Modeling fractured rock mass properties with DFN concepts, theories and issues

Transcription

1 Modeling fractured rock mass properties with DFN concepts, theories and issues Philippe Davy Geosciences Rennes, Univ Rennes, CNRS, France Caroline Darcel, Romain Le Goc Itasca Consultants s.a.s., Ecully, France Contributions Jean-Raynald de Dreuzy, Olivier Bour, Géosciences Rennes, CNRS, France Julien Maillot, Etienne Lavoine, Justine Molron, Diane Doolaeghe (PhD) Raymond Munier, Jan-Olof Selroos, Diego Mas Ivars, Martin Stigsson, SKB, Sweden 1

2 Impact of fractured rock on. 3 fractures per meter!! s h t = x h K x 2

3 Application example Safety assessment for deep nuclear waste disposal Site : area several km 2, depth ~ 500 m Canister Layout: km scale 3

4 Application example Assessing the properties of the (third) geological envelope Observations: the largest database on fracture in the world 4

5 Application example Assessing the properties of the (third) geological envelope Observations: little data compared to the geological complexity 5

6 Application example Assessing the properties of the (third) geological envelope Observations Models Predictions Fracture network model Connected cluster Flowing fractures 6

7 Permeability (K eq ) Application example Assessing the properties of the (third) geological envelope Observations Models Predictions Permeability 10 0 MM PM 10-1 Fracture network model p Fracture density 7

8 Application example Assessing the properties of the (third) geological envelope Observations Models Predictions Elastic modulus 10 0 Fracture network model Elastic modulus fracture density parameter 8

9 Application example Safety assessment for deep nuclear waste disposal Predict contaminant travel time through fractures in the rock mass Fracture model Flow model data 9

10 DFN as a basic concept for fracture media modeling Prior knowledge Data Conceptual DFN Geological mapping Geophysics Hydro logging Deformation Statistical distribution Seismicity Stereology Statistical domains / intrinsic variability Deterministic conditioning Tests ECM DFN Medium model Stochastic conditioned by data statistics Process/genetic model, whose statistics are emerging properties Discrete vs continuum, and upscaling Prediction for applications Flow paths and connectivity Flow intensity (equivalent permeability) Transfer (geothermal, contaminant) Rock deformation (elastic) Rock strength Induced seismicity 10

11 DFN methodology Prior knowledge Data Medium description as a population of discrete (and simple) fractures Close to target systems easy integration of data Made of both statistics and deterministic objects Conceptual DFN But basically a statistical model Extrapolate information between data Model intrinsic and extrinsic variability ECM DFN Medium model Prediction for applications Tool for predictions Bracket possible geological behaviors, or help for understanding data/behavior Tool to find the critical parameters or length scales that are required to improve prediction 11

12 DFN methodology data integration 12

13 From fractured rocks to DFN Data Conceptual Fractured rock geology Fracture object idealized Fracture population DFN North East Roughly Planar discontinuity resulting from rock failure. Cracks, Joints, Faults, Shear zones, Bedding planes Controlled by in situ field conditions and physical processes of fracturing Geologist vs Physicist vs Mining-engineer description emphasize different aspects Lateral dimensions >> thickness 2D planar object Geometrically defined by position, size, orientation, shape Process-based defined by plow, transport, and mechanical properties Density distribution n L, l, θ, φ, number of fractures per unit volume V with a given size l, orientation θ, φ 13

14 From fractured rocks to DFN Data Conceptual Fractured rock geology Fracture object idealized Fracture population DFN North East A thin volume characterized by Its surface per unit volume (p 32 ) Some properties (aperture, stiffness of fracture walls or filling material) An idealized object With simple or complex geometry Whose definition depends on size (e.g. small-scale fracture, large-scale fault zones) Ideally, consistent with hydraulic and mechanical continuity Density distribution n L, l, θ, dl dθ = Density term Size distr. d x, y p l l dl Orientation p θ θ dθ Others p. d 14

15 DFNE 2018 s Fracture Size Seminar From fractured rocks to DFN Fractured rock geology Fracture object idealized Fracture population DFN North East A balance between the system complexity and the facility to integrate data, and to provide a stochastic representations in these fracture population. The notion of fracture size is fully related to the transformation fractured surface fracture object Challenge (or wishes). We rely on the predictions of a schematic model constrained by real data 15

