1. INTRODUCTION

This paper summarizes a series of hydraulic fracture

tests done to observe fracture initiation and growth in a

variety of simple geometries representative of possible

field conditions. The objective of these tests is to directly

examine the initiation and growth of fractures from a

variety of perforation geometries and injection rates, and

also containment at stress or stiffness contrasts. The

work was motivated following an unpublished literature

review of available information on fracture initiation. In

particular, while there is available experimental data on

fracture initiation in a variety of materials (e.g. see [1],

[2], [3], [4]), almost none of the data are on transparent

material allowing direct detailed visualization of the

initiation and early growth (a notable exception is ref

[5]). By using a transparent brittle elastic polymer, the

tests presented here can provide such observations.

2. EXPERIMENTAL SETUP DESCRIPTION

This equipment is designed to provide true-triaxial

stress control on a sample, controlled fluid injection

rate, and continuous visual monitoring of hydraulic

fracture growth from a vertical or inclined wellbore.

Figure 1 is a labeled photograph of the entire

experimental setup. Figure 2 is a close up of the cell

showing the pressure application directions pX, pY and

pZ, and the corresponding viewing directions for the

video cameras (seen in Figure 1) used to visually

record the growth of the hydraulic fractures. Internal

dimensions of the cell are 196 mm wide (X-direction)

by 95-mm deep (Y-direction) by 190-mm tall (Z-

direction). Confining pressure is applied to the

specimen through rubber bladders inflated with

compressed air. During a test the air pressure in the

bladders is monitored with digital pressure sensors.

ARMA 08-321

Observations of Hydraulic Fracture Initiation and

Propagation in a Brittle Polymer

Wu, H., Golovin, E., Shulkin, Yu. and Chudnovsky, A.

University of Illinois at Chicago, Chicago, Illinois, USA

Dudley, J.W.

Shell International Exploration and Production B.V., Rijswijk, The Netherlands

Wong, G.K.

Shell Exploration and Production Company, Houston, Texas, USA

Copyright 2008, ARMA, American Rock Mechanics Association This paper was prepared for presentation at San Francisco 2008, the 42

nd US Rock Mechanics Symposium and 2

nd U.S.-Canada Rock Mechanics Symposium, held in San Francisco, June 29-

July 2, 2008.

This paper was selected for presentation by an ARMA Technical Program Committee following review of information contained in an abstract submitted earlier by the author(s). Contents of the paper, as presented, have not been reviewed by ARMA and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of ARMA, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of ARMA is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgement of where and by whom the paper was presented.

ABSTRACT: This paper summarizes a series of hydraulic fracture tests done to observe fracture initiation and growth in a variety

of multiple-perforation and well orientations. A transparent brittle-elastic polymeric material is used to allow visual monitoring of

the entire initiation and fracture growth process using a variety of fluids and injection rates. Several general observations from the

roughly 40 constant injection rate tests can be made: Breakdown Pressure: only weakly increases with injection rate (~doubles for

rate increase by factor 30-90); Perforation Initiation Sites: fractures tend to initiate from few perforations at low rate with water,

while fractures initiate and grow from almost all perforations at high rate and with high viscosity fluids; Initial Fracture

Orientation: far-field stresses have little influence on the of the initial fractures at the perforations; Final Fracture Orientation:

primarily determined by the far-field minimum in-situ stress; Transition to the Final Orientation: alignment to preferred final

orientation occurs quicker at high injection rate. More significantly, the general pressure behavior of these tests is different from

the breakdown and monotonic pressure decay with growth typically assumed and modeled. The generic behavior observed in these

tests shows a sharp pressure peak with rapid decay following fracture initiation and initial growth, then a roughly steady pressure

‘plateau’ with further fracture growth. Such pressure plateau behavior has also been observed in other hydraulic fracture tests on

rocks and some field data as well, and is incompatible with typical Griffith-type fracture growth assuming zero or constant fracture

toughness, but can be characterized by an increasing fracture toughness with size. Such increasing fracture toughness with fracture

size is typically observed in many engineering materials (so called “R-curve” behavior), and is associated with the growth of a

process zone (damaged or plastic deformation zone) with fracture propagation. Such increasing fracture toughness with fracture

size has also been observed by the authors in concrete.

Fig. 1. Photograph of experimental setup for the hydraulic

fracture tests.

Fig. 2. Photograph of the 3D confinement cell containing a

specimen with an imbedded vertical wellbore. Confining

pressures applied by rubber bladders in directions pX, pY and

pZ as indicated. Video camera recording directions V1, V2 and

V3 also indicated.

Normally the bladder pressure remains stable to within a

few percent during the injection cycle (up to the point

when the fracture reaches the outer boundary of the

specimen). The fracturing fluid injection is controlled

by a precision dual-syringe pump at rates from 1 to 90

cc/min. Tests reported here are done with two fracturing

fluids (water and glycerin) injected into a perforated

aluminum tubing wellbore. Further details of the

specimen preparation, wellbore geometry, fracturing

fluids and test protocol are given in the following

sections.

