PB91-181818
EPA/600/2-91/012
April 1991
FEASIBILITY OF HYDRAULIC FRACTURING OF SOIL
TO IMPROVE REMEDIAL ACTIONS
by
L C. Murdoch, G. Losonsky, P. Quxton,
B. Patterson, I. JOich, B. BrasweU
Center Hill Research Facility
University of Cincinnati
Cincinnati, Ohio 45224
Contract 68-03-3379
Work Assignment No. 8
Project Officer
Michael H. Roulier
. Laboratory
CintinnatCOhio 45268
RISK REDUCTION ENGINNERING LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
CINCINNATI, OHIO 45268
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TECHNICAL REPORT DATA . .
(Please read Instructions on the reverse before complttr
1. REPORT NO.
EPA/600/2-91/012
2.
4. TITLE AND SUBTITLE
Feasibility of Hydraulic Fracturing of Soil . to
Improve Remedial Actions
3.
PB91-181818
5. REPORT DATE
April 1991
6. PERFORMING ORGANIZATION CODE
7. AUTHOH(S)
L.C. Murdoch, G. Losohsky, P. Cluxton, B. Patterson,.
T nirh anH R RracwolT
8. PERFORMING ORG/
ION REPOI
10. PROGRAM ELEMENT NO.
.1Y1J
I. PERFORMING ORGANIZATION NAME AND ADDRESS
University of Cincinnati
Center Hill Research Facility
5995 Center Hill Road
rinrinnati- OH
TF.IYIfl
.CONTRAC
11. CONTRACT/GRANT NO.
68-03-3379 •
12. SPONSORING AGENCY NAME AND ADDRESS
Risk Reduction Engineering Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
P-inrinnati. OH—4S?fiR
13. TYPE OF REPORT AND PERIOD COVERED
fnmnl Pt.P
14. SPONSORING AGENCY CODE
5. SUPPLEMENTARY NOTES
Project Officer:
FPA/finn/11
Michael H. Roulier (513) 569-7796 or FTS 684-7796
6. ABSTRACT
Hydraulic fracturing, a method of increasing fluid flow within the subsurface,
should improve the effectiveness of several remedial techniques, including pump
and treat, vapor extraction, bio-remediation, and soil-flushing. The technique is
widely used to increase the yields of oil wells, but is untested under conditions
typical of contaminated sites.
The project consisted of laboratory experiments, where hydraulic fractures
were created in a triaxial pressure cell, and two field tests, where fractures were
created at shallow depths in soil. The lab tests showed that hydraulic fractures
are readily created in clayey silt, even when it is saturated and loosely-consolidated
Many of the lab observations can be explained using parameters and analyses based
on linear elastic fracture mechanics.
Following the field tests, the vicinity of the boreholes was excavated to reveal
details of the hydraulic fractures. Maximum lengths of the fractures, as measured
from the borehold to the leading edge, averaged 4.0 m, and the average area was 19 m?.
Maximum thickness of sand ranged from 2 to 20 mm, averaging 11 mm. As many as four
fractures were created from a single borehold, stacked one over the other at vertical
spacing of 15 to 30 cm.
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RELEASE TO PUBLIC
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UNCLASSIFIED
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307
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EPA Form 2220-1 (R«v. 4-77) PREVIOUS EDITION is OBSOLETE
1
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NOTICE
The information in this document has been funded by the United States
Environmental Protection Agency under Contract 68-03-3379 to the University of
Cincinnati. It has been subjected to the Agency's peer and administrative review,
and it has been approved for publication as an EPA document. Mention of trade
names or commercial products does not constitute endorsement or recommendation
for use.
11
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FOREWORD
Today's rapidly developing and changing technologies and industrial
products and practices frequently cany with them the increased generation of
materials that, if improperly dealt with, can threaten both public health and the
environment. The U.S. Environmental Protection Agency is charged by Congress
with protecting the Nation's land, air and water resources. Under a mandate of
national environmental laws, the Agency strives to formulate and implement actions
leading to a compatible balance between human activities and the ability of natural
systems to support and nurture life. These laws direct the EPA to perform research
to define our environmental problems, measure the impacts, and search for
solutions.
The Risk Reduction Engineering Laboratory is responsible for planning,
implementing, and managing of research, development, and demonstration
programs to provide an authoritative, defensible engineering basis in support of the
policies, programs, and regulations of the EPA with respect to drinking water,
wastewater, pesticides, toxic substances, solid and hazardous wastes, and Superfund-
related activities. This publication is one of the products of that research and
provides a vital communication link between the researcher and the user
community.
This study was undertaken to determine if hydraulic fracturing, a method of
increasing fluid flow in subsurface soils, could improve the effectiveness of several
remedial action techniques at sites contaminated by hazardous wastes.
E. Timothy Oppelt, Director
Risk Reduction Engineering Laboratory
in
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ABSTRACT
Hydraulic fracturing, a method of increasing fluid flow within the subsurface,
should improve the effectiveness of several remedial techniques, including pump
and treat, vapor extraction, bio-remediation, and soil-flushing. The technique is
widely used to increase the yields of oil wells, but it is untested under conditions
typical of contaminated sites.
The project consisted of laboratory experiments, where hydraulic fractures
were created in a triaxial pressure cell, and two field tests, where fractures were
created at shallow depths in soil. The laboratory tests showed that hydraulic
fractures are readily created in clayey silt, even when it was saturated and loosely-
consolidated. Many of the laboratory observations can be explained using
parameters and analyses based on linear elastic fracture mechanics.
Field tests were conducted during the summers of 1988 and 1989 at sites
underlain by Pleistocene glacial till. During the 1988 test, hydraulic fractures were
successfully created from cemented casing at depths of 2 to 4 m using equipment
designed for fracturing oil wells. The tests were limited to creating one fracture per
well, and they were hindered by the large oil-field equipment, which was difficult to
control because it was designed to operate under flow rates and pressures much
greater than those-used during the test. Many .of the fractures created in 1988
closed completely because they were barren of proppant, a condition that
apparently resulted from insufficient control.
For the 1989 test, a new method of setting casing was designed, and pumps
and blenders designed for injection grouting were used. Casing was set by inserting
a drill rod tipped with a conical point and driving the assembly into the ground. The
rod and point were retracted and a water jet was inserted to cut a disk-shaped notch
beneath the casing. A hydraulic fracture was nucleated at the notch by injecting gel
and sand into the casing. Following fracturing, the rod and point were inserted and
the assembly was driven to a greater depth, where the process was repeated.
Following the tests, the vicinity of the boreholes was excavated to reveal
details of the hydraulic fractures. In general, they were slightly elongate (aspect of
2:3) in plan view, and they were highly asymmetric with respect to their parent
borehole; in each case there was a preferred direction of propagation. The fractures
created in 1988 climbed gently and vented to the ground surface, whereas the ones
created in 1989 were nearly flat-lying, and few of them vented. Maximum lengths of
the fractures in 1989, as measured from the borehole to the leading edge, averaged
4.0 m, and the average area was 19 m2. Maximum thickness of sand in individual
fractures ranged from 2 to 20 mm, averaging 11 mm. As many as four fractures
were created from a single borehole, stacked one over the other at vertical spacings
of 15 to 30 cm.
Four monitoring methods were evaluated: injection pressure, surface uplift,
surface tilt, and electrical resistivity. Results indicate that it should be feasible to
monitor the growth of hydraulic fractures at shallow depths.
It is feasible to create hydraulic fractures at shallow depths in unlithified
sediment, and we recommend that this technology be tested during the remediation
of contaminated sites.
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CONTENTS
Foreword
Abstract
Figures
Tables
Acknowledgment
Introduction 1
Statement of the problem 2
Approach 3
Major Conclusions 4
Laboratory Studies: Summary of Results 4
Field Studies: Summary of Results 6
Recommendations 8
1: Potential Remedial Applications and Previous Investigations of
Hydraulic Fracturing 6
Assessment of Potential Applications 6
Previous Studies of Hydraulic Fracturing 18
2: Observations During Laboratory Experiments 33
Experimental Design 33
Appearance of a Hydraulic Fracture in Center Hill Clay 43
Records of Driving Pressure 54
Summary and Discussion 63
3: Analysis of Hydraulic Fracturing of Soil 67
Predicting the Onset of Hydraulic Fracturing 68
Propagation of a Hydraulic Fracture in Soil 75
Data Quality 116
Discussion 120
4: Setting and Design of the Field Test -1988 122
Site Characteristics 122
Boreholes 132
Method of Fracturing 137
5: Hydraulic Fractures Created During the Field Test 141
Forms of the Hydraulic Fractures 142
Dimensions of Hydraulic Fractures 160
Direction of Propagation 161
Summary: An Idealized Hydraulic Fracture 163
Discussion: Development of the Idealized Fracture 165
6: Setting and Design of the Field Test - 1989 170
Quality Assurance and Control 170
Site Characteristics 170
Method of Fracturing 172
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7: Hydraulic Fractures Created During the Field Test - 1989 181
Quality Assurance and Control 181
Forms of the Hydraulic Fractures 181
Dimensions of the Hydraulic Fractures 204
Thickness Profiles of the Hydraulic Fractures 205
Direction of Propagation 205
Discussion 205
8: Monitoring Hydraulic Fractures 214
Injection Pressure 214
Surface Tilt 229
Surface Uplift 239
Electrical Resistivity .243
Discussion 257
9: Summary and Conclusions 258
Potential Applications 258
Laboratory Studies: Summary of Results 259
Field Studies: Summary of Results 261
References 265
Appendix: Records of Pressure, Volume, Surface Displacement, and
Surface Tilt From 1988 Field Tests 282
VI
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FIGURES
Number Page
1.1. Production rate of an oil well in North Texas as a function of time 9
1.2. Rates of inflow into boreholes in till 11
1.3. Recovery capacity of a flat-lying, circular fracture in a confined
aquifer 17
2.1. Apparatus used for hydraulic fracturing experiments 35
2.2. Cut-away sketch of hydraulic fracturing cell 36
2.3. Grain-size distribution of soils used in the laboratory experiments 39
2.4. Bulk density as a function of moisture content from Proctor tests and
fracture tests 40
2.5. Photograph and sketch of the surface of a hydraulic fracture 44
2.6. Sketches of surfaces of three hydraulic fractures of various lengths 46
2.7. Idealized diagram of the leading edge and propagation paths 47
2.8. Idealized configurations of commonly-occurring fracture lobes 49
2.9. Leading edge of a hydraulic fracture 52
2.10. Length of undyed zone as functions of dyed length and moisture
content 53
2.11. Records of driving pressure as a function of time 55
2.12. Idealized record of driving pressure as a function of time 58
2.13. Records of injection pressure as a function of time for samples of
various moisture contents 60
2.14. Records of injection pressure as a function of time using various
lengths of starter slots 66
2.15. Idealized cross-section of a hydraulic fracture in a laboratory
sample 70
3.1. Critical stress intensity as a function of half-length of starter slot 73
3.2. Critical stress intensity as functions of moisture content and duration
of consolidation .'. 77
3.3. Conceptual model of growth of an idealized hydraulic fracture in
laboratory samples 80
3.4. Geometry used in analyses 84
3.5. Velocities of fluid within a fracture and of the fracture tip 91
3.6. Normalized length of unwetted tip with respect to length of etted
fracture 93
3.7. Normalized driving pressure, aperture, and half-length as functions
of time predicted by analyses 95
3.7a. Average propagation velocities from laboratory experiments 96
3.8. Driving pressure and apertures as functions of length, during
inflation and propagation. The x symbol marks the end of
the fracture 98
3.9. Loading conditions used to develop analytical model 102
3.10. The effect of m on dimensionless driving pressure, half-length and
aperture 104
vu
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Number Page
3. IS. Records of driving pressure as a function of time from experiments
and from analytical solution for samples of various moisture
contents 110
3.16. Records of driving pressure as a function of time from experiments
and from analytical solution for samples that differ only in
the length of their starter slot Ill
3.17. The ratio of wetted to total length of a fracture as a function of
confining stress. Data from Medlin and Masse (1984) 117
3.18. Variation in exponents in eq. (3.40) as functions of confining
stress 118
4.1. Topography and locations of boreholes, vents, and hydraulic
fracturing equipment at the ELDA test site 123
4.2. Geology of the ELDA test site 124
4.3. Stratigraphic section from the vicinity of the ELDA test site 125
4.4. Method of creating small hydraulic fracture to measure the least
horizontalconfining stress 128
4.5. Injection pressure as a function of time during laboratory
experiments (a), and using field apparatus (b) 130
4.6. Grain size distributions in samples of ELDA Till 133
4.7. A borehole used to create hydraulic fractures 136
5.1. Hydraulic fractures HF5, HF6, and HF7. Structural contours are on
the fracture surfaces 144
5.2. Trace of hydraulic fractures HF5 and HF6 146
5.3 Trace of hydraulic fracture HF6 147
5.4 Trace of hydraulic fracture HF7 148
5.5. Hydraulic fracture HF9 150
5.6. Trace of hydraulic fracture HF9 151
5.7. Hydraulic fractures HF10 and HF11 152
5.8. Hydraulic fracture HF12 154
5.9. Geology and trace of hydraulic fracture HF12 155
5.10. Hydraulic fracture HF13 157
5.11. Outline of HF13 showing area where fracture cuts a bed of
upwardly-grading gravel, sand and silt 158
5.12. Trace of hydraulic fracture HF13 159
5.13. Outlines of hydraulic fractures and locations of a backhoe at the
time of fracturing ., 162
5.14. Idealized hydraulic fracture created at the ELDA test site 166
6.1. Scheme for hydraulic fracturing operation performed during the
1989 field test 173
6.2. Fracturing lance, used to prepare boreholes for hydraulic fracturing
during the 1989 field test 177
6.3. Five steps of hydraulic fracturing 178
7.1. Map of ELDA landfill site 182
7.2. Fracture map of trenches B and C 184
7.3. Fracture map of trenches D, E and F 185
7.4. Fracture map of trenches G, H and 1 186
7.5. Cross section B-B' 188
7.6. Cross section C-C 188
7.7. Cross section D-D' 189
vni
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Number £gg£
7.8. Cross section E-E' 189
7.9. Cross section F-F 189
7.10. Cross section G-G' „ - 190
7.11. Cross section H-H' 190
7.12. Map of east wall of trench B 191
7.13. Map of east wall of trench C 192
7.14. Map of east wall of trench D 193
7.15. Map of east wall of trench E 194
7.16. Map of east wall of trench F 195
7.17. Map of east wall of trench G - 196
7.18. Map of east wall of trench H 197
7.19. Map of north wall of trench 1 198
7.20. Fracture thickness for EL6F1, EL6F2 and EL6F3 .206
7.21. Fracture thickness for EL7F1 and EL7F2 20?
7.22. Fracture thickness for EL3F1 and EL3F2 208
7.23. Fracture thickness for EL1F1 and EL1F2 209
7.24. Fracture thickness for EL2F1 and EL2F2 210
7.25. Fracture thickness for EL4F1, EIAF2, E1>*F3 and EL4F4 211
7.26. Fracture thickness for EL5F1, EL5F2 and EL5F3 212
8.1. Pressure records from fracturing tests during 1989 215
8.2. Tiltmeter array from 1989 tests 231
8J. Tilt as a function of time —232
8.4. Hydraulic fracture and surface tilt interpretation of HF5 235
8.5. Hydraulic fracture and surface tilt interpretation of HF6 237
8.6. Hydraulic fracture and surface tilt interpretation of HF7 238
8.7. Thickness and uplift contours for EL6F2 and EL6F3 240
8.8. Thickness and uplift contours for EL7F1 .241
8.9. Thickness and uplift contours for EL7F2 244
8.10. Thickness and uplift contours for EL5F1, EL5F2, EL5F3
andL5F4 245
8.11. Apparent resistivity contour map on borehole 4, following fracture
H4 248
8.12. Apparent resistivity contour map on borehole 6, following fracture
H4 249
8.13. Apparent resistivity contour map on borehole 5, following fracture
H4andH5 250
8.14. Apparent resistivity contour-map on borehole 4, following fracture
H5 251
8.15. Apparent resistivity contour map on borehole 4, following fractures
H4,H5andH7 „ 252
8.16. Apparent resistivity contour map on borehole 7, following fractures
H4,H5,andH7 253
8.17. Apparent resistivity contour map on borehole 4, following fractures
H6 254
8.18. Apparent resistivity contour map on borehole 6, following fracture
H6 255
8.19. Summary of apparent resistivity changes relative to borehole 4
resulting from H4, H5, H6 and H7 256
IX
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TABLES
Number £ag£
1.1. Production rates before and after hydraulic fracture 7
1.2. Inflow rates into glacial till 13
1.3. Some possible constants in Eq. (1.9) 27
2.1. Characteristics of soils used in the study. - 38
3.1. Parameters used in numerical analyses - 89
3.2. Parameters used in analyses shown in figures 112
3.3. Exponents from various analytical solutions 114
3.4. Comparison of constants 115
3.5. Accuracy of laboratory measurements 119
4.1. Conditions of boreholes prior to testing 127
4.2. Saturated hydraulic conductivities of till ~ 131
43. Physical characteristics of silty-clay till 132
4.4. Summary of data from field tests 139
5.1. Dimensions and dips of hydraulic fractures 160
5.2. Azimuths of features of hydraulic fractures 163
7.1. Fracture size 183
7.2. Fracture thickness 200
7.3. Proppant concentration 202
7.4. Flow parameters 203
8.1. Actual and predicted orientations of fractures 234
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ACKNOWLEDGMENTS
The efforts of Doug Ammon, formerly of the USEPA, who initially
recognized the potential of hydraulic fracturing, and the continued support of
Herb Pahren and Mike Rouher of the USEPA have been essential to the
success of this project. Reviews by Herb Pahren, Robert Hartley and Ken
Dotson improved the quality of this report. John Stark, manager of the ELD A
Landfill, gave us permission to conduct the 1988 and 1989 field tests on
property owned by ELDA. Tom Busek, president of the Goettle Construction
Company, gave us permission to conduct tests during 1989 on property owned
by Goettle Construction. Don Steirman, professor of geophysics at the
Univerisity of Toledo, and his assistants conducted the resistivity surveys during
the 1988 field tests. Gary Holzhausen and Howard Egan of Applied
Geomechanics, Santa Cruz, CA, supplied us with tiltmeters and they analyzed
the tilt signals obtained during the 1988 field tests. Mark Roberts and his field
crew from Halliburton Services created the hydraulic fractures during the 1988
tests.
Space limitations prevent us from acknowledging individually a number
of colleagues and associates who contributed to this project. Their efforts have
been greatly appreciated.
XI
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INTRODUCTION
The recovery of hazardous chemicals from contaminated ground is often
difficult and sometimes impossible using established techniques, so earth scientists
have begun to turn to related fields for innovative ideas. In petroleum engineering,
the problem of recovering hydrocarbons from reservoirs is closely analogous to the
problem of recovering contaminants from aquifers. A wide range of techniques has
been developed to enhance the recovery of oil from reservoirs, and one of the most
effective is hydraulic fracturing. This research was motivated by the possibility of
using hydraulic fractures to improve the remediation of contaminated ground.
The basic process of hydraulic fracturing, as it is used in the petroleum
industry, begins with the injection of fluid into a well until the pressure of the fluid
exceeds a critical value and a fracture is nucleated. A granular material, which is
usually sand and is termed a proppant, is pumped into the fracture as it grows away
from the well. Transport of the proppant is facilitated by using a viscous fluid,
usually a gel formed from guar gum and water, to carry the proppant grains into the
fracture. After pumping, proppant holds the fracture open while the viscous gel
breaks down into a thin fluid. The thinned gel is then pumped out of the fracture,
creating a permeable channelway suitable for either the delivery or recovery of
liquid or vapor. As a result of hydraulic fracturing the flow rates of oil wells
commonly increase by factors of 1.5 to 8 (e.g. Howard and Fast, 1970). In some
cases where oil or gas is present in an adjacent formation but initially undetectable
in a well, hydraulic fracturing can dramatically increase the yield and make the well
an economic producer, according to Howard and Fast (1970).
STATEMENT OF THE PROBLEM
Experience from oil wells suggests that hydraulic fracturing could increase
flow rates from wells used to recover ground water contaminants. However, to
realize this increase hydraulic fractures would have to be created and filled with
sand under conditions of contaminated regions. Oil reservoirs are typically deeper
and are composed of different materials than contaminated regions, so the
applicability of fracturing methods used by petroleum engineers is unknown.
Contaminants commonly occur in soils1 that are weaker and more compliant than
limestone or sandstone typical of reservoirs. Effects of soil properties on hydraulic
fractures are difficult to anticipate based on the results of previous studies of
hydraulic fractures in rock. Moreover, most contaminants occur at shallow depths
(several meters to several tens of meters), so intersecting the ground surface and
venting could severely limit the length, and thus the performance of the fracture.
Hydraulic fractures virtually never vent when they are created in oil reservoirs,
which are several hundred to several thousand meters deep, so the practical
problem of creating fractures at shallow depths has yet to be addressed.
Previous investigations of hydraulic fracturing of soil have focused on
methods of preventing fracture initiation, largely ignoring the problems cited above.
As a result, little is known about both the basic problem of the mechanical behavior
1 The termso// is used in this work to mean an unlithified, or uncemented sediment
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of hydraulic fracture propagation in soil, and the applied problem of creating useful,
proppant-filled hydraulic fractures at shallow depths.
APPROACH
The approach of this research was to adapt methods proven for hydraulic
fracturing of rock to applications of hydraulic fracturing of soil. Laboratory
experiments were conducted by creating hydraulic fractures in rectangular samples
of remolded clayey-silt confined in a triaxial pressure cell. Results of those
experiments were analyzed using methods of linear elastic fracture mechanics, a
branch of elasticity theory that is widely used to analyze hydraulic fractures in rock.
Two sets of field experiments were performed by creating hydraulic fractures
in Pleistocene glacial drift at depths of between two and four meters. The first set
was conducted during June 1988 in collaboration with a subcontractor, who used
equipment designed to create hydraulic fractures from oil wells; whereas the second
set was conducted during June and July 1989 by investigators from the Center Hill
Facility, who used equipment that was either rented or designed for the project.
Hydraulic fractures were successfully created during the field tests, and then they
were exposed on the walls of trenches dug with a backhoe. Detailed descriptions of
exposures document the geometries of the fractures, highlighting the potential that
this process should have in remediation of contaminated soil.
MAJOR CONCLUSIONS
The project consisted of studies in the laboratory and in the field, as well as
an investigation of possible applications and a review of previous work. Most
remedial systems requiring fluid flow either into or out of the subsurface could
benefit from hydraulic fracturing. Pump and treat systems are obvious candidates
because they employ procedures resembling those used in petroleum recovery,
where the benefits of hydraulic fractures are without question. The yields of vapor-
producing wells, such as those recovering natural gas or steam, are improved by
hydraulic fracturing, so by analogy we expect that vapor extraction systems could
benefit from this technology. Similarly, hydraulic fracturing could be used in
conjunction with steam stnpping-a process developed to improve yields of oil wells
and currently being tested under remedial conditions. Horizontal, sheet-like
hydraulic fractures placed below a contaminated region could be used as gravity
drains to intercept the leachate from soil flushing systems (Murdoch and others,
1987), improving the effectivness of that remedial action. Bio-remediation systems
stand to benefit in particular because either nutrients for microorganisms, or the
microorganisms themselves, could potentially be delivered as fine-grained solids in
hydraulic fractures.
Laboratory Studies: Summary of Results
1. Hydraulic fracturing in the Center Hill clay (a type CL clayey silt) can be
predicted using methods of linear elastic fracture mechanics, according to
both empirical evaluation and estimates of the size of the crack tip process
zone. Many published methods of analyzing hydraulic fracturing in rock,
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which are based on linear elastic fracture mechanics, can be used to analyze
applications in soil, with appropriate modifications for boundary conditions
(e.g. ground surface), material properties (e.g. elastic constants, leakoff
parameters), and state of stress encountered at shallow depths.
2. The appearance of hydraulic fractures in silt, and clayey silt resemble
published descriptions of hydraulic fractures in rock created during
laboratory experiments. Details of the fracturing process are sensitive to
moisture content of the soil; moisture affects the appearance of the fracture
tip, the magnitude of driving pressure required to initiate fracturing, and the
form of the pressure record during propagation of the fracture. Changes in
all those factors with changes in moisture content are particularly large when
moisture conditions are near the plastic limit of the soil.
3. The critical stress intensity factor can adequately predict the pressure required
to initiate hydraulic fracturing of soil. It is independent of the length of
starter slot (or pre-existing fractures), for the slot lengths used in this study,
and it predicts the driving pressure at the onset of fracturing to within 10
percent, on average. It was more accurate for samples whose moisture
contents (moisture content = wt. water/wt. solid) exceeded 21% and less
accurate for drier samples.
4. The value of the critical stress intensity is highly sensitive to moisture content,
decreasing sharply from roughly 200 kPa cm1/* to 30 kPa cm1/2 as moisture
content increased by a few percent in the range of the plastic limit. Critical
stress intensity goes to zero for samples of Center Hill clay greater than 32%
moisture, although hydraulic fractures are readily created under those
moisture conditions.
5. Theoretical analyses based on linear elastic fracture mechanics and linear
viscous fluid mechanics explain many of the details of the laboratory
experiments, including the development of an unwetted tip, the average
propagation velocity, changes in the form of the pressure record with changes
in slot length or moisture content.
Field Studies: Summary of Conclusions
1. Hydraulic fractures of useful size were created and propped with sand at
shallow depths in glacial drift during field tests in 1988 and 1989.
2. A technique was developed that consistently produced hydraulic fractures
propped with sand in glacial drift. The technique uses a unit, which is readily
available for injection grouting, to inject a slurry of sand and cross-linked
guar gum. To create a fracture, an apparatus composed of an outer casing
and an inner rod was driven out through the bottom of a hollow-stem auger.
The inner rod was removed and a water jet was used to cut a disk-shaped slot
in soil enveloping the casing. Slurry was injected into the casing with a
positive displacement pump, nucleating a hydraulic fracture at the slot.
3. Hydraulic fractures created during the 1989 test were nearly flat-lying; their
steepest dip was 5°. In plan view, they were slightly elongate with aspect
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ratios of 2:3, and they were highly asymetric with respect to their parent
boreholes. They were createdat depths ranging from 1 to 4 m, and the
shapes and sizes of fractures created at depths between 1 and 2 m are known
in detail from excavations. The dimensions are as follows: maximum
distance from the borehole ranged from 0.8 to 7.2 m, and averaged 4.0 m.
Areas covered by the fractures ranged from 0.8 to 36.7 m2, and averaged 19.2
m2. All the fractures contained sand, ranging in maximum thickness from 2
to 20 mm, and the average maximum thickness was 11 mm.
4. The fracturing apparatus facilitates the creation of multiple fractures from a
single borehole. Stacks of flat-lying fractures with vertical spacings from IS
to 30 cm were created with the device.
5. The fractures were highly asymetric with respect to their parent borehole; that
is there was always a preferred direction of propagation. This direction was
related to loading at the ground surface, with the fracture either growing
away from a backhoeparked next to the borehole, or growing in the direction
of maximum slope. This indicates that topography, or surface loading (e.g.
vehicles, buildings), will affect the direction of propagation of shallow
hydraulic fractures.
6. Pressure records, surface uplift, and surface tilt all are available methods of
monitoring hydraulic fractures at shallow depths. Electrical resistivity shows
promise, although further research is required before that method is a
practical monitoring tool.
7. The results of hydraulic fracturing at a site i _, „
consolidated soil or fill are expected to differ markedly from'die results
described here. Further, during this study fractures were created in
unweathered material, so the effects of creating hydraulic fractures in
weathered material is unknown.
RECOMMENDATIONS
The principal recommendation is to expedite further investigation of field
applications. The results of this study indicate that hydraulic fracturing potentially
offers important improvements in the effectiveness of in situ remedial technologies,
particularly at sites underlain by overconsolidated soil or bedrock, and our
recommendation is to develop techniques necessary to assess this potential.
Specifically, we recommend the following:
1. Hydraulic fracturing should be tested during the remediation of several
contaminated sites. Those field tests should assess the impact that hydraulic
fracturing has on several different remedial technologies (e.g. pump and
treat, vapor extraction, soil flushing, bio-remediation). They should also
assess the impact of site conditions (e.g. geology, state of stress, depth of
contamination, etc.).
-------
2. Design and construct equipment intended to create hydraulic fractures at
shallow depths. Equipment should be a compromise between the powerful
and sophisticated ng used during the 1988 test (which lacked the required
control), and the modest and simple unit used during the 1989 test (which
lacked the required power and resiliency).
3. This study focused on creating hydraulic fractures in overconsolidated drift,
and the results of hydraulic fracturing in normally consolidated material may
differ markedly from the results reported here. We recommend that future
studies develop methods of creating hydraulic fractures at shallow depths in
normally consolidated soil, where in situ stresses will favor vertical fractures
that are highly susceptible to venting.
4. Develop techniques of delivering nutrients and microorganisms used for bio-
remediation.
5. Design methods of completing and developing ground water wells intersecting
hydraulic fractures.
6. Adapt or develop analyses to a.) determine treatment parameters from
pressure records (e.g. Nolte and Smith, 1981,1987; Nolte, 1988); b.) predict
the size, shape and orientation of hydraulic fractures at shallow depths,
particularly considering effects of topography; c.) optimize the position and
dimensions of hydraulic fractures based on predictions of the transport of
contaminants in the vicinity of the fractures.
-------
SECTION ONE
POTENTIAL REMEDIAL APPLICATIONS AND PREVIOUS INVESTIGATIONS
The final decision on the use of hydraulic fractures during remediation of
contaminated soilwill depend on whether the benefits they produce outweigh the
effort of creating them. Most of the following report deals with the processes and
problems of creating hydraulic fractures in soil, but it seems prudent at this point to
review some of the potential applications and estimate the order of benefits that can
be expected. Here we will assume that fractures of useful size can be created and
filled with a permeable proppant.
ASSESSMENT OF POTENTIAL APPLICATIONS
Most remedial systems that require fluid flow either into or out of the
subsurface could benefit from the effects expected to accompany hydraulic
fracturing. Pump and treat systems are obvious candidates, as are systems involving
vapor extraction, soil flushing, or steam stripping. Hydraulic fractures offer the
novel possibility of delivering solid material, formed into granules and mixed with
proppant, to the subsurface. Nutrients for microorganisms, or the microorganisms
designed for bio-remediation themselves, could be delivered as solid grains to
contaminated regions.
Filling a hydraulic fracture with material of low permeability, such as a
bentonite-rich soil or grout, was proposed by Buck and others (1980) as a method of
isolating contaminated material. This proposal has been investigated
experimentally in the laboratory (Brunsing and Henderson, 1984), and tested in the
field at a site near Whitehouse, Florida (Brunsing, 1987). The ability to place a flow
barrier beneath a contaminated region without removing overburden is the principal
advantage of this application. The principal drawback lies in the inability to verify
continuity of a low permeability layer. Breaking into segments is a property of
hydraulic fractures that seems to be inevitable. That property, combined with the
presence of objects such as tree roots, will cause discontinuities in the fracture-filling
that would be impossible to predict and difficult to detect using current methods. It
is feasible that hydraulic fractures filled with grout could act as short-term barriers,
or impediments to flow, but the likelihood of undetectable discontinuities inhibits
their use as long-term barriers.
Increasing the rate of flow from a well is expected to be the most widespread
application of hydraulic fracturing in remediation. The magnitude of increase will
be site-specific, but a general estimate of what to expect can be obtained from the
results of related applications and from theoretical analyses.
Records of oil production are irrefutable testimony of the benefits of
hydraulic fracturing, and ratios of production rates are a suitable yardstick with
which to measure those benefits. According to data from several dozen oil wells
(Howard and Fast, 1970; Table 1.1), production ratios (production rate after
fracture/initial rate) are at least 1.5 and range up to very large values. In general,
the ratios range from 1.5 to roughly 10 for wells that were producing before
fracturing, and the ratios are very large for wells showing negligible production prior
to fracturing.
-------
BATE OF OIL PRODUCTION
STATE
Alaska
Calif.
Canada
Colorado
Illinois
Kansas
Louisiana
Michigan
New Hex.
H.Dakota
Ohio
Oklahoma
Penn.
Texas
Heat Vs.
FORMATION
Eeaai sand
Stephana sand
Vaqueros sand
Beaverhill la.
Cardium sand
Villenuve quartz
Weber sand
Cypress sand
McCloakey Is.
Arbuckle la.
Hernnfton la.
Kansas City Is.
Annona Chalk
Hackberry sand
Marauilana sand
Blchfield la.
Graybur* la .
San Andres Is.
Mesa Verde
Madison la.
Berea sand
Bartlesville sand
Baaal sand
Granite wash
Mississippi Is.
Pennsylvanian
Bradford aand
Bron dolomite
Caaerina aand
Canyon limestone
Reklaw sand
Strawn sand
Vilcox sand
Benson aaad
in Barrels of Oil per Day
Before After Ratio
frx Irx (after/before)
1128
20
10
0
50
0
20
4
4
10
6TO>
6
5
30
15
22
15
20
4901
111
0
25
80
120
trace
130
6
6
26
SO
72
10
3.S*
1584
120
70
75
204
4*
110
35
60
40
20501
30
20
115
104
ISO
110
60
5000*
296
60
275
350
650
168
4T5
55
65
230
130
113
35
1100*
66.1*
1.4
6.0
7.0
4.1
5.5
8.7
12.5
4.0
3.1
5.0
4.0
3.0
6.9
6.8
7.3
3.0
10.2
2.6
-
11.0
4.4
* I6
3.6
9.1
10.8
8.8
2.6
1.6
3.5
73.0
18.9
Dakota aand 25 125 5.0
Frontier aand 16 70 4.4
Madison linestone 473 715 1.6
Phosphoria Is. 1050* 3050s 2.9
Tensleep aaand 20 65 3.2
* units of (Hcubio ft./day)
Table 1.1 Data describing the production rates from oil wells before and after
hydraulic fracturing. From Howard and Fast (1970).
-------
Production rates, from either fractured or unfractured wells, typically
decrease as a function of time due to depletion of the reservoir, clogging of pores, or
other processes. Behaviors of fractured wells through time were characterized by
Howard and Fast (1970) in their classic monograph,
"The effect of [hydraulic] fracturing on both short and long term well
productivity has been studied by many investigators, most of whom conclude
that, regardless of the kind of treatment, four basic patterns of production
behavior have been observed.
Type A: Sustained increase in well production accompanied by a
flattening of the production decline curve following treatment.
Type B: Sustained increase in production with the well's highest rate
of production after the treatment declining essentially at the same rate
established before treatment.
Type C: Transitory increase in production lasting from a few months
to several months, after which the well continues to follow the production
decline trend observed prior to treatment.
Type D: No increase in production, with the well continuing to follow
its established, normal production history.
In no case did a treatment have a discernibly detrimental effect on the
production performance of the well."
In one example of a Type A or B result (Fig. 1.1), the production rate at a
well in North Texas increased by a factor of four, from 20 to 80 barrels of oil per day
£opd), and then gradually decreased to 30 bopd over the subsequent seven months.
terestingly, a second hydraulic fracturing job increased the production rate to 80
bopd (Fig. 1.1).
Yields of water wells are also increased by hydraulic fracturing (e.g. review
by Smith, 1989). Thirty years ago Koenig (1960) examined data from wells used for
waterflooding or waste disposal and reported that 78 percent of those wells showed
an increase in yield following hydraulic fracturing. The ratio of yields ranged up to
100, with a median of 5.0. More recently, Stewart (1974,1978) observed increases
in yields from water wells drilled in granite or schist formations in New Hampshire.
Yields of one well reported by Stewart increased from 0.30 to 1.821/s, (ratio of 6.0),
and at another well yields increased from 0.26 to 1.141/s (ratio of 4.4). A
particularly impressive increase in yield of 22 to 25 times is described by Mony
(1989), who cites a water well drilled in gneiss that yielded 0.00771/s prior to
fracturing and 0.16 to 0.191/s after fracturing. Waltz and Decker (1981) used
hydraulic fracturing to stimulate wells in crystalline rock in Colorado and reported
ratios of yields of 1.5 to 2.0. Williamson and Woolley (1980) created hydraulic
fractures from water wells penetrating igneous or metamorphic rocks in Australia,
and cited improvements in specific yield by factors of 5.0 to 6.0. Several other
authors (Hurlburt, 1989; Waltz, 1988; Baski, 1987; Macaulay, 1987) have recently
claimed that hydraulic fracturing of water wells consistently results in increased
yields that are economically significant.
-------
Q
D-
O
PQ
%_^
to
C
o
O
S-,
OH
100
80
60 I-
Hydraulic fracture created
Hydraulic fracture created
0 2 4 6 8 10 12 14 16 18
Time (months)
20
Figure 1.1. Production rate of an oil well in North Texas as a function of time.
-------
Rates of inflow into wells used for waste disposal (Stow and others, 1985;
Wolff and others, 1975; De Laguna, 1966 a and b), or as infiltration galleries are
increased by hydraulic fracturing. Rates of inflow were measured as part of this
project from five open boreholes intersecting sand-filled hydraulic fractures created
in unsaturated glacial drift. The fractures were flat-lying, typically 1 cm in maximum
thickness and as much as 8 m in maximum dimension.
For comparison, inflow rates were measured from three similar boreholes
penetrating unfractured drift. Boreholes intersecting hydraulic fractures are EL2,
EL5, EL6, EL7, whereas those in unfractured ground are TB1, TB2, TB3.
All boreholes were 5 cm in diameter and 2 m deep. Tests were conducted
using Guelph Borehole Permeameter, manufactured by SoilMoisture Inc., Santa
Barbara, Ca. The permeameter enabled us to measure flow rates while maintaining
a constant water depth of one meter above the bottom of the borehole.
Rate of inflow into unfractured boreholes diminished slightly with volume,
approaching steady-state rates after one to three liters. The steady-state rates were
between 0.04 and 0.071/min, depending on the well, and the average rate was 0.055
I/min.
The rate of inflow into the wells intersecting hydraulic fractures also
diminished with time, but larger volumes, as much as several tens of liters, were
required to achieve steady-state. Initially, inflow rates were as rapid as 2 to 31/min,
the upper limit that could be supplied by the permeameter. The rates diminished
with volume, but they were greater than those of the unfractured wells even after
large volumes. For example, the rate of inflow was roughly 0.41/min after 200 liters
of water flowed into EL7, and the rate was 0.175 after 350 liters flowed into EL4.
Steady inflow into the fracture wells occurred at 0301/min.
In the works cited above, effects of a hydraulic fracture were illustrated using
the ratio of flow after fracturing to flow prior to fracturing. The method used to
create the hydraulic fractures precluded measuring inflow at a well before it was
fractured. The average inflow into an unfractured well in the vicinity of a fractured
well will be used to determine the ratios (Table 1.2). Values range from 3.1 to 9.0
for steady-state conditions, and they are typically several times greater than that for
unsteady state (Fig. 1.2).
Inflow into the boreholes that intersect fractures probably would have been
greater if screen and gravel packing was used to prevent collapse. The boreholes
filled with mud to depths of several dm while they contained water during inflow
testing. Nevertheless, the data do suggest that hydraulic fractures in unsaturated
ground could provide marked improvements to remedial systems based on soil
flushing.
