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CNN-PFVS: Integrating Neural Network and Finite Volume Models to Accelerate Flow Simulation on Pore Space Images

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Abstract

Direct numerical simulations of flow on micro-computed tomography (micro-CT) images are extensively used in many disciplines of science and engineering. Recently, we have developed a pore-scale finite volume solver (PFVS) to directly solve for flow on micro-CT images and predict permeability of digital cores. The solver assigns a local conductivity to each voxel based on geometrical and topological constraints. The local conductivity term in PFVS is conventionally calculated by an iterative local scanning algorithm, where the number of iterations depends on the size of the largest flow channel. This can increase the computation time of PFVS significantly if the largest flow channel is reasonably large. In this paper, we apply convolutional neural networks (CNN) to predict local conductivity for each voxel, thus bypassing the iterative algorithm while also preserving the mass conservation in the system by still solving for flow using conventional methods. The network is trained to convert segmented binary images of rocks into a numerical map required for flow simulation by the use of paired image-to-image translation using a ResNet-Style architecture. Comparison of the generated and original coefficient maps shows that the average error is within 1% over the 3D pore geometries used in this study. Then, we compare the absolute permeability results obtained from the original PFVS and the CNN-PFVS and the errors are within 20% with the average of 13.8%. Machine learning improves the computation time significantly especially on the images with large domain size and flow channels. On the samples tested, the speedup factor is 10 times using CNN compared to iterative calculations.

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References

  • Aarnes, J., et al.: Geometrical Modeling, Numerical Simulation, and Optimization: Industrial Mathematics at SINTEF, chapter An introduction to the numerics of flow in porous media using Matlab. Springer, Berlin (2007)

  • Al-Dhahli, A.R., et al.: Three-phase pore-network modeling for reservoirs with arbitrary wettability. SPE J. 18(02), 285–295 (2012)

    Google Scholar 

  • Alpak, F., et al.: Prediction of fluid topology and relative permeability in imbibition in sandstone rock by direct numerical simulation. Adv. Water Resour. 122, 49–59 (2018)

    Google Scholar 

  • Alqahtani, N., et al.: Machine learning for predicting properties of porous media from 2d X-ray images. J. Pet. Sci. Eng. 184, 106514 (2020)

    Google Scholar 

  • Armstrong, R.T., et al.: Modeling the velocity field during Haines jumps in porous media. Adv. Water Resour. 77, 57–68 (2015)

    Google Scholar 

  • Armstrong, R., et al.: Modeling of pore-scale two-phase phenomena using density functional hydrodynamics. Transp. Porous Media 112(3), 577–607 (2016a)

    Google Scholar 

  • Armstrong, R.T., et al.: Beyond Darcy's law: The role of phase topology and ganglion dynamics for two-fluid flow. Phys. Rev. E 94(4), 043113 (2016b)

    Google Scholar 

  • Bakke, S., Øren, P.-E.: 3-D pore-scale modelling of sandstones and flow simulations in the pore networks. SPE J. 2(02), 136–149 (1997)

    Google Scholar 

  • Berg, C.F.: Permeability description by characteristic length, tortuosity, constriction and porosity. Transp. Porous Media 103(3), 381–400 (2014)

    Google Scholar 

  • Berg, S., et al.: Connected pathway relative permeability from pore-scale imaging of imbibition. Adv. Water Resour. 90, 24–35 (2016)

    Google Scholar 

  • Bijeljic, B., Blunt, M.J.: Pore-scale modeling and continuous time random walk analysis of dispersion in porous media. Water Resour. Res. (2006). https://doi.org/10.1029/2005WR004578

    Article  Google Scholar 

  • Bijeljic, B., et al.: Predictions of non-Fickian solute transport in different classes of porous media using direct simulation on pore-scale images. Phys. Rev. E 87(1), 013011 (2013)

    Google Scholar 

  • Blunt, M.J.: Flow in porous media—pore-network models and multiphase flow. Curr. Opin. Colloid Interface Sci. 6(3), 197–207 (2001)

