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.

Analysis of N-nitrosames in water using micellar electrokinetic chromatography (MEKC) and development of online and offline methods of extraction and enrichment of neutral polar analytes

Evaluation of the quality of the environment is essential for human wellness as pollutants in trace amounts can cause serious health problem. Nitrosamines are a group of compounds that are considered potential carcinogens and can be found in drinking water (as disinfection byproducts), foods, beverages and cosmetics. To monitor the level of these compounds to minimize daily intakes, fast and reliable analytical techniques are required. As these compounds are relatively highly polar, extraction and enrichment from environmental samples (aqueous) are challenging. Also, the trend of analytical techniques toward the reduction of sample size and minimization of organic solvent use demands new methods of analysis. In light of fulfilling these requirements, a new method of online preconcentration tailored to an electrokinetic chromatography is introduced. In this method, electroosmotic flow (EOF) was suppressed to increase the interaction time between analyte and micellar phase, therefore the only force to mobilize the neutral analytes is the interaction of analyte with moving micelles. In absence of EOF, polarity of applied potential was switched (negative or positive) to force (anionic or cationic) micelles to move toward the detector. To avoid the excessive band broadening due to longer analysis time caused by slow moving micelles, auxiliary pressure was introduced to boost the micelle movement toward the detector using an in house designed and built apparatus. Applying the external auxiliary pressure significantly reduced the analysis times without compromising separation efficiency. Parameters, such as type of surfactants, composition of background electrolyte (BGE), type of capillary, matrix effect, organic modifiers, etc., were evaluated in optimization of the method. The enrichment factors for targeted analytes were impressive, particularly; cationic surfactants were shown to be suitable for analysis of nitrosamines due to their ability to act as hydrogen bond donors. Ammonium perfluorooctanoate (APFO) also showed remarkable results in term of peak shapes and number of theoretical plates. It was shown that the separation results were best when a high conductivity sample was paired with a BGE of lower conductivity. Using higher surfactant concentrations (up to 200 mM SDS) than usual (50 mM SDS) for micellar electrokinetic chromatography (MEKC) improved the sweeping. A new method for micro-extraction and enrichment of highly polar neutral analytes (N-Nitrosamines in particular) based on three-phase drop micro-extraction was introduced and its performance studied. In this method, a new device using some easy-to-find components was fabricated and its operation and application demonstrated. Compared to conventional extraction methods (liquid-liquid extraction), consumption of organic solvents and operation times were significantly lower.