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Nuclear magnetic resonance is widely used as a probe of pore geometry andfluid composition in well logging. One of the critical assumptions often madeis that the diffusion of fluid molecules is sufficiently fast to warrant thecondition for direct mapping between the surface-enhanced relaxation rate andthe pore geometry. In pores satisfying such a condition, but having asignificant spatial variation of surface relaxivity (rho), one can show thatthe one-to-one mapping may break down. The degree to which the NMR logginginterpretation is affected has not been systematically studied until now. Inthis work, we theoretically investigate the interplay between the poregeometry, internal field and the inhomogeneous surface relaxivity. We develop aperturbative framework and compare its results with exact solutions obtainedfor a class of rho textures in a pore with simple geometry. Its effect isquantified for a wide range of diffusivity and/or rho strength. The resultallows us to set the bounds for the change in the final slope of the relaxationcurve and may serve as a useful guide for logging applications in real rockswith a wide range of pore sizes and fluid diffusivity. We further employ largescale numerical simulations to perform virtual experiments on more complexsituations. Internal field and its gradient distributions were obtained andanalyzed for up to 1.5^3 cm^3 based on tomograms of carbonate rocks. We findthat 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 noshift is observed.

Effect of inhomogeneous surface relaxivity, pore geometry and internal  field gradient on NMR logging:exact and perturbative theories and numerical  investigations