The Application of the Variational Iteration Method for Solving the Problem of Diffusion of Oil and Water in Underground Reservoirs

In this paper, an attempt was made to investigate the diffusion of oil and water in underground reservoirs. Underground water is often withdrawn for agricultural, municipal, and industrial use by constructing and operating extraction wells. Mathematical modeling of this phenomenon was presented as a nonlinear diffusion problem. Variational iteration method was utilized for this purpose. Among the main features of the method are its flexibility and ability to solve nonlinear equations. This technique does not require any discretization, linearization or small perturbations and therefore reduces the numerical computations to a great extent. Numerical examples were examined to show the efficiency of the technique.