2.1. Specimen Preparation The material used in these tests is edible-grade gelatin,

type A. It is an elastic, impermeable, brittle, polymeric

material that can be made with a specific stiffness value

in the range ~10-100 psi. The stiffness is determined by

the gel concentration, specified as a weight percent.

Using larger amounts of gelatin creates stiffer

specimens. The homogeneous specimens are prepared in

the cell with the wellbore in place. The liquid gelatin

(8% by weight) is dissolved in 80 °C water and then

poured into the cell, with the front face down (V1 face in

Figure 2) and the back (face with pY bladder) off. The

entire cell is then placed in a refrigerator and the

specimen is cured at about 0 °C overnight, or about 16

hours. The layered specimens are prepared in a mold that

also holds the wellbore. The first layer is prepared and

cured in the refrigerator at least three hours, then the

second layer is added and cured for an additional three

hours. After the final layer is added the full specimen is

then cured overnight at 0 °C.

2.2. Wellbore Perforation Geometry and

Preparation The wellbore itself is an aluminum tube, 13 mm (0.5

inch) diameter OD, and 1.6 mm (1/16th inch) wall

thickness. The pY layered stress or vertical stiffness

layered tests use a vertical wellbore with only two

perforations, one each in the +/- X-direction at the

middle of the specimen. For the extended perforation

tests two different wellbore orientations and two

different perforation geometries are investigated. The

wellbore is either vertical (along the Z-direction) or at a

45-degree deviation (in XZ-plane). A thin layer of fabric

is glued to the outside of the tubing to provide a strong

adhesion surface for the gelatin. Perforations are made

through 1.6 mm holes drilled in the tubing. Extended

perforation geometries tested are:

Linear:

• Diameter: 1.6 mm (1/16th inch)

• Depth (length of lab-made dental-type pick tool): 3

mm (0.12 in.)

• Density: 0.34 perforations/mm (18 perforations in 50

mm segment, which is a scaled equivalent to 8

shots/foot in 6-inch diameter casing)

• Orientation: For most tests the perforations face in

the +X direction (i.e., pointing toward the V2

recording direction). A few tests were done with the

perforations at angles of 45, 90, 135 and 180 degrees

to the +X direction.

Spiral:

• Diameter, depth and density same as those for the

linear perforations.

• Phasing angle: 45 degrees

• Orientation: Bottom perforation facing in the X

direction (i.e., to the right side of test chamber).

Following the curing of the sample a dental-type pick is

used to create the perforations through the tape into the

specimen. Figure 3 shows the perforation patterns

approximately at fracture initiation for two of the tests

one with a linear perforation pattern, and one with a

spiral perforation pattern.

V1 V2

Linear

V1 V2

Spiral11150501 11290501

V1 V2

Linear

V1 V2

Spiral11150501 11290501

Fig. 3. Photograph of the perforation patterns on vertical

wellbores. V1 and V2 indicate the viewing direction, and the

number corresponds to the test ID.

2.3. Stress Conditions, Fracture Fluids and Test

Protocol An initial set of ~18 tests was done under pressure

control to verify test feasibility and optimize the

specimen preparation and test protocols. These tests are

not documented here. This paper contains the results of

the subsequent optimized tests done under constant

injection rate conditions.

The typical stress configuration is arranged so that the

preferred fracture growth plane is the X-Z plane:

Maximum principal stress: Z-direction, ~7 psi

Intermediate principal stress: X-direction, ~6 psi

Minimum principal stress: Y-direction, ~5 psi

These pressures are relatively large (>10%) compared to

the stiffness of the polymeric material, which has

Young’s modulus in the range 30-60 psi, and provide

sufficient stress contrast to provide roughly vertical

fracture growth in the X-Z plane.

Tests were done with two fracturing fluids of varying

viscosity (at 5 °C): dyed water (~1.5 cP), dyed glycerin

(~7,000 cP). Tests were done at four different injection

rates: 1, 10, ~30, and 87.5 cc/min. The high viscosity

glycerin could not be delivered any faster than ~30

cc/min due to insufficient power in the injection pump.

The typical test protocol is as follows:

1. Synchronize digital data acquisition system and video

recording equipment clocks, and begin pressure/rate data

acquisition.

2. Apply uniformly initial pressures pX, pY and pZ to the

specimen.

3. Inject the chosen fracturing fluid at very slow rate to

completely fill the wellbore through the air outlet valve

on the top of the cell.

4. Close the air outlet valve.

5. Start video recording equipment.

6. Start injection at the specified rate and continue until

fracture reaches specimen boundary.

7. Stop injection and release confining pressures.

8. Stop video and digital recording equipment.

9. Disassemble the test chamber.

10. Photograph any key fracture features of the post-test

specimen.

A summary of the reported tests and their operating

parameters is given in the following section that

discusses the test results.