Wells used for purposes ranging from delivery of water in unsaturated soil to
recovery of oil in reservoirs have shown strikingly similar responses after hydraulic
fracturing - their yield is consistently increased, and the magnitude of increase
ranges up to several orders of magnitude or more. Typically, the ratio of yields is
roughly 1.5 to 8 or 10 for wells that are producing prior to fracturing, but it can be
greater than 10 for wells that are initially poor producers.
10
-------
M
o-
0 15
0.10
0.05
0 15
0.10
0.05
0 OO
0.
0 15
0.10
O.OS
0.00
TB 1
) 1 2
TB 2
° o ° o o - o °
„ 0 0 0 ° c 00 O
o
0 02 0.4 OS 0.6 1.0 1.2 1.4
TB 3
° °V". . . •'
Oo°oo0°»c °° e 0ta000o00°C00coo
o
2
o
3 <
2
1
I
2
1
o o
EL 2
0
0 0
00
0
o
e
J 10 20 30 40 5C
EL 5
0
° °o°Q°°aaoe_0 a eoo ° ° °° o uo-oo"
2 4 6 8 10 12 14 16
EL 6
o
e °
° ° e
B8W>°° . # .'^ssato-.nv
a o z 4 s e 10 iz
Delivered Volume (liters)
Figure 1.2 Rates of inflow into boreholes in till. TB1.TB2.TB3, are test borings,
whereas EL2 through EL7 are borings intersecting hydraulic fractures.
11
-------
x^*
• f-l
^s
w
0)
«4«J
• 1— 1
I— H
0*
U.3 1 ' • • • 1 ' ' ' ' 1 i i i i
o.4 | EL 4 -
0.3 i
*
0.2
0.1
0.0
(
1 1 ° •
» 8 :
o -
o ;
. • i
) 100 200 300 400
2n
• V
1.5
1.0
0.5
OD
: EL 7
j
i o
3 «<
° o o o o o dCo o
0 SK
1 1 1 1
50
100
150
200
Delivered Volume (liters)
Figure 12 (continued).
12
-------
TABLE 1.2 INFLOW RATES INTO SILTY CLAY
Borehole Steady inflow Average Ratio
TB1 0.04
TB2 0.05
TBS 0.075 0.055
EL2 0.20 3.6
EL4 0.175 3.1
ELS 0.50 9.0
EL6 0.20 3.6
EL7 0.40 0.30 73
Predicting Flow to Wells That Intersect Fractures
Early schemes of predicting flow to wells that intersect hydraulic fractures
were based on empirical studies, electrical analogs, and simple theory. Results were
obtained for fractures that were either vertical and rectangular in shape (Prats,
1961, McGuire and Sikora, 1960; Dyes and others, 1958; van Poolen and others,
1958), or horizontal and circular in shape (Landrum and Crawford, 1961; Hartsock
and Warren, 1961; Morrisson and Henderson, 1960). Today, those schemes are
important for simple calculations, but more sophisticated numerical models
(Gringarten, 1982; Cinco-Ley and others, 1981,1978) are available for detailed
analyses.
Many of the available analyses can be used to obtain the specific yield of a
well intersecting a hydraulic fracture, which when divided by the specific yield of the
well without a fracture results in a dimensionless measure of the improvement of
the well. This ratio will be termed the recovery capacity / in the following pages.
Recovery capacity in general depends on conditions of the fracture, such as its size,
shape, aperture, location, and permeability of proppant, and on conditions of the
reservoir or aquifer, such as its permeability, dimension, and the location of the well
within it
Two analyses will provide useful insights: one that shows the importance of
fracture length, relative transmissivity, and radius of influence at steady-state, and
another that shows the importance of fracture length as a function of time. Prats
(1961) analyzed the effect of a vertical fracture of finite permeability ki and
thickness d in a confined aquifer bounded laterally by surfaces of constant pressure.
Relative transmissivity Tt is defined by Prats (1961) as
*.« (1.1)
13
-------
where ks is the permeability of enveloping soil or rock, a is fracture half-length.
Prats describes Tr as the ratio of the ability of fluid to travel along the fracture to the
ability of fluid to travel through the enveloping material and reach the fracture. The
flow at the fracture increases with relative transmissivity for values of Tt between 0
and 1.0. For values of Tt greater than 1.0, however, the effect of T, is negligible
(Prats, 1961) and the fracture behaves at steady-state as if its permeability were
infinite. This result is important because it indicates that in many field cases the
permeability of a propped hydraulic fracture can be assumed to be essentially
infinite, thereby avoiding analytical difficulties associated with fractures of finite
permeability.
Assuming that the relative transmissivity is essentially infinite, the steady-
state recovery capacity is
/ = Mre/rw)/7n(re/(L/4)) (12)
in which rw is the actual radius of the well, and re is the effective radius of the area
drained by the well, and L is the total fracture length. In a field of regularly-spaced
wells, for example, the effective radius is roughly half the spacing between wells.
According to eq. (12) the steady-state behavior of the fracture is the same as
that of a well whose radius is equivalent to L/4. A vertical fracture 10 m long would
behave as a well 25 m in radius, so that the equivalent radius of a fracture can be
much larger than most wells.
Recovery capacity certainly increases with fracture length, but its magnitude
depends on the ratio of fracture length to effective radius. According to this
analysis, the recovery capacity will be greatest when the fracture extends across the
area drained by the well. Assuming L = 2re, the maximum / is
Jam* - 1-44 ln(L/2rv) (1.3)
For example, 2.3 is the maximum recovery capacity of a fracture 10 times as
long as the radius of the unfractured well, whereas the value increases to 5.6 for a
fracture 100 times the well radius, according to this analysis.
As the effective radius increases, the steady-state recovery capacity decreases
and approaches unity. For a single well in a large aquifer, therefore, the steady-
state yield from a fractured well will approach that of one from an unfractured well.
This conclusion is misleading, however, because it ignores potential increases in
yields during the transient period of recovery before steady-state is achieved.
Recovery capacity is typically greatest shortly after fracturing and then it
decreases with time, as shown in Figure 1.1 for example. A solution to the transient
recovery capacity can be obtained in analytical form from dimensionless drawdown
functions for a well and for a fracture. Dimensionless drawdown S^ of a vertical
well in a confined aquifer of thickness h is obtained by assuming the well behaves as
a line sink (Ramey, 1967), so
14
-------
(1.4)
where
I*, = 4tKh/Sr* (1.5)
and K and 5 are the hydraulic conductivity and the storage coefficient of the aquifer,
respectively; t is the time of pumping, p, Q, and r are the drawdown, pumping rate
and radius of the well, respectively. The drawdown function sa«(l/t 1.0 are a result only of the difference in geometry between a sheet-like fracture
and a line-like well.
Many hydraulic fractures created at shallow depths (less than roughly 300 m)
are flat-lying and roughly equant, a geometry that can be approximated by a planar
sink that is flat-lying and shaped like a circular disk. The drawdown function for a
fracture of that geometry in a confined aquifer (e.g. Gringarten and Ramey, 1974;
15.
-------
eqs. 51 and 53) was used in eq. (1.7) to produce Figure 1.3. The ratio of aquifer
thickness 7* to well radius r was held constant and equal to 250, and the fracture was
assumed to be at mid-height in the aquifer (z/T=0.5 where z is the height of the
fracture above the bottom of the aquifer). Recovery capacity was determined as a
function of time for ratios of a/r between 50 and 1000. The radius of the fracture
equals the aquifer thickness when a/r equals 250, and it is four times the aquifer
thickness when a/r equals 1000. Although the dimensionless form is valuable for
many applications, a reference value of fdr may be helpful in some cases: if K = 104
cm/sec, 5 = 0.001, a = 10 m, T = 11.6 m; then tu x 10 = / in days.
Results of the analysis indicate that the recovery capacity at any given time
increases with relative fracture length. Recovery capacity is roughly unity when a/r
= 50, indicating that the recovery from a fracture 50 times the radius of a well will
be similar to that of an unfractured well. As the ratio a/r increases to 1000, the
value of/ increases to 8.0, and even greater values of/ are obtained for earlier times
or longer fractures.
Magnitudes of/ diminish with time because geometric advantages of a planar
sink decrease compared with those of a line sink as water is removed from regions
at increasingly greater distances from the sinks. Even at relatively large values of to,
however, the recovery capacity is significantly greater than 1.0 (Fig. 1.3), indicating
that the fracture is performing better than the well. The performance of the
fracture would be even better if we assumed that the well draining the fracture was
screened for the full thickness of the aquifer, which is a reasonable assumption for
most applications. That case can be approximated by adding 1.0 to the right hand
side ofeq. (1.7), or to values of/ shown in Figure 1.3.
Summary
In the previous section we have seen that hydraulic fracturing increases the
yields (or inflow rates) of oil and gas wells, water wells, and infiltration wells. The
magnitude of increase is consistently between 1.5 and 5 times, routinely as much as
10 times, and in some cases much more than 10 times'. In general, hydraulic
fracturing offers the greatest relative increase to wells which show poor yields prior
to fracturing. Of course, if the initial yield of a recovery well is extremely low, even
the improvement offered by hydraulic fracturing may be insufficient to make
recovery a viable remedial solution. That judgement will depend on analyses of
costs, which exceed the scope of this investigation.
Observations indicate that yields of fractured wells diminish with time, just as
they do at unfractured wells. The relative improvement of the well diminishes
following fracturing, but the effect of the fracture can be important even after many
months or longer. In some cases, wells can be re-stimulated and their yields
increased creating another hydraulic fracture.
A simple theoretical analysis, based on the difference in shape between plane
and line sinks, predicts improvements in specific yield that are similar, both in
magnitude and behavior with time, to improvements observed in the field. It
follows that improvements in yield result principally from the geometric effects of
the fractures.
16
-------
T/r: 250
z/T: 0.5
1000
Figure 13. Recovery capacity of a flat-lying, circular fracture in a confined aquifer.
17
-------
We conclude that the magnitude of increase in yields of contaminant
recovery wells will be similar to that of wells used to recover oil, natural gas, or
water from rock. Hydraulic fractures are expected to increase the yields of recovery
wells in soil or rock by several times, or perhaps up to an order of magnitude.
Detailed predictions of the effects of hydraulic fractures at a particular site will
require more sophisticated analyses, but the general magnitude of the improvement
in yield predicted by the data and analyses described above justifies further
investigation into this process.
PREVIOUS STUDIES OF HYDRAULIC FRACTURING
To some investigators hydraulic fracturing is a blessing, to others it is a curse.
This difference is driven by the effect of fracturing on particular processes, and it
has resulted in two different research goals. When hydraulic fracturing produces
useful results, such as increasing the yield of a well, providing a measure of in situ
stress, or generating insight into geologic process, investigators generally focus on
predicting the characteristics of a fracture (e.g. size, shape, orientation). When
hydraulic fracturing causes problems, such as collapsing a dam, compromising a
permeability test, or bleeding off grout or waste from a borehole, however,
investigators generally focus on predicting, and thus preventing, initiation. To the
latter group, the characteristics of hydraulic fractures are of little interest.
A thorough review of the vast body of published work related to hydraulic
fracturing would fill several volumes, so the following section is intended only as a
brief overview. Other reviews relevant to the present work have been published by
Clearv (1988), Mendelsohn (1984), Veatch (1983 a and b), Geertsma and Haafkens
(1979Y The classic SPE monograph on hydraulic fracturing by Howard and Fast
(1970) is a valuable source, and a revision of that monograph will be published in
the near future.
The Hydraulic Fracture as a Tool
As early as the mid-1930s it was widely recognized by workers in the
petroleum industry that pressurizing a well could fracture the enveloping formation
(Yuster and Calhoun, 1945). The first use of proppants to hold fractures open,
however, was the key to developing a technique of widespread importance. The first
description of the creation of propped fractures is generally attributed to Clark
(1949), who outlined a process that closely resembles the ones used today. Clark
claimed that hydraulic fractures had been created at 32 wells when his paper was
submitted for publication in 1948. Several years later in 1953, a patent of the
hydraulic fracturing method was reissued to R.F. Ferris, a colleague of Clark
(Howard and Fast, 1970).
During the 20 years following Clark's paper the ap
fracturing to oil and gas wells became routine, and by 1968 the technique had been
used at roughly 500,000 wells (Howard and Fast, 1970). Success rates, indicated by
an increased yield after fracturing, were between 75 and 80 percent during the early
years, but they increased to nearly 90 percent by the late 1960s, according to
Howard and Fast (1970).
18
-------
Typical fracturing operations pumped volumes on the order of several
thousand to several tens or thousands of gallons prior to 1970, but in the following
years the sizes of fracturing jobs increased to a million gallons or more. These so-
called massive hydraulic fractures opened oil reserves mat could not be
economically produced using previous methods. Costs involved with creating
massive hydraulic fractures spurred the modern era of research into methods,
materials, analyses and designs of hydraulic fracturing.
Petroleum companies are the primary users of hydraulic fractures, but they
are by no means the only ones. The generation of thermal energy from hot dry
rocks is a technology that makes use of hydraulic fractures to create flow paths in
basement rock. In principle, two wells drilled into hot rock are linked together by
one or more hydraulic fractures (e.g. Murphy, 1982; Ernst, 1980). Cold water is
injected into one well, it flows through the hydraulic fractures and is heated by the
wall rocks, and then is recovered at the other well where it is used to drive turbines
for electrical power. This application was successfully implemented in a small-scale
test at Fenton Hill, New Mexico, where two wells 2.75 km in depth were connected
by a fracture 0.3 km in height (Kerr, 1987; Murphy, 1982). The hydraulic fracture
acted as a heat exchange producing 3 megawatts of power. A second phase of that
project, intended to create larger fractures and produce more power, encountered
difficulties. Two boreholes were drilled to depths 9f 4.6 km, but hydraulic fractures
created at one well failed to intersect the neighboring well, presumably injection
resulted in slippage along many natural joints rather than dilation of a single
fracture (Kerr, 1987). In a related project in Cornwall, England, investigators used
gel to open natural fractures, successfully creating a circulation loop between two
wells. This project was producing 5 megawatts of thermal power after two years of
operation (Kerr, 1987). Similar projects involving the circulation of water through
hydraulic fractures Unking two boreholes have been evaluated in France (Cornet
and others, 1982), and Germany (Rummel and Kappelmeyer, 1982).
Proppant was omitted from fractures created during the projects cited above,
because thermal breakdown of the guar gum-based gel used to transport proppant
could cause sand to plug the well casing during fracturing. A modified gel, intended
for use at high temperatures, was employed by Nakatsuka and others (1982), who
created hydraulic fractures used to recover wet steam at the Nigorikawa geothermal
field in Japan. They injected as much as 81 metric tons of sand per fracture, and
increased the yields of steam or hot water by factors as great as 2.3.
Water wells can be stimulated by hydraulic fracturing, as indicated by data
cited in a previous section. Most of the applications are to water wells in igneous or
metamorphic rock, where the natural permeability is low and the wells are initially
nearly dry (Hurlburt, 1989; Waltz, 1988; Baski, 1987; Macaulay, 1987; Williamson
and Wooley, 1980; Stewart, 1974,1978). The use of proppant in hydraulic fractures
at water wells is unnecessary in many cases because sufficient yields can often be
achieved using water alone (Smith, 1989; Baski, 1987; Williamson and Woolley,
1980). Presumably this occurs because fractures in hard rock can be held open by
asperities on fracture surfaces (Paillet, 1985; Detournay, 1979). Omitting proppant
from a fracture eliminates the need for a blender and a sand supply, considerably
reducing the expense of the fracturing operation.
19
-------
Several other industries that use wells to gain access to the subsurface have
applied hydraulic fracturing. The mining industry, for example, extracts soluble
minerals such as halite, sylvite, sulfur, or uraninite by circulating fluids through
natural ore deposits. Solution mining operations commonly employ two wells, one
to produce and another to inject fluid. Hydraulic fractures are used to increase the
flow rate between the two wells, in a design similar to that of geothermal energy
operations (Haimson and Stahl, 1970).
Various industries have disposed of wastes by injecting them into hydraulic
fractures. In 19S8, injecting radioactive waste into hydraulic fractures was first
considered by the Atomic Energy Commision as a means of disposal (De Laguna,
1966). This application was evaluated for 20 years at the Oak Ridge National
Laboratory (Stow and others, 1985), where radionuclides were mixed with cement-
based grout and injected into a shale formation. The grout formed nearly flat-lying
hydraulic fractures roughly 300m below the ground surface (Stowe and others, 1985;
Holzhausen and others, 1985 a and b; De Laguna, 1966).
Deep well injection is a popular technique of waste disposal that can either
benefit or suffer from hydraulic fracturing. On one hand, hydraulic fracturing
during deep well injection will increase the rate of injection (Bouwer, 1978) and
thereby reduce the. cost of disposal. On the other hand, hydraulic fractures can
propagate upward from the bottom of the disposal well, cutting through low
permeability formations intended to isolate the waste and possibly contaminating
overlying aquifers (Wolff and others, 1975).
The state of stress in the earth's crust is a central topic of interest to
investigators of tectonics, structural geology, earthquake prediction, mining, well
stimulation, soil or rock mechanics, and related disciplines. Hydraulic fracturing has
been used by those scientists since the early 1960s, when Scheidegger (1960,1965),
Kehle (1964), and Fairhurst (1964) proposed that the pressure required to initiate a
hydraulic fracture from a well bore was related to the magnitude of in situ stress.
Their method idealizes a wellbore as a pressurized cavity and assumes that
hydraulic fracturing occurs when the magnitude of tensile stress in the wall of the
cavity exceeds the tensile strength 5 of the formation. Assuming the wellbore is a
long cylindrical cavity in a porous formation, the maximum horizontal compressive
stress is given by
JHinax = 5 + 3St\mm '/>w ~Po (1.8)
in which pw is the pressure in the wellbore at the onset of fracturing, sHmin is the
minimum horizontal compressive stress, and/?0 is the pressure of pore-fluid in the
formation.
To solve eq. (1.8), tensile strength 5 is determined by testing core samples
and the pressures po,pv are obtained from transducer measurements before and
during fracturing. The minimum confining stress Hmirfs generally equated to the
wellbore pressure at the instant the fracture closes shut after pumping has ceased
(termed the instantaneous shut-in pressure, or ISIP). Kehle (1964) presents an
20
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eloquent argument supporting the use of the ISIP in determining Hm» Most
investigators agree that the ISIP is marked by a subtle change in slope of the
pressure record after pumping has ceased, but there are a variety otmethods of
estimating this pressure (e.g. Aamodt and Kuriyagawa, 1982; McLennan and
Roegiers, 1982; Gronseth, 1979; Nolle, 1979; Bjerrum and Anderson, 1972). The
methods of Nplte and Smith (Nolte, 1979,1982; Nolte and Smith, 1981; Smith, 1981;
Nolte and Smith; 1987) are particularly robust, yielding not only Hmmbut leakoff
coefficients, proppant schedules, and other parameters used to design hydraulic
fracture treatments.
Flaws in the walls of boreholes, either natural fractures or cracks created
during drilling or perforating a well, will nucleate hydraulic fractures and cause
errors in in situ stress measurements if they are overlooked (Warpinski, 1983).
Abou-Sayed and others (1978) present theoretical analyses based on linear elastic
fracture mechanics that account for pre-existing cracks in a borehole during in situ
stress measurement. Their analysis requires knowing the size and shape ot pre-
existing fractures intersecting the borehole, information that is generally difficult to
obtain for naturally-occurring fractures. This difficulty is avoided by deliberately
cutting a notch of known dimension in the wall of the borehole to dominate the
effects of natural fractures.
Geologists have recognized natural features that formed by processes closely
resembling hydraulic fracturing. The features are tabular in form and they are filled
by materials that differ in composition or texture from enveloping material. Igneous
sheet intrusions (Pollard, 1978), clastic dikes (Shoji and Takenouchi, 1982),
hydrothermal breccia dikes (Bryant, 1968; Farmin, 1934), and some mineralized
veins (Kesler and others, 1981; Anderson, 1974; Phillips, 1972 and 1973) are
interpreted as resulting from natural processes related to hydraulic fracturing. High
pore pressures induced by seismic shocks accompanying earthquakes (Holzer and
others, 1989) can fracture overlying sediments and erupt at the ground surface as
sand blows, or sand boils (Shoji and Takenouchi, 1982).
Studies of those natural features have certainly benefited from research
conducted by the petroleum industry, but it has by no means been a one-way street.
Natural analogs to hydraulic fractures can be studied directly where they are
exposed at the ground surface, a luxury seldom afforded investigators in the
petroleum industry. Much of what is known about the details of large-scale
fractures has been derived from studies of exposures of igneous dikes and sills. In
their argument for the state of stress as a fundamental control of the orientation of
hydraulic fractures, for example, Hubbert and Willis (1957) first noted the
mechanical similarity between dikes and hydraulic fractures. Then they cited the
similarity between the pattern of dikes at Spanish Peaks, Colorado, and the pattern
of principal stresses calculated by Ode (1957). Later, Pollard (1978,1973) and
Polard and others (1975) showed tiiat dikes and sills are tabular in gross form, but
are discontinuous in detail. The discontinuities are particularly well-developed near
leading edges, where they appear as segments, or elongate lobes. Pollard (1978)
argues, by analogy, that hydraulic fractures should also be discontinuous, and his
argument is supported by later theoretical analyses (Pollard and others, 1982)
showing how a fracture could break into segments in response to small fluctuations
in the in situ state of stress. This insight is significant because it suggests that
hydraulic fractures filled with grout and usedas barriers to flow (Huck and others,
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1980; Brunsing, 1987) could be plagued by imperfections that compromise the
integrity of the barrier. Furthermore, the performance of fractures filled with sand
and used as drains could be reduced if some of the sand is isolated in discontinuous
lobes (Pollard, 1978).
Experiments
Experiments conducted in the laboratory or the field have contributed to
useful applications of hydraulic fracturing. Laboratory experiments are designed
either to measure material properties, to test theories, or to illustrate effects of
processes that are difficult to analyze theoretically. Fracture toughness2 is a
material property, which was introduced to predict fracture in metals (Invin, 1957),
but has been applied the prediction of fracture in rock as well. Traditionally,
fracture toughness has been ignored (set to zero) because the energy required to
overcome viscous forces in large fractures is several orders of magnitude greater
than the energy required to overcome material toughness (Geary, 1980a).
Recently, however, it has been recognized that fracture toughness can affect
aperture and shape in cross-section (Spence and Turcotte, 1985; Nilson and
Griffiths, 1986; Abe and others, 1976), and that natural variations in toughness can
affect the shape of the leading edge of a hydraulic fracture (Thiercelin and others,
1989).
Methods of measuring fracture toughness of rock differ widely in specimen
geometry and type of loading, but they all nave one feature in common: the use of a
large notch, or starter slot, cut in the sample. The starter slot nucleates failure at a
pre-existing fracture of known dimension, thereby avoiding the problem of
characterizing effects of naturally-occurring cracks or flaws. Some methods are
adaptations of ASTM techniques, which apply external loads to measure fracture
toughness of metal specimens (Klepaczko and others, 1984; Ouchterlony, 1982;
Geary, 1978b; Schmidt, 1977), whereas others are patterned after the hydraulic
fracturing process and inject fluid to measure fracture toughness (Clifton and others,
1976; Abou-Sayed, 1977).
Early theories (e.g. Haimson and Fairhurst 1967; Kehle, 1964; Harrison and
others, 1954) predicted that hydraulic fracturing would initiate when the
circumferential stress on the wall of a borehole exceeded the tensile strength of the
formation. This theory was tested by Haimson and Fairhurst (1969) by injecting
fluid into cylindrical samples of hydrostone, a gypsum cement exhibiting properties
similar to natural rock. They observed that during injection the fluid pressure
increased and then abruptly decreased, and they assumed that fracturing, or
breakdown, initiated at the maximum pressure. According to the elastic solution of
Haimson and Fairhurst (1967), breakdown pressure increases linearly with confining
pressure, but both the slope and intercept of breakdown as a function of confining
pressure decrease if injection fluid penetrates the sample prior to fracturing.
2 The l&nn fracture toughness is used in this work only as a nominal criterion of
measuring resistance to fracturing, without any implication to specific criteria,
such as the critical stress intensity factor, critical strain energy release rate, /
integral (Lawn and Wilshaw, 1975), or the fracturability index (Daneshy,
1976b).
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Results of their experiments (as well as those of early studies by Harrison and
others, 1954; and Scott and others, 1953) showed that fluid penetration reduces the
breakdown pressure, similar to the theoretical results. In detail, results of the elastic
theory predicted slightly less breakdown pressures than were actually observed by
Haimson and Fairhurst (1969), a difference they attributed to plastic deformation in
the walls of the borehole that was omitted by their analysis. Medlin and Masse
(1979) performed similar experiments. Their results show that the elastic theory
predicts breakdown pressures at relatively low confining stress, but tends to
overestimate breakdown when confining pressures exceed some critical value, which
depends on rock type. Medlin and Masse (1979) attribute this deviation to plastic
deformation induced by the confining stresses, and they offer a modified theoretical
analysis that is consistent with their results.
Haimson and Fairhurst (1969) also reported that the breakdown depended
on the rate of pressurization; it increased as the rate increased. Zoback and others
(1977) offered an explanation by using an increase in acoustic emissions (AE),
rather than a change in slope of the pressure record, to indicate the onset of
fracturing. According to Zoback and others (1977), during relatively low rates of
pressurization an increase in AE occurred at the same time as the breakdown
pressure. As the rate of pressurization increased, the pressure of fracturing (as
indicated by AE) remained roughly constant, although the breakdown, or maximum
pressure increased dramatically.
Theoretical analyses of fracture propagation have been tested in the
laboratory since the first analyses were proposed. Harrison and others (1954)
created hydraulic fractures in photoelastic gelatin to verify an analysis of hydraulic
fracturing based on elasticity theory and originally published by Sneddon (1946).
Fractures they created experimentally had ratios or length to width that were similar
to those predicted by the simple theory (Harrison and others, 1954; fig, 6).
Moreover, photographs of the experiments revealed fractures that were elliptical in
cross-section, the shape predicted by Sneddon's theory. More recently, Medlin and
Masse (1984) created fractures in rectangular blocks fitted with ultrasonic
transducers to sense the fracture during propagation. Their results show that the
injection fluid lags slightly behind the leading edge, resulting in an unwetted zone at
the tip of the hydraulic fracture. The existence of an unwetted tip was long
suspected on theoretical grounds (Khristianovich and Zheltoy, 1955; Barenblatt,
1962). Rates of growth, dilation, and the pressure record during fracturing in the
experiments were shown to be consistent with two-dimensional, plane-strain
theories of fracture propagation (e.g. Khristianovich and Zheltov, 1955; Geerstma
and de Klerk, 1969; Spence and Turcotte, 1985).
The orientation of hydraulic fractures normal to the least principal stress is a
result obtained nearly universally, from the early studies of Hubbert and Willis
(1957), or Haimson and Fairhurst (1969) to the more recent work of Hanson and
others (1979), and Medlin and Masse (1979). Daneshy (1973) showed that the local
state of stress induced by a cylindrical borehole can cause the initial orientation of a
hydraulic fracture to differ from that favored by far-field conditions. In most of
Daneshy's experiments, fractures contained the axis of the borehole where they
were adjacent to the hole, but the fractures curved or twisted out of their original
plane until they were normal to the direction of least far-field compression at some
distance from the hole. Similar results were obtained by Medlin and Masse (1979),
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who report that the initial orientation of fractures would contain the axis of the
borehole and ignore the presence of shallow notches cut in the wall of the hole at
orientations favorable to the far-field conditions. Deeper notches overcame the
effects of the borehole, nucleating hydraulic fractures in the plane of the notch
instead of parallel to the axis of the borehole. The results or those studies are
important to field applications, such as the tests described in later chapters, where
horizontal fractures are created from vertical boreholes.
Model studies have contributed to the understanding of how hydraulic
fractures behave at interfaces between different materials. This behavior is
important to applications in the petroleum industry where vertical fractures can be
contained within a thin formation by overlying and underlying units that inhibit
propagation. Daneshy (1976) describes results of some of the first experiments
where hydraulic fractures were created in layered media in the laboratory. He
found that the shear strength of the interface was important, with hydraulic fractures
cutting across well-bonded interfaces but unable to cut across poorly-bonded ones.
Anderson (1979) confirmed this result, presenting qualitative evidence that it is the
relative tensile strengths of the materials on either side of the interface, as well as
the shear strength and normal loading on the interface itself that determine whether
a fracture will cross an interface. Other experiments describing the behavior of a
hydraulic fracture approaching an interface are described by Papadapolous and
others (1983), Biot and others (1983), Hanson and others (1978 a and b, 1979), and
Pollard (1973).
The distribution of in situ stresses play an important role in the forms of
hydraulic fractures, according to the results of several laboratory investigations.
Warpinski and others (1982) designed a test cell that allowed the radial load on a
cylindrical rock sample (20 cm in diameter and 20 cm long) to be varied along the
axis of the cylinder. Hydraulic fractures were created in homogeneous samples
where radial loads at the ends of the^cylindrical axis were 2.0 to 2.75 MPa greater
than loads at the center of the axis. They found that a stress contrast of that
magnitude alone was sufficient to inhibit growth of a hydraulic fracture out of the
zone of diminished confining stress. Similar results were obtained by Ahmed and
others (1983), who created fractures in large (1.0 m on a side) blocks of cement
grout to reduce effects of exterior boundaries.
The experiments cited above were conducted to examine effects of
nucleation and growth; other experiments address processes occurring after a
fracture has been created. Of particular interest are processes that could cause a
reduction in permeability of the fracture, either by embedment, or crushing of
proppant grains (Howard and Fast, 1970). A propped fracture mav tend to close if
the normal stress on the fracture is great relative to the strength of the formation,
leading to embedment of the proppant grains. Results from experimental studies
using either chalk or diatomite (Hartley and Bosma, 1985; Strubhar and others,
1984; Strickland, 1985) indicate that embedment is limited to roughly one-half a
grain diameter. Permeability is seriously reduced by embedment when the proppant
layer is one to two grains thick, but it is only moderately reduced when the proppant
is three grains thick, and fracture permeability is unaffected when proppant is
greater than five grains thick (Hartley and Bpsma, 1985). Studies of embedment of
proppant grains into soil have not been published.
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Proppant crushing can occur when the confining stress on the wall of the
fracture exceeds the strength of the proppant particles. According to results of
experiments reported in Howard and Fast (1970), for example, quartz sand can be
crushed at pressures equivalent to depths of two km. At greater depths a high
strength proppant, such as aluminum oxide, is generally recommended. Crushing of
quartz sand should be of no concern to the relatively shallow applications of
remediation.
Experimental investigations of hydraulic fracturing are by no means limited
to the laboratory. Field experiments of most of the applications described in the
previous section have been conducted to test new ideas or verify new theories. In
most field experiments, data are obtained from wells intersecting the fractures, but
in a few experiments data has been obtained from the fractures themselves. The
pioneering paper by Clark (1949) begins with a description of a shallow hydraulic
fracture exposed by excavation. A photograph of the excavation showing a wellbore
intersecting a horizontal fracture propped with sand provided Clark with irrefutable
evidence that fractures could be created using the process he describes.
An extensive suite of field experiments were conducted at the DOE Nevada
Test Site, where hydraulic fractures were created in ash-fall volcanic tuff and
excavated using mining procedures (Northrop and others, 1978). The objectives of
this program were to evaluate proppant distribution, examine characteristics of a
fracture intersecting an interface between different formations, evaluate results of
small-volume fractures as a tool for measuring in situ stress, and compare the size
and geometry of actual fractures to those predicted by theory. Results are described
by Warpinski (1983), Northrop and others (1978), Tyler and Vollendorf (1975), and
references cited therein.
Analyses
Hydraulic fracturing was proven as a technique of increasing the yields of oil
wells long before the physics of the process were understood. As the cost of the
fracturing operation increased, however, it became clear that analyses predicting
fracture geometry (size, shape, orientation) could be used to maximize recovery
performance and minimize expenses. Khristianovich and Zheltov (1955) recognized
that the basic physics of hydraulic fracturing involves two processes: the flow of
liquid within the fracture, and the dilation of the fracture walls due to deformation
of enveloping material. The processes are coupled, though, in that the pressure
distribution resulting from viscous losses during flow is strongly dependent on the
fracture aperture, but the aperture depends on the amount of dilation caused by the
pressure distribution. Dilation of the fracture resulting from material deformation
is calculated, with few exceptions, using elastic, or poro-elastic theory. One of the
exceptions, a study by Medlin and Masse (1982), showed that effects of plastic
deformation during fracturing are detectable in the laboratory, but are undetectable
in field applications of hydraulic fracturing in sedimentary rock. Effects of plastic
deformation are generally ignored. Fluid flow within the fracture is commonly
assumed to be laminar and governed by a linear viscous behavior. Many fracturing
fluids are thixotropic, so nonlinear flow laws have been incorporated into solutions
of hydraulic fracture propagation (Pascal, 1986).
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Two-dimensional analytical solutions to the problem of a linear viscous fluid
driving a fracture in an elastic medium have been derived that yield length,
aperture, and driving pressure as functions of time for the following geometries:
1.) Vertical, circular (Perkins and Kern, 1961; Geerstma and de Klerk, 1969
Abe and others, 1976);
2.) Horizontal, circular (Perkins and Kern, 1961);
3.) Vertical, rectangular with large ratio of length to height (Perkins and Kern,
1961; Nordgren, 1972);
4.) Vertical, rectangular with small ratio of length to height (Khristianovich and
Zheltov, 1955; Geerstma and de Klerk, 1969; Geerstma and Haafkens,
1979; Nilson, 1981; Spence and Turcotte, 1985; Nilson, 1986; Nilson and
Giffiths, 1986).
Analytical solutions show that the growth of an idealized hydraulic fracture,
that is the characteristic length (half-length or radius), L, aperture, A, and fluid
pressure, P, as functions of time, t, can be expressed as simple power functions
L = Ci f" (1.9a)
assuming loss of the injected fluid by flow through the walls of the fractures, or
leakoff, is negligible. The constants C\, €2, €3 depend on details of each solution
(e.g. references cited above), but in general they depend onproperties of the
injection system and the material containing the fracture. The superscripts b, c, and
d, are constants that depend on fracture geometry (Table 1.3). The lengths and
apertures of both types of vertical fractures, for example, are predicted to growth
faster than those of the circular fractures.
It may be possible to detect the mode of growth of a fracture using Table 1.3.
A horizontal, circular fracture is expected to grow by increasing its radius and
compressing adjacent material early in its propagation history, and thus behave as
Case A. With continued pumping, however, the fracture could cease to grow
radially and increase in volume by lifting its overburden (Case B, Table 13), either
because of a mechanical advantage achieved with increasing radius (Pollard, 1973)
or because leakoff near the tip increases the sand concentration preventing flow. In
either case, the change in mode of growth could be detected because the pressures
would begin to increase approaching a slope of unity for Case B in Table 1.3.
Similar applications of principles derived from analytical solutions of vertical
fractures have been described by Nolte and Smith (1981; 1987).
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TABLE 1.3. SOME POSSIBLE CONSTANTS IN EQ. (1.9)
Geometry b c d
Circular
Case A' 2/5 1/5 -1/5
CaseB" 0 1 1
Vertical, Rectangular
small L/H 2/3 1/3 -1/3
large L/H 4/5 1/5 1/5
* Vertical fracture, or deep horizontal fracture. Assumes dilation only by elastic
deformation of adjacent material.
" Shallow, horizontal fracture. Assumes volumetric growth only by lifting
overburden, no radial growth.
Analytical solutions require that the fracture geometry is known, and that it
is a simple geometric shape. Furthermore, details ofthe fracturing procedure, such
as effects of nonlinear fluid Theologies, transport of proppant grains, leakoff, back
stress, fracture toughness, material interfaces, and nonuniform stress distribution in
the host rock cannot be investigated by most analytical solutions. In practice, the
fracture geometry is unknown and effects of those and other details can be crucial in
a design strategy. As a result, sophisticated computer programs have been
developed that offer predictions of the shape of the leading edge of a fracture, and
are able to estimate now a wide range of design parameters affect the length,
thickness, and distribution of proppant within a hydraulic fracture. There are many
dozen, or perhaps more, published descriptions of computer programs used to
simulate hydraulic fractures. The capabilities of those descriptions are reviewed
and compared by Cleary (1988), Palmer and Luiskutty (1986), Advani and others
(1985), Mendelsohn (1984), and Veatch (1983 a and b), so a detailed review seems
unnecessary in the present work. Contributions to the development of computer
codes that predict fracture geometries in three dimensions have been made by
Luiskutty and others (1989), Vandamme and others (1988), Settari (1988), Bouteca
(1988), Acharya (1988), Morita and others (1988), Settari and Cleary (1986), Settari
(1985), Abou-Sayed and others (1984), Settari and Cleary (1984), Cleary and others
(1983 a and b), Settari and Cleary (1982 a and b), Cleary (1978a), Daneshy (1973).
Carter (in Howard and Fast, 1957) presented the first analysis of leakoff, which was
refined by Williams (1970), and generalized to include nonlinear effects by Settari
(1983). Analyses of relevant effects, including fluid rheology (Settari and Price,
1984; Cleary, 1980 a and b), back stress due to pressure of pore-fluids (Keck and
others, 1984; Cleary, 1980 a and b; Ruina, 1978), heat transfer (Meyer, 1989; Keck
and others, 1984; Griffiths and others, 1983; Settari, 1980), proppant transport
(Settari and Price, 1984; Daneshy, 1978; Novotny, 1977), and fracture toughness
(Theircelin and others, 1989; Morita, and others, 1988; Settari, 1985; van Eekelen,
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1980) are commonly included in computer programs analyzing fracture propagation.
One of those programs, described by Boone and others (1989), represents fracture
shape, pore-fluid pressure, and stress in the vicinity of a vertical fracture as a color
image that changes with time on a video monitor.
Interactions between a hydraulic fracture and the ground surface, a topic of
particular interest to the proposed applications, have been analyzed by Pollard and
Holzhausen (1979), and Narendran and Cleary (1983). In related work, interactions
between multiple hydraulic fractures have been analyzed by Narendran and Cleary
(1984), and Hanson and others (1979), and consequences of fracture interactions
have been utilized in design concepts by Warpinski and Branagan (1989), Ernst
(1980), and Huck and others (1980). Theoretical solutions of a fracture
encountering interfaces between materials of differing properties are described by
Lam and Cleary (1984), Weertman (1980), van Eekelen (1980), and Hanson and
others (1978 a and b).
In addition to forecasting the geometry of hydraulic fracture, the results of
theoretical analyses are matched against field measurements, such as injection
pressure or deformation of the ground surface, to estimate geometry after the
fracture has been created. Methods of inverting pressure records were developed in
a series of papers by Nolle and Smith (Nolte, 1988 a and b, 1984,1982,1979; Nolte
and Smith, 1987,1981), and other investigators (e.g. Crockett and others, 1989) have
made contributions as well. The inversion of measurements of surface
deformation-comrnonly obtained using tiltmeters-to estimate the location,
orientation, and dimensions of a hydraulic fracture was described by Davis (1983),
and applied by Holzhausen and others (1985 a and b).
Another application is the optimization of fracture designs, where the output
of a fracture simulator is used as the input of a program that evalutes flow to the
fracture (Anderson and Phillips, 1988) and possibly economic considerations, such
as costs of fracturing materials and rate of return (Howard and Fast, 1970; Veatch,
1983 a and b). A simple method of optimization, based on the cumulative volume
of recovery and described by Elbel and Sookprasong (1987), is relevant to the
application of hydraulic fracturing during remediation.
