Pore Scale Computational Fluid Dynamic Modeling: Approaches for Permeability Modeling and Particle Tracking Using Lattice Boltzmann Methods

Abstract

Knowledge of colloid mobility is important for understanding nutrient cycling, the transport of some contaminants, and for developing environmental remediation systems such as geologic filters. The interaction forces between colloids and soil materials are central to colloid transport and immobilization. These forces act at the microscale (nanometers to microns) and include: fluid drag (friction), Brownian motion, gravity and buoyancy, and fluid chemical forces (including DLVO and van der Waals mechanisms). Most vadose zone studies, however, consider colloids at the continuum scale in terms of solute transport mechanisms using parametrized forms of the advection-dispersion equation and absorption isotherms. A comprehensive, generally applicable, well-documented and publicly available framework for simulating colloids at the microscale is still lacking. Colloid transport and mobility are mechanisms that fundamentally occur at the microscale. As such, representation of the pore-structure needs to be obtained that is meaningful for the pore-scale fluid flow field and colloid mobility (pore-scale colloidal force balances cause the colloidal transport field to be different from the fluid flow field). At the same time, the pore-structure needs to be relevant for continuum-scale experiments or simulations. There are two ways by which a pore-structure can be obtained: by direct three-dimensional imaging (typically with x-ray tomographic techniques) or by reconstruction techniques that yield a synthetic, but presumably representative, pore-structure. Both techniques are examined in this dissertation, but the synthetic route must be used if little micro-scale information is available. This dissertation addresses three main objectives. In chapter 2 it addresses the relation between image quality obtained with two different x-ray tomography techniques (a synchrotron and an industrial scanner) and the obtained flow field. Chapter 3 discusses the development of the LB-Colloids software package, while chapter 4 applies the code to data obtained from a breakthrough experiment of nanoparticulate TiO2. In chapter 2, pore-scale flow fields for Berea sand stone and a macropore soil sample were obtained with lattice Boltzmann simulations which were volume-averaged to a sample-scale permeability and verified with an observed sample-scale permeability. In addition, the lattice Boltzmann simulations were verified with a Kozeny-Carman equation. Results indicate that the simulated flow field strongly depends on the quality of the x-ray tomographic imagery and the segmentation algorithm used to convert gray-scale tomography data into binary pore-structures. More complex or advanced segmentation algorithms do not necessarily produce better segmentations when dealing with ambiguous imagery. It was found that the KC equation provided a reliable initial assessment of error when predicting permeability and can be used as a quick evaluation of whether simulations of the micro-scale flow field should be pursued. In the context of this study, this chapter indicated that LB is able to generate relevant pore-scale flow fields that represent sample-scale permeabilities. However, because the remainder of the study was focused on the development of a pore-scale colloid mobility framework we decided to focus primarily on synthetically-generated pore-structures. This also allowed us to focus on actual mechanisms that were free of imaging and segmentation artifacts. Chapter 3 discusses the development of the LB-Colloids package. This simulation framework is able to simulate large collections of individual colloids through pore representations and porous media. The general workflow for users is as follows: 1) Obtain a pore structure by tomographic imaging or by synthetic means. The latter can be accomplished though the included PSPHERE module which is able to generate a random porous medium using user-supplied porosity and particle size. 2) The pore-scale fluid flow field in the porous medium is generated with a lattice Boltzmann method and a user-specified body force that controls the volume averaged Darcy velocity. 3) Mobility and attachment/detachment of colloids is simulated by accounting of the force balance (fluid drag, Brownian motion, gravity and buoyancy forces, and fluid-chemical forces including DLVO and van der Waals mechanisms). Colloid mobility is carried out at a submicron to nanometer scale and requires grid refinement of the LB flow field. To speed up computations the fluid-chemical forces are precomputed for every grid cell. Because of computational considerations, the LB-Colloids package is presently only able to deal with 2D representations of the porous medium. Code-development and testing (chapter 4) would have taken too long for a full 3D approach. The main draw-back of the 2D approach is that these cannot accurately represent 3D pore-structures. However, no fundamental “new” mechanisms are needed for a 3D approach and we expect that this can be easily built into the clean and well-documented LB-colloids code. The LB-Colloids framework is applied on data obtained from a break-through experiment of TiO2 nanoparticles. Because LB-Colloids is still a 2D code an inverse method was needed to represent the experimental data. In our inversions we calibrated the ratio of pore diameter and colloid radius, the LB body force, nanoparticle density, fluid ionic strength, and surface chemical properties (colloid and porous media zeta potentials). A sensitivity analysis showed that the objective function used for the inversions was most sensitive to the pore-size to colloid ratio, closely followed by surface area, both of which had severe constraints due to the 3D to 2D conversion. Limitations of the two-dimensional particle tracking method and grid discretization approach used in LB-Colloids are identified. Future extension of the LB-Colloid software using the existing mathematical approach to particle tracking is recommended.