1. A Study of the Non-Linear Seepage Problem in Porous Media via the Homotopy Analysis Method.
- Author
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You, Xiangcheng, Li, Shiyuan, Kang, Lei, and Cheng, Li
- Subjects
POROUS materials ,NONLINEAR equations ,PRESSURE drop (Fluid dynamics) ,SIMILARITY transformations ,ANALYTICAL solutions ,SEEPAGE - Abstract
A non-Darcy flow with moving boundary conditions in a low-permeability reservoir was solved using the homotopy analysis method (HAM), which was converted into a fixed-boundary mathematical model via similarity transformation. Approximate analytical solutions based on the HAM are guaranteed to be more accurate than exact analytical solutions, with relative errors between 0.0089% and 2.64%. When λ = 0, the pressure drop of the Darcy seepage model could be instantaneously transmitted to infinity. When λ > 0, the pressure drop curve of the non-Darcy seepage model exhibited the characteristics of tight support, which was clearly different from the Darcy seepage model's formation pressure distribution curve. According to the results of the HAM, a moving boundary is more influenced by threshold pressure gradients with a longer time. When the threshold pressure gradients were smaller, the moving boundaries move more quickly and are more sensitive to external influences. One-dimensional, low-permeability porous media with a non-Darcy flow with moving boundary conditions can be reduced to a Darcy seepage model if the threshold pressure gradient values tend to zero. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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