nmrlog

Nuclear Magnetic Resonance Log

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Objective

The development of the nuclear magnetic resonance (NMR) log was fueled by the desire

to obtain an estimate of permeability from a continuous measurement. Previous work

had relied on empirical correlations with porosity and irreducible water saturation.

Unfortunately, these correlations are an order of magnitude in accuracy. Other

alternatives such as the Repeat Formation Tester (RFT) tool provide permeability from

mini-well tests, but are not continuous but discrete measurements. Therefore the primary

objective of the NMR log was to obtain a continuous estimate of permeability and

irreducible water saturation. Subsequent work of indicating shale content and estimating

of clay bound water has further the applications of this tool.

Theory

The basic principle of nuclear magnetic resonance logging has been known and

documented for many years[Wyllie, (1963), Pirson (1963)]. In fact, the first field

application was introduced by Pan Geo Atlas Corp in California in 1960. The delay in

widespread development has been due to the inability to construct a tool, which can be

operated in the environmental conditions of the wellbore. High tech solutions have

negated these factors and therefore have made this tool available for use.

Two properties of nuclei identified by the NMR are magnetic moment and nuclear spin.

Magnetic moment is the attempt of a nucleus to align itself parallel to an imposed

magnetic field. The nuclear spin is the rotation of the nucleus about an axis similar to a

gyroscope. Hydrogen exhibit these properties, C, O, Mg, Ca, Si do not. If a strong

magnetic field is applied the spinning protons will tend to align in a direction parallel to

the applied field, much like small bar magnets or magnetic compass needles. This

process is called polarization. If the applied field is on a sufficient time to create order

and then abruptly turned off, the tendency is for chaos to occur and the aligned protons to

revert to their previous state. The return to chaos is not instantaneous, but a given

relaxation time is required. The duration and magnitude of the relaxation time is the

basis of NMR logging.


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The precessing motion is the turning tendency or torque of a proton when realigning from

the applied field to the earth’s magnetic field. This is analogous to a spinning top

revolving away from the center axis as it loses energy with respect to the gravitational

field (Figure 1). The precessing protons induce an alternating voltage in a coil.

Figure 1. Precessing motion of a hydrogen nuclei about the static magnetic field similar

to a top precessing about the gravitational field. [Oilfield Review, 1997]

This voltage is related to the number of protons influenced and the rate these protons

revert to disorder. The precession frequency, or the resonance frequency, is called the

Larmor frequency, fL, and is proportional to the strength of the polarization field,

fL = * HE (Eq. 1)

where

is the gyromagnetic ratio of the proton (Y = 4.2576 x 103 Hz/G)

He is the earth’s magnetic field

The Larmor frequency in the earth's field varies roughly from 1300 to 2600 Hz,

depending on location. The precessing protons, still acting like small magnets, sweep out

oscillating magnetic fields just as many radio antennas transmit electromagnetic fields.

The logging tool receives the tiny radio frequency signals (a few microvolts) from the

precessing protons in the formation.

The NML tool measures the free precession of proton nuclear magnetic moments

in the earth's magnetic field as shown in Figure 2. A strong DC polarizing magnetic field,

Hp, is applied to the formation in order to align proton spins approximately perpendicular


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to the earth's field (HE). The characteristic time constant for the exponential buildup of

this spin polarization is called T1, spin-lattice relaxation time. The polarizing field must

be applied for a period roughly five times T1 for full polarization to occur. At the end of

polarization, the field is turned off rapidly.

Figure 2. Nuclei response to an external polarizing field, Hp, and subsequent decay to the

earth’s magnetic field, He. [Schlumberger, 1989]

The amplitude of the recorded signal, fL, will exponentially decay due to variations in the

polarizing field. This means the spin orientation becomes out of phase with others in the

transverse plane - a transverse relaxation process. The time constant for the transverse

relaxation process is called T2, the transverse decay time. Measuring the decay of the

precessing transverse signal is the heart of the NMR pulse-echo measurement. Figure 3

is an illustration of the decay response.


