Development of a Probabilistic Bayesian Model for Tracking of Submerged Oil during Operational Response

Chao Ji

Submerged oil may be found to persist at depth following a well blowout or a sunken ship/vessel/tanker oil spill, due to high crude oil density, loss of light fractions, and/or other factors, as was observed after the Deepwater Horizon (DWH) spill in the Gulf of Mexico in 2010. The deep and long-lasting features of submerged oil bring challenges to the detection and modeling of submerged oil, sometimes resulting in low efficiency of detection by autonomous underwater vehicles and ship-based Rosette, and mixed results of oil trajectory modeling. The objectives of the thesis are to develop a data-driven submerged oil spill model, SOSim (Submerged Oil Simulator) that assimilates available field submerged oil concentration observations and available predictions from other models to make time updated forecasts on submerged oil concentration and trajectory and based on the SOSim forecasts, to design real-time submerged oil field sampling plans by applying environmental and geostatistical sampling methods.<o:p></o:p>To realize these objectives, a time-updated statistical model on the submerged oil concentration distribution is proposed based on advection-diffusion theorems and Bayesian statistical methods to compute the posterior distribution of the model parameters based on the field likelihood function and a prior likelihood function determined by other models’ predictions. Maximum a posterior method is then used to infer the unknown parameters and time-updated predictions are made with the inferred parameters. The predictions are made in 2D and transformed to 3D by adding the depth coordinates using the information about isopycnal layers containing oil. Uncertainty estimates are provided by predictions using the uncertainty bound of the parameters obtained by using the Wilks theorem. SOSim provides a probability map informing the location and depths and reflects the relative concentration distributions of the submerged oil. The developed model is demonstrated on a synthetic inertial circle case and versus field data collected during the DWH spill. The model predictions agree well in moving directions and relative concentration profiles of the real observations.<o:p></o:p>The predictions are further applied to design sampling plans. Systematic random, kriging-based sampling method as well zig-zag patterns are applied inside the region with a high probability of submerged oil presence predicted by SOSim to collect samples. The sampled data are then input to SOSim to update the predictions and provide information for future samplings. A recommendation to choose a sampling method is given based on the availability of sampling devices and other available prior information. The proposed sampling methods are applied to the DWH spill and the results show that the use of the SOSim model predictions significantly improves the sampling efficiency.<o:p></o:p>Overall, SOSim provides a new probabilistic approach for modeling and sampling submerged oil. The model does not need hydrodynamic field information and uncertainty estimates are provided using probability theory. The proposed sampling plans based on SOSim predictions are also shown to be more efficient than plans used during the DWH oil spill in terms of informing subsequent SOSim forecasts. Future applications and improvements of the model include determining exact locations for oil spills, making predictions using other physical quantities such as dissolved oxygen anomalies, and using machine learning algorithms to improve the model.<o:p></o:p>

Development of a Probabilistic Bayesian Model for Tracking of Submerged Oil during Operational Response

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