Rapid surface-to-volume ratio and tortuosity measurement using Difftrain

A finite element approach to forward modeling of nuclear magnetic resonance measurements in coupled pore systems

Porous media characterized by a hierarchy of length scales are ubiquitous in industry and nature, and include carbonate rocks, cements, heterogeneous catalysts, and biological cells. Nuclear magnetic resonance (NMR) is a popular tool for studying liquid-saturated porous materials, where the spin relaxation rate is generally considered proportional to pore size. However, in porous granular media, the relaxation rate is modified by diffusion between the intraparticle and interparticle pores. The observed relaxation rates do not reflect the pore size under such conditions. Deconvolving the various contributions of surface relaxation, geometry, and diffusion is nontrivial, and forward models are a powerful technique for elucidating the underlying pore structure. Various forward models have been proposed previously, including analytic solutions and random walk simulations. Here, a finite element method is adopted to simulate the diffusion of nuclear magnetization in a coupled pore geometry. We validate our model against existing solutions and use the simulations to determine the surface relaxivity of powdered silica by matching experimental results. The finite element approach is more versatile than other modeling methods, allowing direct visualization of the diffusing magnetization and being trivially extensible to multidimensional NMR exchange experiments.

Pulsed second order field NMR for real time PGSE and single-shot surface to volume ratio measurements

Pulsed field gradient nuclear magnetic resonance provides a powerful tool for the measurement of particle diffusion and mobility. When these particles are contained in a porous medium, the diffusive process is influenced by the pore boundaries, and their effect on diffusion measurements provides information about the pore space. The acquisition of the apparent diffusion coefficient and its dependence on time, in the short time limit, reveals the surface to volume ratio of the porous medium, and in the long time limit, its tortuosity. With conventional pulsed field gradient techniques, processes where pore boundaries are evolving on the sub-second time scale cannot be resolved. Using pulsed second order magnetic fields in conjunction with one-dimensional imaging and the pulse sequence Difftrain, this paper presents a proof of concept for the first ever real time single-shot surface to volume NMR measurement.

Spatial fluctuations of fluid velocities in flow through a three-dimensional porous medium

We use confocal microscopy to directly visualize the spatial fluctuations in fluid flow through a three-dimensional porous medium. We find that the velocity magnitudes and the velocity components both along and transverse to the imposed flow direction are exponentially distributed, even with residual trapping of a second immiscible fluid. Moreover, we find pore-scale correlations in the flow that are determined by the geometry of the medium. Our results suggest that despite the considerable complexity of the pore space, fluid flow through it is not completely random.

Structure, diffusion, and permeability of protein-stabilized monodispersed oil in water emulsions and their gels: a self-diffusion NMR study

Self-diffusion NMR is used to investigate monodispersed oil in water emulsions and the subsequent gel formed by removing the water through evaporation. The radius of the oil droplets in the emulsions is measured using a number of diffusion methods based on the measurement of the mean squared displacement of the oil, water, and tracer molecules. The results are consistent with the known size of the emulsions. Bragg-like reflections due to the restricted diffusion of the water around the oil droplets are observed due to the low polydispersity of the emulsions and the dense packing. The resulting data are fitted to a pore glass model to give the diameter of both the pools of interstitial water and the oil droplets. In the gel, information on the residual three-dimensional structure is obtained using the short time behavior of the effective diffusion coefficient to give the surface to volume ratio of the residual protein network structure. The values for the surface to volume ratio are found to be consistent with the expected increase of the surface area of monodisperse droplets forming a gel network. At long diffusion observation times, the permeability of the network structure is investigated by diffusion NMR to give a complete picture of the colloidal system considered.

A rapid measurement of flow propagators in porous rocks

NMR flow propagators have been obtained for brine flowing through Bentheimer sandstone using the rapid DiffTrain pulse sequence. In this way, 8 flow propagators at different observation times Delta were acquired in 67 mins, compared to 7 h for the same measurements implemented with conventional pulsed field gradient (PFG) sequences. DiffTrain allows this time saving to be achieved through the acquisition of multiple displacement probability distributions over a range of Delta in a single measurement. If only the propagator moments are required, this experiment time can be further reduced to 9 mins through appropriate sparse sampling at low q values. The propagator moments obtained from DiffTrain measurements with dense and sparse q-space sampling are shown to be equivalent to those obtained from conventional PFG measurements.