Date post: | 30-Dec-2015 |
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Geothermal ApplicationSummerSummerSchoolSchool
Heat extractionfrom a sloped sandstone aquifer
Vertical cross section of the model domain
Geothermal ApplicationSummerSummerSchoolSchool
Spatial Discretization
• 3 super elements• 3000 quad elements, including 1000 covering the sloped aquifer• Areally Meshing option
FEFLOW Mesh Generation, Step 1
Geothermal ApplicationSummerSummerSchoolSchool
• Triangularize• Areal-Joining (via Supermesh) of the sloped aquifer, twice
Spatial Discretization
FEFLOW Mesh Generation, Step 2
Geothermal ApplicationSummerSummerSchoolSchool
Model Set-Up
FEFLOW Basic Settings
• 2D (default)
• Problem Class:Flow and Heat (steady flow, steady
transport)
• Vertical problem projection
Geothermal ApplicationSummerSummerSchoolSchool
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
Model Set-Up
Geothermal ApplicationSummerSummerSchoolSchool
Flow Problem - Boundary Conditions
• Impermeable border (default)
• 1st-kind boundary condition at an arbitrary node, e.g., upper left: h = 0 m
Model Set-Up
Geothermal ApplicationSummerSummerSchoolSchool
Heat-Transport Problem - Boundary Conditions
Implemented as 1st-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 ApplicationSummerSummerSchoolSchool
Heat-Transport Problem - Initials
• Reference temperature: To = 20°C
Model Set-Up
Geothermal ApplicationSummerSummerSchoolSchool
Numerical Solution
FEFLOW Options
• Direct equation solver
Geothermal ApplicationSummerSummerSchoolSchool
FEFLOW Result
Conductive temperature distribution
Numerical Solution
Geothermal ApplicationSummerSummerSchoolSchool
Base model – Save…
Geothermal ApplicationSummerSummerSchoolSchool
• 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
Model Extension
FEFLOW Basic Settings
Geothermal ApplicationSummerSummerSchoolSchool
Flow Problem – Material parameters
• Global:Expansion coefficient = 0.0004 K-1
Input 4 [10-4] K-1
Water density as a function of temperature (after Perrochet)
Model Extension
Geothermal ApplicationSummerSummerSchoolSchool
Numerical Solution
FEFLOW Result
No convection cells
Geothermal ApplicationSummerSummerSchoolSchool
Flow Problem – Material parameters
Aquifer of higher hydraulic conductivity
• Join (via Supermesh): K = 0.005 m/s Input 50 [10-4] m/s
Model Extension
Geothermal ApplicationSummerSummerSchoolSchool
Convection cells develop in aquifer
Numerical Solution
FEFLOW Result
Geothermal ApplicationSummerSummerSchoolSchool
Numerical Solution
FEFLOW Result
Convection cells develop in aquifer
Geothermal ApplicationSummerSummerSchoolSchool
Load base model …
Geothermal ApplicationSummerSummerSchoolSchool
• 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 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 andre-injection (of cooled water) into aquifer
Model Extension
Flow Problem - Boundary Conditions
Geothermal ApplicationSummerSummerSchoolSchool
• Remove 1st-kind B.C. (h = 0 m)
• Set 2nd-kind B.C. (via Nodal):
Model Extension
Flow Problem - Boundary Conditions
Geothermal ApplicationSummerSummerSchoolSchool
Heat-Transport Problem - Boundary Conditions
Implemented as 1st-kind B.C. at injection nodes (via Nodal):
Temperature of re-injected water: 20°C
• T = 20°C
Model Extension
Geothermal ApplicationSummerSummerSchoolSchool
• Temporal and control data:
Final time: 10000 days
Model Extension
FEFLOW Basic Settings
Geothermal ApplicationSummerSummerSchoolSchool
Numerical Solution
FEFLOW Result