NMR imaging methods are provided for determining the spatial petrophysical properties of materials. These methods employ the generation of separate Mo, T1 and T2 images from which various petrophysical characteristics may be obtained, such as free fluid index, porosity, pore sizes and distributions, capillary pressure, permeability, formation factor and clay content.

NMR imaging of materials

We describe experiments on a two-dimensional granular Couette system consisting of photoelastic disks undergoing slow shearing. The disks rest on a smooth surface and are confined between an inner wheel and an outer ring. Only shearing from the inner wheel is considered here. We obtain velocity, particle rotation rate (spin), and density distributions for the system by tracking positions and orientations of individual particles. At a characteristic packing fraction, ${\ensuremath{\gamma}}_{c}\ensuremath{\simeq}0.77,$ the wheel just engages the particles. In a narrow range of $\ensuremath{\gamma},$ $0.77l~\ensuremath{\gamma}l~0.80$ the system changes from just able to shear to densely packed. The transition at ${\ensuremath{\gamma}}_{c}$ has a number of hallmarks of a critical transition, including critical slowing down, and an order parameter. For instance, the mean stress grows from $0$ as $\ensuremath{\gamma}$ increases above ${\ensuremath{\gamma}}_{c},$ and hence plays the role of an order parameter. Also, the mean particle velocity vanishes at the transition point, implying slowing down at ${\ensuremath{\gamma}}_{c}.$ Above ${\ensuremath{\gamma}}_{c},$ the mean azimuthal velocity decreases roughly exponentially with distance from the inner shearing wheel, and the local packing fraction shows roughly comparable exponential decay from a highly dilated region next to the wheel to a denser but frozen packing further away. Approximate but not perfect shear rate invariance occurs; variations from perfect rate invariance appear to be related to small long-time rearrangements of the disks. The characteristic width of the induced ``shear band'' near the wheel varies most rapidly with distance from the wheel for $\ensuremath{\gamma}\ensuremath{\simeq}{\ensuremath{\gamma}}_{c},$ and is relatively insensitive to the packing fraction for the larger $\ensuremath{\gamma}$'s studied here. The mean particle spin oscillates near the wheel, and falls rapidly to zero away from the shearing surface. The distributions for the tangential velocity and particle spins are wide and show a complex shape, particularly for the disk layer nearest to the shearing surface. The two-variable distribution function for tangential velocity and spin reveals a separation of the kinematics into a slipping state and a nonslipping state consisting of a combination of rolling and translation.

Kinematics of a two-dimensional granular Couette experiment at the transition to shearing

Measurements were made of two components of the average and fluctuating velocities, and of the local self-diffusion coefficients in a flow of granular material. The experiments were performed in a 1 m-high vertical channel with roughened sidewalls and with polished glass plates at the front and the back to create a two-dimensional flow. The particles used were glass spheres with a nominal diameter of 3 mm. The flows were high density and were characterized by the presence of long-duration frictional contacts between particles. The velocity measurements indicated that the flows consisted of a central uniform regime and a shear regime close to the walls. The fluctuating velocities in the transverse direction increased in magnitude from the centre towards the walls. A similar variation was not observed for the streamwise fluctuations. The self-diffusion coefficients showed a significant dependence on the fluctuating velocities and the shear rate. The velocity fluctuations were highly anistropic with the streamwise components being 2 to 2.5 times the transverse components. The self-diffusion coefficients for the streamwise direction were an order-of-magnitude higher than those for the transverse direction. The surface roughness of the particles led to a decrease in the self-diffusion coefficients.

/pdf/local-measurements-of-velocity-fluctuations-and-diffusion-fprva4f5lp.pdf

Local measurements of velocity fluctuations and diffusion coefficients for a granular material flow

The complementary use of computer simulations and analogue simulations to explore the physics of multiparticle systems is demonstrated. Applications to problems of current interest (e.g. non-equilibrium pattern formation, granular flow, and the physics of disordered materials) are emphasized. The ability to describe complex systems in quantitative terms using concepts such as fractal geometry and scaling and the development of new theoretical approaches has led to substantial progress during the past ten years, but we still seem quite far from a general theoretical understanding of many of the problems discussed in this review. The impact of computer technology and the ability to manufacture essentially monodisperse polymer microspheres with well controlled properties (such as magnetic moment, charge, size, porosity and density) is illustrated.

