What NMR Measures

Listening to the Fluids

Every other porosity log reads the rock: density counts electrons, neutron counts hydrogen everywhere, sonic times the matrix. NMR is different. It listens only to the hydrogen nuclei in the pore fluids. The tool polarizes those protons in a strong magnet, tips them with a radio pulse, and records the magnetization as it decays. A CPMG echo train traces that decay, an exponential:

where $T_2$ is the transverse relaxation time and $M_0$, the amplitude at time zero, counts how many hydrogen nuclei there are.

The Amplitude Is Porosity

Because the signal counts fluid hydrogen, $M_0$ is simply the fluid-filled porosity. And because the rock matrix carries no mobile hydrogen, it is invisible to NMR. That is the first great advantage: the NMR porosity needs no grain density and no lithology assumption, unlike the density and neutron logs, which must be told what the matrix is. In a complex or unknown mineralogy, where those logs stumble, NMR still reads porosity straight.

The Decay Carries Pore Size

The second advantage hides in the decay rate. A proton relaxes faster when it bumps into a pore wall, so fluid in small pores, with lots of wall per unit volume, decays quickly (short $T_2$), while fluid in big pores decays slowly (long $T_2$). The single $T_2$ here is the simplest case; a real rock has many pore sizes and so many decay rates at once, and untangling them gives the T2 distribution, a direct picture of the pore-size spectrum. That is the next section.

References

• Coates, G. R., Xiao, L., and Prammer, M. G. (1999). NMR Logging Principles and Applications. Halliburton Energy Services.
• Dunn, K.-J., Bergman, D. J., and LaTorraca, G. A. (2002). Nuclear Magnetic Resonance: Petrophysical and Logging Applications. Pergamon.