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

Xiangcheng You (), Shiyuan Li, Lei Kang and Li Cheng
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Xiangcheng You: State Key Laboratory of Petroleum Resources and Prospecting, College of Petroleum Engineering, China University of Petroleum-Beijing, Beijing 102249, China
Shiyuan Li: State Key Laboratory of Petroleum Resources and Prospecting, College of Petroleum Engineering, China University of Petroleum-Beijing, Beijing 102249, China
Lei Kang: State Key Laboratory of Petroleum Resources and Prospecting, College of Petroleum Engineering, China University of Petroleum-Beijing, Beijing 102249, China
Li Cheng: State Key Laboratory of Petroleum Resources and Prospecting, College of Petroleum Engineering, China University of Petroleum-Beijing, Beijing 102249, China

Energies, 2023, vol. 16, issue 5, 1-13

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.

Keywords: low permeability; non-Darcy flow; homotopy analysis method (HAM); moving boundary (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2023
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