Nuclear magnetic resonance diffusion with surface relaxation in porous media

Valfouskaya, A.; Adler, P. M.; Thovert, Jean‐François; Fleury, Marc

doi:10.1016/j.jcis.2005.08.021

Cited by 29 publications

(19 citation statements)

References 29 publications

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“…This scaling is also consistent with the one found by , and Valfouskaya et al (2006). They show that for zero surface relaxtivity an universal curve exists for a porous media.…”

Section: Scaling In Random Walk Simulationssupporting

confidence: 91%

NMR for equilateral triangular geometry under conditions of surface relaxivity—analytical and random walk solution

et al. 2006

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We consider analytical and numerical solution of NMR relaxation under the condition of surface relaxation in an equilateral triangular geometry. We present an analytical expression for the Green's function in this geometry. We calculate the transverse magnetic relaxation without magnetic gradients present, single-phase, both analytically and numerically. There is a very good match between the analytical and numerical results. We also show that the magnetic signal from an equilateral triangular geometry is qualitatively different from the known solution: plate, cylinder, and sphere, in the case of a nonuniform initial magnetization. Nonuniform magnetization close to the sharp corners makes the magnetic signal very fast multiexponential. This type of initial configuration fits qualitatively with the experimental results by Song (Phys.

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“…This scaling is also consistent with the one found by , and Valfouskaya et al (2006). They show that for zero surface relaxtivity an universal curve exists for a porous media.…”

Section: Scaling In Random Walk Simulationssupporting

confidence: 91%

NMR for equilateral triangular geometry under conditions of surface relaxivity—analytical and random walk solution

et al. 2006

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“…In the opposite limit, where the texture of δρ(r) is such that its variation occurs on length scales much shorter than the pore geometrical length-scale (Eq.16), the effect of such finely inhomogeneous δρ should be muted via diffusive averaging-out. This is the case considered in Valfouskaya et al [38] which considered a texture with a random variation uncorrelated beyond the voxel size, much smaller than the typical grain size, in a stochastically generated 3D porous medium. Our numerical simulations on random glass bead packs with similar textures of δρ also yielded results consistent with these observations.…”

Section: Discussionmentioning

confidence: 99%

“…Our result provides a useful theoretical framework and quantitative bounds for more complex situations addressed mainly through numerical simulations. [38,39,41] Further development through comparison to exact solution [55] and systematic numerical simulations [56] are underway.…”

Section: Discussionmentioning

confidence: 99%

Effects of inhomogeneous partial absorption and the geometry of the boundary on population evolution of molecules diffusing in general porous media

Ryu

2009

Phys. Rev. E

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We consider aspects of the population dynamics, inside a bound domain, of diffusing agents carrying an attribute which is stochastically destroyed upon contact with the boundary. The normal mode analysis of the relevant Helmholtz equation under the partially absorbing, but uniform, boundary condition provides a starting framework in understanding detailed evolution dynamics of the attribute in the time domain. In particular, the boundary-localized depletion has been widely employed in practical applications that depend on geometry of various porous media such as rocks, cement, bones, and cheese. While direct relationship between the pore geometry and the diffusionrelaxation spectrum forms the basis for such applications and has been extensively studied, relatively less attention has been paid to the spatial variation of the boundary condition. In this work, we focus on the way the pore geometry and the inhomogeneous depletion strength of the boundary become intertwined and thus obscure the direct relationship between the spectrum and the geometry. It is often impossible to gauge experimentally the degree to which such interference occur. We fill this gap by perturbatively incorporating classes of spatially-varying boundary conditions and derive their consequences that are observable through numerical simulations or controlled experiments on glass bead packs and artificially fabricated porous media. We identify features of the spectrum that are most sensitive to the inhomogeneity and apply the method to the spherical pore with a simple hemi-spherical binary distribution of the depletion strength and obtain bounds for the induced change in the slowest relaxation mode.

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“…The measure of T 1 is time-consuming, so T 2 is usually used to reflect the physical properties and fluid characteristics of the sample. Based on NMR diffusion with a surface relaxation model [17], nuclear relaxation in a single pore of a sample can be described by relaxation time.…”

Section: Experimental Principle and Processmentioning

confidence: 99%

“…Sci. 2017, 7, 300 8 of 13 a surface relaxation model [17], nuclear relaxation in a single pore of a sample can be described by relaxation time.…”

Section: Experimental Principle and Processmentioning

confidence: 99%

Experimental Study of Imbibition Characteristics of Silica Sol in Coal-Measure Mudstone Matrix

et al. 2017

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Coal-measure mudstone is a typical dual-porosity media, and grouting in a matrix system is dominantly controlled by the imbibition effect for silica sol. This paper studies the imbibition effect using mudstone in the Huaibei mining area and silica sol as grouting material as an example. Groutability, driving force, and diffusion difficulty affecting the imbibition effect were tested by a mercury porosimeter, nanoparticle size analyzer, optical contact-angle measuring device, surface tension meter, and rotary viscosity meter. After finely grinding a mudstone sample, a pressureless imbibition process was conducted through nuclear magnetic resonance equipment for 216 h to study colloid spontaneous migration and phase characteristics. Results show that silica sol absorption rate follows a power function and that the spectrograms of T 2 are distributed in a triple peak pattern, with a tendency to move to the right of vertex time. The paper lays a theoretical and experimental foundation for field grouting in the coal mine.

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Nuclear magnetic resonance diffusion with surface relaxation in porous media

Cited by 29 publications

References 29 publications

NMR for equilateral triangular geometry under conditions of surface relaxivity—analytical and random walk solution

NMR for equilateral triangular geometry under conditions of surface relaxivity—analytical and random walk solution

Effects of inhomogeneous partial absorption and the geometry of the boundary on population evolution of molecules diffusing in general porous media

Experimental Study of Imbibition Characteristics of Silica Sol in Coal-Measure Mudstone Matrix

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