Different “average” nuclear magnetic resonance relaxation times for correlation with fluid-flow permeability and irreducible water saturation in water-saturated sandstones

Fluid-flow properties of porous media, such as permeability k and irreducible water saturation S_wi, can be estimated from water ¹H nuclear magnetic resonance (NMR) relaxation data, but there are basic questions regarding data processing and interpretation. We found that S_wi and k are better estimated if different forms of “average” relaxation time are used. NMR longitudinal relaxation data for a suite of 106 water-saturated clean sandstones were used. Sandstones represent a specialized class of porous media, where even for small porosity, substantially all pore space is connected. The sandstones exhibit distributions of relaxation times ranging over factors from at least 10 to more than 10³. We tried several forms of “average” relaxation time T. One family of Ts is p>^1/p, where lim p→0 gives the geometric mean. The best estimator we found for S_wi uses a form of average relaxation time only, rather than relaxation time cutoff. The time used can be any of several forms of T, giving more emphasis to short times than the geometric mean does. On the contrary, the best T for estimating permeability without other information is precisely the geometric mean. The best estimates of permeability came from fits of ln (k/Φ) using Ts with emphasis at slightly longer times. While S_wi is better estimated by using all the data points (starting from our minimum 0.4 ms), k is better estimated by sta- rting at a few ms, that is by ignoring a non-negligible fraction of the signal for some samples. These results can be obtained also by using computations that do not need to invert multiexponential relaxation data, and good results are obtained even with only a few data points. The results are compatible with the reasonable picture, where high surface-to-volume pores, giving signal components with short relaxation times but not contributing to the permeability, are important in determining the fraction of the wetting phase which remains trapped in the solid matrix after displacement with a nonwetting phase. © 1997 American Institute of Physics.