Adaptive Dynamic Multilevel Simulation of Fractured Geothermal Reservoirs

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An algebraic dynamic multilevel (ADM) method for fully-coupled simulation of flow and heat transport in heterogeneous fractured geothermal reservoirs is presented. Fractures are modeled explicitly using the projection-based embedded discrete method (pEDFM), which accurately represents fractures with generic conductivity values, from barriers to highly-conductive manifolds. A fully implicit scheme is used to obtain the coupled discrete system including mass and energy balance equations with two main unknowns (i.e., pressure and temperature) at fine-scale level. The ADM method is then developed to map the fine-scale discrete system to a dynamic multilevel coarse grid, independently for matrix and fractures. To obtain the ADM map, multilevel multiscale coarse grids are constructed for matrix as well as for each fracture at all coarsening levels. On this hierarchical nested grids, multilevel multiscale basis functions (for flow and heat) are solved locally at the beginning of the simulation. They are used during the ADM simulation to allow for accurate multilevel systems in presence of parameter heterogeneity. The resolution of ADM simulations is defined dynamically based on the solution gradient (i.e. front tracking technique) using a user-defined threshold. The ADM mapping occurs algebraically using the so-called ADM prolongation and restriction operators, for all unknowns. A variety of 2D and 3D fractured test cases with homogeneous and heterogeneous permeability maps are studied. It is shown that ADM is able to model the coupled mass-heat transport accurately by employing only a fraction of fine-scale grid cells. Therefore, it promises an efficient approach for simulation of large and real-field scale fractured geothermal reservoirs. All software developments of this paper is publicly available at
Original languageEnglish
Article number100061
Pages (from-to)1-24
Number of pages24
JournalJournal of Computational Physics: X
Publication statusPublished - 2020


  • Adaptive mesh refinement
  • Flow in porous media
  • Fractured porous media
  • Geothermal energy
  • Mass-heat transfer coupling
  • Multiscale simulation


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