Heat extraction from a sloped sandstone aquifer

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Heat extractionfrom a sloped sandstone aquifer

Vertical cross section of the model domain


Spatial Discretization

• 3 super elements• 3000 quad elements, including 1000 covering the sloped aquifer• Areally Meshing option

FEFLOW Mesh Generation, Step 1


• Triangularize• Areal-Joining (via Supermesh) of the sloped aquifer, twice

Spatial Discretization

FEFLOW Mesh Generation, Step 2


Model Set-Up

FEFLOW Basic Settings

• 2D (default)

• Problem Class:Flow and Heat (steady flow, steady

transport)

• Vertical problem projection


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


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


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


Heat-Transport Problem - Initials

• Reference temperature: To = 20°C

Model Set-Up


Numerical Solution

FEFLOW Options

• Direct equation solver


FEFLOW Result

Conductive temperature distribution

Numerical Solution


Base model – Save…


• 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



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


Numerical Solution

FEFLOW Result

No convection cells


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


Convection cells develop in aquifer

Numerical Solution

FEFLOW Result


Numerical Solution

FEFLOW Result

Convection cells develop in aquifer


Load base model …


• 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



• Remove 1st-kind B.C. (h = 0 m)

• Set 2nd-kind B.C. (via Nodal):

Model Extension



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


• Temporal and control data:

Final time: 10000 days

Model Extension



Numerical Solution

FEFLOW Result

Documents

Heat extraction from a sloped sandstone aquifer