Application of experimental and numerical models to the physics of multiparticle systems

Particle self-diffusion has a significant effect on mixing and thus on performance of rotating cylinder systems such as rotary kilns and drum mixers. We study experimentally the radial mixing of monodisperse beads of different colors in a quasi-two-dimensional cylinder rotated in the continuous flow regime. In this regime a shallow surface layer of particles flows steadily while the rest of the material rotates as a solid body. The initial distribution of tracer particles is taken to be radially symmetric and cylinder is taken to be half full. Both facilitate estimation of the particle self-diffusivity since the evolving concentration distribution during mixing in this case is radial for most part and the mixing in these conditions is shown to be dominated by diffusion of particles. A qualitative study of the mixing is carried out using digital photography. Radial number fraction profiles of the tracer particles are obtained by bulk sampling. Since mixing occurs only in the flowing layer, mixing is considered in terms of “passes” defined as the number of times the material in the bed entirely flows through the layer. Experimental results indicate that the mixing per pass decreases with increasing rotational speed, increases with increasing particle size, and is nearly independent of cylinder size. The mixed state captured by digital photography and the measured radial concentration profiles are well described by a convective diffusion model, using diffusivity as a fitting parameter. The diffusivity obtained from the model follows the scaling proposed by Savage [“Disorder, diffusion, and structure formation in granular flow,” Disorder and Granular Media, edited by A. Hansen and D. Bideau (Elsevier, Amsterdam, 1993), pp. 255–285] and a simple expression for the diffusivity is obtained in terms of the particle diameter and the static and dynamic angles of repose.

Radial mixing of granular materials in a rotating cylinder: Experimental determination of particle self-diffusivity

The mixing of a packed bulk material consisting of non-cohesive mechanically identical particles during shearing is modelled mathematically with the aid of a diffusion equation. In this paper, an equation relating the diffusion coefficient proportionally to the shear rate is derived. This prediction was verified experimentally by shearing experiments using a Couette apparatus. The model bulk consisted of vertically packed cylindrical metal rods, marked by colouring.

Theoretical and experimental investigations into local granulate mixing mechanisms

The velocity profiles and volume concentrations of free water and the solids matrix of flowing pastes can be mutually determined independently via flow experiments in an NMR tomograph. This supplies direct proof of the relative displacement of free water in flowing pastes. The two phases can be distinguished with the help of NMR by their different magnetic relaxation times ( T 2 ). It is possible to measure the wall-slip of the two phases and, hence, to differentiate between the shear and slip shares of the total volumetric flow. When the evaluation of the flow experiments is based on a material law, the accompanying material functions can then be derived for pastes or suspensions from the velocity and concentration distributions. For example, as in the case of the fully-developed steady-state pipe flow, without any additional assumptions or corrections as is normally necessary for capillary rheometry. Through the use of NMR, it is possible to correlate the rheological features of the material in question, its flow behaviour and its flow-induced structural changes.

NMR flow imaging of pastes in steady-state flows

The small-scale mixing densely packed bulk material was modelled by Buggisch and Loffelmann in 1989, starting from a diffusion approach which had been developed previously. An equation could be deduced which the diffusion coefficient appears to be proportional to the shear rate. This model coception was confirmed through shearing experiments using a Couette apparatus. The model bulk consisted of vertically packed metal rods of various diameters, parts of which were marked by colours. The present paper investigates the influence of the particle size distribution upon the mixing process. It is to be expected that the distribution of the particle size has an influence upon the package structure of the bulk and hence, amongst other things, upon the shear rate, and, eventually, upon the intensity of the diffusion. It has been possible to confirm this prediction through shearing experiments with the model bulk in the Couette apparatus.

Experimental investigation into the influence of the particle size distribution upon the local mixing mechanisms in a flowing bulk material

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Theoretical and experimental investigations into local granulate mixing mechanisms

NMR flow imaging of pastes in steady-state flows

Experimental investigation into the influence of the particle size distribution upon the local mixing mechanisms in a flowing bulk material