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Heat extraction from a sloped sandstone aquifer

Heat extraction from a sloped sandstone aquifer. Vertical cross section of the model domain. Spatial Discretization. FEFLOW Mesh Generation, Step 1. • 3 super elements • 3000 quad elements, including 1000 covering the sloped aquifer • Areally Meshing option. Spatial Discretization.

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Heat extraction from a sloped sandstone aquifer

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  1. Heat extractionfrom a sloped sandstone aquifer Vertical cross section of the model domain

  2. Spatial Discretization FEFLOW Mesh Generation, Step 1 •3 super elements•3000 quad elements, including 1000 covering the sloped aquifer•Areally Meshing option

  3. Spatial Discretization FEFLOW Mesh Generation, Step 2 •Triangularize•Areal-Joining (via Supermesh) of the sloped aquifer, twice

  4. Model Set-Up FEFLOW Basic Settings •2D (default) •Problem Class: Flow and Heat (steady flow, steady transport)•Vertical problem projection

  5. Model Set-Up Flow Problem - Material parameters •Global: K = 10-7 m/s Input 0.001[10-4] m/s•Join (via Supermesh): K = 10-4 m/s for the sloped aquifer

  6. Model Set-Up Flow Problem - Boundary Conditions •Impermeable border (default)•1st-kind boundary condition at an arbitrary node, e.g., upper left: h = 0 m

  7. Model Set-Up Heat-Transport Problem - Boundary Conditions Geothermal gradient: 35 K/km Implemented as 1st-kind boundary condition on the top and bottom border (via Border-Option) •top: T = 20°C•bottom: T = 90°C

  8. Model Set-Up Heat-Transport Problem - Initials •Reference temperature: To = 20°C

  9. Numerical Solution FEFLOW Options •Direct equation solver

  10. Numerical Solution FEFLOW Result Conductive temperature distribution

  11. Base model – Save…

  12. Model Extension FEFLOW Basic Settings • Problem Class: Flow and Heat (steady flow, transient transport)• Temporal and control data:Automatic time stepping, FE/BE time integrationFinal time: 36500 days (100 years)Error tolerance: 10-4 Input 0.1[10-3]Least-square upwinding for numerical stabilization

  13. Model Extension Flow Problem – Material parameters •Global: Expansion coefficientb= 0.0004 K-1 Input 4[10-4] K-1 Water density as a function of temperature (after Perrochet)

  14. Numerical Solution FEFLOW Result No convection cells

  15. Model Extension Flow Problem – Material parameters Aquifer of higher hydraulic conductivity•Join (via Supermesh): K = 0.005 m/s Input 50[10-4] m/s

  16. Numerical Solution FEFLOW Result Convection cells develop in aquifer

  17. Numerical Solution FEFLOW Result Convection cells develop in aquifer

  18. Load base model …

  19. Model Extension Flow Problem - Boundary Conditions Pumping (heat extraction) from aquifer and re-injection (of cooled water) into aquifer • Pumping rate of 250 m3/h, or 6000 m3/d, over 500 m system width: 12 m2/d (2D) • Distributed vertically over 40 m aquifer height, the outflux due to pumping is0.3 m/d •An inner Neumann-B.C. acts in two directions simultaneously, thus the B.C. value is half the flux: q = 0.15 m/d

  20. Model Extension Flow Problem - Boundary Conditions • Remove 1st-kind B.C. (h = 0 m) • Set 2nd-kind B.C. (via Nodal):

  21. Model Extension Heat-Transport Problem - Boundary Conditions Temperature of re-injected water: 20°C Implemented as 1st-kind B.C. at injection nodes (via Nodal): •T = 20°C

  22. Model Extension FEFLOW Basic Settings •Temporal and control data:Final time: 10000 days

  23. Numerical Solution FEFLOW Result

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