Fracture Growth in Layered and 

Discontinuous Media

Norm Warpinski
© 2011 Halliburton. All Rights Reserved. 2

Fracture growth in complex media

 Extensive research into affects of important parameters

In situ stresses

Material properties

Interfaces

Layering

Fracture toughness

Heterogeneities

Core Photo

Projected 

Borehole FMS 

Image

F11

F10

F9

F8

F7

F6

F5

F4

F3

F2

F1

4675

4676

4677

4678

2-1/2 in.

Core dia.

DOE/GRI M-Site core through

Mounds Drill Cuttings 

Injection Experiment
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Hydraulic Fracture Growth

 In Situ Stress 

 Dominant factor in 

controlling hydraulic 

fracture growth

 Mineback tests showing 

fracture termination at high 

stress layer

DOE Mineback results showing effects of in situ stress contrasts
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Fracture Height Growth

 In situ stress

 Example equilibrium calculation

Requires:

 Stress

 Pressure

 Fracture toughness

 In general, more complex 

equations are used

Modulus

Layers

/ 2

sin 2 1

2 2 1

H

K

H

h

P

Ic

h H P

1 – stress in reservoir

2 – stress in bounding layers

P – pressure in fracture

H – fracture height

h – reservoir thickness

0

100

200

300

400

500

600

700

0 200 400 600 800 1000

Height (ft)

Pressure (psi)

Kic=1500

Kic=5000

Simonson et al., SPE, 1978
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Modeling fracture growth

 Calibrated 

models using 

diagnostics

Verify data 

and behavior

Example in the 

Bossier 

sandstone in 

East Texas

11700

11800

11900

12000

12100

12200

12300

12400

12500

12600

12700

12800

12900

13000

13100

13200

13300

-800

-700-600

-500

-400

-300-200-100

0 100 200 300 400 500 600 700 800

Distance Along Fracture (ft)

MD (ft)

9:05-10:08am

10:08-11:05am

11:05-12:13pm

perfs

Late events after 

net pressure drop

Minor fracturing in 

York; not modeled

Frac model 

geometry

11700

11800

11900

12000

12100

12200

12300

12400

12500

12600

12700

12800

12900

13000

13100

13200

13300

-800

-700-600

-500

-400

-300-200-100

0 100 200 300 400 500 600 700 800

Distance Along Fracture (ft)

MD (ft)

9:05-10:08am

10:08-11:05am

11:05-12:13pm

perfs

9:05-10:08am

10:08-11:05am

11:05-12:13pm

perfs

Late events after 

net pressure drop

Minor fracturing in 

York; not modeled

Frac model 

geometry

12100

12200

12300

12400

12500

12600

12700

0 150

Gamma R...

Logs : D-14 Gr ...

Rocktype Stress (... Modulu...

0 1

Permea...

0 200

Compo...

FracproPT Lay er Properties

Sand/Shale

Cotton Va...

Cotton Va...

Cotton Va...

Cotton Va...

Cotton Va...

Shale Lo...

Shale Lo...

Shale Lo...

100 200 300 400 500 600 700

Concentration of Proppant in Fracture (lb/f t2)

0 0.07 0.14 0.21 0.28 0.35 0.42 0.49 0.56 0.63 0.70

Proppant Concentration (lb/ft2)

Griffen et al., SPE 84489
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Fracture Height Growth

 Modulus variations

Limited effect due to 

influence on width

Van Eekelen

formulation

Interfacial effect

 Fracture toughness 

behavior at interfaces

 Not observed in field

Interface

Low-modulus 

material

High-modulus 

material

Propagation 

Direction

Fracture

Mineback example showing behavior of 

fracture at a material property interface

2

1

2

1

1

2

3 1

4

1

log

19

12 1

2 h

H

G

G

h

H

G

H G

L
© 2011 Halliburton. All Rights Reserved. 7

Fracture Height Growth

 Fracture toughness

Generally assumed to 

have a small effect

Relatively low fracture 

toughness for rocks

Potential for scale 

effects that might 

constrain growth 

(Shlyapobersky)

4000

5000

6000

7000

8000

9000

0 500 1000 1500 2000 2500

Depth (ft)

Fracture Toughness (psi- in)

Sandstones

Non-reservoir lithologies

dy

H y

H y

p y

H

K

H

H

I

/ 2

/ 2

/ 2

1 /2

/2

Equation for calculating stress intensity factor, Rice (in Fracture, Liebowitz, 1968)

Data from DOE Multiwell experiment in 

Piceance basin, Colorado
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Fracture Height Growth

 Composite layering

 Mineback photos 

suggest a wide variety 

of mechanisms are 

interplaying

 Fracture diagnostics 

have shown the same 

behavior

Microseismic

Downhole tiltmeters

~ 2 ft
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Fracture Height Growth

 Observed layering 

effects at DOE/GRI 

M-Site

Microseismic 

and downhole 

tiltmeter 

measurements of 

fracture height

In situ stress 

measurements

Treatment 

pressure

4200

4300

4400

-500 -250 0 250 500

ALONG FRACTURE LENGTH (ft)

DEPTH (ft)

MWX-2

C SAND

FRAC 5C

480 bbl

Borate

Gel

Minifrac

3500

4000

4500

0 10 20 30 40

TIME (min)

PRESSURE (psi)

Pressure Well

Above Upper

Bounding Stresses

4100

4300

4500

3000 3500 4000 4500

STRESS (psi)

DEPTH (ft)

C SAND

Small Stress

Contrast

Above
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Discontinuities

 Fracture growth across 

discontinuities in the rock 

mass has been extensively 

studied

Depends upon

 Stress

 Material properties

 Angle of approach

 Models

 Mineback

 Laborataory

Propagation

Cement 

Fracture

Jeffrey & Zhang, 

2009, SPE 119351

DOE mineback tests
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Discontinuities

 Fracture behavior as 

influenced by a wide range of 

discontinuities have been 

observed in minebacks and 

other tests

Faults

Cleats

Fracture 

Strands

Coal

DOE mineback tests

Bureau of Mines Report 9083, 

Diamond & Oyler, SPE 22395, 

Diamond CBM Symposium 11/87, 

Lambert SPE 15258
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Hydraulic Fracture Growth

 Summary

Hydraulic fractures influenced by heterogeneities 

within the reservoir

 Any change in properties/uniformity

In situ stress is the dominant influence

 Large stress contrasts contain fractures

Layering and interfaces result in inefficient growth

Models available to simulate/mimic behavior