Pore-Size Measurement from Eigenvalues of Magnetic Resonance Relaxation

Nonground eigenvalues are widely disregarded in magnetic resonance relaxation measurements of porous media due to difficulties involved in their measurement, detection, and the derivation of physically meaningful parameters from them. Such nonground eigenvalues may be experimentally observed in relaxation measurements, such as the relaxation correlation of ${T}_{1}\ensuremath{-}{T}_{2}$, and yield information on the pore size and surface relaxivity of porous media without calibration through other independent measurements. Nonground eigenvalue analysis of ${T}_{1}\ensuremath{-}{T}_{2}$ measurements on Berea sandstone undertaken at three static magnetic fields produces pore sizes consistent with those obtained through x-ray microtomography and SEM measurements. Similar agreement is found for a Bentheimer sandstone with a more complex pore geometry. A phase-encoding imaging variant of this method measures the imbibition confinement-size profile in Berea sandstone. It is suggested that the existence of nonground eigenmodes may be much more prevalent in simple magnetic resonance relaxation measurements than previously considered. Therefore, it is possible to measure pore size by matching numerical Brownstein-Tarr solutions with those of experiments in a wide variety of samples and magnetic resonance methods.