Geothermal Application 1 Summer School Heat extraction from a sloped sandstone aquifer Vertical cross section of the model domain

Geothermal Application 2 Summer School Spatial Discretization 3 super elements 3000 quad elements, including 1000 covering the sloped aquifer Areally Meshing option FEFLOW Mesh Generation, Step 1

Geothermal Application 3 Summer School Triangularize Areal-Joining (via Supermesh) of the sloped aquifer, twice Spatial Discretization FEFLOW Mesh Generation, Step 2

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

Geothermal Application 5 Summer School Flow Problem - Material parameters Global: K = m/s  Input [10 -4 ] m/s Join (via Supermesh): K = m/s for the sloped aquifer Model Set-Up

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

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

Geothermal Application 8 Summer School Heat-Transport Problem - Initials Reference temperature: T o = 20°C Model Set-Up

Geothermal Application 9 Summer School Numerical Solution FEFLOW Options Direct equation solver

Geothermal Application 10 Summer School FEFLOW Result Conductive temperature distribution Numerical Solution

Geothermal Application 11 Summer School Base model – Save…

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

Geothermal Application 13 Summer School Flow Problem – Material parameters Global: Expansion coefficient  = K -1  Input 4 [10 -4 ] K -1 Water density as a function of temperature (after Perrochet) Model Extension

Geothermal Application 14 Summer School Numerical Solution FEFLOW Result No convection cells

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

Geothermal Application 16 Summer School Convection cells develop in aquifer Numerical Solution FEFLOW Result

Geothermal Application 17 Summer School Numerical Solution FEFLOW Result Convection cells develop in aquifer

Geothermal Application 18 Summer School Load base model …

Geothermal Application 19 Summer School Pumping rate of 250 m 3 /h, or 6000 m 3 /d, over 500 m system width: 12 m 2 /d (2D) Distributed vertically over 40 m aquifer height, the outflux due to pumping is 0.3 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 Pumping (heat extraction) from aquifer and re-injection (of cooled water) into aquifer Model Extension Flow Problem - Boundary Conditions

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

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

Geothermal Application 22 Summer School Temporal and control data: Final time: days Model Extension FEFLOW Basic Settings

Geothermal Application 23 Summer School Numerical Solution FEFLOW Result