Numerical estimation of electrical resistivity in digital rocks using GPUs

Authors

  • T.S. Khachkova Trofimuk Institute of Petroleum Geology and Geophysics of SB RAS https://orcid.org/0000-0002-1595-7142
  • V.V. Lisitsa Trofimuk Institute of Petroleum Geology and Geophysics of SB RAS https://orcid.org/0000-0003-3544-4878
  • G.V. Reshetova The Institute of Computational Mathematics and Mathematical Geophysics of SB RAS (ICM&MG SB RAS)
  • V.A. Tcheverda Trofimuk Institute of Petroleum Geology and Geophysics of SB RA

DOI:

https://doi.org/10.26089/NumMet.v21r326

Keywords:

digital rock physics, finite-difference method, iterative methods, electrical resistivity, numerical upscaling

Abstract

We present a numerical algorithm for computing the electric field in digital rock samples and estimating their electrical resistivity (conductivity). The main peculiarity of the algorithm is its applicability tostrongly heterogeneous models including partially saturated and multi-mineral rock samples. The algorithm is based on the iterative Krylov-type solver preconditioned by the inverse Laplace operator for homogeneous media. The preconditioner is computed using the spectral method in directions orthogonal to the direction of the main electric current, whereas the series of 1D problems are solved by the Thomas algorithm. We implement the algorithm using GPUs, which allows us to use a single GPU to solve the problems for samples whose size is up to 4003 voxels.

Author Biographies

T.S. Khachkova

V.V. Lisitsa

G.V. Reshetova

V.A. Tcheverda

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Published

27-09-2020

How to Cite

Хачкова Т.С., Лисица В.В., Решетова Г.В., Чеверда В.А. Numerical Estimation of Electrical Resistivity in Digital Rocks Using GPUs // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2020. 21. 306-318. doi 10.26089/NumMet.v21r326

Issue

Section

Methods and algorithms of computational mathematics and their applications

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