The work cited above includes some notable contributions, but it is by no
means an exhaustive survey of papers that address useful applications of hydraulic
fracturing; there are many more. With few exceptions, those papers are targeted to
applications where hydraulic fractures are created in rock at depths in excess of
several hundred meters. Use of the significant body of existing information for the
purposes of this research, therefore, will depend on the extent to which hydraulic
fracturing of rock at great depth resembles hydraulic fracturing of soil at shallow
depths.
The Hydraulic Fracture as a Problem
Hydraulic fracturing of soil at shallow depths has, in the past, generally been
regarded as a problem. This is because many soil engineering techniques, which
require increasing ambient pore pressures, will be ruined if they induce hydraulic
fracturing-with the exception of hydraulic fractures created to measure in situ
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stresses in soil (Leach, 1977; Massarsch and others, 1975; Tavenas and others, 1975;
Bjemim and Anderson, 1972).
Applications
The collapse of a dam is perhaps the most severe consequence of accidental
hydraulic fracturing. One example occurred at the Teton Dam, Idaho, where
excessive rates of seepage were noted downstream of the dam shortly after the
reservoir behind it was filled in 1976. Seepage rates increased and soon a muddy
flow appeared at the downstream toe of the dam. The flow eroded a gully, which
cut through the dam from the downstream toe upward to the crest. Fourteen people
died and 400 million dollars of property damage resulted from the subsequent
failure. An investigation of the tragedy concluded that hydraulic fracturing, due to
increases in pore pressure accompanying filling of the reservoir, probably
contributed to the dam failure (Jaworski and others, 1979; and references therein).
Elsewhere, hydraulic fracturing was attibuted as the cause of leaks that ultimately
led to the failure of 14 dams in Oklahoma and Mississippi, and other darns in
California, Brazil, and China, according to Sherard (19/2), and Jaworski and others
(1979).
Ironically, hydraulic fracturing was known to workers in the oil industry as a
problem before it was used to stimulate wells. Yuster and Calhoun (1945)
recognized that a sudden increase in the rate of inflow during a waterflooding
operation (a technique of injecting water in one well to sweep oil toward a recovery
well) without an increase in pressure could be caused by hydraulic fracturing, or in
their terminology, pressure parting. Hydraulic fracturing caused by excessive
injection pressures can reduce the area swept out by the waterflood. New methods
of estimating the maximum allowable pressure without causing fracturing during a
waterflood continue to be developed (Singh and Agarwal, 1990).
In situ permeability of soil is commonly calculated by holding a constant
pressure and measuring the rate at which water flows into a borehole. Bjerrum and
others (1972) point out that hydraulic fractures can be created if the borehole
pressure used in a permeability test is greater than a critical value, which they relate
theoretically to the overburden load and these soil properties: poisson ratio,
coefficient of lateral pressure, tensile strength, and compressibility. They claim that
if hydraulic fracturing goes undetected dunng a test, values of permeability •
calculated from the resulting data can be as much as three orders of magnitude
greater than the actual in situ permeability.
In some applications, hydraulic fracturing can be either an asset or a liability,
depending on the details of the application. The disposal of liquid waste by
injection into wells, outlined in the previous section, is one example. Injection
grouting is another. Some designs require grout to uniformly permeate pores in the
vicinity of an injection point (borehole), and the specifications of these designs
cannot be met if grout flows preferentially into hydraulic fractures (Wong and
Farmer, 1974). Moreover, hydraulic fracturing during grouting could result in
problems, such as deforming a neighboring foundation, lifting a concrete cut-off
from its seat, or markedly increasing the amount of grout required to complete a job
(Morgenstern and Vaughn, 1963). Interestingly, however, hydraulic fracturing can
29
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also play a useful role in grouting practices. Zhang (1989) indicates that
intentionally creating hydraulic fractures during grouting increases the rate of
penetration of grout in some formations, and it effectively seals formations by
creating an interlocking network of grout sheets. The technique is especially useful
in formations, such as karstic limestone cut by clay- and sand-filled caves, where
conventional grouting techniques are ineffective. Moreover, the load-bearing
capacity of large diameter piles in silty sand is increased by creating grout-filled
fractures following pile driving, according to Zhang (1989).
Experiments
The goal of many experimental investigations of the applications described
above is to predict the pressure at which hydraulic fracturing occurs under a
particular set of laboratory conditions. A noteworthy set of experiments is described
by Jaworski and others (1979 and 1981), who examined hydraulic fractures in the
vicinities of model wellbores and dam faces. They injected water into cubic blocks
of soil, slowly increasing injection pressure and recording flow rate until a marked
increase in flow rate indicated the onset of fracturing. This technique is common
for other investigations of hydraulic fracturing of soil, although it differs from
studies of hydraulic fracturing of rock (e.g. Medlin and Masse, 1979; Zoback and
others, 1977; Haimson and Fairhurst, 1967,1970; Harrison and others, 1954; Scott
and others, 1953), which hold flow rate constant and monitor pressure. Jaworski
and others (1979) cut slots in the faces of samples and applied pressure to the slots
to simulate the role of joints or pre-existing cracks as stress concentrators. Cutting a
slot in a sample to nucleate a fracture is common practice in tests designed to
measure fracture toughness, as mentioned above.
Significant results of Jaworski and others (1979 and 1981) are as follows:
1. The pressure required to induce hydraulic fracturing from a cylindrical
borehole is linearly related to confining stress. A similar relation was observed for
the pressure required to induce hydraulic fracturing in rock by Medlin and Masse
(1979), and Haimson and Fairhurst (1967,1970).
2. A large amount of variation was observed in the fracturing pressures,
suggesting that fracturing pressure from an open borehole would be difficult to
predict. Fracturing pressure was affected by many factors, such as pre-existing flaws
in the soil, that could neither be eliminated nor characterized.
3. The fracturing pressure depended on soil properties, increasing with the
number of blows used to compact the sample. It increased as the water content
decreased.
4. A discontinuity, such as a slot, will nucleate a hydraulic fracture in soil,
and the presence of the discontinuity reduces the pressure required to induce
fracturing.
In a later study, Mori and Tamura (1987) created hydraulic fractures from
cylindrical holes in cylindrical soil samples, using much the same technique as
Jaworski and others (1979). Their results confirm the linear relation between
30
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fracturing pressure and confining stress. Mori and Tamura conducted tests using
various rates of injection, concluding that the fracturing pressure increased as the
rate of pressurization increased. Hydraulic fracturing pressures in rock also
increase with rate of pressurization, according to Hairnson and Fairhurst (1967 and
1970), and Zoback and others (1977).
In one suite of tests, Mori and Tamura applied an axial load that was less
than the radial load. Hydraulic fractures were formed either inclined or normal to
the axial hole, leading Mori and Tamura to conclude that shear failure controls
hydraulic fracturing of cohesive soil. This conclusion contradicts a large body of
solid evidence for hydraulic fracturing being a tensile phenomena in other materials.
It seems likely that the peculiar orientations of fractures observed by Mori and
Tamura resulted from boundary conditions on their test samples. As Medlin and
Masse (1979) point out, a cylindrical hole will tend to create a hydraulic fracture
containing the axis of the hole. The fracture will change orientations, however, as it
grows away from the hole and into a region of different stresses-such as would have
been the case under the applied stress conditions used by Mori and Tamura. Large
changes in orientations during propagation are accomplished by curving, twisting, or
breaking into segments (Pollard and others, 1982), resulting in irregular or intricate
fracture forms. The results that are briefly described by Mori and Tamura are
consistent with behavior as tensile, or Mode I fractures (Lawn and Wilshaw, 1975),
propagating in an abruptly changing stress field; their conclusion that hydraulic
fractures in cohesive soil behave as shear failures is unconvincing.
An apparatus used to create hydraulic fractures is described by Sun and Ting
(1988), who claim that it offers advantages over apparatuses described previously.
Their device is designed to create a hydraulic fracture from a cylindrical hole in a
cylindrical sample, which is a standard configuration. The principal novelty appears
to be that the pressure acting on the cylindrical hole can be controlled
independently from pore pressure in soil adjacent to the hole. This is done by lining
the hole with a permeable layer and then inserting a flexible bladder along the
length of the lined hole; inflating the bladder controls pressure on the wall of the
hole, whereas wetting the liner controls pore pressure in the soil.
Analyses
Studies seeking methods of preventing fracture initiation commonly employ
analyses of stresses in the vicinity of pressurized holes. Hydraulic fracturing is
assumed to occur when tensile stresses exceeds the tensile strength of the material.
Analyses of this type were first based on elastic solutions and used to predict
hydraulic fracturing of rock (e.g. Harrison and others, 1954; Schiedegger, 1960;
' ~>64; Haimson and Fairhurst, 1967),
Kehle, 1964; Haimson and Fairhurst, 1967), but have been applied directly to
predict hydraulic fracturing of soil (Mori and Tamura, 1987; Jaworski and others,
1979 and 1981). Jaworski and others (1979) point out some discrepancies between
theory and data, not the least of which is a large amount of variability in the data.
This observation leads them to conclude that the criteria represented by the simple
theory were insufficient to reliably predict the pressure required to cause fracturing
from an open borehole in soil.
31
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Bjemim and others (1972), who were concerned with inhibiting hydraulic
fracturing during field permeability tests, included in their analysis the effect that
driving a piezometer would have on state of stress prior to fracturing. They assume
that when a piezometer is inserted, the soil adjacent to it yields, and the radial and
circumferential stresses change by an amount that depends on the compressibility of
the soil. The radial stress always increases when a piezometer is inserted; by a
factor of 1.5 for highly compressible soil to as much as 5.2 for relatively
incompressible soil. The circumferential stress at the wall of the piezometer,
however, will decrease by a factor of as much as 0.6 for highly compressible soil, or
increase by as much as 2.1 for relatively incompressible soil. Deformation resulting
from pushing a piezometer into the ground, thus, could either increase or decrease-
depending on the compressibility of the soil-the pressure required to initiate
fracturing, according to the analysis of Bjemim and others (1972).
An analysis of the conditions required to create a hydraulic fracture
specifically in unconsolidated sediment is presented by Horsrud and others (1982),
who use coupled elastic and plastic solutions. Fracture initiation pressures can be
reduced by plastic deformation to roughly 10 percent less than that predicted by
elastic theory, according to their results. Medlin and Masse (1979) presented both
experimental and theoretical evidence confirming that plastic deformation around a
borehole reduced the pressure required for fracture initiation.
Predicting the maximum pressure achievable without causing a hydraulic
fracture during injection grouting has been an elusive task. The limiting pressure is
recognized to increase with depth; values of 22.6 to 102 kPa/m (1.0 to 4.5 psi/ft) of
depth are used in regulations defining maximum allowable pressure (Dickinson,
1988). Those gradients apparently are determined empirically. Morgenstern and
Vaughn (1963) suggest that a Mohr-Coulomb failure criterion could be adopted to
predict hydraulic fracturing during grouting, although the mode of failure-shear-
implied by that criteria is unfounded for hydraulic fractures. The analysis of Wong
and Farmer (1973) assumes tensile failure and uses an elastic analysis, which
includes pore-pressure effects, to examine the initiation of a hydraulic fracture
during grouting. This approach is consistent with established methods (e.g.
Haimson and Fairhurst, 1967), although it is unclear how well it predicts grouting
pressures.
Wong and Farmer (1973) present both a stress analysis and an energy
balance approach to analyze the propagation of hydraulic fractures formed during
injection grouting. Their analyses assumes that many hydraulic fractures radiate
outward and are closely spaced within a certain distance from the borehole. In
contrast, the majority of published analyses as well as field and laboratory evidence
suggests that only one, or at most a few, fractures grow away from the borehole.
Wong and Farmer (1973) indicate that their analyses predict pressures during
propagation that greatly exceed those observed in the field.
32
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SECTION TWO
LABORATORY EXPERIMENTS OF HYDRAULIC FRACTURING OF SOIL
The purpose of studying hydraulic fracturing of soil has traditionally been to
provide methods of preventing fracture initiation during geotechnical engineering
operations. This is because hydraulic fracturing can result in failures during, for
example, injection grouting, permeability testing, deep-well injection, or dam
construction. As a result of the focus on fracture initiation little is known about the
physical appearance, mechanical behavior, or methods of analyzing the growth of a
hydraulic fracture in soil.
In contrast, a wide range of useful applications has been developed for
hydraulic fracturing of rock. These applications have prompted a broad scope of
investigations; consequently a great deal is known about hydraulic fractures in rock.
The goal of the following section is to apply methods of studying hydraulic
fractures in rock to aid in understanding hydraulic fractures in soil. Laboratory tests
were conducted using a bench scale apparatus designed to create hydraulic fractures
in soil. Observations from the laboratory tests, including the appearance of the
fractures and injection pressures as a function of time and moisture content, are
described in the following section.
During the laboratory tests, hydraulic fractures were created by injecting
fluid into samples confined within a triaxial loading cell. The fractures were
observed directly by looking through a transparent loading plate in the experimental
apparatus, and phenomena related! to fracturing were observed indirectly by
measuring the pressure of injected fluid as a function of time. The direct
observations, combined with descriptions of fracture surfaces from samples split
open after testing, yield the important details of the appearance of a hydraulic
fracture in clay. Records of injection pressure as a function of time are used to
obtain critical pressures at which fracturing takes place. The critical pressure varies
over an order of magnitude, depending on the moisture content of the clay and
other factors. Moreover, shapes of the records also depend on moisture content,
and the nature of this dependency will be described in the following section. Before
the observations can be described, it will be necessary to explain the design of the
apparatus, the techniques of preparing a sample, and the procedures of conducting a
test.
EXPERIMENTAL DESIGN
The experiments were designed to create hydraulic fractures by injecting
glycerin into rectangular blocks of soil confined in a triaxial pressure cell. An
experimental apparatus and testing procedure were developed to reveal physical
characteristics of the fractures ana to yield data describing the fracture toughness of
soil. Rhodamine dye was added to the glycerin to highlight areas of the fracture
surface wetted by the fluid. The pressure of the injection fluid was monitored as a
function of time so that fracture toughness could be calculated. Details of the
33
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design of the apparatus and the method of sample preparation are described in the
following sections.
Apparatus
The experimental apparatus consists principally of a pump system, a fracture
cell, and a data acquisition computer (Fig. 2.1). The pump system is used to inject
fluid at a constant rate into a sample contained in the fracture cell. Typically, the
pressure of the injected fluid increases until fracturing occurs, then decreases during
fracture propagation. The computer is used to monitor injection fluid pressures as a
function of time and to control the flow rate of the pump.
The fracture cell is a rectangular chamber (inside dimensions are 10 cm by
10 cm by 39 cm) with one moveable side that is used as a loading plate (Fig. 2.2).
The loading plate is transparent, so that the interior of the cell can be inspected
during a test. The other five sides of the chamber are lined with neoprene bladders.
The three principal stresses on the sample are controlled independently by adjusting
air pressures in the bladders.
A hole in the loading plate allows access to a soil sample inside the chamber.
A spacer plate, placed between the loading plate and the sample, contains a
pressure-tight fitting for tubing three mm in diameter. The tubing extends from the
pump through the loading and spacer plates and into a thin slot cut in the sample
The pump used to inject fluid into the sample consists of two hydraulic
cylinders dnven by a threaded rod attached to a stepper motor. Hydraulic fluid is
forced out of the cylinders and into the lower chamber of a pressure interface
device, which thereby forces dyed glycerin out of an upper chamber and into the
fracturing cell (Fig. 2.1). The flow rate of the pumping system is controlled by
regulating the rate of rotation of the stepper motor. Other details of the design and
operation of the pumping system are given in Murdoch and others (1987).
A flow rate of 0.225 ml/min was used for all the tests described in the
following pages. The Reynolds Number associated with flow of glycerin in the slot
at that flow rate is 0.01, and in hydraulic fractures it was less because the aperture
of the fractures was less than that of the slot. Laminar flow was assumed to occur in
the fractures based on the small Reynolds Number.
Pressure of the injection fluid as a function of time was the primary data
recorded during each test. A transducer, accurate to 0.3 kPa, positioned roughly 20
cm upstream of the slot was used to measure pressure once every 200 msec.
Pressure losses due to flow from the transducer to the tip of the starter slot are on
the order of the accuracy of the transducer, according to calculations using standard
methods (Streeter, 1971), so the pressure measured at the transducer will be taken
to be the pressure within the slot.
The injection pressure was recorded as a disk file and it was displayed as a
function of time on a video monitor. Accordingly, during a test it was possible to
34
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000
o
000000000
ooooooooo
000000000
Figure 2.1. Apparatus used for hydraulic fracturing experiments. A. Fracturing cell;
B. Pressure transducer; C. Gauges and regulators of confining
pressure; D Fluid pressure interface; E. Pump; F. Computer for data
acquisition and control
35
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bladder
Loading
Plate
to pump
Figure 2.2. Cut-away sketch of hydraulic fracturing cell.
36
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observe the pressure record on the monitor, and to see the trace of a hydraulic
fracture on the edge of the sample.
Physical Characteristics of the Soils
Two soils were used in the laboratory experiments. Most experiments were
conducted using a yellow-brown colluvial clayey silt derived from a pit adjacent to
the Center Hill Research Facility, Cincinnati, Ohio. That soil will be termed the
Center Hill clay. Approximately one half m3 of moist Center Hill clay was
excavated and stored in air-tight drums, which served as a repository of sample
material during testing. Several experiments were conducted using a different soil, a
light-brown alluvial silt obtained from an exposure overlooking the Ohio River near
the River Downs Racetrack, Cincinnati, Ohio. That material will be termed the
River Downs silt.
All samples were molded into shape for the fracturing experiments. A suite
of standard analyses was conducted on remolded Center Hill clay and River Downs
silt to determine their basic physical characteristics. Two samples of each soil were
analyzed, and they are nearly identical in physical characteristics.
The Center Hill clay is a type CL soil, according to the USCS classification
based on Atterburg Limits (Table 2.1). It behaves as a plastic material in Atterburg
tests over the range of moisture contents used during the fracturing tests (moisture
contents were between the liquid and plastic limits). The River Downs silt is type
ML, and it shows plastic behavior over a much narrower range of moisture contents
(Table 2.1). Moisture contents during fracturing tests of the River Downs silt were
less than the plastic limit of that material.
Analysis of grain sizes indicates that the Center Hill clay is dprninantly silt
and lesser amounts of clay (Table 2.1; Fig. 2.3). Trace amounts of limestone
fragments occur in the soil naturally, but they were removed before the soil was
used in the fracturing tests. The River Downs silt is mostly silt, with minor amounts
of clay. Siderite concretions occur in the silt. These were removed by sieving.
Results from Proctor Tests (ASTM D698) indicate that the maximum density of the
Center Hill clay occurs when the moisture content (wt. water/wt.solid) is!9.7%.
The moisture contents of samples used in the fracturing tests ranged from 19 to
33%; typically greater than optimum moisture content. Bulk densities of samples
used in the fracturing tests are either equivalent to or slightly greater than densities
from the Proctor Tests (Fig. 2.4).
Sample Preparation
Techniques of preparing soil samples were developed to yie
rectangular samples of a desired composition, water content and c<
ield uniform
[consolidation
history. Samples were prepared in rectangular molds the same size as the inside of
the fracturing cell. A mold resembled a rigid box with a top that moved like a piston
to consolidate the sample. Geotextile along two sides of the sample facilitated
drainage during consolidation.
37
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TABLE 2.1. CHARACTERISTICS OF SOILS USED IN THE STUDY
CENTER HILL CLAY
Atterburg Limits CHI CH2 AVE
(wt. water/wt. solid)
Liquid Limit 0.429 0.438 0.433
Plastic Limit 0.198 0.200 0.199
Plastic Index 0.231 0.238 0.234
Shinkage Limit 0.188
Grain size
Gravel 0 0
Sand 0.03 0.03
Silt 0.61 0.62
Clay 0.36 0.35
Proctor Test (ASTM D698)
Moisture Content of Greatest Density: 0.197
Maximum Dry Density: 1.68 gm/cm3 (104.7 lb/ft3)
Maximum Wet Density: 2.01 gm/cm3 (126.0 lb/ft3)
RIVER DOWNS SILT
Atterburg Limits RD1 RD2 AVE
Liquid Limit 0.221 0.234 0.227
Plastic Limit 0.208 0.200 0.204
Plastic Index 0.013 0.034 0.023
Grain size
Gravel 0.02 0.0
Sand 0.05 0.06
Silt 0.81 0.82
Clay 0.12 0.12
Proctor Test (ASTM D698)
Moisture Content of Greatest Density: 0.165
Maximum Dry Density: 1.73 gm/cm3 (108.2 lb/ft3)
Maximum Wet Density: 2.06 gm/cm3 (128.7 lb/ft3)
38
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I
£
h
~
«
0
cm
1UU
90
80
70
60
50
40
30
20
10
ft
& Center Hill clay
J*
i
r^
•
0.001
0.010 0.100
Grain size (mm)
1.000
A
ao
100
90
80
70
60
50
40
30
20
10
River Downs silt
0.001
0.010 0.100
Grain size (mm)
1.000
Figure 23. Grain-size distribution of soils used in the lab experiments.
39
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o
o
• Proctor test
O Fracture test
2.05
1.95
1.85
1.75
0.16 0.20 0.22 0.24 0.26 0.28 0.30 0.32
Moisture (wt. waler/wt. solid)
2.10
a 2.05
2.00
i
Q
11.
River Downs silt
Proctor test
Fracture test
95
1.90 ' • • • •
0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22
Moisture (wt. water/wt. solid)
Figure 2.4. Bulk density as a function of moisture content from Proctor tests and
fracture tests.
40
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Two methods were used to prepare a sample; one that involved compaction
and consolidation, and another that involved compaction alone. When samples
were to be consolidated, a layer of soil roughly 2 cm thick was compacted with 30 to
40 blows of a drop-weight hammer. The upper surface of the layer was scarified to a
depth of 0.5 to 1.0 cm and another layer of similar thickness was added and
compacted. That process was repeated until the soil in the mold was 10.5 cm thick.
Four sample molds were filled and then placed beneath the corners of a pallet upon
which there were four drums of water. The weight of water in the drums exerted a
vertical stress of 69 kPa on the samples. Samples were consolidated under that load
for as many as 14 days.
A pneumatic press (SoilTest Model CN-425A) was used to load samples that
were prepared only by compaction. The press was modified by attaching a special
rectangular load shoe (5.8 cm x 9.8), so that the entire width of the sample mold was
loaded by each blow. A layer of soil 2 cm thick was compacted by 80 blows from the
press, and a pressure of 139 kPa was applied during each blow. The layer was
scarified and another layer added and compacted. That process was repeated until
the sample mold was filled to a depth of roughly 12 cm. The sample was removed
from the mold and trimmed with a wire saw to a height of 10 cm.
A narrow slot (0.04 mm in aperture) was cut through the middle of each
sample (Fig. 2.2) using a special blade-like tool. The slots were rectangular in shape
with the long axis of the rectangle spanning the width of the sample. The short axis
of the rectangle, or slot length, ranged from 12 to 72 mm depending on the size of
the blade used to cut the slot. A hole 3 mm in diameter was cut along the center of
the long axis.
The purpose of the slot was to provide a starting fracture that was much
larger than existing flaws in the sample. The slot was necessary because
measurements of critical stress intensity require knowing the length of a fracture
when it begins to propagate (Tada and others, 1985). Natural discontinuities
resembling fractures several mm long were common in the samples, so a starter slot
of at least 12 mm in length was used to nucleate hydraulic fractures.
A film of silicone grease was applied to the surfaces of the sample to inhibit
leaking of the injected fluid where a fracture intersected the sample surface. The
grease provided an adequate seal and, because it was nearly transparent, allowed
the trace of the fracture on the surface of the sample to be observed through the
plexiglass loading plate.
The starter slot was filled with glycerin prior to each test to ensure that air
was expelled from the slot. The loading plate was then secured and the cell
positioned so that the starter slot was horizontal, eliminating a static pressure
gradient normal to the slot (Fig. 2.2).
Confining pressures were applied to the sample by inflating neoprene
bladders in the fracturing cell with air. Three sets of pressure gauges and regulators
provided independent control of each of the three confining stresses. Most tests
were conducted using confining pressures between 35 and 70 kPa (5 to 10 psi).
Typically, the confining pressure normal to the starter slot was 20 percent less than
the other two confining pressures, which were equal to one another. This loading
41
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configuration was used to promote the growth of a hydraulic fracture in the plane of
the starter slot. If all three confining loads were equal or if the minimum load was
in the plane of the starter slot, the hydraulic fracture would twist or curve yielding
complicated forms that were difficult to duplicate.
A Typical Test
Events occurring during the fracturing tests followed a consistent pattern.
..„ r illy, pressure increased nearly linearly with time early in the test. At some
point the slope of the pressure record began to flatten, reaching zero slope as the
pressure peaked and then becoming negative as the pressure decreased with
continued injection.
A thin (on the order of 0.05 mm) fracture trace typically could be first seen
on the surface of the sample roughly at the time of maximum injection pressure.
Most traces were nearly straight, although in many cases they consisted of a family
of straight, sub-parallel segments arranged either en echelon or staggered. The
location of the fracture tip was difficult to establish because the aperture tapered
gradually until it became undetectable. Thus the tip could be located within
approximately one cm, but the trace was too thin to locate the tip precisely.
The fracture trace grew at cm-long intervals, initially appearing as lines so
thin they could barely be seen and then slowly widening to narrow slits with a
recognizable aperture. Growth appeared essentially the same when magnified
roughly ten times; greater magnification was impossible using available instruments.
Although it was impossible to follow the tip of the fracture trace during propagation,
the average rate of propagation could be determined from the total fracture length
and the total time of injection; it was on the order of 0.5 to 1.0 mm/sec. Medlin and
Masse (1984; fig. 9), who used an apparatus similar to the one described above and
injected at 0.5 ml/sec (roughly twice the flow rate used here), report that the
propagation rate decreases with time from 2 mm/sec early in a test to 0.2 mm/sec
late in the test.
A fracturing test was terminated by stopping the pump and opening a
pressure relief valve, which allowed the injection fluid to flow back into the injection
tube as the fracture closed. The dyed glycerin was promptly removed from the
fracture to inhibit staining of the sample by flow unrelated to the process of
hydraulic fracturing.
The sample was removed from the fracturing cell and pulled open along the
plane of the fracture. A rough, finely-dimpled surface was formed where pristine
portions of the samples were pulled apart. In contrast, the surface of the hydraulic
fracture was relatively flat, or marked by angular steps. This contrast is important
because the leading edge of the hydraulic fracture was undyed, but could be readily
distinguished from pristine clay by the difference in textures.
42
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APPEARANCE OF A HYDRAULIC FRACTURE IN CENTER HILL CLAY
More than five dozen experiments were conducted with the Center Hill clay
using a variety of loading conditions, sample preparation techniques, moisture
contents and durations of consolidation. Hydraulic fractures were created during
every experiment, except in a few cases when the injection tube was plugged with
clay as it was inserted. Examination and description of the appearance of each
fracture revealed features of the fractures that occur in virtually every case. Most of
those features exhibited slight variations, depending on the conditions of the test,
but they were consistently identified in some form. The features were described in
notes and they were traced onto transparent mylar. In the following section, the
typical attributes will be used to describe an idealized hydraulic fracture in the
Center Hill clay.
In gross form most fractures were nearly symmetric with respect to the axis of
the starter slot. The fractures created during the toughness experiments were
roughly planar; other experiments resulted in fractures that curved or twisted into
complicated forms that will be omitted from the following descriptions. The half-
length of a fracture (measured from the hole along the axis of the slot to the leading
edge) was roughly uniform along the width (measured parallel to the axis of the
starter slot), although half-lengths were slightly shorter near the edges than in the
center of most fractures.
Some fractures were asymmetric with respect to their width, that is their
lengths were several cm greater along one side than along the other. In some cases,
the lengths were greater on the side of the injection tube, whereas in other cases the
side opposite the injection tube was longer. In virtually all cases, however, the
asymmetry was mirrored across the axis of the starter slot. Slight leakage at one
side of the sample, either out of the slot or out of the fracture itself, apparently
caused this type of asymmetry. Leakage in most instances occurred during
Eropagation, according to direct observations through the loading plate, so it had
ttle effect on the early stages of nucleation and growth of the fracture.
The typical test revealed a continuous, parent fracture adjacent to the starter
slot. The parent fracture broke into discontinuous, lobate planes with increasing
distance from the injection hole. Dye staining formed irregular dendritic patterns
near the ends of the lobes, but the leading edge of the fracture was beyond the zone
reached by the dyed glycerin and is unstained. These features define four distinct
zones, arranged in increasing distance from injection hole: 1.) starter slot; 2.) parent
fracture; 3.) fracture lobes; 4.) and an unwetted zone at the leading edge.
Starter Slot
The starter slot appears on the surface of a cleaved sample as a smooth strip
with a shallow trough, which is one half of the injection hole, along the axis of the
strip (Fig. 2.5). The width of the strip depends on the length of the blade used to cut
the slot.
43
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J_aJ
0
10cm
Figure 2.5. Photograph and sketch of the surface of a hydraulic fracture, a.) starter
slot; b.) parent fracture; c.) lobes; d.) unwetted tip. Lines on the
sketch are prominent linear features on the fracture surface. Heavy
lines represent overlap of fracture lobes, as shown in the inset.
44
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Parent Fracture
The main, or parent hydraulic fracture appears as a continuous dyed surface
that lies roughly within the plane defined by the starter slot (Fig. 2.5). Locally,
parent fractures are twisted or curved, with most of the distorted regions located
near the edges of a sample (top of Fig. 2.5). Those distortions are minor, however;
the fracture rarely deviates by more than 10° from the orientation of the slot.
The surface of a parent fracture is generally flat, but in detail it is marked by
irregularities that have as much as one cm of relief. Some of the irregularities are
rounded bulges or dimples. More typically the surface is marked by elongate
features; narrow ridges, grooves or angular steps (fig. 2.5). Ridges and grooves
typically have one mm or less of relief and the fracture surface on either side of
them lies in the same plane. Steps are where the fracture surface abruptly changes
height over a narrow interval.
Steps range in size from less than one mm high and several mm long, to 5
mm high and nearly as long as the entire fracture (Fig. 2.6). Lengths of ridges and
grooves are on the order of several mm, typically shorter than the steps. The
direction of the long axes of the linear features differ, depending on where the
feature occurs on the fracture surface. Where they occur near the starter slot, the
long axes are perpendicular 19 the axis of slot. At the other end of the fracture, near
the tip, the steps are perpendicular to a tangent across the leading edge. Within the
parent fracture, the axes are sub-parallel to one another and within 20° of the line
formed by the edge of the sample. As the edge of the sample is approached,
however, the linear features curve outward at increasingly higher angles, and at the
edge itself the axes are inclined 45° or more (Fig. 2.6).
Steps, grooves and ridges on fracture surfaces are by no means unique to
hydraulic fractures in soil; they have been described on the surfaces of tensile
fractures in a variety of materials, ranging from glass to metal, plastic or rock
(Williams, 1984; Pollard and others, 1982, and references cited therein; Pollard,
1978; Pollard and others, 1975; Daneshy, 1973; Tetelman and McEvily, 1967). A
common interpretation is that the steps indicate the direction of propagation when
the leading edge of the fracture is at the location of the step (Pollard and others,
This interpretation is consistent with the patterns of steps on the surfaces of
fractures in soil. The typical pattern of steps is shown in Figure (2.7), from which
the leading edge at several different times during growth is inferred. The inference
suggests that propagation began near the center of the slot and the fracture grew
toward the edges as it increased in length (Fig. 2.7). Upon reaching the edge of the
sample, the fracture grew roughly parallel to it. Propagation at the edges of the
sample apparently lagged behind the center because the direction of growth there
has an outward component. Thus, the fracture trace on the surface of a sample,
viewed through the plexiglass loading plate, was oblique to the direction of
propagation of the fracture contained within the sample. In some cases, as in Figure
2.5, linear features suggest that propagation began near one side of the sample.
Directions of propagation were slightly divergent within the fracture, and
strongly divergent near the edges. As a result, all except the center-most of the
45
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5
cm
10
Figure 2.6. Surfaces of three hydraulic fractures of various lengths. Lines on
fracture surfaces are linear features and hatch marks on the lines
indicate the lower side of a step. Fractured, but undyed areas are
stipled. Heavy lines indicate overlap of lobes, as in Fig. 15.
46
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Figure 2.7. Idealized diagram of the position of the leading edge and the path of
propagation during growth of a hydraulic fracture in the experiments.
Inferred from the results of several dozen tests.
47
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propagation paths eventually fan outward to intersect the edges of the sample (Fig.
A few steps on fracture surfaces were nearly parallel to the axis of the starter
fracture-at a high angle to the steps that indicate propagation direction (Fig. 2.6a
and b). The axes of the high-angle steps are several cm in length and they are nearly
straight to gently arcuate. Their location is variable; some of them occur in the
vicinity of the starter slot, whereas others are in the vicinity of the leading edge. In
many cases, a high-angle step on a fracture surface is related to a smaller fracture
that either overlies or underlies the surface. The origin of the high-angle steps is
unknown, but they are similar to rib marks, which were observed by Daneshy (1973),
who used them to infer the position of the leading edge of the hydraulic fracture
prior to the termination of a test.
Lobes
A continuous parent fracture breaks into a family of fracture lobes as the
leading edge is approached from the starter slot (Fig. 2.6 and 2.7). The transition
from continuous fracture to discontinuous lobes is smooth, marked by slight twisting
or curving of lobes with respect to the parent fracture. Lobes occurred in virtually
all the tests, although shapes and sizes of the lobes differ markedly between
samples.
Lobes range from nearly equant to highly elongate, with aspect ratios from
1:1 to 1:10. In a few cases, fracture lobes originated at the starter slot and the entire
fracture consisted of a family of elongate lobes; a continuous parent fracture was
absent (upper right side of rig. 2.6c). The major axes of elongate lobes are within a
few degrees of parallel to the edges of the sample.
Fine steps or ridges are present on the surfaces of fracture lobes. Axes of
steps are parallel to the major axis near the center of a lobe, but curve outward as
the leading edge is approached. At the leading edge of a lobe, the steps are nearly
perpendicular to the edge. The elongate lobes, therefore, are inferred to have
widened as they increased in length.
As many as several dozen lobes are present in any given sample, and they
range in size over more than an order of magnitude. The width of the largest lobe is
typically on the order of several cm, roughly one third of the width of the sample.
Intermediate-sized lobes, whose widths are on the order of several mm, occur along
the leading edges of the larger lobes. Other lobes that are even smaller, roughly one
mm in width, fringe the edges of the intermediate-sized lobes.
Several of the larger lobes, the ones bounded by unfractured soil, occur in
each sample. Each one of these lobes is in close proximity to one or more
neighbors. Three types of spatial arrangement between neighboring lobes were
identified during the tests. They are as follows (Fig. 2.8):
1. Neighboring: Lobes are coplanar, and their edges are separated by a narrow
band of unfractured material.
48
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Figure 2.8. Idealized configurations of commonly-occurring fracture lobes, a.
Neighboring lobes; b. En echelon overlapping lobes; c. Staggered
overlapping lobes; d. Superposed lobes.
49
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2. Overlapping: Lobes lie in slightly different planes, and their edges slightly
overlap.
3. Superposed: Lobes are roughly parallel. When viewed normal to the plane of
the fracture, one lobe entirely overlaps the adjacent lobe.
Neighboring and overlapping lobes are the most common, occurring in nearly
all samples. Typically, the wider lobes tend to be overlapping whereas the smaller
ones are neighboring. The sense of overlap between lobes was consistent in some
samples, so that traces of the lobes would appear en echelon on a surface normal to
the long axis of the sample. In other cases, however, the sense of overlapping
reversed itself, so that traces of lobes would appear staggered on the normal surface.
Typically, the sense of overlap was inconsistent, with some lobes en echelon and
others staggered in any given sample (Fig. 2.6).
Superposed lobes, or pair of lobes with a large amount of overlap, occurred
most commonly when the magnitudes of the applied stresses differed by a relatively
large amount. Superposed lobes were rare in tests where the applied load normal to
the starter slot was 80 percent of the loads parallel to the slot (the relative loading
typical of all tests described in Section 3). Highly overlapping lobes were more
common, occurring in roughly half the samples, when the normal load was between
30 and SO percent of the parallel load.
Steps on the surfaces of superposed lobes were used to infer the path taken
by the lobe as it grew, and some of the results are rather surprising. Typically,
superposed lobes appear to be overlapping lobes that widen laterally as they grow in
length (Fig. 2.8d). In some cases, however, the steps indicate that the lobe widened
laterally and then propagated back toward the starter slot. In a few cases,
superposed lobes are roughly circular features that are nearly isolated from both
other lobes and the parent fracture. Small fractures, several mm in length, oriented
normal to the lobes are the only connection that could be identified between those
superposed lobes and their neighbors. Steps indicate that these isolated fractures
grew outward in a radial pattern from the small connecting fractures.
The axes of boundaries between adjacent lobes typically can be traced back
toward the starter slot to steps on the surface of a fracture (Fig. 2.6). This was
observed on several scales; from boundaries between the larger lobes which can be
traced to steps on the surface of the parent fracture, to the boundaries between the
smallest lobes which can be traced back to fine steps on a fracture surface.
Pollard (1978) has argued that linear features, such as steps, ridges or
grooves, on the surface of a tensile fracture result from the coalescence of lobes
during growth of the fracture. The close spatial relationship between the
boundaries between lobes and the axes of the linear features in the experiments
described above support Pollard's argument. Moreover, Pollard cites the
development of lobes, steps, ridges and grooves over a wide range of scales (eight
orders of magnitude) and in materials ranging from glass to metal and rock. The
results of this study indicate that the appearance of hydraulic fractures in clay-rich
soil is similar to hydraulic, or other tensile, fractures in general.
50
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Unwetted Tip
A thin band of fractured, but undyed soil ocurred at the leading edge of many
of the hydraulic fractures. This undyed zone was identified on the surfaces of split
samples based on surface texture and color. The zone lacked dye staining, so it
could readily be distinguished from the surface wetted by rhodamine-laced
glycerine. The break created when the sample was pulled apart had a rough,
dimpled surface and lacked linear features such as steps or ridges (Fig. 2.9). In
contrast, the surface in the undyed zone was smooth and nearly planar, marked only
by fine steps. In some cases, a fine step in the undyed zone could be traced back
into the stained region of the hydraulic fracture (Fig. 2.9).
The similarity in surface textures suggests that the undyed zone represents
part of the hydraulic fracture that has not been wetted by the injection fluid, and
unwetted tip. Accordingly, the hydraulic fractures extended from the bole along the
axis of the starter slot to the leading edge of the undyed zone.
The length of the undyed zones varied greatly from one sample to another.
In general among samples of similar moisture content and consolidation history, the
length of the undyed zone was roughly proportional to the length of the dyed zone
(Fig. 2.10). This suggests that those lengths are related by
Luw = mLw + Lw (2.1)
where m is the slope dLuvt/dL>, and L^ is the intercept. First order regression lines
are shown in Figure 2.6 for measurements taken from samples of different moisture
content.
The length of the unwetted tip relative to the length of the wetted fracture,
the parameter m in eq. (2.1), depends on moisture content of the sample (Fig. 2.10).