16 Data integration Data from different support and scales Outcrop mapping Number of 2D fracture traces t per orientation range: n 2d (t, θ) Range of scales 1-10 m (outcrops), 100m-10km (aerial photos) Data Borehole fracture intensity Tunnel mapping Number of fractures that fully intersect the core, per unit borehole length, per orientation range: n 1d (θ) Investigation scale = borehole length (~1km) Fracture scale= borehole diameter (~80mm) to xxx 2D traces on the tunnel wall n 2d (t, θ) 1D fracture intensity n 1d (θ) for fractures that fully intersect the tunnel (scale > 5m) Geophysical data 3D information with fracture size and orientation But: not complete and low resolution (how many fractures are revealed by geophysics)? Challenge: Reducing uncertainty of DFN by conditioning to geophysical data 16

17 DFN model for data integration Stereology Data Conceptual 1. A 3D model n 3d l, θ = d 3d θ l a 3d Prior knowledge Data Conceptual Medium model Prediction for applications 2. Stereology rules Observation parameters P, fracture parameter F n(p) = න Probability P, F n 3d F df all Φ: angle between the fracture and the observation structure Outcrop Observation parameter: nb of fracture trace length t on a surface S n 2d t, θ = π 2 Γ a 3d 2 Γ a 3d d 3d θ sin Φ t a 3d+1 Piggott, A. (1997), Fractal relations for the diameter and trace length of disc-shaped fractures, J. Geophys. Res., 102(B8),

18 DFN model for data integration Stereology Data Conceptual 1. A 3D model n 3d l, θ, φ = d 3d θ l a 3d x fracture length, l Prior knowledge Data Conceptual Medium model Prediction for applications 2. Stereology rules Observation parameters P, fracture parameter F n(p) = න Probability P, F n 3d F df all Φ: angle between the fracture and the observation structure Borehole Observation parameter: nb of fractures B borehole diameter, L borehole length radius, r If l min < B and a 3d > 3 n 1d h, θ, φ = π 2 d 3d θ cos Φa3d 2 1 ε a 3d, Φ a 3d 3 a 3d 2 a 3d 1 B3 a 3d Piggott, Davy, P., A. C. (1997), Darcel, Fractal O. Bour, relations R. Munier, for the and diameter J. R. d. and Dreuzy (2006), A trace note on length the angular of disc-shaped correction fractures, applied J. to Geophys. fracture intensity Res., profiles along 102(B8), drill core, J. Geophys. Res., 111(B11), /2005jb004121,

19 DFN model for data integration Checking consistency Distribution model n 3d l, θ = d 3d θ l a 3d Data Conceptual outcrops 3D density term d 3D a 3D =3.5 Outcrops dip Darcel, C., P. Davy, O. Bour, and J. De Dreuzy (2006), Discrete fracture network for the Forsmark site, SKB Reports, R-06-79, 94 pp, Svensk Kärnbränslehantering AB, Stockhölm. 19

20 DFN model for data integration Checking consistency cores Distribution model n l, θ = d 3d θ l a 3d Data Conceptual outcrops 3D density term d 3D a 3D =3.5 Outcrops Borehole Rock unit m m m 10-3 Shear zone dip 3D consistency between borehole information (10 cm) and outcrop mapping (50cm -5m) Difference between the background fracture pattern and shear zones Increase of the fracture density by a factor 10 for low-angle dipping fracture sets No change for high-angle dipping fracture sets 20

21 DFN model for data integration a 3D DFN density pattern from 1D cores (Forsmark, Sweden) Data Conceptual Calculated from cored-borehole fracture density data Geological domain length investigation: 1-km * 10 boreholes Fracture size investigation: 10-cm (borehole diameter to.) Orientations of fractures Darcel, C., R. Le Goc, and P. Davy (2013), Development of the statistical fracture domain methodology application to the Forsmark site. SKB Rep. R , 94 pp, Svensk Kärnbränslehantering AB, Stockhölm.. 21

22 depth (m) depth DFN model for data integration a 3D DFN density pattern from 1D cores (Forsmark, Sweden) Data Conceptual Calculated from cored-borehole fracture density data Geological domain length investigation: 1-km * 10 boreholes Fracture size investigation: 10-cm (borehole diameter to.) Density of fractures density (horizontal fractures) density (vertical fractures) Classes Classes average density exp(-depth/60m) exp(-depth/500m) mean horizontal mean vertical Darcel, C., R. Le Goc, and P. Davy (2013), Development of the statistical fracture domain methodology application to the Forsmark site. SKB Rep. R , 94 pp, Svensk Kärnbränslehantering AB, Stockhölm.. 22