3. TEST RESULTS

A summary of the tests with extended perforation

patterns is given in Table 1. This table identifies the test

ID and parameters, and also the observed stresses and

net pressure (Pnet= Pinj – Pmin) at breakdown. Some

general observations about the tests are presented first,

then the behavior with respect to rate and perforation

pattern are presented. This is followed by the

observations in stress and stiffness layered systems.

3.1. General Observations These tests show complex fracture systems growing

from the extended perforation sections, but the most

interesting observation is that the majority (>80%)

showed a generic pressure behavior illustrated in Figure

4. Pressure increases rapidly until fracture initiation

(Point A), then decreases rapidly to Point B, and then

roughly stabilizes for the remainder of the injection

cycle (Points B-C-D). This pressure ‘plateau’ is roughly

constant, but can have a slight decline (shown here),

increase, or combination thereof.

Water - 10cc/min

Inclined Spiral

Test ID: 01240601

0

1

2

3

4

5

250 300 350 400 450

Elapsed time (sec)

Net Pre

ssure

(psi)

0

2

4

6

8

10

Inj. R

ate

(cc/m

in) .

Pinj Inj.Rate

A

BDC

Fig. 4. Generic pressure behavior observed during tests. A, B,

C, D mark points discussed in text.

This pressure behavior is different from that predicted

using classical hydraulic fracture theory [6] under

constant injection rate in a zero or constant fracture

toughness material in a homogeneous medium. In that

case a monotonically decreasing pressure is expected,

with the net pressure proportional to the inverse cube

root of time (i.e., Pnet ∝ t-1/3

). To explicitly check for this

behavior, fits to the log(Pnet) versus log(tinj) between

Points A and B (example given in Figure 5) were done.

The results are given in Table 1 and illustrated in Figure

6. Although two tests (ID 11170501 and 02070601)

have the predicted inverse cube root for the initial

propagation exponent, it is clear that the propagation

exponent observed widely varies, and does not appear to

be related to the rate, fluid or perforation geometry, and

is always less than or equal to 1/3 in magnitude.

Water - 10cc/min

Inclined Spiral

Test ID: 01240601

Decline Fit: y = 3.80x-0.146

1

10

1.00 10.00 100.00

Time After Breakdown (sec)

Ne

t P

res

su

re (

ps

i)

Data

Fig. 5. Example plot illustrating the initial pressure decline

exponent determination.

Initial Post-Breakdown Pressure Decline Exponent

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

Test Sequence #

Init

ial P

res

su

re P

rop

. E

xp

on

en

t

1 cc/min

10-11 cc/min

30 cc/min

87.5 cc/min-1/3

gly.waters s s

Perf. Configuration: s = spiral; si = spiral inclined; others linear

si s s s si si

Fig. 6. Initial net pressure propagation exponents for the

extended perforation tests. No clear relationship exists

between the decline exponent and rate, fluid type or geometry.

3.2. Breakdown Net Pressure Variations Overall there is only a weak dependence of the

breakdown pressure on injection rate, with the

breakdown pressure increasing roughly a factor of 2-3

for an increase in injection rate of a factor 30-90. Figure

7 is a summary plot of the net pressure at breakdown

versus injection rate for all the tests. The spiral-glycerin

tests show a clear increasing trend (but without duplicate

tests to assess scatter). The linear perforation/water fluid

tests show there is significant scatter in these data, even

excluding tests at zero confining stresses. The scatter

may be related to non-uniform and/or repeatable stresses

near the wellbore. These may be associated with residual

stresses from the curing process, variable adhesion

properties between the wellbore fabric and polymer, or

some other cause.

Table 1. Extended perforation tests summary. Tests of similar shading have similar injection rate and well/perforation geometry.

Test IDWell

Orientation

Perf

Pattern

Lowest Perf

Orientation

Injection

Rate

(cc/min)

