Abstract
Predicting the petrophysical properties of rock samples using micro-CT images has gained significant attention recently. However, an accurate and an efficient numerical tool is still lacking. After investigating three numerical techniques, (i) pore network modeling (PNM), (ii) the finite volume method (FVM), and (iii) the lattice Boltzmann method (LBM), a workflow based on machine learning is established for fast and accurate prediction of permeability directly from 3D micro-CT images. We use more than 1100 samples scanned at high resolution and extract the relevant features from these samples for use in a supervised learning algorithm. The approach takes advantage of the efficient computation provided by PNM and the accuracy of the LBM to quickly and accurately estimate rock permeability. The relevant features derived from PNM and image analysis are fed into a supervised machine learning model and a deep neural network to compute the permeability in an end-to-end regression scheme. Within a supervised learning framework, machine and deep learning algorithms based on linear regression, gradient boosting, and physics-informed convolutional neural networks (CNNs) are applied to predict the petrophysical properties of porous rock from 3D micro-CT images. We have performed the sensitivity analysis on the feature importance, hyperparameters, and different learning algorithms to make a prediction. Values of R2 scores up to 88% and 91% are achieved using machine learning regression models and the deep learning approach, respectively. Remarkably, a significant gain in computation time—approximately 3 orders of magnitude—is achieved by applied machine learning compared with the LBM. Finally, the study highlights the critical role played by feature engineering in predicting petrophysical properties using deep learning.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
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, EH, Sain, R, Saxena, N, Ricker, S, Wiegmann, A, Zhan, X: Digital rock physics benchmarks-Part I: Imaging and segmentation. Computers and Geosciences 50, 25–32 (2013). https://doi.org/10.1016/j.cageo.2012.09.005
Dong, H, Blunt, MJ: Pore-network extraction from micro-computerized-tomography images. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 80(3), 1–11 (2009). https://doi.org/10.1103/PhysRevE.80.036307
Mostaghimi, P, Blunt, MJ, Bijeljic, B: Computations of Absolute Permeability on Micro-CT Images. Mathematical Geosciences 45(1), 103–125 (2013). https://doi.org/10.1007/s11004-012-9431-4
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, EH, Sain, R, Saxena, N, Ricker, S, Wiegmann, A, Zhan, X: Digital rock physics benchmarks-part II: Computing effective properties. Computers and Geosciences 50, 33–43 (2013). https://doi.org/10.1016/j.cageo.2012.09.008
Guibert, R, Nazarova, M, Horgue, P, Hamon, G, Creux, P, Debenest, G: Computational Permeability Determination from Pore-Scale Imaging: Sample Size, Mesh and Method Sensitivities. Transport in Porous Media 107(3), 641–656 (2015). https://doi.org/10.1007/s11242-015-0458-0
Tembely, M, AlSumaiti, AM, Jouini, MS, Rahimov, K: The effect of heat transfer and polymer concentration on non-Newtonian fluid from pore-scale simulation of rock X-ray micro-CT. Polymers 9(10), 509 (2017). https://doi.org/10.3390/polym9100509
Blunt, MJ, Bijeljic, B, Dong, H, Gharbi, O, Iglauer, S, Mostaghimi, P, Paluszny, A, Pentland, C: Pore-scale imaging and modelling. Advances in Water Resources 51, 197–216 (2013). https://doi.org/10.1016/j.advwatres.2012.03.003
Lecun, Y, Bengio, Y, Hinton, G: Deep learning. Nature 521(7553), 436–444 (2015). https://doi.org/10.1038/nature14539
Van Der Linden, JH, Narsilio, GA, Tordesillas, A: Machine learning framework for analysis of transport through complex networks in porous, granular media: A focus on permeability. Physical Review E 94(2), 1–16 (2016). https://doi.org/10.1103/PhysRevE.94.022904
Ling, J, Kurzawski, A, Templeton, J: Reynolds averaged turbulence modelling using deep neural networks with embedded invariance. Journal of Fluid Mechanics 807, 155–166 (2018). https://doi.org/10.1017/jfm.2016.615