23 DFN methodology scaling issues 23

24 Issue 1. Scaling laws Filling the scale gap between measures Data Conceptual cores outcrop Lineament maps scale (m)

25 Issue 1. Scaling laws Filling the scale gap between measures Data Conceptual Very few data compared to the natural complexity and modeling objectives The scaling law is a key relationship, which should be based on strong arguments 25

26 logarithmic slope density distribution, n(l) Issue 1. Scaling laws Scaling and density parameters Data Conceptual A first-order local measure of the quantity (number) of fractures n D (l): number of fractures per unit D-dimension volume, per unit fracture size l Number l, l + dl n D l = V D dl An upscaling parameter Dimensionless Measure the ratio of fractures for different length scales a D l 1, l 2 = log n D l 1 n D l 2 / log l 1 l fracture trace length, l (m) a D l = l n dn D dl = d log n D l d log l 26

27 logarithmic slope density distribution, n(l) Issue 1. Scaling laws Scaling and density parameters Data Conceptual A first-order local measure of the quantity (number) of fractures n D (l): number of fractures per unit D-dimension volume, per unit fracture size l Number l, l + dl n D l = V D dl A density parameter: d D l = n D l l a D l (eq. n D l = d D l l a D) fracture trace length, l (m) 27

28 logarithmic slope density distribution, n(l) Issue 1. Scaling laws Scaling and density parameters Data Conceptual THE power-law model The only function without characteristic scales n D l, θ = d D (θ) l a D with d D and a D independent of l over a (fairly large) range of fracture sizes fracture trace length, l (m) 28

29 n 2d (l) Issue 1: Scaling law Which scaling? Data Conceptual THE LAXEMAR FRACTURE SYSTEM (SWEDEN) fracture traces outcrops 0.5m-10m Darcel, C., et al. (2009), R Statistical methodology for discrete fracture model including fracture size, orientation uncertainty together with intensity uncertainty and variability, SKB fracture trace length (m) 29

30 Issue 1: Scaling law Which scaling? Data Conceptual THE LAXEMAR FRACTURE SYSTEM (SWEDEN) fracture traces 5 Davy, P., R. Le Goc, C. Darcel, O. Bour, J.-R. de Dreuzy, and R. Munier (2010), A likely universal model of fracture scaling and its consequence for crustal hydromechanics, J. Geophys. Res., 115(B10), 1-13, doi: /2009jb density term, d 2d exponent, a 2d Forskmark Laxemar Simpevarp 30

31 n 2d (l) Issue 1: Scaling law Which scaling? Data Conceptual 10 2 outcrops 0.5m-10m outcrop model 1 a~2.2 outcrop model 2 a~ fracture trace length (m) Davy, P., R. Le Goc, C. Darcel, O. Bour, J.-R. de Dreuzy, and R. Munier (2010), A likely universal model of fracture scaling and its consequence for crustal hydromechanics, J. Geophys. Res., 115(B10), 1-13, doi: /2009jb

32 n 2d (l) Issue 1: Scaling law Which scaling? Data Conceptual 10 2 outcrops 0.5m-10m outcrop model 1 a~2.2 outcrop model 2 a~ fracture trace length (m) Davy, P., R. Le Goc, C. Darcel, O. Bour, J.-R. de Dreuzy, and R. Munier (2010), A likely universal model of fracture scaling and its consequence for crustal hydromechanics, J. Geophys. Res., 115(B10), 1-13, doi: /2009jb

33 Issue 1: Scaling law the critical scales (i.e., the dual of scaling) Data Conceptual The contribution of fractures to a physical process Π l MAXΠ C l = න l n3d l dl l min Physical process l MAXΠ C l = න l n3d l l d(ln l) l min Contribution of DFN to the physical process Π 33

34 Issue 1: Scaling law the critical scales (i.e., the dual of scaling) Data Conceptual The contribution of fractures to a physical process Π l C l = MAX lmin Π l n 3d l l d(ln l) Π l n 3d l l Scale, l 34

35 Issue 1: Scaling law the critical scales (i.e., the dual of scaling) Data Conceptual The contribution of fractures to a physical process Π l C l = MAX lmin Π l n 3d l l d(ln l) The Queen s regime Prediction depends on the capacity to detect the position and properties of the largest fractures geophysics 35