Rhodamine stain was present over the entire fracture surface-an unwetted tip was
completely absent-for samples containing less 'than 21% moisture. The relative
length of the unwetted tip m increases as moisture content increases from 21 to
28%. Within that range, the relative length m is roughly linearly related to moisture
content, according to Figure 2.10. The relative length is greatest, roughly 25%, at
moisture contents between 27 and 28%, and it diminishes as moisture content
increases to values greater than 28% (Fig. 2.10). The trend at moistures greater
than 28% is based on only a few measurements.
The measurements of undyed zones made on different fracture surfaces and
compiled in Figure 2.10 could be used to infer different stages in the growth of the
unwetted tip of a single, idealized fracture. We must make this inferrence with
caution, however, because it assumes that the glycerin stops moving when
propagation ceases. That assumption requires that capillary forces are unable to
cause flow after the pump is turned off. To crudely examine the effects of capillary
forces, droplets of dyed glycerin were placed on narrow, flat-lying cracks exposed on
the surfaces of samples of Center Hill clay. The glycerin flowed 6 to 12 mm into the
dry cracks due solely to capillary suction. The dye produced dendritic patterns
similar to those at the leading edges of the hydraulic fractures.
51
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0
5cm
Figure 2.9. Leading edge of a hydraulic fracture. Lines on the sketch indicate linear
features as in Figures. 2.5 and 2.6.
52
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2.5
0.0 2.5 5.0 7.5 10.0
Dyed Length (cm)
12.5
0)
O
Q)
73
CJ
0.25
0.20
0.15
0.10
0.05
o.oof
073
O
0 :
o
0 o .
) O O •-•--••-•-•- • • :
'a ^^ oVo 0.22 0.24 0.28 0.28 0.30
Moisture Content
Figure 2.10. Length of undyed zone as functions of dyed length and moisture
content (upper figure). Ratio of undyed to dyed length as a function
of moisture content (lower figure).
53
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Capillary forces will certainly affect flow in the vicinity of an unwetted tip
during propagation, and it seems likely that those forces could cause the glycerin to
advance toward the tip even after propagation has ceased. We conclude that the
lengths of undyed zones shown in Figure 2.6 are the lower limits of the lengths of
the unwetted tips during propagation. Likewise, we must accept the possibility that
some of the variation in m with moisture content described above could be
influenced by changes in post-propagation flow, rather than by changes in the rate of
growth of the unwetted tip itself.
RECORDS OF DRIVING PRESSURE
Driving pressure Pa, the difference between the internal fluid pressure and
the confining stress normal to a fracture, is a fundamental quantity in analyses of a
hydraulic fracture (Kristianovich and Zheltov, 1955; Perkins and Kern, 1961;
Geerstma and de Klerk, 1969; Pollard, 1973, Nolle and Smith, 1981; Crockett and
others, 1989). As such, Fd is a valuable quantity in the diagnosis of fracture
behaviour and it is routinely recorded as a function of time during both laboratory
experiments and commercial applications in the field (Nolle, 1988 a and b; Medlin
and Masse, 1984; Zoback and Pollard, 1978; Zoback and others, 1977; Hubbert and
Willis, 1957). Records of driving pressure were made during all the experiments
conducted during this research to compare with similar records from experiments in
rock and to examine how various parameters affect the record. During the
experiments, driving pressure within the starter slot was obtained by measuring the
pressure of the injection fluid as it entered the fracturing cell and subtracting the
pressure in the pneumatic bladder acting normal to the slot
The records of driving pressure as a function of time, hereafter termed
records, were obtained for a variety of conditions. They will be described in the
following section.
Reproducing the Records
Early in the experimental program a suite of four tests was conducted to
examine whether the records could be reproduced. Four samples were prepared
from a common batch of soil and consolidated together beneath the loading pallet
described above. The properties of the samples were similar: densities were within
0.01 gm/cm3 and moisture contents differed by less than one percent. Slot lengths,
applied loads and other factors were identical.
Forms of the records for the four samples (Fig. 2.11) are similar,
characterized by the following periods:
Period I: Nearly constant positive slope
Period II: Slope diminishes, but remains positive
Period III: Slope is negative
54
-------
ctf
0 50 100 150 200
Time (sec)
Figure 2.11. Records of driving pressure as a function of time from tests conducted
on similar samples.
55
-------
The records are nearly identical during Period I. The boundary between
Period I to Period II was identified by marking the location of the break in slope
typical of Period I. Three of the records in Figure 2.11. show smooth changes m
slope, whereas one of the records shows an abrupt step in the record. Pressures
marking the boundaries between periods are indicated by short markers on the
records.
The driving pressures marking the change in slope are within 1.0 kPa for
three of the samples, and they range over 4.1 kPa, from 22.8 to 26.8 kPa, for all four
samples. The driving pressures average 25.4 kPa and show a standard deviation of
1.86 kPa, which is within seven percent of the average.
The forms during Period II are similar for three of the records, showing a
gradual decrease in slope. The other record is marked by two short intervals during
which the slope changes drastically as the pressure decreases and then increases
abruptly. That record is similar to the others, however, if the two short intervals are
ignored. Slight, abrupt changes in pressure were observed in other records, but their
occurrence was unpredictable.
The maximum driving pressure marks the boundary between Periods II and
HI, and it ranges over 3.7 kPa (from 27.0 to 30.7 kPa), roughly the same range as the
boundaries between Period I and II. The record showing the least pressure between
Periods I and n yields the greatest pressure between Periods n and HI. The average
maximum pressure is 28.8 kPa, and the standard deviation is 2.03 kPa.
During Period III, driving pressure decreases and approaches a constant
slope that is similar for three of the records. A constant slope is approached by the
record of the fourth sample, but it is steeper than the other three. Slopes of two of
the records diminish with continued propagation during Period III.
The records appear to be reproducible in both form and magnitude up to the
time of maximum pressure. Variations in the pressures markingthe boundaries of
the Periods are within 10 percent of the total driving pressure. The records during
Period m are similar in form, but their magnitude at any given time ranges over 10
kPa or more.
The forms of the records described above resemble the records presented by
Medlin and Masse (1984) and Daneshy (1976a), both of whom used apparatus
similar to the one used here but conducted their experiments using limestone or
sandstone. The principal difference between the records from tests where rock is
fractured and those in Fig. 2.11 is the slope early in Period III; it is generally steeper
when rock is fractured. However, considerable differences are seen in the forms of
records of hydraulic fracturing tests using rock, and some of them are nearly
identical to those in Figure 2.11 (e.g. Daneshy, 1976a; fig. 6).
Previous studies of hydraulic fracturing of soil (Mori and Tamura, 1987;
Jaworski and others, 1981; Jaworski and others, 1979; Bjerrum and others, 1972)
have measured the rate of flow into a sample while keeping pressure constant, and
then slightly increasing injection pressure until fracturing occurs. The records of
those studies are typically presented as injection pressure plotted with respect to
56
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flow rate, and they are difficult to compare to the records from tests presented here
where injection rate was held constant.
Fracture Development with Respect to the Record
Most tests were terminated sometime during Period III, but several tests
were terminated during Periods I and II in an effort to correlate the development of
a fracture to the form of the record. Samples similar to the ones described in the
previous paragraph were prepared so that the pressures marking the boundaries
between Periods could be anticipated. The surfaces of fractures terminated at
different times are shown in Figure 2.6a through c. The times when each of those
tests was terminated are shown on an idealized record (Fig. 2.12).
Most tests terminated during Period I showed a starter slot enveloped by
unfractured soil; a hydraulic fracture was absent. In two cases, small hydraulic
fractures were observed even though the tests were terminated prior to a break in
slope in the pressure record. These incipient fractures were less than 1.0 cm longer
than the starter slot, and short unwetted zones occurred at their leading edge.
Tests terminated during Period II, however, show well-developed hydraulic
fractures several cm in maximum length. The edges of the fracture during Period II
typically are contained within the sample, that is the fracture has not yet reached the
edge of the sample (Fig. 2.6a).
Another test was terminated early in Period III, roughly five seconds after
the maximum pressure. The sample from this test contains a fracture that is longer
than the one terminated during Period II, and it has intersected the edges of the
sample (Fig. 2.6b).
The third sample shown in Figure 2.6c was terminated several tens of
seconds into Period III and it shows a fully-developed fracture cutting from one
edge of the sample to another.
Those observations indicate that the break in slope of the record (Fig. 2.11)
indicates that hydraulic fracturing is taking place. In some cases, incipient fracturing
apparently occurs prior to the break in slope. Incipient fracturing cannot be
detected on the pressure records, at least by the methods of recording pressure used
for this work, so we will assume that fully-developed fracturing starts at the break in
slope. The driving pressure at the break in slope Pa is taken as the critical driving
pressure required to initiate fracturing.
Following the onset of fracturing, driving pressure continues to increase
during Period II and then decrease dunng Period III. Increasing driving pressure
during propagation indicates a period of stable growth of a hydraulic fracture,
whereas decreasing pressures indicate unstable growth (Tetelman and McEvily,
1967; Zoback and others, 1977; and Zoback and Pollard, 1978). These terms are
used because if the driving pressure were held constant a stable fracture would be
held open but would not propagate, whereas an unstable fracture would continue to
propagate at constant pressure. Thus, the three Periods of the injection record
relate to three different processes during a test:
57
-------
e
o
d-
c
o
d
(DQO
e
o
— o
do
(00.1
— d
J3CID
dd
**Ou
wo
et-
Time
Figure 2.12. Idealized record of driving pressure as a function of time. Letters
correspond to times of termination of tests resulting in fractures
shown in Figure 2.6a, b, and c.
58
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Period I: Inflation of the starter slot
Period II: Stable propagation of a hydraulic fracture
Period III: Unstable propagation
In an earlier section linear features were used to infer that the fracture
initiated within the sample and then grew outward to the edges as it increased in
length. This interpretation is supported by the images shown in Figure 2.6, and
suggests that stable growth occurs from the time when the fracture initiates to when
it intersects the edges of the sample.
Williams (1984) presents one explanation relating this behavior to the
geometry of the specimen. He shows that a notched rectangular specimen will be
under conditions of plane strain at its center, whereas it willbe under plane stress
near its edges. The resistance of a material to fracturing in plane strain is less than
in plane stress, because conditions of plane strain reduce plastic deformation at the
crack tip (Williams, 1984). According to this explanation, the increase in driving
pressure during Period II occurs as the fracture grows from the center of the sample
into material offering greater resistance to propagation. Williams' arguments are
based on a sample whose outer surface is unconfined, whereas the samples used in
this study were confined in a triaxial pressure cell. Friction between the outer
surfaces of a sample and the walls of the fracturing cell would further inhibit
propagation as a fracture grew toward the edge of the sample.
Zoback and Pollard (1978) show that propagation of a hydraulic fracture can
be initially stable, regardless of the geometry of the sample. They attribute this
stability to viscous losses in driving pressure in the incipient fracture. It is possible
that a similar mechanism contributes to the stable propagation during Penod n.
Effects of Moisture Content
Suites of samples were prepared by placing soil of differing moisture content
into the sample molds. Soil in the molds was consolidated for 10 to 14 days, until
displacement during loading was negligible. The resulting samples differed in
moisture content and bulk density, but were otherwise similar. It is possible that
moisture content varied slightly within .the samples, due to incomplete equilibration.
Drainage during consolidation was only possible through geotextiles on the two
sides of the sample that were parallel to the starter slot, however, so that moisture
contents would be uniform along the planes of the fractures. Fractures were created
in the samples and the results of one suite of tests, which is representative, is shown
in Figure 2.13.
The form of the record of injection pressure is markedly affected by
increasing the moisture content of a sample. During Period I, it causes a slight
decrease in the slope, but the most striking effects are seen during Periods II and HI.
The pressure marking the transition between Periods I and II diminishes as
moisture content increases. Furthermore, the slopes of both Periods II and ID
become more gentle, resulting in a flattening of the curved part of the record.
59
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100 -
ctf
PH
0 50 100 150
Time (sec)
Figure 2.13. Records of injection pressure as a function of time for samples of
various moisture contents.
60
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Driving pressures required to initiate hydraulic fracturing decrease by an
order of magnitude, from more than 100 kPa to 10 kPa, by increasing the moisture
content of the samples by only six percent. Once propagation begins, theperiod of
stable growth, Period n, becomes longer as moisture contents increase. The
transition from stable to unstable fracture growth, indicated by a change from
positive to negative slope on the record, is well-defined for relatively dry samples
but it becomes subtle for relatively wet samples. Despite this subtlety, however,
periods of both stable and unstable growth could be identified in all tests.
Explanation of the effects of moisture content on the fracture process will
require development of several theoretical models in Section 3, but an explanation
of how the slope dPa /dt differs with moisture content during Period I can be readily
explained. The starter slot is inflating during Period I and the different slopes
appear to be related to an increase in modulus as moisture content decreases.
According to Tada (1985) the volume of a pressurized slot in plane strain is
V = 2-ffPAwai(l -v*)/£: (2.2)
where w is fracture width, a is the fracture half length, v is Poissons ratio, and £ is
the elastic modulus. Differentiating with respect to time and assuming1 that
dV=Qdt (2.3)
where Q is the rate of injection yields
d?d /dt = QE/[2* fl2w(l - v2)] (2.4)
neglecting the effect of the small hole along the axis of the slot. The slope during
Period I is linearly related to elastic modulus of the sample, according to eq. (2.4).
Uniaxial compression tests conducted on the clay show that the elastic modulus
decreases by at least an order of magnitude over the range of water contents of the
samples. We conclude that a decrease of elastic modulus could cause the observed
change in slopes of the records. The changes in slope, however, are small compared
with the change in modulus. This probably results from volume changes in tubing
and the pressure interface of the pumping system, which contribute to the slope
during Period I but are overlooked in eqs. (2.3 and 2.4).
Effect of Slot Length
The effect of varying the length of the starter slot is summarized in Figure
2.14, which shows the records from four experiments conducted on similar samples
This assumption requires that none of the glycerin leaked out of the fracture into
the clay.
61
-------
Half-length: 0.61 cm
100 200 300 400
Time (sec)
Figure 2.14. Records of injection pressure as a function of time using various lengths
of starter slots.
62
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differing only by the lengths of their slots. Other experiments conducted on pairs of
similar samples (one large sample split into two) confirm the features shown in
Figure 2.14.
A decrease in the pressure at which fracturing occurs Pat is the most striking
effect of increasing slot length. The relationship between Pa and half-length of the
slot a is characterized by the empirical function
Pdr=Cfl» (2.5)
in which C - 39.3 and n = -0.61. Many other materials, including rock, steel,
ceramics and glass, show a relationship similar to eq. 2.5, with values of C related to
fracture toughness of the material, and values of n varying slightly from -0.5
(Williams, 1984; Lawn and Wilshaw, 1975; Daneshy, 1976b; Clifton and others,
1976).
The pressure at which failure occurs is by no means the only effect of
increasing the length of the starter slot; the shape of the record is also affected.
Records from tests using shorter slots show a period of stable growth, during which
period of stable growth becomes longer and driving pressure increases
by a smaller amount-several kPa-during stable growth. During unstable growth,
the amounts of decrease of driving pressure are less for fracture started from the
longer slots than from the shorter ones (Fig. 2.14).
SUMMARY AND DISCUSSION
Observations in the preceding section suggest a scenario for the development
of a hydraulic fracture in soil that is straightforward, yet more detailed than previous
works (Mori and Tamura, 1987; Brunsing and Henderson, 1984; Jaworski and
others, 1981; Bjerrum and others, 1972). The early stage of injection at a constant
rate was characterized by inflation of the starter slot, which resulted in a roughly
linear increase in driving pressure. A hydraulic fracture formed when the driving
pressure reached some critical value, the magnitude of which diminished with either
an increase in the length of the slot, or a decrease in the moisture content of the
soil. Driving pressure continued to increase during the early stages of propagation.
At some point, either at the onset of propagation or after the fracture had reached
some critical length, the injection fluid lagged behind the leading edge of the
fracture leaving an unwetted zone at the tip. Once it began to form, the length of
the unwetted tip increased roughly in proportion to the length of the wetted zone of
the fracture.
The slope of the pressure record decreases from roughly the onset of
propagation, resulting in a concave downward form. The forms of the records
differed in detail, however, depending on the length of the starter slot and the
moisture content. A short slot resulted in a record that was tightly concave, with the
pressure diminishing sharply following the onset of propagation. A longer slot
caused the concavity of the record to broaden, so that the pressure increased slowly
63
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and then decreased slowly during propagation. Keeping the slot length constant, but
decreasing the moisture content resulted in a similar change in the shape of a
record: it was sharply concave when the samples were relatively dry, but it became
broader and flatter as the moisture content increased.
Moisture content affected the development of the unwetted tip as well. An
unwetted tip was absent, that is stain covered the entire fracture surface in samples
less than 21% in moisture (roughly the plastic limit). As moisture content increased,
the length of the unwetted tip relative to the length of the dyed fracture increased,
until it reached a maximum length of 0.25cm in samples of 28% moisture.
Preliminary evidence indicates that the unwetted tip decreases in relative length as
moisture content increases to values greater than 28%.
The growth of the unwetted tip appears to be a fundamental feature of
hydraulic fractures in Center Hill clay at moisture greater than the plastic limit
That feature is by no means unique to day; unwetted zones at the leading edge of
hydraulic fractures in rock have been observed in experiments by Medlin and Masse
(1984). Their apparatus differed from the one used in this research in that theirs
was fitted with ultrasonic transducers which yielded data on aperture and fluid
content as a fracture was growing. They observed marked attenuation of the
ultrasonic signals near the tip of a growing fracture and inferred that the tip of the
fracture was filled with air. Results from one of their experiments (Medlin and
Masse, 1984; fig. 6) indicates that the unwetted zone first forms at the starter slot, it
grows to length Lw and then is roughly constant as the length of the wetted zone Lu
increases during propagation. This differs slightly from our results, which indicate
that Lw increases with Lw.
Similarity between surface textures of the unwetted tip and the wetted
fracture, as well as the continuity of linear features from the wetted fracture to the
unwetted tip indicate that the unwetted tip is open and a pan of the fracture itself.
This is in contrast to so-called decohesion zones, or process zones, identified or
postulated from studies of fracturing of metal, polymer or rock. The process zone is
an interval over which the material becomes separated. In tensile fractures, of
which hvdraulic fractures are a special case, processes of decohesion involve the
nucleation and growth of voids or microfractures (Williams, 1984; Tetejman and
McEvily, 1967). The process zone is characterized by vestiges of material cohesion
resulting from the strength of intact material remaining between voids, and as such
it differs from the fracture itself where the material is completely separated and
cohesion is absent. Process zones composed of clusters of voids have been
described at the tips of fractures in metals (Shockey and others, 1979; Tetelman and
McEvily, 1967; Irwin, 1957) and polymers (Williams, 1984; Weidmann and Doell,
1979). Ouchterlony (1982) postulates a process zone in rock that consists of dilating
microfractures, which produce acoustic signals that are commonly used to monitor
the fracturing process in rock (Ouchterlony, 1982; Zoback and others, 1977). Time-
lapsed sequences of photographs by Knauss (1976) capture the coalescence of voids
resulting in the formation of fracture surfaces in polymers.
Phenomena occurring in the process zone of a fracture in clay have received
little attention. In normally-consolidated kaolin, micron-sized voids occurring
between aggregates of grains were observed to grow by coalescing during the early
stages of shear loading (Smart and Dickson, 1979). To our knowledge, processes at
64
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the tip of a fracture in clay under tensile loading have yet to be studied, but it seems
reasonable to assume that those processes involve microfracturing or void growth
ahead of the fracture itself. Whatever processes are involved, the zone in which
they occur appears to be ahead of, and distinct from, the unwetted tip.
In cross-section, an idealized hydraulic fracture in clay is inferred to be
composed of a zone wetted by pressurized injection fluid, an unwetted zone near the
tip where fluid pressure is zero, and a process zone in front of the tip where
decohesion of the clay takes place. The idealized cross-section is shown in Figure
2.15, where lobes are assumed to be absent for simplicity.
Hydraulic fracturing of clay was inevitable in the laboratory experiments; it
occurred in all samples that could be properly prepared. We tried to inhibit
fracturing by increasing the water content and softening the clay. The wettest
sample that could be prepared as described above, however, could be hydraulically
fractured and the appearance of the fracture in that sample resembled that of drier
samples. Samples or extremely high water contents were too soft to be handled and
we were unable to prepare them using the procedures described.
65
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0.
H
1 Wetted Fracture 1 "°
. .,,,,,»,,,,f,,m,,/M/M/SS///ff///////M/^^^ •
TJ
O
O
PA
CO
CO
N
O
^^
l»l
•<".'.".»
Figure 2.15.> Wealized cross-section of a hydraulic fracture in clay.
66
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SECTION THREE
ANALYSIS OF HYDRAULIC FRACTURING OF SOIL
Since the work of Kristianovich and Zheltov in the mid-1950s, the
principles of elasticity theory have been used to analyze the onset and
propagation of hydraulic fractures in rock. Those principals have resulted
in a significant body of published papers describing both methods of
formulating and solving for various fracture geometries and boundary
conditions, and techniques of applying those methods to design field
applications. Details of the methods vary considerably, but the use of
elasticity theory to determine deformation of material enveloping the
fracture is virtually universal.
The broad knowledge-base of published analyses based on elasticity
theory would be an extremely valuable tool in designing hydraulic fractures
under near-surface conditions. The application of such methods to analyze
the hydraulic fracturing of soil, however, is currently untested. The
appearance of fractures created in clay resembles the appearance of hydraulic
fractures created in rock, as well as.that of tensile fractures in a range of
other materials. This semblance is encouraging, but appearance alone is
insufficient to provide grounds for adopting a mechanical theory. Previous
investigators of hydraulic fracturing of soil (Mori and Tamura, 1987; Horsrud
and others, 1982; Jaworski and others, 1981 and 1979; Massarsch, 1978; Leach,
1977; Wong and Farmer, 1973; Bjerrum and others, 1972; Morgenstern and
Vaughan, 1963) have developed analyses based on theories of elasticity or
plasticity to provide predictions of pressures required to induce hydraulic
fracturing from a cylindrical hole in soil. Those analyses are also
encouraging, but they are limited to predicting initiation from a borehole
and reveal little about the behaviour of the fracture itself.
Is elasticity theory applicable to hydraulic fracturing of clay? The
purpose of the following chapter is to answer that question by analyzing
critical aspects of the lab experiments. The method of analysis will be
acceptable if it can predict or explain:
1. The onset of fracturing
2. Essential features of a hydraulic fracture
3. Forms of pressure records observed during propagation
Those criteria will be addressed using analyses based on linear elastic
fracture mechanics, a branch of elasticity theory. Results of the analyses
will be compared with the results of lab experiments, and the degree to which
they are similar will determine applicability of the approach.
The analyses that will be developed are intended to predict effects,
principally the growth of an unwetted zone at the fracture tip, that are
commonly ignored by investigators who study hydraulic fractures in rock.
Unwetted zones do develop in hydraulic fractures cutting rock, however, so
the results of the analyses may be relevant to hydraulic fractures in both
67
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The growth of unwetted zones at the tips of hydraulic fractures in
rock is particularly well documented by Medlin and Masse (1984). Those
investigators used an apparatus that was similar to the one used in this
work. One important difference, however, is that their apparatus was
fitted with ultrasonic transducers yielding information on fracture
length, aperture, and fluid content during propagation. The experimental
method used in this work was only able to yield pressures during
propagation.
The primary goal of the following chapter is to explain results of
lab experiments of hydraulic fracturing of soil. Certain experimental
results of Medlin and Masse will also be used in the following chapter
because they offer data describing propagation.
PREDICTING THE ONSET OF HYDRAULIC FRACTURING
The stresses in the vicinity of a straight fracture in an infinite
elastic medium are concentrated at the fracture tip. In the vicinity of
the tip, stresses are proportional to r where r is the radial distance
from the tip. That relation results in a singularity in the stresses at
the fracture tip itself, at r = 0. The strength of the singularity is
characterized by the stress intensity factor K which is given by (Inglis,
1957; Tada and others, 1985)
K = <7/7uTflb) (3.1)
where a is the applied stress, a the half-length of the fracture, and f(b)
is a function of the geometry of the fracture and the enveloping material.
The driving pressure P (Secor and Pollard, 1975) of a hydraulic
fracture is the difference between the internal fluid pressure p, which
tends to open the fracture, and the confining stress
-------
provide a means of predicting the driving pressure required to initiate
fracturing.
Critical stress intensities of soil were determined through eq. (3.1)
by obtaining a critical driving pressure P at the first change in slope
of the pressure record from the lab experiments described in Chapter Two.
Other accepted methods, such as those decribed by Ouchterlony (1982) for
fracture toughness testing of rock, pick the critical load at fracturing
based on a certain (5 percent) deviation from linearity of the record of
load with respect to crack opening displacement (COD). Measurements of
COD were impossible to make using our apparatus, however, and our
observations suggested that fracturing occurs at, or perhaps even slightly
before, the first change in slope of the pressure record.
In general, the function f(b) in eq. (3.1) is equal to unity under
the ideal conditions of a straight slot of zero initial aperture in an
elastic medium of infinite extent. It is less than unity and can be taken
as a correction factor for practical constraints such as finite sample
size. Tada and others (1985) give expressions for f(b) for a straight
slot containing an axial hole, and for a straight slot embedded in a
rectangular sample of finite size. Those conditions represent relevant
corrections for the experimental apparatus used in this work. However,
correction factors determined for the geometries of the lab apparatus are
minor (within five percent of 1.0), so f(b) was set equal to 1.0 in the
determinations of K . The critical stress intensity was calculated using
(3.3)
Tests were conducted to determine the relation between AT, and the
1C
length of the starter slot (Octerlony, 1982). These tests consisted of
preparing sets of similar samples and cutting slots of a different length
in each sample. Sixteen sets of samples of Center Hill clay were
prepared, where one set consisted of four full-length samples, two sets
consisted of three full-length samples, and the other sets consisted of
one full-length sample cut in half to give two half-length samples. One
set of three full-length samples composed of River Downs silt was also
tested. The samples were fractured using procedures described in Chapter
Two and K was determined using eq. (3.3).
According to the results of those tests (Fig. 3.1), doubling the
length of the starter slot resulted in an average variation of 0.104
(variation was determined as the absolute value of the difference between
two measurements divided by their average). That average value includes
the results of several sets of unusually large variation (one value of
1.0, and two others greater than 0.4). Nevertheless, the average
variation caused by doubling the length of the initial fracture is similar
to the variation of 0.081 observed among results from four identical
samples described in the previous chapter.
69
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200
180
^120
PH.100
^08°
w~eo
40
20
0
O—O Center Hill clay
,o
D—Q River Downs silt
0.0
1.0
2.0 3.0
&i (cm)
4.0
Figure 3.1. Critical stress intensity as a function of half-length of
starter slot for similar samples of Center Hill clay and River
Downs silt.
70
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The critical stress intensity of rock and metal is observed to
increase slightly as a function of slot length, if the slot length is less
than a critical value that depends on £fc and a tensile yield strength
(e.g. Ochterlony (1982); Schmidt (1977); Kaufmann and Nelson (1974), and
references therein). As the length of the starter slot increased in the
experiments using soil, the critical stress intensity decreased for ten of
the sample sets, it increased for four of the sets, and it both increased
and decreased for two sets of samples (Fig. 3.1). Although K^ decreased
for more sample sets than it increased, there appears to be no systematic
relation between K and a. It is unclear whether K is independent of a
1C K
for the Center Hill clay, or whether the critical length for that
dependence is less than the slot lengths used in this study.
The results of the previous two paragraphs indicate that K^ can be
used to predict (within roughly 10 percent) the driving pressure required
to propagate a hydraulic fracture in Center Hill clay. Likewise, the few
tests conducted using River Downs silt suggest that ATfc can be used to
predict hydraulic fracturing in that material as well. It is apparent
from Figure (3.1), however, that the value of K^ varies over more than an
order of magnitude for samples of the Center Hill Clay. Thus, some method
of anticipating K will be required to make a useful prediction of the
1C
onset of propagation.
Moisture content and duration of consolidation varied from one sample set
to another, and they both have a marked affect on the critical stress
intensity. Among samples that were prepared by compaction alone, K^ is
greatest, roughly 200 kPa cm172, at moisture contents between 0.17 and 0.21.
The critical stress intensity decreases abruptly to roughly 35 kPa cm ,
however, as moisture content increases from 0.21 to 0.22. The moisture
content of this sharp change in K is slightly wetter than the plastic limit
of the soil. Further increases in moisture slightly decrease the average K^,
although the decrease is small and K^ is practically independent of moisture
content over the range 0.22 to 0.30.
Critical stress intensity is neglible for samples of moisture content
greater than 0.32. This means that the break in slope of the pressure record,
from which the onset of fracturing was inferred, occurs when the pressure of
the injection fluid is equal to the confining stress. Hydraulic fractures
produced during these tests are physically indistinguishable from other
fractures produced when ATfc is greater than zero.
Consolidation appears to toughen the Center Hill clay (Fig 3.2b).
Critical stress intensity of samples that were consolidated for four days
using procedures described in the previous chapter are greater than they are
for the compacted samples of similar moisture. Moreover, increasing the
71
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duration of consolidation to 14 days further increases K, according to
Figure 3.2b. The forms of the three curves in Figure 3.2b are similar,
however; they all show K^ decreasing markedly (from roughly 200 kPa cm to
between 30 to 50 kPa cm ) over a few percent of moisture.
Limited tests conducted on the River Downs silt show that K is four or
Ie
five times less than K of the Center Hill clay at similar moisture content
(Fig. 3.2). This result suggests that fractures will develop in the silt at
lower driving pressures than in the clay, if the two materials contain the
same weight percent water. Lab experiments to confirm this suggestion were
not conducted, but it is consistent with the common behavior of the two
materials; the silt readily fractures and crumbles, whereas the clay tends to
resist crumbling when pieces of the material are worked manually.
Discussion
The critical stress intensity is a material property of clay that depends
on moisture content and duration of consolidation, according to the results of
this investigation. Driving pressure marking the onset of propagation of a
hydraulic fracture in the Center Hill clay could be roughly predicted by
estimating K^ from water content and consolidation history and measuring the
length of a pre-existing fracture. The effects of other parameters, such as
compaction effort, will also affect K (e.g. Jaworski and others, 1979)
although the present study was limited to effects of moisture content and
duration of consolidation, the requirements of an acceptable theory of
hydraulic fracturing of soil, the ability to predict propagation of a
pre-existing fracture, appears to be satisfied by the critical stress
intensity factor.
The use of K as a fracture criterion generally requires that the
fracture process zone, where inelastic behavior such as microcracking or void
coalescence occurs, is small compared with the dimensions of the fracture and
the specimen (Tada and others, 1985; Williams, 1984; Ouchterlony, 1982; Rice,
1968). Schmidt (cited in Ouchterlony, 1982) describes a method of estimating
the size of the process zone based on a maximum normal stress criterion. That
method tacitly assumes that the dilation of microcracks is the dominant
phenomena occurring in the process zone, an assumption that is accepted for
rocks (Ouchterlony, 1982) and seems reasonable for clayey soil as well. The
maximum length of the process zone L is given by
L = 0.269 [K l(a + a )]2 (3.3a)
P Ie y c
where a is the mean confining stress, and a is the tensile yield stress
required to open microcracks in the process zone. Several investigators have
72
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a
o
cfl
0.15
0.20 0.25 0.30
Moisture (wt. water/wt.solid)
0.35
a
o
(d
CU
— Compacted
A Consolidated 4 days
O Consolidated 14 days
0.15
0.20 0.25 0.30
Moisture (vi. -water/Trt.solid)
0.35
Figure 3.2 Critical stress intensity of Center Hill clay as functions of
moisture content and duration of consolidation. Filled circles
on lower plot are for River Downs silt.
73
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described methods of measuring tensile yield strength of soil (Snyder and
Miller, 1985; Snyder, 1980; Vomocil and Chancellor, 1967; Farrell and others,
1967), but all of those methods make use of special equipment that was
unavailable during this study. The tension of pore-water, however, could be
taken as a tensile yield strength because dilation of microcracks in the
process presumably must overcome the pore-water tension. In a sample of 0.20
moisture under load in the fracturing cell, the pore-water tension was 60 kPa,
according to measurements made using a tensiometer (SoilMoisture Model 2100).
Measurement of a sample containing 0.27 moisture yielded inconclusive results,
perhaps because the sample was saturated and the gauge attached to the
tensiometer was only able to measure suction; the tensile strength of the 0.27
material will be assumed to be zero. The critical stress intensity for 0.20
moisture is roughly 180 kPa cm , whereas for 0.27 moisture it is 50 kPa
cmre (Fig. 3.2).
The maximum length of the process zone ranges from 0.47 cm for 0.20
moisture down to 0.13 cm for 0.27 moisture, according to eq. (3.3a) and data
in the proceeding paragraph. The length of the initial slots ranged from 1.22
to 5.05 cm, and the length from the end of the slot to the end of the sample
was greater than 5 cm. The process zone in the Center Hill clay was always at
least several times smaller than both the initial starter slot and the sample.
This suggests that K^ should be a reasonable predictor of fracturing,
according to Tada and others (1985) and Williams (1984), who state that the
accuracy of K improves as L diminishes to lengths significantly less than
the length of the starter slot or the sample. It is apparent from eq. 3.3a
that L decreases as either tensile strength or confining stress increase, so
p
that the accuracy of K should improve as confining pressures increase to
values greater than the 69 kPa used in the lab. Confining pressures of most
anticipated field applications, for example, would exceed 69 kPa. The
relation between the size of the process zone and the accuracy of JTfc also may
explain why the drier samples, which have the larger process zones, exhibit
the greatest variability of K (e.g. Fig. 3.1).
Ie
We recognize that in some cases incipient fracturing may occur at driving
pressures less than those marked by a break in slope in the record. A change
in slope of the pressure record was the only method available to detect the
onset of fracturing during the present work. Values of critical stress
intensity presented here should be taken as apparent intensities for the onset
of fully-developed hydraulic fracturing and they may overestimate the critical
stress intensity obtained from other types of tests, such as a compact tension
test or three-point bend test (Tada and others, 1985).
The method described above is by no means the only one that uses
principals of linear elastic fracture mechanics to predict the onset of
tensile fracturing of soil. Briones and Uehara (1977b) cracked rectangular
beam-shaped samples of soil in a bending apparatus and proposed a material
characteristic (their eq. 9) that is equivalent to
74
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(3.4)
where a is assumed to be the tension of pore fluid, and a is an effective
t f
length of pores, or microcracks in the soil. Their expression is based on the
classic works of Griffith (1920) and Irwin (1957), and it is identical in form
to eq. (3.1). The tension of pore fluid can readily be determined using a
tensiometer, but Briones and Uehara (1977b) were unable to determine
appropriate effective sizes of pores in their soil samples, and thus were
unable to determine K through eq. (3.4).
Ie
Snyder (1980) and Snyder and Miller (1985) use methods of linear elastic
fracture mechanics to develop another analysis predicting the tensile fracture
of soil. They recognized the importance of pore size and shape in nucleating
tensile fractures, and they were fully aware of the practical difficulty of
measuring critical shapes and sizes of pores. To address this problem, Snyder
(1980) introduces a parameter based on the degree of saturation that is
intended to characterize the role of pore size and shape in the fracturing
process. According to Snyder (1980), this approach to characterizing the role
of existing flaws yields results that can explain both his own data and
published data on tensile cracking of soil. Various other investigators
(Rogowski and others, 1968; Farrell and others, 1967; Kirkham and others,
1959) have used methods based on elasticity theory to estimate tensile
strength of soil without explicitly considering the effects of pores or
microcracks.
The approach used here differs only slightly from that of previous
workers. The principal difference—we cut a large slot to nucleate a fracture
whereas they omitted the slot-is significant because our method explicitly
addresses the role of existing cracks in a sample.
PROPAGATION OF A HYDRAULIC FRACTURE IN SOIL
Predicting or explaining essential features of both the hydraulic
fractures themselves and the pressure records during propagation are two more
requirements of the analysis. Meeting those requirements will be accomplished
by including effects of propagation in the analysis. The propagation of a
hydraulic fracture involves two basic processes, the flow of liquid within the
fracture and the dilation of the fracture due to deformation of the enveloping
medium. The processes are coupled in that the pressure distribution resulting
from viscous losses during fluid flow is strongly dependent on fracture
aperture, and the aperture depends on the pressure distribution. Flow within
the fracture will be treated using methods of fluid mechanics, and dilation of
the fracture will be treated using methods of elasticity theory.
Another condition, one that ensures equilibrium propagation, must also be
considered. In keeping with the approach of linear elastic fracture mechanics
we will require that the criteria for onset of fracturing is maintained
75
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throughout propagation. Accordingly, during equilibrium propagation the
pressure distribution within the fracture must always result in the critical
stress intensity. The fracture is considered to be out of equilibrium if
the stress intensity exceeds the critical value, and propagation will cease
if the stress intensity is less than the critical value. Other methods of
maintaining equilibrium propagation are described by Geertsma and Haafkens
(1979).
Conceptual Model
A conceptual model of fracture growth is the sequence of events
describing the progression from an inflated slot to a typical fracture in
the lab samples. This model of growth will be inferred from lab
observations and from simple reasoning, and it will used as a framework for
formulating theoretical analyses of propagation.
The model begins with a narrow slot cut in the material (Fig. 3.3).
The slot is inflated at a constant volumetric rate, resulting in an increase
in fluid pressure and an increase in the intensity of stresses at the edge
of the slot. All the inflow during inflation results in dilation of the
slot, so the flow rate diminishes along the fracture and must be zero at the
tip. The fracture begins to propagate when the stress intensity equals the
critical stress intensity for the material, according to the principles
described earlier. Separation of material at the fracture tip during the
onset of propagation occurs in response to the intensity of stress within
the enveloping material. The stress intensity depends only on the magnitude
and distribution of pressure, and it is independent of properties governing
the flow of the fluid in the fracture. Indeed, separation of material at
the fracture tip will occur when the critical stress intensity is achieved
even if the fluid in the fracture is totally immobile and unable to fill the
newly formed region (e.g. Clifton and others, 1976).
This concept is important because it suggests that the newly-formed
region at the tip can be unfilled by injected fluid immediately following
the onset of propagation. In other words, the tip of the fracture could be
unwetted from the start of fracture growth. The lab experiments conducted
for this work were unable to yield conclusive information about the fracture
tip at the onset of propagation; however, Medlin and Masse (1984, fig. 6)
clearly show that the unwetted region forms at the onset of hydraulic
fracturing of rock.
The lengths of unwetted zones appeared to be proportional to the
lengths of the wetted parts of fractures in the lab experiments conducted on
clay samples of similar moisture content. In relatively moist samples, the
length of the unwetted zone appeared to be linearly related to the length of
the wetted zone from the start of the fracturing, whereas in drier samples
we inferred that a critical fracture length was required before the linear
relation was observed. The latter observation is consistent with our model
if we postulate that a short unwetted zone forms at the onset of fracturing
in the drier samples and grows slowly until the critical fracture length is
76
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1.
2.
3.
Figure 3.3. Conceptual model of the growth of an idealized hydraulic
fracture in lab samples.
77
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reached.
The conceptual model is summarized in four steps shown in Figure 3.3.
1. Pre-existing starter slot cut in a sample
2. Inflation of the slot leading to an increase in stress intensity,
depicted by stipling at the tips of fractures in Figure 3.3.
