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

Osman, H.; Salama, Amgad; Sun, Shuyu; Bao, Kai

doi:10.1063/1.4711178

Cited by 6 publications

(3 citation statements)

References 9 publications

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“…This approach is so-called multipoint flux mixed finite element (MPFMFE). In the last decade, the implementation of MPFA into single-phase or multiphase flow models for 2-D and 3-D problems has been deeply discussed [12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Multiphase flow simulation with gravity effect in anisotropic porous media using multipoint flux approximation

2015

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Please cite this article as: Negara, A., Salama, A., Sun, S., Multiphase flow simulation with gravity effect in anisotropic porous media using multipoint flux approximation, Computers & Fluids (2015), doi: http://dx.doi.org/ 10. 1016/j.compfluid.2015.02.012 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. AbstractNumerical investigations of two-phase flows in anisotropic porous media have been conducted. In the flow model, the permeability has been considered as a full tensor and is implemented in the numerical scheme using the multipoint flux approximation within the framework of finite difference method. In addition, the experimenting pressure field approach is used to obtain the solution of the pressure field, which makes the matrix of coefficient of the global system easily constructed. A number of numerical experiments on the flow of two-phase system in two-dimensional porous medium domain are presented. In this work, the gravity is included in the model to capture the possible buoyancy-driven effects due to density differences between the two phases. Different anisotropy scenarios have been considered. From the numerical results, interesting patterns of the flow, pressure, and saturation fields emerge, which are significantly influenced by the anisotropy of the absolute permeability field. It is found that the two-phase system moves along the principal direction of anisotropy.2 Furthermore, the effects of anisotropy orientation on the flow rates and the cross flow index are also discussed in the paper.

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Section: Introductionmentioning

confidence: 99%

Multiphase flow simulation with gravity effect in anisotropic porous media using multipoint flux approximation

2015

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“…We also adapt the experimenting field approach developed by Sun et al (2012) which solves a set of local problems and construct the global system automatically, Salama et al 2014. This scheme has been rigorously tested against a number of cases in both single and two-phase systems including anisotropy, e.g., Osman et al 2012, Negara et al 2013. Multipoint flux approximation has grown following two independent routes.…”

Section: Numerical Algorithmmentioning

confidence: 99%

Numerical investigation of nanoparticles transport in anisotropic porous media

Salama

Negara

El-Amin

et al. 2015

Journal of Contaminant Hydrology

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In this work the problem related to the transport of nanoparticles in anisotropic porous media is investigated numerically using the multipoint flux approximation. Anisotropy of porous media properties are an essential feature that exist almost everywhere in subsurface formations. In anisotropic media, the flux and the pressure gradient vectors are no longer collinear and therefore interesting patterns emerge. The transport of nanoparticles in subsurface formations is affected by several complex processes including surface charges, heterogeneity of nanoparticles and soil grain collectors, interfacial dynamics of double-layer and many others. We use the framework of the theory of filtration in this investigation. Processes like particles deposition, entrapment, as well as detachment are accounted for. From the numerical methods point of view, traditional twopoint flux finite difference approximation cannot handle anisotropy of media properties. Therefore, in this work we use the multipoint flux approximation (MPFA). In this technique, the flux components are affected by more neighboring points as opposed to the mere two points that are usually used in traditional finite volume methods. We also use the experimenting pressure field approach which automatically constructs the global system of equations by solving multitude of local problems. This approach facilitates to a large extent the construction of the global system. A set of numerical examples is considered involving two-dimensional rectangular domain. A source of nanoparticles is inserted in the middle of the anisotropic layer. We investigate the effects of both anisotropy angle and anisotropy ratio on the transport of nanoparticles in saturated porous media. It is found that the concentration plume and porosity contours follow closely the principal direction of anisotropy of permeability of the central domain.

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“…In this work, we only implement the MPFA O-method. MPFA Omethod (later simply called MPFA) has been widely implemented for simulating the fluid flow behavior in anisotropic porous media, either single-phase or multiphase flow [Keilegavlen et al, 2012;Wolff et al, 2012;Osman et al, 2012;Negara et al 2013], as well as to the problem of conduction heat transfer in anisotropic porous media [Salama et al 2013b]. MPFA method provides advantage in particular when the discretizations are not aligned with the principal directions of permeability in the model.…”

Section: Multipoint Flux Approximation and Its Numerical Discretizationmentioning

confidence: 99%

Density-Driven Flow Simulation in Anisotropic Porous Media: Application to CO2 Geological Sequestration

2014

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Carbon dioxide (CO 2 ) sequestration in saline aquifers is considered as one of the most viable and promising ways to reduce CO 2 concentration in the atmosphere. CO 2 is injected into deep saline formations at supercritical state where its density is smaller than the hosting brine. This motivates an upward motion and eventually CO 2 is trapped beneath the cap rock. The trapped CO 2 slowly dissolves into the brine causing the density of the mixture to become larger than the host brine. This causes gravitational instabilities that is propagated and magnified with time. In this kind of density-driven flows, the CO 2 -rich brines migrate downward while the brines with low CO 2 concentration move upward. With respect to the properties of the subsurface aquifers, there are instances where saline formations can possess anisotropy with respect to their hydraulic properties. Such anisotropy can have significant effect on the onset and propagation of flow instabilities. Anisotropy is predicted to be more influential in dictating the direction of the convective flow. To account for permeability anisotropy, the method of multipoint flux approximation (MPFA) in the framework of finite differences schemes is used. The MPFA method requires more point stencil than the traditional two-point flux approximation (TPFA). For example, calculation of one flux component requires 6-point stencil and 18-point stencil in 2-D and 3-D cases, respectively. As consequence, the matrix of coefficient for obtaining the pressure fields will be quite complex. Therefore, we combine the MPFA method with the experimenting pressure field technique in which the problem is reduced to solving multitude of local problems and the global matrix of coefficients is constructed automatically, which significantly reduces the complexity. We present several numerical scenarios of density-driven flow simulation in homogeneous, layered, and heterogeneous anisotropic porous media. The numerical results emphasize the significant effects of anisotropy in driving the migration of dissolved CO 2 along the principal direction of anisotropy even if the porous medium is highly heterogeneous. Furthermore, the impacts of the increase of density difference between the brine and the CO 2 -saturated brine with respect to the onset time of convection, the CO 2 flux, and the CO 2 total dissolved mass are also discussed in this paper. Motivation and backgroundNowadays, global warming issue has become the world-widely discussed topic due to the change of climate on the Earth. One of the causes of the global warming is the greenhouse gasses emission, i.e., the release of CO 2 into the atmosphere due to the use of fossil fuels in the industry activities such as power plant, refineries, petrochemical industries, oil and gas processing, etc. The amount of CO 2 concentration in the atmosphere has steadily increased particularly in the last century, from 280 ppm (prior to the industrial revolution) to 390 ppm (at the current time) with annual increase of 1 to 2 ppm [Firoozabadi ...

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

Cited by 6 publications

References 9 publications

Multiphase flow simulation with gravity effect in anisotropic porous media using multipoint flux approximation

Multiphase flow simulation with gravity effect in anisotropic porous media using multipoint flux approximation

Numerical investigation of nanoparticles transport in anisotropic porous media

Density-Driven Flow Simulation in Anisotropic Porous Media: Application to CO2 Geological Sequestration

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