permeabilityscalingandflowstructuresin …massonr/momasmultiphasique2015/... · 2015. 10. 14. ·...

$: PERMEABILITYSCALINGANDFLOWSTRUCTURESIN …massonr/MOMASMultiphasique2015/... · 2015. 10. 14. · What is a fracture? Geology Ubiquitous: Fault, Fracture, Joint, Diaclase Plate tectonics,$
Jean-Raynald de Dreuzy1, Olivier Bour1, Caroline Darcel2, PhilippeDavy1, Jocelyne Erhel3, Romain Le Goc2, Julien Maillot1,2, Yves Méheust1,

Géraldine Pichot2

1 Géosciences Rennes, UMR CNRS 6118, University of Rennes 1, France2 Itasca Consultants S. A., Group HCItasca, Ecully, France

3 IRISA/INRIA, University of Rennes 1, France

PERMEABILITY SCALING AND FLOW STRUCTURES INFRACTURE NETWORKS

What is a fracture?Why fractures matter?

2

What is a fracture? Geology Ubiquitous: Fault, Fracture, Joint, Diaclase Plate tectonics, sismology

3

San Francisco (1906)Magnitude 8,2San Andreas

(Californie, USA)

Simpevarp (Suède)100 m

Simpevarp (Suède)1 m

Energy Minerals Division; Gas shale tricky to understandBrian Cardott (EMD Gas Shale Committee member).http://www.aapg.org/explorer/divisions/2006emd.cfm/

Ivory Coast

core Lineament mapsoutcrop

10-3 10-2 10-1 100 101 102 103 104 105

scale (m)

What is a fracture? Geology Ubiquitous: Fault, Fracture, Joint, Diaclase Plate tectonics, sismology

Mathematical modeling 2D features in 3D space (lower dimensionality)

Hydraulics Flow barriers, flow highways High permeablity, low storativity Low surface/volume features

Long, J. C. S., et al. (1985), A Model for Steady Fluid Flow inRandom Three-Dimensional Networks of Disc-Shaped

Fractures, Water Resources Research, 21(8), 1105-1115.

Maryka, J., et al. (2004), Numerical simulation of fracture flowwith a mixed-hybrid FEM stochastic discrete fracture network

model, Computational Geosciences, 8(3).

Martin, V., et al. (2005), Modeling fractures and barriers asinterfaces for flow in porous media, SIAM Journal in

Scientific Computing, 26, 1667-1691.

Tsang, C. F., et al. (2008),Simple model representations oftransport in a complex fractureand their effects on long-termpredictions, Water Resources

Research, 44(8), 13.

Geology Ubiquitous: Fault, Fracture, Joint, Diaclase Plate tectonics, sismology

Mathematical modeling 2D features in 3D space (lower dimensionality)

Hydraulics Flow barriers, flow highways High permeablity, low storativity Low surface/volume features

Mechanics Dynamic, Chaotic Energy dissipation

Physics Statistics, emergence

What is a fracture?

Stauffer, D., and A. Aharony (1992),Introduction to percolation theory, second

edition, Taylor and Francis, Bristol.

Why fractures matter? Negative fracture perception Waste storage, connectivity issues Interacting energetic and environmental applications

Positive impact of fractures on resources oil and gas recovery 3D volume (geothermal energy STES) Groundwater (India, Africa) , Aquifer (connectivity)

Fractures (more generally geological complexity) Source of uncertainty Coexistence of services (storage, resources, environment)

Requires CONTROL Observations, Monitoring Modeling Data processing, calibration, assimilation

6

7

Fracture versus rock permeability

10-5 10-4 10-3

10-11

10-10

10-9

10-8

10-7

10-6

10-5

Equivalent fr

acture perm

eability

n=0.01m-1

n=0.1m-1

Keq

(m/s

)

a (m)

mm100 m Matrix permeability

n=0.001m-1

L/n

L

Km

W

a: hydraulic aperture

High Fracture DensitiesExtreme flow channeling

Small Permeability

8

Flow structures in natural fractured mediaMultiple-scale Channeling and limited permeability

9

Fracture scale

Network scaleStripa

http://www.imstunnel.com/page_03.htmBolmen channels 2

Quality of Water from CrystallineRock Aquifers in New England, NewJersey, and New York, 1995–2007http://pubs.usgs.gov/sir/2011/5220/

80 % of flow100 % of flow

Stripa, Olsson [1992]

Why are flows so channelled andpermeability so limited?

