H34A-01 16:00h
High-resolution Imaging of Multiphase Porous Media: Impact of Pore-scale Geometry and Topology and Fractional Wettability
In multiphase porous media systems, the distribution of immiscible fluids is strongly dependent on the pore-scale geometry and topology as well as the wettability characteristics of the media. Previous studies of multiphase systems have used either indirect methods or required destruction of the sample, thus eliminating the ability correlate fluid distribution and characteristics and the pore-scale properties. Synchrotron X-ray tomography can be used to nondestructively obtain high-resolution (on the order of 1-10 micron), three-dimensional images of multiphase porous media systems. A series of column experiments were conducted where nonwetting phase was entrapped at residual saturation. Grain size, media uniformity, and wettability properties were varied among the columns. These columns were imaged at the GeoSoilEnviroCARS tomography beamline at the Advanced Photon Source. Algorithms, developed by our group, were used to (1) obtain the physically-representative network structure of the void space including the pore body and throat distribution, coordination number, and aspect ratio; (2) characterize the entrapped fluid phase properties (e.g., volume, sphericity, orientation, surface area); and (3) correlate the porous media and fluid properties.
H34A-02 16:15h
A Grain-based Algorithm for Constructing Physically Representative Network Mappings of Porous Media
Constructing physically representative network mappings of porous media is a highly challenging problem that, once solved, will facilitate large advances in understanding fluid dynamics and mechanics in complex geometrical systems. High-resolution, three-dimensional imaging is quickly becoming a routine tool for visualizing porous materials. However, algorithms for quantitatively analyzing these systems are lacking. In this work, we will present a new grain-based algorithm that can be used to construct physically representative network mappings of granular materials and to extract quantitative statistics for the material. The algorithm is fundamentally different than previous techniques in that it utilizes the granular structure of the medium as the basic foundation for extracting the pore network structure. The resulting network files are in the same format as the network files used in single and multiphase flow pore-scale models. Here, this algorithm is applied to a variety of computer-generated media, laboratory-grade glass beads, sands, and several natural media systems. Results from these analyses highlight the accuracy and robustness of the algorithm over a range of image resolutions and system types.
H34A-03 16:30h
Navier Stokes Pore Scale Modeling of Two-Phase Flow through an Artificial Porous Medium
Two-phase immiscible flows in a lattice-like flow-cell fabricated for studying flow through porous media were analyzed. A computational grid for two-phase viscous fluid flows through the artificial porous medium was developed, and the fluid flows conditions for a range of capillary numbers were evaluated. Time variation of the averaged front movement for various conditions are evaluated the nature of the flow regimes was assessed. The cross-over from Invasion Percolations (IP) flow to Diffusion-Limited Aggregations (DLA) flow in the lattice flow-cell was found. The fractal dimension was calculated and the breakthrough saturations for various Darcy velocities and viscosity ratios were also evaluated. The results from Navier Stokes simulations were compared with the results from Poiseuille/capillary pressure modeling and with previously published results.
H34A-04 16:45h
Volume of fluid (VOF) simulation of two-phase incompressible fluid flow through interconnected pores and fracture networks
A volume of fluid (VOF) method based on the Los Alamos National Laboratory two-dimensional RIPPLE code was used to model transient, partially saturated incompressible fluid flows through porous matrices and interconnected factures. The fluid/fluid interface was implicitly represented and tracked by fractional volume of fluid (VOF) information defined on the center of each grid cell. Complex interface dynamics such as coalescence and fragmentation are automatically handled by tracking the evolutions of the VOF data. The curvature of the interface, and consequently the pressure difference due to surface tension, are also computed using the VOF data. A two-step projection method was used to solve the incompressible Navier-Stokes equations, aided by an incomplete Cholesky conjugate gradient (ICCG) solution technique for the pressure Poisson equation. Solid grains and fracture walls were modeled as interior obstacles. The contact angle between the fluid interface and solid obstacles is directly specified as a boundary condition, with different values assigned to advancing and receding fluid-fluid-solid contacts. The method can handle two-phase fluid flow problems with large density ratios.
H34A-05 17:00h
Lattice Boltzmann Simulations of Permeability in Statistically Reconstructed Three-Dimensional Pore Structures
Water flow and related processes at the pore scale essentially occur in three dimensions. Unfortunately, it is often difficult and expensive to obtain reliable "images" of the 3D pore structure. Several techniques are available to statistically generate 3D pore structures from 2D microscope images of thin sections of rock and soil. In general, these techniques use two-point correlation functions and/or lineal path distribution functions to reconstruct a 3D pore space such that it has similar spatial properties as the 2D original. Such reconstructions show great promise because they allow detailed study of 3D pore-scale processes without the need of actually sampling the medium in 3D. However, since only 2D information is used, and isotropy is assumed, the question remains whether the reconstructed media are functionally identical to the 3D originals. In this study we try to answer this question by reconstructing pore structures of idealized media. Lattice-Bolzmann simulations are carried out to compare the permeabilities of the original and reconstructed media. Subsequently, we will reconstruct some 3D pore structures of thin soil sections (with known permeabilities) and use Lattice-Bolzmann simulations to obtain insight into the mobile/immobile water fractions as well as the tortuoisity of the flow paths.