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Figure 3. Pulse echo sequence and refocusing. [Oilfield Review, 1997]

In Figure 3, the spin precession begins with a 90 pulse. To enhance the signal and to

measure the true transverse relaxation rate, subsequent pulses are reversed to 180. The

result is dephasing of the precessing protons to produce what is called a spin echo. By

reversing the spins, the protons continue to precess, in the same transverse plane as

before, but now the slowest one is in first and the fastest one last. If the protons return at

the same rate, they all will arrive at the same time. However, if a perturbation occurs, the

protons will arrive at varying times. This perturbation or dephasing creates the decline in

the amplitude response. The process is repeated hundreds of times, resulting in an

exponentially decaying sine wave with time constant T2* and frequency fL as shown in

Fig. 4.


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Figure 4. Pulse echo response [Schlumberger, 1989]

Because the large polarizing field cannot be turned off instantaneously, much of the

signal amplitude could be lost. To compensate for this effect, the polarizing field is

allowed to oscillate at the Larmor frequency for a few cycles; this "ringing" field keeps

the proton spins aligned perpendicular to HE.

The time delay ( approximately 25 to 30 ms) after the beginning of the free precession, is

to take advantage of the short relaxation times for hydrogen protons in solids or bound to

surfaces and the longer relaxation times of the bulk fluids in the pore space.

Consequently, the delay in observing the signal records only the bulk or movable fluids

in the pore space. The measurement presented by the log is called the free fluid index

(FFI) or free fluid porosity (f). This quantity is derived from the extrapolated signal

amplitude at the beginning of free precession.

The time constant T2 characterizes the transverse magnetization signal decay. The decay

comes from three sources:

a. intrinsic - the intrinsic bulk relaxation rate in the fluids,

b. surface - the surface relaxation rate, a formation environmental effect


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c. diffusion - the diffusion-in-gradient effect, which is a mix of environmental

and tool effects.

a. Relaxation time is dependent on fluid type and location of the fluid in the pores; i.e.,

the wettability of the rock. Bulk-fluid relaxation is caused primarily by the natural spin-

spin magnetic interactions between neighboring protons. The relative motions of two

spins create a fluctuating magnetic field at one spin due to the motion of the other. These

fluctuating magnetic fields cause relaxation.

Molecular motions in water and light oils are much more rapid, so the relaxation is very

inefficient with long decay times. As the liquids become more viscous, the molecular

motions are slower, and therefore are closer to the Larmor frequency. Thus viscous oils

relax relatively efficiently with short T1 and T2 decay times (Fig. 5).

Figure 5. Bulk relaxation time versus fluid viscosity [Oilfield Review, 1997]

It should be noted that for liquids with low viscosities, the diffusion-in-gradient effects

dominate the T2 rates; subsequently decreasing with reduced viscosity. The diffusion-in-

gradient mechanism does not affect Tl as shown in Figure 5.

b. Grain surface relaxation is the most important process affecting relaxation times. The

surface relaxation rate depends on the ability of the protons in the fluids to make multiple

interactions with the surface. Brownian motion prevails therefore the path of the

precessing proton is a random diffusion process. The probability of colliding with the


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grain surface is higher in small pores than in larger pores. The result is a more rapid

relaxation rate in the small pores.

Figure 6. Diagram of pore size on grain surface relaxation [Oilfield Review, 1997]

c. In the relaxation from diffusion some protons do not receive correct phase adjustment.

This leads to a further, though not significantly large, increase in the T2 relaxation rates

for water and oil. Gas, because of its high diffusion mobility, has a large diffusion-in-

gradient effect. This is used to differentiate gas from oil.

The pulse-echo measurements are analyzed in terms of multiple exponentially decaying

porosity components. The amplitude of each component is a measure of its volumetric

contribution to porosity. Figure 7 illustrates the various components.


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Figure 7. Schematic model describing possible partition of the NMR signal into the

various components.

Applications

The NMR log has the advantage of differentiating between the various fluid components

residing in the pore spaces. For example, the sandstone formation shown in Figure 8

illustrates the free water, oil, capillary bound and clay bound water fractions.

