Wait Time

Key Takeaways

• The physical basis for the wait time requirement is the T1 longitudinal relaxation process: after the preceding echo train acquisition, the longitudinal magnetization M_z has been perturbed from equilibrium by the RF pulses, and the Bloch equations govern its recovery as M_z(t) = M_0 * (1 - exp(-t/T1)), where M_0 is the equilibrium magnetization proportional to the hydrogen content (porosity) and T1 is the longitudinal relaxation time of the fluid in that pore environment; for a wait time W equal to T1, the magnetization recovers to 63 percent of M_0; for W = 2*T1, to 86 percent; for W = 3*T1, to 95 percent; for W = 5*T1, to 99.3 percent; an NMR log acquired with W = 1*T1 will underestimate porosity by 37 percent if no polarization correction is applied, which is a critical error for reservoir characterization; in practice, the T1 distribution of formation fluids spans a wide range (water in small pores 1 to 10 ms, water in large pores 100 to 1,000 ms, light oil 1 to 100 ms, heavy oil 1 to 10,000 ms, gas at reservoir conditions 4,000 to 8,000 ms at typical HPHT conditions), and the wait time must be set to at least 3 times the longest T1 in the formation for the longest T1 component to be fully represented in the measured T1 distribution; for gas reservoirs, this requires wait times of 10,000 to 20,000 ms (10 to 20 seconds) per cycle, dramatically reducing the measurement speed for a given logging run speed.
• Multi-wait-time NMR logging acquisition modes acquire echo trains at two or more different wait times to simultaneously measure T1 and T2 distributions and to correct for partial polarization of long-T1 components: a fast acquisition (short wait time, typically 200 to 500 ms) samples the short-T1 components (clay-bound water, capillary-bound water in small pores) with high SNR but misses long-T1 components; a slow acquisition (long wait time, typically 5,000 to 12,000 ms) samples all T1 components but with reduced SNR per unit depth from the longer cycle time; the ratio of the two acquisitions at the same depth allows calculation of the T1/T2 ratio (the ratio of longitudinal to transverse relaxation time, which is approximately 1.0 for water in small pores, 1.5 to 2.0 for water in large pores, and much greater for gas and viscous oil), providing a direct gas and oil indicator from the NMR log without requiring resistivity data; Schlumberger's CMR (Combinable Magnetic Resonance) tool and Baker Hughes' MRILTM (Magnetic Resonance Imaging Log) use variants of the multi-wait-time acquisition to provide T1-T2 maps that distinguish light oil, gas, water, and heavy oil in the same formation interval, enabling fluid typing without requiring neutron or density logs for the gas-sand discrimination that NMR alone cannot resolve from T2 data.
• The relationship between wait time and logging speed determines the depth resolution and depth sampling of the NMR log: in a moving logging tool, the measurement for a given depth interval is acquired as the tool passes through that interval; if the logging speed is 300 m/hr (5 m/min) and the wait time plus echo train acquisition time is 4 seconds per cycle, the tool moves 0.33 meters during each cycle; at this speed and cycle time, the depth sampling is approximately one measurement per 0.33 meters, providing adequate sampling for standard reservoir description; if the wait time is increased to 12 seconds (for a gas-bearing formation requiring long T1 coverage), the depth sampling at the same logging speed becomes one measurement per 1 meter, which may be too coarse to resolve thin beds below 2 to 3 meters thickness; the logging engineer must therefore either reduce the logging speed (from 300 to 100 m/hr for the same depth sampling with the longer wait time) or accept reduced thin-bed resolution; commercial NMR logging practice in gas reservoirs typically uses logging speeds of 60 to 120 m/hr with 8,000 to 12,000 ms wait times to achieve the combination of adequate polarization (95 percent or more of gas signal recovered) and acceptable depth resolution (one measurement per 0.3 to 0.5 m at 60 m/hr speed).
• Laboratory NMR measurement of core samples for petrophysical calibration uses much longer wait times than logging tools because there is no time constraint from logging speed: a MARAN or Oxford Instruments benchtop NMR spectrometer measuring the T2 distribution of a 1.5-inch diameter core plug can use wait times of 30,000 to 60,000 ms (30 to 60 seconds) between pulse sequences, ensuring complete T1 relaxation for even the longest-T1 fluids (gas, light crude, large-pore brine) and providing the most accurate porosity and pore size distribution measurements possible from the NMR technique; laboratory NMR core analysis (measuring T2 distribution at multiple saturations during a capillary desaturation experiment or drainage-imbibition cycle) provides the T2 cutoff calibration (the T2 value below which pores are capillary-bound and do not contribute to producible fluid) that is applied to the logging NMR T2 distribution to calculate free fluid porosity (producible porosity) and bound fluid porosity (clay-bound water plus capillary-bound water) in the reservoir; the laboratory T2 cutoff (typically 33 ms for sandstones and 92 ms for carbonates in the convention established by Coates et al. (1999)) is calibrated against capillary pressure data (centrifuge or mercury injection) and production data, and the wait time used in the laboratory measurement must be long enough to ensure that the clay-bound water (with T2 of 0.5 to 3 ms and T1 of similar magnitude) has fully relaxed before the next measurement, requiring wait times of at least 10 times the minimum T2 in the sample.
• Partial polarization correction is applied to NMR logs acquired at wait times shorter than 5 times the longest T1 to recover the porosity of incompletely polarized fluid components: the polarization correction multiplies the apparent amplitude of each T2 component by the factor 1/(1 - exp(-W/T1_i)), where W is the wait time and T1_i is the T1 of the i-th fluid component; this requires knowledge of the T1 of each component, which is obtained from the T1/T2 ratio (approximately 1.5 to 2.0 for water, measurable from multi-wait-time data) and from the T2 distribution (which is directly measured in the standard Carr-Purcell-Meiboom-Gill echo train acquisition); the polarization correction is most important for gas-bearing formations at short wait times (gas T1 at reservoir conditions of 4,000 to 8,000 ms means that a 5,000 ms wait time recovers only 46 to 71 percent of the gas signal without correction), and the correction must be applied before fluid typing (gas identification from the long T1/T2 ratio) to avoid underestimating gas porosity and consequently overestimating water saturation from the NMR log; modern NMR log processing software (Schlumberger's Optima, Halliburton's T2 MAP, and Baker Hughes' MRILTM processing) applies polarization corrections automatically when the acquisition parameters are provided, and quality-control checks on the polarization correction are performed by comparing corrected NMR porosity to independently measured total porosity from density or neutron logs.