Numerical investigation of nanoparticles transport in anisotropic porous media

Abstract

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.

Flow and Transport in Tight and Shale Formations: A Review

“…Salama et al [145,146] also developed what they called the experimenting field algorithm in which the matrix of coefficients of a linear system is constructed automatically, rather than being inputted manually. This technique has been tested in various cases and shows to be very effective (Salama et al [147][148][149], Wu et al [150], Negara et al [151,152], and El-Amin et al [153]). Furthermore, Salama et al [154] and Salama [155] developed a technique that numerically solves the problem of flow towards a well in an efficient manner.…”

Adaptive Time-Splitting Scheme for Nanoparticles Transport with Two-Phase Flow in Heterogeneous Porous Media

“…In the following we introduce the governing equations briefly, (for details see Refs. [22,23,24,25,26,28,29]:…”

“…So, The transport equation of the nanoparticles in the water phase is given as ( [18,21,19,20,22,23,24,25,26,28,29]),…”

“…[25], they have introduced numerical and dimensional analyses of nanoparticles transport with a twophase flow in porous media. Salama et al [26] have investigated the problem of transport of nanoparticles in anisotropic porous media numerically using the multipoint flux approximation. Recently, Chen et al [27] presented a numerical simulation of drag reduction effects by hydrophobic nanoparticles adsorption method in water flooding processes.…”

A Multiscale Time-Splitting Discrete Fracture Model of Nanoparticles Transport in Fractured Porous Media

“…El-Amin et al [3][4][5][6][7] developed some models of transport of nanoparticles in a two-phase flow in porous media. The problem of nanoparticles transport in anisotropic porous media using the multipoint flux approximation was investigated by Salama et al [8] . Chen et al [9] introduced a numerical simulation of drag reduction effects by hydrophobic nanoparticles adsorption method in water flooding processes.…”