Fracturing Fluid

Initial

Propagation

Exponent

Pz Px Py

Stress

Contrast

X-Y

Stress

Contrast

Z-Y

Pnet

10200501 Vertical linear 0 1 Dyed water -0.241 9.0 8.0 7.0 1.0 2.0 2.7

10310501 Vertical linear 0 1 Dyed water -0.170 9.5 5.5 6.5 -1.0 3.0 4.4

11030501 Vertical linear 0 87.5 Dyed water -- 11.0 10.4 9.0 1.4 2.0 5.2

11090501 Vertical linear 0 87.5 Dyed water -0.032 7.4 6.3 5.0 1.3 2.4 4.8

11110501 Vertical linear 0 1 Dyed water -0.212 7.5 6.0 5.5 0.5 2.0 2.8

11150501 Vertical linear 0 87.5 Dyed water -0.206 7.3 6.1 5.0 1.1 2.3 5.2

11170501 Vertical linear 0 10 Dyed water -0.330 7.3 6.1 4.8 1.3 2.5 3.5

11220501 Vertical spiral 0 87.5 Dyed water -0.066 7.1 6.1 5.1 1.0 2.0 3.7

11290501 Vertical spiral 0 1 Dyed water -0.187 6.7 5.7 4.3 1.4 2.4 3.1

12010501 Vertical spiral 0 10 Dyed water -0.167 7.0 6.1 4.8 1.3 2.2 3.6

12060501 Vertical linear 180 87.5 Dyed water -0.132 0.0 0.0 0.0 0.0 0.0 3.2

01060601 Vertical linear 0 87.5 Dyed water -0.239 7.6 6.4 4.8 1.6 2.8 6.7

01100601 Vertical linear 45 87.5 Dyed water -0.265 7.5 6.5 5.3 1.2 2.2 6.9

01120601 Vertical linear 90 87.5 Dyed water -0.047 7.3 6.2 4.6 1.6 2.7 6.9

01130601 Inclined 45º spiral 0 87.5 Dyed water -0.070 7.4 6.4 4.9 1.5 2.5 6.2

01180601 Vertical linear 135 87.5 Dyed water -0.014 7.0 6.0 4.8 1.2 2.2 7.4

01190601 Inclined 45º spiral 0 1 Dyed water -0.129 6.7 5.6 4.9 0.7 1.8 3.0

01200601 Vertical linear 180 87.5 Dyed water -0.235 7.1 5.9 3.6 2.3 3.5 6.2

01240601 Inclined 45º spiral 0 10 Dyed water -0.146 7.2 6.3 4.9 1.4 2.3 4.7

02020601 Vertical spiral 0 11 Dyed glycerin -0.197 0.0 0.0 0.0 0.0 0.0 4.9

02070601 Vertical spiral 0 30 Dyed glycerin -0.332 6.8 5.9 5.0 0.9 1.8 6.9

02090601 Vertical spiral 0 1 Dyed glycerin -- 6.8 6.1 4.7 1.4 2.1 2.5

02140601 Vertical spiral 0 10 Dyed glycerin -0.161 7.1 6.2 4.6 1.6 2.5 6.1

Stresses (psi) @ Breakdown

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

0 20 40 60 80 100

Injection Rate (cc/min)

Pn

et

at

Bre

akd

ow

n (

psi)

Vert-spiral-gly. Vert.-linear-water

Vert.-spiral-water Incl.-spiral-water

Test at Zero Pxyz

Fig. 7. Summary plot of breakdown pressure versus injection

rate. Tests are grouped by wellbore inclination-perforation

geometry-fluid

Within this scatter, no further conclusions are warranted

with respect to net breakdown pressure dependence on

wellbore deviation, perforation geometry or injection

fluid.

3.3. Fracture Initiation and Growth Behavior Figure 8 is an example of bi-wing fracture growth from

two perforations. The growth rate of the equivalent area

circle fracture is plotted with the pressure and injection

rate data. This test is explicitly simulated in a companion

paper [7]. In the extended perforation tests the injection

rate does have an impact on the number of perforations

from which fractures initiate. At low water injection rate

only a few perforations tend to initiate fractures, while at

high rates virtually all the perforations initiate with a

fracture. For spiral perforation geometry extended

growth is generally limited to those initial fractures

favorably oriented relative to the minimum in-situ stress.

For the linear geometry most of the initiated fractures

continue to grow throughout the injection. Figures 9 to

11 show the fracture growth patterns for spiral

perforation geometry, dyed-water injection tests at rates

of 1, 10 and 87.5 cc/min, respectively. Figures 12 to 14

show the same but for the linear perforation geometry.

For the higher viscosity glycerin, however, most

perforations tended to grow fractures even at low rates.

The initial fracture orientations are not generally in the

preferred direction perpendicular to the far-field

minimum in-situ stress. This is evident in the above

figures, and can be seen best in the deviated wellbore

tests, such as the one shown in Figure 15. The initial

fracture orientation is probably dictated by details of the

perforation geometry, and differences between the local

near-wellbore stresses and those in the far-field.

3.4. Fracture Containment in Layered Systems Several tests were done to observe fracture growth

containment behavior at contrasts in stiffness or stress

between layers. For stiffness contrast, specimens with a

soft central layer bounded by two stiffer layers are

tested. The central layer is made from a 7% gelatin

solution, with stiffer bounding layers made from 10%,

12% or 14% gelatin solution. For stress contrast, two

spacer plates of 6 mm thick foam-core poster board are

inserted next to the top and bottom third of a

homogeneous specimen. A 1 mm thick aluminum plate

is placed between the bladder and foam boards to

confine the bladder and enable the desired stress contrast

of several psi between the center and top and bottom

zones of the specimen. This plate is also used in the

stiffness-contrast specimens for similar reasons.

3.4.1. Containment at a Stiffness Contrast The tests on stiffness-layered specimens showed full

containment for bounding layers of 14% gelatin. The

contained fracture usually halted within a millimeter or

two of the interface, but in several cases curved to

almost parallel to interface before halting. This crack

“kinking” behavior has been reported previously by the

authors [8]. For bounding layers made with less than

14% gelatin some part of the fracture propagated into

the bounding layer, either directly or with a small kink.