FRACTURE SCALE Fracture roughness Fracture sealing/dissolution (chemistry) Fracture closing/opening (mechanical)NETWORK SCALE Fracture length distribution Global connectivity (network effects) Effective transmissivity variability (orientations, depth) Local connectivity (intersections) Mechanical-issued correlation patterns (fracture

organization)10


FRACTURE SCALE Fracture roughness Fracture sealing/dissolution (chemistry) Fracture closing/opening (mechanical)NETWORK SCALE Fracture length distribution Global connectivity (network effects) Effective transmissivity variability (orientations, depth) Local connectivity (intersections) Mechanical-issued correlation patterns (fracture

organization)11

=1arithmetic meanparallel model

KN=K(d,L) exp[w(d,a).s2(log K1)/2]

=-1harmonic meanin series model

=0geometric mean

2D Poissonian fracture networksa: length distribution parameterd: density parameters2(log K1): fracture log-permeability variance

de Dreuzy, J. R., et al. (2001a), Hydraulic properties of two-dimensional random fracture networks following a power law length distribution: 2-Permeability of networks based on log-normal distribution of apertures, Water Resources Research, 37(8), 2079-2095.de Dreuzy, J. R., et al. (2001b), Hydraulic properties of two-dimensional random fracture networks following a power law length distribution: 1-Effective connectivity, Water Resources Research, 37(8).de Dreuzy, J. R., et al. (2002), Permeability of 2D fracture networks with power-law distributions of length and aperture, Water Resources Research, 38(12).

K(d=dc)~L-1

K(d>dc)~d

MODELS ARE MUCH TOO PERVIOUSReduction for sparse networks by

tortuosity and BOTTLE NECKSBUT

Large fractures prevent sparsityand enhance permeability


FRACTURE SCALE Fracture roughness Fracture sealing/dissolution (chemistry) Fracture closing/opening (mechanical)NETWORK SCALE: bottle necks versus large fractures Fracture length distribution Global connectivity (network effects) Effective transmissivity variability (orientations, depth) Local connectivity (intersections) Mechanical-issued correlation patterns (fracture

organization)13

Permeability of rough fractures

Méheust, Y., and J. Schmittbuhl (2000), Flow enhancement of a rough fracture, Geophysical Research Letters, 27(18).Méheust, Y., and J. Schmittbuhl (2001), Geometrical heterogeneities and permeability anisotropy of rough fractures, Journal of Geophysical Research-Solid Earth, 106(B2),2089-2102.14

http://www.comsol.com/products/4.2/

15

Local aperture distributionTruncated Gaussian with abounded self-affine correlation pattern http://www.comsol.com/products/4.2/

00

02

1/

2

2

2

1/

ifa

ifaec=aap

frac

m

c

aa

fracm

a/am

16

Frac

ture

aper

ture

and t

rans

missi

vity d

istrib

ution

show

nby

dash

ed an

d soli

d lin

es re

spec

tively

.

10-2 10-1 100 101 102

10-4

10-3

10-2

10-1

100

101 Aperturec=1.5

Transmissivityc=1.5

p(T l/T

lm)

Tl/Tlm

10-2 10-1 100 101 102

10-4

10-3

10-2

10-1

100

101Aperture

c=1.5p(

a /a

m)

a/am

00

02

1/

2

2

2

1/

ifa

ifaec=aap

frac

m

c

aa

fracm

2

23/1

3/23/12 2

/exp

3β1

2π1 cβT

T=TpT

From local apertureto local transmissivity


T~a3

Effective permeability KAnormalized by the equivalent parallel platepermeability K1

17


0 1 20,0

0,5

1,0

Reduction by a factor of 4

cfrac

Single Fracture


1K

K A

Roughness:Reduction factor of K :2 to 4 at most


FRACTURE SCALE: reduction factor of 2 to 4 at most Fracture roughness Fracture sealing/dissolution (chemistry) Fracture closing/opening (mechanical)NETWORK SCALE: bottle necks versus large fractures Fracture length distribution Global connectivity (network effects) Effective transmissivity variability (orientations, depth) Local connectivity (intersections) Mechanical-issued correlation patterns (fracture organization)COMBINATION FRACTURE/NETWORK

