Flow and Solute Transport in Saturated Porous Media: 1. The Continuum Hypothesis

Salama, Amgad; Geel, Paul J. Van

doi:10.1615/jpormedia.v11.i4.60

Cited by 40 publications

(28 citation statements)

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“…The governing equations describing flow and transport in porous media are based on the continuum approach in which field variables are continuous functions of space and time, Salama and van Geel [7], [8]. Consider the second order elliptic problem that models single phase flow in porous media.…”

Section: Mathematical Formulationmentioning

confidence: 99%

A finite difference, multipoint flux numerical approach to flow in porous media: Numerical examples

Osman

Salama

Sun

et al. 2012

AIP Conference Proceedings

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Abstract. It is clear that none of the current available numerical schemes which may be adopted to solve transport phenomena in porous media fulfill all the required robustness conditions. That is while the finite difference methods are the simplest of all, they face several difficulties in complex geometries and anisotropic media. On the other hand, while finite element methods are well suited to complex geometries and can deal with anisotropic media, they are more involved in coding and usually require more execution time. Therefore, in this work we try to combine some features of the finite element technique, namely its ability to work with anisotropic media with the finite difference approach. We reduce the multipoint flux, mixed finite element technique through some quadrature rules to an equivalent cell-centered finite difference approximation. We show examples on using this technique to single-phase flow in anisotropic porous media.

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Section: Mathematical Formulationmentioning

confidence: 99%

A finite difference, multipoint flux numerical approach to flow in porous media: Numerical examples

Osman

Salama

Sun

et al. 2012

AIP Conference Proceedings

Self Cite

View full text Add to dashboard Cite

show abstract

“…and recently Salama & van Geel (2008a) proposed a set of requirements such that proper upscaling may be achieved. They require that, 1.…”

Section: Requirements For Proper Averagingmentioning

confidence: 99%

“…The answer to this question turns out to be yes as will be explained in the next section. Salama & van Geel (2008a) provided an interesting analogy that sheds light on the possibility to adopt the continuum approach to phenomena occurring in porous media. They stated that an observer closer to a given porous medium will be able to see details of the porous medium (at least at the surface) that an observer from far distant would, generally, ignore.…”

Section: Introductionmentioning

confidence: 99%

“…These length scale constraints were introduced for proper upscaling based on the pioneering work of several researchers including (Whitaker, Gray, Hassanizadeh, Bear, Bachmat, Quintard, Slattery, Cushman, Marle and many others). Recently, (Salama & van Geel, 2008a) have postulated the conditions required for proper upscaling such that one may get the correct set of equations subject to the constraints pertinent to adhering to these conditions, as will be explained later. This set of macroscopic point equations, in which macroscopic field variables are defined at yet a larger scale than their microscopic counterpart, represents the governing conservation laws at the new macroscale.…”

Section: Introductionmentioning

confidence: 99%

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Solute Transport With Chemical Reaction in Singleand Multi-Phase Flow in Porous Media

El-Amin¹,

Salama²,

Sun³

2011

Mass Transfer in Multiphase Systems and Its Applications

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“…In addition to the three popular models, another modelling methodology based on the continuum hypothesis as applied to porous media has been suggested. In this framework, field variables represent continuous functions of space and time, and the governing conservation equations are described in the form of differential equations [34][35][36]. Zhao et al [3][4][5] used a combination of the finite element method and the finite difference method to simulate wormhole generation and propagation in carbonate rocks.…”

Section: Introductionmentioning

confidence: 99%

Parallel simulation of wormhole propagation with the Darcy–Brinkman–Forchheimer framework

Salama

Sun

2015

Computers and Geotechnics

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The acid treatment of carbonate reservoirs is a widely practiced oil and gas well stimulation technique. The injected acid dissolves the material near the wellbore and creates flow channels that establish a good connectivity between the reservoir and the well. Such flow channels are called wormholes. Different from the traditional simulation technology relying on Darcy framework, the new Darcy-Brinkman-Forchheimer (DBF) framework is introduced to simulate the wormhole forming procedure. The DBF framework considers both large and small porosity conditions and should output better simulation results than the Darcy framework. To process the huge quantity of cells in the simulation grid and shorten the long simulation time of the traditional serial code, a parallel code with FORTRAN 90 and MPI was developed. The experimenting field approach to set coefficients in the model equations was also introduced. Moreover, a procedure to fill in the coefficient matrix in the linear system in the solver was described.After this, 2D dissolution experiments were carried out. In the experiments, different configurations of wormholes and a series of properties simulated by both frameworks were compared. We conclude that the numerical results of the DBF framework are more like wormholes and more stable than the Darcy framework, which is a demonstration of the advantages of the DBF framework. Finally, the scalability of the parallel code was evaluated, and we conclude that superlinear scalability can be achieved.

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Flow and Solute Transport in Saturated Porous Media: 1. The Continuum Hypothesis

Cited by 40 publications

References 0 publications

A finite difference, multipoint flux numerical approach to flow in porous media: Numerical examples

A finite difference, multipoint flux numerical approach to flow in porous media: Numerical examples

Solute Transport With Chemical Reaction in Singleand Multi-Phase Flow in Porous Media

Parallel simulation of wormhole propagation with the Darcy–Brinkman–Forchheimer framework

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