H43J-01
Pore-scale Simulations of Drainage of Heterogeneous and Anisotropic Porous Media
A numerical model, based on smoothed particle hydrodynamics (SPH), was used to simulate pore-scale liquid and gas flow in synthetic two-dimensional porous media consisting of non-overlapping grains. The model was used to study the effects of pore- scale heterogeneity and anisotropy on the relationship between the average saturation and the Bond number (strength of the gravitational field acting on fluid density differences relative to capillary forces). Pore-scale anisotropy was created by using co-oriented non-overlapping elliptical grains, and heterogeneity was created by inserting a micro-fracture in the middle of the porous domain consisting of non- overlapping circular grains. The effect of the wetting fluid properties on drainage was also investigated. It is shown that pore-scale heterogeneity and anisotropy can give rise to saturation/Bond number relationships and entry (bubbling) pressures that depend on the flow direction, suggesting that these properties should be described by tensor rather than scalar quantities.
H43J-02
Drainage Studies Using Pore-Scale Approaches
The process of drainage has wide spread applications in soil hydrology, irrigation, and the remediation of contaminants in the subsurface. In this paper, we present the comparison of experimental and pore-scale modeling results for drainage. Using a HD-500 microCT system, X-ray tomographic images (21 micron voxels) of saturation during a drainage experiment were obtained in a porous medium consisting of 20/30 mesh (590- 840 microns) Accusand. Utilizing the segmented microtomographic images of the pore space, we modeled drainage using two pore-scale approaches: (1) the pore-morphology-based simulator (PMBS) developed by Hilpert and Miller (2001), and (2) a Lattice Boltzmann (LB) model. Invasion pathways and pressure-saturation relations obtained from both the PMBS and the LB model were compared with those obtained from experiments. The results of PMBS modeling displayed good agreement with experimental observations, except at high suction and low water saturation values, where both CT resolution and model assumptions become an issue. The LB model is currently being refined, and the results of these simulations will also be presented.
H43J-03
Quasi-Static Pore-Scale Network Models for Studying Pc-Sw-anw Relationship in Drainage and Imbibition
We have developed two types of quasi-static pore-scale network models to simulate drainage and imbibition experiments in two-phase in a porous medium. These models are used to study relationship among capillary pressure (Pc), saturation (Sw), and interfacial area (anw). The first one is a standard pore-scale network model consists of pore bodies and pore throats connected to each other in a 3-D regular lattice structure. The second model has an irregular structure with no well-defined pore throat or pore body. It is based on the exact geometry of a 2-D micro-model. Using the first pore-scale network, through simulating primary and scanning drainage and imbibition, we have generated two surfaces fitted to capillary pressure, saturation, and interfacial area (Pc-Sw-anw) points as well as to relative permeability, saturation and interfacial area (kr-Sw-anw) points. The two fitted three-dimensional surfaces show very good correlation coefficients with the data points. We show that interfacial area can be considered as an essential variable for diminishing or eliminating the hysteresis observed in capillary pressure- saturation (Pc-Sw) and the relative permeability-saturation (kr-Sw) curves. The second pore-scale network is used to simulate a set of drainage and imbibition experiments carried out in a micromodel. In order to define boundaries of pores, medial axis transform has been used in the network development. We show the utility of our model by reproducing the observed microscale distribution of the two fluids. We are also able to obtain measured Pc-S, and anw-S curves with a very good accuracy. This network model will be used to design future two-phase flow experiments in the micro model.
H43J-04
Investigating Interfacial Area in a Multiphase Porous System Using Computed Microtomography and Lattice-Boltzmann Simulations
The interface that exists between immiscible fluids plays an important role in multiphase flow and transport in subsurface environments. In this study interfacial area per volume was investigated using computed microtomographic image data and lattice-Boltzmann simulations. A multicomponent lattice-Boltzmann model was used to simulate air-water drainage and imbibition experiments. The pore geometry for the simulations was generated using computed microtomographic image data from the experiments. Based on analysis of the Reynolds, Capillary and Bond number it was determined that capillarity was the dominating force in the experiments, thus gravity, viscous and inertial forces were not taken into account in the simulations. Both pressure and flux boundary conditions were investigated with the simulations. The flux boundary conditions reflect the conditions in the experiments. The pressure boundary conditions are consistent with the more traditional methods for measuring capillary pressure - saturation curves. Simulations with both boundary conditions are in good agreement for the capillary pressure saturation curves. Comparisons between experimental and simulated capillary pressure - saturation curves show relatively good agreement. A preliminary comparison between nonwetting - wetting phase interfacial area per volume estimates indicates good agreement for drainage, however, the simulated interfacial area estimates for imbibition were significantly higher than those obtained in the experiments. The exact cause of the high estimates during imbibition is currently under investigation.
