Some analytical solutions for fluid flow in and around a single fracture in a porous formation based on singular integral equation

Pouya, Ahmad; Vu, Minh‐Ngoc; Pham, Duc Tho; Trieu, Hung Truong; Sang, Nguyen Xuan; To, Quy‐Dong; Nguyen-Thoi, T.

doi:10.1016/j.enganabound.2020.05.012

Cited by 1 publication

(1 citation statement)

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“…Many scholars have overlooked the permeability of soil layers (especially when rock permeability is low) due to the significant role that fractures play in water transport, focusing solely on the flow capacity of fractures (referred to as “one region flow,” i.e., clear flow in fractures). In the early days, the fluid transport study in the fractured porous medium primarily focused on the flow capacity of a single fracture, examining the effects of fracture aperture (Méheust & Schmittbuhl, 2000; Zheng et al., 2008; Lenci, Putti, et al., 2022; Lenci, Méheust, et al., 2022), surface roughness (Boutt et al., 2006), and fluid properties (Felisa et al., 2018; Lavrov, 2014) on the flow capacity of a single fracture through theoretical deductions (Nashawi, 2008; Pouya et al., 2020), numerical simulations (Miyoshi et al., 2003; Xie et al., 2015), and laboratory experiments (Qian et al., 2005, 2007). The description of the flow capacity of a single fracture was initially based on the cubic law (Witherspoon et al., 1980).…”

Section: Introductionmentioning

confidence: 99%

A Semi‐Analytical Solution for the Equivalent Permeability Coefficient of the Multilayered Porous Medium With Continuous Fracture

Zhang,

Liu

2024

Water Resources Research

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Fractures significantly alter the permeability characteristics of the natural porous media, especially for the multilayered porous medium system. The most direct and effective approach to assess the hydraulic conductivity of a multilayered porous medium with continuous fracture is to determine its equivalent permeability coefficient (EPC). A mathematical model with second‐order accuracy is established to analysis the permeability characteristics of the multilayered porous medium incorporating a continuous fracture. The Navier‒Stokes equation is used to govern the clear fluid motion in the continuous fracture, and the seepage fluid motion in the multilayered porous matrix is governed by the Brinkman‒Darcy equation. The semi‐analytical solutions for the velocity profile and EPC of the present model are derived under the conditions of the jumping stress at the fracture‐matrix interface and the continuous velocity at the matrix(i)‐matrix(i +1) interface. The Lattice Boltzmann method, finite element method, and one domain method simulations are conducted to verify the deduced semi‐analytical solutions of the velocity profile. Furthermore, the calculated EPC of the present multilayered model is in good agreement with that of the existing classic models (i.e., one region: fracture, two regions: fracture‐matrix, three regions: fracture‐matrix1‐matrix2, and multilayered porous medium without fracture). Parameter sensitivity reveals that increasing the thickness, dip angle, and porosity of the fractured porous media increases the flow velocity, while an increase in the stress jump coefficient can result in the opposite effect. This implies that porous layers containing fracture are more susceptible to erosion, particularly under conditions of steep dip angle and strong permeability.

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