A new formulation of the dispersion tensor in homogeneous porous media

Valdés‐Parada, Francisco J.; Lasseux, Didier; Bellet, Fabien

doi:10.1016/j.advwatres.2016.02.012

Cited by 19 publications

(13 citation statements)

References 31 publications

(64 reference statements)

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“…An alternative strategy, requiring consideration of only adjoint variables, has been proposed by Valdés-Parada, Lasseux & Bellet (2016). It consists in solving the system which holds since the microscopic equation applies in the unit cell (Mei & Vernescu 2010).…”

Section: The Flow In a Porous Mediummentioning

confidence: 99%

Flow over natural or engineered surfaces: an adjoint homogenization perspective

Bottaro

2019

J. Fluid Mech.

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Natural and engineered surfaces are never smooth, but irregular, rough at different scales, compliant, possibly porous, liquid impregnated or superhydrophobic. The correct numerical modelling of fluid flowing through and around them is important but poses problems. For media characterized by a periodic or quasi-periodic microstructure of characteristic dimensions smaller than the relevant scales of the flow, multiscale homogenization can be used to study the effect of the surface, avoiding the numerical resolution of small details. Here, we revisit the homogenization strategy using adjoint variables to model the interaction between a fluid in motion and regularly micro-textured, permeable or impermeable walls. The approach described allows for the easy derivation of auxiliary/adjoint systems of equations which, after averaging, yield macroscopic tensorial properties, such as permeability, elasticity, slip, transpiration, etc. When the fluid in the neighbourhood of the microstructure is in the Stokes regime, classical results are recovered. Adjoint homogenization, however, permits simple extension of the analysis to the case in which the flow displays nonlinear effects. Then, the properties extracted from the auxiliary systems take the name of effective properties and do not depend only on the geometrical details of the medium, but also on the microscopic characteristics of the fluid motion. Examples are shown to demonstrate the usefulness of adjoint homogenization to extract effective tensor properties without the need for ad hoc parameters. In particular, notable results reported herein include:(i)an original formulation to describe filtration in porous media in the presence of inertial effects;(ii)the microscopic and macroscopic equations needed to characterize flows through poroelastic media;(iii)an extended Navier’s condition to be employed at the boundary between a fluid and an impermeable rough wall, with roughness elements which can be either rigid or linearly elastic;(iv)the microscopic problems needed to define the relevant parameters for a Saffman-like condition at the interface between a fluid and a porous substrate; and(v)the macroscopic equations which hold at the dividing surface between a free-fluid region and a fluid-saturated poroelastic domain.

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Section: The Flow In a Porous Mediummentioning

confidence: 99%

Flow over natural or engineered surfaces: an adjoint homogenization perspective

Bottaro

2019

J. Fluid Mech.

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“…The procedure described above to compute H * and F was followed by different authors [24,[29][30][31][32]56]. A more elegant approach which does not require the microscopic flow problem solution can be used, as developed earlier [57]. In fact, the microscopic velocity can be expressed in terms of the closure and macroscopic quantities as [15]…”

Section: Closure Problem Under a Closed Formmentioning

confidence: 99%

Origin of the inertial deviation from Darcy's law: An investigation from a microscopic flow analysis on two-dimensional model structures

