Anisotropic Permeability in Porous Media

Rice, Philip A.; Fontugne, Daniel J.; Latini, Raimondo G.; Barduhn, Allen J.

doi:10.1021/ie50726a005

Cited by 47 publications

(24 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For specimens n = 1, 4 the R values obtained are respectively 0.79 and 0.83, while for n = 2, 3 the R values obtained are 0.27 and 0.51. Based on Guibert et al and Rice et al, where isotropy is suggested to be the case when R > 0.75 and 0.65 < R < 0.84 respectively, specimens n = 1,4 are much closer to being isotropic (Guibert et al, 2015, Rice et al, 1970) has the largest variation between

k_{\min}^{p}, k_{i n t}^{p}

and

k_{\max}^{p}

and therefore exhibits the largest degree of anisotropy.…”

Section: Discussionmentioning

confidence: 99%

Estimation of anisotropic permeability in trabecular bone based on microCT imaging and pore-scale fluid dynamics simulations

et al. 2017

View full text Add to dashboard Cite

In this paper, a comprehensive framework is proposed to estimate the anisotropic permeability matrix in trabecular bone specimens based on micro-computed tomography (microCT) imaging combined with pore-scale fluid dynamics simulations. Two essential steps in the proposed methodology are the selection of (i) a representative volume element (RVE) for calculation of trabecular bone permeability and (ii) a converged mesh for accurate calculation of pore fluid flow properties. Accurate estimates of trabecular bone porosities are obtained using a microCT image resolution of approximately 10 μm. We show that a trabecular bone RVE in the order of 2 × 2 × 2 mm3 is most suitable. Mesh convergence studies show that accurate fluid flow properties are obtained for a mesh size above 125,000 elements. Volume averaging of the pore-scale fluid flow properties allows calculation of the apparent permeability matrix of trabecular bone specimens.For the four specimens chosen, our numerical results show that the so obtained permeability coefficients are in excellent agreement with previously reported experimental data for both human and bovine trabecular bone samples. We also identified that bone samples taken from long bones generally exhibit a larger permeability in the longitudinal direction. The fact that all coefficients of the permeability matrix were different from zero indicates that bone samples are generally not harvested in the principal flow directions. The full permeability matrix was diagonalized by calculating the eigenvalues, while the eigenvectors showed how strongly the bone sample's orientations deviated from the principal flow directions. Porosity values of the four bone specimens range from 0.83 to 0.86, with a low standard deviation of ± 0.016, principal permeability values range from 0.22 to 1.45 ⋅ 10 −8 m2, with a high standard deviation of ± 0.33. Also, the anisotropic ratio ranged from 0.27 to 0.83, with high standard deviation. These results indicate that while the four specimens are quite similar in terms of average porosity, large variability exists with respect to permeability and specimen anisotropy. The utilized computational approach compares well with semi-analytical models based on homogenization theory. This methodology can be applied in bone tissue engineering applications for generating accurate pore morphologies of bone replacement materials and to consistently select similar bone specimens in bone bioreactor studies.

show abstract

k_{\min}^{p}, k_{i n t}^{p}

and

k_{\max}^{p}

and therefore exhibits the largest degree of anisotropy.…”

Section: Discussionmentioning

confidence: 99%

Estimation of anisotropic permeability in trabecular bone based on microCT imaging and pore-scale fluid dynamics simulations

et al. 2017

View full text Add to dashboard Cite

show abstract

“…It may be noted that large values of h correspond to a rapid transfer of heat between the phases (LTE) and small values of h gives rise to relatively strong LTNE effects. Although the porous medium is anisotropic, the preferential orientation of the grains constituting the medium renders it isotropic in the direction parallel to the stratification (Rees [16], Rice et al [17]). For this reason, the porous medium could be taken as being horizontally isotropic.…”

Section: Problem Formulationmentioning

confidence: 99%

Boundary and thermal non-equilibrium effects on convective instability in an anisotropic porous layer

