Modeling Fluid Flow in Fractured Porous Media with the Interfacial Conditions Between Porous Medium and Fracture

Hosseini, N.; Khoei, A.R.

doi:10.1007/s11242-021-01648-5

Cited by 14 publications

(3 citation statements)

References 25 publications

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“…(2010) derived the expression for the equivalent permeability coefficient of symmetric fracture‐matrix models under the velocity slip interface boundary condition (called the “B‐J” boundary (Beavers & Joseph, 1967)). However, for the study of flow field characteristics of some irregular and complex fracture‐matrix models, most of it is based on numerical simulation methods such as Lattice Boltzmann method (LBM) (Landry et al., 2014; Landry & Karpyn, 2012), FEM (Hosseini & Khoei, 2021; Salimzadeh et al., 2017), and Finite difference method (FDM) (Z. Q. Huang et al., 2014; Yan et al., 2016).…”

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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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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“…An enhanced version of DFN, based on the concept of fractured porous media, was proposed for modeling fluid flow in both the rock matrix and discrete fractures, where the flux interaction between them is allowed (Hoteit and Firoozabadi 2008b;Choo and Lee 2018;Berre et al 2019). Meanwhile, combined with the finite difference, finite element and finite volume methods, the DFN-based methods have gained many successes in simulation of hydraulic process as well as mechanical deformation (Gupta and Duarte 2018;Wang et al 2019bWang et al , 2020Hosseini and Khoei 2021;Wang et al 2022).…”

Section: Introductionmentioning

confidence: 99%

Investigating Effects of Heterogeneity and Fracture Distribution on Two-Phase Flow in Fractured Reservoir with adaptive time strategy

et al. 2022

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Modeling of fluid flow in porous media is a pillar in geoscience applications. Previous studies have revealed that heterogeneity and fracture distribution have considerable influence on fluid flow. In this work, a numerical investigation of two-phase flow in heterogeneous fractured reservoir is presented. First, the discrete fracture model is implemented based on a hybrid-dimensional modeling approach, and an equivalent continuum approach is integrated in the model to reduce computational cost. A multilevel adaptive strategy is devised to improve the numerical robustness and efficiency. It allows up to 4-levels adaption, where the adaptive factors can be modified flexibly. Then, numerical tests are conducted to verify the the proposed method and to evaluate its performance. Different adaptive strategies with 3-levels, 4-levels and fixed time schemes are analyzed to evaluate the computational cost and convergence history. These evaluations demonstrate the merits of this method compared to the classical method. Later, the heterogeneity in permeability field, as well as initial saturation, is modeled in a layer model, where the effect of layer angle and permeability on fluid flow is investigated. A porous medium containing multiple length fractures with different distributions is simulated. The fine-scale fractures are upscaled based on the equivalent approach, while the large-scale fractures are retained. The conductivity of the rock matrix is enhanced by the upscaled fine-scale fractures. The difference of hydraulic property between homogeneous and heterogeneous situations is analyzed. It reveals that the heterogeneity may influence fluid flow and production, while these impacts are also related to fracture distribution and permeability.

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“…The increase in temperature with increased depth in the Earth, known as the geothermal gradient, is not uniform around the globe as this temperature rises in a range of 2-3 • C per 100 m of depth on average [2]. There are many numerical methods for related studies, such as the finite element method, which can provide a general analysis [3], and the boundary element method, which allows for more accurate calculation [4]. Numerical methods cannot quantify transfer in porous media as sufficiently as analytical methods.…”

Section: Introductionmentioning

confidence: 99%

Dimensionless Characterization to Estimate Horizontal Groundwater Velocity from Temperature–Depth Profiles in Aquifers

Jiménez-Valera

Alhama

2022

Mathematics

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The outcome of a dimensionless characterization study in a two-dimensional porous media domain in which groundwater flows at a constant horizontal velocity is presented in this report. Using spatial discrimination, the dimensionless groups that govern the solution patterns are determined from dimensionless governing equations. As a boundary condition on the surface, the case of constant temperature is studied. From the mathematical deduction of the groups, a characteristic horizontal length emerges. This length determines the region in which temperature–depth profiles are affected by flow. Existing analytical solutions have been shown to be invalid due to the severe assumption that the horizontal thermal gradient has a constant value. Therefore, universal solutions based on pi theorem have been obtained for the characteristic horizontal length, temperature field, temperature–depth profiles and horizontal temperature profiles. Dependencies between dimensionless groups have been depicted by universal curves, abacuses and surfaces. These graphical solutions are used in an easy way to estimate groundwater velocity from experimental temperature measurements in the form of an inverse problem. In addition, an easy and fast protocol for estimating fluid flow velocity and groundwater inlet temperature from temperature profile measurements is proposed. This protocol is applied in a scenario of groundwater discharge from a quaternary aquifer to a salty lagoon located in the southeast of Spain.

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Modeling Fluid Flow in Fractured Porous Media with the Interfacial Conditions Between Porous Medium and Fracture

Cited by 14 publications

References 25 publications

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

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

Investigating Effects of Heterogeneity and Fracture Distribution on Two-Phase Flow in Fractured Reservoir with adaptive time strategy

Dimensionless Characterization to Estimate Horizontal Groundwater Velocity from Temperature–Depth Profiles in Aquifers

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