18

10-1 100 101 10210-710-610-510-410-310-210-1100101102

n(l)~ LD2d=1.75 l-a2d=2.75

n(l)/

LD

fracture length, l

Multi-Scale Discrete Fracture Network models (DFNs)

19

Field-based DFNs Power-law length distribution Orientation distribution Correlation patterns (mechanics) Fracture density Fracture roughness Fracture aperture Intersection structure Matrix permeability

Simplifications Keep connected clusters Keep large fractures

Hydraulic simulations Large scale, highly resolved 3D

Odling, N. E. (1997), Scaling and connectivity of joint systems insandstones from western Norway, Journal of Structural Geology,

19(10), 1257-1271.Bour, O., et al. (2002), A statistical scaling model for fracture

network geometry, with validation on a multiscale mapping of ajoint network (Hornelen Basin, Norway), Journal of Geophysical

Research, 107(B6).

Hornelen, Norway

Broad power-law length distribution n(l)~l-a withlmin<l<L

Large number of fractures: ~15 103

L=50

l min

MP_FRAC

Multi-scale DFN hydraulic simulations

20




MP_FRAC

Network Fracture

Network+

Fracture

.a3h=0

Log a3

Flow equation PermeameterBoundary conditions

KN KF

KN+F

K=QL/(DhS)

Combined fracture- andnetwork-scale effects

21

Fracture Network Flows withuniform apertures

KN

Flows withdistributed apertures

KN+Fde Dreuzy, J.-R., Y. Méheust, and G. Pichot (2012), Influence of fracture scale heterogeneity onthe flow properties of three-dimensional Discrete Fracture Networks (DFN), J. Geophys. Res.-Earth Surf., 117(B11207), 21 PP.

Effective permeability KN+ADense Networks

22

0 1 20,0

0,5

1,0


cfrac

Single Fracture


1K

K FN

Hihgly limited effects

Effective permeability KN+ASparse Networks

23

0 1 20,0

0,5

1,0


cfrac

Single Fracture


1K

K FN

Additional reduction by a factor of 2 to 3

Effective permeability KN+FPercolation Networks

24

0 1 20,0

0,5

1,0


cfrac

Single Fracture


1K

K FN

Additional reduction by a factor of 5 to 10


FRACTURE SCALE: reduction factor of 2 to 4 at most Fracture roughness Fracture sealing/dissolution (chemistry) Fracture closing/opening (mechanical)NETWORK SCALE: bottle necks versus large fractures Fracture length distribution Global connectivity (network effects) Effective transmissivity variability (orientations, depth) Local connectivity (intersections) Mechanical-issued correlation patterns (fracture organization)COMBINATION FRACTURE/NETWORK: reduction factor of 2 to 10

25


FRACTURE SCALE: reduction factor of 2 to 4 at most Fracture roughness Fracture sealing/dissolution (chemistry) Fracture closing/opening (mechanical)NETWORK SCALE: bottle necks versus large fractures Fracture length distribution Global connectivity (network effects) Effective transmissivity variability (orientations, depth) Local connectivity (intersections) Mechanical-issued correlation patterns (fracture organization)COMBINATION FRACTURE/NETWORK: reduction factor of 2 to 10

26

Mechanical induced organization of thefracture network (preliminary results)

27

High connectivity

Low connectivityTypical trace

map view1.0 1.5 2.0

0.01

0.1

1 BCBSAC

K

P32

AS

UFM

Poisson

Reduction factor of K :3 to 10


FRACTURE SCALE: reduction factor of 2 to 4 at most Fracture roughness Fracture sealing/dissolution (chemistry) Fracture closing/opening (mechanical)NETWORK SCALE: bottle necks versus large fractures Fracture length distribution Global connectivity (network effects) Effective transmissivity variability (orientations, depth) Local connectivity (intersections) Mechanical correlation patterns: reduction factor of 3 to 10COMBINATION FRACTURE/NETWORK: reduction factor of 2 to 10

28

Impact of Intersection length (l2)

