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. 1
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, f L, and is proportional to the strength of the polarization field, f L = * H E (Eq. 1) where is the gyromagnetic ratio of the proton (Y = 4.2576 x 10 3 Hz/G) H e 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, H p, is applied to the formation in order to align proton spins approximately perpendicular 2
to the earth's field (H E ). The characteristic time constant for the exponential buildup of this spin polarization is called T 1, spin-lattice relaxation time. The polarizing field must be applied for a period roughly five times T 1 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, H p, and subsequent decay to the earth s magnetic field, H e. [Schlumberger, 1989] The amplitude of the recorded signal, f L, 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 T 2, 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. 3
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 T 2 * and frequency f L as shown in Fig. 4. 4
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 H E. 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 T 2 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 5
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 spinspin 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 T 1 and T 2 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 T 2 rates; subsequently decreasing with reduced viscosity. The diffusion-ingradient mechanism does not affect T l 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 6
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 T 2 relaxation rates for water and oil. Gas, because of its high diffusion mobility, has a large diffusion-ingradient 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. 7
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 T 2 for each component, reflects the 8
rate of relaxation, which is dominated by relaxation at the grain surface. T 2 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 T 2 times in the top diagram indicates small pores with large surface-tovolume ratios and low permeability. In contrast, the bottom diagram has longer T 2 times indicating larger pores and thus higher permeability. Figure 9. Two examples of varying T2 distribution indicating different permeabilities [Oilfield Review, 1997] 9
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; or if an independent porosity measurement is available, FFI (1 S wi ) (Eq. 2) S wi FFI 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, T 1, 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]. 9 2.3 4.3 k 1.6x10 t 1 (Eq. 4) This relationship is not valid for carbonates due to differences in pore geometry. 10
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 porosity 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 densityderived 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. 11
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. 12
Figure 12. Example from North Sea micaceous sandstones of permeability logging from nuclear magnetic resonance log, [Oilfield Review, 1997] 13
Figure 13. NMR example from Gulf of Mexico, [Oilfield Review, 1997] 14