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Multi-exponential Analysis of Water NMR Spin–Spin Relaxation in Porosity/Permeability-Controlled Sintered Glass

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Abstract

Measuring time constants in multi-exponential decay phenomena is crucial in many areas of knowledge. However, besides the inherent difficulties to the mathematical structure of the problem analysis, noisy experimental data can make the task considerably difficult. One important example is nuclear magnetic resonance (NMR) logging data obtained from measurements of water and hydrocarbons in porous rocks from oil fields. To minimize the uncertainties, it is important to design experiments under controlled conditions. In this paper, we report a systematic study of high (500 MHz) and low (15 MHz)-field NMR \(T_2\) relaxation times performed on artificial sintered sand-glass samples saturated with water. Porosity and permeability were controlled by selecting the range of grains, and then applying a specific sintering temperature protocol to produce samples with different porous sizes, constant porosity, but varying permeability. The structure of porous was verified by microtomography and scanning electron microscopy techniques. Porosity and permeability were measured, respectively, by the free-gas expansion and steady-state methods. We analyze the NMR data using three different approaches: (1) Laplace inversion with optimized regularization based on measured noise level, (2) bi-exponential, and (3) q-exponential nonlinear least-squares. Upon a careful measurement protocol, we report that all methods yield essentially similar \(T_{2}\) distributions.

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Notes

  1. Actually, two surface relaxativities are presented: one relating to longitudinal relaxation on the surface and another to transversal process.

  2. A porous sample with permeability equal to 1 Darcy allows a flow of \(1~{\text {cm}}^{3}/{\text {s}}\) of a fluid with viscosity of 1 mPa s under a pressure gradient of 1 atm/cm acting across an area of 1 cm\(^{2}\).

  3. The residue of regularized solutions as a function of the regularization coefficient, even for the nonnegatively constrained problem considered here, is usually non-decreasing.

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Acknowledgements

We are grateful to technicians and researchers of CENPES/PETROBRAS laboratories for the microtomography images, porosity and permeability measurements. We also would like to thank E.H.C.P. Sinnecker and J. P. Sinnecker for the susceptibility measurements. This work was supported by CAPES, CNPQ, and PETROBRAS, Project 2015/00275-5.

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Authors and Affiliations

  1. Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150 Ed. Cesar Lattes, Urca, Rio de Janeiro, RJ, CEP 22290-180, Brazil

    B. Chencarek, M. S. Nascimento, A. M. Souza, R. S. Sarthour & I. S. Oliveira

  2. Centro de Pesquisas e Desenvolvimento Leopoldo Américo Miguez de Mello-CENPES/PETROBRAS, Av. Horácio Macedo, 950, Cidade Universitária, Rio de Janeiro, RJ, 21941-915, Brazil

    M. S. Nascimento, B. C. C. Santos & M. D. Correia

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  1. B. Chencarek
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  7. I. S. Oliveira
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Correspondence to I. S. Oliveira.

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Chencarek, B., Nascimento, M.S., Souza, A.M. et al. Multi-exponential Analysis of Water NMR Spin–Spin Relaxation in Porosity/Permeability-Controlled Sintered Glass. Appl Magn Reson 50, 211–225 (2019). https://doi.org/10.1007/s00723-018-1050-x

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  • DOI: https://doi.org/10.1007/s00723-018-1050-x

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