H34A-06 17:15h
Development Of A Least-Squares Finite-Element Based Lattice Boltzmann Method For Modeling Fluid Flow In Porous Media
In the last few decades, lattice Boltzmann method (LBM) has been developed as a promising method for simulating fluid flow in natural porous media. Traditional LBM, however, is restricted to a uniform grid. This limitation seriously affects further applications of LBM, where representations of complex pore geometry requires a very fine uniform lattice, thus necessitating additional computing resources. In this study, a new numerical model of LBM utilizing least-squares finite element in space and Crank-Nicolson method in time is developed. The new method is able to solve fluid flow in domains that contain complex or irregular geometric boundaries by using finite-element method's flexibility and numerical stability, while employing accurate least-squares optimization. Fourth-order accuracy in space and second-order accuracy in time are derived from the method for a pure advection equation on a uniform mesh; while high stability is implied from a von Neumann linearized stability analysis. Implemented on unstructured mesh through an innovative element-by-element approach, the proposed method requires fewer grid points and much less memory compared to traditional LBM. Accurate numerical results are presented through two-dimensional incompressible Poiseuille flow, Couette flow and flow past a circular cylinder. Finally, the proposed method is applied to estimate the permeability of a randomly generated porous media, which further demonstrates its inherent geometric flexibility.
H34A-07 17:30h
Dispersion in Porous Media from Pore-scale Network Simulation
We study macroscopic (~cm to ~m scale) dispersion using pore-scale network simulation. A Lagrangian-based transport model incorporating flow and diffusion is applied in a diamond lattice of throats with square cross-section whose radius distribution is the same as computed for Berea sandstone. We use physically consistent rules using a combination of stream-tube routing and ideal mixing to transport particles across pore junctions. Asymptotic behavior is only being seen after movement through many throats. The approach to asymptotic behaviour is analysed by looking at the distribution of transit times between pores and is found to be dependent on heterogeneity and Peclet number. A comprehensive comparative study of longitudinal and transverse dispersion with experiments in consolidated and unconsolidated media indicates that the model can quantitatively predict the asymptotic macroscopic dispersion coefficients over a broad range of Peclet numbers, 0 $<$ Pe $<$ 100000. We discuss the correlation between longitudinal and transverse dispersion coefficients.
H34A-08 17:45h
Numerical modeling of surface and water phase contributions to the electrical properties of partially saturated sandstones
Non-invasive techniques, such as ground penetrating radar, electrical resistivity tomography, and spectral induced polarization have found increasing application for the (time-lapse) monitoring of vadose zone dynamics. Critical to the usefulness of such techniques is the capability to link hydrological quantities of interest, such as moisture content, to the geophysical properties measured by non-invasive methods. Existing relationships are invariably empirical in nature, and should be calibrated on a site-by-site basis. Fundamental investigation of the electrical response of partially saturated natural porous media appears to be necessary to improve on the reliability of the hydro-geophysical relationships. We investigated the electrical response of a partially saturated, weakly consolidated sandstone via pore scale modelling, based on a digital representation of the porous medium. We created this representation purely on the basis of experimental grain-size distribution and porosity data, by using a synthetic, non-overlapping and gravitationally stable packing of spheres. Then we generated a digital representation of this medium by discretizing it in voxels. We simulated primary drainage by preforming a morphological analysis of the digital pore space. The pore-scale distribution of the phases at discrete pressure steps is computed using Laplace equation for a spherical interface and zero contact angle. Then we simulated the direct current response and the dielectric response of the multiphase system at each degree of saturation by means of finite-difference and finite-element solutions to the relevant partial differential equations. Both volume and surface pathways were taken into account. We compared the model results with laboratory data on DC resistivity and electrical permittivity of the studied sandstone. Three different approaches to model surface conductivity in simulating the DC response have been implemented and tested, reaching the conclusion that surface and volume conduction through the bulk of the aqueous phase do not act in parallel, but significant interaction of the two pathways may occur at low water saturation and/or in presence of a significant clay fraction. It is notable that the same pore-scale model is capable of reproducing both the DC response and the dielectric response of the same medium, on the basis of the same elementary principles.