A Physics-Driven Approach using Single-Pore-Modes (SPM) for Estimating an Average Pore Radius and Surface Relaxativity from NMR Data

The method of Nuclear Magnetic Resonance (NMR) has found a wide range of application in geophysics. At the largest scale SNMR as a surface based method covers volumes up to thousands of cubic meters, at laboratory scale NMR can handle samples as small as cuttings from drilling. Here we focus on unconsolidated material with the purpose to derive hydraulic properties from NMR relaxation curves at laboratory scale. Until now several methods for fitting NMR data are used. All approaches utilize a mono-, multi- or stretched-exponential relationship to explain NMR decay curves. Brownstein and Tarr (1979) showed that even for single pores a decay curve composes of several mono-exponential modes which superimposes to a multi-exponential signal. Thus, common multi-exponential approaches can lead to a misinterpretation of the decay time spectrum, when purely seen as a pore radius distribution. The mono-exponential modes introduced by Brownstein and Tarr (1979) occur by solving the general diffusion equation, which can be calculated for different pore geometries. In this study we used a cylindrical geometry to describe the pore space in analogy to Kozeny (1927). Thus, the solution is given for decay times T, extended by a term for the bulk relaxation and intensities I by equation 1 and 2.