H43J-05
Structural - entropic characterization of porous media and systematic derivation of flow properties
A new systematic approach is described for the characterization of porous media and the application of the characterization to derivation and analysis of transport and mechanical properties. The strategy is as follows. 1. The connectivity of the structure is defined. In granular systems it is based on the inter-granular contact network and in cellular solids on the skeleton. The connectivity is characterized by a new fabric tensor. This description makes it possible to quantify structural parameters, such as skeletal pores and throats. 2. An entropic description of the structure is formulated, for which the fabric tensor provides a volume function. This function is the analogue of a Hamiltonian in conventional statistical mechanics. The fundamental 'quasi- particles' in this formalism are not grains or pores, but rather smaller basic volume elements, named quadrons. In systems of N grains and mean grain coordination number z, there are zN quadrons in 2D and 6(z-2)N in 3D. 3. The entropic formalism is used to extract the distribution of the throat size as expectation values over the partition function. 4. The distributions of throat sizes and pore coordination numbers are used to extract an equivalent network of the same structural characteristics as the original porous material. 5. Using existing techniques, it is then possible to compute both the permeability of the equivalent network to flow (of one or more phases) and its electrical conductivity when saturated with brine water. The commonality of these properties as expectation values over the partition function makes it possible to derive first-principles conductivity- permeability relations. The advantages of this strategy are discussed, as well as the difficulties involved in each stage and our progress in the implementation of the programme.
H43J-06
Pore-scale Simulation of the Effects of Colloid Deposition on Fluid Flow and Solute Transport
High-energy, synchrotron-based x-ray difference micro-tomography was used to resolve the pore structure of a granular porous medium, as well as colloidal deposits within the pore space, with near-micron-scale resolution. This detailed structural information was used to define internal boundary conditions for three-dimensional lattice Boltzmann (LB) simulations of the effects of the colloidal deposits on pore fluid flow. Colloid accumulation was observed to be highly heterogeneous at the pore scale. As colloids accumulated in the pore space, the mean tortuosity increased and the tortuosity distribution became multi-modal, indicating the development of macro- scale heterogeneity. These changes in the geometry of the pore space also greatly reduced the bulk permeability of the porous medium. In addition, a time-series of measurements was used to observe the dynamics of the deposition process in a single sample with successive colloid loading. The pore structure evolved to become increasingly complex over time. LB simulations of solute transport indicated that these changes in pore structure produced anomalous diffusion behavior.
H43J-07
Imaging and Modeling of Colloid Retention Processes in Unsaturated Pore Experiments
Colloid transport in natural porous media (soil) is an important environmental concern due to effects and outcomes of such processes as colloid-facilitated transport of contaminants, transport of bio-colloids and nano- sized materials, and bacterial remediation. Retention of colloids in saturated porous media is mostly associated with retention of colloids at solid-water interface (SWI) and straining. In unsaturated porous media, colloids may be additionally retained at air-water interface (AWI) and contact line. While colloid transport in saturated porous media has achieved better understanding and theoretical prediction, colloid transport in unsaturated porous media poses more uncertainties mostly associated with colloid retention on AWI and contact line. Additionally, dynamic nature of natural soil processes indicates the importance of hydrodynamic conditions, which have to be accounted for in prediction of colloid transport. The objective of the current work is to provide insight into the relative importance of retention forces (colloid and hydrodynamic forces) and retention sites (AWI and contact line) of colloids at the interface- and pore-scale through combined experimental and numerical approaches. These include visualization of colloid behavior employing a micro-fluid channel and a confocal microscope, performing an estimate of colloid forces governing colloid interfacial interactions and retention, and numerical simulation of the flow field and colloid retention in the channel using the Lattice-Boltzmann method (LBM). Coupling of colloid and hydrodynamic forces in natural media presents a challenge, but it can be attempted in model systems such as presented in the current study. Despite the ideal nature of both colloids and porous media some important results on the role of colloid interfacial behavior in colloid transport can be inferred. Expanding these results to larger scales would be the next step needed in the future.
H43J-08
Flow and anomalous transport through a three-dimensional pore
Flow and transport through porous media is a ubiquitous and fundamental geologic process. Three-dimensional Navier-Stokes flow and transport simulations are conducted for a single pore throat between cubic-packed grains 1-2 mm in diameter to advance our fundamental understanding of porous media processes. The grains are considered either spherical or ellipsoidal, and flow between the grains at different Reynolds number is oriented along or across the long axis of the grains. Discharge varied linearly with imposed pressure gradients directly verifying Darcy's Law at the single-pore scale. Vortices are present near the pore throats with narrower and deeper pore throats displaying a series of vortices. The vortices drive non-Fickian tailing of solutes resulting in power-law residence time distributions. Different tailing behavior is observed since the vortices are sensitive to grain shape and flow orientation. Over-all, solute transport through single pores cannot be described by a one-dimensional advection-dispersion equation where "dispersive" transport follows Fick's Law. This suggests that the transport process is below a continuum scale and that anomalous transport characterizes the single-pore scale. At this scale, Darcy's Law holds but Fick's Law does not.