3. The inflated slot begins to grow when the £, = £fc. Part of the
newly-formed fracture is unfilled by injected fluid.
4. The fracture increases in length and partly fills with fluid. A
region at the tip of the fracture remains unfilled, and the
length of the unfilled region increases during propagtion. Lab
measurements suggest that the length of the unfilled region is
linearly related to the length of the wetted fracture, although
that relation is only approximate.
Analysis of Propagation
Two analyses will be used to examine the conceptual model and to predict
the records of driving pressure as a function of time. Both analyses are
based on linear elastic fracture mechanics, although they differ markedly in
level of complexity. The first analysis that is presented solves the problem
of coupled fluid flow and elastic dilation and requires numerical procedures
implemented in a lengthy computer program, whereas the other one neglects the
effects of fluid flow and results in a simple analytical expression.
Both analyses treat the fractures in two dimensions normal to the axis of
the starter slot. The lengths of fractures produced in the lab were roughly
uniform with respect to their width, so that the appearance of the fracture in
a cross-section normal to the axis of the slot is nearly independent of
location along the width. The fractures gapped open at the sample edges, but
the aperture at the edges was probably less than within the sample due to
friction between the sample and the apparatus. That edge effect, as well as
effects related to the development of lobes at the leading edge of the
fracture are assumed to be negligible in this formulation. The hole along the
axis of the slot will be ignored because including it will markedly increase
the complexity of the analyses while adding little insight.
The experimental apparatus was designed to restrict deformation parallel
to the axis of the starter slot, placing the entire sample in conditions of
plane strain deformation. It will be assumed that plane strain conditions
exist at the leading edge of the fracture, and those conditions will be
adopted for the analyses. Shear stresses induced at the edges of the sample
by the dilation of the fracture will be ignored, and consideration of plane
stress conditions at the edge of a notched sheet as described by Williams
78
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(1984; p. 99) seem unwarranted in light of the edge constraint applied by the
experimental apparatus.
The numerical analysis is designed to obtain a distribution of pressure
within the fracture that simultaneously satisfies equations describing the
elastic dilation, viscous fluid flow, and stress intensity. An iterative
procedure, which converges in less than ten iterations for most cases, was
developed for this purpose. The procedure makes use of the Schwarz-Neumann
alternating technique introduced by Pollard and Holzhausen (1979) to analyze
static hydraulic fractures, and similar iterative methods are used by Nilson
and Griffiths (1986), Cleary and Wong (1985), and Narandren and Cleary (1983)
to analyze propagation.
A variety of other methods of analyzing a propagating hydraulic fracture
whose geometry resembles the one described here are available (e.g. Nilson,
1986; Spence and Turcotte, 1985; Biot and others, 1982; Geerstma and de Klerk,
1969). The method of solution used in this work was adopted because it is
straightforward, yet versatile enough to accomodate a wide range of
modifications that may be required in the future.
Overview of the Approach of the Numerical Analysis
The analysis begins by assuming fluid is injected at a constant rate at
the midpoint of a pre-existing fracture (Fig. 3.4). Symmetry about the
midpoint is assumed and allows us to only treat one half of the fracture. The
fracture is embedded in an elastic medium of infinite extent along cartesian
axes x and v, and it is of width w along the z axis. The fracture, which is
of half-length a{, lies on the x axis and the v axis is normal to the plane of
the slot. Displacements along the z axis are assumed to be zero, reducing the
problem to one of plane strain in the x-y plane.
An initial period of injection inflates'the pre-existing fracture but
does not result in propagation. Pressure within the fracture increases during
inflation and propagation begins when K = K . Propagation is assumed to
continue such that the equality K = K is always maintained.
The history of growth is analyzed by treating a series of fractures each
of which contains a slightly larger volume of fluid than the last. The time
since injection began, which yields a growth history, is obtained by dividing
the volume of a fracture by the volumetric rate of injection. The volume can
only be determined after selecting a fracture length and solving for a
pressure distribution, so different methods of changing fracture volume are
needed for stationary or moving fractures. During inflation of a pre-existing
fracture, volume is increased by incrementing the driving pressure at the
fracture tip, whereas during propagation volume is increased by incrementing
fracture length.
This method of solution is termed quasi-steady (Nilson, 1986) in that it
ignores dynamic effects in the elastic solutions; transient terms only enter
79
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X
Figure 3.4 Geometry used in analyses.
80
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in the mass balance used to solve the flow equations. Dynamic effects are
insignificant, however, when the velocity of a fracture is much slower than
the speed of elastic waves in the solid enveloping the fracture. As Nilson
(1986) points out, viscous effects in the fluid filling a hydraulic fracture
will limit propagation velocity to much less than the wave speeds of elastic
solids, so the quasi-steady approach seems to be justified for hydraulic
fractures.
Inflation of a Pre-existing Fracture
The steps used to analyze inflation of a pre-existing hydraulic fracture
are outlined below.
1. Assume an initial length for the pre-existing fracture and assign the
locations of nodal points starting at the midpoint and ending at the tip.
2. Assume a uniform pressure over the fracture that is less than the critical
pressure for propagation.
3. Determine apertures at nodal points from elastic solution.
4. Use an expression for flow in the fracture to determine a new pressure
distribution at the nodal points. Apertures from step 3 yield effective
hydraulic conductivities along the fracture. Mass balance requires that
all the flow into the fracture is accomodated by dilation, so that the
flow rate decreases along the fracture length and is zero at the tip. At
the midpoint, second-type boundary conditions are used to satisfy the
constant inflow rate. At the tip, a first-type condition satisfies the
stress intensity requirement, that K < K .
5. Use the new pressure distribution to determine new apertures and iterate
from step 2 through 4 until convergence criteria are satisfied. The
criteria for convergence used in this work include: a.) the maximum
difference between pressures on two successive iterations is less than a
certain value, typically two percent of the maximum pressure, b.) the
inflow rate determined by finite differences is within a certain value,
typically two percent, of the the specified inflow rate, c.) flow rate at
die tip is essentially zero, d.) mass balance at an arbitrary point along
the fracture is satisfied withiil a certain value, typically five percent.
6. Determine fracture volume by integrating aperture over the length of the
fracture, and determine the time since injection began by dividing
fracture volume by the volumetric rate of injection. Save the variables
of interest.
7. Increase the pressure at the tip and repeat steps 2 through 6.
8. Repeat step 7 until the stress intensity exceeds the critical stress
intensity. Estimate the pressure at the tip so that K = K . This
estimate is achieved by interpolation between the previous two solutions
and the observation that stress intensity varies nearly linearly with
81
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small changes in pressure at the tip.
9. Repeat steps 2 through 6 for the estimated critical pressure at the tip and
check whether K = K^. If this check is satisfied (within two percent)
then the current time and pressure distribution mark the onset of
propagation of the pre-existing fracture. Additional iteration is
required if the check is not satsified, but this was rarely needed.
Propagation of an Inflated Fracture
Two schemes are used to analyze propagation, one that assumes the fluid
reacheshe crack tip and another that tracks the leading edge of the
fluid and results in an unwetted tip. The former is the simpler of the
two and will be described first.
1. Increase the length of the fracture by a small increment and reassign
locations of nodal points so that the new fracture is covered by the same
number of points as the old one. Assign a uniform pressure distribution.
Convergence is improved by assuming the initial pressure satisfies the
stress intensity requirement for a uniformly distributed pressure in a
fracture of the new half-length.
2. Determine apertures from an elastic solution.
3. Use an expression for flow in the fracture to determine a new pressure
distribution. Apertures from step 3 yield effective hydraulic
conductivity along the fracture. The difference between the current
apertures and those at the previous time step yields the mass balance in
the flow equation. At the midpoint, second-type boundary conditions are
used to satisfy the constant inflow rate. At the tip, a first-type
condition is used to obtain the stress intensity requirement, that KI -
5. Use the new pressure distribution to determine new apertures and iterate
through step 4 until the convergence criteria are satisfied.
Oscillations between successive iterations are common in this iterative
sheme, as illustrated by Narandren and Cleary (1983). The rate of
convergence is improved by using a weighted average of the previous two
iterations until the solution is close to convergence (Nilson and
Griffiths, 1986). The final two iterations lacked a weighting factor to
ensure that the maximum difference criteria (criteria a. above) is
satisfied.
6. Determine stress intensity and compare with critical stress intensity. If
the stress intensity is within two percent of the critical value, then
the solution for the current fracture length is complete. If the
critical stress intensity is not satisfied, another solution is obtained
using a slightly different pressure at the tip. A third solution is then
obtained using a new pressure at the tip. Selection of that new pressure
82
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is based on the observation that stress intensity is nearly linearly
related to the specified pressure at the tip. Thus, the previous two
solutions are used to estimate a new tip pressure that results in the
critical stress intensity. In many cases, the critical stress intensity
was satisfied after convergence of the first solution, and it was always
satisfied by the linear scheme described above when the increment ,pf
crack growth was less than five percent of the crack length and fi < 1.0,
where n = qi*ElK*e with q the volumetric inflow rate, // dynamic viscosity,
and E elastic modulus. Larger values of n resulted in numerical
instabilities and an alternate method based on adjusting the input *
pressure was used to obtain convergence. Those larger values of n
exceed the range of lab experiments, so the alternate method was
unnecessary for the present work.
7. Save variables of interest (e.g. time, driving pressure, length, aperture)
and increase fracture length by a small increment. Reassign the
locations of nodal points and determine an initial pressure distribution.
Repeat steps 2 through 6.
8. Repeat step 7 until the desired fracture length is reached.
Injected fluid completely filling the fracture is a tacit assumption of
the analysis described above; however, results of that analysis show that
the velocity of fluid near the fracture tip is less than the velocity of
the fracture tip itself (Fig. 3.5). This suggests that the fluid is
unable to keep pace with the fracture and the the assumption of a
completely filled fracture is incorrect (Abe and others, 1976). The
analysis was modified to track the position of the wetted front by
integrating the fluid velocity at the tip over each time step. The
integration was done using a finite difference scheme that is backward in
time, which amounts to using the velocity over the previous time step to
predict the location of the wetted front at a new time step. As a
result, during the first increment of crack growth the fracture front
moves forward a small increment but the fluid front remains stationary
because its velocity at the previous time step was zero.
The method used to assign locations of nodal points was modified during
tracking of the wetted front. The modified method generated one set of
points that were spaced evenly between the midpoint of the fracture and
the wetted front, and another set of points that were spaced evenly
between the wetted front and the fracture tip. Driving pressures were
positive and resulted from the pressure of the injection fluid over the
first set of points, whereas they were negative and assumed to be equal
to the confining load over the second set. The first set of points was
used to solve the flow equation and both sets were used to solve for
apertures and stress intensity.
Outline of the Analysis
Implementing the method of solution requires the fracture to be
discretized into many small segments defined by the nodal points. Apertures
and stress intensities are obtained by integral methods cast as summations
83
-------
1.000
>
>
0.100
0.010
0.001
fracture
0.0 0.2 0.4 0.6 0.8 1.0 j 1.2
Fracture Length (a/a ^ ^P
Figure 3.5. Velocities of fluid within a fracture and of the fracture tip,
scaled to the velocity of fluid entering the fracture, v .
84
-------
over values calculated at each segment, and pressures are obtained using a
finite-difference method based on the mid-points of the segments. Details of
calculating apertures, stress intensities and pressures are described below.
Consider a fracture loaded by a uniform driving pressure P over the
be
segment b <, x <> c, where b and c are nodal points bounding the segment. The
aperture at any point x on the fracture resulting from a load on that segment
is (Erdogan, 1962; Tada and others, 1985)
- sinlb/a)(a2- x2)in 1 (3.5)
assuming plane strain deformation.
A driving pressure of arbitrary distribution P(x) over the entire
d
fracture can be approximated by a series of loads, each of which is uniform
over a segment and equal to P(x ), where x is the midpoint of a segment.
d nip mp
Summing the contributions of each segment yields the aperture at any point.
Assuming there are a total of n segments, where the ith segment is bounded on
the left side by b and on the right side by c leads to
4(1 - y2) r_ r a2-ex t
P.l(c.- x) cosh'1 L_ - (b- x) coslf1-
E *~ 'L ' a\x -
z =
+ (suf'c./a - sin-1fci/fl)(a2- x2)1'2 1 (3.6)
An expression for the stress intensity is obtained using a similar approach
85
-------
n
i = -n
- [1 - (c/o)]- [1 -
which is based on an equation for stress intensity due to loading over a
single segment given by Tada and others (1985).
Pressures
Pressures within the fracture are determined by satisfying conditions
governing laminar flow that is one-dimensional along the fracture length.
Assuming the change in aperture is small over any given segment and the fluid
is linearly viscous, then the flow law within that segment is of the form
q = • (<53/C/0(aPd/ax) (3-8)
where q is the volumetric flow rate per unit width of the fracture, and n is
the dynamic viscosity of the fluid within the fracture. In general, the
constant C depends on Reynolds number R and wall roughness. If the walls of
the fracture are perfectly smooth, GI decreases from 1.5 for J?e of roughly one
or greater to 12 for R,« 1-0 (Schlichting, 1960). Wall roughness tends to
increase the value of C and the magnitude of the increase depends on Rf.
Detournay (1979) reviews experimental studies of the role of wall roughness on
flow through a fracture.
The Reynolds Number during flow through a narrow slot is (Detournay,
1979)
(3.9)
which yields R = 5 x 10"4 for conditions of the lab experiments. The effects
of the roughness of the fracture walls will be ignored, so a value of C^ 12
will be used (Schlichting, 1960).
Conservation of mass requires
dJ/ar = -Bqldx (3.10)
assuming that the fluid is incompressible, that no fluid is stored within the
86
-------
pumping system, and that no fluid leaks off through the walls of the fracture.
All those assumptions can be relaxed by modifying the conservation equation.
Nilson (1986) shows how to include effects of compressibility of injected
fluid and storage within the pumping system. A simple but widely-used
analysis of leakoff was first described by Carter (in Howard and Fast, 1957),
and more general analyses of the problem are treated by Settari (1983), Dean
and Advam (1984) and Pascal (1986), among others.
Substituting eq. (3.8) into (3.10) yields
dS/dt = BTIto dPIdx + T tfPJdx2 (3.11)
o d
where the transmissivity 7 is
T = S3/fiCl (3.12)
Boundary conditions at the midpoint of the fracture require that
x = 0 (3.13)
where q is the total flow rate per unit width of the fracture and 8 is the
^o f o
aperture at the midpoint. The pressure at the fracture tip must also be
specified to control stress intensity and ensure that K = K during
propagation, so
Pd = P.. * - « (3.14)
The flow equation was solved for the boundary conditions described above
using an implicit finite difference scheme. Nodal points in the finite
difference scheme were midpoints of segments in the elastic solution. Several
methods of spacing the points along the fracture were evaluated, but
uniformly-spaced points yielded the most satisfactory results. Other methods,
which were designed to decrease spacing in the vicinity of the fracture tip,
proved to be less stable than the uniform spacing even when the finite
difference scheme was written to account for non-uniform spacing. The
following description is valid only 'for uniformly-spaced nodal points,
although it is readily modified to accomodate non-uniform spacing.
A second-order finite difference approximation of eq. (3.11) is obtained
using Taylor series expansion and the resulting expression is written in
implicit form as
,- « <3-15a>
where
87
-------
- [(T.I- T^MJ*2] (3.15b)
(3.15c)
(3.15d)
<3'15e>
in which the subscripts i are indices of the the nodal points and the
superscripts j indicate an increment of time. The total volume per unit width
of the fracture is V, and the nodal spacing is Ax. The boundary condition at
the midpoint of the fracture eq. (3.13) requires
a= 0 (3.16a)
^= -27/Jjc2 (3.16b)
c= 2TJAX2 (3.16c)
m= (6\ - d\'l)/[(V j - V H)/?o] - qJAx (3.16d)
whereas the boundary condition at the tip is written
«n= 0 (3.17a)
&n= 1.0 (3.17b)
cn= 0 (3.17c)
The resulting set of n equations was written in tridiagonal form and solved
using a commercially-available inversion algorithm.
Tracking the length of the wetted zone a was done by integrating the
velocity at the tip over time. The fluid velocity v at the tip is obtained
to first order by the backward difference
(3.18)
-------
where m is the number of segments wetted by fluid. The change in length of
the wetted part of the fracture a during a time step is established by
and GW is determined at any given time by summing the increments of growth
during the previous time steps.
This approach assumes that pressure within the unwetted zone is constant,
which is a reasonable simplification although we recognize that it tacitly
ignores the matching of pressures and velocities at the interface between the
injected fluid and the fluid filling the tip. It also ignores capillary
effects at the boundary between the fluid front and the unwetted tip, as well
as contributions that the rate of change of pressure distribution and crack
length have on stress intensity (e.g. Cleary and Wong, 1985; eq. 16). The
analysis described above could be modified to consider all of those effects,
and such modifications could be important in predicting various details of
hydraulic fractures. However, we expect that the major conclusions drawn from
the analyses will be unaffected, so those modifications will be deferred for
future work.
Results
Numerical analyses were conducted using parameters resembling those of
the Center Hill clay at moisture contents between 0.26 and 0.27 (Table 3.1).
The driving pressure on the unwetted zone P was assumed to be zero,
daw
implying that the fluid pressure equals the confining stress along that zone.
In its present formulation, the analysis is unable to account for effects such
TABLE 3.1 PARAMETERS USED IN NUMERICAL ANALYSIS
*«•'
I* :
C:
i
Klc:
ai:
0.00375 cm2/s
175 cp
12
50 kPa cm1/2
1.0 cm
u:
£:
P :
dnw
w:
m:
0.3
10 MPa
0
34
30
as capillary forces, and leakoff, both of which will affect the distribution
of pressure at the tip. Accordingly, P should be taken as an effective
daw
stress that crudely accounts for the factors omitted in the analysis, and its
value was estimated based on the form of pressure records generated by the
analysis.
89
-------
The results show that an unwetted tip begins to develop at the onset of
fracturing (Fig. 3.6) and then increases in length during propagation. This
result essentially confirms the conceptual model. Moreover, it shows that the
difference between the velocity of the fracture and the velocity of the fluid
near the tip could be the process responsible for the development of a
fracture with an unwetted tip.
The numerical model predicts (Fig. 3.6) that the length of the unwetted
zone a increases rapidly compared with that of the wetted fracture a^ during
an early period of propagation (a^ < 1.5). Following this early period, the
relative rate of growth of a diminishes and is roughly constant with a slope
of 0.2 for a > 2.0.
Measurements made on fracture surfaces created in the lab (Fig. 2.10)
show that the average slope a la for samples of moisture content 0.26 to
0.27 is between 0.19 and 0.21; similar to that predicted by the analysis (Fig.
3.6). Lengths of undyed zones are a few mm less than that of unwetted zones
predicted by the numerical analysis. Those differences are considered small,
however, and could be due to advancement of the dyed fluid by capillary
forces, a process ignored in the analysis.
Other results of modeling conducted using the numerical analysis indicate
consequences of the development of an unwetted tip on driving pressure,
fracture length and aperture as functions of time. These consequences are
highlighted by comparing results from two analyses; one in which an unwetted
tip was allowed to develop as a result of differences between fluid and
fracture velocity, and another in which the development of an unwetted tip was
prevented by requiring that the fracture remaincompletely filled with
fluid. Driving pressure, aperture, and fracture length, have been normalized
to the values of those variables at the onset of propagation. The normalized
variables include
/*= tit, (3.20a)
in
a*, a/a. (3.20c)
5'- 816 . (3.20d)
ofnc
where the subscript frx indicates the value at the onset of fracturing, and
the subscript o indicates the value at the origin. All the starred variables
have values less than 1.0 during inflation, and values equal to 1.0 at the
onset of fracturing according to this definition.
Growth of an unwetted tip has a marked effect on the driving pressure,
90
-------
2.00
cd
0.00
.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0
~*
Figure 3.6 Normalized length of unwetted tip with respect to length of
wetted fracture, from numerical simulation (solid line) and from
lab experiments (data points).
91
-------
aperture and fracture length as functions of time (Fig. 3.7). The driving
pressure increases linearly during inflation and then abruptly decreases at
the onset of propagation when growth of the unwetted tip is prevented (Fig.
3.7). Similar results were obtained using a wide range of fluid viscosity,
elastic modulus, and critical stress intensity if development of the unwetted
tip was prevented. The analysis that tracks die fluid front and results in an
unwetted tip shows that driving pressure continues to increase after
propagation has beguo^. Indeed, the slope of the pressure record very early in
propagation (1.0 < f < 1.25) is only slightfy less than during inflation.
Driving pressure continues to increase until t = 2, when it reaches a maximum
and then decreases at later times (Fig. 3.7).
Those results have several implications with respect to the lab
observations. They indicate that growth of an unwetted tip can cause the
early propagation of a fracture to be stable, and that unstable propagation
takes place after the fracture has grown to some finite length. Records of
driving pressure from the lab experiments consistently show an early period of
stable growth followed by a period of unstable growth. We conclude that this
behavior results from the early growth of the unwetted zone that was observed
on the surfaces of fractures created in the lab.
Clifton and others (1976) performed experiments where they prevented
fluid from entering a hydraulic fracture by lining a starter hole with a
flexible membrane. Stable propagation was observed when the membrane was in
place, and unstable propagation when the membrane was omitted. Their results,
which are supported by theoretical analyses, confirm the conclusion that lack
of fluid penetration results in stable propagation. The numerical analyses
also indicate that fracturing may occur before a noticable change in the slope
of the pressure record. This is because the onset of fracturing itself may
cause only a minor change in slope, and it is only after the fluid enters the
fracture that the slope of the record changes markedly. That could explain
the observation of short, incipient fractures in experiments terminated
slightly before a change in slope of the pressure record. It also could
explain the observations of Zoback and others (1977), who measured acoustic
emissions from rock samples to detect the beginning of hydraulic fracturing
during lab experiments. They observed increased acoustic emissions while the
slope of their pressure records was constant and concluded that the beginning
of fracturing was undetectable on the pressure records.
Fracture length and aperture are affected by the growth of the unwetted
tip (Fig. 3.7), according to the analysis. The rate of growth of the fracture
is reduced, whereas the rate of dilation is increased when the unwetted tip is
allowed to grow. Analyses ignoring the formation of the unwetted tip
therefore apparently will overestimate length and under estimate aperture.
This has important implications in designing field applications of hydraulic
fractures where length and aperture are important variables affecting the
performance in delivery or recovery.
The actual magnitude of the propagation velocity predicted when the
unwetted tip is 0.58 mm/sec, whereas that predicted by the other analysis is
0.81 mm/sec (determined from slopes of Figure 3.7 and /,_= 4.72 sec, which is
tn
92
-------
1.25
0.00 ^
0.0 1.0 2.0 S.O 4.0 5.0 6.0 7.0 6.0
3.5
S.O
-------
determined from Table 3.1 and eq. 3.2Sc). Propagation velocities in the lab
experiments, determined by dividing half-length by duration of propagation,
ranged widely from 0.2 to 1.05 mm/sec (Fig. 3.7a). Both theoretical analyses
predict velocities that are within the range of observed velocities. A linear
regression of the lab data, however, indicates that the average propagation
velocity was 0.57 to 0.59 mm/sec for moisture contents between 0.26 and 0.28;
the analysis considering an unwetted tip predicts this velocity with
remarkable accuracy, whereas the other analysis overestimates it. The rate of
growth of the unwetted tip itself varies during propagation (Fig. 3.7). The
tip grows rapidly while driving pressure increases during stable propagation.
Growth rate diminishes during the transition from stable to unstable
propagation, and it is roughly constant later in the period of unstable
growth. Our experiments were unable to yield data on growth rate of the tip,
however, Medlin and Masse (1984; fig. 6) show that the tip grows rapidly at
the onset of propagation, and then the growth rate diminishes and is roughly
constant during further propagation.
Driving pressure and aperture were calculated along the length of the
fracture during inflation, at the onset of propagation, and during propagation
(Fig. 3.8). During inflation driving pressure varies roughly linearly along
the fracture, except in the vicinity of the tip where the slope flattens to
zero gradient and thus zero flow at x = a.. At the onset of propagation
driving pressure is nearly constant, varying a few percent over the length of
the fracture. As the fracture lengthens during propagation a zone of low
driving pressure, corresponding to the unwetted tip, appears and increases in
length.
Stable propagation early in the growth of a hydraulic fracture has been
attributed to large viscous losses during flow in a narrow region at the tip
(Zoback and others, 1977; Zoback and Pollard, 1978). The results of this work
show that, at least for conditions of the lab experiments, we do not expect a
large decrease in pressure due to viscous dissipation in the tip. This is
because dilation of the fracture reduces the flow' rate along the length of the
fracture, according to eq. (3.10). As the tip is approached the decrease in
aperture is offset by a decrease in flow rate, so that the pressure gradient
determined through eq. (3.8) is gentle. A steeper gradient is obtained if the
dilation of the fracture is ignored.
The pre-existing fracture has a nearly elliptical form during inflation
(Fig. 3.8). During propagation the form is grossly elliptical, but it is
marked by a slight upward concavity centered on the leading edge of the
pressurized fluid. Similar fracture profiles were obtained by Nilson and
others (1985; fig. 3).
Analytical Solution
The numerical solution described above is cumbersome to use because it
requires as much as an hour of execution time on a desk-top computer (IBM 386,
16 Mhz) to complete an analysis. Making two simplications in the problem will
allow a simple analytical expression to be developed that captures much of the
94
-------
0.20 0.25
Moisture
0.30
0.35
Figure 3.7a. Average propagation velocities from lab experiments. Linear
regression line suggests a slight dependence on moisture
content.
95
-------
1.3
1.0
*,0.8
DH
0.5
0.3
0.0
3.0
2.5
2.0
1.5
1.0
0.5
0.0
3.4
13.8
0.0 0.5 1.0 1.5 2.0 2.5 3.0
t = 13.8
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Figure 3.8. Driving pressure and apertures as functions of fracture length
during inflation (t < 1.0) and propagation. The symbol x marks
the end of a fracture.
96
-------
essence of the numerical solution but requires only a few seconds to compile
and execute. The results of the numerical solution showed that driving
pressure varies only slightly within the fracture, so that one of the
simplifications will be to assume that the driving pressure within the wetted
fracture is constant. This is the same as ignoring the pressure losses due to
viscous dissipation during flow. As a result, the analytical solution will be
unable to predict the growth of the unwetted tip. Both the numerical solution
and the lab data, however, suggest that the length of the unwetted tip is
roughly linearly related to the length of the wetted zone. The other
simplification, therefore, is to assume that the length of the unwetted dp is
proportional to the length of the wetted pan of the fracture.
The geometry of the problem is the same as that used for the numerical
solution and described in a previous section (Fig. 3.4). The fracture is
filled with fluid to a point b along the x axis, and the pressure p of the
fluid is uniform along 0 * x £ b. Fluid pressure along an unwetted tip, the
interval b ^ x £ a, is zero. During inflation the entire fracture is filled
with fluid, so a = b before propagation begins. When the unwetted tip
develops during propagation b will be less than a, with the length of the
unwetted zone equal to o - ft. The relationship between a and b is assumed to
follow that observed in the experiments and expressed in eq. 2.4.
Fluid pressure within the fracture is opposed by a confining stress a
acting normal to the plane of the fracture. Accordingly, the driving pressure
is (p - o) on 0 ^ x £ b, and -a on b < x s a.
Static analyses will be used to obtain driving pressure, aperture and
half-length. Those analyses will be made functions of time by treating a
series of fractures of slightly different volumes, and then determining the
time since injection began by dividing fracture volume by volumetric rate of
injection. This quasi-static approach is the same as the one used in the
numerical analysis.
The fracture will be assumed to be in equilibrium, so that the stress
intensity must equal the critical stress intensity K throughout propagation.
In the analyses of Kristianovich and Zheltov (1959), and Geertsma and de Klerk
(1969) equilibrium propagation is obtained by adjusting either the length of
the unwetted tip, or the driving pressure to eliminate stress concentration at
the tip; they set K to zero.
A solution to the problem can be obtained by superimposing solutions for
two different loading conditions (Fig. 3.9): a.) the load equals p along 0 s x
£ b and 0 along b < x s a; and b.) the load equals -a along 0 £ x £ a. A
solution to similar boundary conditions was obtained by Barenblatt (1962).
The mode I stress intensities K^ volumes V, and apertures at the origin 5 of
fractures for conditions a and b are (Tada and others, 198S)
97
-------
nun
TT! I f TT! t f
illllllllk
Illllllllt
Figure 3.9. Loading conditions used to develop analytical model.
98
-------
K^= pi na (2/n) sm'lb/a (3.21a)
V= (4pa2w/£) [sin'Wi + (bla) /I - (bla)2 (3.21b)
5 = (ZnpalnE) [sm'lb/a + bla cosb'la/b] (3.2Ic)
CU
JT= -av IE (3.21e)
D
$ = ^aaiE (3.21f)
OD
where the E, the plane strain modulus, is £'/(! - u2), and £' is the elastic
modulus and u is Poisson's ratio. Adding the two solutions and introducing
the driving pressure P from eq (3.2) yields
K = / na [PO - a (1 - 0)] (3.22a)
I d
(3.22b)
(3.22c)
where the terms 6, y and 0 depend only on the length of the unwetted zone
0 = (2/7T) sin'1 bla (3.22e)
\p = (2ln) [smlbla + bla / 1 - (bio)* ] (3.22f)
0 = sm'b/a + Wa cosha/^ (3.22g)
The rate of injection Q is constant, and assuming that both the fluid and the
pumping system are incompressible, and that none of the fluid flows out of the
fracture, then
V = Qt (3.23)
where t is the time since pumping began. Substituting eq. (3.23) into eq.
99
-------
(3.22b) yields
/ = (2ita2w/QE) [Pw - (7(1 - \i/)] (3.24)
d
For convenience driving pressure, time, half-length and aperture at the origin
will be normalized in terms of those variables at the onset of fracturing, so
(3.25a)
a . = at (3.25b)
char i x '
I fc = 2rra2 wP IQE (3.25c)
char c dc * * '
d. = APalE (3.25d)
char dc c '
Dividing eq. (3.22a) by eq. (3.25a) and solving fpr normalized driving
pressure P in terms of normalized half-length a
-in , _ /* A, 14 £ jg)
Similarly
(3.28)
^t
ff = ff/P. = ff (nay IK (3.29)
dc i b '
fl = fl/«. (3.30)
In the plots that follow normalized driving pressure, half-length and *
aperture were obtained as functions of dimensionless time by incrementing a
and using eqs. (3.26) through (3.30).
Effects of Growth of an Unwetted Tip
According to the solution derived above driving pressure, half-length,
and aperture as functions of time depend on the growth of the unwetted tip,
manifested as the ratio b/a, and on the magnitude of dimensionless confining
100
-------
stress. Observations described in Chapter Two suggest that the length of the
unwetted tip is linearly related to the wetted length after the fracture has
reached some critical length a . Rearranging eq. (2.4)
cr
b/a = (ma + al(a + ma) (3.31)
to
where m is the ratio of wetted to unwetted length.
Results from the lab tests showed that m and a are roughly constant for
cr ° '
a soil of a particular moisture content, but they both increase as moisture
decreases. For the purpose of this section, I will assume that m and a are
material constants that govern* the growth of the unwetted tip according to eq.
(3.10). The effects of m, a , and a on dimensionless driving pressure,
half-length, and aperture are shown in Figures 3.10 through 3.12. In those
Figures, the quantities used to form^he dimensionless groups require that
inflation of the slot occurs during (/ < 1.0), and propagation occurs during
<£ > 1-0).
When m = oo the unwetted zone is absent and eqs. 3.26 through 3.28 reduce
P* = *-in (3.32a)
c* = r"3 (3.32b)
6* = r*1/3 (3.32c)
for values of / > 1.0. Driving pressure shows a sharp decrease following the
onset of propagation for m = o> (Figure 3.10). The rate of growth of the
fracture (slope of Figure 3.1Gb) is greatest at the onset of propagation, and
diminishes slightly with time. The rate of dilation (slope of Figure 3.10c)
is greatest before propagation begins, when the slot is dilating. Aperture
continues to increase during propagation, but the rate at which it does so
diminishes with time.
Finite values of m change the form of the pressure record significantly;
driving pressure increases slightly early in propagation, and then decreases
at later times (Fie. 3.10). Thus, the presence of the unwetted tip results in
an early period of stable propagation followed by an unstable period. The
period of stable propagation is brief for large values of m, but increases in
duration as m decreases in value. The rate of growth of the unwetted tip,
embodied in m, therefore tends to stablize fracture growth.
Fracture length and aperture are also affected by m (Figure 3.10). The
rate of growth of the fracture diminishes as m decreases. The decrease in
growth rate is offset by an increase in the dilation rate, so that
conservation of volume is maintained. Accordingly, the fracture becomes
shorter and fatter as the relative length of the unwetted tip increases.
101
-------
0129466789 10
0123458789 10
3.5
3.0
2.5
* 2.0
*0
1.5
1.0
0.5
0.0
0123466789 10
t*
Figure 3.10 The effect of parameter m on dimensionless driving pressure,
half-length and aperture. Other parameters are constant: a _
1.0, a* = 0.5.
er
102
-------
Experimental data suggest that in some samples the unwetted tip develops
after the fracture reaches a critical length a . Observations early in the
growth of fractures in those samples are unavailable, so we will simply assume
that the unwetted tip grows slowly from the onset of propagation and more
rapidly when the critical length is reached. This suggests that eq. 3.31
should be modified for the period beginning at the onset of propagtion and
ending when a = a . We will use
cr
b/a = (mf + 1.0)/(fl + Wjfl) (3.33)
for a. < a < a , which is the same form as eq. 3.31. The parameter m was
i cr 1
set equal to three times m to determine curves in Figure 3.11.
A flattening of the slope of the driving pressure record is the principal
effect of increasing a to values greater than the half-length of the slot.
cr
The change in slope ocqurs when the unwetted tip begins to grow according to
eq. (3.31), so that as a increases the point when the slope flattens occurs
cr
at progressively latter times (Fig. 3.11). Increasing the critical length
results in an increase in fracture length, which reflects early growth that is
unimpeded by the constraining effects of the unwetted tip. As we saw in the
previous figure, an increase in growth rate is accompanied by a decrease in
dilation rate (Fig. 3.12).
The normalized confining stress affects the forms of the records, as
shown in Figure 3.12, because it is the driving pressure over the unwetted
zone. The duration* of the stable period early in propagation increases with
the magnitude of a . The rate of growth, of the fracture is reduced, and the
rate of dilation enhanced by increasing a (Fig. 3.12).
The same confining stress was used in all the lab experiments, so there
are no data on the effects of confining stress from this study. However,
dimensionless confining stress is a function of both K and a, through eq.
(3.29). We saw in a previous section that K^ of a soil increases as moisture
content decreases. The effects of increasing a shown in Figure 3.12,
therefore, could occur either by decreasing K^, say by increasing water
content, or by increasing the slot length.
Results from the proceeding analysis indicate that the unwetted tip makes
the soil appear artificially tough. It causes driving pressures to increase,
growth rates to diminish and dilation rates to increase. The magnitude of
these effects depend on the length of the unwetted zone relative to the
fracture length, when the zone begins to grow, and the magnitude of the
confining stress acting normal to the zone.
103
-------
0123466789 10
0123466789 10
*0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
0123466788 10
t*
Figure 3.11 The effect of parameter a on dimensionless driving pressure,
ei
half-length and aperture. Other parameters are constant: m = 6,
ml = 3m, a = 0.5.
104
-------
1.50 r—. 1 •
0123466789 10
3.5,,—, , , ,
0123458789 10
1.0
0.5 °-75 •
0123456760 10
Figure 3.12 The effect of parameter a on dimensionless driving pressure,
half-length and aperture. Other parameters are constant: m = 6,
a* - 1.0.
er
105
-------
Comparison With Results From The Lab
Variations in forms of records of driving pressure observed in the lab
experiments can be explained using the analysis described above. To do so, we
must first include effects of a defonnable pumping system on the form of the
pressure record. Volumetric distortion of the pumping system causes fluid to
either be stored when pressure is increasing or released when pressure is
decreasing, so that the flow rate into the fracture will differ from the flow
rate of the pump. Distortion can be included in the analysis by modifying
eq. (3.22b) to
V = V + V= (2ita2w/E) [Pw - a(\ -
-------
1.50
0.00
0
50
100
150
200
p (kPa)
Figure 3.13 Volume stored in pumping system as a function of fluid
pressure fluid pressure. Dashed line is second-order regression.
107
-------
(3.39b)
v i
which reduces to eq. (3.28) when C = 0. Values of C^ ranged from 0.02 to 2.0
during the experiments, depending on the modulus of the soil and the slot
length.
Dilation of the experimental apparatus affects the forms of pressure
records by changing the time scale according to eq. (3.39). The
characteristic time increases, reducing the slope of the record during
inflation, as the apparatus becomes more compliant. The form of the pressure
record during propagation is especially affected early in propagation when a
large value of C causes the record to steepen (Fig. 3.14). As a result, the
slope of the record during early stable propagation may be nearly
indistinguishable from the slope during inflation of the starter slot. The
term C also results in a steepening of the record early in the unstable
period of propagation. Steep slopes during this period are commonly observed
in both field and lab investigations of hydraulic fracturing of rock, where
large moduli could result in large values of C.
The rates of growth and dilation of the fracture both increase
dramatically, indicating an increase in the volumetric growth rate, as
C increases (Fig. 3.14). The volumetric rate of growth of the fracture
increases, even though the pump is running at a constant rate, because fluid
is released from storage in the pumping apparatus when driving pressures
diminish during unstable propagtion. Accordingly, the flow rate into the
fracture will be greater than the flow rate of the pump during unstable
propagation. This conclusion is confirmed by observations of minute bubbles
in glycerin flowing through a translucent tube leading to the fracturing cell;
their velocity was less during inflation and stable propagation than it was
during unstable propagation.
The revised expression for / in eq. (3.39) was used to compare results
from the analytical solutions to the forms of records from the experiments.
Results from the lab experiments showed that the form of the record of driving
pressure depended on both the moisture .content and the slot length. As
moisture content decreases, the driving pressure required to initiate
fracturing increases, the period of stable growth early in propagation
shortens, and the downwardly concave shape of the record becomes tighter.
Similar changes in the records occur when the slot length decreases.
Records of driving pressure are similar to results from the analytical
solution (Figs. 3.15 and 3.16) using parameters listed in Table 3.2. The
parameters were estimated from lab data, except m which was adjusted to yield
the best fit to the data—using m estimated from lab data yields driving
pressures that greatly exceed the ones that were observed. The general forms
of the records for samples of different moisture content are predicted by the
analysis. The driving pressure at the break in slope and the duration of the
early period of stable growth are within a few percent of those observed. The
108
-------
0.00
0.0 1.0 2.0 3.0 4.0 5.0
5.0
4.0
3.0
2.0
1.0
6.0
4.0
* 3.0
<0
2.0
1.0
0.0
10.0
0.0 1.0 2.0 3.0 4.0 6.0
10.0
0.0 1.0 2.0 3.0 4.0 6.0
Figure 3.14. Driving pressure, half-length and aperture as functions of
time and compliance of pumping system, m: 10; a : 1.0;
109
-------
100
75
cti
DH
50
25
0
-T 1 r
-i 1 "
0
50 100 150
Time (sec)
Figure 3.15. Records of driving pressure as a function of time from
experiments and from analytical solution (dashed) for samples of
various moisture contents.
