Two-dimensional analytical solutions for a two-pump free product recovery system

As of 1986, more than 12,000 incidents of oil spills were identified throughout the country. When an immiscible oil, lighter than water, leaks above an unconfined aquifer, it migrates down under the influence of gravity and eventually reaches the ground water surface. The floating oil on the ground water surface is called the free product. A model was developed to estimate the free product recovery by a two-pump operation in a two-dimensional aquifer. Governing equations were obtained in terms of free product thickness and water table drawdown by vertical averaging of the mass balance equations for the oil and water phases. Simultaneous analytical solutions of these two coupled equations were obtained by applying an integral transform. The analytical solutions estimate the temporal and spatial variation of free product thickness and drawdown. Results were presented graphically to illustrate these variations for a particular set of model parameters