  Nuclear magnetic resonance is widely used as a probe of pore geometry and
fluid composition in well logging. One of the critical assumptions often made
is that the diffusion of fluid molecules is sufficiently fast to warrant the
condition for direct mapping between the surface-enhanced relaxation rate and
the pore geometry. In pores satisfying such a condition, but having a
significant spatial variation of surface relaxivity (rho), one can show that
the one-to-one mapping may break down. The degree to which the NMR logging
interpretation is affected has not been systematically studied until now. In
this work, we theoretically investigate the interplay between the pore
geometry, internal field and the inhomogeneous surface relaxivity. We develop a
perturbative framework and compare its results with exact solutions obtained
for a class of rho textures in a pore with simple geometry. Its effect is
quantified for a wide range of diffusivity and/or rho strength. The result
allows us to set the bounds for the change in the final slope of the relaxation
curve and may serve as a useful guide for logging applications in real rocks
with a wide range of pore sizes and fluid diffusivity. We further employ large
scale numerical simulations to perform virtual experiments on more complex
situations. Internal field and its gradient distributions were obtained and
analyzed for up to 1.5^3 cm^3 based on tomograms of carbonate rocks. We find
that the texture of rho based on the internal field gradient induces a small,
but observable shift, compared to a random noise generated texture for which no
shift is observed.
