Analytical solutions for steady downward flow of a wetting fluid in unsaturated soil using the Adomian decomposition method

Investigating and simulating the steady water flow in an unsaturated soil column containing oil is one of the most important studies in the field of optimizing oil extraction processes. In order to simulate this flow, governing equation for this field should be solved. The governing equation is strongly nonlinear with limited analytical solutions in the literature. In this paper, analytical solutions have been developed for the nonlinear equation in different soil properties using Adomian Decomposition Method (ADM). A total of three soils with different pore size distribution index are considered in this research. These pore size distribution indexes are 2, 3 and 4 for cases 1, 2 and 3, respectively. Results for the presented analytical solutions are capillary pressure head verses elevation in the unsaturated soil column containing oil. To investigate the accuracy of the derived analytical solutions, capillary pressure head values are obtained from a numerical solution and compared with the presented analytical solution values for all cases. An excellent agreement is observed between analytical and numerical results for three cases. These analytical solutions can be used as a benchmark for verification and efficiency assessment of numerical methods.