What NMR Measures

Chapter 10, NMR Logging

Learning objectives

  • Explain that an NMR tool sees only the hydrogen in the pore fluid, never the matrix
  • Read the echo train M(t)=M0exp⁡(−t/T2)M(t) = M_0\exp(-t/T_2), its amplitude as the porosity once the hydrogen index is divided out
  • Predict how a gas-filled pore space changes the amplitude but not the porosity
  • Read T2 as the pore size through T2=r/(3 ρ2)T_2 = r/(3\,\rho_2) and say why the surface matters

Listening to the Fluids

Every other porosity log reads the rock. The density log counts electrons, the neutron log counts hydrogen wherever it sits, including in the grains and the clay, and the sonic log times the matrix. An NMR tool listens to one thing: the hydrogen nuclei in the pore fluid. It polarises them in a strong magnet, tips them with a radio pulse, and records the magnetisation as it decays. A train of echoes (the CPMG sequence of Carr and Purcell, 1954, and Meiboom and Gill, 1958) traces that decay, here a single exponential:

M(t)=M0 e−t/T2,M(t) = M_0\,e^{-t/T_2},

where T2T_2 is the relaxation time and M0M_0 the amplitude at time zero. The train has two readings, where it starts and how fast it falls, and Figure 10.1 lets you pull them apart.

At 5890 ft, in the upper oil sand, the echo train starts at 22.9 pu: 23.2 % ofporosity times a hydrogen index of 0.99 for 19 % water and 81 % oil. Divided by thatindex the amplitude gives 23.2 %, the well's porosity, with no matrix told to thetool; the density log, expecting 2.65 g/cc, reads the same 23.2 %. With pores 3.0 μmin radius and a surface relaxivity of 10 μm/s, the echoes decay with a T2 of 100 ms;pores a third the radius would decay with 33.3 ms from the same amplitude.(a) The echo train040080010000102030 puTime (ms)porosityT2 100 ms(b) T2 against pore radius0.1110101001000Pore radius (μm)T2 (ms)sandstone, 10 μm/slimestone, 3 μm/s(c) Porosity down the well01020305800600062006400Porosity (%)Depth (ft)NMR 23.2amp. 22.9density 23.2Key: (a) solid, the echo amplitude, with the echoes as dots (thinned), the dashed line the porosity itmust return, the dotted curve the same rock with pores a third the radius, the vertical dotted line thetime T2 at which the amplitude is 1/e. (b) orange, a sandstone surface; teal, a limestone surface; thelarge dot the pores you set, the small one a third the radius. (c) orange, the NMR porosity; greydashed, the raw amplitude; black dots, the density porosity with a 2.65 g/cc matrix, every 5 ft; thedotted line the depth read.Amplitude at t = 0 22.9 pu (23.2 % porosity times a hydrogen index of 0.99). Hydrogen index 0.99 (19 %water (0.96), 81 % oil (1.00)). Density porosity 23.2 % (matrix 2.65 g/cc assumed; this bed's is2.65 g/cc). T2 100 ms (pores 3.0 μm, relaxivity 10 μm/s). Porosity from the amplitude 23.2 % (theamplitude over the hydrogen index; the well's own 23.2 %).

Where the Train Starts: the Porosity

The amplitude is proportional to the hydrogen in the pore fluid (Doveton, 1999), so a fluid contributes in proportion to its hydrogen index HIHI, the hydrogen it holds in a unit volume relative to pure water (Hertel et al., 2016). For a half foot of porosity ϕ\phi holding water and a hydrocarbon,

M0=ϕ [Sw HIw+(1−Sw) HIhc],M_0 = \phi\,\bigl[S_w\,HI_w + (1 - S_w)\,HI_{hc}\bigr],

in porosity units (pu), where one pu is the signal of one per cent of the rock's volume as water. Ogbon-1 has no NMR log, so the figure models one from the well's own porosity and water saturation. At 5890 ft, in the upper oil sand, the porosity is 23.2 %, the pores hold 19 % water and 81 % oil, and the hydrogen index of that mixture is 0.99, so the train starts at 22.9 pu. Divide by the index and the 23.2 % comes back. No grain density went in and no lithology was told to the tool: the grains hold no mobile hydrogen, so NMR does not see them.

The density log is not so lucky. It needs the matrix density, and at 6080 ft, in the tight limestone, a density log told a sandstone's 2.65 g/cc reads 5.1 % where the well's porosity is 8.5 %, because this bed's grains are 2.71 g/cc (Section 4.2 shows the effect). The amplitude there, 8.4 pu over an index of 0.99, returns the 8.5 %. Tell the density log the limestone, or set the figure's matrix to limestone, and the two logs agree. In the other direction, a dolomite matrix, 2.87 g/cc, told to the density log at 5890 ft reads 32.2 % in a sandstone of 23.2 %, while the amplitude has not moved.

The index matters when the fluid changes. Gas holds little hydrogen for its volume: replace the oil of the upper oil sand with gas and the index falls from 0.99 to 0.53, so the same 23.2 % gives 12.2 pu, not 22.9 pu. Divided by the index it is still 23.2 %, but an amplitude read without that correction would call a gas-bearing rock tight. The figure takes the tool as fully polarised, the fluids as the Rock Physics anchor's, and the well as it is in the virgin zone; a real tool reads the invaded zone near the hole (Section 2.3). What NMR measures is the total pore fluid, which includes the water bound to clay (Section 4.6).

How Fast It Falls: the Pore Size

A proton relaxes when it meets the pore wall, so a fluid in a pore with much wall for its volume relaxes quickly, and a fluid in a large pore slowly. For a sphere of radius rr the wall per volume is S/V=3/rS/V = 3/r, and with a surface relaxivity ρ2\rho_2 the rate is 1/T2=ρ2S/V1/T_2 = \rho_2 S/V, so

T2=r3 ρ2.T_2 = \frac{r}{3\,\rho_2}.

Doveton (1999) gives ρ2\rho_2 as about 10 μm/s for quartz, the sandstone surface, and about 3 μm/s for calcite, the limestone surface. In the figure, pores of 3.0 μm radius in the sandstone have a T2 of 100 ms; shrink them to 1.0 μm and the T2 falls to 33.3 ms while the amplitude, 22.9 pu, does not move. The same 3.0 μm pores in a limestone have a T2 of 333 ms, because the calcite wall relaxes the fluid more slowly. So a T2 is a pore size only once the surface relaxivity is known, and the pore size is one number here, where a real rock has many. Section 10.2 takes up the sum of their decays.

References

  • Carr, H. Y., and Purcell, E. M. (1954). Effects of diffusion on free precession in nuclear magnetic resonance experiments. Physical Review, 94(3), 630-638. doi:10.1103/PhysRev.94.630
  • Doveton, J. H. (1999). Application of resistivity-porosity crossplot analysis to nuclear magnetic resonance logging data. Kansas Geological Survey Open-file Report 99-51.
  • Hertel, S. A., Anger, B. C., Smith, K., and Appel, M. (2016). Hydrogen index measurements of highly saline brines under pressures up to 15,000 psi and temperatures up to 300 °F. Society of Core Analysts paper SCA2016-042.
  • Meiboom, S., and Gill, D. (1958). Modified spin-echo method for measuring nuclear relaxation times. Review of Scientific Instruments, 29(8), 688-691. doi:10.1063/1.1716296

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