Modeling of non-Darcy flow through anisotropic porous media: Role of pore space profiles

Veyskarami, Maziar; Hassani, Amirhossein; Ghazanfari, Mohammad Hossein

doi:10.1016/j.ces.2016.05.020

Cited by 37 publications

(16 citation statements)

References 27 publications

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“…To further establish whether equation (2) suitably describes real geologic porous media representing different processes inducing pore geometry variation, we focused on the results from groups of previous laboratory experiments where geologic samples were deformed through compression (Dan et al, 2016;Gostick et al, 2006;Jones, 1987;Ma et al, 2015;Ma et al, 2016;Schrauf & Evans, 1986;Zhou et al, 2015), torsion (Okumura et al, 2009), shearing (Javadi et al, 2014;Wang, 2017), or decompression (Lindoo et al, 2016;Takeuchi et al, 2009), and from modeling experiments where pore networks with ducts of different shapes were systematically varied (Veyskarami et al, 2016), like we did with our CFD simulations discussed below. The complete details on the data set including the type of geologic porous media, the geometry-varying processes represented, and the fitted parameters are provided in Table S4 in the supporting information.…”

Section: Resultsmentioning

confidence: 99%

“…In the CFD modeling, we first investigated an idealized pore geometry with sinusoidal walls in an axissymmetric framework (Figure 3a), following previous investigations where basic pore configurations were adopted to reveal the underlying physical mechanism for complex flow and transport phenomena (Bolster et al, 2014;Veyskarami et al, 2016). The pore geometry can be fully characterized by two dimensionless numbers, the aspect ratio (L/R t ) and fluctuation (R b /R t ), where L is the longitudinal length of the pore and R t and R b are the radii at the pore throat and pore body, respectively.…”

Section: Methodsmentioning

confidence: 99%

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Universal Relationship Between Viscous and Inertial Permeability of Geologic Porous Media

Zhou

Chen

Wang

et al. 2019

Geophysical Research Letters

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Fluid flow through geologic porous media is represented by Darcy's law and its inertial and nonlinear extension, the Forchheimer equation. These relationships equate the product of the driving potential gradient and phenomenological coefficients representing momentum resistance and dissipation to flux. From decades of research, the coefficient of viscous permeability (kv) in Darcy's law is largely predictable, but this is not the case for the coefficient of inertial permeability (ki) in the Forchheimer equation. Synthesizing results from thousands of laboratory and field flow tests and pore‐scale flow model results, we show that ki can be predicted from kv via the equation ki = 1010kv3/2 across 12 and 20 orders of magnitude in kv and ki, respectively. Since it is related with ki, kv is thus sufficient for predicting flow across viscous to inertial regimes for most geologic porous media.

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Section: Resultsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Universal Relationship Between Viscous and Inertial Permeability of Geologic Porous Media

Zhou

Chen

Wang

et al. 2019

Geophysical Research Letters

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“…Various origins of the deviation were mentioned in a heuristic way in the literature. Among them, one can mention pore roughness [42,43], loss of kinetic energy in restrictions and constrictions [44], development of inertial cores [9,45], bends in the flow paths [46], formation of a hydrodynamic boundary layer [15], change in spatial distribution of the kinetic energy within the structure [47], flow tortuosity [48], and pore-throat curvature [49]. Some authors distinguished contributions due to linear losses in pores and channels and quadratic losses in contractions and expansions [50].…”

Section: Introductionmentioning

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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“…Then the REV determined by nonDarcy coefficient and the REV determined by inherent permeability should be consistent, but more studies have shown that the non-Darcy coefficient is not only related to the intrinsic permeability of media. Evans and Civan [52], Geertsma [53], and Macdonald et al [54] found that nonDarcy coefficient is also related to the effective porosity of the pore medium; Li and Engler [55] and Veyskarami et al [56] proposed that, for isotropic media, several correlations relate to petrophysical parameters (in particular , k, and the tortuosity ); Knupp and Lage [57] also pointed out that is related to the inherent permeability and inertia coefficient , where represents the microform resistance exerted by the solid porous substrate; that is to say, it depends on the geometry of the solids in each basic representative volume of the porous medium. It is noteworthy that and are independent parameters.…”

Section: Discussionmentioning

confidence: 99%

Study on the REV Size of Fractured Rock in the Non-Darcy Flow Based on the Dual-Porosity Model

2018

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Modeling of non-Darcy flow through anisotropic porous media: Role of pore space profiles

Cited by 37 publications

References 27 publications

Universal Relationship Between Viscous and Inertial Permeability of Geologic Porous Media

Universal Relationship Between Viscous and Inertial Permeability of Geologic Porous Media

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

Study on the REV Size of Fractured Rock in the Non-Darcy Flow Based on the Dual-Porosity Model

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