A Study of the Non-Linear Seepage Problem in Porous Media via the Homotopy Analysis Method

A non-Darcy flow with moving boundary conditions in a low-permeability reservoir was solved using the homotopy analysis method (HAM), which converted into fixed-boundary mathematical model via similarity transformation. Approximate analytical solutions based on HAM are guaranteed to be more accurate than exact solutions, relative errors between 0.0089% and 2.64%. When λ = 0, pressure drop of Darcy seepage could instantaneously transmitted infinity. > curve exhibited characteristics tight support, clearly different from model’s formation distribution curve. According results HAM, is influenced by threshold gradients longer time. were smaller, boundaries move quickly sensitive external influences. One-dimensional, porous media can reduced if gradient values tend zero.