    Google Scholar 

  • Blunt, M.J.: Multiphase Flow in Permeable Media: A Pore-Scale Perspective. Cambridge University Press, Cambridge (2017)

    Google Scholar 

  • Blunt, M., King, P.: Macroscopic parameters from simulations of pore scale flow. Phys. Rev. A 42(8), 4780 (1990)

    Google Scholar 

  • Blunt, M., King, P.: Relative permeabilities from two-and three-dimensional pore-scale network modelling. Transp. Porous Media 6(4), 407–433 (1991)

    Google Scholar 

  • Blunt, M.J., et al.: Detailed physics, predictive capabilities and macroscopic consequences for pore-network models of multiphase flow. Adv. Water Resour. 25(8–12), 1069–1089 (2002)

    Google Scholar 

  • Blunt, M.J., et al.: Pore-scale imaging and modelling. Adv. Water Resour. 51, 197–216 (2013)

    Google Scholar 

  • Chhatre, S.S., et al.: A blind study of four digital rock physics vendor labs on porosity, absolute permeability, and primary drainage capillary pressure data on tight outcrop rocks. In: Annual Symposium of the Society of Core Analysts (2017)

  • Chung, T., et al.: Approximating permeability of microcomputed-tomography images using elliptic flow equations. SPE J. 24, 1–154 (2019)

    Google Scholar 

  • Chung, T., et al.: Voxel agglomeration for accelerated estimation of permeability from micro-CT images. J. Pet. Sci. Eng. 184, 106577 (2020)

    Google Scholar 

  • Coenen, J., et al.: Measurement parameters and resolution aspects of micro X-ray tomography for advanced core analysis. In: Proceedings of International Symposium of the Society of Core Analysts (2004)

  • Dong, H., Blunt, M.J.: Pore-network extraction from micro-computerized-tomography images. Phys. Rev. E 80(3), 036307 (2009)

    Google Scholar 

  • Erofeev, A., et al.: Prediction of porosity and permeability alteration based on machine learning algorithms. Transp. Porous Media 128(2), 677–700 (2019)

    Google Scholar 

  • Flannery, B.P., et al.: Three-dimensional X-ray microtomography. Science 237(4821), 1439–1444 (1987)

    Google Scholar 

  • Hazlett, R.: Simulation of capillary-dominated displacements in microtomographic images of reservoir rocks. Multiphase Flow Porous Media 20, 21–35 (1995)

    Google Scholar 

  • Hughes, R.G., Blunt, M.J.: Pore scale modeling of rate effects in imbibition. Transp. Porous Media 40(3), 295–322 (2000)

    Google Scholar 

  • Hurley, N. F., et al.: Multiscale digital rock modeling for reservoir simulation, Google Patents (2015)

  • Huynh-Thu, Q., Ghanbari, M.J.E.I.: Scope of validity of PSNR in image/video quality assessment. Electron. Lett. 44(13), 800–801 (2008). https://doi.org/10.1049/el:20080522

    Article  Google Scholar 

  • Kamrava, S., et al.: Linking morphology of porous media to their macroscopic permeability by deep learning. Transp. Porous Media 131(2), 427–448 (2020)

    Google Scholar 

  • Khayrat, K., Jenny, P.: A multi-scale network method for two-phase flow in porous media. J. Comput. Phys. 342, 194–210 (2017)

    Google Scholar 

  • Kingma, D.P., Ba, J.: Adam: a method for stochastic optimization. arXiv preprint http://arxiv.org/abs/05322 (2014)

  • Lie, K.A., et al.: Open-source MATLAB implementation of consistent discretisations on complex grids. Comput. Geosci. 16(2), 297–322 (2012)

    Google Scholar 

  • Lindquist, W.B., et al.: Medial axis analysis of void structure in three-dimensional tomographic images of porous media. J. Geophys. Res. Solid Earth 101(B4), 8297–8310 (1996)