110
-------
0 25 50 75 100 125 150
t (sec)
the length of the starter dot.
in
111
-------
slope of the records during unstable propagation steepens with increasing
moisture content in both the analysis and the lab data
The effect of changing the slot length is predicted by the analysis (Fig.
3.16). Driving pressure at the break in slope increases, the duration of
stable propagation decreases, and the slope during unstable propagation
increases as the length of the initial slot decreases.
The analysis overestimates the driving pressure during unstable
propagation in all the examples (Fig. 3.15 and 3.16). Small amounts of the
injection fluid leaking out of the edges of the sample, due to imperfect seals
between the samples and the apparatus, probably caused the driving pressure
during propagation to be less than that predicted by the analysis.
TABLE 3.2. PARAMETERS USED I N ANALYSES
Curve
Moi s t u re m K
kPa cm1'2
/
c
( sec)
C a.
c i
(cm)
Fi
Fi
g.3.15
a
b
c
g.3.16
a
b
0
0
0
0
0
.29
.26
.23
.27
.27
75
30
50
30
30
22
41
186
63
63
28
50
150
100
95
0
0
5
0
0
.05
.30
.0
.088
.354
1
1
1
1
0
.22
.22
.22
.22
.61
In both Figure 3.15 and 3.16 the parameter m was selected to yield
results that matched experimental data. Values of m are an order of magnitude
greater than those obtained from experimental observations, so that the length
of unwetted tip required for the analytical solution to resemble the observed
pressure records is considerably less than the length of the undyed zones on
fracture surfaces. This suggests either that the effective length of the
unwetted tip may be shorter than the undyed zone observed on fracture
surfaces, or that the driving pressure acting over the unwetted tip may be
greater than the negative confining stress.
Comparison with Other Solutions
Several other two-dimensional analytical solutions have been published
describing the growth of a hydraulic fracture having a geometry resembling the
one used here. Khristianovich and Zheltov (1959) solve the case where the
fracture has an identical geometry, but the distribution of driving pressure
differs slightly from the one used here. They assume that the driving
pressure is a maximum at the center of the fracture and diminishes due to
viscous losses to 0 at a point b, which is less than the total length of the
112
-------
fracture. The variable driving pressure is approximated by a statically
equivalent driving pressure that is uniformly distributed and acts over 0 & x
£ 6' (b' is obtained from Khristianovich and Zheltov, 1959; eqs. 6 and 7).
Thus, the driving pressure they use is uniform but its magnitude depends on
fluid viscosity, whereas the pressure used here is uniform but independent of
viscosity.
The analysis of Kristianovich and Zheltov includes a zone at the tip of
the fracture where fluid pressure is equal to the fluid pressure in the
confining material. In contrast, the analyses used here assumes that the
pressure along the tip zone is zero, and is independent of the pressure of
pore-fluid in the soil. Our assumption is certainly valid for
partially-saturated soil, where the pressure of the pore fluid is less than
zero. The assumption seems reasonable for saturated soils of low permeability
as well. This is because the dilation of the crack itself must reduce the
pressure within the tip, and the tune required for those low pressures to
equilibrate with pore-fluid pressures would be longer than the few seconds
that the tip remains unfilled by injection fluid. In any case, the assumption
used here marks one end and the one of Khristianovich and Zbeltov marks the
other end of the range of possible pressures within the tip zone.
Geerstma and DeKlerk (1969) solve a problem whose geometry is similar to
the one used here, except they provide for a distribution of pressure within
the fracture that varies from a maximum at x = 0 to zero at x = b. They
obtain the pressure distribution by integrating over the interval 0 s x b an
equation for flow through a narrow rectangular channel, and assuming that the
pressure within the fracture is zero over b < x s a. Both Geerstma and
DeKlerk, and Kristianovich and Zheltov introduce an unwetted zone remove the
stress singularity at the fracture tip. This concept, which is applied to
brittle fracture by Barenblatt (1962) and to ductile fracture by Dugdale
(1963), is mechanically different from the one used in this work. We show
that the unwetted tip can develop due to a difference between the velocities
of the fluid and the fracture, and the length of the unwetted zone is
therefore related to differences between the two velocities. In the other
model, the length of the unwetted zone is related to the magnitude of JTfc and
is independent of the relative velocities. These differences are subtle, but,
inasmuch as the size of the unwetted zone strongly affects the length and
aperture of a fracture, the mechanism for growth of that zone plays an
important role in predicting fracture dimensions.
Spence and Turcotte (1985) built on the work of Geerstma and DeKlerk by
deriving an analytical solution that includes effects of both viscous
dissipation of pressure in the fracture and finite fracture toughness. The
general solution of Spence and Turcotte requires numerical integration;
however, for specific cases where the system is dominanted by either fracture
toughness or viscous dissipation the solution reduces to algebraic
expressions. Predicting the migration of igneous sheet intrusions was the
primary goal of Spence and Turcotte, and they have omitted an investigation of
the pressure distribution at the tip of a hydraulic fracture.
Perkins and Kern (1961) present a solution for a long, rectangular
113
-------
fracture that is elliptical in shape in sections taken normal to the long
axis. They obtain a pressure distribution by using an equation for flow
through a narrow elliptical channel, and assuming the driving pressure is zero
at the end of the channel. Nordgren (1972) modified the solution of Perkins
and Kern (1961) to include effects of dilation and leakoff on the pressure
distribution in the fracture. Both Perkins and Kern (1961) and Nordgren
(1972) ignore the problem of stress concentration at the tip of the fracture,
so conditions of equilibrium propagation are not explicitly satisfied.
Medlin and Masse (1984) and Geerstma and Haafkens (1979) point out that
the analytical solutions described above can be written as power law functions
relating driving pressure, half-length, and aperture to time
P= c f (3.40a)
0
a - d £ (3.40b)
8 = e f (3.40c)
The solution derived for this work reduces to a set of power law
functions by setting bla = 1.0, which is the same as setting the
length of the unwetted tip to zero (eq. 3.32). Values of the
exponents given by the present solution (using bla = 1.0) are
identical to those derived by Geerstma and DeKlerk, and by Spence and
Turcotte (Table 3.3), and they are similar to values from
Kristianovich and Zheltov.
—TABLE 3.3. EXPONENTS FROM VARIOUS ANALYTICAL SOLUTIONS
_ JL JL JL
Kristianovich and Zheltov**
Kristianovich and Zheltov
Geerstma and DeKlerk
Spence and Turcotte
Perkins and Kern
This work (bla = 1.0)
P
-0.3
-1/4
-1/3
-1/3
+1/5
-1/3
JL
0.6
1/2
2/3
2/3
4/5
2/3
£
0.4
1/2
1/3
1/3
1/5
1/3
* Values cited by Medlin and Masse (1984)
** Based on eqs. (33), (36) and (45) of Kristianovich and Zheltov (1959)
The values are markedly different from those given by Perkins and Kern
(1961), however. In particular, the solution of Perkins and Kern
(1961) yields a positive value for /?, whereas the others yield
114
-------
negative values. Positive value of /? indicates that driving pressure
increases throughout propagation, whereas pressure was observed to
decrease in the experiments suggesting that a negative value of /S is
appropriate.
Forms of the constants c, d, e from the present solution are
similar to those given by Spence and Turcotte for a fracture whose
resistance to propagation due to fracture toughness is much greater
than resistance to now (Table 3.4). Fracture toughness enters as the
same power for both
-TABLE 3.4. COMPARISON OF CONSTANTS
Constant Spence and Turcotte This paper
1'3 r . , il/3
2K*w (1 - o2)
QE'
.1/405/4 'W
d 0.5599
3/41
, Q.5685 P
-------
time on a log-log scale. They found that apparent values of x and £
decrease, whereas ft increases as confining stress increases (Figure
3.17).
The experimental apparatus of Medlin and Masse resulted in
conditions resembling two-dimensional plane strain, so the analysis
described above was used to examine the effect of confining stress on
apparent values of the exponents. The ratio bla is independent of a,
but increases with confining stress according to Medlin and Masse
(1984; fig. 7). Figure 3.17. is based on figure 7 in Medlin and
Masse, but values of bla have been extrapolated for the purpose of
this analysis. A driving pressure at failure of approximately 500 psi
is apparent from figure 3 (Medlin and Masse, 1984), and this value
will be used to determine a for all the calculations--^, and slot
length are assumed to be constant. The apparent value, of ft jvas
determined by linear regression of the logarithms of P. and t , and
the other exponents were determined in a similar manner.
The analysis is able to predict the experimental values of ft
throughout the range of confining pressures. At relatively low
confining pressure, ft increases with confining pressure, but it
remains roughly constant at intermediate to high confining pressure.
Figure 3.18 shows that increasing a tends to increase ft, whereas
decreasing the length of the unwetted tip, with a according to Figure
3.17, tends to decrease ft. At confining pressures greater than 14 MPa
these effects apparently balance one another according to the data of
Medlin and Masse and the results of the analysis. We conclude that
those changes in the form of the pressure record, expressed as changes
in ft, can be explained by the effect of confining stress acting on the
unwetted tip.
The analysis yields values of x and £ that exceed those observed
in the experiments of Medlin and Masse. Flow out of the fracture and
into the enveloping material, or leakoff, is a possible explanation of
the discrepency. The present analysis is unable to account for
leakoff, but the analysis of Nordgren (1972) shows that leakoff will
decrease the values of x and e. Moreover as Medlin and Masse (1974)
point out, conservation of mass requires that £ + £ = 1.0 if no
leakoff occurs, and that sum will be less than 1.0 if leakoff does
occur. At equal confining stress, sums of x and £ determined
experimentally by Medlin and Masse (Fig. 3.18) are all less than 1.0
and those sums decrease with increasing confining pressure. This
information substantiates the conclusion that leakoff is a possible
explanation for why the data of Medlin and Masse on x and £ are less
than the results of the analysis.
DATA QUALITY
The objective stated in the Quality Assurance Project Plan (memo
116
-------
Ctf
1.00
0.98
0.96
0.94
0.92
4.0
(J
8.0
12.0
10
20
30
40
a (MPa)
16.0
50
Figure 3.17 The ratio of wetted to total length of a fracture as a function
of confining stress. Data from Medlin and Masse (1984).
117
-------
X
-0.35
0.70
0.65
0.60
0.55
0.50
0.45
(1)
0.40
0.40
0.35
0.30
0.25
0.20
10
10
20
30
20
30
a (MPa)
16.0
.1
40
40
50
O
50
60
Figure 3.18. Variation of exponents in eq. (3.40) as functions of confining
stress. Data from Medlin and Masse (1984), solid line from
analytical solution. 1Q
llo
-------
submitted to David L. Smith, 3 October 1988), was to make measurements
of Kie that can be duplicated to within IS percent. In Chapter Two,
we showed the results of four tests conducted on similar samples. The
three of the four values of initiation pressure were tightly
clustered, they were within 2.5 percent of their average value. The
fourth measurement was less than the other three. The average of all
four measurements is 25.4 kPa and that fourth value is 22.8 kPa, which
is 10 percent less than the average. Critical stress intensity is
determined directly from initiation pressure, and so it will have the
same range of values as described above.
Earlier in this chapter, results showed that doubling the slot
length caused variations of K that averaged 10.4 percent. The
critical stress intensity both increases and decreases as the slot
length increases, indicating that the variations that were observed
reflect experimental error, rather than a systematic dependence on
slot length as reported by Ouchterlony (1982).
Critical stress intensity measurements can be duplicated to
within 15 percent of an average value using the methods described in
the text.
The principal measurements, the methods of obtaining them, and
the accuracies of those methods are presented in Table (3.5).
TABLE 3.5. EXPERIMENTAL MEASUREMENTS
Measurement Method Accuracy
Sample size scale ±0.1 cm
Length of slot micrometer ±0.001 cm
Density Weight/Volume ±0.01 gm/cc
Confining pressure Gauge ±0.005 kPa
Injection pressure Transducer ±0.002 kPa
Injection rate pump calibration 0.00003 cc/sec
Ar calculation 0.007 kPa cm"2
Pressure gauges and transducers were purchased at the beginning
of the project, and were maintained in good working order. Gauges
used to measure confining pressure were calibrated using a pressure
transducer. The transducers were calibrated at the factory.
The precision of the critical stress intensity measurements is
impossible to assess because published values of that parameter are
unavailable for soil.
All the tests that we set out to conduct were accomplished during
the study. Completeness was 100 percent.
119
-------
The results are expected to represent K determined using
similar techniques of sample preparation, experimental apparatus, and
method of loading. Experimental methods that facilitate detecting the
onset of fracturing, perhaps by acoustic or optical methods, probably
will show that fracturing occurs slightly prior to the break in slope
of the injection record, which was used in this study to infer
fracturing. As a result, critical stress intensity measurements
obtained by those methods will be less than those cited here.
DISCUSSION
A satisfactory analysis of hydraulic fracturing of soil should
yield a method of predicting the driving pressure at the onset of
fracturing as well as the forms of pressure records during
propagation, and it should explain the development of essential
features of a fracture, according to requirements put forth in the
introduction of this chapter. Elements of linear elastic fracture
mechanics were used to develop various analyses to test against those
requirements.
The critical stress intensity at the onset of fracturing is
independent of the length of the initial slot, and appears to be a
material property of the soil used in this study that will serve as an
acceptable predictor of fracturing. Moreover, theoretical estimates
suggest that the size of the process zone at the tip of a fracture in
the Center Hill clay ranges from one to a few mm, which is small
compared to lengths of initial slots and further supports the
applicability of K^ as a predictor of fracturing.
The critical stress intensity of the Center Hill clay ranged over
an order of magnitude for various moisture contents and durations of
consolidation, so that that lab data will only yield rough estimates
of conditions in the field. An in-situ method of determining K
would yield values more suitable for field applications.
Nevertheless, the lab results are significant in that they show that
ATie is a meaningful property describing fractures in clay.
The development of a hydraulic fracture in the Center Hill clay
at moisture contents less than 0.21 includes the growth of an unwetted
zone at the tip of the fracture. A theoretical analysis of coupled
fluid flow and elastic deformation shows that the velocity of fluid
near the tip of a fracture is less than the velocity of the fracture
itself, thus providing a mechanism for the development of the unwetted
tip. Tracking the position of the fluid front by the theoretical
model yields lengths of the unwetted and wetted parts of the fracture
that are similar to lengths observed on the surfaces of fractures
created in the lab. Detailed analyses of the rate of growth of the
120
-------
unwetted tip as a function of moisture content (e.g. Figure 2.10) are
the subject of future investigations.
An early period of stable propagation, characterized by
increasing driving pressures, was observed in nearly every lab test.
Stable propagation early in the growth of a hydraulic fracture can be
explained by an increase in resistance to propagation resulting from
growth of an unwetted tip. This explanation is confirmed by results
of both numerical and analytical solutions to fracture growth. An
alternate explanation of stable propagation resulting from large
viscous losses due to flow in a narrow region near the tip of a
growing fracture (Zoback and others, 1977; Zoback and Pollard, 1978)
could also explain the lab data but it is inconsistent with the
results of the numerical analysis.
Results of the numerical solution using parameters typical of the
lab experiments show that the fluid pressure within a fracture is
nearly uniform. This suggests that a simple analytical analysis,
which assumes uniform pressure, could provide insight into the general
behavior of the fractures. Pressure records from the lab can be
reproduced usin| the analytical model by selecting an appropriate
function describing the growth of the unwetted zone. The analytical
model also provides an explanation of the dependence of the form of
pressure records on confining stress, which was observed in hydraulic
fracturing experiments conducted using rock specimens (Medlin and
Masse, 1984).
The methods of linear elastic fracture mechanics meet the
requirements of an acceptable model of hydraulic fracturing of soil.
Modifications of the analysis to account for large-scale plastic
yielding at the fracture tip appear to be unnecessary. The present
methods could readily be adapted to account for appreciable plastic
yielding during hydraulic fracturing (e.g. Biot and others, 1982),
although measurements that are more detailed than those used here
would be required before such methods seem warranted.
Much of the published analyses on hydraulic fracturing of rock
appear to be generally applicable to hydraulic fracturing of soil.
Analyses that track the position of the wetted front, such as those by
Abe and others (1976), Roegiers and others (1982), Griffiths and
Nilson (1986), or Nilson (1986), appear to be particularly well-suited
to predicting hydraulic fracturing of soil.
Analyses that assume that the fracture is completely filled with
fluid will overestimate lengths and underestimate apertures as
compared with analyses that allow for the development of an unwetted
tip. Inasmuch as fracture length and aperture control the performance
of a fracture in delivery and recovery, it is clear that understanding
processes at the fracture tip will improve the ability to design field
applications of hydraulic fractures in either soil or rock.
121
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SECTION FOUR
SETTING AND DESIGN OF THE FIELD TEST-1988
The 1988 field test was conducted at a site 10 km north of downtown Cincinnati on
the western side of the valley of Mill Creek, a southerly-flowing tributary of the Ohio
River. The site is on the southeastern side of an area owned by the ELBA Company, who
currently uses it as a municipal landfill.
Investigation and preparation of the test site took place during several months in
Spring 1988. The actual test, however, only required 12 hours and was completed in one
day, 15 June 1988. Ten hydraulic fractures were created during the test. Field evaluation
of the results of the test took place during the six weeks following the test.
SITE CHARACTERISTICS
The vicinity of the test site is an area of gently sloping ground bounded on the
northwest by a vertical face and on the southwest by moderate slopes into an excavated
trough (Fig. 4.1). The southern side of the trough is bounded by a north-facing vertical cut,
the eastern end of which is shown on the southwestern corner of Figure 4.1. The ground
surface at the time of the test had been excavated during operations at the landfill to
several meters below the natural ground surface.
The site itself is an elongate strip trending N20E and roughly 80 m long. The
northern end of the site is on a gentle, south-facing slope, whereas the southern end of the
site is on level ground (Fig. 4.1). The slope of the ground surface is important because it
apparently affected forms of the fractures.
Geology
Glacial till, probably of Dlinoian age, underlies the test site. The thickness of the till
is unknown, but it is more than several tens of meters. Three stratigraphic units were
identified in the till based on exposures in vertical faces near the site, on boring logs, and
on exposures in trenches cut in the test site (Fig. 4.2 and 4.3). The upper till unit, Unit 1, is
0.5 to 2 m thick and consists of massive light brown-grey clay and silt containing 5 to 15
percent rock fragments. Coarse gravel, cobbles, fragments of limestone and organic matter
are disseminated through Unit 1.
The middle unit, Unit 2, is dominantly flat-lying beds that fine upward from coarse
gravel to clay. A typical bed consists of orange-brown cobbles and gravel at the base that
grades upward to orange-brown coarse and fine sand, to light brown silt, and to light
brown clay at the top. The graded beds range in thickness from 0.1 to 0.4 m, and in most
exposures are several m to several tens of m in lateral extent. Locally, the forms of the
beds are irregular and highly contorted with large changes in thickness occurring over
several m. An example of the irregular bed forms is shown in Figure. 5.9. Massive beds of
grey clav and silt are locally interfingered with graded beds. The total thickness of Unit 2
ranges from 3 to 7 m.
122
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Scale
5 10
nrwtars
15
\
o Well location
13 Well I.D.
'»n Vent
Strati graphic
contact
Topographic contours In
meters above MSL
Location of
hydraul Ic
fracturing
equipment
Figure 4.1. Topography and locations of boreholes, vents, and hydraulic fracturing
equipment at the ELDA test site.
123
-------
Unit 3: Mouiv, iiity day
o Well location
-- Stratlorophlc
contact
Topographic contours In
meters above MSL
Figure 4.2. Geology of the ELD A test site.
124
-------
UNIT1
Weathered till topsoil, 0 to 0.3 m thick.
Light brown to grey, massive clay and silt
containing 5 to 15 percent disseminated
gravel, cobbles and rock fragments.
Roots common.' One half to 2 m thick.
Sharp, planar contact.
UNIT 2
Light brownish-grey, massive silt. One m thick,
thins south of site.
Upwardly-grading beds and lenses of gravel, sand
silt and clay that range from 0.1 to 0.4 m thick;
and massive to laminated beds of grey silty-clay
0.2 to 1.0 m thick. Irregular, contorted bed-
forms common. Total thickness 4 to 7 m.
Irregular contact.
UNIT 3
Light grey, massive, silty-clay containing 5 to 20
percent disseminated gravel, cobbles and rock
fragments. Irregular lenses of silt, or yellow-brown
sand present locally. Lower contact not exposed, at
least 8 m thick.
Figure 43. Stratigraphic section from the vicinity of the ELDA test site.
125
-------
The upper surface of a light brown, massive silt bed several dm in thickness marks
the contact between Units 1 and 2. The contact is planar and nearly flat-lying, differing in
elevation by roughly 0.1 m over the study area.
The lower till unit, Unit 3, consists of massive, grey silty-clay containing 5 to 20
percent disseminated rock fragments. Pods and beds of light grey silt, or brown sandy-
gravel occur locally. The lower contact is not exposed, so the thickness of Unit 3 is
unknown. The upper surface of the massive grey clay of Unit 3 marks the contact between
Units 2 and 3. The contact varies in elevation by several meters in the vicinity of the site.
Hydraulic fractures were created in Units 2 and 3. Fractures at boreholes 2 and 13
were in Unit 2, the one at borehole 12 propagated upward from Unit 3 into Unit 2, and the
others were contained within Unit 3.
Hydrology
Eleven of the 14 boreholes drilled during exploration of the site were dry when we
created the hydraulic fractures. In those boreholes that did contain water, the water depths
were less than 20 cm at the time of fracturing. Some other boreholes contained water
several days prior to fracturing, but the day before fracturing we found soft mud, but no
standing water, at the bottom of those holes (Table 4.1).
A regional water table is present several tens of meters or more below the level of
the boreholes, but it was insignificant to the test.
During testing the silty clay that comprises most of the till was unsaturated (ratio of
water volume to pore volume of 29%). Water that was observed in boreholes apparently
drained from perched zones within sand and gravel lenses in the till.
Effects of the hydrologic conditions in a borehole on the results of hydraulic
fracturing were undetectable.
In situ State of Stress
The state of stress in the till was measured in situ using a method of analyzing
injection pressure after creating a small-volume (10-20 ml) hydraulic fracture. The
method of analysis of the pressure record is used routinely for research in rock mechanics
(Zoback and Pollard, 1978; Gronseth, 1979), but the apparatus used to create the small
hydraulic fractures in soil was designed for this project.
The apparatus consists of a heavy-walled steel pipe (1/2" Nominal Schedule 80
pipe, O.D.: 2.13 cm; I.D: 1.42 cm) fitted with a conical point. The point consists of an outer
beveled ring attached to the pipe, and an inner, bullet-shaped point attached to a steel rod
extending the length of the pipe. A cap fits on the end of the pipe and prevents the rod
and inner point from moving when the pipe is driven into the ground.
126
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TABLE 4.1. CONDITIONS OF BOREHOLES PRIOR TO TESTING.
BOREHOLE DEPTH OF CONDITIONS
CASING (m) (6/9/88) (6/13/88^ (6/14/881
2 2.76 DRY DRY N/A
3 1.39 N/A* N/A N/A
4 3.65 DRY DRY DRY
5 1.64 DRY DRY DRY
6 1.86 DRY MUDDY DRY
7 1.83 DRY MUDDY DRY
8 1.89 N/A 1.45" 1.77
9 1.86 0.88 MUDDY MUDDY
10 2.10 1.98 1.58 2.07
11 1.98 DRY DRY DRY
12 1.99 1.47 1.80 1.80
13 2.01 1.18 MUDDY MUDDY
14 1.85 DRY DRY DRY
15 2.23 1.24 1.71 1.77
*: N/A, data not available.
**: Water level in m below ground surface.
To measure lateral stress the pipe is pushed into the ground using a post-hole
driver (Fig. 4.4); we were able to drive the pipe to depths of 2 m in both till and colluvium.
The rod and inner point is retracted exposing soil at the bottom of die pipe. A coring
point, shaped like a thin-walled rube 0.63 cm in diameter, is driven into the soil at the
bottom of the pipe and cuts a cylindrical hole roughly 10 on in length (Fig. 4.4). Water is
injected into the pipe using a positive displacement pump and the pressure is monitored
using a pressure transducer and a data acquisition computer. Lateral pressure of the soil
against the pipe seals the system and a hydraulic fracture is created from the cylindrical
hole at the bottom of the pipe (Fig. 4.4).
The least compressive in situ lateral stress is obtained by assuming that it is equal
to the pressure of the injection fluid when a hydraulic fracture closes after pumping has
ceased. This pressure is commonly termed the instantaneous shut-in pressure, ?«. When
the pump is turned off after a hydraulic fracture has been created, the pressure of the
injection fluid commonly shows two well-defined periods of behavior (Medlin and Masse,
1984). During the first period, the pressure decreases rapidly as fluid flows out of both the
borehole and the fracture and into the enveloping material. The rate of decrease of
pressure diminishes, however, as the fracture closes. During the second period, the
pressure decreases slowly, at a nearly constant rate, as the fluid leaks only out of the walls
of the borehole.
There are a variety of methods used to infer P*; from the record of injection
pressure as a function of time (e.g. McLennan and Roegiers, 1982; Aamodt and
Kuriyagawa, 1982; Gronseth, 1979; Zoback and Pollard, 1978; Nolte, 1979; Muskat, 1937).
127
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s^
®=-
•::•' Fracture from
: '.'• small diameter
Lance tip'-'-'
Small core::.:^
cutter ~
Figure 4.4. Method of creating small hydraulic fracture to measure the least
horizontal confining stress.
128
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A relatively simple method, suggested by Medlin and Masse (1984), is to use the maximum
pressure during the second period of pressure decline. This pressure is obtained by fitting
a straight line to the record and recording the earliest point of intersection between the
line and the record (Fig. 4.5).
According to the experiments of Medlin and Masse (1984), ?« obtained in this
manner can over-estimate the actual applied stress, and the amount of over-estimation
depends on the rate of flow out of the fracture and other factors. Roughly one dozen
experiments were conducted using the laboratory apparatus described earlier to test
whether this method of obtaining Pig would yield the confining stress in soil. Hydraulic
fractures were created from a cylindrical hole 0.63 cm in diameter and 10 cm long (the
same size as in the field apparatus) cut in Center Hill clay. The results are encouraging;
Ptsi obtained from the method described above was typically within five percent of the
confining stress applied to the sample (Fig. 4.5a).
In the field at the ELDA site, tests were conducted at a depth of 1.2 m in silty-clay
till (Unit 3). The injection pressure rapidly increased to 1200 kPa and then abruptly
decreased indicating the onset of fracturing (Fig. 4.5b). We turned off the pump after 60
seconds, at which time the pressure decreased rapidly for roughly 10 seconds and then the
rate of decrease started to diminish. The rate of decrease became roughly linear at 65
seconds. A second test was conducted by turning on the pump until the pressure reached a
peak and started to diminish (indicating further propagation), and then turning off the
pump. The pressure record of the second test is similar to that of the first (Fig. 4.5b).
Fluctuations in pressure during the linear part of the second test probably resulted from
vibrations caused by heavy earth-moving equipment operating nearby.
An instantaneous shut-in pressure of 320 kPa was obtained during the test at the
ELDA site (Fig. 4.5b). The transducer was 2.15 m above the fracture, so a correction for
the static pressure gradient was added to obtain an estimate of the lateral confining
pressure. The vertical confining stress is assumed to be the unit weight of the till times the
depth of the test.
Using those methods, the lateral confining stress is inferred to be 340 kPa (roughly
50 psi), and the vertical confining stress roughly 26 kPa (3.9 psi). The ratio of vertical to
lateral confining stress is 1:13 at a depth of 1.2 m.
Hydraulic Conductivity
Saturated hydraulic conductivity, K«, of till was measured in situ at several locations
using a Guelph borehole permeameter, a device manufactured by Soilmoisture Equipment
Company, Santa Barbara, CA. The device is designed to measure Kg in boreholes
penetrating unsaturated porous media. In general, the device uses a Mariotte bottle device
to hold a constant level of water in a borehole, and allows flow rate out of the well to be
measured as a function of time. A test is conducted until the flow rate becomes constant.
Details of the operation of the Guelph Permeameter are available from the manufacturer.
The saturated hydraulic conductivity is obtained from the steady-state solution of
flow from a cylindrical hole in an unsaturatedporous media (Reynolds and Elrick, 1985).
Two methods of solving for K« are available. The most accurate method requires
measurements of flow rate at two different heads (water levels in the borehole). This
129
-------
o
Q_
25
100
75
to
D
(0
s 50
i_
Q_
25
0
Injection pressure
. Applied
Load
a
CL
1250
1000
750
500
250
Pump on
off
100 200 300 400 500
Depth: 1.2 m
ELDA Landfill
Hmin
Pump on | off | on j off
0 50 100 150 200 250
Time (sec)
Figure 4.5a. Injection pressure as a function of time during a lab experiment. 4.6b.
Injection pressure as a function of time at the ELDA test site using
field apparatus designed to estimate lateral confining stress.
130
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method requires a homogeneous porous media, and will yield erroneous values if layers or
discontinuities are present.
Another method of determining Kg requires measurements of flow rate at only one
value of head, and it can be applied in layer media. The accuracy of this method is less
than of the method described above because this one requires an estimation of the ratio
of KS and the matric flux potential. Fortunately, however, the ratio can be estimated from
descriptions of the till to yield values K« that are within 20 percent of Kg determined by
other methods, according to Elrick and others (1988). This accuracy is considered
sufficient for our purposes.
Both methods of calculating Ks were used, but we found that the method requiring
two measurements typically yielded unsatisfactory values of Kg (values were less than 0).
As a result, the method requiring one measurement and an estimation of the ratio of Kg
and matric flux potential was used for all estimates of Kg.
In general, the saturated hydraulic conductivity of silty clay is between 1.5 x
cm/sec and 1.9 x 10-7 cm/sec, whereas those measured in silty sands and gravels are an
order of magnitude or more greater; between 1.0 x 10-5 cm/sec and 3.5 x 10-s cm/sec.
Measurements of Kg were made at five locations, and the values are tabulated below
(Table 4.2).
Physical Characteristics of the Till
A suite of tests was performed in the laboratory on samples of the ELD A Till to
determine standard geotechnical characteristics. The tests were conducted by Patricia
Strube, a geotechnical soils analyst at the Center Hill Research Facility. The methods
used to make the measurements are described in the ASTM Handbook on Soil Testing.
Samples from four shelby tubes pushed into the till at the ground surface were used for the
analyses.
TABLE 4.2. SATURATED HYDRAULIC CONDUCTIVITIES OF TILL
Location
1
2
3
4
5
Depth (cm)
40
45
150
30
42
Material
silty clay
silty clay
silty clay
silty sand
and gravel
silty sand
and gravel
K» (cm/sec)
7.5 x 10-7 to 1.5 x 106
1.0x10* to 1.4x10*
1.9 x 10-7 to 8.9 xlO-7
1.0xlO-sto2.4xl05
3.0 xlO-5 to 3.5X105
131
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TABLE: 4.3 PHYSICAL CHARACTERISTICS OF SILTY-CLAY TILL
Atterburg
Limits
Liquid 22.6 22.9 24.8
Plastic 12.5 10.5 11.4
Shrinkage 19.8 15.5 15.3
P.I. 10.1 12.4 13.4
Grain sizes (by wt.)
Gravel 0.13 0.18
Sand 0.29 0.28
Silt 0.36 0.31
Clay 0.22 0.23
Void Ratio: 0.34
Porositv: 0.25
Moisture: 11.6 13.5
Degree of
Saturation: 0.29
Bulk Unit Weight: 2268kg/m3 (141.6 lb/ft3)
Bulk S.G.: 22
Drv Unit Weight: 2031kg/m3 (126.8 lb/ft3)
0.10
0.34
0.34
0.22
ET4
25.0
15.7
9.3
0.11
033
0.37
0.19
AVE
23.8
12.5
16.8
11.3
Specific gravity, solids:
2.68
The characteristics of the ELD A Till are similar to those of other tills analyzed by
Strube in the vicinity of Cincinnati. It is a hard soil, requiring more than 30 blows during a
standard penetration test (Navfac, 1982), and it is relatively dense (bulk unit weight of
2268kg/m3 or 141.6 lb/ft3) compared with colluviai soil or alluvium.
The till is well-graded from particles of clay size to sand size or larger. Cobble- to
boulder-sized rock fragments are common in field exposures, although they were absent
from the sample used for the grain size analysis (Table 43; Fig. 4.6).
Results from tests of the Atterburg Limits plot above the A line and indicate that the till is
a CL type soil, in the nomenclature of the Unified Soil Classification System (ASTM
D248,
BOREHOLES
Eleven boreholes were hydraulically fractured during the field test. Most borings
are approximately 10 m from their neighbors (Fig. 4.1), except at the southern end of the
site where a cluster of four borings are each 2.5 m from their nearest neighbor (Fig. 4.1).
132
-------
u.i. HA*
tOO. 4-1
n
i "
* >•
r
0
1
DAB WVI ontwo M MOO U.I
m i v H « i « « in i
"
t
— -^^
1
MO 1M M 10
COMUI
WMM
•"" —
sssa
r
.
^
^
nANDAASKVf NUMHH
U*» M 40 J070JCM
1 1 1 >
.
—
*»
1 1
T
---
•s
1
X,
i^
ri«o 71
I I
X.
^ ,
MAM S« HUWCTItt
Figure 4.6. Grain size distributions in samples of ELDA Till.
133
-------
U i HAMUV MVt OttMMO M NCMU U.L llAMUJO WV1 NUXMB
u
Ml
4 1 1
1
100
10
H
1
V K H
r^-<
10
1 i
•
^
*
1
1 1
1
V.
0 1* M »
1 I 1
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• JC
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0.1
J
^
0 7(
*DO*I40 71
1 '
X
^
O.I
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OOJ
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\
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\
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s
4.00J
'
•^
S*^-
DC
u i II««UD im OKMNO M torn u.i. SIUOAJO tun NUMHB
i 1 1
. _
—
1 IK 1 » » ft
,)B
-
1
to-.
-
'
^
1 4 * IWUUK
r
" ,
N
1 '
•x^
'
>OJC XI 70 100' I«O Ml
*^
^
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(
-
y
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— H
«AD«10N CUIVU
134
-------
Depths to the bottom of casing ranged between 1.64 m and 1.95 m at nine of 11
boreholes. The other two boreholes were deeper; 2.72 m and 3.81 m (Table 4.1).
Design
Boreholes were designed for the purpose of creating hydraulic fractures. In
general, a borehole consists of a steel tube cemented into a boring, and open at both ends
(Fig. 4.7). A basket is fixed to the lower end of the casing to prevent cement from plugging
the bottom of the borehole. The open boring extends several dm below the basket ana is
partly filled with fragments (cuttings) of till. A narrow notch, oriented normal to the axis
of the borehole, is cut in the wall of the boring several cm below the bottom of the casing.
Roughly horizontal hydraulic fractures were expected to develop, and the boreholes
were designed to nucleate a horizontal fracture at the notch. Although the expectations of
horizontal hydraulic fractures were correct, most of the fractures initiated at or above the
basket, not at the notch.
Specifications
Borings were made with a Marmon-Herrington drill rig using an auger 7.62 cm (3
in.) in diameter. The auger was pulled out of the hole after each 0.3 m (Ifoot) of drilling
so that samples of the cuttings could be collected. Each boring required between 30 and
90 minutes to complete.
The borings were drilled several dm beyond the depth at which we intended to cut
the notch because cuttings filled a zone several dm deep at the bottom of the hole. Tools
to retrieve cuttings from the bottom of the hole were unavailable during drilling.
Notches were cut in the walls of the boring using a mechanical device. The device
consisted of a talon-shaped blade (made from tool steel 0.3 cm thick) mounted on the
bottom of a PVC tube which fit snugly into the boring. The blade was mounted on a rod
attached to the inner wall and extending the full length of the tube.
To cut a notch, the blade was brought flush with the tube and the apparatus
inserted into the boring until it rested on the top of cuttings at the bottom of the boring.
The blade was then slightly extended by twisting the rod at the ground surface. The entire
apparatus was rotated, cutting a shallow notch in the wall of the boring. Then the blade
was extended further and the notch was deepened by continuing to rotate the apparatus.
When the operation was complete, the wall of the boring contained a notch 3.75 cm
deep and 0.3 cm thick (Fig. 4.7). Notches of those dimensions were observed when the
boreholes were excavated.
The boreholes were cased with steel tubing 3.75 cm in outer diameter and 3 mm in
wall thickness (1 1/4" Nominal Schedule 80 steel pipe). The tubing was obtained at a local
plumbing supply store.
Baskets were constructed of annular disks of 3/4" (nominal) plywood, plastic foam
and fine steel mesh. Three foam disks were placed on the end of the casing, and a steel
135
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Bentonite
Gaskets
Support ring
' ' ^
0 5 10
cm
Portland cement
JN; Ijqi—Basket
«-Notch
Boring partly filled
with cuttings
Figure 4.7. A borehole used to create hydraulic fractures.
136
-------
mesh disk placed beneath them. The outside diameter of those disks was 8 cm, slightly
larger than the inside diameter of the boring. The plywood disk served as a support for
the other disks, steel band was secured beneath the basket to prevent it from slipping off
the end of the casing (Fig. 4.7).
When the casing and basket assembly was inserted into a boring, the plastic and
steel disks were flush with the boring walls. Bentonite pellets were placed on top of the
basket to seal the annulus between the casing and the wall of the boring. Portland cement,
which contained an additive that inhibits shrinking, was poured in the annulus to secure
the casing into the borehole. The result was a cemented casing whose lower end was open
to the till.
METHOD OF FRACTURING
Hydraulic fractures were created by workers from Halliburton Services, a company
specializing in creating hydraulic fractures for the petoleum industry. Most of the methods
used during the test are similar to methods used in the hydraulic fracturing of oil wells.
We modified the methods slightly, however, because of the shallow depths of the
boreholes.
Equipment
The fracturing equipment was mounted on five vehicles: a truck containing a
blender and a positive displacement pump, two trucks containing sand, a truck containing
water, and a van containing monitoring and control equipment.
Three pumps were used in the operation: a Triplex positive displacement pump,
and two centrifugal pumps, one upstream and one downstream from the blender. The
positive displacement pump can generate a maximum of 41,000 kPa (6000 psi), whereas
the centrifugal pumps can produce a maximum of between 400 and 550 kPa (60 and 80
psi) and flow rates of 2.4 to 2.8 m3/min (630 to 750 gals/min).
The Injection Fluid
Sand and several chemicals were added to water in the blender to improve the
performance of the fracturing operation. To increase the viscosity of the fluid, we added a
guar gum base gel at a concentration of 2.5kg/m3 (0.025 Ibs/gal), and a cross-linking
chemical at a concentration of 0.05kg/m3 (0.0005 Ibs/gal). A buffer was used to reduce
the pH of the fracturing fluid to between four and five, which is optimal for use of the gel.
The guar gum gel increases the viscosity of the water from 1 to 15 cP. The cross-
linking chemical causes the gel to become thixotropic, with an apparent viscosity of 100 to
200 cP and an apparent shear strength of roughly 25 Pa, according to laboratory tests
conducted with a rotational viscometer. The high viscosity and shear strength of the gel
facilitates the transport of sand into the fracture. Typically, another chemical is blended
into the fluid to cause the gel to break down several hours after injection. The breaking
chemical improves removal of gel, greatly increasing the permeability of the propped
fracture.
