Explicit calculation of nuclear-magnetic-resonance relaxation rates in small pores to elucidate molecular-scale fluid dynamics

Abstract

A model linking the molecular-scale dynamics of fluids confined to nano-pores to nuclear magnetic resonance (NMR) relaxation rates is proposed. The model is fit to experimental NMR dispersions for water and oil in an oil shale assuming that each fluid is characterised by three time constants and Lévy statistics. Results yield meaningful and consistent intra-pore dynamical time constants, insight into diffusion mechanisms and pore morphology. The model is applicable to a wide range of porous systems and advances NMR dispersion as a powerful tool for measuring nano-porous fluid properties.Understanding molecular-scale fluid dynamics in micro-and meso-porous materials is central to understanding a wide range of industrially-important materials and processes: rocks for petroleum engineering; zeolites for catalysis; calcium-silicate-hydrates for concrete construction; bio-polymers for food production to name but a few. A molecular-scale model of fluid in a pore is depicted in Fig. 1. In this general picture, one considers fluid within the body of the pore and a surface layer of fluid at the pore wall. The pore body fluid behaves much as a bulk fluid, free to diffuse in three dimensions with motion characterised by a correlation time τ b . The surface layer diffuses in just two dimensions (2D) with motion characterised by a slower correlation time τ . Molecular exchange is envisaged between the surface layer and the bulk fluid characterised by a desorption time τ d and a corresponding adsorption time linked to τ d by the requirements of mass balance. This model therefore simplifies the complex intra-pore dynamics of real fluids to three characteristic time constants,τ b , τ and τ d . Aspects of this general model, henceforth referred to as the 3τ model, are widely used throughout literature [1][2][3][4][5][6][7][8].Nuclear magnetic resonance (NMR) relaxation analysis is a uniquely powerful tool to access molecular correlation times of fluids in porous media [1][2][3][4][5][6][7][8][9]. It is rivalled only by small-angle scattering techniques, especially with neutrons, but has the advantage of being widely available using laboratory-scale equipment. Two NMR relaxation methods are especially valuable. NMR relaxation dispersion (NMRD) measurement of the frequency dependence of the nuclear (usually 1 H) spin-lattice relaxation time (T 1 ) of fluid molecules in the low-frequency range (kHz to MHz) is sensitive to fluid correlation times. Second, the T 1 -T 2 correlation experiment measures the ratio of T 1 to the nuclear spin-spin relaxation time T 2 . This is especially sensitive to different relaxation mechanisms.However, for the NMR methods to be useful, a model is required to link fluid molecular dynamics in pores to NMR relaxation rates. Several models have been proposed (for example, [1,2,6,7,10]) but that which builds most successfully on the general dynamics of the model illustrated in Fig. 1 in terms of fitting experimental data is due to Korb and co-workers [3-6, 10]. Korb's model reproduces the fundamental form ...

A model for the interpretation of nuclear magnetic resonance spin-lattice dispersion measurements on mortar, plaster paste, synthetic clay and oil-bearing shale

“…The expressions required to describe all the combinations of spin-pair interactions which contribute to the relaxation dispersion for a specific system have been presented [8,9]. The 3τ model is applied to four systems: an oilbearing shale (water and oil), a plaster paste, mortar and saponite clay.…”

“…(17)- (20) from Ref. [9] using parameters in Table 1 for surface oil. The exponential is introduced to account for the desorption of surface oil into bulk oil.…”

“…(17)- (20) from Ref. [9] using parameters in Table 1. The final parameters and fit outcomes are listed in Table 1.…”

“…(17)- (20) from Ref. [9] with the parameters listed in Table 1 for water. Optimum fits are obtained for τ b ≈ 10-40 ps with the wide range reflecting the uncertainty in determining the asymptotic limit of the dispersion at the higher frequencies.…”

“…By placing the effective paramagnetic layer below the surface, the long-time limit of G(t) decays as t −2 (rather than t −1 when all spin species are contained in a pure 2D layer) leading to fundamentally different T −1 1 dispersions and a different value of the time constant τ when the model is fit to experimental data. The t −2 dependence of G(t) has been previously demonstrated theoretically and computationally [6,8,9]. A second innovation is that we integrate across the full thickness of the fluid to correctly account for the strong distance-dependence of the dipolar interaction.…”