Pollock, J, Stoecker-Sylvia, Z, Veedu, V, Panchal, N, Elshahawi, H: Machine learning for improved directional drilling. In: Proceedings of the Annual Offshore Technology Conference, Vol. 4, Offshore Technology Conference, pp. 2496–2504 (2018), https://doi.org/10.4043/28633-ms
Sudakov, O, Burnaev, E, Koroteev, D: Driving digital rock towards machine learning: Predicting permeability with gradient boosting and deep neural networks. Computers and Geosciences 127, 91–98 (2019). https://doi.org/10.1016/j.cageo.2019.02.002
Wu, J, Yin, X, Xiao, H: Seeing permeability from images: fast prediction with convolutional neural networks. Science Bulletin 63(18), 1215–1222 (2018). https://doi.org/10.1016/j.scib.2018.08.006
Araya-Polo, M, Alpak, FO, Hunter, S, Hofmann, R, Saxena, N: Deep learning–driven permeability estimation from 2D images. Computational Geosciences 24, 571–580 (2020). https://doi.org/10.1007/s10596-019-09886-9
Araya-Polo, M, Alpak, FO, Hunter, S, Hofmann, R, Saxena, N: Deep learning-driven pore-scale simulation for permeability estimation. In: 16th European Conference on the Mathematics of Oil Recovery, ECMOR 2018, Vol. 2018, European Association of Geoscientists and Engineers, EAGE, pp. 1–14 (2018), https://doi.org/10.3997/2214-4609.201802173
Alqahtani, N, Armstrong, RT, Mostaghimi, P: Deep learning convolutional neural networks to predict porous media properties. In: Society of Petroleum Engineers - SPE Asia Pacific Oil and Gas Conference and Exhibition 2018, APOGCE 2018, Society of Petroleum Engineers (2018), https://doi.org/10.2118/191906-ms
Andrew, M: A quantified study of segmentation techniques on synthetic geological XRM and FIB-SEM images. Computational Geosciences 22, 1503–1512 (2018). https://doi.org/10.1007/s10596-018-9768-y
Miao, X, Gerke, KM, Sizonenko, TO: A new way to parameterize hydraulic conductances of pore elements: A step towards creating pore-networks without pore shape simplifications. Advances in Water Resources 105, 162–172 (2017). https://doi.org/10.1016/j.advwatres.2017.04.021
Rabbani, A, Babaei, M: Hybrid pore-network and lattice-Boltzmann permeability modelling accelerated by machine learning. Advances in Water Resources 126, 116–128 (2019). https://doi.org/10.1016/j.advwatres.2019.02.012
Alpak, FO, Gray, F, Saxena, N, Dietderich, J, Hofmann, R, Berg, S: A distributed parallel multiple-relaxation-time lattice Boltzmann method on general-purpose graphics processing units for the rapid and scalable computation of absolute permeability from high-resolution 3D micro-CT images. Computational Geosciences 22(3), 815–832 (2018). https://doi.org/10.1007/s10596-018-9727-7
Alpak, FO, Araya-Polo, M: Rapid computation of permeability from Micro-CT images On GPGPUs. In: 16th European Conference on the Mathematics of Oil Recovery, ECMOR 2018, European Association of Geoscientists and Engineers, EAGE (2018), https://doi.org/10.3997/2214-4609.201802184
Alpak, FO, Zacharoudiou, I, Berg, S, Dietderich, J, Saxena, N: Direct simulation of pore-scale two-phase visco-capillary flow on large digital rock images using a phase-field lattice Boltzmann method on general-purpose graphics processing units. Computational Geosciences 23(5), 849–880 (2019). https://doi.org/10.1007/s10596-019-9818-0
Mosser, L, Dubrule, O, Blunt, MJ: Reconstruction of three-dimensional porous media using generative adversarial neural networks. Phys. Rev. E 96, 043309 (2017). https://doi.org/10.1103/PhysRevE.96.043309[https://link.aps.org/doi/10.1103/PhysRevE.96.043309]
Tembely, M, Attarzadeh, R, Dolatabadi, A: On the numerical modeling of supercooled micro-droplet impact and freezing on superhydrophobic surfaces. International Journal of Heat and Mass Transfer 127, 193–202 (2018). https://doi.org/10.1016/j.ijheatmasstransfer.2018.06.104
Funding
The authors received financial support from ADNOC and Khalifa University supercomputing resources (HPCC) made available for conducting the research reported in this paper.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Tembely, M., AlSumaiti, A.M. & Alameri, W. A deep learning perspective on predicting permeability in porous media from network modeling to direct simulation. Comput Geosci 24, 1541–1556 (2020). https://doi.org/10.1007/s10596-020-09963-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10596-020-09963-4