water, gauss/cm3
Mi(0)	=	magnitude of the initial magnetization from the ith component of relaxation gauss/cm3
M(0)	=	magnitude of the initial magnetization, gauss/cm3
M(t)	=	measured magnetization at time t, gauss/cm3
Mx(t)	=	transverse magnetization at time t, gauss/cm3
Mz	=	strength of magnetic field, gauss/cm3
Mz(t)	=	longitudinal magnetization at time t, gauss/cm3
NE	=	number of echoes
Pc	=	capillary pressure, dynes/cm2
Q	=	quality factor of a resonant circuit
Rt	=	true formation resistivity, ohm-m
(S/V)i	=	ratio of pore surface (S) to fluid volume (V), of the ith pore, 1/cm
(S/V)pore	=	ratio of pore surface (S) to fluid volume (V), 1/cm
Sw	=	water saturation, %
Swirr	=	irreducible water saturation, %
Swb	=	clay-bound water saturation, %
Sxo	=	flushed-zone saturation, %
t	=	time, seconds
T	=	temperature, °C
T1	=	longitudinal relaxation time, seconds
T1bulk	=	pore-fluid bulk-T1 relaxation time, seconds
T1surface	=	pore-surface T1 relaxation time, seconds
T2	=	transverse relaxation time, seconds
T2bulk	=	pore-fluid bulk-T2 relaxation time, seconds
T2cutoff	=	T2 cutoff value, seconds
T2diffusion	=	pore-fluid T2 relaxation time in a magnetic field gradient, seconds
T2DW	=	upper limit of the measured T2 for water, seconds
T2gm	=	T2 geometric mean value, seconds
T2i	=	pore-fluid surface T2 relaxation time of the ith component, seconds
T2surface	=	pore-fluid surface T2 relaxation time, seconds
TDW	=	dual wait time—the value of TE such that diffusion, rather than surface relaxation, is the dominant relaxation mechanism, seconds
TE	=	CMPG interecho spacing, seconds
TK	=	absolute temperature, K
Tp	=	pulsing time, seconds
TW	=	polarization (wait) time, seconds
TWL	=	polarization time, long, seconds
TWS	=	polarization time, short, seconds
Vshale	=	shale volume, %
x, y, z	=	cartesian space coordinates
γ	=	gyromagnetic ratio—the ratio of the magnetic dipole moment to the mechanical angular momentum, Hz/gauss
ΔTE	=	incremental change in echo spacing, seconds
ΔTW	=	incremental change in wait time, seconds
η	=	fluid viscosity, cp
ξ	=	apparent T1/T2 ratio of fluid
ρ1	=	T1 surface relaxivity, cm/sec
ρ2	=	T2 surface relaxivity, cm/sec
τ	=	time over which an oscillating field is applied
ϕ	=	porosity, %
ϕe	=	effective porosity, %
ϕeff	=	effective porosity, %
ϕH	=	hydrocarbon porosity, %
ϕi	=	calibrated porosity associated with all pores of the i th pore size
ϕt	=	total porosity, %
ϕw	=	water porosity, %
χ	=	goodness of fit

Acknowledgements

The authors of this chapter wish to acknowledge the help provided by the many former and current staff of Halliburton Energy Services who have been involved with the development of NMR logging. All figures except Fig. 3E.21 were provided courtesy of Halliburton Energy Services.

References

SI Metric Conversion Factors

cm2/sec	×	1.0*	E + 02	=	mm2/sec
cp	×	1.0*	E − 03	=	Pa•s
°C	273.15		=	K
dynes/cm2	×	1.0*	E − 01	=	Pa
ft	×	3.048*	E − 01	=	m
ft/min	×	5.080*	E − 03	=	m/sec
°F		(°F + 459.67)/1.8		=	K
gauss	×	1.0*	E − 04	=	Tesla
in.	×	2.54*	E − 02	=	m
ohm-m	×	1.0*	E − 02	=	ohm-cm
psi	×	6.894 757	E + 00	=	kPa

*

Conversion factor is exact.