Diffusion and Gas

A Third Relaxation

On top of bulk and surface relaxation comes a third mechanism: diffusion. As a molecule wanders through the tool's magnetic-field gradient it feels a changing field, loses phase, and decays faster. The extra rate is

where $D$ is the molecular diffusion coefficient, $G$ the gradient, and $T_E$ the echo spacing. The lever is $D$: it is utterly different between fluids, gas diffusing about forty times faster than water, and oil slower still.

D Separates the Fluids

Because $D$ is a fluid property independent of pore size, it gives NMR a second axis. Plot diffusion coefficient against T2 and the fluids fall into separate fields: slow oil low, water in the middle, fast gas high. The D-T2 map is the modern workhorse of NMR fluid typing, sorting water from oil from gas even when their T2 distributions overlap.

Catching Gas

Gas is the prize. Its high $D$ makes diffusion, not pore size, dominate its relaxation, so gas is pinned at short T2 however large its pores, sitting against the diffusion ceiling drawn on the map. And because the ceiling depends on the echo spacing, widening $T_E$ sweeps it leftward and drives the gas T2 shorter still, while the liquids barely move. Running two echo spacings and watching what shifts is the standard field trick to confirm gas, an independent check on the density-neutron crossover and the high T1/T2 of the last section.

References

• Akkurt, R. et al. (1996). NMR logging of natural gas reservoirs. The Log Analyst, 37(6).
• Hurlimann, M. D. and Venkataramanan, L. (2002). Quantitative measurement of two-dimensional distribution functions of diffusion and relaxation. Journal of Magnetic Resonance, 157.