POROSITY, PERCOLATION THRESHOLDS, AND WATER RETENTION BEHAVIOR OF RANDOM FRACTAL POROUS MEDIA

Fractals are a relatively recent development in mathematics that show promise as a foundation for models of complex systems like natural porous media. One important issue that has not been thoroughly explored is the affect of different algorithms commonly used to generate random fractal porous media on their properties and processes within them. The heterogeneous method can lead to large, uncontrolled variations in porosity. It is proposed that use of the homogeneous algorithm might lead to more reproducible applications. Computer codes that will make it easier for researchers to experiment with fractal models are provided. In Chapter 2, the application of percolation theory and fractal modeling to porous media are combined to investigate percolation in prefractal porous media. Percolation thresholds are estimated for the pore space of homogeneous random 2-dimensional prefractals as a function of the fractal scale invariance ratio b and iteration level i. Percolation in prefractals occurs through large pores connected by small pores. The thresholds increased beyond the 0.5927 porosity expected in Bernoulli (uncorrelated) networks. The thresholds increase with both b (a finite size effect) and i. The results allow the prediction of the onset of percolation in models of prefractal porous media. Only a limited range of parameters has been explored, but extrapolations allow the critical fractal dimension to be estimated for many b and i values. Extrapolation to infinite iterations suggests there may be a critical fractal dimension of the solid at which the pore space percolates. The extrapolated value is close to 1.89 -- the well-known fractal dimension of percolation clusters in 2-dimensional Bernoulli networks. The results of Chapters 1 and 2 are synthesized in an application to soil water retention in Chapter 3

Distribution of multiphase fluids in porous media: comparison between lattice Boltzmann modeling and micro-x-ray tomography

Journal ArticleA parallel implementation of the three-dimensional Shan-and-Chen multicomponent, multiphase lattice Boltzmann method (LBM) was used to simulate the equilibrium distributions of two immiscible fluids in porous media. The simulations were successfully validated against cone-beam x-ray microtomographic data on the distribution of oil (decane), water, and air phases in a 5-mm cube of porous medium composed of packed quartz sand grains. The results confirm that LBM models allow for the straightforward incorporation of complex pore space geometry determined from x-ray microtomography measurements and that simulated wetting and nonwetting phase distributions are consistent with x-ray observations on both macroscopic and microscopic scales

Developing Benthic Class Specific, Chlorophyll-a Retrieving Algorithms for Optically-ShallowWater Using SeaWiFS

This study evaluated the ability to improve Sea-Viewing Wide Field-of-View Sensor (SeaWiFS) chl-a retrieval from optically shallow coastal waters by applying algorithms specific to the pixels’ benthic class. The form of the Ocean Color (OC) algorithm was assumed for this study. The operational atmospheric correction producing Level 2 SeaWiFS data was retained since the focus of this study was on establishing the benefit from the alternative specification of the bio-optical algorithm. Benthic class was determined through satellite image-based classification methods. Accuracy of the chl-a algorithms evaluated was determined through comparison with coincident in situ measurements of chl-a. The regionally-tuned models that were allowed to vary by benthic class produced more accurate estimates of chl-a than the single, unified regionally-tuned model. Mean absolute percent difference was approximately 70% for the regionally-tuned, benthic class-specific algorithms. Evaluation of the residuals indicated the potential for further improvement to chl-a estimation through finer characterization of benthic environments. Atmospheric correction procedures specialized to coastal environments were recognized as areas for future improvement as these procedures would improve both classification and algorithm tuning

Solute and Bacterial Transport through Partially-Saturated Intact Soil Blocks

Steady-state transport of water, chloride and bacteria was measured through intact blocks of Maury and Cecil soils, under partially saturated conditions. Major objectives were to determine if transport occurs uniformly or via preferential flow paths, and if soil physical properties could be used to predict breakthrough. The blocks were instrumented with TDR probes and mounted on a vacuum chamber containing 100 cells that collected eflluent. After each experiment the blocks were sampled for soil physical properties. The fluxes showed no spatial autocorrelation and the eflluent variance was not statistically different between soils. Less than 3% of the influent bacteria appeared in the effluent. Maximum bacterial breakthrough occurred after 0.25 water-filled pore volumes had been leached, and was greater for Cecil soil than for Maury soil. The chloride breakthrough curves were fitted to the convection dispersion equation. The best predictor of dispersivity was volumetric water content (R2 = 0.28, P \u3c 0.01), with dispersivity increasing with decreasing water content. Lower water contents lead to more tortuous flow paths and thus, a broadening of the velocity distribution. Soil structural controls on solute dispersion under partially saturated conditions are likely to be indirect, and related to differences in water content at given flux produced by differences in pore-size distribution

Biogenic Macroporosity and lts Lattice Boltzmann Method Permeability in the Karst Biscayne Aquifer

