In this study we have applied 2D NMR experiments where the spatial inhomogeneous magnetic field (Bi) inside a porous sample is correlated to respectively internal gradient (G0), diffusion coefficient (D), and transverse relaxation time (T2) of a confined liquid. Experiments were performed on samples having different pore system geometry and heterogeneity, leading to different types of confinement of the liquid. The results show that the correlation between G0 and Bi is more sensitive to the type of confinement, and thus also of the pore geometry and heterogeneity, compared to the corresponding correlations involving D and T2.

The two most successful methods of estimating the distribution of NMR relaxation times from two dimensional data are firstly a data compression stage followed by application of the Butler-Reeds-Dawson (BRD) algorithm, and secondly a primal dual interior point method using a preconditioned conjugate gradient (PCG). Both of these methods have been presented in the literature as requiring a truncated singular value decomposition of matrices representing the exponential kernels. Other matrix factorisations are applicable to each of these algorithms, and which demonstrate the different fundamental principles behind the operation of the algorithms. In the case of the data compression approach the most appropriate matrix decomposition specifically designed for this task is the rank-revealing QR (RRQR) factorisation. In the case of the interior point method, the most appropriate method is the LDL factorisation with diagonal pivoting, also known as the Bunch-Kaufman-Parlett factorisation. The details of these differences are discussed, and the performances of the algorithms are compared numerically.

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Contains abstracts and full texts of Diffusion Fundamentals V conference

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A selection of papers presented at the 11th International Bologna Conference Magnetic Resonance in Porous Media (MRPM 11), September 2012, Surrey, UK

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Contains full texts of Diffusion Fundamentals IV conference

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