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Accelerated Computational Micromechanics for Reactive Flow in Porous Media (2312.15554v1)

Published 24 Dec 2023 in math.NA and cs.NA

Abstract: Reactive transport in permeable porous media is relevant for a variety of applications, but poses a significant challenge due to the range of length and time scales. Multiscale methods that aim to link microstructure with the macroscopic response of geo-materials have been developed, but require the repeated solution of the small-scale problem and provide the motivation for this work. We present an efficient computational method to study fluid flow and solute transport problems in periodic porous media. Fluid flow is governed by the Stokes equation, and the solute transport is governed by the advection-diffusion equation. We follow the accelerated computational micromechanics approach that leads to an iterative computational method where each step is either local or the solution of a Poisson's equation. This enables us to implement these methods on accelerators like graphics processing units (GPUs) and exploit their massively parallel architecture. We verify the approach by comparing the results against established computational methods and then demonstrate the accuracy, efficacy, and performance by studying various examples. This method efficiently calculates the effective transport properties for complex pore geometries.

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References (42)
  1. Two-scale expansion with drift approach to the taylor dispersion for reactive transport through porous media. Chemical Engineering Science, 65:2292–2300, 2010.
  2. G. Allaire and A.-L. Raphael. Homogenization of a convection-diffusion model with reaction in a porous medium. Comptes Rendus Mathematique, 344:523–528, 2007.
  3. Validation of a numerical method based on fast fourier transforms for heterogeneous thermoelastic materials by comparison with analytical solutions. Computational Materials Science, 87:209–217, 2014.
  4. A penalization method to take into account obstacles in incompressible viscous flows. Numerische Mathematik, 81:497–520, 1999.
  5. C. A. J. Appelo and D. Postma. Geochemistry, groundwater and pollution. CRC press, 2004.
  6. Y. Baqer and X. Chen. A review on reactive transport model and porosity evolution in the porous media. Environmental Science and Pollution Research, 29:47873–47901, 2022.
  7. J. Bear and Y. Bachmat. Introduction to modeling of transport phenomena in porous media, volume 4. Springer Science & Business Media, 2012.
  8. A numerical spectral approach for solving elasto-static field dislocation and g-disclination mechanics. International Journal of Solids and Structures, 51:4157–4175, 2014.
  9. A fast fourier transform-based mesoscale field dislocation mechanics study of grain size effects and reversible plasticity in polycrystals. Journal of the Mechanics and Physics of Solids, 135:103808, 2020.
  10. N. Bertin and L. Capolungo. A fft-based formulation for discrete dislocation dynamics in heterogeneous media. Journal of Computational Physics, 355:366–384, 2018.
  11. K. Bhattacharya and P. Suquet. A model problem concerning recoverable strains of shape-memory polycrystals. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 461:2797–2816, 2005.
  12. Distributed optimization and statistical learning via the alternating direction method of multipliers. Foundations and Trends in Machine Learning, 3:1–122, 2011.
  13. R. Carbonell and S. Whitaker. Dispersion in pulsed systems—ii: theoretical developments for passive dispersion in porous media. Chemical Engineering Science, 38:1795–1802, 1983.
  14. Z. Chen and H. Chen. Pointwise error estimates of discontinuous galerkin methods with penalty for second-order elliptic problems. SIAM Journal on Numerical Analysis, 42:1146–1166, 2004.
  15. The development of discontinuous galerkin methods. In Discontinuous Galerkin methods: theory, computation and applications, pages 3–50. Springer, 2000.
  16. A fast numerical scheme for computing the response of composites using grid refinement. The European Physical Journal-Applied Physics, 6:41–47, 1999.
  17. A fully-coupled flow-reactive-transport formulation based on element conservation, with application to co2 storage simulations. Advances in Water Resources, 42:47–61, 2012.
