Lattice Boltzmann modeling of fluid flow and solute transport in karst aquifers

A novel modeling approach is applied to karst hydrology. Long-standing problems in karst hydrology and solute transport are addressed using Lattice Boltzmann methods (LBMs). These methods contrast with other modeling approaches that have been applied to karst hydrology. The motivation of this dissertation is to develop new computational models for solving ground water hydraulics and transport problems in karst aquifers, which are widespread around the globe. This research tests the viability of the LBM as a robust alternative numerical technique for solving large-scale hydrological problems. The LB models applied in this research are briefly reviewed and there is a discussion of implementation issues. The dissertation focuses on testing the LB models. The LBM is tested for two different types of inlet boundary conditions for solute transport in finite and effectively semi-infinite domains. The LBM solutions are verified against analytical solutions. Zero-diffusion transport and Taylor dispersion in slits are also simulated and compared against analytical solutions. These results demonstrate the LBM’s flexibility as a solute transport solver. The LBM is applied to simulate solute transport and fluid flow in porous media traversed by larger conduits. A LBM-based macroscopic flow solver (Darcy’s law-based) is linked with an anisotropic dispersion solver. Spatial breakthrough curves in one and two dimensions are fitted against the available analytical solutions. This provides a steady flow model with capabilities routinely found in ground water flow and transport models (e.g., the combination of MODFLOW and MT3D). However the new LBM-based model retains the ability to solve inertial flows that are characteristic of karst aquifer conduits. Transient flows in a confined aquifer are solved using two different LBM approaches. The analogy between Fick’s second law (diffusion equation) and the transient ground water flow equation is used to solve the transient head distribution. An altered-velocity flow solver with source/sink term is applied to simulate a drawdown curve. Hydraulic parameters like transmissivity and storage coefficient are linked with LB parameters. These capabilities complete the LBM’s effective treatment of the types of processes that are simulated by standard ground water models. The LB model is verified against field data for drawdown in a confined aquifer.

Lattice Boltzmann Modeling of Fluid Flow and Solute Transport in Karst Aquifers

A novel modeling approach is applied to karst hydrology. Long-standing problems in karst hydrology and solute transport are addressed using Lattice Boltzmann methods (LBMs). These methods contrast with other modeling approaches that have been applied to karst hydrology. The motivation of this dissertation is to develop new computational models for solving ground water hydraulics and transport problems in karst aquifers, which are widespread around the globe. This research tests the viability of the LBM as a robust alternative numerical technique for solving large-scale hydrological problems. The LB models applied in this research are briefly reviewed and there is a discussion of implementation issues. The dissertation focuses on testing the LB models. The LBM is tested for two different types of inlet boundary conditions for solute transport in finite and effectively semi-infinite domains. The LBM solutions are verified against analytical solutions. Zero-diffusion transport and Taylor dispersion in slits are also simulated and compared against analytical solutions. These results demonstrate the LBM’s flexibility as a solute transport solver. The LBM is applied to simulate solute transport and fluid flow in porous media traversed by larger conduits. A LBM-based macroscopic flow solver (Darcy’s law-based) is linked with an anisotropic dispersion solver. Spatial breakthrough curves in one and two dimensions are fitted against the available analytical solutions. This provides a steady flow model with capabilities routinely found in ground water flow and transport models (e.g., the combination of MODFLOW and MT3D). However the new LBM-based model retains the ability to solve inertial flows that are characteristic of karst aquifer conduits. Transient flows in a confined aquifer are solved using two different LBM approaches. The analogy between Fick’s second law (diffusion equation) and the transient ground water flow equation is used to solve the transient head distribution. An altered-velocity flow solver with source/sink term is applied to simulate a drawdown curve. Hydraulic parameters like transmissivity and storage coefficient are linked with LB parameters. These capabilities complete the LBM’s effective treatment of the types of processes that are simulated by standard ground water models. The LB model is verified against field data for drawdown in a confined aquifer.

Geochemical determination of the fate and transport of injected fresh wastewater to a deep saline aquifer

Deep well injection into non-potable saline aquifers of treated domestic wastewater has been used in Florida for decades as a safe and effective alternative to ocean outfall disposal. The objectives of this study were to determine the fate and transport of injected wastewater at two deep well injection sites in Miami Dade County, Florida, USA. Detection of ammonium in the Middle Confining units of the Floridan aquifer above the injection zone at both sites has been interpreted as evidence of upward migration of injected wastewater, posing a risk to underground sources of drinking water. Historical water quality data, including ammonia, chloride, temperature, and pH from existing monitoring wells at both sites from 1983 to 2008, major ions collected monthly from 2006 and 2008, and a synoptic sampling event for stable isotopes, tritium, and dissolved gases in 2008, were used to determine the source of ammonium in groundwater and possible migration pathways. Geochemical modeling was used to determine possible effects of injected wastewater on native water and aquifer matrix geochemistry. Injected wastewater was determined to be the source of elevated ammonium concentrations above ambient water levels, based on the results of major ion concentrations, tritium, dissolved noble gases and 15N isotopes analyses. Various possible fluid migration pathways were identified at the sites. Data for the south site suggest buoyancy-driven vertical pathways to overlying aquifers bypassing the confining units, with little mixing of injected wastewater with native water as it migrated upward. Once it is introduced into an aquifer, the injectate appeared to migrate advectively with the regional groundwater flow. Geochemical modeling indicated that CO 2-enriched injected wastewater allowed for carbonate dissolution along the vertical pathways, enhancing permeability along these flowpaths. At the north site, diffusive upward flow through the confining units or offsite vertical pathways were determined to be possible, however no evidence was detected for any on-site confining unit bypass pathway. No evidence was observed at either site of injected wastewater migration to the Upper Floridan aquifer, which is used as a municipal water supply and for aquifer storage and recovery.

A study of branching fluid networks for enhancing the performance of thermal -fluid devices

Compact thermal-fluid systems are found in many industries from aerospace to microelectronics where a combination of small size, light weight, and high surface area to volume ratio fluid networks are necessary. These devices are typically designed with fluid networks consisting of many small parallel channels that effectively pack a large amount of heat transfer surface area in a very small volume but do so at the cost of increased pumping power requirements. ^ To offset this cost the use of a branching fluid network for the distribution of coolant within a heat sink is investigated. The goal of the branch design technique is to minimize the entropy generation associated with the combination of viscous dissipation and convection heat transfer experienced by the coolant in the heat sink while maintaining compact high heat transfer surface area to volume ratios. ^ The derivation of Murray's Law, originally developed to predict the geometry of physiological transport systems, is extended to heat sink designs which minimze entropy generation. Two heat sink designs at different scales are built, and tested experimentally and analytically. The first uses this new derivation of Murray's Law. The second uses a combination of Murray's Law and Constructal Theory. The results of the experiments were used to verify the analytical and numerical models. These models were then used to compare the performance of the heat sink with other compact high performance heat sink designs. The results showed that the techniques used to design branching fluid networks significantly improves the performance of active heat sinks. The design experience gained was then used to develop a set of geometric relations which optimize the heat transfer to pumping power ratio of a single cooling channel element. Each element can be connected together using a set of derived geometric guidelines which govern branch diameters and angles. The methodology can be used to design branching fluid networks which can fit any geometry. ^