Figure 16 shows the progress of fracture growth in a

specimen made with top, middle, bottom gelatin

concentrations of 12%, 7%, 14%, respectively. The

fracture remains contained through most of the

propagation, only penetrating the right-hand side of the

upper 12% layer near the end of the injection.

Similar to the observations from the extended

perforation zone tests, we generally see fracture growth

from both perforations at higher water injection rates

(10 cc/min or greater), but usually only growth from one

perforation at low rates (1 cc/min).

3.4.2. Containment at a Stress Contrast The stress-layered tests (in a homogeneous medium)

showed very limited growth into the upper layer, but

more extensive into the lower layer. The stress analysis

for this situation is derived in Appendix 5. Figure 17

shows the progress of fracture growth for a

homogeneous specimen and 2 cc/min water injection

rate. The estimated 3.2 psi stress barrier effectively

prevents the fracture from extending upward, but it does

grow down partially into the bottom higher-stress zone

on the right side. This could be due to a lower stress

contrast or more gradual stress transition between the

middle and bottom stress zones than that between the

middle and upper zones. This may arise from frictional

effects since this position is furthest from the X and Z

pressure bladders located on the right and top,

respectively.

Experimental Data

Simulation, increasing toughness

Simulation, constant toughness

Experimental Data

Simulation, increasing toughness

Simulation, constant toughness

Simulation, constant toughness

Simulation, increasing toughness

Experimental Data

Simulation, constant toughness

Simulation, increasing toughness

Experimental Data

Simulation, constant toughness

Simulation, increasing toughness

Experimental Data

Fracture half

length

Equivalent area

fracture radius

HF Growth in polymeric material

Experimental Data

Simulation, increasing toughness

Simulation, constant toughness

Experimental Data

Simulation, increasing toughness

Simulation, constant toughness

Simulation, constant toughness

Simulation, increasing toughness

Experimental Data

Simulation, constant toughness

Simulation, increasing toughness

Experimental Data

Simulation, constant toughness

Simulation, increasing toughness

Experimental Data

Fracture half

length

Equivalent area

fracture radius

Fracture half

length

Fracture half

length

Equivalent area

fracture radius

HF Growth in polymeric material

Fig. 8. Bi-wing fracture growth from two perforations, test ID 06060601 (note ID not in Table 1). Injection pressure and rate

versus time shown in lower left graph, and radius of circle with equivalent area to fracture is shown in upper left graph. Simulation

curves from companion paper show consistent fit with an increasing toughness model, but not with a constant toughness model

[7].

b: v1,v2b: v1,v2

a: v1 ,v2a: v1 ,v2

c: v1,v2c: v1,v2

e: v1e: v1

d: v1,v2d: v1,v2

e: v2e: v2

112950501

0

2

4

6

13:50:53 13:58:05 14:05:17 14:12:29 14:19:41Tes t tim e (hh:m m :ss )

pnet (

psig

)

ed

cb

a

112950501

0

2

4

6

13:50:53 13:58:05 14:05:17 14:12:29 14:19:41Tes t tim e (hh:m m :ss )

pnet (

psig

)

ed

cb

a

11290501

Fig. 9. Net pressure versus time and fracture initiation and growth pattern for test ID 11290501, dyed water injection at 1 cc/min.

Views v1 and v2 are along the minimum and intermediate stress directions, respectively.

a: v1 ,v2a: v1 ,v2

c: v1 ,v2c: v1 ,v2

b: v1 ,v2b: v1 ,v2

d: v1 ,v2d: v1 ,v2

e: v2e: v2

e: v1e: v1

12010501

0

2

4

6

14:28:36 14:29:37 14:30:37 14:31:38 14:32:38 14:33:39Tes t tim e (hh:m m :ss )

pn

et (

psig

)

ed

cb

a

12010501

0

2

4

6

14:28:36 14:29:37 14:30:37 14:31:38 14:32:38 14:33:39Tes t tim e (hh:m m :ss )

pn

et (

psig

)

ed

cb

a

Fig. 10. Net pressure versus time and fracture initiation and growth pattern for test ID 12010501, dyed water injection at 10

cc/min. Views v1 and v2 are along the minimum and intermediate stress directions, respectively.

