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A theoretical model of NMR surface relaxation in porous media Jourabchi, Parisa

Abstract

A model has been developed to express the relaxation time constant of pore water hydrogen protons in porous geological materials. This model is based on the dipolar interactions of the protons with the naturally found paramagnetic ions near the surface of the solid, modulated by the diffusive motion of the pore water molecules. The effect of a uniform nonmagnetic coating on the solid, which physically separates the water molecules from the paramagnetic ions, is incorporated in the developed model of surface relaxation rate, 1/T1S. A three-dimensional model pore space is defined as a rectangular prism in a sheet-like pore structure. The motion of the molecules is described as two-dimensional diffusion parallel to the solid pore walls, and one-dimensional diffusion perpendicular to the surfaces. The dipolar interaction is considered between hydrogen protons associated with the water molecules, and a layer of randomly distributed paramagnetic ions on the solid. The protons' distance of closest approach to the layer of paramagnetic ions is determined by the thickness of substance coating the solid surface. The resulting expression for 1/T1S involves a number of parameters, some of which can be eliminated by considering the normalized relaxation rates: 1/T1S for the coated sample divided by that of the uncoated sample. Other unknown parameters are used to set bounding limits on the predicted normalized relaxation rates, T1S(plain)/T1S(coated). The predicted trend in T1S(plain)/ T1S(coated) with increasing coating thickness can be approximated by a logarithmic decline for thicknesses up to 2nm. This predicted decay in normalized relaxation rate with increasing coating thickness is more gradual than the trend predicted by previous models. As a result, the application of the developed model to measured relaxation times reported in studies of coated and plain samples is capable of providing realistic estimates of coating thicknesses. [Scientific formulae used in this abstract could not be reproduced.]

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