Oil and water interaction: a mathematical modeling approach


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A thesis Submitted in Partial Fulfillment of the Requirements for the Degree of MASTER of SCIENCE in MATHEMATICS from Texas A&M University-Corpus Christi in Corpus Christi, Texas.
The physical characteristics of oil are subject to a complex transformation in the marine environment as a result of different biogeochemical processes that begin developing from the initial interaction between oil and sea water. The qualities of oil change at the initial direct interaction is due to a mixture of physical, chemical and biological alterations and degradations. This thesis explores the changes in the main physical characteristics of the spilled oil that occur after the oil spill. To study these interdependent changes a coupled ordinary differential equations (ODE) system was developed and solved numerically using MATLAB. The primary purpose of the thesis was to develop a mathematical model that describe the behavior and final outcome of pollutants such as oil and oil products in marine environments. The model includes the following oil spill process: evaporation, spreading, emulsification, loss of volume, and viscosity. The results were compared with other mathematical models published in the literature. It confirmed the area increase and viscosity increase of oil slick in other models of the field. In addition, the model developed corrected volume decrease in connection to the area increase over time as a result of adding a Biodegradation term to the right hand side of the volume rate equation. The model will be useful for comparing theoretical results with real spills data in the Gulf of Mexico, Arabian Gulf, and N’kossa in the Republic of Congo. Also, it will be helpful using results of such a comparison to adjust parameters and mathematical model of the system of equations under consideration. Results for the case study indicate that the model can predict the fate and transport of oil spills in the sea with reasonable accuracy over a relatively short period of time.
Mathematics and Statistics
College of Science and Engineering