In this paper, we introduce a pore-scale model for reactive flow and transport in evolving porous media exhibiting two competing mineral phases. By formal two-scale asymptotic expansion in a level-set framework an effective micro-macro model is derived. As such, our approach comprises flow and transport equations on the macroscopic scale including effective hydrodynamic parameters calculated from representative unit cells. Conversely, the macroscopic solutes' concentrations alter the unit cells' geometrical structure by triggering dissolution or precipitation processes. The numerical implementation of such micro-macro models poses several challenges, especially in terms of geometry representation and computational complexity. In this research, the Voronoi implicit interface method is applied to characterize and evolve the two-mineral structure and first-order convergence is obtained in a test case where analytical solutions are available. Furthermore, we present a sophisticated overall solution strategy for the introduced fully coupled nonlinear micro-macro problem and conduct numerical simulations. In doing so, the significant performance enhancements arising from machine learning techniques are evaluated. To this end, a convolutional neural network is trained on (realistic) unit cell geometries for permeability prediction and deployed in a micro-macro simulation. The outcome is compared to the respective results obtained by classical methods in terms of predictive power and computational effort.


  1. convolutional neural network
  2. evolving porous media
  3. micro-macro model
  4. multiphase solid
  5. reactive transport
  6. upscaling

MSC codes

  1. 35B27
  2. 68T07
  3. 76V05

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Information & Authors


Published In

cover image Multiscale Modeling & Simulation
Multiscale Modeling & Simulation
Pages: 433 - 461
ISSN (online): 1540-3467


Submitted: 16 November 2020
Accepted: 2 November 2021
Published online: 22 March 2022


  1. convolutional neural network
  2. evolving porous media
  3. micro-macro model
  4. multiphase solid
  5. reactive transport
  6. upscaling

MSC codes

  1. 35B27
  2. 68T07
  3. 76V05



Funding Information

Deutsche Forschungsgemeinschaft https://doi.org/10.13039/501100001659 : 2170, 2339

Funding Information

Vedecká Grantová Agentúra MŠVVaŠ SR a SAV https://doi.org/10.13039/501100006109 : 1/0709/19, APVV-19-0460

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