Partial Differential Equation
MetadataShow full item record
PublisherThe University of Arizona.
RightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction, presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
AbstractFor the offshore oil industry, a primary concern is an accidental oil spill. Potentially, oil can spill from the platform during the extraction or from the tanker during the transportation, in both cases will flow into the nearby sea. After an oil spill occurs, to prevent it from polluting even more areas and recover the polluted area, scientists want to understand the process of oil spreading on the sea. In this dissertation, we study the phenomena of oil spreading on water surface. We address a reduced model that captures the local dynamics of an oil slick spreading on flowing water surface and provides an insight on the trend of the spreading process. When the underlying water is locally steady, a full PDE model is analyzed to yield the velocity of the oil slick and its spreading rate. For spreading on a water surface where the flow is locally contracting towards the center of the oil slick, a stationary state is found for the oil slick. For an oil slick spreading on a water surface where the flow is locally expanding towards the edge the slick, the asymptotic spreading rate of the slick and a quasi-steady state are found in this case. We also develop numerical schemes that simulate the dynamics of an oil slick spreading on steady water surface and surface with expanding water flow. For modeling the evolution of crude oil, we introduce a dimension reduction for systems with slow relaxation and develop a multilayer stochastic model. Using the multilayer reduced model, we are able to estimate a single observable quantity of oil based on its past states, without further knowledge on the 'microscopic structure' inside the crude oil. Through synthetic data experiments, our reduced model is demonstrated to have an improved accuracy when implemented with data assimilation methods and can maintain stability while predicting a future state when no data is available.
Degree ProgramGraduate College