137
-------
Potassium chloride was added to the fluid at a concentration of three percent by
weight. The KC1 is an additive that is used routinely to inhibit the swelling or clay
minerals in hydraulic fractures created by the oil industry. In addition, this material
increases the electrical conductivity of the fluid and was used to improve the resolution of
fractures by electrical geophysical techniques.
Dye was added to the fluid to stain the fracture surfaces and make them easier to
identify during excavation. Three types of dye were tested during the experiment:
rhodamine, fluorescein, and fluorescent orange paint pigment. Dye was mixed at a
concentration of 1:500 in the first few fractures but it was more dilute (1:1000 to 1:2000) in
the last few fractures.
Ottawa sand was mixed with the fracturing fluid to prop open the fractures. Two
different sizes of sand, very coarse-grained, 12/20 mesh, and medium-grained, 20/40
mesh, were used. Concentrations of sand ranged from 9% to 18% by volume (2 to 4 Ibs.
sand/gal, fluid).
The Fracturing Procedure
During routine fracturing operations of oil wells, water is pumped from the water
truck and mixed with sand and chemicals in the blender. A centrifugal pump pulls the
mixture of water, sand and chemicals from the blender and creates input head for the
positive displacement pump. Injection into the borehole is accomplished using the
positive displacement pump. Flow rates and injection pressures are monitored in the van.
During our tests, the procedure differed slightly from above in that we used the
centrifugal pump at the downstream end of the blender to inject fluid into the borehole.
The positive displacement pump was used intermittently, when pressures in excess of 550
kPa (80 psi) were required to initiate fracturing.
The fracturing procedure began by filling the casing with water, so the initial
fracture would be created with water rather than gel.' Pipes were connected from the
borehole to the trucks containing the fracturing equipment, which were parked on the
northeastern edge of the site (Fig. 4.1).
Injection using the centrifugal pump caused pressures measured at the borehole to
increase to between 400 and 550 kPa (60 and 80 psi) within several minutes. In some
cases, a fracture was created soon after the pressure reached 60 to 80 psi, but in other
cases 5 to 10 minutes were required before fracturing. Injection pressure was increased
using the positive displacement pump if a fracture was not created after approximately 10
minutes, injection pressures of as great as 820 kPa (120 psi) were required to initiate
fracturing at some boreholes (Table 4.4).
The onset of fracturing was determined by an abrupt decrease in the injection
pressure. Injection pressures decreased to between 69 and 275 kPa (10 and 40 psi) during
the propagation of most of the fractures (Table 4.4). Records of the pressures and
volumes as functions of time are presented in the Appendix.
Injection was terminated at the shallow boreholes when fluid vented to the ground
surface, and at the deeper boreholes injection was terminated after a predetermined
138
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volume of injection. Each fracture was created in less then ten minutes. The pipes
extending from the pump truck to the borehole was uncoupled at the borehole
immediately after termination of injection. Roughly 100 liters (several tens of gallons) of
injection fluid flowed back out of the fracture into the borehole and onto the ground
following uncoupling.
Flow rates of between 0.075 and 0.42 m3/min (20 and 90 gal/min) were used to
create the fractures. In general, the flow rate was low during peak pressure and increased
as the pressure decreased and the fracture began to grow. Details of the history of flow
rates, however, are poorly known because the flow meter used by Halliburton Services was
often clogged with sand and non-functional. Clogging apparently occurred because the
flow rates that were used were less than those designed to be measured by the meter.
The total volumes of fluid and sand pumped out of the blender were estimated by
the operator of the pump truck. Typically the fractures required 0.38 to 0.76 m3 (100 to
200 gals) of fluid, but the volume ranged from as little as 0.076 m3 to as much as 1.51 m3.
The volume of sand pumped to the fractures was typically 0.056 to 0.14 m3 (2 to 5
ft3), but it ranged from less than 0.03 to as much as 0.85 m3 (30 ft3). These estimates are
greater than the volume contained in fractures because they do not account for material
that remained in the pipes after fracturing, or that flowed out during venting.
TABLE: 4.4. SUMMARY OF DATA FROM FIELD TESTS
Id
FLUID
Volume Dye
m3 (gal)
13
11
12
2
10
4
9
5
8
7
6
1.51 (400
0.11
0.45
0.46
0.57
0.57
0.76
0.76
0
0.38
(30
120
110
150
150
200
(20
(0
(10
0.57 (150
rh
rh
rh
rh
rh
fo+fl
fo+fl
fo
fo
fo
fo+fl
SA
Volume
m3
0.28-0.42
0.057
0.08-0.14
0.85
0.22-0.24
0.17-0.22
0.08-0.14
0.03-0.08
0
0.03-0.08
0.14
JSTD
Gr.Size
20/40
20/40
20/40
12/20
12/20
12/20
20/40
20/40
20/40
20/40
20/40
PRESSURE
Max. Propagation
kPa(BSi) kPa
620 90
340 50
410 60
410 60
410 60
760 ( 10
820 (120
410 (60
3700 (540
550 (80
550 (80
140-340
140
140
140-280
340
480
200-275
410
..
550
200
rh: rhodamine red
fo: fluorescent orange pigment
fl: fluorescein
Shown in the order in which the fractures were created.
139
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The amount of sand observed in some of the fractures was much less than the
amount pumped from the blender. For example, 0.122 m3 (4.2 ft3) of sand filled the
fracture at borehole 13 (details of this calculation are described in Section 6), but 0.28 to
0.42 m3 (10 to 15 ft3) were pumped from the blender. Approximately 0.1 m3 of the
missing sand is inferred to nave been deposited in pipes extending from the pump truck to
the boring, and roughly 0.05 m3 flowed out of the fracture during venting.
Hydraulic fracturing was attempted at eleven boreholes, and fractures were
successfully created at ten of those boreholes. Hydraulic fracturing did not occur at
borehole 8. Two attempts were made to fracture borehole 8; during the first injection
pressures reached 1720 kPa (250 psi), and during the second injection pressures reached a
maximum of 3700 kPa (540 psi). Following both attempts, we discovered plugs of sand
several dm from the bottom of the casing that presumably blocked the injection fluid. The
cause of the sand blockage is unclear. One explanation is that the gel in the injection fluid
broke down and was unable to adequately transport sand. The flow of the gel is sensitive
to heat and could have been affected by the ambient temperature (which was 38 ° C on
the day of the test), according to Mark Roberts, field engineer with Halliburton Services.
Shortcomings of the Equipment
Shortcomings of the hydraulic fracturing equipment used during the test are all
related to scale: the equipment was designed to create fractures one to several orders of
magnitude larger than the ones we created. As a result sensing devices such as flow
meters and pressure transducers used by Halliburton were unable to accurately measure
the low flow rates and pressures of the test.
The blending system was unable to consistently deliver a quality mixture of
injection fluid at the relatively low volumes required. This resulted in variations in fluid
properties between fractures, according to observations of the fluid flowing back out of
fractures. In some cases, especially during the last several fractures, the viscosity of the
injection fluid was low and this could have been partly responsible for sand settling out
before reaching the subsurface.
The fracturing equipment was practically immobile, so pipes as long as 50 m were
used to connect the injection pump to the boreholes. The volume of the long pipes was on
the same order as the volume of the fractures, which reduced the control of the fracturing
process. Moreover, in many cases it appeared that sand settled in the pipes before
reaching the fracture.
The team from Halliburton Services made every effort to adapt their equipment to
the highly atypical conditions of our tests. The shortcomings cited above in no way reflect
the manner in which the equipment was operated. The shortcomings do indicate,
however, that conventional equipment used to create hydraulic fractures at oil wells will
be too large to create hydraulic fractures of the size used during this test. Future
applications would benefit from equipment designed for the pressures, flow rates, and
volumes required to create and prop open hydraulic fractures at shallow depths (tens of
meters).
140
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SECTION FIVE
HYDRAULIC FRACTURES CREATED DURING THE FIELD TEST-1988
These two observations, 1) an abrupt decrease in the pressure of the
injection fluid, and 2) venting of the fluid several m or more from the point of
injection, were critical because they are strong evidence that hydraulic fracturing of
soil occurred during the field test. There was little information at the time of the
test, however, about fracture geometry, that is the size, shape, orientation, location,
and thickness of the fractures. Those parameters largely control how the fracture
will affect the recovery of ground water, and so they are of fundamental importance
to the goals of this research.
The geometries of the fractures were determined by excavation and mapping.
The day after the fractures were created, we mapped the locations of the vents and
prepared to excavate the vicinity of each borehole. Two days later a backhoe was
rented and brought to the site to begin excavation. The strategy used during
excavation was to first cut a trench from the vent to the parentborehole. The
fracture was identified at the vent and traced along the trench during excavation.
The trench was extended beyond the borehole until the fracture could no longer be
identified in the trench walls. Then another trench was cut perpendicular to the first
one. Subsequent trenches were placed to intercept the fracture at critical locations
based on existing exposures.
The locations of trenches were selected to give the maximum amount of
information on the forms of the fractures, while keeping the amount of excavation
to a minimum. In general, the technique was successful, but in a few cases
(boreholes 2,4, and 9) the fractures could not be identified during excavation, so a
full array of trenches was not completed. Careful investigation following excavation
did reveal the locations of fractures at borehole 9, but the backhoe was no longer
available to complete excavation.
Two boreholes that were incompletely excavated (2 and 4) were several
meters deeper than the others and they lacked a vent from which to start excavation.
We discovered a fracture adjacent to borehole 2, but the fracture was poorly
developed so excavation was discontinued. At borehole 4, the maximum depth that
could be reached by the backhoe was 0.3 m above the bottom of the casing.
Monitoring techniques indicated that a fracture developed at borehole 4, but after
considerable effort we were unable to locate the fracture.
Traces of fractures on the walls of the trenches were identified and marked
with brightly-colored flagging. Many of the fractures lacked sand and could be
identified only after detailed excavation revealed traces of dye staining.
The appearance of the fractures on the walls of the trenches depended on
the material filling them. Where fractures were filled with sand, they appeared as
thin white layers in the grey till. Gel mixed with the fracturing fluid allowed some
hydraulic fractures to be identified because the gel appeared as a mucous-like or
rubbery film on the fracture surfaces. Many of the fractures lacked sand or gel and
could be identified only by trace amounts of dye on the fracture surfaces.
Rhodamine was the most effective dye, staining fracture surfaces deep purple (a
color that was readily distinguished from natural iron oxide stain, which is dark red).
141
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Fluorescent paint pigment yielded satisfactory results, although the distribution of
the pigment was less uniform than the distribution of the rhodamine stain. The
paint pigment fluoresced and could be detected in the field using a UV lamp.
However, the UV lamp was not used routinely to detect the dye because the
florescence could only be detected when the trenches were covered with a tarp to
reduce ambient lighting. Both of those dyes effectively stained fracture surfaces
when mixed with injection fluid at concentrations of roughly 1:500, and they could
be detected on fracture surfaces at concentrations of 1:1000 to 1:2000. Fluorescein
dye was ineffective at staining the surfaces of fractures, even though it resulted in a
strongly-colored injection fluid.
FORMS OF THE HYDRAULIC FRACTURES
Hydraulic fractures were created at shallow depths so that they could be
excavated and mapped in detail. The purpose of the excavation and mapping was to
determine physical characteristics of the fractures, such as their size, shape,
orientation, and thickness. This information is necessary to the design or hydraulic
fractures in remedial actions, to infer processes of fracturing, and to highlight
features of the fractures that are undesirable. Identifying the undesirable features
will allow us to develop techniques that will inhibit their formation.
The geometry of each hydraulic fracture, that is its size, shape and
orientation, was determined by mapping exposures of the traces of the fractures on
the walls of trenches. Sections obtained! from the trench walls were compiled into
maps showing the surface of the fracture in plan.
The sections were made by measuring the location of the fracture traces
relative to a horizontal datum, which was constructed by positioning fine string with
a hand level and securing it to the trench wall. The location of a fracture trace
could be mapped to within a few cm using this technique. Sections were mapped at
a scale of 1:12 and reduced to the sizes shown in the following pages. The locations
of most of the fracture traces are accurate to within one line width on the following
sections.
The fractures shown in the following maps and sections represent exposures
that could be confirmed because they contained sand, dye, or gel. The
concentration of those materials decreased as the leading edge of a fracture was
approached, and we determined the leading edge as the last exposure of injected
material. Commonly, however, an unfilled fracture extended several dm or more
ahead of the point that was mapped as the leading edge. The unfilled fractures
probably were caused by hydraulic fracturing, but they were omitted from the
sections because their origin was uncertain.
The forms of each of the hydraulic fractures will be described in the
following pages. An idealized form has been inferred from the descriptions and will
be presented at the end of this section.
142
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Borehole Four
A hydraulic fracture could not be identified in two trenches cut adjacent to
borehole Four. Monitoring of injection pressure and surface tilts indicates that a
hydraulic fracture was formed, but we were unable to excavate deep enough to
reach it.
Borehole Five
A hydraulic fracture occurs on the northern side of borehole five (the
fracture will be referred to as HFS). In general, the fracture is continuous in the
vicinity of the borehole, and it splits into two lobes several m north of the borehole
(Fig. 5.1). One lobe vented on the northwestern side, and the other remained in the
subsurface on the northeastern side of the borehole (Fig. 5.1).
The northwestern lobe is shaped like a trough that plunges 20° to 30° toward
the borehole (Figs. 5.1 and 5.2). Each side of the trough is roughly planar and the
sides differ in stnke by 135°. The sides of the trough split near the ground surface,
and they vent as separate fractures striking roughly tangential to the major axis of
the fracture. As the hydraulic fracture approaches the ground surface it flattens for
several dm, and then curves abruptly upward one dm below the ground surface. The
fracture is nearly vertical where it intersects the ground surface at the point of
venting (Fig. 5.2).
The northeastern lobe of HFS splits from the northwestern lobe roughly 1.5
m north of the borehole. The dip of the northwestern lobe is slightly greater than
that of the northeastern lobe, so that the northwestern lobe climbs above its
neighbor with increasing distance from the borehole. In plan view, the two lobes are
separated by unfractured ground; no overlap was observed (Fig. 5.1).
A vertical fracture striking N62E cuts the host till adjacent to the open
interval and the bentonite-filled zone of the borehole. At 15 cm above the bottom
of the casing (adjacent to the bentonite), the dip of the fracture flattens abruptly
over severalcm. Within 20 cm of the bottom or the casing, the fracture dips 25° to
the south, and this dip is typical of most of the fracture. The vertical fracture is
apparently unrelated to the notch at borehole five.
Borehole Six
Hydraulic fracture six resembles HF5 in that it consists of a steeply dipping
fracture adjacent to the borehole, a zone that is flat-lying in the vicinity of the
borehole, and several shallowly dipping lobes (Fig. 5.1). The vertical fracture is
relatively large compared with HF5; it is at least one m in length and it extends
upward from the notch to a height of 1.25 m (Figs. 5.1,5.2 and 5.3). The strike of
the vertical fracture is N23W, nearly perpendicular to that of the vertical fracture at
HFS.
The hydraulic fracture is nearly flat-lying within approximately two m of the
borehole, a distance that is similar to the depth of initiation of the fracture. At a
143
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Elevation of frx surface
(m ibov» bonom of eulng *s)
— Wan of trench
Figure 5.1. Hydraulic fractures HF5, HF6, and HF7. Structural contours are on the
fracture surfaces.
144
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distance of one to two meters from the borehole, the fracture changes orientation
abruptly, curving upward to dip shallowly toward the borehole (Fig. 52).
A large fracture lobe extends south of the borehole to a vent roughly 8 m to
the WSW. This lobe is roughly planar in form and dips toward the borehole at 14°
(Figs 5.2 and 5.3). In plan, the large lobe is elongate with an aspect ratio of roughly
2:1. The borehole is near the end of the long axis of the lobe (Fig. 5.1).
The fracture trace along the major axis of the large lobe is, in general,
straight from where the fracture begins to turn upward to the vent. In detail,
however, the fracture is gently-stepped, consisting of riser intervals that are 20 to 40°
steeper than the average dip of the fracture. The riser intervals are a dm or less in
length and they are spaced roughly one m apart along the fracture. Till cut by the
fracture was studied carefully for variations in texture or composition that could be
related to the location of risers, but no such variations were found. The step-like
form of the trace appears to be unrelated to variations in till detectable in hand
sample.
Two smaller lobes were identified; one of them is at the same elevation as
the large lobe and extends to the SSE, whereas the other is 1.5 m above the large
lobe and extends to the north where it vents roughly three m from the borehole (Fig.
The upper, northern lobe apparently is connected to the vertical fracture in
the vicinity of borehole. There are several isolated fracture segments a few dm in
length exposed between the lobe and the vertical (Fig. 5.2), but apparently a direct
connection of the upper lobe and the vertical fracture was removed during
excavation.
The vent at the large lobe resembles the vents at HF5 in that the fracture
trace flattens (Fig. 5.3) and then turns abruptly upward when it is within one dm of
the ground surface (Figs. 5.2 and 5.3). The strike of the fracture at the vent is sub-
parallel to the strike of the vertical fracture at the borehole.
The vent at the smaller, northern lobe of HF6 resembles the other vents, but
the fracture flattens at an unusually shallow depth of 3 to 8 cm. The fracture cuts
beneath the ground surface at this shallow depth for 0.5 m before turning upward
and venting.
Borehole Seven
Hydraulic fracture seven is the smallest observed during excavation. The
fracture is steeply dipping adjacent to the borehole and it flattens gradually with
increasing distance from the borehole (Fig. 5.4). The dip of the fracture decreases
to 25° toward the borehole roughly at 0.5 m from the vent. The average dip of HF7
was greater than the other fractures because the transition from vertical to gently-
dippmgfracture was relatively gradual. This behavior is important because it shows
that HF7 intersected the ground surface after growing a small distance from the
parent borehole, compared with the lengths other fractures (Figs. 5.1 and 5.4).
145
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Figure 5.2. Trace of hydraulic fractures HF5 and HF6 on the northern wall of the
longest east-west-trending trench shown in Figure 5.1. Boreholes are
projected onto the section.
146
-------
Eut
Notch
South wu of tr«n<*
M«t«f»
Figure 53. Trace of hydraulic fracture HF6 on the southern wall of the same trench
as in Figure 52.
147
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Silty clay till
10-20% Cobbles
Gravelly sand
limestone fragment
Detail from opposite wall
Figure 5.4. Trace of hydraulic fracture HF7 on the western wall of the trench cut
along the major axis of the fracture. The section was made prior to
excavating the tranverse trench shown in Figure 5.1.
148
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In other respects, HF7 resembles the other fractures. The steeply dipping
part of HF7 cuts the open zone below the basket and contains the axis of the boring.
It is apparently unrelated to the notch. In plan view, the fracture is slightly elongate,
with an aspect ratio of 1.5:1. The borehole is at the end of the long axis (rig. 5.1).
The vent at HF7 is typical: the fracture flattens as it approaches the ground surface,
reaches a depth of 0.2 m and cuts abruptly upward venting as a vertical fracture
nearly 1 m in length and striking parallel to the vertical fracture at the borehole.
A lens of gravelly-sand and limestone fragments is cut by HF7. The fracture
cuts beneath one limestone fragment, upward through a narrow space between
neighboring fragments, and then flattens, assuming roughly the path it was taking
before reaching the fragments. Limestone fragments appeared to affect the path of
the fracture only locally.
Borehole Nine
The form of HF9 resembles the large lobe at HF6 in that it is roughly
elongate, and the parent borehole is near one end of the major axis (the
northeastern boundary of the fracture was not excavated and is inferred). The
fracture is fiat-lying in the vicinity of the borehole, but most of the fracture dips
shallowly (17°) to the southeast toward the borehole (Figs. 5.5 and 5.6).
The fracture trace from borehole to vent along the major axis of HF9 is
nearly straight, marked only by gentle steps spaced roughly 1 m from each other
(Fig. 5.6). The trace resembles those of HF5 and HF6 (Fig. 52 and 5.3).
A vertical fracture cuts upward from the notch to the basket of HF9. At the
basket, the vertical fracture flattens abruptly, rolling over and becoming flat-lying in
the vicinity of the borehole. The exposures of the vertical fracture are marked in
Figure 5.6, but the size of the fracture was impossible to determine because the
edges were removed during excavation. The vertical fracture strikes N63W, which is
at a high angle to the strike of the fracture at the vent.
Borehole 10
The hydraulic fractures at borehole 10 consists of two lobes extending from
the borehole in opposite directions, to the northeast and southwest. The two lobes
meet at a vertical fracture intersecting the borehole. The vertical fracture is roughly
2 m along strike and 1 m in height, which is similar in size to vertical fractures at
HF6 and HF7. The lobes dip between 20 and 25° toward the borehole and are
roughly planar (Fig. 5.7).
Vents occur at three locations, two on the southwestern lobe and one on the
northeastern lobe. At the vents, the strikes of the fractures are roughly parallel to
the vertical fracture intersecting the borehole (Fig. 5.7).
The northeastern lobe cuts across a hydraulic fracture created from borehole
11 (Fig. 5.7), which was created prior to HF10. The line of intersection of the two
fracture planes was shallow, so it was excavated by hand and studied carefully. We
149
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—~ Leading edge of fracture
///// Vent
O Borehole
Wall of trench
Vertical
fracture
— Elevation of frx surface
bottom fff culn0)
Figure 5.5. Hydraulic fracture HF9. Structural contours are on fracture surfaces.
The northeastern edge of the hydraulic fracture was fracture was
covered and has been inferred.
150
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Bor«hol« *9
Silty clay 1111
10-20% cobtl.i
Vartlcal Iractwa
Figure 5.6. Trace of hydraulic fracture HF9 on the southwestern side of the trench
that cuts the major axis of the fracture.
151
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Vertical fracture
Fracture
Intersection
Vertical
fracture
v meter '
Leading edge of fracture
///// Vent l*Bh"1 *™ awrox-)
@ Borehole
Wall of trench
Elevation of frx surface
Im obovt bottom
of casing #10)
Figure 5.7. Hydraulic fractures HF10 and HF11.
152
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could find no indication that the presence of the earlier fracture (HF11) affected the
shape, size, distribution of sand, or any other characteristic of HF10.
Borehole 11
The hydraulic fracture at borehole 11 consists of a main lobe extending to
the southwest, and a smaller lobe that lies above and to the west of the main one.
The main lobe is slightly elongate in plan with an aspect ratio of 1.5:1. The
borehole is at the end of the long axis (Fig. 5.7). The fracture surface is roughly
planar, dipping 20° toward the borehole. The main lobe cuts the borehole adjacent
to the basket, 0.1 m above the notch.
A vertical fracture occurs at the borehole and extends to the SSW. The
bottom of the fracture lies on the notch, and it cuts upward through the main lobe.
The vertical fracture breaks into segments above the main lobe, but it appears to be
connected to the smaller lobe. The connection was removed during excavation.
The strike of the vertical fracture is at a high angle to that of the vents.
Although this relationship between strikes was observed at HF9, it is atypical. It is
possible, however, that vertical fractures oriented parallel to vents were present at
HF9 and HF11 because the excavations would have removed fractures of that
orientation at those boreholes.
Borehole 12
The form of HF12 resembles a plunging trough (Fig. 5.8) formed by two
crudely planar sides and a narrow zone that curves sharply. Both sides of the trough
dip shallowly toward the borehole, and the strikes of the sides differ by 60°. The
northwestern lobe of HF5 also has a trough-like form, but the angle between the
sides at HF5 is more shallow than it is at HF12.
The excavation of HF12 was unusual because the easternmost trench cuts
roughly parallel to the leading edge of the fracture-other trenches cut the leading
edges of fractures at high angles. Exposures in that trench show six lobes fringing
the edge of the fracture. The orientation of the lobes could be determined in a few
locations at which the lines of their major axes intersected the parent borehole. The
lobes range from several dm to 1 m in width and they appear to be longer than they
are wide.
The contact between till Units 2 and 3 occurs roughly 0.5 m below the ground
surface at HF12. The fracture initiates in massive silty clay of Unit 3 and cuts across
the contact into beds of gravelly sand and silt in Unit 2 (Fig. 5.9). The geology
exposed on the east wall of the long trench cutting HF12 was mapped in detail to
examine the relationship between bedding and the form of the fracture.
The plunge of the trace of the fracture flattens slightly over a meter-long
interval where HF12 cuts across the upper surface of a bed of gravelly sand slightly
east of the center of the section shown in Figure 5.9. Bedding is irregular, however,
and the fracture cuts partly through the gravelly sand and partly through the
153
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— Loading «dga of frortura
Illll Vent w—"d •"" •*""•'
O Borahol*
••" ™~ Woll Oi II 6fldk
— Elevation of frx sirfac*
frn BbuM • datun O.&n
tt»M batlon «r Mine)
Figure 5.8. Hydraulic fracture HF12. Lobes inferred from discontinuous exposures
of the fracture on the walls of the trench.
154
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Orange-brown gravelly sand
local sill beds
Figure 5.9. Geology and trace of hydraulic fracture on the eastern wall of the trench
cutting the major axis of the hydraulic fracture HF12.
155
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overlying silty clay. To the east of this zone, the fracture cuts across several beds
and there appears to be negligible effect on the form of the trace. As the fracture
approaches the ground surface it flattens and then curves sharply upward, a form
resembling most other vents.
The trace of HF12 shown in Figure 5.9 is remarkably similar to traces of
HF5, HF6, and HF9, where the fractures cut relatively homogeneous silly-clay.
Apparently, bedding in the till affected the form of the trace of HF12 only slightly-
flattening it near the center of Fig. 5.9. The sharp trough-like form of HF12 is
unusual, however, and could be a result of bedding or other heterogeneities in the
till. Exposures were insufficient to make that determination.
Borehole 13
The fracture in the vicinity of borehole 13 is the largest one that could be
excavated. It is also unusual in several respects other than size. In particular, the
fracture is nearly flat-lying and the overlying ground is sloping, whereas at the other
fractures the ground is flat-lying and the fracture slopes.
At least four lobes and a main parent fracture compose HF13 (5.10 and
5.11). Typically, a lobe splits and either overlies or underlies the main fracture so
that the two overlap in plan (Fig. 5.10). This differs from fractures at the other
boreholes where lobes are adjacent and they rarely overlap in plan. The lobes at
HF13 are roughly parallel and separated by roughly 0.3 m of unfractured till. As a
result, the traces of two fracture planes were commonly found on the walls of
trenches cutting HF13 (Fig. 5.12).
Junctions between the main fracture and lobes are well-exposed in two
locations, at the eastern and southern sides of HF13. The junctions are several m in
length and the lines they form intersect the borehole. The other two junctions are
covered, and their locations and orientations are inferred (Fig. 5.12). Double lines
are used to indicate junctions in Figures 5.10 and 5.11, and short solid lines at each
end of the double lines indicate lobes associated with each junction.
The hydraulic fracture is crudely basin-shaped in the vicinity of the borehole,
but it flattens and is nearly flat-lying at distances greater than several meters from
the borehole. Most of the southern half of the fracture, for example, differs by less
than a few cm from horizontal.
In plan view, HF13 resembles the other hydraulic fractures. It is elongate,
with an aspect ratio of 2:1, and the borehole is near one end of the major axis. The
longest dimension of the fracture, as measured from the borehole, lies roughly in
the direction of the slope of the overlying ground surface (Fig. 5.10 and 5.11).
The vent at F13 is down slope from the borehole, and it occurs where the
elevation of the ground surface is slightly greater than that of the bottom of the
casing-the vent is 0.75 m above the bottom of the casing. The fracture curves
sharply upward at the vent (Fig. 5.12).
Two vertical fractures occur adjacent to the borehole; one is parallel to the
long axis of the fracture, whereas the other differs in strike by 125°. Both vertical
156
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e-
Orientation of
faint surfaca
Leading edga or rracnra
Hill Vont
BWBhole
13 Well 1.0.
Elevation of frx surfoce
0.13m
Ma* batum of oahal
Figure 5.10. Hydraulic fracture HF13 showing structural contours fracture surfaces.
Double lines mark the intersections of fracture lobes.
157
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8"
Orl»ntotlon of
ground *urfoc«
'.•:::.7;:.:. Froetu-* cutting tondy
i*>3»S flrovtl Ixd
Figure 5.11. Outline of HF13 showing area where fracture cuts a bed of upwardly-
grading gravel, sand and silt Fracture cuts massive silty-clay till
where unstipled.
158
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South
West wal of trench
Figure 5.12. Trace of hydraulic fracture HF13 and graded beds on the western wall
of the trench cutting the major axis of the fracture. Graded beds
exposed above the fracture trace have been omitted.
159
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fractures cut till adjacent to the bentonite seal in the borehole, and are above the
level of the notch. The main, sub-horizontal hydraulic fracture is contiguous with
the vertical fractures, and is unrelated to the notch (Fig. 5.11,5.12).
Till in the vicinity of HF13 consists of massive silty-clay and graded beds of
silty and sandy-gravel (Unit 2). Most of the fracture is in massive silty clay, but it
intersects a graded bed roughly midway between the borehole and the vent (Fig.5.11
and 5.12). The bed is 02 m at its thickest and grades from gravel at the base to silt
at the top. The fracture cuts relatively soft silt at the top of the bed.
The flat-lying orientation of HF13 is atypical compared with the other
fractures, which are dipping. The graded bed could have affected the orientation of
HF13 because the silt appeared to be less tough than the enveloping silty clay.
However, much of HF13 is horizontal where it cuts through massive silty clay,
material that lacks stratification. It is inferred that the general flat-lying orientation
of HF13 results from factors other than stratification. In particular, the slope of the
overlying ground surface could have affected the dip of the fracture. This inference
should be checked with a theoretical analysis, but here it will allow us to ignore the
orientation of HF13 in developing an idealized model of a hydraulic fracture.
DIMENSIONS OF THE HYDRAULIC FRACTURES
The plan areas of most of the fractures were between 10 m2 and 30 m2 (Table
5.1), according to measurements made from the maps described in the previous
section. One fracture (HF13) was much larger, covering an area of 90 m2, and
another fracture was smaller (HF7 was 2.2 m2) than most of the others (Table 5.1).
TABLE: 5.1. DIMENSIONS AND DIPS OF HYDRAULIC FRACTURES
FQC Depth Plan Area Max. Length Ave. Dip
£m) (m2) (m)
HF2 2.77 unknown unknown shallow
HF4 3.84 unknown unknown shallow
HF5 1.64 13 3.6 25°
HF6 1.85 28 6.4 15°
HF7 1.83 2.2 1.8 variable
HF9 1.75 20 5.5 17°
HF10 1.83 12 3.3 22°,25°
HF11 1.67 9 4.1 24°
HF12 1.98 30 8.2 14°
HF13 1.83 90 13.5 sub-horiz.
The greatest length of all exposed fractures occurred between the parent well
and the vent. The maximum length of most of the fractures, where length is
160
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measured from the injection well to the leading edge of the fracture, is typically
between 3 and 8 m. The longest fracture is 13.5 m, and the shortest one is 1.8 m
(Table 5.1).
Ratios of maximum length to depth of initiation typically range between 1.5
and 4, with a maximum of 7.4 and a minimum of 1.0. Fractures HF2 and HF4 did
not vent and were too deep to excavate completely, so their lengths are unknown.
Many of the hydraulic fractures are approximately planar between the
borehole and the vent. The average dips of the fractures are similar; all of them are
within 5° of a 20° dip. The exception is HF13, which is sub-horizontal (Table 5.1).
DIRECTION OF PROPAGATION
Most of the fractures are asymmetric in plan with respect to the borehole.
Thus, the fractures acquire a preferred, or dominant direction of propagation as
they grow away from their parent boreholes. The dominant direction of
propagation, the azimuth of the line between the borehole and a vent, ranges from
northeast to west to southeast (Table 5.2). The direction of propagation of HF13 is
nearly parallel to the direction of maximum slope of the overlying ground surface,
which is 225° (Fig. 5.10 and Table 5.2). At the other fractures, however, the
direction of propagation is unrelated to known geologic or topographic features.
The direction of propagation is related to the location of the backhoe used to
prevent movement of the casing during fracturing. In most cases, the fractures
propagated away from the backhoe. The two exceptions, HF7 and the southwestern
lobe of HF10, are small fractures that propagated toward the backhoe, venting near
the front wheels of the vehicle (Fig. 5.13). No fractures propagated beneath the
backhoe.
Theoretical analyses indicate that hydraulic fractures will propagate hi
directions of decreasing confining stress. Apparently the weight of the backhoe
resulted in vertical stress gradients that were great enough to affect the propagation
of the underlying hydraulic fracture.
The dominant direction of propagation is related to the trend of the
hydraulic fracture at the vent, and to the vertical hydraulic fractures adjacent to the
borehole. Strikes of vertical fractures at the vent are nearly perpendicular to the
dominant direction of propagation in every fracture (Fig. 5.13 and Table 5.2). At
most fractures, the strike of a vertical fracture at the borehole is also nearly
perpendicular to the propagation direction (Fig. 5.13 and Table 5.2). In a few cases,
however, the strikes of fractures adjacent to the borehole (e.g. HF9, HF11) are at
high angles to the direction of propagation, and in one case (HF13), two vertical
fractures differing in strike by 125° were observed. The formation of those fractures
is poorly understood, but it could be similar to the results of laboratory experiments
where hydraulic fractures were created from cylindrical holes in clay.
161
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r
Locotlon of
hydraulic
fracturing
equipment
|
Scale
L
_L
_L
5 10
meters
J
15
o Well location
Backhoe
/v_^—-Borehole frx
fv,
H_V
Hydraulic frx
Figure 5.13. Outlines of hydraulic fractures and locations of a backhoe at the time of
fracturing.
162
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TABLE 5.2: AZIMUTHS OF FEATURES OF HYDRAULIC FRACTURES.
HF5
HF6
HF7
HF9
HF10
HF11
HF12
HF13
Propagation
Direction
325, 282
225,10
150
326
206, 39
205,240
175
200
Vent
Fix
60
165
62
35
124
130
75
105
Borehole
Frx
62
157
58
117
128
18
_
265, 20
In some experiments, two co-planar fractures were created, whereas in other
experiments, three fractures in a trigonal pattern (striking roughly 120° from
another) were created from the cylindrical hole. Haimson and Fairhurst (1970) also
describe laboratory experiments where both co-planar and trigonal patterns of
hydraulic fractures were created from cylindrical holes in rock. Our experiments
and those of Haimson and Fairhurst (1970) show that the two patterns of fractures
are possible, although additional work is required to determine the factors that
actually cause these patterns to develop.
SUMMARY: AN IDEALIZED HYDRAULIC FRACTURE CREATED DURING
THE FIELD TESTS
Forms of hydraulic fractures created during the field test differ in detail, but
there are certain characteristics that are common to nearly all the fractures. The
common traits were used to infer an idealized hydraulic fracture created in the field
tests. The form of the idealized fracture consists of four zones, which are arranged
in increasing distance from the parent borehole (Fig. 5.14):
1. Zone One: a sub-vertical orientations adjacent to the borehole.
2. Zone Two: a flat-lying orientation in the vicinity of the borehole (within
several m).
3. Zone Three: a planar to trough-like feature dipping gently toward the
borehole. This zone composes most of each hydraulic fracture.
4. Zone Four: a steeply-dipping orientation occurring within several dm of the
ground surface.
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Zone One
Zone One is characterized by one or more vertical fractures containing the
axis of the borehole and initiating along the open interval below the casing, vertical
fractures were observed at all boreholes except HF12, where the bottom of the
borehole was poorly exposed during initial excavation and the trench was flooded
before we could complete excavation.
Two vertical fractures whose strikes differed by roughly 120° occurred at
HF13, whereas single fractures were found adjacent to the other borings. More
than one fracture may have occurred adjacent to some of the other borings, and they
were removed during excavation of the trenches.
Vertical fractures typically flatten upward and become sub-horizontal at the
bottom of the basket or adjacent to the bentonite-filled segment of the borehole,
one to several dm above the notch. The change in orientation typically is quite
abrupt, occurring over a length of several cm and having a radius of curvature of one
to two cm.
There are several exceptions to the above generalizations. One is at
borehole 7, where a vertical fracture rolls over gradually over a length of 1 to 1.5 m.
At two other boreholes (HF10 and HF6) vertical fractures propagate a meter or
more above the bottoms of the casing before they roll over and become sub-
horizontal. None of the vertical fractures extended from the bottom of a borehole
to the ground surface.
A sub-horizontal fracture propagated from the notch at borehole HF6, but
none of the other notches contained a hydraulic fracture. The notch at HF6 was two
cm below the basket, whereas it was four to eight cm below the basket at the other
boreholes.
The features of Zone One are a result of the nucleation of hydraulic
fractures in the vicinity of an open borehole. It appears that nucleation occurs as a
vertical fracture in the wall of the open boring. The vertical fracture propagates
outward and upward and rolls over to a shallowly-dipping fracture either at or above
the top of the open interval.
The notches cut in the walls of the borehole were ineffective at nucleating
hydraulic fractures. Presumably this occurred because the notches were too shallow
to affect the concentration of stress in the vicinity of the borehole. A notch of larger
diameter is expected to be more effective at nucleating a horizontal hydraulic
fracture at the borehole. We were unable to create a larger notch using the simple
mechanical device designed for the project.
Zone Two
Zone Two is characterized by a subhorizontal fracture occurring within
several m of the parent borehole. The subhorizontal fracture surrounds the
borehole in some cases (e.g. HF6 and HF12). In other cases (HF5 and HF9) the
subhorizontal fracture is limited to one side of the borehole, typically the side
opposite the main body of the fracture.
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The subhorizontal fracture of Zone Two is absent from some of the fractures
(e.g. HF7, HF10 and HF11), and it is unclear whether this Zone is typical. A
hydraulic fracture lacking Zone Two would resemble 5.14 except the vertical
fracture of Zone One would roll over to the shallowly-dipping fracture of Zone
Three.
Zone Three
Zone Three composes most of the idealized hydraulic fracture. It is slightly
elongate in plan, with aspect ratios between 1.5:1 and 2:1, and the major axis lies
along a line between the parent borehole and the vent The length of the fracture in
Zone Three is roughly three times the depth where the fracture rolls over in Zone
One.
The fracture in Zone Three is, in general, planar to slightly trough-like and it
„ *_._.J .*.!_._ 1_ _ __ _. l_ ._. 1 ._. *-.+. ._._--_L1_. ^-/W\ fJm^*m _.«*_««. IB. KI^BVJB. K^ *1 ^-ft «««J ^Cft\ T«« *1»«
dips toward the borehole at roughly 20° (dips range between 12° and 25°). In the
field, this Zone is commonly composed of several distinct lobes, which taken
together result in the idealized form shown in Figure 5.14.
Traces of the fracture in Zone Three are remarkably straight over the length
of the zone. In detail, however, the traces are slightly stepped (Fig. 5.14b); they
consist of straight segments of approximately one meter connected by risers of
roughly 0.1 m (e.g. Figs. 3.7,3.8,3.11).
In plan, Zone Three is asymmetric with respect to the borehole. At some of
fractures (HF5, HF7 and HF10, HF11), the borehole lies at the edge of the fracture,
whereas at others the borehole is contained within the fracture but it lies much
closer to one end than to the other. The borehole lies between the load applied by
the backhoe and the fracture of Zone Three.
The major axis of the idealized fracture is perpendicular to the strike of the
vertical fracture in Zone One.