11220501

0

2

4

6

14:29:20 14:29:37 14:29:54 14:30:12 14:30:29Tes t tim e (hh:m m :s s )

pnet (

psig

)

edc

ba

11220501

0

2

4

6

14:29:20 14:29:37 14:29:54 14:30:12 14:30:29Tes t tim e (hh:m m :s s )

pnet (

psig

)

edc

ba

b: v1,v2b: v1,v2

a: v1,v2a: v1,v2

c: v1 ,v2c: v1 ,v2

e: v1e: v1

d: v1,v2d: v1,v2

e: v2e: v2

Fig. 11. Net pressure versus time and fracture initiation and growth pattern for test ID 11220501, dyed water injection at 87.5

cc/min. Views v1 and v2 are along the minimum and intermediate stress directions, respectively.

a: v1 ,v2a: v1 ,v2e: v2e: v2

d: v1 ,v2d: v1 ,v2c: v1,v2c: v1,v2

b: v1,v2b: v1,v2

11110501

0

2

4

6

13:03:22 13:10:34 13:17:46 13:24:58 13:32:10 13:39:22Tes t tim e (hh:m m :s s )

pn

et

(psig

)

ed

c

ba

11110501

0

2

4

6

13:03:22 13:10:34 13:17:46 13:24:58 13:32:10 13:39:22Tes t tim e (hh:m m :s s )

pn

et

(psig

)

ed

c

ba

e: v1e: v1

Fig. 12. Net pressure versus time and fracture initiation and growth pattern for test ID 11110501, dyed water injection at 1 cc/min.

Views v1 and v2 are along the minimum and intermediate stress directions, respectively.

a: v1 ,v2a: v1 ,v2

b: v1,v2b: v1,v2

d: v1,v2d: v1,v2

c: v1,v2c: v1,v2

11170501

0

2

4

6

13:18:29 13:20:30 13:22:31 13:24:32 13:26:33Tes t tim e (hh:m m :s s )

pn

et (

psig

)

d

c

b

a

11170501

0

2

4

6

13:18:29 13:20:30 13:22:31 13:24:32 13:26:33Tes t tim e (hh:m m :s s )

pn

et (

psig

)

d

c

b

a

Fig. 13. Net pressure versus time and fracture initiation and growth pattern for test ID 11170501, dyed water injection at 10

cc/min. Views v1 and v2 are along the minimum and intermediate stress directions, respectively.

e: v1e: v1

a: v1 ,v2a: v1 ,v2

d: v1 ,v2d: v1 ,v2c: v1 ,v2c: v1 ,v2

b: v1,v2b: v1,v2

e: v2e: v2

11150501

0

2

4

6

14:20:53 14:21:11 14:21:28 14:21:45 14:22:02 14:22:20Tes t tim e (hh:m m :s s )

pnet (

psig

)

ed

c

ba

11150501

0

2

4

6

14:20:53 14:21:11 14:21:28 14:21:45 14:22:02 14:22:20Tes t tim e (hh:m m :s s )

pnet (

psig

)

ed

c

ba

Fig. 14. Net pressure versus time and fracture initiation and growth pattern for test ID 11150501, dyed water injection at 87.5

cc/min. Views v1 and v2 are along the minimum and intermediate stress directions, respectively.

d: v1 v2

Water

87.5cc/min

Inclined

Spiral

01130601

0

2

4

6

8

0 15 30 45 60Time (s )

Net

pre

ssure

(psig

)

pnet(= pf - sc,3)

a

d

cb

Water

87.5cc/min

Inclined

Spiral

01130601

0

2

4

6

8

0 15 30 45 60Time (s )

Net

pre

ssure

(psig

)

pnet(= pf - sc,3)

a

d

cb

a: v1 v2 b: v1 v2 c: v1 v2

Fig. 15. Net pressure versus time and fracture initiation and growth pattern for test ID 01130601, dyed water injection at 87.5

cc/min. Views v1 and v2 are along the minimum and intermediate stress directions, respectively.

0

2

4

6

8

50 100 150 200 250 300

Elapsed Time (sec)

Net

Pre

ssu

re (

psi)

Water - 10cc/min

Stiffness layered:

t:m:b - 12%:7%:14%

Test ID: 021408_2

D

C

BAt

m

b

0

2

4

6

8

50 100 150 200 250 300

Elapsed Time (sec)

Net

Pre

ssu

re (

psi)

Water - 10cc/min

Stiffness layered:

t:m:b - 12%:7%:14%

Test ID: 021408_2

DD

C

BBAAt

m

b

Fig. 16. Net pressure versus time and fracture growth pattern for stiffness-layered specimen, test ID 021408_2, dyed water

injection at 10 cc/min. View is along V1 (minimum stress) direction. Note limited breakthrough (on right only) into top layer

between photos C and D. Note, test ID is not in Table 1.

0

2

4

6

8

0 100 200 300 400 500 600 700

Elapsed Time (sec)

Net

Pre

ss

ure

(p

si)

Water - 2 cc/min

Y-stress layered

Test ID: 020808

σσσσyt=5.8 psi

σσσσyb=5.8 psi

D

C

m

b

A

σσσσym=2.6 psi

B

0

2

4

6

8

0 100 200 300 400 500 600 700

Elapsed Time (sec)

Net

Pre

ss

ure

(p

si)

Water - 2 cc/min

Y-stress layered

Test ID: 020808

σσσσyt=5.8 psi

σσσσyb=5.8 psi

D

C

m

b

A

σσσσym=2.6 psi

B

Fig. 17. Estimated net pressure versus time and fracture growth pattern for Y-stress layered test (ID 020808), dyed water injection

at 2 cc/min. View is along V1 (minimum stress) direction. Note visible penetration (furthest on right side) into bottom layer in

photos C and D. Note, test ID is not in Table 1, and σy stress derivation given in appendix.

