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Permeability from 3D Porous Media Images: a Fast Two-Step Approach

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Abstract

An efficient methodology to calculate absolute permeability of porous media using a two-step algorithm is developed. In the first step, the creeping flow equations over the pore space are translated into a Darcy flow problem with the pore space being represented by appropriately chosen local flow conductivities. In the next step, a combined renormalization group and multi-level iterative Laplace solver approach is used to upscale the local conductivities to obtain the effective permeability for the full domain. The accuracy and computational efficiency of the proposed two-step local conductivity–Laplace scheme (LC-LAP) are tested against a FFT (fast Fourier transform) accelerated solver which uses a semi-implicit method for the pressure-linked equation (SIMPLE-FFT) and against a solver that features the GPGPU implementation of the multiple-relaxation-time lattice Boltzmann method (MRT-LBM). A detailed comparison is made by computing permeabilities from all three methods over model geometries and digitized images obtained from micron-scale-resolution computerized tomography (micro-CT) of sandstone rocks of varying porosities and heterogeneity levels. We observe an agreement between our method and either benchmark methods (SIMPLE-FFT and MRT-LBM) that is similar to the agreement between both benchmarks. On the samples tested, the computational performance advantage of the LC-LAP approach ranges from 10- to 40-fold compered to SIMPLE-FFT and 8- to 25-fold compared to MRT-LBM. The proposed method is suitable for fast computations and for computations over very large volumes (due to much lower memory and compute resource requirements) for determining single-phase permeabilities of medium- to high-permeability rocks.

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Acknowledgements

The authors gratefully acknowledge productive discussions with Shell colleagues, Justin Freeman, Kunj Tandon, Nitish Nair, Nishank Saxena, Ronny Hoffmann, and Steffen Berg. Rock geometries used in the benchmarking section and results from SIMPLE-FFT and MRT-LBM methods provided by Jesse Dietderich, Matthias Appel, Steffen Berg, and Nishank Saxena are also gratefully acknowledged.

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  1. J. M. Vianney A. Koelman

    Present address: Center for Computational Energy Research, Dutch Institute for Fundamental Energy Research, Eindhoven University of Technology, Eindhoven, The Netherlands

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  1. Shell India Markets Pvt. Ltd., Shell Technology Center, Bangalore Hardware Park, Devanahalli Industrial Park, Bengaluru, 562149, India

    Umang Agarwal & J. M. Vianney A. Koelman

  2. Shell International Exploration and Production Inc., Shell Technology Center, 3333 Hwy 6, Houston, TX, 77082, USA

    Faruk Omer Alpak

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  1. Umang Agarwal
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Agarwal, U., Alpak, F.O. & Koelman, J.M.V.A. Permeability from 3D Porous Media Images: a Fast Two-Step Approach. Transp Porous Med 124, 1017–1033 (2018). https://doi.org/10.1007/s11242-018-1108-0

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