We focus on two major problems in the study of paleokarst of the Biscayne aquifer in southeastem Florida: ( 1 ), current conceptual models of karst aquifers do not adequately characterize much of the eogenetic rnacropore system within the carbonate rocks of the Biscayne aquifer, and (2) standard laboratory core-analysis rnethods cannol be used lo accurately measure the permeability of highly macroporous carbonate core samples

Pore-Scale Behavior of Darcy Flow in Static and Dynamic Porous Media

Lattice-Boltzmann numerical simulations are conducted to explore the pore-scale flow behavior inside modeled porous media over the Darcy regime. We use static (fixed) and dynamic (rotating) particles to form the porous media. The pore flow behavior (tortuosity) is found to be constant in the static medium within the Darcy range. However, the study reveals distinctively different flow structures in the dynamic case depending on the macroscopic Darcy flow rate and the level of internal energy imposed to the system (via the angular velocity of particles). With small Darcy flow rates, tortuous flow develops with vortices occupying a large portion of the pore space but contributing little to the net flow. The formation of the vortices is linked to spatial fluctuations of local pore fluid pressure. As the Darcy flow rate (and, hence, the global fluid pressure gradient across the medium) increases, the effect of local pressure fluctuations diminishes, and the flow becomes more channelized. Despite the large variations of the pore-scale flow characteristics in the dynamic porous media, the macroscopic flow satisfies Darcy's law with an invariant permeability. The applicability of Darcy's law is proven for an internally disturbed flow through porous media. The results raise questions concerning the generality of the models describing the Darcy flow as being channelized with constant (structure-dependent) tortuosity and how the internal sources of energy imposed to the porous media flow are considered

Lattice Boltzmann modeling: an introduction for geoscientists and engineers

Lattice Boltzmann models have a remarkable ability to simulate single- and multi-phase fluids and transport processes within them. A rich variety of behaviors, including higher Reynolds numbers flows, phase separation, evaporation, condensation, cavitation, buoyancy, and interactions with surfaces can readily be simulated. This book provides a basic introduction that emphasizes intuition and simplistic conceptualization of processes. It avoids the more difficult mathematics that underlies LB models. The model is viewed from a particle perspective where collisions, streaming, and particle-particle/particle-surface interactions constitute the entire conceptual framework. Beginners and those with more interest in model application than detailed mathematical foundations will find this a powerful "quick start" guide. Example simulations, exercises, and computer codes are included. Working code is provided on the Internet

Lattice Boltzmann simluation of solute transport in heterogeneous porous media with conduits to estimate macroscopic continuous time random walk model parameters

We use Lattice Boltzmann models to simulate solute transport in porous media traversed by open fractures or other conduits. Our particular interest is to simulate moderate Reynolds number flow in the conduits to study the effect of eddy mixing and matrix diffusion on solute breakthrough curve. These "double-porosity" systems represent an area of significant interest in environmental fluid mechanics. We fit the resulting solute breakthrough curves (BTCs) with macroscopic Continuous Time Random Walk (CTRW) models. CTRW is a non-perturbative upscaling method effectively used to model a wide range of transport phenomena in heterogeneous media. In this approach, the impact of system fluctuations on effective transport is modeled by a joint probability density function (s, t) which describes each particle transition over a distance and direction, s and time t and characterizes the random walk both in space and time. The associated effective transport PDE is characterized by a time memory term, which is a functional of the transition time distribution. The porous media are simulated using a real numbered solids fraction that damps the inertial components of the flow leading to a Darcy s Law solution. Solute transport in the porous medium is simulated with anisotropic dispersion. In the open conduits, standard fluid flow and diffusive transport are solved. The combination of Lattice Boltzmann methods and CTRW models will help elucidate the relationship between the microscopic parameters of the flow (microgeometry, Reynolds numbers) and the macroscopic parameters of transport. Our ultimate goal is the application of the CTRW models to large- scale hydro-geological systems

Forecasting Water Demands in South Florida in the Context of Everglades Restoration: Retrospective

AbstractTraditional economic forecasts had consistently underestimated the hypergrowth of South Florida and its need for freshwater from the 1970s through the 1990s. It was hypothesized that the continued rapid growth of urban and farm water use into the 2000–2030 period would undermine efforts to restore the Everglades. To test this hypothesis, the corresponding author had hybridized two widely used regional economic modeling tools: the static, single-period Impact Analysis for Planning (IMPLAN); and the dynamic multiperiod Regional Economic Modeling Inc. (REMI) to forecast population and water use for the period from 2010–2030. In the present paper, these early forecasts are compared to actual census and water use counts for 2010 and 2015. Some of these early forecasts are found to be surprisingly accurate while others seriously overshoot the mark. The on-target forecasts validate the basic hybrid model while the other “deviant” forecasts measure the success of the radical antidrought policies and the region’s economic reaction to the financial collapse. This retrospective provides a new metric for measuring actual changes in the paradigm of water consumption