Amélie Neuville Advanced Materials and Complex Systems group (AMCS) University of Oslo Norway
The Research Council of Norway Postdoc within a PETROMAKS project Mobility grant for young researchers YGGDRASIL, project 202527 PICS between Norway and France AMCS Oslo, University of Oslo Eirik Flekkøy Knut Jørgen Måløy Mihailo Jankov Ken Tore Tallakstad Marion Erpelding EOST Strasbourg, University of Strasbourg Renaud Toussaint Jean Schmittbuhl Alain Cochard University of Glasgow Daniel Koehn University of Mainz Olivier Schwarz
Photo P Thomas
Photo JP Malet
Dr M Royon / Wikimedia Commons Image GEIE
3 2 1
Laser profiler (mm) (mm) Neuville et Al. Hydraulic Processes (2011) (mm)
Photogrammetry
Computer tomography scan Neuville et Al. Hydraulic Processes (2011)
(mm) Aperture (mm) Open fracture Correlation of the topography + hypothesis on the type of displacement (normal/shear/ ) 2.7 2.6 2.5 2.4 2.3 2.2 (mm) Sealed fracture (mm) Aperture (mm) 14 12 10 8 6 4 (mm)
Natural aperture Self-affine aperture (mm) (mm) (mm) (mm) (mm)
Navier-Stokes V ρ + V. V t Advection-diffusion equation Depend on = p + η V + f ext T +.( VT ) =.( χ T ) t fluid viscosity, density pressure gradient r p η, ρ Rock/fluid thermal diffusivities Fracture aperture a(x,y) χ r, χ f y z x Fluid injection (P 0,T 0 ) T r (t =0) = 200 C a(x,y) T r (t)? Fluid pumping (P L,T f?) Scale: individual fracture
Finite differences (FD) model o Lubrications approximations = Equations averaged across the aperture Smooth roughness (Here: self-affine aperture) Velocity contained in the mean plane (x,y) z V parabolic Diffusive heat flux along z Advectiveheat flux in the mean plane (x,y) z T quartic o Constant rock temperature
Rough apertures (self-affine) a( x, y) Main flow 2D-hydraulic flow norm ( x, y ) inertial forces Re = = 0.23 viscous forces q r Averaged temperature T ( x, y) = a V ( x, y, z) T ( x, y, z) dz a V ( x, y, z) dz Neuvilleet Al. Phys. Rev. E(2010) Neuville et Al. C.R. Geosci.(2010)
Velocity Temperature
Control of the large scales modes on the hydro-thermal variations Fourier filtering of the aperture Neuville et Al. GJI (2011) Aperture y x
Control of the large scales modes on the hydro-thermal variations Aperture y x Main flow Hydraulic flow Main flow -ln(t * ) Neuville et Al. GJI (2011)
Mean geometrical aperture known Not enough information to model the hydro-thermal behavior Permeability known Thermal exchange efficiency over-estimated if neglecting the roughness Large scale variation of the aperture known Good estimation of the permeability and thermal efficiency
Effect of sharp morphology? Full Navier Stokes equation solved in 3D + Natural convection Full advection-diffusion heat equation solved in 3D, in fluid androck Dynamical modeling Transientregime, Morphology evolution
Comes from Lattice gas methods Discrete space and time Discrete velocity directions Fictitious particles, 1 particle/node in a given direction Variables: booleans showing particle occupation Boltzmann methods Average in a mesoscopicvolume of particles occupation in a given direction Here: 2 particles distributions, 2 lattices Hydraulics mass particle distribution Conservation of mass and momentum Thermics Internal energy particle distribution Conservation of internal energy and energy flux
FLUID ROCK Space unit: average aperture A/20 Time unit: 0.125[A/(40)] 2 x (0.016/χ r ) Reynolds number: 0.17 Péclet number: 46 Temperature unit: arbitrary (fixed by fluid injection temperature and rock temperature) χ /χ r = 0.17 (realistic)
Space unit: average aperture A/20 Time unit: 0.125[A/(40)] 2 x (0.016/χ r ) Reynolds number: 0.17 Péclet number: 46 Temperature unit: arbitrary (fixed by fluid injection temperature and rock temperature) χ /χ r = 0.17 (realistic)
ROCK FLUID V x V x * V x V z * Recirculation SmallReynolds number (Re 0.17) β=28 β=102 V x * FLUID x10-3 x10-3 V * z z V z z x x V x * V x *
Temperature ROCK ROCK FLUID χ f z x * (x) * * Reynolds number: 0.17 Péclet number: 46
Temperature * * * (x) Linear fit, exp(-x/r // ) Linear fit, exp(-x/r) Corner: R / R // = 1.7 x ROCK
R / R // 1 2 p L 1 2 L β p p=20, L=10, β=28 p=20, L=50, β=?
Re = 0.17 Pe = 46
Vx Vz
Temperature T* Compared to the temperature obtained in FD with lubrication approximation
P = P0 + bsin(2π t * P ) = P0 + bsin(2π t * Re = 1.8 ) Vx Vz
Temperature (quasi stationnary regime) Re = 1.8 Pe = 201 Temperature difference, without-with time dependent pressure
Boussinesq approximation g T v p v v t v r ρ ε η ρ + + = +. Thermal expansion coefficient ε Reynolds number: 0.05 Péclet number: 0.46
Vx Velocity Z Vz
Possible mechanism to explain frequencies induced by tremor/aseismic events? Stress change
t+ t e.g. Cochard et Rice J Mech Phys Solids (1997)
Example of stress within the fluid (LB computation) : Shear stress -- dimensionless
Radiation Temperature Planck law +corrections
Bottom: rough surface: Epoxy plate surface cast Numerical topography: photogrammetry Zone observed withthe IR camera
Top surface: transparent to the IR Polyethylen(plastic bag) Germanium plate with anti-reflexion coating
Free surface
Hydro-thermal Due to the fracture roughness, channeling of Hydraulic flow Temperature (energy) Large scale variations are important Thermal exchange less efficient than flat model with same permeability Inside the asperity with steep slopes: Recirculation Fluid trapped Few advectivethermal exchanges, even with a time dependent pressure
Hydro-thermal modeling using LB methods Advantages Full hydraulic and heat equations solved in 3D Fluid recirculation Natural convection Dynamic modelling Direct computation of stress within the fluid Possibility to couple fluid LB simulation with solid and wave modelling 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: also holds for the chemical species concentration o Crystallization/dissolution
Experimentation with an infrared camera Observation of temperature evolution Experimental setup Feasibility study Observing the temperature of a fluid circulating in a fracture On going / further work Calibration / precision of the setup Thermal and infrared properties of each material in the setup Comparison with numerical simulations Link with field measurements