Mechanochemically mediated anisotropy of fluid flow in fractured rock

Transcription

1 Mechanochemically mediated anisotropy of fluid flow in fractured rock Philipp S. Lang, Morteza Nejati, Adriana Paluszny, and Robert W. Zimmerman Imperial College London, UK PMPM and UK InterPore Joint Annual Meeting 2016 Edinburgh, UK

2 Introduction Understanding fluid flow direction and magnitude in fractured rock is fundamental to the design of subsurface sequestration, production and disposal The fractures that are considered most likely to be hydraulically conductive are those critically oriented with respect to the in situ stress field This is usually attributed to slip-induced dilation, as the stress acting on these fractures approaches their frictional strength Barton, Zoback, & Moos, Geology (1995) 2

3 Permeability Anisotropy in Fractured Rock Flow anisotropy on two scales Fracture network - orientation - connectivity Barton, Eng. Geol. (1973) Individual fractures - shear-induced dilation - normal-stress dependent compression Bonnet et al., Rev. Geophys. (2001) Matsuki et al., Int. J. Rock Mech. Min. Sci. (2001) 3

4 Upscaling Averaging Methods Volume Average: Flow has vertical component Surface Average: Flow has only horizontal component Wu et al., Discrete Continuous Dyn. Syst. Ser. B (2002) When using surface averaging to upscale permeability, the implicit assumption is that a pressure gradient in e.g. x- direction causes flow in the same direction only. The error of the resulting diagonalization depends on the underlying spatial discretization and the arbitrarily imposed reference system, i.e., the reference frame at which boundary conditions are prescribed. 4

5 Upscaling Assumptions Effective permeability of spatially periodic medium k min k max K = Volume averaging, full tensor K = Surface averaging, diagonalized tensor Durlofsky, Water Resour. Res. (1991) K =

6 Upscaling Issues on the Network Scale The applicability of upscaling depends on a separation of length scales. Effective: REV, spatially periodic Equivalent: no REV, no separation of scales Renard & de Marsily, Adv. Water Resourc. (1996) Bonnet et al., Rev. Geophys. (2001) 6

7 Upscaling Issues on the Fracture Scale Surfaces created by a fracturing process are fractal across all length scales. It follows that there is no obvious a priori homogenization length scale for the contact or flow problem. Whether scaling relationships for laboratory derived models exist is not clear. Barton, Eng. Geol. (1973) Modified after Wei & Hudson, ISRM (1988) 7

8 Modelling Approach Represent largest features explicitly Largest fractures in the network Largest roughness wavelengths of the fractures Solve the contact problem on both scales Solve the flow problem on both scales Both flow and contact converge with decreasing cut-off scale 8

9 Two-Scale Contact-Flow Model Linear-elastic model of fracture opening and closure at network scale (FE) Fractures are planar discontinuities Internal pressure opens fractures, triaxial confining stress then causes closure Displacement and traction fields over fracture surfaces result Contact and transmissivity at fracture scale (BE/FV) Rough, fractal surface model for each fracture Opposing surfaces are offset by the average shear displacement, and compressed under the average normal traction 9

10 Fracture Surfaces Fracture surfaces roughness is fractal across all scales Aperture fields, however, may have a homogenization length scale above which the resulting transmissivity remains invariant Roughness spectrum to (a), a tensile fracture This length scale is a function of shear displacement and reflects that the opposing surfaces are correlated above some roughness wavelength The existence of such a homogenization scale for the aperture field is an open question Even pure tensile fractures have a minimum mismatch resulting form surface damage Mismatch length scale 10

11 Conjugate Fractures Example Opening Tractions upon closure In-plane permeability eigenvector B A Hydraulic aperture and shear direction Single Fracture Contact and Flow A B 11

12 Fractured Rock Mass Model Discrete 200-fracture model Power-law size distribution (r = [5,15] m, exp = -2.0) Uniform random orientation Young's modulus 60 GPa, Poisson's ratio 0.15 Intact rock permeability: 1E-15 m 2 Friction coefficient between fracture surfaces: 0.6 Single fracture models Two surfaces with Hurst exponent of 0.8 Roughness-length scaling h rms = 0.01 L H Small-roughness wavelength mismatch Displacements 12

13 Orientation Dependent Transmissivity Fractures close to a critical stress state (A) possess a larger void space with more pronounced channels due to openingclosure related shear. Fractures far from this stress state (B) show more porous medium-like flow fields. This reflects the amount of shear during closure and the acting normal traction. A A B B 13

