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.

Organic carbon sources and their transfer in a gulf of Mexico coral reef ecosystem

Coral reefs face unprecedented threats throughout most of their range. Poorly planned coastal development has contributed increased nutrients and sewage contamination to coastal waters, smothering some corals and contributing to overgrowth by macroalgae. My approach to assessing the degree to which coral reef ecosystems have been influenced by terrestrial and anthropogenic organic carbon inputs is through the use of carbon (C) and nitrogen (N) stable isotopes and lipid biomarkers in a marine protected area, the Coral Reef System of Veracruz: Parque Nacional Sistema Arrecifal Veracruzano (PNSAV) in the southwest Gulf of Mexico. Firstly, I used a C and N stable isotope mixing model and a calculated fatty acid (FA) retention factor to reveal the primary producer sources that fuel the coral reef food web. Secondly, I used lipid classes, FA and sterol biomarkers to determine production of terrestrial and marine biogenic material of nutritional quality to pelagic and benthic organisms. Finally, I used coprostanol to determine pollutant loading from sewage in the suspended particulate matter. Results indicate that phytoplankton is the major source of essential metabolite FA for marine fish and that dietary energy from terrestrial sources such as mangroves are transferred to juvenile fish, while seagrass non-essential FA are transferred to the entire food web mainly in the rainy season. Sea urchins may be the main consumers of brown macroalgae, especially in the dry season, while surgeon fish prefer red algae in both dry and rainy seasons. C and N isotopic values and the ratio C:N suggest that fertilizer is the principal source of nitrogen to macroalgae. Thus nitrogen supply also favored phytoplankton and seagrass growth leading to a better nutritional condition and high retention of organic carbon in the food web members during the rainy season when river influence increases. However, the great star coral Montastrea cavernosa nutritional condition decreased significantly in the rainy season. The nearest river to the PNSAV was polluted in the dry season; however, a dilution effect was detected in the rainy season, when some coral reefs were contaminated. In 2013, a new treatment plant started working in the area. I would suggest monitoring δ¹⁵N and the C: N ratio in macroalgae as indicators of the nitrogen input and coprostanol as an indicator of human feces pollution in order to verify the efficiency of the new treatment plant as part of the management program of the PNSAV.