Upscaled models of flow and transport in faulted sandstone: boundary condition effects and explicit fracture modelling

2004 ◽  
Vol 10 (2) ◽  
pp. 173-181 ◽  
Author(s):  
Eric A. Flodin ◽  
Louis J. Durlofsky ◽  
Atilla Aydin
Keyword(s):  
Boundary Condition ◽  
Flow And Transport

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.

scholarly journals New features of version 3 of the HYDRUS (2D/3D) computer software package

2018 ◽  
Vol 66 (2) ◽  
pp. 133-142 ◽  
Author(s):  
Jiří Šimůnek ◽  
Miroslav Šejna ◽  
Martinus Th. van Genuchten
Keyword(s):  
Boundary Condition ◽  
Graphical User Interface ◽  
Software Package ◽  
Computer Software ◽  
Transport Processes ◽  
Flow And Transport ◽  
Software Packages ◽  
3D Software ◽  
Growth Features ◽  
Hydrus 1D

AbstractThe capabilities of the HYDRUS-1D and HYDRUS (2D/3D) software packages continuously expanded during the last two decades. Various new capabilities were added recently to both software packages, mostly by developing new standard add-on modules such as HPx, C-Ride, UnsatChem, Wetland, Fumigant, DualPerm, and Slope Stability. The new modules may be used to simulate flow and transport processes in one- and two-dimensional transport domains and are fully supported by the HYDRUS graphical user interface (GUI). Several nonstandard add-on modules, such as Overland, Isotope, and Centrifuge, have also been developed, but are not fully supported by the HYDRUS GUI. The objective of this manuscript is to describe several additional features of the upcoming Version 3 of HYDRUS (2D/3D), which was unveiled at a recent (March 2017) HYDRUS conference and workshop in Prague. The new features include a flexible reservoir boundary condition, expanded root growth features, and new graphical capabilities of the GUI. Mathematical descriptions of the new features are provided, as well as two examples illustrating applications of the reservoir boundary condition.

One-Dimensional Fin-Tip Boundary Condition Correction II

2001 ◽  
Vol 22 (5) ◽  
pp. 35-40 ◽  
Author(s):  
D. C. Look Jr ◽  
Arvind Krishnan
Keyword(s):  
Boundary Condition ◽  
One Dimensional

Sturm-Liouville Problem for Stationary Differential Operator with Nonlocal Two-Point Boundary Conditions

2006 ◽  
Vol 11 (1) ◽  
pp. 47-78 ◽  
Author(s):  
S. Pečiulytė ◽  
A. Štikonas
Keyword(s):  
Boundary Condition ◽  
Differential Operator ◽  
Boundary Conditions ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Liouville Problem ◽  
Complex Case ◽  
Qualitative Behavior ◽  
Point Boundary ◽  
Sturm Liouville

The Sturm-Liouville problem with various types of two-point boundary conditions is considered in this paper. In the first part of the paper, we investigate the Sturm-Liouville problem in three cases of nonlocal two-point boundary conditions. We prove general properties of the eigenfunctions and eigenvalues for such a problem in the complex case. In the second part, we investigate the case of real eigenvalues. It is analyzed how the spectrum of these problems depends on the boundary condition parameters. Qualitative behavior of all eigenvalues subject to the nonlocal boundary condition parameters is described.

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