Permeability and pore connectivity: A new model based on network simulations

[1] The purpose of this paper is to model the effect of pore size heterogeneity and pore connectivity on permeability. Our approach is that of conceptual modeling based on network simulations. We simulated fluid flow through pipe networks with different coordination numbers and different pipe radius distributions. Following a method widely used in percolation theory, we sought “universal” relationships (i.e., independent of lattice type) between macroscopic properties such as permeability k and porosity ϕ, and, pore geometry attributes such as hydraulic radius rH, coordination number z, and so forth. Our main result was that in three-dimensional simple cubic, FCC, and BCC networks, permeability obeyed “universal” power laws, k ∝ (z − zc)β, where the exponent β is a function of the standard deviation of the pore radius distribution and zc = 1.5 is the percolation threshold expressed in terms of the coordination number. Most importantly, these power law relationships hold in a wide domain, from z close to zc to the maximum possible values of z. A permeability model was inferred on the basis of the power laws mentioned above. It was satisfactorily tested by comparison with published, experimental, and microstructural data on Fontainebleau sandstone.

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