Lattice boltzmann modeling of fluid flow to determine the permeability of a karst specimen

A limestone sample was scanned using computed tomography (CT) and the hydraulic conductivity of the 3D reconstructed sample was determined using Lattice- Boltzmann methods (LBM) at varying scales. Due to the shape and size of the original sample, it was challenging to obtain a consistent rectilinear test sample. Through visual inspection however, 91 mm and 76 mm samples were digitally cut from the original. The samples had porosities of 58% and 64% and produced hydraulic conductivity values of K= 13.5 m/s and K=34.5 m/s, respectively. Both of these samples were re-sampled to 1/8 and 1/64 of their original size to produce new virtual samples at lower resolutions of 0.542 mm/lu and 1.084 mm/lu, while still representing the same physical dimensions. The hydraulic conductivity tended to increase slightly as the resolution became coarser. In order to determine an REV, the 91 mm sample was also sub-sampled into blocks that were 1/8 and 1/64 the size of the original. The results were consistent with analytical expectations such as those produced by the Kozeny-Carman equation. A definitive REV size was not reached, however, indicating the need for a larger sample. The methods described here demonstrate the ability of LBM to test rock structures and sizes not normally attainable.

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.

Characterization and modeling of multi-conductor transmission line using Finite-difference Time-Domain method

A two-dimensional, 2D, finite-difference time-domain (FDTD) method is used to analyze two different models of multi-conductor transmission lines (MTL). The first model is a two-conductor MTL and the second is a threeconductor MTL. Apart from the MTL's, a three-dimensional, 3D, FDTD method is used to analyze a three-patch microstrip parasitic array. While the MTL analysis is entirely in time-domain, the microstrip parasitic array is a study of scattering parameter Sn in the frequency-domain. The results clearly indicate that FDTD is an efficient and accurate tool to model and analyze multiconductor transmission line as well as microstrip antennas and arrays.

Dynamic fault tree analysis with PEWMA modeling of event rates and Bayesian updating of material balance parameters using MCMC

This research explores Bayesian updating as a tool for estimating parameters probabilistically by dynamic analysis of data sequences. Two distinct Bayesian updating methodologies are assessed. The first approach focuses on Bayesian updating of failure rates for primary events in fault trees. A Poisson Exponentially Moving Average (PEWMA) model is implemnented to carry out Bayesian updating of failure rates for individual primary events in the fault tree. To provide a basis for testing of the PEWMA model, a fault tree is developed based on the Texas City Refinery incident which occurred in 2005. A qualitative fault tree analysis is then carried out to obtain a logical expression for the top event. A dynamic Fault Tree analysis is carried out by evaluating the top event probability at each Bayesian updating step by Monte Carlo sampling from posterior failure rate distributions. It is demonstrated that PEWMA modeling is advantageous over conventional conjugate Poisson-Gamma updating techniques when failure data is collected over long time spans. The second approach focuses on Bayesian updating of parameters in non-linear forward models. Specifically, the technique is applied to the hydrocarbon material balance equation. In order to test the accuracy of the implemented Bayesian updating models, a synthetic data set is developed using the Eclipse reservoir simulator. Both structured grid and MCMC sampling based solution techniques are implemented and are shown to model the synthetic data set with good accuracy. Furthermore, a graphical analysis shows that the implemented MCMC model displays good convergence properties. A case study demonstrates that Likelihood variance affects the rate at which the posterior assimilates information from the measured data sequence. Error in the measured data significantly affects the accuracy of the posterior parameter distributions. Increasing the likelihood variance mitigates random measurement errors, but casuses the overall variance of the posterior to increase. Bayesian updating is shown to be advantageous over deterministic regression techniques as it allows for incorporation of prior belief and full modeling uncertainty over the parameter ranges. As such, the Bayesian approach to estimation of parameters in the material balance equation shows utility for incorporation into reservoir engineering workflows.

Centrifuge modeling of oblique pipe-soil interaction in dense and loose sand

Due to relative ground movement, buried pipelines experience geotechnical loads. The imposed geotechnical loads may initiate pipeline deformations that affect system serviceability and integrity. Engineering guidelines (e.g., ALA, 2005; Honegger and Nyman, 2001) provide the technical framework to develop idealized structural models to analyze pipe‒soil interaction events and assess pipe mechanical response. The soil behavior is modeled using discrete springs that represent the geotechnical loads per unit pipe length developed during the interaction event. Soil forces are defined along three orthogonal directions (i.e., axial, lateral and vertical) to analyze the response of pipelines. Nonlinear load-displacement relationships of soil defined by a spring, is independent of neighboring spring elements. However, recent experimental and numerical studies demonstrate significant coupling effects during oblique (i.e., not along one of the orthogonal axes) pipe‒soil interaction events. In the present study, physical modeling using a geotechnical centrifuge was conducted to improve the current understanding of soil load coupling effects of buried pipes in loose and dense sand. A section of pipeline, at shallow burial depth, was translated through the soil at different oblique angles in the axial-lateral plane. The force exerted by the soil on pipe is critically examined to assess the significance of load coupling effects and establish a yield envelope. The displacements required to soil yield force are also examined to assess potential coupling in mobilization distance. A set of laboratory tests were conducted on the sand used for centrifuge modeling to find the stress-strain behavior of sand, which was used to examine the possible mechanisms of centrifuge model test. The yield envelope, deformation patterns, and interpreted failure mechanisms obtained from centrifuge modeling are compared with other physical modeling and numerical simulations available in the literature.

Biomechanical modeling of parotid glands morphing in head & neck radiation therapy treatments

Durante i trattamenti radioterapici dei pazienti oncologici testa-collo, le ghiandole parotidee (PGs) possono essere indebitamente irradiate a seguito di modificazioni volumetriche-spaziali inter/intra-frazione causate da fattori quali il dimagrimento, l’esposizione a radiazioni ionizzanti ed il morphing anatomico degli organi coinvolti nelle aree d’irraggiamento. Il presente lavoro svolto presso la struttura di Fisica Medica e di Radioterapia Oncologica dell’A.O.U di Modena, quale parte del progetto di ricerca del Ministero della Salute (MoH2010, GR-2010-2318757) “ Dose warping methods for IGRT and Adaptive RT: dose accumulation based on organ motion and anatomical variations of the patients during radiation therapy treatments ”, sviluppa un modello biomeccanico in grado di rappresentare il processo di deformazione delle PGs, considerandone la geometria, le proprietà elastiche e l'evoluzione durante il ciclo terapeutico. Il modello di deformazione d’organo è stato realizzato attraverso l’utilizzo di un software agli elementi finiti (FEM). Molteplici superfici mesh, rappresentanti la geometria e l’evoluzione delle parotidi durante le sedute di trattamento, sono state create a partire dai contorni dell’organo definiti dal medico radioterapista sull’immagine tomografica di pianificazione e generati automaticamente sulle immagini di setup e re-positioning giornaliere mediante algoritmi di registrazione rigida/deformabile. I constraints anatomici e il campo di forze del modello sono stati definiti sulla base di ipotesi semplificative considerando l’alterazione strutturale (perdita di cellule acinari) e le barriere anatomiche dovute a strutture circostanti. L’analisi delle mesh ha consentito di studiare la dinamica della deformazione e di individuare le regioni maggiormente soggette a cambiamento. Le previsioni di morphing prodotte dal modello proposto potrebbero essere integrate in un treatment planning system per metodiche di Adaptive Radiation Therapy.