2017

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Inertial flow in porous media occurs in many situations of practical relevance among which one can cite flows in column reactors, in filters, in aquifers, or near wells for hydrocarbon recovery. It is characterized by a deviation from Darcy's law that leads to a nonlinear relationship between the pressure drop and the filtration velocity. In this work, this deviation, also known as the nonlinear, inertial, correction to Darcy's law, which is subject to controversy upon its origin and dependence on the filtration velocity, is studied through numerical simulations. First, the microscopic flow problem was solved computationally for a wide range of Reynolds numbers up to the limit of steady flow within ordered and disordered porous structures. In a second step, the macroscopic characteristics of the porous medium and flow (permeability and inertial correction tensors) that appear in the macroscale model were computed. From these results, different flow regimes were identified: (1) the weak inertia regime where the inertial correction has a cubic dependence on the filtration velocity and (2) the strong inertia (Forchheimer) regime where the inertial correction depends on the square of the filtration velocity. However, the existence and origin of those regimes, which depend also on the microstructure and flow orientation, are still not well understood in terms of their physical interpretations, as many causes have been conjectured in the literature. In the present study, we provide an in-depth analysis of the flow structure to identify the origin of the deviation from Darcy's law. For accuracy and clarity purposes, this is carried out on two-dimensional structures. Unlike the previous studies reported in the literature, where the origin of inertial effects is often identified on a heuristic basis, a theoretical justification is presented in this work. Indeed, a decomposition of the convective inertial term into two components is carried out formally allowing the identification of a correlation between the flow structure and the different inertial regimes. These components correspond to the curvature of the flow streamlines weighted by the local fluid kinetic energy on the one hand and the distribution of the kinetic energy along these lines on the other hand. In addition, the role of the recirculation zones in the occurrence and in the form of the deviation from Darcy's law was thoroughly analyzed. For the porous structures under consideration, it is shown that (1) the kinetic energy lost in the vortices is insignificant even at high filtration velocities and (2) the shape of the flow streamlines induced by the recirculation zones plays an important role in the variation of the flow structure, which is correlated itself to the different flow regimes.

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“…It is important to mention that in the method of volume averaging, the values for effective transport coefficients and the validity of average transport equations have been proven independently from each other. In addition, the effects of the multiphase and multiscale information captured by the transport coefficients at a lower length scale on the global behaviour of the system are almost never validated or proven . Therefore, these tasks remain incomplete.…”

Section: Introductionmentioning

confidence: 99%

“…In addition, the effects of the multiphase and multiscale information captured by the transport coefficients at a lower length scale on the global behaviour of the system are almost never validated or proven. [35][36][37] Therefore, these tasks remain incomplete.…”

Section: Introductionmentioning

confidence: 99%

CFD analysis of bed textural characteristics on TBR behaviour: Kinetics, scaling‐up, multiscale analysis, and wall effects

Uribe¹,

Cordero²,

Zárate³

et al. 2018

Can J Chem Eng

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A simulation of a trickle bed reactor aided by computational fluid dynamics was implemented. With a Eulerian approach, geometrical characteristics were explicitly considered and two simultaneous heterogeneous reactions were included, hydrodesulphurization (HDS) and hydrodenitrogenation (HDN). This was performed in order to achieve the following: (1) attain further insight into a proper scaling‐up procedure to be able to obtain the same hydrodynamics and kinetics behaviour in two reactors of different length and diameter scales; (2) develop a multiscale analysis regarding the communication of information between scales through the construction of a porous microstructure model from which the geometrical information of the microscale is captured by the effective transport coefficients (which affect the overall reactor behaviour); (3) investigate the effect of operation condition variations on hydrodynamics and kinetics; and (4) assess the deviations and further differences observed from average to punctual conversion values and the assumptions from kinetic literature models through a preliminary multiscale analysis. The CFD results were validated against experimental pressure drop data as well as HDS and HDN conversion theoretical data. An excellent agreement was found. The model produces a significant improvement in hydrodynamic parameter prediction, achieving 5 times better accuracy in predicting pressure drops and 50 % improvement in holdup prediction. The fully coupled model predicts HDS conversion with 96 % accuracy and HDN conversion with 94 % accuracy. Results suggest that the best way to obtain similar kinetic and hydrodynamic behaviour in TBRs with different lengths and diameter length scales is by equaling the liquid holdup true(ϵγtrue) or the mass velocities (L‐G).

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A new formulation of the dispersion tensor in homogeneous porous media

Cited by 19 publications

References 31 publications

Flow over natural or engineered surfaces: an adjoint homogenization perspective

Flow over natural or engineered surfaces: an adjoint homogenization perspective

Origin of the inertial deviation from Darcy's law: An investigation from a microscopic flow analysis on two-dimensional model structures

CFD analysis of bed textural characteristics on TBR behaviour: Kinetics, scaling‐up, multiscale analysis, and wall effects

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