4. DISCUSSION AND CONCLUSIONS

The fractures observed in the extended perforations are

significantly more complex than would typically be

modeled. More over, these fractures and even the simple

bi-wing fractures show a general pressure behavior

different from the breakdown and monotonic pressure

decay with growth that is typically assumed and

modeled. The generic behavior observed in these tests

shows a sharp pressure peak with rapid decay following

fracture initiation and initial growth, then a roughly

steady pressure ‘plateau’ with further fracture growth.

This plateau behavior has also been observed in other

hydraulic fracture tests ([3], [4]) and field data as well

[9]. It is incompatible with typical Griffith-type fracture

growth assuming zero or constant fracture toughness, but

can be characterized by increasing fracture toughness

with size. Such increasing fracture toughness with

fracture size is typically observed in many engineering

materials (so called “R-curve” behavior), and can be

associated with the growth of a process zone (damaged

or plastic deformation zone) with fracture propagation.

Such increasing fracture toughness with fracture size has

also been observed in concrete [10].

It may well be possible to model these fractures with a

constant toughness by using different assumptions, such

as multiple propagating fractures and/or non-Poiseuille

flow conditions. The former is generally not done in

practice as we usually have no data to determine the

appropriate number and size and geometry of the

multiple fractures. The latter requires altering the basic

hydraulic fracture governing equations to account for

frictional flow, which is also a complexity with typically

unknown properties. By modeling these fractures with a

variable toughness (a physical effect well known in

many materials), we can retain the simplicity of a single

fracture and lubrication theory and successfully match

the observed pressure behavior. This theoretical model

for predicting hydraulic fracture pressure behavior such

as that observed in these tests is presented in a

companion paper [7].

Specific observations from the tests results can be

summarized as follows:

•Breakdown Pressure: only weakly increases with

injection rate (pressure ~doubles for rate increase by

factor 30-90);

•Perforation Initiation: higher injection rates and higher

fluid viscosity lead to fracture growth at almost all

perforations;

•Initial Fracture Orientation: far-field stresses have little

influence on the orientation of the initial fractures at the

perforations;

•Final Fracture Orientation: primarily determined by the

far-field minimum in-situ stress;

•Transition to the Final Orientation: alignment to

preferred final orientation occurs faster at high injection

rate.

ACKNOWLEDGEMENTS

The authors would like to thank the Shell companies for

permission to publish, and Rob Jeffrey and Alexei

Savitski for constructive review of the paper.

REFERENCES

[1] Hubbert, M.K., and D.G. Willis (1957) Mechanics of

hydraulic fracturing, Transactions of AIME, 210, 153-

166.

[2] Haimson, B., and C. Fairhurst, (1969) Hydraulic

fracturing in porous-permeable materials, Journal of

Petroleum Technology, 811-817.

[3] Dudley, J.W., J. Shlyapobersky, A. Chudnovsky and S.

Glaser (1997) Laboratory Investigation of Fracture

Processes in Hydraulic Fracturing, Annual Report, Gas

Research Institute Report GRI-97/0300, Shell E&P

Technology Co., Houston, November.

[4] C.J. de Pater, B. Bohloli, J. Pruiksma and A. Bezuijen

(2003) Experimental study of hydraulic fracturing in

sand, In Proceedings of 39th US Rock Mechanics

Symposium, Cambridge, MA, 22-26 June.

[5] Bunger, A.P., E. Detournay and R.G. Jeffrey (2005)

Crack tip behavior in near-surface fluid-driven fracture,

C.R. Mecanique, 333, pp.299-301.

[6] See, for example, M. Economides, "Unified Fracture

Design," 2002 ORSA Press, page 55, Table 4-4, which

shows the well bore pressure for a radial fracture is

proportional to the pump time raised to a power of

minus one-third.

[7] Chudnovsky, A., F. Fan, Yu. Shulkin, H. Zhang, J.W.

Dudley and G.K. Wong (2008), Hydraulic Fracturing

Revisited, In Proceedings of the 42nd US Rock

Mechanics Symposium, San Francisco, CA, 29 June –

2 July.

[8] Wu, H., A. Chudnovsky, J.W. Dudley and G.K. Wong

(2004), A Map of Fracture Behavior in the Vicinity of

an Interface, In Proceedings of the 6th North American

Rock Mechanics Symposium, Houston, TX, 5-9 June.

[9] Shlyapobersky, J., W.W. Walhaug,, R.E. Sheffield and

P.T. Huckabee (1988) Field Determination of

Fracturing Parameters for Overpressure Calibrated

Design of Hydraulic Fracturing, SPE 18195, 63rd SPE

Annual Technical Conference, Houston, 2-5 October.