36 Issue 1: Scaling law the critical scales (i.e., the dual of scaling) Data Conceptual The contribution of fractures to a physical process Π l C l = MAX lmin Π l n 3d l l d(ln l) Π l n 3d l l Scale, l 36

37 Issue 1: Scaling law the critical scales (i.e., the dual of scaling) Data Conceptual The contribution of fractures to a physical process Π l C l = MAX lmin Π l n 3d l l d(ln l) The democratic regime The smaller fractures control the physical process what is the smaller relevant size 37

38 Issue 1: Scaling law the critical scales (i.e., the dual of scaling) Data Conceptual The contribution of fractures to a physical process Π l C l = MAX lmin Π l n 3d l l d(ln l) Π l n 3d l l Scale, l 38

39 Issue 1: Scaling law the critical scales (i.e., the dual of scaling) Data Conceptual The contribution of fractures to a physical process Π l C l = MAX lmin Π l n 3d l l d(ln l) Intermediary bodies The process is controlled by structures of intermediate sizes How to make relevant measurements 39

40 n 2d (l) Issue 1: Scaling law the critical scales (i.e., the dual of scaling) Data Conceptual 1. a 3D model deduced from 2d data n 3d l ~n 2d l l outcrops lineaments 2. the contribution of fractures to a physical process fracture trace length (m) E l = න Π l n 3d l l d(ln l) Physical process 40

41 Issue 1: Scaling law the critical scales (i.e., the dual of scaling) Data Conceptual Ex. Surface-controled processes Π l ~l 2 p 32 Mechanical properties of fractured rocks controlled by surface friction Permeability of dense networks 10 1 outcrops lineaments n 3d (l) * l l c Π l n 3d l l fracture size, l (m) 41

42 Issue 1: Scaling law the critical scales (i.e., the dual of scaling) Data Conceptual Ex. Percolation-controlled process Π l ~l 3 Network connectivity Permeability of networks close to the percolation threshold Mechanical properties of frictionless fractures 10 2 outcrops lineaments n 3d (l) * l 3+1 l c Π l n 3d l l fracture size, l (m) 42

43 Issue 1: Scaling law the critical scales (i.e., the dual of scaling) Data Conceptual Ex. contribution of a fracture to deformation ε~ S V τ k s +E o /l = S V τ 1 k s 1+l s /l Π l ~ l2 1+l s /l Π l n 3d l l fracture size, l (m) 43

44 DFN methodology physical rationale for scaling 44

45 Issue 1: Scaling law A physical rationale from genetic model Prior knowledge Data Conceptual Medium model Prediction for applications Fracture networks = population dynamics Nucleation Growth Arrest Davy, P., R. Le Goc, and C. Darcel (2013), A model of fracture nucleation, growth and arrest, and consequences for fracture density and scaling, Journal of Geophysical Research: Solid Earth, 118(4), , doi: /jgrb

46 Issue 1: Scaling law A physical rationale from genetic model 1. Nucleation Nucleation rate nሶ N t Pdf of nuclei size p N (l) nሶ N l = nሶ N (t) p N l 2. Growth ~ stress intensity factor K m ~l m/2 The Charles law: dl dt = C la stationary distribution n D l = nሶ N C. l a 1 P N l Davy, P., R. Le Goc, and C. Darcel (2013), A model of fracture nucleation, growth and arrest, and consequences for fracture density and scaling, Journal of Geophysical Research: Solid Earth, 118(4), , doi: /jgrb

47 Issue 1: Scaling law A physical rationale from genetic model 3. Arrest / Stop Large amount of T-intersection 47

48 Issue 1: Scaling law A physical rationale from genetic model 3. Arrest / Stop The Mosaic network 48

49 Issue 1: Scaling law A physical rationale from genetic model 3. Arrest / Stop The Mosaic network Size distribution Distance from one object to another ~ object size Densité of objects: ρ = N/V Average distance d~ρ 1/D D=space dimension n(l) l = ρ 1/D 49

50 Issue 1: Scaling law A physical rationale from genetic model 3. Arrest / Stop The hierarchical network Size distribution Fracture energy depends on fracture size An intersection should likely stop the smallest fracture Size ~ average distance of larger fractures l~ N l >l V 1/D = Cumulative l 1/D n(l) self-similar distribution n D l = Dγ D l D+1 50

51 Issue 1: Scaling law A physical rationale from genetic model 3. Arrest / Stop The hierarchical network 20 cm self-similar distribution n D l = Dγ D l D+1 10 km 51

