Calculation of the permeability of porous media using hydrodynamic cellular automata

The permeability of two-dimensional porous media is calculated numerically as a function of porosity using the hydrodynamic cellular automata (lattice gas) approach. Results are presented for systems with up to 22 million sites (8192×2688). For randomly distributed solid obstacles whose macroscopic dimensions are much longer than the mean free path of particles in the fluid, the permeability varies with porosity as (–0.6)/(1–) for>0.7. When the solid obstacles are much smaller than the mean free path of particles in the fluid, i.e., when they form a dust of point objects, then such a relationship no longer holds and the permeability is more than an order of magnitude smaller than for the former case. The program used for the simulations is discussed and a listing is presented in the Appendix which achieved a sustained speed of 185 million sites updated per second on a single processor of the Cray-YMP. (On a Sun Sparc Workstation, the same program ran about 100 times slower.)     

Probing porous media with gas diffusion NMR.

We show that gas diffusion nuclear magnetic resonance (GD-NMR) provides a powerful technique for probing the structure of porous media. In random packs of glass beads, using both laser-polarized and thermally polarized xenon gas, we find that GD-NMR can accurately measure the pore space surface-area-to-volume ratio, S/V rho, and the tortuosity, alpha (the latter quantity being directly related to the system's transport properties). We also show that GD-NMR provides a good measure of the tortuosity of sandstone and complex carbonate rocks.     

Numerical study on permeability characteristics of fractal porous media

The fractal Brownian motion is utilized to describe pore structures in porous media. A numerical model of laminar flow in porous media is developed, and the flow characteristics are comprehensively analyzed and compared with those of homogeneous porous media. Moreover, the roles of the fractal dimension and porosity in permeability are quantitatively described. The results indicate that the pore structures of porous media significantly affect their seepage behaviors. The distributions of pressure and velocity in fractal porous media are both non-uniform; the streamline is no longer straight but tortuous. When Reynolds number Re 1, the dimensionless permeability is independent of Reynolds number, but its further increase will lead to a smaller permeability. Moreover, due to the higher connectivity and enlarged equivalent aperture of internal channel network, the augment in porosity leads to the permeability enhancement, while it is small and insensitive to porosity variation when ε 0.6. Fractal dimension also plays a significant role in the permeability of porous media. The increase in fractal dimension leads to the enhancement in pore connectivity and a decrease in channel tortuosity,which reduces the flow resistance and improves the transport capacity of porous media.     

Tortuosity measurement and the effects of finite pulse widths on xenon gas diffusion NMR studies of porous media.

We have extended the utility of NMR as a technique to probe porous media structure over length scales of approximately 100-2000 microm by using the spin 1/2 noble gas 129Xe imbibed into the system's pore space. Such length scales are much greater than can be probed with NMR diffusion studies of water-saturated porous media. We utilized Pulsed Gradient Spin Echo NMR measurements of the time-dependent diffusion coefficient, D(t), of the xenon gas filling the pore space to study further the measurements of both the pore surface-area-to-volume ratio, S/V(p), and the tortuosity (pore connectivity) of the medium. In uniform-size glass bead packs, we observed D(t) decreasing with increasing t, reaching an observed asymptote of approximately 0.62-0.65D(0), that could be measured over diffusion distances extending over multiple bead diameters. Measurements of D(t)/D(0) at differing gas pressures showed this tortuosity limit was not affected by changing the characteristic diffusion length of the spins during the diffusion encoding gradient pulse. This was not the case at the short time limit, where D(t)/D(0) was noticeably affected by the gas pressure in the sample. Increasing the gas pressure, and hence reducing D(0) and the diffusion during the gradient pulse served to reduce the previously observed deviation of D(t)/D(0) from the S/V(p) relation. The Pade approximation is used to interpolate between the long and short time limits in D(t). While the short time D(t) points lay above the interpolation line in the case of small beads, due to diffusion during the gradient pulse on the order of the pore size, it was also noted that the experimental D(t) data fell below the Pade line in the case of large beads, most likely due to finite size effects.     

Electromagnetic—acoustic evaluation of the permeability of porous media

The generation of ultrasound in a porous water-saturated medium subjected to rapid electromagnetic heating is considered. The irradiation provides the Joule heating of narrow and electrically high resistive pore throats, which interconnect cavities within the medium and, consequently, determine the permeability of the medium. Because of the small throat sizes, the sound generation is accompanied by considerable thermal flows going out from the throats into a relatively cold environment. Due to the latter, the output of the ultrasonic measurement allows one to estimate the rate of the thermal exchange process. A common geometric model of fluid flows and electric currents throughout a complicated network of intergranular cavities and their interconnecting throats is used for calculating the permeability of a rock on the basis of the determined values of the thermal exchange rate.     

A difference-fractal model for the permeability of fibrous porous media

In this Letter, a difference-fractal model for the permeability of viscous flow through fibrous porous media is proposed. Since fractal objects have well-defined geometric properties, and are discrete and discontinuous, we apply the difference approach to developing the fractal model. The model of non-dimensional permeability is expressed as a function of porosity and fractal dimension. To verify the validity of the proposed model, the predicted permeability values are compared with those of experimental measurements. A good agreement between the prediction of the fractal model and the existing experimental data from the literature is found.     

