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Percolation connectivity, pore size, and gas apparent permeability: Network simulations and comparison to experimental data
Author(s) -
Li M.,
Tang Y. B.,
Bernabé Y.,
Zhao J. Z.,
Li X. F.,
Li T.
Publication year - 2017
Publication title -
journal of geophysical research: solid earth
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.983
H-Index - 232
eISSN - 2169-9356
pISSN - 2169-9313
DOI - 10.1002/2016jb013710
Subject(s) - permeability (electromagnetism) , slippage , relative permeability , percolation threshold , exponent , pressure drop , porous medium , percolation (cognitive psychology) , radius , gaseous diffusion , materials science , thermodynamics , porosity , chemistry , physics , composite material , electrical resistivity and conductivity , biochemistry , linguistics , philosophy , computer security , electrode , quantum mechanics , neuroscience , membrane , biology , computer science
Abstract We modeled single‐phase gas flow through porous media using percolation networks. Gas permeability is different from liquid permeability. The latter is only related to the geometry and topology of the pore space, while the former depends on the specific gas considered and varies with gas pressure. As gas pressure decreases, four flow regimes can be distinguished as viscous flow, slip flow, transition flow, and free molecular diffusion. Here we use a published conductance model presumably capable of predicting the flow rate of an arbitrary gas through a cylindrical pipe in the four regimes. We incorporated this model into pipe network simulations. We considered 3‐D simple cubic, body‐centered cubic, and face‐centered cubic lattices, in which we varied the pipe radius distribution and the bond coordination number. Gas flow was simulated at different gas pressures. The simulation results showed that the gas apparent permeability k app obeys an identical scaling law in all three lattices, k app ~ ( z ‐ z c ) β , where the exponent β depends on the width of the pipe radius distribution, z is the mean coordination number, and z c its critical value at the percolation threshold. Surprisingly, ( z ‐ z c ) had a very weak effect on the ratio of the apparent gas permeability to the absolute liquid permeability, k app / k abs , suggesting that the Klinkenberg gas slippage correction factor is nearly independent of connectivity. We constructed models of k app and k app / k abs based on the observed power law and tested them by comparison with published experimental data on glass beads and other materials.