    Google Scholar 

  • Liu, M., Mostaghimi, P.: Characterisation of reactive transport in pore-scale correlated porous media. Chem. Eng. Sci. 173, 121–130 (2017a)

    Google Scholar 

  • Liu, M., Mostaghimi, P.: Pore-scale simulation of dissolution-induced variations in rock mechanical properties. Int. J. Heat Mass Transf. 111, 842–851 (2017b)

    Google Scholar 

  • Liu, M., et al.: Impact of mineralogical heterogeneity on reactive transport modelling. Comput. Geosci. 104, 12–19 (2017a)

    Google Scholar 

  • Liu, Z., et al.: Pore-scale characterization of two-phase flow using integral geometry. Transp. Porous Media 118(1), 99–117 (2017b)

    Google Scholar 

  • McClure, J.E., et al.: A novel heterogeneous algorithm to simulate multiphase flow in porous media on multicore CPU–GPU systems. Comput. Phys. Commun. 185(7), 1865–1874 (2014)

    Google Scholar 

  • Meakin, P., Tartakovsky, A.M.: Modeling and simulation of pore-scale multiphase fluid flow and reactive transport in fractured and porous media. Rev. Geophys. (2009). https://doi.org/10.1029/2008RG000263

    Article  Google Scholar 

  • Menke, H.P., et al.: Dynamic three-dimensional pore-scale imaging of reaction in a carbonate at reservoir conditions. Environ. Sci. Technol. 49(7), 4407–4414 (2015)

    Google Scholar 

  • Molins, S., et al.: An investigation of the effect of pore scale flow on average geochemical reaction rates using direct numerical simulation. Water Resour. Res. (2012). https://doi.org/10.1029/2011WR011404

    Article  Google Scholar 

  • Mostaghimi, P., et al.: Simulation of flow and dispersion on pore-space images. SPE J. 17(04), 1131–131141 (2012)

    Google Scholar 

  • Mostaghimi, P., et al.: Computations of absolute permeability on micro-CT images. Math. Geosci. 45(1), 103–125 (2013)

    Google Scholar 

  • Mostaghimi, P., et al.: Numerical simulation of reactive transport on micro-CT images. Math. Geosci. 48(8), 963–983 (2016)

    Google Scholar 

  • Mostaghimi, P., et al.: Cleat-scale characterisation of coal: an overview. J. Nat. Gas Sci. Eng. 39, 143–160 (2017)

    Google Scholar 

  • Notay, Y.: An aggregation-based algebraic multigrid method. Electron. Trans. Numer. Anal. 37(6), 123–146 (2010)

    Google Scholar 

  • Øren, P.-E., Bakke, S.: Reconstruction of Berea sandstone and pore-scale modelling of wettability effects. J. Pet. Sci. Eng. 39(3–4), 177–199 (2003)

    Google Scholar 

  • Ovaysi, S., Piri, M.: Direct pore-level modeling of incompressible fluid flow in porous media. J. Comput. Phys. 229(19), 7456–7476 (2010)

    Google Scholar 

  • Ovaysi, S., Piri, M.: Multi-GPU acceleration of direct pore-scale modeling of fluid flow in natural porous media. Comput. Phys. Commun. 183(9), 1890–1898 (2012)

    Google Scholar 

  • Rabbani, A., Babaei, M.J.: Hybrid pore-network and lattice-Boltzmann permeability modelling accelerated by machine learning. Adv. Water Resour. 126, 116–128 (2019)

    Google Scholar 

  • Rabbani, A., et al.: Pore network extraction using geometrical domain decomposition. Adv. Water Resour. 123, 70–83 (2019)

    Google Scholar 

  • Raeini, A.Q., et al.: Validating the generalized pore network model using micro-CT images of two-phase flow. Transp. Porous Media 130(2), 405–424 (2019)

    Google Scholar 

  • Ramstad, T., et al.: Pore-scale simulations of single-and two-phase flow in porous media: approaches and applications. Transp. Porous Media 1–28 (2019)

  • Rassenfoss, S.: Digital rocks out to become a core technology. J. Petrol. Technol. 63(05), 36–41 (2011)

    Google Scholar 

  • Salazar-Tio, R. (2014). System and method for multi-phase segmentation of density images representing porous media, Google Patents.

