The effect of surface roughness on Nuclear Magnetic Resonance relaxation

Abstract

Most theoretical treatments of Nuclear Magnetic Resonance (NMR) measurements of porous media assume ideal pore geometries for the pores (i.e. slabs, spheres or cylinders) with welldefined surface-to-volume ratios (S/V). This same assumption is commonly adopted for naturally occurring materials, where the pore geometry can differ substantially from these ideal shapes. In this paper the effect of the roughness of the pore surface on the T₂ relaxation spectrum is studied. By homogenization of the problem using an electrostatic approach it is found that the effective surface relaxivity can increase dramatically in the presence of rough surfaces. This leads to a situation where the system responds as a pore with a smooth surface, but with significantly increased surface relaxivity. As a result the standard approach of assuming an idealized geometry with known surface to-volume and inverting the T₂ relaxation spectrum to a pore size distribution is no longer valid. The effective relaxivity is found to be fairly insensitive to the shape of the roughness but strongly dependent on the width and depth of the surface geometry.