Self-Calibrating Low-Field NMR Measurements of Pore Size.

Portable and bench-top NMR relaxation measurements provide an invaluable analytical tool to infer sample microstructure and composition, enabling the non-destructive analysis of a wide range of materials from cements and rocks, to emulsions and food. However, a weakness in these measurements is that their quantification of pore size typically requires calibration with other analytical techniques. The determination of pore size with NMR relaxometry relies on the relation that a pore's contribution the relaxation rate is proportional to the surface-to-volume ratio of the pore ( Δ 1/T2 = ρ S/V ) [2] and in practice ρ, the surface relaxivity, must either use 'typical' values for the sample type or for accurate measurements be calibrated by other techniques such as Mercury Injection Capillary Pressure measurements. Such destructive analyses are undesirable for rare or valuable samples or impossible to obtain as is often the case in NMR well logging.

Alternatively, NMR diffusion measurements can be directly related to pore size and in combination with T2 measurements to determine ρ [3], and so a single DT2 measurement can provide a self-calibrated measurement of pore size. This approach still requires a number of predetermined physical parameters such as the bulk diffusion coefficient, tortuosity and heterogeneity length scale of the pore structure, because diffusion based pore size measurements can only accurately characterize pore sizes near the characteristic diffusion length of the encoding. To address this limitation, we propose a new method based on analyzing multiple DT2 maps with varied diffusion encoding times and an improved signal model. With multiple diffusion times, the values of the apparent diffusion coefficient correctly describe a wider range of restricted diffusion behavior in samples with wide PSD and large pores, and so do not require predetermined parameters in addition to acquiring multiple NMR DT2 data. Laboratory experiments on glass beads packs with beads diameters ranging from 50 μm to 500 μm are used to validate the new method.

[1] Blümich, B., J. Perlo, and F. Casanova. "Mobile single-sided NMR." Progress in Nuclear Magnetic Resonance Spectroscopy 52.4 (2008): 197-269.
[2] R.L. Kleinberg, NMR well logging at Schlumberger, Concepts in Magnetic Resonance, 13 (2001) 396-403.
[3] Zielinski, L., R. Ramamoorthy, C. Cao Minh, K. Al Daghar, R. H. Sayed, and A. F. Abdelaal, 2010, Restricted diffusion effects in saturation estimates from 2D diffusion-relaxation NMR maps: Presented SPE Annual Conference