  • Schlüter, S., et al.: Image processing of multiphase images obtained via X-ray microtomography: a review. Water Resour. Res. 50(4), 3615–3639 (2014)

    Google Scholar 

  • Shabro, V., et al.: Finite-difference approximation for fluid-flow simulation and calculation of permeability in porous media. Transp. Porous Media 94(3), 775–793 (2012)

    Google Scholar 

  • Sorbie, K., Skauge, A.: Can network modeling predict two-phase flow functions? Petrophysics 53(06), 401–409 (2012)

    Google Scholar 

  • Sudakov, O., et al.: Driving digital rock towards machine learning: predicting permeability with gradient boosting and deep neural networks. Comput. Geosci. 127, 91–98 (2019)

    Google Scholar 

  • Szegedy, C., et al.: Inception-v4, inception-resnet and the impact of residual connections on learning. In: Thirty-First AAAI Conference on Artificial Intelligence (2017)

  • Valvatne, P.H., Blunt, M.J.: Predictive pore-scale modeling of two-phase flow in mixed wet media. Water Resour. Res. (2004). https://doi.org/10.1029/2003WR002627

    Article  Google Scholar 

  • Wang, Y., et al.: Computations of permeability of large rock images by dual grid domain decomposition. Adv Water Resour. Res. 126, 1–14 (2019a)

    Google Scholar 

  • Wang, Y.D., et al.: Enhancing resolution of digital rock images with super resolution convolutional neural networks. J. Pet. Sci. Eng. 182, 106261 (2019b)

    Google Scholar 

  • Wang, Y., et al.: Accelerated computation of relative permeability by coupled morphological and direct multiphase flow simulation. J. Comput. Phys. 401, 108966 (2020a)

    Google Scholar 

  • Wang, Y.D., et al.: Physical Accuracy of Deep Neural Networks for 2D and 3D Multi-Mineral Segmentation of Rock micro-CT Images. arXiv preprint http://arxiv.org/abs/05322 (2020b)

  • Wildenschild, D., Sheppard, A.P.: X-ray imaging and analysis techniques for quantifying pore-scale structure and processes in subsurface porous medium systems. Adv. Water Resour. 51, 217–246 (2013)

    Google Scholar 

  • Yang, J.: Multi-scale simulation of multiphase multi-component flow in porous media using the Lattice Boltzmann Method, Imperial College London (2013). https://doi.org/10.25560/18928

  • Yang, X., et al.: Direct numerical simulation of pore-scale flow in a bead pack: comparison with magnetic resonance imaging observations. Adv. Water Resour. 54, 228–241 (2013)

    Google Scholar 

  • Zacharoudiou, I., Boek, E.S.: Capillary filling and Haines jump dynamics using free energy Lattice Boltzmann simulations. Adv. Water Resour. 92, 43–56 (2016)

    Google Scholar 

  • Zhang, Y., et al.: On the challenges of greyscale-based quantifications using X-ray computed microtomography. J. Microsc. 275(2), 82–96 (2019)

    Google Scholar 

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Authors and Affiliations

  1. School of Minerals and Energy Resources Engineering, The University of New South Wales, Sydney, Australia

    Traiwit Chung, Ying Da Wang, Ryan T. Armstrong & Peyman Mostaghimi

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  1. Traiwit Chung
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  4. Peyman Mostaghimi
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Correspondence to Peyman Mostaghimi.

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Chung, T., Da Wang, Y., Armstrong, R.T. et al. CNN-PFVS: Integrating Neural Network and Finite Volume Models to Accelerate Flow Simulation on Pore Space Images. Transp Porous Med 135, 25–37 (2020). https://doi.org/10.1007/s11242-020-01466-1

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