Amélie Neuville (1,2), Renaud Toussaint (2), Eirik Flekkøy (1), Jean Schmittbuhl (2)

Transcription

1 Amélie Neuville (1,2), Renaud Toussaint (2), Eirik Flekkøy (1), Jean Schmittbuhl (2)

2 Thermal exchanges between a hot fractured rock and a cold fluid Deep geothermal systems Enhanced Geothermal Systems Soult-sous-Forêts (Alsace, France) Cooper Basin (Australia) Example of parameters Hydraulic flow : 25 l/s Temperature at injection : 60 C Temperature at pumping : 200 C 1 km 2 km 3 km 1 4 km km 2 A. Gallien, from AREVA documents

3 Fracture have a complex morphology Variable fracture aperture Impermeable bulk Effect of the morphology of fractures on the Hydraulic flow? Heat exchange between fluid and rock? Fluid injection (P 0,T 0 ) T f (t)? T r (t =0) = 200 C T r (t)? Fluid pumping (P L,T f?) Scale: individual fracture

4 Equations Navier-Stokes Advection-diffusion equation Hydro-thermal models Finite differences (FD) model o Lubrications approximations = Equations averaged across the aperture Velocity contained in the mean plane (x,y) Diffusive heat flux along o o Advective heat flux in the mean plane (x,y) Constant temperature rock Self-affine aperture: Smooth roughness Depend on fluid viscosity pressure gradient Rock/fluid thermal diffusivities Fracture aperture a(x,y)! y x a(x,y) T η ρ p Main flow V parabolic quartic Lattice Boltmann (LB) model o Statistical method Fictitious mass and energy particles o No terms discarded in the equations o Single asperity with steep slopes, Sharp roughness

5 Rough apertures (self-affine) a( x, y) Main flow 2D-flow norm ( x, y) q ρ Averaged temperature T ( x, y) = a V ( x, y, ) T ( x, y, ) d a V ( x, y, ) d Neuville et Al. Phys. Rev. E (2010) Neuville et Al. C.R. Geosci. (2010)

6 Inverse of the heat exchange Efficiency(Γ) Thermal exch. less efficient than parallel plates separated by A Thermal exch. more efficient than parallel plates separated by A 1 Less permeable than parallel plates separated by A * Γ=1.02 H= More permeable than parallel plates separated by A Thermal exch. less efficient than flat model with same permeability Expected thermal efficiency deduced from the hydraulic efficiency A: mean geometric aperture Hydraulic exchange efficiency (H)

7 Aperture y x Hydraulic flow -ln(t * ) Neuville et Al. GJI (2011)

8 Fourier filtering of the aperture a(x,y): Hydraulic Thermal (H n - H ref )/ H ref and ( Γ n -Γ ref )/ Γ ref : Difference between the efficiencies in the filtered (H n, Γ n ) and in the fully rough geometries (H ref, Γ ref ) n = 1 Average aperture kept Parallel case n Morphology is better described H n converge towards H ref Γ n converge towards Γ ref

9 x Velocity vectors ROCK FLUID V x V Recirculation at small Reynolds number (Re 0.003) x Velocity vectors V x V x Compared to velocity obtained in FD with lubrication approximation x x

10 Temperature Time evolution ROCK χ r FLUID χ f * (x) * * R / R // = 1.09 x Reynolds number: Péclet number: 0.5 FLUID ROCK R R //

11 L p=20, L=10, β=28 p=20, L=30, β=74 At small Pe: thermal exchange slighlty less good with the asperity Qualitative behavior consistent with the lubrication approximation

12 Smooth roughness Due to roughness, channeling of Hydraulic flow Temperature (energy) Large scale variations are important Thermal exchange less efficient than flat model with same permeability Sharp roughness (cavities) Inside the asperity with steep slopes: Recirculation Fluid trapped Few advective thermal exchanges How to stimulate these asperities? Oscillating pressure gradient? Change the Peclet number? On going simulation s using LB methods

13 Advantages Full hydraulic and heat equation solved in 3D Fluid recirculation Other questions which could be addressed with LB methods: Long term behavior of geothermal systems o Diffusion in the rock and liquid Chemical effects? o Advection-diffusion equation: o Hydro-thermal modeling using LB methods also holds for the chemical species concentration Crystalliation/dissolution Coupling the pressure variations in space and time with mechanical effects?

14 A. Neuville, R. Toussaint and J. Schmittbuhl (2010) Fracture roughness and thermal exchange: A case study at Soult-sous-Forêts. Comptes Rendus Geoscience, 347(7-8): A. Neuville, R. Toussaint and J. Schmittbuhl (2010) Hydro-thermal flows in a self-affine rough fracture, Physical Review E, 82, A. Neuville, R. Toussaint and J. Schmittbuhl (2011) Hydraulic transmissivity and heat exchange efficiency of rough fractures: a spectral approach. Geophysical Journal International

15 * P = P0 sin(2π t / p) p=64