The relationship of problems in biomedical MRI to the study of porous media.

The NMR methods that are used to characterize inanimate porous media measure relaxation times and related phenomena and material transport, fluid displacement and flow. Biological tissues are comprised of multiple small, fluid-filled compartments, such as cells, that restrict the movement of the bulk solvent water and whose constituents influence water proton relaxation times via numerous interactions with macromolecular surfaces. Several of the methods and concepts that have been developed in one field of application are also of great value in the other, and it may be expected that technical developments that have been spurred by biomedical applications of MR imaging will be used in the continuing study of porous media. Some recent specific studies from our laboratory include the development of multiple quantum coherence methods for studies of ordered water in anisotropic macromolecular assemblies, studies of the degree of restriction of water diffusion in cellular systems, multiple selective inversion imaging to depict the ratios of proton pool sizes and rates of magnetization transfer between proton populations, and diffusion tensor imaging to depict tissue anisotropies. These illustrate how approaches to obtain structural information from biological media are also relevant to porous media. For example, the recent development of oscillating gradient spin echo techniques (OGSE), an approach that extends our ability to resolve apparent diffusion changes over different time scales in tissues, has also been used to compute surface to volume measurements in assemblies of pores. Each of the new methods can be adapted to provide spatially resolved quantitative measurements of properties of interest, and these can be efficiently acquired with good accuracy using fast imaging methods such as echo planar imaging. The community of NMR scientists focused on applications to porous media should remain in close communication with those who use MRI to study problems in biomedicine, to their mutual benefits.     

Direct pore-level modeling of incompressible fluid flow in porous media

We present a dynamic particle-based model for direct pore-level modeling of incompressible viscous fluid flow in disordered porous media. The model is capable of simulating flow directly in three-dimensional high-resolution micro-CT images of rock samples. It is based on moving particle semi-implicit (MPS) method. We modify this technique in order to improve its stability for flow in porous media problems. Using the micro-CT image of a rock sample, the entire medium, i.e., solid and fluid, is discretized into particles. The incompressible Navier–Stokes equations are then solved for each particle using the MPS summations. The model handles highly irregular fluid–solid boundaries effectively. An algorithm to split and merge fluid particles is also introduced. To handle the computational load, we present a parallel version of the model that runs on distributed memory computer clusters. The accuracy of the model is validated against the analytical, numerical, and experimental data available in the literature. The validated model is then used to simulate both unsteady- and steady-state flow of an incompressible fluid directly in a representative elementary volume (REV) size micro-CT image of a naturally-occurring sandstone with 3.398 μm resolution. We analyze the quality and consistency of the predicted flow behavior and calculate absolute permeability using the steady-state flow rate.     

SPIRAL-SPRITE: a rapid single point MRI technique for application to porous media.

This study presents the application of a new, rapid, single point MRI technique which samples k space with spiral trajectories. The general principles of the technique are outlined along with application to porous concrete samples, solid pharmaceutical tablets and gas phase imaging. Each sample was chosen to highlight specific features of the method.     

Quantitative measurements of injections into porous media with contrast based MRI

Porous flow occurs in a wide range of materials and applies to many commercially relevant applications such as oil recovery, chemical reactors and contaminant transport in soils. Typically, breakthrough and pressure curves of column floods are used in the laboratory characterization of these materials. These characterization methods lack the detail to easily and unambiguously resolve flow mechanisms with similar effects at the core scale that can dominate at the aquifer or oil field scale, as well as the effects of geometry that control the flow at interfaces as in a perforated well or the inlet of an improperly designed column. Non-invasive imaging techniques such as MRI have been shown to provide a far more detailed characterization of the properties of the solid matrix and flow, but usually focus on the intrinsic flow properties of porous media or matching a numerical model to a complex flow system. We show that these MRI techniques, utilizing paramagnetic tagging in combination with a carefully controlled and ideal flow system, can quantitatively characterize the effects of geometry and intrinsic flow properties for a point injection into a core. The use of a carefully controlled and 'idealized' system is essential to be able to isolate and match predicted effects from geometry and extract subtle flow processes omitted in the model that would be hidden in a more heterogeneous system. This approach provides not only a tool to understand the behavior of intentional boundary effects, but also one to diagnose the unintentional ones that often degrade the data from routine column flood measurements.     

The features of gas hydrate dissociation in porous media at warm gas injection

Results of numerical simulation of warm gas injection into a porous medium initially saturated with gas and gas hydrate, accompanied by gas hydrate dissociation, are presented. It is shown that depending on parameters at the outer boundary of the medium (permeable or impermeable to the gas flow) hydrate dissociation can occur both at the frontal boundary and in the extended region.     

Two-dimensional gas flows under heterogeneous combustion of solid porous media

Two-dimensional unsteady gas flows in porous media with heterogeneous-combustion centers are investigated under forced filtration and free convection. With the use of numerical methods, it is shown that complex gas flows including vortex ones can arise under the combustion of solid porous media. In the case of forced filtration, the gas tends to flow around the heated portion of an object preferring to flow along cold regions. Under natural convection, the vortex gas flows, which can exist for a reasonably long time and strongly affect the oxidizer inflow into the reaction zone, arise at the initial moment of the process in the combustion zone and in its vicinities.