Prediction of Permeability from Euler Characteristic of 3D Images

Z. Liu1, A. Herring2, V. Robins2, R. T. Armstrong1

1School of Petroleum Engineering, University of New South Wales, Kensington, New South Wales, Australia
2Department of Applied Mathematics, Research School of Physics and Engineering, Australian National University, Canberra, Australian Capital Territory, Australia

This paper was prepared for presentation at the International Symposium of the Society of Core Analysts held in
Vienna, Austria, 27 August - 1 September 2017

The determination of absolute permeability in porous media is of great importance in hydrocarbon extraction, subsurface groundwater investigation and carbon dioxide sequestration. Permeability can be determined from empirical formulations, such as Katz- Thompson, which correlates permeability with percolation threshold. Alternatively, recent research using 2D micro-fluidic experiments and numerical simulations have demonstrated that permeability can be derived from the Euler characteristic (a topological invariant) and the number of grains, which is independent of percolation threshold. However, whether or not these new findings are applicable for three-dimensional porous media has not been verified. How to determine the number of grains also remains a question. Herein, we examine new formulations for characterizing permeability in porous media. We generate three types of stochastic models, simulate single-phase flow using Lattice Boltzmann method and calculate absolute permeability. We find that permeability in 3D pore space does not scale with the same correlation as previously published work on 2D porous media. One possible explanation to this difference is that the number of grains does not capture the resistant force in three-dimensional space. We propose a modified equation by incorporating the void ratio, which is pore volume divided by solid volume. We find that the permeability scales with the Euler characteristic, number of grains and void ratio in 3D porous media and that the scaling is unique for distinctly different stochastic models. These findings provide a new means to characterize the absolute permeability of 3D porous media from pore-scale images of distinctly different grain and pore geometries without the need of numerical simulation.

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