14 Full Permeability Tensor: Arbitrary Fracture Networks The upscaled permeability/flow should not depend on the imposed coordinate axes Periodic boundary conditions are impractical for unstructured meshes of arbitrary fracture networks Using three flow simulations and sampling regions of arbitrary choice, the full permeability tensor can be evaluated using a least-squares approximation (FE) Ax = b 14

15 Full Permeability Tensor: Locally Anisotropic Coefficients Fractures with the largest effect on macroscopic flow are likely those with the largest shear displacement Effective permeability This shear is accompanied by flow anisotropy To incorporate the mechanical effects on flow in fractured rock this fracture-scale transmissivity anisotropy has to be taken into account Matrix permeability Fracture transmissivit Element-wise constant diffusion coefficients in tensor form need be supported 15

16 Anisotropic Permeability of Rock Mass The preferential flow direction, represented by the eigenvector k max, tends to lie inbetween the two planes that represent critically stressed fracture orientations Mechanical model Length correlated k max = 4.13 k med = 2.89 E-11 m2 k min =

17 Anisotropic Effects of Fracture Compaction Fracture permeabilities are known to change over time due to thermo-hydromechanical-chemical processes Since these processes depend on the state of stress, they should be expected to affect fractures differently based on their orientation Using multi-scale multi-physics simulations, we show that orientation dependent compaction provides additional explanation for the observation that near-critically stressed fractures are hydraulically more conductive 17

18 Pressure Solution as Compaction Mechanism Pressure enhanced solubility of contacting asperities with respect to hydrostatically stressed free surface Diffusive process of mass transfer Confining pressure and dissolution of contacts result in convergence of surfaces Precipitation of dissolved mass over free surface 18

19 dissolution precipitation Numerical Pissolution/Precipitation Model (BE) D x 2 c x + ρ sk d ρ f w Ω s kt σ x ln c(x) c eq = 0 (FV) Laminar, depth-averaged Reynolds lubrication flow in non-contact areas (FV) Free-face precipitation, proportional to 1/(dist. from contact area) 19

20 Fracture Compaction due to Pressure Solution Contact patches grow and flatten Contact stress concentrations decrease From reversible to irreversible compaction Increasing discrepancy between mechanical and hydraulic aperture 20

21 Orientation Dependent Compaction The stress-dependent opening-closure process, combined with the difference in normal pressure, leads to fractures near a critical stress (A') state being less affected by pressure-solution compaction than those with different stress ratios (B'). A B 21

22 Orientation Dependent Compaction Contact Ratio Time Time Contact Ratio Time 22

23 Single Fracture: Anisotropic Flow Effects of Compaction The mechanically induced anisotropy of fracture transmissivity increases during compaction Percolation seals the shear-parallel flow structures first 23

24 Fracture Network: Anisotropic Flow Effects of Compaction Pressure-solution compaction, if an active process in fractures in the system, acts to increase mechanically induced permeability anisotropy and the resulting preferential flow direction 24

25 Discussion Parameter free model of fractured rock permeability (...μ) As any solution to non-linear problems with distributed parameters, sensitive to Boundary conditions Initial conditions Parameter distribution extremes Specifically, for contact problem in fractured rock Stress ratio, confinement Opening-closure model, opening pressure, no propagation Largest fractures Fracture intersections? Mechanical stability of fracture geometries? 25

26 References Lang, PS, A Paluszny, and RW Zimmerman (2014), Permeability tensor of three-dimensional fractured porous rock and a comparison to tracemap predictions, Journal of Geophysical Research: Solid Earth, 119(8), Lang, PS, A Paluszny, and RW Zimmerman (2015), Hydraulic sealing due to pressure solution contact zone growth in siliciclastic rock fractures, Journal of Geophysical Research: Solid Earth, 120(6), Lang, PS, A Paluszny, and RW Zimmerman (2016), Evolution of fracture normal stiffness due to pressure dissolution and precipitation, International Journal of Rock Mechanics and Mining Sciences, submitted. Nejati, M, A Paluszny, and RW Zimmerman (2015), On the use of quarter-point tetrahedral finite elements in linear elastic fracture mechanics, Engineering Fracture Mechanics, 144, Nejati, M, A Paluszny, and RW Zimmerman (2015), A disk-shaped domain integral method for the computation of stress intensity factors using tetrahedral meshes, International Journal of Solids and Structures, 69 70, Nejati, M, A Paluszny, and RW Zimmerman (2016), A finite element framework for modeling internal frictional contact in three-dimensional fractured media using unstructured tetrahedral meshes, Computer Methods in Applied Mechanics and Engineering, submitted. 26