Shivakumara

Lee

Mamatha³

et al. 2011

J Mech Sci Technol

View full text Add to dashboard Cite

The effects of boundary and local thermal non-equilibrium on the criterion for the onset of convection in a sparsely packed horizontal anisotropic porous layer are investigated. A two-field temperature model each representing the solid and fluid phases separately is used and the flow in the porous medium is described by the Brinkman extended-Darcy model. The lower boundary is rigid, while the upper boundary is considered to be either rigid or free with fixed temperature conditions at the boundaries. The stability equations are solved numerically using the Galerkin method to extract the critical stability parameters. The influence of local thermal non-equilibrium, mechanical and thermal anisotropy parameters representing the fluid and solid phases is assessed on the stability characteristics of the system. The existing results are obtained as limiting cases from the present study.

show abstract

“…Over one hundred measurements of the value of the permeability ratio, r k , have been collated by who, along with Rice et al (1970), have summarised and assessed the wide variety of techniques that have been employed for measuring r k in both cohesive and non-cohesive media. Whilst some r k values were reported to be greater than 10 and also some to be less than 0.5, these occurred for varved clays, rocks and shallow clays; where laminations, cracking and holes from plant roots or burrowing animals could have impacted on measurements.…”

Section: Anisotropy Measurementsmentioning

confidence: 99%

Permeability anisotropy due to consolidation of compressible porous media

et al. 2006

View full text Add to dashboard Cite

The characterisation of flow through porous media is important for all solid-liquid separation and fluid transport realms. The permeability of porous media can be anisotropic and furthermore, the extent of anisotropy can be increased as a result of an applied compressive force. However, the understanding of how anisotropy develops is incomplete. An overview of research on permeability anisotropy is given and an expression for predicting anisotropy as a function of void ratio is offered. The two underlying assumptions of the proposed model are: flow in different directions occurs within the same network of pores and deformation is primarily due to the compression of the particles in the direction of the applied force rather than due to particle rearrangement. The assumption of network connectivity allows permeability anisotropy to be described as a function of flow path tortuosity only. Results are presented for hydraulic anisotropy measured in lignite that has been upgraded by a compression dewatering method known as mechanical thermal expression. The lignite permeability is shown to be up to eight times greater in the direction perpendicular to compression, suggesting that the rate of dewatering could be significantly increased by choosing the drainage to also be perpendicular to the direction of the applied compressive force. It is illustrated that the proposed anisotropy model can be used to accurately predict the experimentally determined permeability anisotropy ratios for lignite, as well as for other materials including sand, clay and kaolin. Nomenclature aLength of the major axis of a particle (m) a 0 Initial length of the major axis of a particle (m) A Anisotropy due to particle shape and orientation (-) 366 O.N. Scholes et al. bLength of the minor axis of a particle (m) b 0 Initial length of the minor axis of a particle (m) C K Kozeny shape factor (-) c Empirical constant (-) d Empirical constant (-) e Void ratio, which equals [volume of voids]/[volume of solids] (m 3 /m 3 ) e 0 Maximum void ratio where permeability isotropy exists (m 3 /m 3 ) e 1 First measured void ratio (m 3 /m 3 ) e max Maximum void ratio (m 3 /m 3 ) e opt Void ratio at optimum density of the modified proctor test (m 3 /m 3 ) F Formation resistivity factor (-)

show abstract

Anisotropic Permeability in Porous Media

Abstract: Fontugne and Raimondo Latini are former graduate students of the above department.This paper was presented as part of the Symposium on Flow Through Porous Media, Washington, D. C.,

Cited by 47 publications

References 9 publications

Estimation of anisotropic permeability in trabecular bone based on microCT imaging and pore-scale fluid dynamics simulations

Estimation of anisotropic permeability in trabecular bone based on microCT imaging and pore-scale fluid dynamics simulations

Boundary and thermal non-equilibrium effects on convective instability in an anisotropic porous layer

Permeability anisotropy due to consolidation of compressible porous media

Contact Info

Product

Resources

About