Anomalous diffusion in porous media

Ferreira, J. A.; Pena, Gonçalo; Romanazzi, Giuseppe

doi:10.1016/j.apm.2015.09.034

Cited by 23 publications

(13 citation statements)

References 42 publications

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“…3(b), in which the left boundary is treated as an injection well (line source) and the right boundary is treated as a production well (line sink). We consider a heterogeneous porous medium and choose the permeability function K(x) as given in [74]. The permeability function is given by…”

Section: Waterflooding In a Rectilinear Geometry With A Heterogeneous Permeability Fieldmentioning

confidence: 99%

Modeling and simulation of surfactant–polymer flooding using a new hybrid method

Daripa

Dutta

2017

Journal of Computational Physics

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Chemical enhanced oil recovery by surfactant-polymer (SP) flooding has been studied in two space dimensions. A new global pressure for incompressible, immiscible, multicomponent two-phase porous media flow has been derived in the context of SP flooding. This has been used to formulate a system of flow equations that incorporates the effect of capillary pressure and also the effect of polymer and surfactant on viscosity, interfacial tension and relative permeabilities of the two phases. The coupled system of equations for pressure, water saturation, polymer concentration and surfactant concentration has been solved using a new hybrid method in which the elliptic global pressure equation is solved using a discontinuous finite element method and the transport equations for water saturation and concentrations of the components are solved by a Modified Method Of Characteristics (MMOC) in the multicomponent setting. Numerical simulations have been performed to validate the method, both qualitatively and quantitatively, and to evaluate the relative performance of the various flooding schemes for several different heterogeneous reservoirs.

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Section: Waterflooding In a Rectilinear Geometry With A Heterogeneous Permeability Fieldmentioning

confidence: 99%

Modeling and simulation of surfactant–polymer flooding using a new hybrid method

Daripa

Dutta

2017

Journal of Computational Physics

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“…Therefore, it can be easily used with any of the available models for dispersion in the literature. Here, we use a common model for porous media, which is used in Ghesmat and Azaiez 18 and Ferreira et al 17 The dispersion is given by…”

Section: Dispersionmentioning

confidence: 99%

“…18 This model is also popular in recent (non-stability) works on dispersion in porous media. 17 Therefore, we employ this model here (see Section V).…”

Section: Introductionmentioning

confidence: 99%

Studies on dispersive stabilization of porous media flows

Daripa

Gin

2016

Physics of Fluids

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Motivated by a need to improve the performance of chemical enhanced oil recovery (EOR) processes, we investigate dispersive effects on the linear stability of three-layer porous media flow models of EOR for two different types of interfaces: permeable and impermeable interfaces. Results presented are relevant for the design of smarter interfaces in the available parameter space of capillary number, Peclet number, longitudinal and transverse dispersion, and the viscous profile of the middle layer. The stabilization capacity of each of these two interfaces is explored numerically and conditions for complete dispersive stabilization are identified for each of these two types of interfaces. Key results obtained are (i) three-layer porous media flows with permeable interfaces can be almost completely stabilized by diffusion if the optimal viscous profile is chosen, (ii) flows with impermeable interfaces can also be almost completely stabilized for short time, but become more unstable at later times because diffusion flattens out the basic viscous profile, (iii) diffusion stabilizes short waves more than long waves which leads to a "turning point" Peclet number at which short and long waves have the same growth rate, and (iv) mechanical dispersion further stabilizes flows with permeable interfaces but in some cases has a destabilizing effect for flows with impermeable interfaces, which is a surprising result. These results are then used to give a comparison of the two types of interfaces. It is found that for most values of the flow parameters, permeable interfaces suppress flow instability more than impermeable interfaces. Published by AIP Publishing.

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“…For the history of FC, see the articles Ross 6 and Machado et al 7 The FC has applications in the reaction diffusion equations [8][9][10] and is used to explain the well-known phenomena of anomalous diffusion observed in experiments. 9,[11][12][13] The time fractional diffusion equations are obtained by replacing time derivative with fractional derivative in time variable to explain the sub-diffusion or super diffusion. 14,15 In this article, we are interested in determination of the solution, ie, u(x, t), and the space-dependent source term, ie, f(x), for the equation…”

Section: Introductionmentioning

confidence: 99%

An inverse problem for a family of two parameters time fractional diffusion equations with nonlocal boundary conditions

Ali

Malik

2017

Math Methods in App Sciences

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The determination of a space-dependent source term along with the solution for a 1-dimensional time fractional diffusion equation with nonlocal boundary conditions involving a parameter > 0 is considered. The fractional derivative is generalization of the Riemann-Liouville and Caputo fractional derivatives usually known as Hilfer fractional derivative. We proved existence and uniqueness results for the solution of the inverse problem while over-specified datum at 2 different time is given. The over-specified datum at 2 time allows us to avoid initial condition in terms of fractional integral associated with Hilfer fractional derivative. KEYWORDS bi-orthogonal system of functions, Hilfer fractional derivative, Mittag-Leffler function, nonlocal boundary conditions Math Meth Appl Sci. 2017;40:7737-7748.wileyonlinelibrary.com/journal/mma

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Anomalous diffusion in porous media

Cited by 23 publications

References 42 publications

Modeling and simulation of surfactant–polymer flooding using a new hybrid method

Modeling and simulation of surfactant–polymer flooding using a new hybrid method

Studies on dispersive stabilization of porous media flows

An inverse problem for a family of two parameters time fractional diffusion equations with nonlocal boundary conditions

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