Extracting connectivity paths in digital core images using solution of partial minimum eigenvalue problem
-
Serguei Yu. Maliassov
and
Yuri V. Vassilevski
Abstract
We show theoretically and numerically that the lowest non-trivial eigenvector function for a specific eigenproblem has almost constant values in high conductivity channels, which are different in separate channels. Therefore, based on these distinct values, all separate connected clusters of open pores can be identified in digital cores.
Funding statement: The work is supported by the Ministry of Science and Higher Education of the Russian Federation, Agreement 075-10-2021-093, Project MMD-RND-2265.
Acknowledgment
The authors would like to thank Dr. Yalchin Efendiev for fruitful discussions and valuable suggestions.
References
[1] E. T. Chung, Y. Efendiev, and W. T. Leung, Constraint energy minimizing generalized multiscale finite element method. Computer Methods in Applied Mechanics and Engineering 339 (2018) 298–319.10.1016/j.cma.2018.04.010Search in Google Scholar
[2] Y. Efendiev, J. Galvis, and T. Y. Hou, Generalized multiscale finite element methods (gmsfem). J. Comput. Phys. 251 (2013) 116–135.10.1016/j.jcp.2013.04.045Search in Google Scholar
[3] Y. Efendiev and W. T. Leung, Multicontinuum homogenization and its relation to nonlocal multicontinuum theories. J. Comput. Phys. 474 (2023), 111761.10.1016/j.jcp.2022.111761Search in Google Scholar
[4] W. R. Franklin, S. V. G. de Magalhaes, and E. N. Landis, Fast 3-D Euclidean connected components. In: 3rd ACM SIGSPATIAL International Workshop on Spatial Gems (SpatialGems 2021), November 2, 2021 (Ed. J. Krumm), ACM, 2021.Search in Google Scholar
[5] A. V. Knyazev, Preconditioned eigensolvers. In: Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide (Eds. Z. Bai, J. Demmel, J. Dongarra, A. Ruhe, and H. van der Vorst), SIAM, Philadelphia, PA, 2000, pp. 352–368.Search in Google Scholar
[6] I. Lashuk, M. Argentati, E. Ovtchinnikov, and A. Knyazev, Preconditioned Eigensolver LOBPCG in hypre and PETSc, Vol. 55. Springer, Berlin–Heidelberg, 2007, pp. 635–642.10.1007/978-3-540-34469-8_79Search in Google Scholar
[7] M. A. Shubin, Pseudodifferential Operators and Spectral Theory. Springer, 2001.10.1007/978-3-642-56579-3Search in Google Scholar
[8] P. Thore and A. Lucas, Extracting connectivity paths in 3d reservoir property: A pseudo skeletonization approach. Computers and Geosciences 171 (2023), 105262.10.1016/j.cageo.2022.105262Search in Google Scholar
[9] Y. Zhang, A. Azad, and A. Buluc, Parallel algorithms for finding connected components using linear algebra. J. Parallel and Distributed Computing 144 (2020), 14–27.10.1016/j.jpdc.2020.04.009Search in Google Scholar
© 2023 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Explaining breakthrough behaviour in shale rock: influence of capillary effects and geomechanics
- Non-local discretization of the isoneutral diffusion operator in a terrain-following climate ocean model
- Numerical model of Earth ionosphere F region based on three-dimensional transport and ambipolar diffusion equations
- Extracting connectivity paths in digital core images using solution of partial minimum eigenvalue problem
- The study of the local sensitivity of functionals of the optimal solution to observational data and the heat flux input data in a variational assimilation problem for the sea thermodynamics model
- Multiresolution approximation for shallow water equations using summation-by-parts finite differences
Articles in the same Issue
- Frontmatter
- Explaining breakthrough behaviour in shale rock: influence of capillary effects and geomechanics
- Non-local discretization of the isoneutral diffusion operator in a terrain-following climate ocean model
- Numerical model of Earth ionosphere F region based on three-dimensional transport and ambipolar diffusion equations
- Extracting connectivity paths in digital core images using solution of partial minimum eigenvalue problem
- The study of the local sensitivity of functionals of the optimal solution to observational data and the heat flux input data in a variational assimilation problem for the sea thermodynamics model
- Multiresolution approximation for shallow water equations using summation-by-parts finite differences
