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Analytical predictions and lattice Boltzmann simulations of intrinsic permeability for mass fractal porous media

Abdullah Cihan, Michael C. Sukop, John S. Tyner, Edmund Perfect and Haibo Huang
Analytical predictions and lattice Boltzmann simulations of intrinsic permeability for mass fractal porous media (in Fractals, E. Perfect, Y. Pachepsky and M. A. Martin)
Vadose Zone Journal (February 2009) 8 (1): 187-196

Abstract

We derived two new expressions for the intrinsic permeability (k) of fractal porous media. The first approach, the probabilistic capillary connectivity (PCC) model, is based on evaluating the expected value of the cross-sectional area of pores connected along various flow paths in the direction in which the permeability is sought. The other model is a modified version of Marshall's probabilistic approach (MPA) applied to random cross matching of pores present on two parallel slices through a fractal porous medium. The Menger sponge is a three-dimensional mass fractal that represents the complicated pore space geometry of soil and rock. Predictions based on the analytical models were compared with estimates of k derived from lattice Boltzmann method (LBM) simulations of saturated flow in virtual representations of Menger sponges. Overall, the analytically predicted k values matched the k values from the LBM simulations with <14% error for the deterministic sponges simulated. While the PCC model can represent variation in permeability due to the randomization process for each realization of the sponge, the MPA approach can capture only the average permeability resulting from all possible random realizations. Theoretical and empirical analyses of the surface fractal dimension (D (sub 2) ) for successive slices through a random Menger sponge show that the mean D (sub 2) value <D (sub 2) > = D (sub 3) - 1, where D (sub 3) is the three-dimensional mass fractal dimension. Incorporating <D (sub 2) > into the MPA approach resulted in a k that compared favorably with the modal value of k from LBM simulations performed on 100 random realizations of a random Menger sponge.


ISSN: 1539-1663
Serial Title: Vadose Zone Journal
Serial Volume: 8
Serial Issue: 1
Title: Analytical predictions and lattice Boltzmann simulations of intrinsic permeability for mass fractal porous media
Title: Fractals
Author(s): Cihan, AbdullahSukop, Michael C.Tyner, John S.Perfect, EdmundHuang, Haibo
Author(s): Perfect, E.
Author(s): Pachepsky, Y.
Author(s): Martin, M. A.
Affiliation: University of Tennessee, Biosystems Engineering & Soil Science, Knoxville, TN, United States
Affiliation: University of Tennessee, Department of Earth and Planetary Sciences, Knoxville, TN, United States
Pages: 187-196
Published: 200902
Text Language: English
Publisher: Soil Science Society of America, Madison, WI, United States
References: 29
Accession Number: 2009-032704
Categories: SoilsHydrogeology
Document Type: Serial
Bibliographic Level: Analytic
Annotation: Includes appendix
Illustration Description: illus. incl. 4 tables
Secondary Affiliation: U. S. Department of Agriculture-ARS, USA, United StatesUniversidad Politecnica de Madrid, ESP, SpainFlorida International University, USA, United States
Country of Publication: United States
Secondary Affiliation: GeoRef, Copyright 2017, American Geosciences Institute. Abstract, Copyright, Soil Science Society of America. Reference includes data from GeoScienceWorld, Alexandria, VA, United States
Update Code: 200918
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