52 Collisions rate The UFM model a collision model for fracture growth model Prior knowledge Model parameters System dimension D=3 Nuclei size l N = 0.3 Nucleation rate nሶ N ln_0.15 ln_0.3 ln_0.5 Growth law: dl dt = C Gl a, a = 3 Dimensionless time t c time for a nuclei to have an infinite size t c = l N 1 a 1 C G a t* 52

53 The UFM model a collision model for fracture growth model Prior knowledge Model parameters System dimension D=3 Nuclei size l N = 0.3 n(l) Nucleation rate nሶ N Growth law: dl dt = C Gl a,a = 3 Dimensionless time t c time for a nuclei to have an infinite size t c = l N 1 a 1 C G a Dimensionless time: Fracture length 53

54 density distribution function nucleation regime Issue 1: Scaling law A physical rationale from genetic model A dual physics that explains data and predicts critical length scale Low concentration l c 10-3 High concentration growth regime UFM arrest regime fracture length 54

55 density distribution function nucleation regime Issue 1: Scaling law A physical rationale from genetic model A (likely) universal Fracture model (UFM) with a two-power-law scaling distribution n l = nሶ o C. l a n l = d UFM l D l c transition Length l c = d UFM C G ሶ n N 1 D+1 a growth regime UFM arrest regime fracture length 55

56 Issue 1: Scaling law A need for a better knowledge of geological processes m = 3 Etienne Lavoine s PhD ( ). Development of fracture network from (simplified) mechanical rules Nucleation probability ~ σ m, with m a selectivity parameter Increase of fracture correlation, decrease of fractal dimensions 56

57 DFN methodology predictions in applications 57

58 DFN predictions the construction of the and their critique Prior knowledge Data A DFN model is a conceptual framework, where model statistical properties are either bootstrapped from data (Poisson-process based ), or providing emerging properties (genetic ) Conceptual Medium model Prediction for applications A DFN model contains tuning parameters Structure (statistical distributions, spatial correlations) Heuristic laws relating fracture and geological/physical properties: Transmissivity = f(size, orientation, stress), Stiffness = f(size, stress) However, a DFN model is limited in reproducing the geological complexity How to prove that the geological system is part of the solution space. Data indicators able to discriminate between? 58

59 DFN predictions Connectivity Connectivity and percolation parameter The percolation parameter P controls statistically the DFN connectivity and the size of the largest connected cluster [Bour and Davy, 1998; Dreuzy et al., 2000]: P = π2 8 නn l l3 dl Percolation threshold p c (~2.5): percolation value at which the DFN is connected towards system boundaries by a critical cluster of fractures Model with a = 4 l min = 1 L = 20 p [1.5; 2.5; 5] p p c No flow p = p c critical flow With "red" links p p c Many flow paths, flow dominated by density effects 59

60 DFN prediction indicators which measures to calibrate The equivalent permeability K eq = Q T h A flow intensity indicator, rather than an intrinsic property of the system Vary with scale L Directly defined with permeameter conditions, indirectly from pumping tests 60

61 DFN prediction indicator which measures to calibrate The flow structure (channeling indicator) p 32 Q = 1 V (σ f S f Q f ) 2 (σ f S f Q f 2 ) Comparable with, and smaller than p 32 Inverse of the average distance between flow paths Measurable in boreholes or tunnels Vary with scale L p 32 Q is a measure of the exchange surface between flow and rock for geochemistry or geothermal applications 61

62 depth (m) DFN prediction indicator Channeling Channeling index: p 32 Q = 1 (σ f S f Q f ) 2 V (σ f S f Q 2 f ) (distance) -1 between main flow paths 0 number of fractures per meter Total sealed open Transmissivity m 2.s -1 Maillot, J., P. Davy, R. L. Goc, C. Darcel, and J. R. d. Dreuzy (2016), Connectivity, permeability, and channeling in randomly distributed and kinematically defined discrete fracture network, Water Resour. Res., 52(11), , doi: /2016WR

63 DFN prediction indicator Channeling Channeling index: p 32 Q = 1 (σ f S f Q f ) 2 V (σ f S f Q 2 f ) (distance) -1 between main flow paths Kinematic Model Poisson's Model constant T f same size and orientation distributions 0.4 [p 32 ] Q Maillot, J., P. Davy, R. L. Goc, C. Darcel, and J. R. d. Dreuzy (2016), Connectivity, permeability, and channeling in randomly distributed and kinematically defined discrete fracture network, Water Resour. Res., 52(11), , doi: /2016WR p 32 63

