T1, T2, and Fluid Typing

Two Relaxations

So far this chapter has used only $T_2$, the decay of the signal after the protons are tipped into the transverse plane. NMR also has $T_1$, the recovery of the magnetization along the field, the time the protons take to re-align with it. They are different physics, and $T_1 \geq T_2$. What makes $T_1$ useful is that the tool does not wait for it: before each measurement the protons are given a wait time $T_W$ to re-align, and a fluid with the longitudinal time $T_1$ has recovered only the share

of its magnetization when the pulses begin (Akkurt and co-authors, 1995). A wait of three times $T_1$ gives 95 %. A fluid that is not polarized does not show in the T2 spectrum, and that is the lever: two fluids with the same T2 but different T1 can be told apart by how much of each a short wait leaves behind. Ogbon-1 has no NMR log, so every spectrum in the figure is a what-if built from the porosity and the water saturation of the half foot read.

Water, Oil and Gas Differ in T1

Brine in a rock relaxes at the pore walls, and there $T_1$ is only 1 to 1.5 times $T_2$ (US Patent 6,366,087): water with a $T_2$ of 300 ms has a $T_1$ of 450 ms, and the water in the small pores a few ms. A light hydrocarbon liquid does not wet the rock and relaxes at its bulk rate; the same patent gives its $T_1$ as roughly 1 to 3 seconds, and at low viscosity $T_1$ and $T_2$ are equal (Hirasaki and co-authors, 2002), so the figure puts its oil at the middle of the range, 2000 ms. A gas is the slowest: Akkurt and co-authors give 3 to 6 s for supercritical methane, and Vinegar and co-authors (US Patent 5,498,960) about 4 s for methane at 0.2 g/cc and 200 °F, close to the 4400 ms that Table 2 of US Patent 6,366,087 prints for a Gulf of Mexico sandstone and that the figure uses.

The gas differs in a second way. It diffuses fast: Table 2 gives it a diffusion coefficient 13 times the brine's, and in the gradient of the tool diffusion shortens its $T_2$ to 39.9 ms, though its $T_1$ is 4400 ms. The figure's tool, 17 gauss/cm and an echo spacing of 1.2 ms, is the example tool of US Patent 5,498,960, not a specification of any tool; Section 10.5 builds the diffusion contrast. And it carries fewer hydrogen atoms in a given volume: at the anchor of the Rock Physics book its density is 0.20 g/cc, and its hydrogen index is 0.42, against 1.00 for the oil and 0.96 for the brine (the patent gives 0.2 to 0.6 for a gas; Table 2 prints 0.38).

A Short Wait and a Long Wait

Run the measurement twice. After a long wait, 8000 ms in the figure, everything is polarized: the water 100 %, the oil with its T1 of 2000 ms 98 %, a gas with 4400 ms 84 %. After a short wait of 1500 ms the water, with its 450 ms, is 96 % polarized, but the oil only 53 % and the gas 29 %. The water is the same in both spectra; the hydrocarbon is not. The two waits, 8 s and 1.5 s, are Akkurt and co-authors' example of what they call the differential spectrum method.

The Difference Spectrum

Subtract the spectrum after the short wait from the one after the long wait. What the short wait polarized fully cancels; what it left behind remains. At 6170 ft in the main sand, where the rock is 25.6 % pore space and 35 % of the pores hold water, the oil is 16.5 % of the rock, and the difference holds 7.6 pu: 7.5 pu of oil and only 0.2 pu of water. The oil's part is its volume times its hydrogen index times the polarization it gains between the waits, 45 %; dividing it by the last two, 1.00 and 45 %, returns the 16.5 % the figure started from. That return is exact only because the figure built its spectrum from that volume: in a log the volume is the unknown, and the hydrogen index and the $T_1$ are assumed.

For a gas the same steps show the cost of the low hydrogen index. If the hydrocarbon at that depth were gas (Ogbon-1 holds oil, so this is a what-if), the 16.5 % of gas would show as only 5.9 pu after the long wait, its hydrogen index of 0.42 times a polarization of 84 %, and the difference would hold 3.8 pu of gas, its 0.42 times the 55 % it gains. The product of the hydrogen index and the polarization is what the patent calls the effective hydrogen index.

Where T2 Alone Fails

A gas relaxes at 39.9 ms in the gradient. Where the water in the large pores relaxes as fast, a T2 of 45 ms before diffusion and 41.4 ms seen, the two peaks share 68 % of their T2 range and the spectrum after either wait cannot say which is which. The difference can: the water, with a $T_1$ of 67.5 ms, is fully polarized by 1500 ms and cancels, and the difference holds 3.8 pu, all of it gas. That is the case for $T_1$: it separates fluids that $T_2$ puts on top of each other.

What the Method Assumes

The difference is not a saturation until a $T_1$ and a hydrogen index have been chosen for the hydrocarbon; the figure takes them from the sources, and a log would have to assume them. The short wait must also be long enough for the water. Set the short wait to 500 ms and the water's $T_2$ to 600 ms, so that its $T_1$ is 900 ms, and the water is polarized only 43 %: it supplies 2.5 pu of a 15.0 pu difference, and the hydrocarbon's part is no longer the whole. A slower oil gives more difference only until the long wait stops polarizing it: at a $T_1$ of 5000 ms the oil is 26 % and 80 % polarized and the difference holds 8.9 pu of oil, but 5000 ms is outside the range the patent gives for a light liquid. A viscous oil breaks the assumption $T_2 = T_1$ altogether. And where there is no slow fluid the difference is empty: at 6240 ft, in the water leg, the same waits leave 0.7 pu, the large-pore water that 1500 ms does not quite polarize. Ogbon-1's own brine and oil are not these fluids, which are the Rock Physics anchor's; the well freezes its own for its logs.

References

• Akkurt, R., Vinegar, H. J., Tutunjian, P. N., and Guillory, A. J. (1995). NMR logging of natural gas reservoirs. SPWLA 36th Annual Logging Symposium, Paris, June 1995.
• Vinegar, H. J., Akkurt, R., and Tutunjian, P. N. (1996). NMR logging of natural gas in reservoirs. US Patent 5,498,960, Shell Oil Company, granted 12 March 1996. uspto.report/patent/grant/5498960.
• Coates, G. R., and Hou, L. B. NMR logging apparatus and methods for fluid typing. US Patent 6,366,087 B1, priority 30 October 1998. patents.google.com/patent/US6366087.
• Hirasaki, G. J., Lo, S.-W., and Zhang, Y. (2002). NMR properties of petroleum reservoir fluids. 6th International Conference on Magnetic Resonance in Porous Media, Ulm, Germany, 8-12 September 2002.