Radionuclide Transport in Fractured Porous Media—Analytical Solutions for a System of Parallel Fractures with a Flux-Type Boundary Condition

1997 ◽  
Vol 117 (2) ◽  
pp. 223-233 ◽  
Author(s):  
Chu-Tien Chen ◽  
Shih-Hai Li
Keyword(s):  
Boundary Condition ◽  
Porous Media ◽  
Analytical Solutions ◽  
Fractured Porous Media ◽  
Radionuclide Transport ◽  
Type Boundary ◽  
Type Boundary Condition

Heat Transfer in Composite Spheroids

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Rajai Alassar
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Prolate Spheroid ◽  
Published Data ◽  
Composite Sphere ◽  
Legendre Series ◽  
The Third ◽  
Type Boundary ◽  
Type Boundary Condition ◽  
The Impact

Abstract Heat transfer from a composite prolate spheroid under the third-type boundary condition is investigated using a Legendre series expansion. The model is verified against published data on cooling boiled eggs and also against the asymptotic solution of a composite sphere. The impact of Biot number on the heat transfer in spheroids with realistic dimensions and properties, such as eggs and olives, is investigated. The results are also presented for varying conductivity ratios and fractional volume of the inner part of the spheroid.

scholarly journals A Computational Workflow for Flow and Transport in Fractured Porous Media Based on a Hierarchical Nonlinear Discrete Fracture Modeling Approach

Energies ◽  
2020 ◽  
Vol 13 (24) ◽  
pp. 6667
Author(s):  
Wenjuan Zhang ◽  
Waleed Diab ◽  
Hadi Hajibeygi ◽  
Mohammed Al Kobaisi
Keyword(s):  
Boundary Condition ◽  
Porous Media ◽  
Boundary Conditions ◽  
Large Scale ◽  
Fractured Porous Media ◽  
Small Scale ◽  
Flow And Transport ◽  
Fracture Length ◽  
Discrete Fracture ◽  
Computational Workflow

Modeling flow and transport in fractured porous media has been a topic of intensive research for a number of energy- and environment-related industries. The presence of multiscale fractures makes it an extremely challenging task to resolve accurately and efficiently the flow dynamics at both the local and global scales. To tackle this challenge, we developed a computational workflow that adopts a two-level hierarchical strategy based on fracture length partitioning. This was achieved by specifying a partition length to split the discrete fracture network (DFN) into small-scale fractures and large-scale fractures. Flow-based numerical upscaling was then employed to homogenize the small-scale fractures and the porous matrix into an equivalent/effective single medium, whereas the large-scale fractures were modeled explicitly. As the effective medium properties can be fully tensorial, the developed hierarchical framework constructed the discrete systems for the explicit fracture–matrix sub-domains using the nonlinear two-point flux approximation (NTPFA) scheme. This led to a significant reduction of grid orientation effects, thus developing a robust, applicable, and field-relevant framework. To assess the efficacy of the proposed hierarchical workflow, several numerical simulations were carried out to systematically analyze the effects of the homogenized explicit cutoff length scale, as well as the fracture length and orientation distributions. The effect of different boundary conditions, namely, the constant pressure drop boundary condition and the linear pressure boundary condition, for the numerical upscaling on the accuracy of the workflow was investigated. The results show that when the partition length is much larger than the characteristic length of the grid block, and when the DFN has a predominant orientation that is often the case in practical simulations, the workflow employing linear pressure boundary conditions for numerical upscaling give closer results to the full-model reference solutions. Our findings shed new light on the development of meaningful computational frameworks for highly fractured, heterogeneous geological media where fractures are present at multiple scales.

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