[10] Shlyapobersky, J., M.A. Issa, M.A. Issa, M.S. Islam,

J.W. Dudley, Y. Shulkin and A. Chudnovsky (1998),

Scale Effects on Fracture Growth Resistance in

Poroelastic Materials, SPE 48929, Proceedings of the

Society of Petroleum Engineers Annual Technical

Conference, New Orleans, LA, 27-30 September.

APPENDIX - STRESS ANALYSIS FOR STRESS-

LAYERED LOADING

This appendix provides an analysis of the stress in a

uniform sample that is loaded non-uniformly by

inserting relatively thin spacers between the specimen

and the loading plate, behind which is the pressurized

bladder. Fig. A.1 shows the loading arrangement. Note

that for the analysis below ‘x’ is the non-uniform

loading direction, y is the direction perpendicular to this

and parallel to the layering, and z is the direction

perpendicular to the layering (thus the x and y directions

are swapped relative to the definitions in the test

described in section 2).

For the displacements conditions where there is

sufficient pressure p to fully contact the central specimen

layer with the loading plate we have the compatibility

equations:

h2

h2

h1

l d

pE

h2

h2

h1

l d

pE

·x

z

y·x

z

y

Fig. A1. Schematic geometry in the non-uniform loading

direction. For this analysis ‘x’ is the horizontal direction, y is

out of the page and z is the vertical direction.

yyyxxx εεεεεεε ===∆−=)2()1()2()1( , (A.1)

where ld /=ε∆ is given.

For this homogeneous material Hook’s law is written as:

)(1

),(1 )1()1()1()1(

xyyyxxEE

νσσενσσε −=−= (A.2)

)(1 )2()2(

yxxE

νσσεε −=∆+ , (A.3a)

)(1 )2()2(

xyyE

νσσε −= (A.3b)

From (A.2) and (A.3) it follows

)(1 2

)1(

yxx

Eνεε

νσ +

−= , (A.4a)

)(1 2

)1(

xyy

Eνεε

νσ +

−= (A.4b)

)(1 2

)2(ενεε

νσ ∆++

−= yxx

E, (A.5a)

)(1 2

)2(εννεε

νσ ∆++

−= xyy

E (A.5b)

According to (A.4) and (A.5),

εν

σσ ∆−

+=2

)1()2(

1

Exx (A.6a)

εν

νσσ ∆

−+=

2

)1()2(

1

Eyy (A.6b)

The force equilibrium condition requires

xxx phhhh )2(2 21

)2(

2

)1(

1 +=+ σσ (A.7)

yyy phhhh )2(2 21

)2(

2

)1(

1 +=+ σσ (A.8)

Combining (A.6a) and (A.7) yields

εσ

εσ

∆⋅+

⋅−

+=

∆⋅+

⋅−

−=

21

1

2

)2(

21

2

2

)1(

21

,2

2

1

hh

h

v

Ep

hh

h

v

Ep

xx

xx

(A.9)

From (A.9) we can determine the condition on px to

insure contact and a positive compressive stress in the

loading direction in the central layer (i.e., 0)1(>xσ ):

ε∆⋅+

⋅−

>

21

2

2 2

2

1 hh

h

v

Epx (A.10)

With (A.6.2) equation (A.8) yields

εν

σ

εν

σ

∆⋅+

⋅−

+=

∆⋅+

⋅−

−=

21

1

2

)2(

21

2

2

)1(

21

2

2

1

hh

h

v

Ep

hh

h

v

Ep

yy

yy

(A.11)

From (A.11) we can determine the condition on py to

insure positive compression in the y direction, 0)1(>yσ :

εν

∆⋅+

⋅−

>

21

2

2 2

2

1 hh

h

v

Epy (A.12)

Finally, since this is a homogeneous material:

zzz p==)2()1(

σσ (A.13)

In the stress contrast experiment described in section

3.4.2 we have the following parameters (in the

coordinate system used in this appendix):

psippsippsip

psiEld

mmhmmh

zyx 7,6,5

,45)1/(,071.0/

,65,40

2

21

===

=−==∆

==

νε

where the plane-strain modulus of 45 psi is the value

required to simulate the fracture growth shown in Figure

8. Substituting these data into (A.9) and (A.11), we

obtain

psix 56.244.256524

071.0652455)1(

=−=⋅+

⋅⋅⋅−=σ

psix 75.575.056524

071.040455)2(

=+=⋅+

⋅⋅+=σ

psi

psi

y

y

38.675.05.06

78.444.25.06

)2(

)1(

=⋅+=

=⋅−=

σ

σ

We also verify the px and py values of 5 and 6 psi,

respectively, satisfy the compression condition equations

A.10 and A.12:

psipx 44.2071.06524

65245 =⋅

⋅+

⋅⋅>

psip y 22.1071.06524

6525.045 =⋅

⋅+

⋅⋅⋅>