On the Validity of the Relationship 1/T=1/T B+1/T S+1/T D in NMR Techniques With Regards to Permeability Estimation of Natural Porous Media

One of the most relevant feature of geophysical techniques based on nuclear magnetic resonance is their ability to estimate the permeability of natural porous media, since other geophysical techniques, as the use of the formation factor and neutron well-logs, allow to quantify the volume of water in the media. Permeability is conventionally obtained from decay time of the total resonance signal. However, the fluid in the pores of a medium normally has different mobility degree that can be differentiated by the NMR results. Therefore, a detailed estimation of permeability requires decomposing the total resonance signal as a function of the decay times corresponding to the three mechanisms that contribute to the signal: the intergranular free fluid, the surface layer, and the diffusion relaxation mechanism. The relationship currently used to make this decomposition states that the exponential decay rate attributed to the total resonance signal is the sum of the three existing decay rates. We demonstrate that this relationship is not generally applicable in porous media, showing the contradiction with the much more widely accepted relationships as well as computation examples from three typical decay rates in a single pore and from sandstone with bulk and surface relaxation mechanisms. Consequently, we conclude that the assertion whereby the permeability of any porous medium does not depend on the decay time of the free fluid is an overstatement, since it only applies to very small pore sizes.