64 Forsmark, Sweden DFN case study 64

65 Case study (Forsmark, Sweden) GeoDFN GeoDFN UFM All fractures (open + sealed) P 32 d = 4.76 m -1 d l c =3m p 32 measured at 10 cm (borehole diameter): 4.76 m -1 Transition between power laws l c : 3 m Volume : (100 m) 3 Orientation distribution: bootstrapped from Forsmark 65

66 Case study (Forsmark, Sweden) the issue of clogging HydroDFN In the application, 75% of the total fracture surface measured at the core diameter scale is sealed 25% is open or partly open The HydroDFN is a subset of the GeoDFN Fracture sealed with hematite stained adularia (Sandström et al, 2008) 66

67 Case study (Forsmark, Sweden) scaling transmissive DFN HydroDFN l c -open UFM 25% of GeoDFN DFN backbone, fractures coloured by total flow. Fracture with flow smaller than 1% of max. flow are transparent. d l c lc,open =10m Genetic model, small fractures clogged 67

68 Case study (Forsmark, Sweden) scaling transmissive DFN HydroDFN α-open UFM 25% of GeoDFN DFN backbone, fractures coloured by total flow. Fracture with flow smaller than 1% of max. flow are transparent. d l c =3.3m Genetic model, all fractures equally clogged 68

69 Case study (Forsmark, Sweden) scaling transmissive DFN HydroDFN rmin-krmin 25% of GeoDFN DFN backbone, fractures coloured by total flow. Fracture with flow smaller than 1% of max. flow are transparent. d l c Poisson-process model, single power-law 69

70 p Case study (Forsmark, Sweden) Connectivity l c -open Percolation parameter Geo-DFN lc-open a-open r min -k rmin α-open 10 5 r min -k rmin system size (m) p c 70

71 depth (m) Case study (Forsmark, Sweden) Scaling fracture transmissivity Fracture transmissivity Varies in orders of magnitude Likely depends on fracture size Likely depends on normal stress number of fractures per meter Total sealed open Transmissivity m 2.s -1 71

72 Case study (Forsmark, Sweden) Permeability scaling Permeability geometric average data scale 72

73 Case study (Forsmark, Sweden) Permeability scaling Permeability geometric average 10 0 Structure l c -open α-open Transmissivity Constant fracture transmissivity T f T f ~l T f ~ e σ n σc T f ~l α e σ n σc data Genetic (small) Genetic (all) Poisson-process scale r min -k rmin 73

74 Theory Permeability scaling Below p c, the connected backbone is a ~plane and permeability decreases as scale 1 Above p c, the connected backbone is a complex structure with fractures in series and parallel. Above p c, the average permeability is highly dependent on the scaling of transmissivity with fracture size de Dreuzy, J.-R., P. Davy, and O. Bour (2001), Hydraulic properties of two-dimensional random fracture networks following a power law length distribution 2. Permeability of networks based on lognormal distribution of apertures, Water Resour. Res., 37(8), /2001WR900010, de Dreuzy, J.-R., P. Davy, and O. Bour (2002), Hydraulic properties of two-dimensional random fracture networks following power law distributions of length and aperture, Water Resour. Res., 38(12), /2001WR001009,

75 P10q Case study (Forsmark, Sweden) Channeling and scaling Channeling indicator m Structure l c -open α-open Transmissivity Constant fracture transmissivity T f T f ~l T f ~ e σ n σc T f ~l α e σ n σc l c -open, T=cte l c -open, T=l f l c -open, T=f() l c -open, T=f(,l f ) a-open, T=cte a-open, T=l f KFM08A m 1/L s scale r min -k rmin 75

76 DFN framework, overview Prior knowledge Data Conceptual DFN DFN is basically a combination of statistics and deterministic objects, that aims to extrapolate information with sound DFN (medium description as a population of discrete idealized fractures) allows for an easy integration of data DFN is also a tool to find the critical parameters or length scales that should be measured to improve prediction DFN can be used for flow and mechanical applications Not all DFN are equivalent ECM DFN Medium model Prediction for applications Issues Issue 1. Scaling is a critical component of the DFN framework Issue 2. Any prior knowledge, theoretical or empirical, is welcome Issue 3. A DFN is a stochastic model, which contains intrinsic variability and extrinsic controls Issue 4. Calibrating DFN model is not enough, validating is a prerequisite 76