An improved approximation for hydraulic conductivity for pipes of triangular cross-section by asymptotic means

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Date

2021-01-28

Authors

Keane, Laura
Moyles, Iain
Hall, Cameron

Journal Title

Journal ISSN

Volume Title

Publisher

Springer

Abstract

In this paper, we explore single-phase flow in pores with triangular cross-sections at the pore-scale level. We use analytic and asymptotic methods to calculate the hydraulic conductivity in triangular pores, a typical geometry used in network models of porous media flow. We present an analytical formula for hydraulic conductivity based on Poiseuille flow that can be used in network models contrasting the typical geometric approach leading to many different estimations of the hydraulic conductivity. We consider perturbations to an equilateral triangle by changing the length of one of the triangle sides. We look at both small and large triangles in order to capture triangles that are near and far from equilateral. In each case, the calculations are compared with numerical solutions and the corresponding network approximations. We show that the analytical solution reduces to a quantitatively justifiable formula and agrees well with the numerical solutions in both the near and far from equilateral cases.

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Keywords

Asymptotic analysis, Hydraulic conductivity, Poiseuille flow, Porous media flow, Triangular flow

Citation

Keane, L.M., Hall, C.L. & Moyles, I.R. An improved approximation for hydraulic conductivity for pipes of triangular cross-section by asymptotic means. J Eng Math 126, 12 (2021). https://doi.org/10.1007/s10665-020-10079-y