Figure 8. Example of a well-sorted water-wet sandstone formation

Capillary bound water adheres to the smaller pore spaces and interstices, tightly bound by

surface tension of the fluids. This water will always remain in the formation, and is

known as irreducible water. Clay bound water is the volume of water attached to the

surfaces of the clay particles. Since clays have large surface-to-volume ratios, the

relative volume of clay- bound water is large.

The NMR provides two useful measurements. The amplitude depends on the volume of

each fluid component, and therefore is directly proportional to porosity. Figure 9

illustrates two samples with similar porosity. Note the amplitude in both are

approximately the same. Second, the decay rate, or T2 for each component, reflects the


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rate of relaxation, which is dominated by relaxation at the grain surface. T2 is determined

primarily by the pore surface-to-volume ratios. Therefore the decay rate is related to the

pore size distribution and fluid type and viscosity in the pore spaces. Referring to Figure

9, the short T2 times in the top diagram indicates small pores with large surface-to-

volume ratios and low permeability. In contrast, the bottom diagram has longer T2 times

indicating larger pores and thus higher permeability.

Figure 9. Two examples of varying T2 distribution indicating different permeabilities

[Oilfield Review, 1997]


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A principal measurement of the NML tool is the free fluid index, FFI; a measure of the

movable fluid (oil and water) in the pore spaces. It is defined as;

)1(wi

SFFI (Eq. 2)

or if an independent porosity measurement is available,

FFI

wiS 1 (Eq. 3)

With an estimate of irreducible water saturation and porosity, any of the log correlations

can be applied to determine permeability. The FFI represents the effective porosity.

Here, effective porosity is defined as that which contains free, movable fluid.

The NML measurement has been effectively used to identify water-productive intervals

in heavy oil- or tar- bearing reservoirs. The NML log responds to these very heavy crudes

as if they were solids; with little or no FFI is measured. Thus, any FFI signal indicates

free water in the formation. Because of the large viscosity contrast between water

(viscosity less than 1 cp) and the tar-like crudes (viscosity of several hundred centipoise),

a formation with any free water will be predominately water productive.

The spin-lattice relaxation time, T1, is a property of the rock and fluid wetting the pore

surfaces and therefore related to pore size. Since permeability is also related to pore size,

an empirical relationship was established from 80 sandstone cores from around the world

[Kenyon, et al,1988].

3.43.2

1

9106.1 txk

(Eq. 4)

This relationship is not valid for carbonates due to differences in pore geometry.


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Comparison of Porosity Logs

Comparing one porosity measurement with another leads to new information about the

makeup of the formation. Traditionally, neutron and density- porosity logs are combined,

sometimes by simple averaging. In rnany cases, the lithology effects on the neutron

porosity tend to cancel those on the density porosity, so that the average derived poros-

ity is correct. If there are only two lithologies in a water or oil filled formation, then

porosity and the fraction of each rock mineral can be determined using a crossplot

technique. In gas zones, neutron- derived porosity reads low, if not zero, whereas density-

derived porosity reads slightly high. This leads to the classic gas crossover signatures

useful feature.

Figure 10. Comparison of NMR and neutron porosity. Note NMR can discriminate

between capillary bound and clay-bound fluids.


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NMR T2 distributions provide for fluid discrimination. Since fluids confined to small

pores near surfaces have short T2 relaxation times and free fluids in large pores have

large T2 relaxation times, partitioning the T2 distributions allows discrimination between

the different fluid components (Figure 11). Adding the amplitudes of the observed fluid

T2 components together gives a total NMR porosity which usually agrees with the

density porosity in water-filled formations. In gas zones, the NMR depends on the

hydrogen content similar to neutron porosity.

Figure 11. NMR T2 time distributions identifying free fluid, clay-bound and capillary

bound water components.


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Figure 12. Example from North Sea micaceous sandstones of permeability logging from

nuclear magnetic resonance log, [Oilfield Review, 1997]


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Figure 13. NMR example from Gulf of Mexico, [Oilfield Review, 1997]

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