InterPore2023

Employing GPUs to compute effective properties of porous media from μCT scans in desktop computers

25 May 2023, 10:45

1h 30m

Poster Presentation (MS10) Advances in imaging porous media: techniques, software and case studies Poster

Speaker

Mr Pedro Cortez Lopes (Universidade Federal Fluminense)

Description

Image acquisition techniques are increasingly being employed for material characterization. For example, X-ray Mirco-Computed Tomography ($\mu$CT) can be seen in multiple works that study media such as reservoir rocks [2,3], and fibrous and woven materials [4,5], to cite a few. This sort of approach usually involves 3D numerical simulations at the microstructure, which is represented as a grid of voxels, to compute the effective properties of the sample. For $\mu$CT scans, these simulations can be significantly large and with high memory allocation, to the point that clusters or even supercomputers might be required. One of the ways to perform these simulations is via the voxel-based Finite Element Method (FEM), where each voxel is taken as an element, thus eliminating the task of meshing the domain, and favouring the adoption of lightweight matrix-free schemes. We have been exploring memory-efficient implementations of such method for Numerical Homogenization, as it can be seen in [1], where massively parallel (GPU) solvers are detailed for thermal conductivity and elasticity analyses. We have also recently implemented solvers for other phenomena, such as Stokes flow in porous media, to compute permeability. The motif in these implementations is not storing data that can be recomputed on demand, and tackling the trade-off in computational cost with acceleration provided by graphics cards. Here, we aim to present how our solvers can be used to characterize segmented $\mu$CT samples with personal hardware in a sensible time frame. Image-based meshes with hundreds of millions of voxels can be studied with less than 8 GB, taking seconds or no more than a few minutes per simulation. This enables analyses on $\mu$CT images with upwards of 400${}^3$ voxels in desktop computers equipped with relatively accessible GPUs. It will be shown that even a personal laptop can be used for thermal conductivity or electrical resistivity analyses of such dimensions. Further, a case-study in the context of Digital Petrophysics will be presented, where the electrical resistivity, linear elastic stiffness, and absolute permeability of sandstone $\mu$CT samples are computed employing our tools and methods, in workstations equipped with a single GPU, of either 8 or 12 GB RAM. These analyses would not be feasible with such limited memory allocation if not for the matrix-free approach, nor would they take minutes if not for the massively parallel solver.

References

[1] Lopes, P. C. F., Pereira, A. M. B., Clua, E. W. G., and Leiderman, R. (2022). A GPU implementation of the PCG method for large-scale image-based finite element analysis in heterogeneous periodic media. Computer Methods in Applied Mechanics and Engineering, 399:115276.

[2] Andrä, H., Combaret, N., Dvorkin, J., Glatt, E., Han, J., Kabel, M., Keehm, Y., Krzikalla, F., Lee, M., Madonna, C., Marsh, M., Mukerji, T., Saenger, E. H., Sain, R., Saxena, N., Ricker, S., Wiegmann, A., and Zhan, X. (2013). Digital rock physics benchmarks—part i: Imaging and segmentation. Computers & Geosciences, 50:25–32.

[3] Andrä, H., Combaret, N., Dvorkin, J., Glatt, E., Han, J., Kabel, M., Keehm, Y., Krzikalla, F., Lee, M., Madonna, C., Marsh, M., Mukerji, T., Saenger, E. H., Sain, R., Saxena, N., Ricker, S., Wiegmann, A., and Zhan, X. (2013). Digital rock physics benchmarks—part ii: Computing effective properties. Computers & Geosciences, 50:33–43.

[4] Semeraro, F., Ferguson, J. C., Panerai, F., King, R. J., and Mansour, N. N. (2020). Anisotropic analysis of fibrous and woven materials part 1: Estimation of local orientation. Computational Materials Science, 178:109631.

[5] Semeraro, F., Ferguson, J. C., Acin, M., Panerai, F., and Mansour, N. N. (2021). Anisotropic analysis of fibrous and woven materials part 2: Computation of effective conductivity. Computational Materials Science, 186:109956.