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Transport in Porous Media

, Volume 95, Issue 3, pp 535–550 | Cite as

Tomography-Based Characterization and Optimization Of Fluid Flow Through Porous Media

  • A. Akolkar
  • J. PetraschEmail author
Article

Abstract

Numerical simulations to characterize fluid flow through porous media have been carried out using tomography-derived real geometry data that has been manipulated using digital image processing techniques to obtain a wide range of porosities. Two kinds of porous media have been analyzed: (a) a reticulated porous ceramic (RPC) foam and (b) a packed bed of CaCO3 particles. The porosity of the media is varied via morphological operations between 0.727 and 0.913 in case of the RPC and between 0.329 and 0.824 in case of the packed bed. A mesh generator based on the pore space indicator function is then used to generate unstructured tetrahedral grids from the processed tomography data. Fluid flow simulations are carried out for Reynolds numbers ranging from 0.1 to 200 and the results are used to determine the permeability and the Dupuit–Forchheimer coefficient in each case. The results are then compared with existing analytical models and the applicability of the models is examined. In the RPC case, the Happel–Brenner (parallel-flow) model predicts the permeability with a normalized root mean square error (NRMSE) of 11.8 % across the porosity range and Modified Ergun (Macdonald et. al) model predicts the Dupuit–Forchheimer coefficient within a NRMSE of 13.5 %. In the packed-bed case, the Brinkman drag model predicts the permeability within a NRMSE of 8.26 % across the porosity range and the Modified Ergun model predicts the Dupuit–Forchheimer coefficient within an NRMSE of 5.94 %. For each material, an adjusted Kozeny constant is determined. For the RPC, the Kozeny constant is evaluated at 7.73 and for the CaCO3 packed bed, it is found to be 6.10, leading to predictions of the permeability with an NRMSE of 4.16 and 3.37 %, respectively.

Keywords

Tomography Fluid Flow Porosity Permeability Dupuit–Forchheimer 

List of Symbols

Variables

a

Particle-size distribution constant (−)

A0

Specific surface area (m2)

b

Constant in Cooke’s Dupuit–Forchheimer coefficient correlation (−)

c0

Inverse dimensionless permeability (−)

c1

Dimensionless Dupuit–Forchheimer coefficient (−)

CΔ

Relative convergence of pressure drop with mesh refinement (−)

CV

Relative convergence of pressure drop with sample size (−)

d

Diameter (hydraulic) (m)

df

Fiber diameter (m)

dnom

Nominal diameter (m)

dp

Particle diameter (m)

dsolid

Solid phase hydraulic diameter (m)

dvoid

Void phase hydraulic diameter (m)

fd

Friction factor due to fiber deflection (−)

F

Dupuit–Forchheimer coefficient (m−1)

k4, k5

Constants in Davies’ equation (−)

kK

Kozeny constant (−)

K

Permeability (m2)

L

Sample length (m)

LREV

Edge length of representative elementary volume (REV) (m)

m

Constant in Cooke’s Dupuit–Forchheimer coefficient correlation (−)

n

Generic constant in relations for Dupuit–Forchheimer coefficient correlation (−)

Ne

Effective pore number (−)

P

Pressure (Pa)

r

Radial distance in sample volume (m)

Re

Reynolds number (−)

s2

Two-point correlation function (−)

uD

Darcean velocity vector (ms−1)

uD

Darcean velocity (ms−1)

V

Sample volume (m3)

z

Distance along sample axis (m)

Greek symbols

Δ

Mesh representative edge length (m)

ε

Sample porosity (−)

μ

Dynamic viscosity (Pa s)

Subscripts

Br

Brinkman drag model

Ch

Chen fibrous bed model

CK

Carman–Kozeny model

Cond

Conduit flow model

Dav

Davies fibrous bed model

DPLS

Direct Pore Level Simulation

E

Ergun correlation for Dupuit–Forchheimer coefficient

G

Geertsma correlation

HB

Happel–Brenner parallel flow model

Ky

Kyan fibrous bed model

M

Modified Ergun (Macdonald et al.) correlation

s2a

Two-point correlation approximation

W

Ward correlation

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Mechanical and Aerospace EngineeringUniversity of FloridaGainesvilleUSA
  2. 2.Vorarlberg University of Applied SciencesDornbirnAustria

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