A numerical study of the relationship between NMR relaxation and permeability in sands and gravels

Abstract

ABSTRACTThe accuracy of NMR‐derived permeability estimates in sands and gravels are examined through simulations on numerical grain packs composed of uniform spherical grains. The packs consisted of randomly packed grains, with grain sizes set to represent a range corresponding to sands and gravels. The material properties for each pack were quantified through numerical analysis and the NMR response was simulated for a range of surface relaxivity values. The agreement between the numerically‐derived permeability estimates and the permeability estimates derived using the Schlumberger‐Doll Research (SDR) and Seevers equations was evaluated. Use of the SDR equation assumes that the relaxation of the bulk pore fluid can be neglected. The NMR‐derived permeability estimates were calculated using each equation for the cases where relaxation was assumed to occur in one of the two major diffusion regimes. We found that permeability is most accurately estimated in all packs through use of the Seevers equation with the empirical constant set equal to 1. We showed that the contribution of bulk fluid relaxation should be accounted for in materials with grain radii greater than 1.2e‐4m (fine sand) and surface relaxivity values less than 1.0e‐3 m s−1. In practice, this range of surface relaxivity values and grain sizes corresponds to situations where the measured relaxation time is greater than approximately one‐third the value of the bulk fluid relaxation time .