  18. Reactive transport in porous media for CO2 sequestration: Pore scale modeling using the lattice Boltzmann method. Computers & Geosciences, 98:9–20, 2017.
  19. R. Glowinski and Y. Kuznetsov. On the solution of the Dirichlet problem for linear elliptic operators by a distributed Lagrange multiplier method. Comptes Rendus de l’Académie des Sciences-Series I-Mathematics, 327:693–698, 1998.
  20. R. Glowinski and P. Le Tallec. Augmented Lagrangian and operator-splitting methods in nonlinear mechanics. SIAM, 1989.
  21. Reactive transport modeling of the enhancement of density-driven CO2 convective mixing in carbonate aquifers and its potential implication on geological carbon sequestration. Scientific reports, 6:24768, 2016.
  22. A volume penalization method for incompressible flows and scalar advection-diffusion with moving obstacles. Journal of Computational Physics, 231:4365–4383, 2012.
  23. Lattice boltzmann pore-scale model for multicomponent reactive transport in porous media. Journal of Geophysical Research: Solid Earth, 111, 2006.
  24. M. Karimi and K. Bhattacharya. A learning-based multiscale model for reactive flow in porous media. arXiv:2309.10933, 2023.
  25. M. Karimi and K. Bhattacharya. A learning-based multiscale model for reactive flow in porous media. Preprint, arXiv:2309.10933, 2023.
  26. Programming Massively Parallel Processors. Morgan-Kaufman, 2016.
  27. R. A. Lebensohn and A. Needleman. Numerical implementation of non-local polycrystal plasticity using fast fourier transforms. Journal of the Mechanics and Physics of Solids, 97:333–351, 2016.
  28. A computational method based on augmented Lagrangians and fast Fourier transforms for composites with high contrast. CMES(Computer Modelling in Engineering & Sciences), 1:79–88, 2000.
  29. V. Monchiet and G. Bonnet. A polarization-based FFT iterative scheme for computing the effective properties of elastic composites with arbitrary contrast. Experimental Mechanics, 89:1419–1436, 2012.
  30. H. Moulinec and F. Silva. Comparison of three accelerated FFT-based schemes for computing the mechanical response of composite materials. International Journal for Numerical Methods in Engineering, 97:960–985, 2014.
  31. H. Moulinec and P. Suquet. A fast numerical method for computing the linear and nonlinear mechanical properties of composites. Comptes Rendus de l’Académie des sciences. Série II. Mécanique, physique, chimie, astronomie, 1994.
  32. H. Moulinec and P. Suquet. A fast numerical method for computing the linear and nonlinear mechanical properties of composites. Comptes Rendus de l’Académie des Sciences Paris, 318:1417–1423, 1994.
  33. Convergence of iterative methods based on Neumann series for composite materials: Theory and practice. International Journal for Numerical Methods in Engineering, 114:1103–1130, 2018.
  34. C. S. Peskin. Flow patterns around heart valves: a digital computer method for solving the equations of motion. Yeshiva University, 1972.
  35. S. Salimzadeh and H. Nick. A coupled model for reactive flow through deformable fractures in enhanced geothermal systems. Geothermics, 81:88–100, 2019.
  36. Reactive transport in evolving porous media. Reviews in Mineralogy and Geochemistry, 85:197–238, 2019.
  37. J. A. Sethian and P. Smereka. Level set methods for fluid interfaces. Annual review of fluid mechanics, 35:341–372, 2003.
  38. Fluid flow and reactive transport around potential nuclear waste emplacement tunnels at yucca mountain, nevada. Journal of Contaminant Hydrology, 62:653–673, 2003.
  39. An FFT-based Galerkin method for the effective permeability of porous material. International Journal for Numerical Methods in Engineering, 123:4893–4915, 2022.
  40. An FFT-based Galerkin method for homogenization of periodic media. Computers & Mathematics with Applications, 68:156–173, 2014.
  41. Validity of cubic law for fluid flow in a deformable rock fracture. Water resources research, 16:1016–1024, 1980.
  42. H. Zhou and K. Bhattacharya. Accelerated computational micromechanics and its application to polydomain liquid crystal elastomers. Journal of the Mechanics and Physics of Solids, 153:104470, 2021.

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