29 With an analytical image method adapted from Long [1985]

10-6 10-4 10-2 1000,00

0,25

0,50

0,75

1,00

l1

Teq

(l2)/

T1

l2

IntersectionLimiting

l 2

0

l 1

1

2ln

1~

l

l

Reduction factor of K :2 to 4


FRACTURE SCALE: reduction factor of 2 to 4 at most Fracture roughness Fracture sealing/dissolution (chemistry) Fracture closing/opening (mechanical)NETWORK SCALE: bottle necks versus large fractures Fracture length distribution Global connectivity (network effects) Effective transmissivity variability (orientations, depth) Local connectivity (intersections): reduction factor of 2 to 3 Mechanical correlation patterns: reduction factor of 3 to 10COMBINATION FRACTURE/NETWORK: reduction factor of 2 to 10

30

Modeling frameworksRelevant-RealisticSimple-Tractable

31

« Historical » modelling frameworks

32

Warren and Root (1963), The Behavior ofNaturally Fractured Reservoirs, Society ofPetroleum Engineers Journal, September,

245-255.

Double Porosity

Neretnieks, I. (1980), Diffusion in the RockMatrix: An Important Factor in

Radionucleside Retardation?, Journal ofGeophysical Research, 85(B8), 4379-4397.

Neuman SP (1987) Stochastic continuumrepresentation of fractured rock permeability as

an alternative to the REV andfracture network concepts. Proceedings of the

28th US Symposium, Tucson, Arizona

Stochastic Continuum

Snow, D. T. (1969), Anisotropic permeabilityof fractured media, Water Resources

Research(5), 1273-1289.

Discrete FractureNetwork

Long, J. C. S., et al. (1982), Porous MediaEquivalents for Networks of Discontinuous

Fractures, Water Resources Research, 18(3), 645-658.

Simpevarp (Sweden) 1 m

Stripa, 1980s

L

LO

G10

()

K

-9

-12

-15

-18

-21

-24 cm m km 100 km

Clauser, C. (1992), Permeability of crystalline rock, EosTrans. AGU, 73(21), 237-238.

10-1 100 101 10210-710-610-510-410-310-210-1100101102

n(l)~ LD2d=1.75 l-a2d=2.75

n(l)/

LD

fracture length, l

Multi-Scale DFN models: building simplifications

33




Hornelen, Norway

Broad power-law length distribution n(l)~l-a withlmin<l<L

Large number of fractures: ~15 103

L=50

l min

MP_FRAC

Equivalent Permeability,controls on the flow structure

34 de Dreuzy, J. R., Y. Méheust, G. Pichot (2012), Influence of fracture scale heterogeneity on the flow properties of three-dimensional discrete fracturenetworks (DFN), Journal of Geophysical Research-Solid Earth, 117.

< 1 > 1= 1

Bottlenecks Parallel paths

KN

KN+F K0

KF KN

KN+F K0

KF KN

KN+F K0

KF

Reference Multi-Scale DFN modelsAlternative modeling concepts

35




Elementary cellStructured Interacting Continua

Multiple-scaleRenormalizationGroup Method

Gavrilenko, P., and Y. Guéguen (1998), Flow in fractured media: A modifiedrenormalization method, Water Resources Research, 34(2), 177-191.

Discrete Double-PorosityD. Roubinet

Elementary cellSingle Rate Mass Transfer

Comparisonto double porosityComparison

to Multiple Interacting Continua

Pruess, K., and T. N. Narasimhan (1985), A practical method for modeling fluid and heat-flowin fractured porous-media, Society of Petroleum Engineers Journal, 25(1), 14-26.

Discrete multiple-porosity media

36

Multi-scale Fractured Media Fracture structures Network complexity Fracture/Matrix interactions

Hydraulic DFN MP_FRAC High-resolution 3D flow simulations Training basic

Alternative modeling concepts Structured Interacting Continua Multiple-scale permeability Discrete Double porosity

Calibration and Testing Synthetic training Field testing




Conclusions

Hydraulics in fractured media Large structures are essential Details matter!

Permeability Scaling and sampling Variable, High channeling

Modeling Main discrete structrues Multi-porosity

37




permeabilityscalingandflowstructuresin …massonr/momasmultiphasique2015/... · 2015. 10. 14. ·...

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