Zone Four
In Zone Four, the idealized fracture curves upward and is subvertical where
it intersects the ground surface. The vertical fracture in Zone Four typically extends
to a depth of ten cm, although depths range from a maximum of 30 cm at HF9 to a
minimum of 2 cm at the northern lobe of HF6. The vertical fracture of Zone Four
is 0.5 m to 1.5 m along strike. It is perpendicular to the major axis of Zone Three,
and it is roughly parallel to the vertical fracture in Zone One.
DISCUSSION: DEVELOPMENT OF THE IDEALIZED FRACTURE
A general history of the development and growth of the idealized fracture
Fig. 5.14J will improve our understanding of the processes that occurred during the
leld test. In the following section, we will use the results of experiments of
hydraulic fracturing of rock or soil and the results of theoretical analyses based on
linear elastic fracture mechanics to infer a conceptual model of the development of
the idealized fracture.
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Load- due to
backhoe
I
beokhoe
vent
1 11*"^ If— .
:; noToh
Zone 2.1. 2
Figure 5.14a. Idealized hydraulic fracture created at the ELDA test site. Inferred
from exposures of fractures created beneath level ground, a.) Oblique
view, bo Section along major axis of the fracture.
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When pumping begins at the start of the fracturing procedure, the pressure
within the borehole increases, affecting the state of stress until failure occurs in the
till enveloping the open interval of the borehole. The initial fracture is vertical,
containing the axis of the borehole and apparently is unrelated to the notch.
Several investigators have reported results from the laboratory indicating
that hydraulic fractures nucleated from cylindrical holes in rock will contain the axis
of the hole, even though the applied far-field state of stress favored an orientation
normal to the axis f Medlin and Masse, 1979; Daneshy, 1973; Haimson and
Fairhurst, 1969). Similar results occurred when hydraulic fractures were created
from cylindrical holes in soil using the apparatus described in Part I.
This result can be explained by an analysis of stresses in the vicinit
pressurized cylindrical hole in an elastic medium where the principal confining
stresses act parallel or normal to the axis of the hole (Poulos and Davis, 1974). The
analysis shows that pressure within the hole can induce tensile stresses in the
enveloping medium that act parallel to the circumference of the hole. Stresses
acting parallel to the axis of the hole, however, are unaffected by pressure within the
hole. Accordingly, tensile stress adjacent to a vertical borehole develop normal to a
vertical plane, regardless of the relative magnitudes of the principal confining
stresses. The vertical fractures observed adjacent to the boreholes apparently result
from those tensile stresses.
A disk-shaped notch should favor the nucleation of a fracture in the plane of
the notch, assuming the minimum applied compression is normal to the notch.
Indeed, this was the reason the notches were created. It is clear from the results of
the field test that the notches had little effect on the nucleation of hydraulic
fractures. Failure to nucleate a horizontal fracture at the borehole is a significant
shortcoming of the design of the borehole because it reduces the overall size of the
hydraulic fractures. This occurs because the vertical fractures at the borehole grow
upward before rolling over, essentially reducing the depth of initiation and limiting
the length of the fracture prior to venting.
The development of a vertical fracture could be inhibited by decreasing the
length of the open interval in the boring, and by increasing the depth of penetration
of the notch. Recently, we have used a high-velocity water jet to cut notches that
extend IS to 25 cm into till, many times larger than the ones cut mechanically during
the field test.
Once formed, the vertical fracture grows outward and upward climbing
above the open interval of the borehole. At some point, either adjacent to or
several dm to one meter above the basket, the vertical fracture changes orientation,
or rolls over, flattening abruptly to a shallow dip. Typically, the fractures roll over
to a nearly flat-lying orientation, but in some cases they dip 15° to 25° toward the
borehole. This change of orientation appears to occur as the fracture grows out of a
zone where stresses are influenced by the pressurized borehole and into a zone
influenced by the far-field stresses.
The idealized fracture then grows roughly horizontally as much as several m
away from the borehole and changes orientation again, curving upward to dip
roughly 20° toward the borehole. This change in orientation is inferred to result
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from a mechanical interaction between the fracture and the overlying ground
surface. The interaction has several effects on the propagating fracture, all of which
are related to the removal of resistance of the material above the ground surface.
Perkins and Kern (1961), for example, analyze one effect of mechanical interaction
by comparing the aperture of a shallow circular horizontal fracture, which dilates by
lifting the overburden, to the aperture of a deep circular fracture, which dilates by
compressing the overburden. They show that fracture apertures depend on the size
of the fracture relative to its depth, expressed as the ratio of radial length a to depth
of initiation d. Apertures of the two fractures are equal when a/d = 1.33, but the
aperture of the fracture that lifts the overburden greatly exceeds that of the other
fracture when a/d > 1.33.
Pollard and Holzhausen (1979) show how mechanical interaction could cause
a fracture to turn upward and propagate toward the ground surface. They
calculated the stress intensity factors, K\ and K\\, for a two-dimensional, static, planar
fracture of half-length a in an elastic medium bounded by a free surface (the ground
surface). The direction of propagation of the fracture can be predicted using the
relative magnitudes of K\ and An, according to theories proposed by Cottrell and
Rice (1979) or other investigators cited by Pollard and Holzhausen (1979). Those
theories state that non-zero values ofKu lead to propagation out of the plane of the
original fracture. The results of Pollard and Holzhausen indicate that K\\ of a
horizontal fracture increases as a/d increases; K\\ is negligible when a/d < 0.3, it
increases gradually when 0.3 < a/d < 1.0, and it increases rapidly when a/d > 1.0
(Pollard and Holzhausen, 1979; fig 5). This is because the upper surface of a
horizontal fracture is displaced farther from the axial plane than the lower surface,
resulting in shear at the tip and non-zero values of AH.
Those results suggest that the depth of initiation is critical to propagation
path. A horizontal fracture considerably shorter than the depth of initiation will
propagate horizontally, but as the fracture length approaches that depth the fracture
will tend to curve out of plane and propagate upward.
The analyses described in the previous paragraph are for static fractures, and
as such they are limited to the favored direction of a miniscule extension of a
stationary planar fracture. Dynamic analyses, which track the movement of a
fracture as it propagates, show how the interactions described above affect fracture
form. Narandren and Cleary (1983) present the results of a dynamic analysis
predicting the path of propagation or a horizontal hydraulic fracture beneath a free
surface. The results (Narandren and Cleary 1983; fig. 9) show that the fracture is
nearly flat-lying when it is short relative to its depth, but the dip increases noticeably
when a/d > 0.7. The analysis was terminated when a/d = 1.55 and the fracture
curves upward yielding a shape suggestive of the cross-section of the idealized
fracture (Fig. 5.14b and Narandren and Cleary 1983; fig. 9).
Results of theoretical analyses outlined above indicate that we should expect
a hydraulic fracture to begin to propagate toward the ground surface after it has
grown away from the parent borehole a distance approximately equal to the depth
of initiation. Thus, the analyses indicate that the maximum length a fracture
reaches before venting is scaled to its depth of initiation. This implies that we could
have increased the sizes of the fractures created during the test by using deeper
boreholes.
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The idealized fracture grows at nearly a constant dip once it begins to
propagate toward the ground surface (neglecting vertical growth at the borehole).
Processes causing the dip to remain constant are unclear because available analyses
(i.e. Pollard and Holzhausen, 1979; Narandren and Geary, 1983) suggest that the
dip will increase as the fracture climbs and the effect of the ground surface
increases. One possibility is that during upward growth the vertical stress, resulting
from the weight of the overburden at the fracture tip decreases, whereas the lateral
stress remains constant. Thus the tendency to steepen, due to effects of the ground
surface, is balanced by a tendency to flatten, due to an increase in the ratio of lateral
to vertical stress at the tip. This possibility must still be checked
The dip of the idealized fracture is uniform in general, but it varies slightly in
detail, resulting in gentle step-like features. The steps suggest that slight deviations
from the average dip are rapidly corrected by the fracture curving back to the initial
orientation. Cotterell and Rice, who analyze the stability of slightly-curved Mode I
cracks, show how a small deviation from the optimal path will result in a step-like
form in a fracture (Cotterell and Rice, 1980; fig. 10).
Many analyses of hydraulic fractures assume that they are symmetric with
respect to the axis of the borehole, but most of the fractures created in the field test
were asymmetric. The hydraulic fracture created beneath sloping ground (HF13) is
elongate in the downslope direction. Where the ground is level, however, applied
loads seem to influence the direction of propagation because the dominant
directions of propagation are typically away from the backhoe parked near each
borehole. Apparently gradients in vertical stress, caused by either topography or
applied loads, affect the dominant direction of propagation of horizontal or
shallowly-dipping hydraulic fractures. This conclusion raises the intriguing
possibility of artificially loading the ground surface to cause fractures to propagate
in a particular direction.
It is reasonable to expect that hydraulic fractures of similar size and shape as
those described here could be created under conditions similar to the ELD A site. It
would be misleading, however, to suggest that similar hydraulic fractures can be
expected at any site. The large lateral stresses in the till at the ELD A site certainly
affected the dips of the fractures, and thus the sizes that they could achieve before
venting. Measuring in situ stresses will be a vital first step in predicting the
orientation of hydraulic fractures.
The principles of linear elastic fracture mechanics, specifically the
applications to hydraulic fracturing of rock, seem to offer general explanations of
the development of the idealized fracture created in till at the ELD A site.
Predicting the forms of hydraulic fractures at other sites, however, will require a
theoretical model specifically tailored to analyze conditions of the near-surface.
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SECTION SIX
SETTING AND DESIGN OF THE FIELD TEST - 1989
Hydraulic fracturing field tests of 1989 were performed at two sites. Oni
me as the field test of 1988, located 10 km north of downtown Cincinnati:
One was
the same as the field test of 1988, located 10 km north of downtown Cincinnati near
the southeastern corner of the ELD A Company landfill. The other is located IS
miles north of the ELD A landfill, on the grounds of the Goettle Construction
Company.
Hydraulic fracturing at the ELD A landfill site took place in June and July,
1989. Field analysis of the fractures, including trench mapping, took place in July
and August, 1989. Preliminary testing of the hydraulic fracturing apparatus was
performed at the Goettle Construction Company site in March and April, 1989.
Hydraulic fractures for fracture monitoring purposes were created at the Goettle
site in July, 1989. Fractures created at the ELDA site were exposed by excavating a
network of trenches, whereas fractures at the Goettle site were not exposed. As a
result, more is known about the fractures and subsurface at the ELDA site, and the
following chapters will focus on that site.
QUALITY ASSURANCE AND CONTROL
The success of the hydraulic fracturing effort is one measure of quality
assurance steps taken during the execution of this project. The fact that fractures of
similar shape and size were created repeatedly, at different times and locations, is a
measure or the success of quality control.
All instruments used during the fracturing process were calibrated according
to industry standards. Calibration of custom designed instruments, such as the
gauge for measuring the flow rate of the injection pump, was conducted in a series
of identical tests, performed by different staff researchers. Dosages of chemical
ingredients of fracturing gels were measured with margins of error no greater than
0.1%, hence exceeding petroleum industry standards. Accuracy achieved in
measuring borehole depths and notch lengths was comparable to accuracy
demanded by field analysis of the fractures (see Section 7).
SITE CHARACTERISTICS
The vicinity of the ELDA test site is an area of gently sloping ground
bounded on the southwest by a steep slope, three to four meters tall, and on the
northeast by a moderate to steep descent into a deep (> 10 m) trough. The ground
surface at the time of the test was the product of sou excavation for fill purposes,
and it was three to four meters below the natural ground surface. The ELDA
fracturing site is a gently sloping, elongate strip, trending N55W, roughly 50 m long
and 10 m wide.
The area used during 1989 is in the vicinity of the area used during 1988. We
estimate that the southeastern end of the 1989 site is 40 to 60 m south of the
southwestern corner of the area shown in Figure 4.2. Accurate correlation of the
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two sites was not attempted because all the features shown in Figure 4.2 were
removed during excavation activities between autumn 1988 and spring 1989.
Geology
The ELD A site is underlain by glacial till (Illinoian?), composed mostly of
clayey silt to silty clay. The stratigraphic level is slightly higher (5 to 10 m) than that
of the site of the 1988 test. A two meter section of the stratigraphy, exposed in
trenches used to examine the fractures, is described in the following section.
Description of Soil Profiles in Trenches
The soil profile is generally uniform in the SE-NW direction, according to
observations in trenches. Gravelly till lies at the top of the soil sectionjust beneath
the ground surface. The thickness of the gravelly till increases to the NW, from 20
cm at the SE end of trench A, to 30 cm at the midpoint of trench A, 20 m away from
the SE end, to 50 cm at the NW end of the trench.
Organic-rich silty clay to clayey silt underlies the gravelly till. The thickness
of the organic silty clay is 40 cm at both ends of trench A, but it pinches to half that
thickness at the midpoint of the trench.
Massive brown silt, 25 to 30 cm thick, underlies the organic silt. At the NW
end of the trench, the massive silt is directly underlain by a 90 cm thick unit of
laminated silty clay, with interbedded clayey silt. At the SE end and at the midpoint
of the trench, the massive silt and the laminated silty clay are separated by other
units. At the midpoint of the trench, a 50 cm thick sequence of interbedded, 10 cm
thick, laminated clay and 10 to 20 cm thick massive brown silt underlies the upper
massive silt. At the SE end, 50 cm of clayey silt with interbedded silty clay lie below
the massive silt. At both the SE end and the midpoint of the trench, the 50 cm thick
sequence of silt and clay is underlain by 105 to 110 cm of laminated silty clay with
interbedded clayey silt.
At the NW end of the trench, the laminated silty clay is underlain by 20 cm of
loam, followed by 20 cm of gravelly till, at the bottom of the trench. At the
midpoint of the trench, the laminated silty clay is underlain by 10 cm of gravel at the
bottom of the trench, and at the SE end of the trench, the laminated silty clay
reaches to the bottom of the trench.
Moisture Contents
Moisture contents of three samples extracted from the western intersection
of Trenches A and F, were measured in accordance with the ASTM Standard
Designation D 2216-80. The three samples represent three different soil types,
described above, under Site Characteristics.
Sample 1, extracted 77 cm above the horizontal datum, represents the
organic-rich silty clay to clayey silt, which occurred just below the gravelly till
throughout the trench network. Its moisture content is 23.7%.
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Sample 2, extracted 44 cm above the datum line, represents the massive,
brown silt, lenses of which also extend across the entire trench network. Its
moisture content is 14.6%.
Sample 3, extracted 15 cm above the datum, consists of laminated siltv clay.
Although the layer from which Sample 3 was removed lies above the lowest lens of
massive silt, the sample represents the same type of soil that constitutes the one-
meter-thick, laminated silty clay unit pervasive in the lower half of the entire trench
network. Its moisture content is 25.2%.
METHOD OF FRACTURING
Figure 6.1 illustrates the equipment and sequence of operations involved in
hydraulic fracturing. Figure 6.2 shows details of the drive head used to prepare a
borehole for hydraulic fracturing. Figure 63 outlines five steps of hydraulic
fracturing.
Equipment
Equipment used to prepare and pump gel and sand mixtures for hydraulic
fracturing included two water tanks, two gel mixing tanks (labeled a in Figure 6.1),
two blenders for crosslinking and adding sand (d in Figure 6.1), a water pump, a gel
pump (b in Figure 6.1), hoses for gel transfer (c in Figure 6.1), and a grout pump to
inject proppant into the subsurface (e in Figure 6.1). Equipment used to create
boreholes for fracturing included rod and casing (fin Figure 6.1; also see Figure
6.2), a drive head with pointed tip (Figure 6.2), a water jet rod to create starter
notches, a high-pressure pump for the water jet, and an electrically powered
jackhammer to drive the fracture lance into the ground. Monitoring equipment
included an IBM-PC compatible, portable (laptop) computer (h in Figure 6.1), a
pressure transducer (g in Figure 6.1), and a motorized power generator.
The two water tanks were made of plastic, and had capacities of 1.1 nr1 (300
gal.) each. The two^longate eel tanks were made of galvanized steel, and had
capacities of 0.95 nr (250 gal.) each. The two blenders for crosslinking and adding
sand were part of a grouting pump system by Chem-Grout Company of Chicago,
Illinois, and they had capacities of 0.2 nr (50 gal.) each. Rotary mixing blades
within the blenders were powered by a diesel engine, which also powered the
moyno-type grouting pump. Crosslinked gel and sand were fed from the blenders
directly into the grouting pump, which pumped the blend downhole and into the
fractures.
At the Goettle site, a five horsepower centrifugal pump moved water from a
nearby lake into the two water tanks, and from the water tanks into the gel tanks.
At the ELDA site, the water pump was not needed, because the water tanks were
filled directly from a water truck, and water flowed downhill from the water tanks
into the gel tanks.
An eight horsepower, 7.6 cm (3 in) centrifugal pump rapidly circulated gel in
the gel tank to hydrate the guar gum, and to prevent the formation of lumps, or
"fisheyes," in the gel. The same pump also moved gel from the gel tanks into the
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a. mixing tank
b. circulation pump
o. valve
d blender
e Injection pump
f. borehole
g. transducer
h. data acquisition
Figure 6.1. Scheme for hydraulic fracturing operation performed during the 1989
field test
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crosslinking blenders. Gel circulated from the gel tank, into the pump, and back
into the geltank through 5 cm (2 in) tubing (Figure 6.1). A "T" valve (labeled c in
Figure 6.1) in the tubing diverted the hydrated gel into the crosslinking blenders,
also through plastic tubing.
A Zenith Supersport 286 laptop personal computer, with 40 megabyte hard-
drive was linked to the pressure transducer, which was attached to the borehole
casing, in order to monitor pressure changes in the proppant pumping hose (the
pipeline) at or above ground surface.
The Injection Fluid
Guar gum-based chemical mixtures were added to the injected water to
create a gel capable of carrying sand into the fractures. A complex derivative of
guar gum, manufactured by Halliburton Services company - a major service
company to oilfields in the United States - was used in the first four fractures
created at the ELDA site. A simple guar gum, manufactured by Hi-Tek Polymers,
Inc., was used in the remaining fractures, including twelve at the ELDA site, and
five at the Goettle site.
Comparison of the two gel products led to the conclusion that the simple,
nonderivitized guar gum system manufactured by Hi-Tek Polymers is better suited
for shallow, environmental applications than the highly derivitized system
manufactured by Halliburton Services. The chemical kinetics of the nonderivitized
gel corresponds better to the requirements of fracturing at shallow depths.
Guar gum-based gels consist of four main ingredients, which are added to
water in a particular, timed order, causing a three-step chemical process. The
ingredients include guar gum powder, buffering powder or solution, crosslinking
powder or solution, and breaking powder or solution. The three steps are, in order,
gelling, crosslinking, and breaking. Gelling and crosslinking increase the viscosity of
water by one and two orders of magnitude, respectively. Breaking reduces the
viscosity back down to almost that of water (1 cP), after a period of time sufficiently
long to allow completion of the fractures.
Gelling increases the viscosity of water from 1 cP to about 15 to 20 cP,
caused by the addition of about 3.6 to 4.8 kgs of guar gum powder per cubic meter
(0.03 to 0.04 Ibs/gal) of buffered, pH-neutral water. Halliburton's WG-18 gum
powder, known as a CMHPG (Carboxyl-methyl-hydroxyl-propyl-guar) gum, was
required in doses of 4.8 to 5.03 kgs/nr (0.04 to 0.042 Ibs/gal) to obtain the
necessary viscosity. Doses of 3.6 kg/mj (0.03 Ibs/gal) were insufficient. Hi-Tek
Polymer's Jaguar 408-D gum powder, known as a "standard guar," was required in
doses of 036 to 3.95 kg/nr3 (0.03 to 0.033 Ibs/gal).
Halliburton's WG-18 guar gum required 0.3 kg/m3 (0.0025 Ibs/gal) of an
acidic buffering agent, containing 60% sulfamic acid, supplied by Halliburton
Service Company under the name of BA-2. In conjunction with Hi-Tek Polymer's
Jaguar 408-D guar gum, a buffer is required only if the water is pH-neutral or
slightly caustic, because the guar gum increases the pH of neutral (pH=7.0) water to
about 7.5 or 8.0, whereas a pH value of 7.0 is needed for the successful hydration of
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the guar gum powder to form a gel. Cincinnati City Water used at the ELD A site
was slightly acidic, so that a buffer was not needed. Lake water used at the Goettle
site was slightly caustic, with a pH of 7.5 to 8.0, so that a buffering agent was needed.
Calcium chloride, added in doses of 4.8 to 5.4 kg/nr (0.04 to 0.045 Ibs/gal), served
both as a buffer, and as an inhibitor of swelling in clays. Calcium chloride crystals
were added to Goettle Lake Water before the guar gum powder, to allow sufficient
time for the crystals to dissolve.
Once guar gum powder is added to water, sufficient time must pass for the
guar to hydrate before the required viscosity is reached and a crosslinker may be
added. The hydration time is only about 5 minutes for the Halliburton gel, whereas
it is 20 to 30 minutes for the Hi-Tek Polymers gel. This is the first of two critical
differences between the chemical kinetics of the two gel systems applied during
fracturing at the ELDA site (only Hi-Tek Polymers gel was applied at the Goettle
site for the fractures described in this report). Both gel systems require several
minutes of agitated mixing of the guar gum, to avoia formation of small lumps of
gum, called "fish-eyes" in the oilfield hydraulic fracturing industry.
The viscosity of the hydrated gel is increased to 100 to 200 cP by the addition
of a crosslinker. The crosslinker supplied by Halliburton, called CL-19, contains 11
to 30% ethyJene glycol, and it was added to the hydrated gel in doses of 1.9 to 2.8
cm* per cnT (0.0005 to 0.00075 gal per gal). The Hi-Tek Polymers gel required
borate as a crosslinker, available under the brand name "Borax," and it was added to
the hydrated gel in doses of 0.24 to 0.68 kg/nr3 (0.002 to 0.0057 Ibs/gal). The
kinetics of the crosslinking reaction are different for the two systems compared in
this study. The Halliburton gel typically requires five to six minutes of vigorous
agitation for crosslinking to occur. The High-Tek Polymers gel, on the other hand,
is crosslinked almost instantly, within seconds after the crosslinker is introduced
under vigorous agitation. This is the second of the two critical differences between
the chemical kinetics of the Halliburton and Hi-Tek Polymer gel systems.
Concomitantly to the addition of crosslinker, breaker was added to ensure
the eventual breakdown of the gel to a liquid solution with viscosity almost equal to
that of water. Laboratory tests showed the final viscosity of broken gels to be about
2 cP, for both the Halliburton and Hi-Tek Polymers gels. The breaker supplied by
Halliburton, called GBW-3, contains at least 60% of an unspecified carbohydrate
material, and it was added in doses of 0.095 to 0.099 kg/nr (0.0008 to 0.00083
Ibs/gal). The breaker supplied by Hi-Tek Polymers, called Breaker-F, contains a
cellulase enzyme, and it was added in doses of 0.12 to 0.30 kg/nr (0.001 to 0.0025
Ibs/gal). The time required to break down the gel to the final viscosity was 18 to 24
hours for the Halliburton gel, and 24 to 48 hours for the Hi-Tek Polymers gel.
Although this contrast between the Halliburton and Hi-Tek Polymers systems may
influence scheduling of the application of newly created fractures for remediation
purposes, the contrast is nonessential because it does not affect the fracturing
process itself.
The two critical differences between the chemical kinetics of the Halliburton
and Hi-Tek Polymers gel systems noted above - the different times required for
hydration and crosslinking of the gels - render the Hi-Tek Polymers gel system
more suitable for application to hydraulic fracturing for remediation purposes. The
relatively small volumes required for our application makes the long hydration times
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necessary for Hi-Tek Polymers gel tolerable, since tanks of hydrated but
uncrosshnked gel sufficiently large to fill several fractures can be prepared in
advance. Moreover, the pumping rate of the system we used is limited by the time
required to completely mix a batch of gel, crosslink and sand, so the rapid
crosslinking of the High Tek Polymers gel decreased the time required to mix each
batch and thus improved the efficiency of our procedure. The gel and crosslink
system from Halliburton is designed for procedures used to create hydraulic
fractures in the oil industry, which benefit from short hydration times and delayed
crosslinking.
The Fracturing Procedure
The borehole used to create fractures during the 1989 tests was designed to
inhibit the formation of vertical fractures adjacent to the bore (as in the 1988 tests),
and to facilitate the creation of stacks of multiple fractures. A device (Fig. 6.2),
which we term a "fracturing lance", is the central element of the design. The lance,
illustrated in Figure 6.2, consists of casing (EX casing) and an inner rod (EW drill
rod), both of which are tipped at one end with hardened cutting surfaces that are
formed into a conical point. A drive head at the other end of the lance secures both
the casing and the rod. Individual segments of rod and casing were 1.52 (5 ft) long,
and they were threaded together as required by borehole depth, which ranged from
9.6 to 3.9m (2 ft to 12 ft).
To prepare for fracturing, the lance was driven 0.1 to 0.2 m below the bottom
of a borehole; either an open hole or through a hollow-stem auger (Fig. 63). The
rod was removed leaving till exposed at the bottom of the casing. Lateral pressure
of the soil on the wall of the casing effectively sealed the casing in the ground, much
as cement sealed steel pipe in the borehole during the 1988 tests. Another
apparatus, composed of steel tubing with a narrow (diam. 0.025 cm; 0.01 in) orifice
at one end, was inserted into the casing. Water injected into that apparatus with a
pressure washer pump (rated at 17.2 kPa; 2500 psi,0.02 nr/rnin; 5 gpm) formed a
jet that cut laterally into the soil. The water jet was rotated, producing a disk-
shaped notch extending up to 40 cm away from the borehole (Fig. 6.3). A simple
device, built from a steel tape extending the length of a tube and making a right
angle bend at the end of the tube, was inserted into the casing and used to verify and
measure the radius of the slot. A hydraulic fracture was created, using a procedure
that will be described in detail below, and then the rod and point were reinserted
and the lance advanced from 7 to 50 cm. The rod and point were retracted and the
procedure repeated, creating a second fracture 7 to 50 cm below the first one.
Several fractures were created, stacked one on top of another, from a common
borehole.
The actual procedure of hydraulic fracturing was commenced by engaging
the injection pump-a Robbins and Meyers Moyno 2J6 CDQjmmp was on the
grouting rig used in the test (e in Figure 6.1). At least 0.02 m~ (5 gall of water were
pumped downhole first, followed by a. pad of at least 0.02 nr (5 gal) of
uncrosslinked gel (without sand). The gel was crosslinked and sand added in
concentrations ranging from 240 to 1438 kg of sand per cubic meter of gel (2 to 12
Ibs/gal). Two sizes of sand were used in the tests; #5 sand ranges from 0.8 to 1.8
mm with a median of 1.5 mm, whereas #7 sand ranges from 0.4 to 0.9 mm with a
176
-------
Drive head
Cutting sleeve
Point
Figure 6.2. Fracturing lance, used to prepare boreholes for hydraulic fracturing
during the 1989 field test
177
-------
1
Casing^
Extension
rod
Lance tip
Pressure from coll
seals casing
Hydraulic fracture
Figure 63. Five steps of hydraulic fracturing: (1) create borehole; (2) extend
borehole beyond casing; (3) remove rod and tip of fracturing lance;
(4) create starter notch with water jet; (5) create fracture by injecting
proppant into notch.
178
-------
median of 0.75 mm. The sand-laden gel was pumped downhole at a rate of 0.02 to
0.04 mr/min (5 to 10 gpm).
Injection pressure measured at the top of the borehole increased rapidly to at
least 138 kPa (20 psi). As soon as fracturing commences - typically about 30
seconds after initial engagement of the injection pump - the pressure dropped
abruptly to about 68.9 kPa (10 psi). As pumping progressed, the pressure gradually
decreased, although changes in gel viscosity, sand concentration, or pumping rate
cause temporary pressure fluctuations.
Assuming unlimited supply of gel and sand, pumping of proppant into the
growing fracture would continue until either the fracture vents, or the pump jams.
The latter occurs if there is "screen-out", either at the tip of the fracture or at the
borehole, causing immobilized sand to back up into the injection hose, or even into
the injection pump. At that point, pressure measured by the transducer increases
dramatically, and the operation must cease.
Most fracturing episodes performed as part of this study were complete when
the planned volume of proppant had been injected.
Discussion of the Fracturing Method
The 1989 tests showed that hydraulic fractures can be created and propped
with sand using a simple apparatus intended for injection grouting. An apparatus
similar to the one we used should be readily available for rent throughout the
United States, and several manufacturers offer similar units for sale.
Use of the lance is more rapid than drilling a borehole and cementing casing,
as we did in 1988. Moreover, the technique is versatile; a hole fractured using the
lance method can be completed with a gravel pack and screen, or the hole can be
left unscreened if a well is not required.
The design of the fracturing lance facilitates the creation of multiple
fractures. Of course, methods of creating multiple fractures are well-known in the
oil industry, but they commonly require sophisticated packers and explosive charges
to perforate casing. The technique used in this research is intended to take
advantage of the shallow depths and penetrability of soil, where those sophisticated
methods are unnecessary.
There are several drawbacks to the method used during the 1989 tests. The
blenders were underpowered, so that mixing sand with crosslinked gel was time
consuming. As a result, the rate of blending a batch of sand-laden gel was
increased, limiting the injection rate. A more powerful blender, and perhaps
another blender design would improve the design.
The progressive cavity pump used to inject slurry suffered excessive wear,
and the rotor and stator had to be replaced after pumping almost llm3 (2900 gal)
of gel-sand mixtures. The progressive cavity grouting pump, while effective for high
concentrations of #7 (0.75 mm grain size) size sand, proved ineffective - it jammed
- for even moderate to low concentrations of the coarser (1.5 mm grain size), #5
179
-------
sand. We are currently evaluating several other styles of pump for future
applications.
Use of the fracturing lance requires creating hydraulic fractures during
drilling of a borehole, rather than after completion or the well. This means that
drilling is interupted for fracturing to take place, a practice that would increase the
time required to drill each well. Techniques of isolating a zone to be fractured using
straddle packers, a common practice in oil wells and water wells, are currently being
considered as an alternative to the use of the fracturing lance. In some cases,
creating a fracture below the bottom of a borehole and then drilling down through it
could result in the deposition of mud, as a skin between the bore and the fracture.
Completion and development techniques, which eliminate well-bore skin from the
vicinity of hydraulic fractures, will be crucial to obtaining the maximum
performance from fractured wells.
180
-------
SECTION SEVEN
HYDRAULIC FRACTURES CREATED DURING THE FIELD TEST - 1989
In contrast to fractures created during the field test of 1988, fractures created
in 1989 are filled with 5 to 25 mm of sand, making them clearly visible. As in the
1988 field test, fractures were excavated with a backhoe, creating a network of
trenches two m deep. Detailed mapping of the trench walls revealed the geometry
of the fractures.
A 40 m long, longitudinal trench (trench A, Fig. 7.1) intersects all seven
boreholes, and roughly coincides with the minor axes of the elliptical fractures. A 5
to IS m long, transverse trench also intersects each of the seven boreholes (trenches
B - H), roughly coinciding with the major axes of the fractures. A 6 m long trench
(trench I), parallel to the longitudinal trench, intersects one of the transverse
trenches (trench G).
A horizontal datum line, extending along the entire trench network, was used
during mapping. Smooth trench surfaces were cut by knives to allow precise
measurement of fracture thicknesses. Dyed proppant sand was barely
distinguishable from undyed sand, but the thickness of proppant made dye
unnecessary, in contrast to fractures created during the 1988 field test.
Excavation of the trenches was completed one week after creation of the last
fracture. Mapping and analysis of the fractures commenced immediately, and
continued for three weeks. This section presents the results of mapping and
measuring fracture traces in the nine trenches.
QUALITY ASSURANCE AND CONTROL
To assure consistent quality of data, measurements were periodically
repeated by different field investigators. Datum lines were checked daily to correct
for sagging or other potential sources of inaccuracy.
Accuracy achieved in field analysis of fractures was comparable to accuracy
standards for similar analyses of structural field data related to geomechanical
studies, or to petroleum exploration and production.
FORMS OF THE HYDRAULIC FRACTURES
At the ELDA site, we created 20 fractures from 7 boreholes, spaced 3.5 to 10
m apart horizontally, and roughly defining a straight line, as shown in Figure 7.1.
The boreholes are located on a 10 to 15 m wide bench, bounded to the southwest by
a 5 m tall, steep ascent, and to the northeast by a 10 m deep descent. The boreholes
are located 2 to 5 m away from the wall. Individual boreholes contain 2 to 5
fractures, spaced 0.1 to 03 m apart vertically at the borehole, as indicated in Table
181
-------
a- c
oo
to
0 10
meters
Contours In meters
Figure 7.1. Map of Elda Landfill site. Solid lines are
topographic contours; dotted lines are trench
outlines. Locations of boreholes and cross
sections are also shown.
-------
TABLE 7.1: FRACTURE SIZE
Fracture
EL1F1
EL1F2
EL2F1
EL2F2
EL3F1
EL3F2
EUF1
EUF2
EL4F3
EL/4F4
EL5F1
EL5F2
EL5F3
EL5F4
EL5F5
EL6F1
EL6F2
EL6F3
EL7F1
-EL7F2
Depth
(m)
1.5
1.7
1.5
1.7
1.5
1.7
0.9
1.2
1.5
1.8
1.1
1.2
1.5
1.6
1.6
1.4
1.6
1.9
1.3
—
Major
Axis
(m)
8.0
4.5
5.0
3.0
8.0
5.0
5.0
7.0
5.0
4.5
8.0
7.0
3.0
1.0
~_
6.0
8.5
5.5
7.0
7.0
Minor
Axis
(m)
5.0
2.0
3.5
2.0
3.5
2.5
4.0
4.0
4.5
3.5
5.0
6.0
2.5
1.0
....
5.0
5.5
4.5
5.5
5.0
Max Dist
From BH
(m)
7.2
3.8
4.0
1.2
6.0
4.6
3.8
4.6
3.0
2.5
3.2
3.8
2.0
0.8
....
5.0
7.0
4.0
4.4
5.8
Aspect
Ratio
(m)
1.6
2.3
1.4
1.5
2.3
2.0
13
1.8
1.1
1.3
1.6
12
12
1.0
.._
1.2
15
1.2
1.3
1.4
Area
(m2)
31.4
7.1
13.7
4.7
22.0
9.8
15.7
22.0
17.7
12.4
31.4
33.0
5.9
0.8
..._
23.6
36.7
19.4
30.2
27.5
183
-------
\ c \
Figure 7.2. Fracture map of trenches B and C. Thickest line shows outline of
topmost fracture.
184
-------
meter
D
Figure 7.3. Fracture map of trenches D, E and F. Thickest line shows outline of
topmost fractures.
185
-------
A\
\H ..'
meter
Figure 7.4. Fracture map of trenches G, H and I. Thickest line shows outline of
topmost fractures.
186
-------
Outlines and Dips of Fractures
A network of nine interconnected trenches, shown in Figure 7.1, exposes the
fractures and reveals their shapes. Most of the fractures are elliptical in outline,
with aspect ratios (length of major axis divided by length of minor axis) ranging from
1.0 (fracture EL5F4 in Figure 7.4) to 2.3 (fracture EL6F2 in Figure 7.2; Table 7.1).
The major axes of the fractures are roughly parallel to the dip direction of the
ground surface, which is generally parallel to the transverse trenches (trenches B -
H) and perpendicular to the wall along the southwest edge of the bench (Figures
7.1-7.4).
Many of the fractures are flat and subhorizontal in cross section, with dips
ranging from 0 degrees (fractures E16F2 in Figure 7.12, E13F1 in figure 7.14, E14F1
in Figure 7.17, and EL5F1 and EL5F3 in Figure 7.18); to 5 degrees (fractures
EL3F2 in Figure 7.14, and EL1F1 in Figure 7.15). Some fractures are subhorizontal
near the borehole, and dip toward the borehole by up to IS degrees near the
fracture margin,'thus resembling a shallow bowl or plate (fractures EL6F1 in Figure
7.12, EL7F2 In Figure 7.13, and EL4F3 and EL4F4 in Figure 7.17).
The deepest point of each fracture, which coincides with the borehole in
almost all cases, is located near the end of the major axis, close to the wall along the
southwest edge of the bench (Figures 7.1-7.4). The only notable exception is
fracture EL4F5 (Figure 7.17), in which the deepest point is located approximately
1.3 m north of the borehole, and the borehole is located near the center of the
fracture, but closer to the downslope (northeast) edge of the fracture than to the
wall along the southwest side of the bench (Figures 7.1 and 7.17).
Venting of Fractures
Five of the fractures created at the ELD A site vented onto the slope
northeast of the bench. Fractures EL1F1 and EL2F2 both vented along the same
horizon. Fractures EL2F1 and EL3F1 each vented along horizons above the EL1F1
venting horizon. Finally, fracture EL3F2 vented along both the EL3F1 and EL1F1
venting horizons. The vertical distance between the three venting horizons is about
30cm.
Fluid that vented from all of those fractures was virtually devoid of sand,
even though the fluid was laden with sand when injected. Sand proppant filled all
the fractures, but it terminated several m before the point of venting, according to
exposures on transverse trenches cut along lines between boreholes and vents. Two
scenarios seem possible: either the aperture of the fractures in the vicinity of the
vents was too small to permit the passage of sand, or sand was deposited because
the gel that was carrying it leaked off-this is termed "tip-screenout" by Smith and
others (1987). In either case, the gel was separated from the sand by straining
through immobilized sand at the fracture tip.
187
-------
5 ra
EL6
B
B
Figure 7.5. Cross section B-B'. See Figure 7.1 for location.
5 m
EL7
Figure 7.6. Cross section C-C. See Figure 7.1 for location.
188
-------
Figure 7.7. Cross section D-D'. See Figure 7.1 for location.
Figure 7.8. Cross section E-E'. See Figure 7.1 for location.
Figure 7.9. Cross section F-F. See Figure 7.1 for location.
189
-------
Figure 7.10. Cross section G-G'. See Figure 7.1 for location.
EL5
H
Figure 7.11. Cross section H-H1. See Figure 7.1 for location.
190
-------
I meter
EL6
TRENCH B
EAST WALL
Figure 7.12. Map of east wall of trench B, showing fracture
traces, borehole and ground surface (dashed).
-------
1 meter
EL7
TRENCH C
EAST WALL
Figure 7.13. Map of east wall of trench C, showing fracture
traces, borehole and ground surface (dashed).
Thick fracture is filled with perlite.
-------
1 METER
EL3
vo
TRENCH D
EAST WALL
Figure 7.14. Map of east wall of trench D, showing fracture
traces, borehole and ground surface (dashed).
-------
1 meter ELI
TRENCH E - EAST WALL
Figure 7.15. Map of east wall of trench E, showing fracture
traces, borehole and ground surface (dashed).
-------
1 meter
VO
TRENCH F
EAST WALL
Figure 7.16. Map of east wall of trench F, showing fracture
traces, borehole and ground surface (dashed).
-------
1 meter
vo
EL4
TRENCH G - EAST WALL
Figure 7.17. Map of east wall of trench G, showing fracture
traces, borehole and ground surface (dashed).
-------
10
1 meter
EL5
TRENCH H - EAST WALL
Figure 7.18. Map of east wall of trench H, showing fracture
traces, borehole and ground surface (dashed).
-------
1 meter
00
TRENCH I - NORTH WALL
Figure 7.19. Map of north wall of trench I, showing fracture
traces and ground surface (dashed).
-------
Continuity of Fractures
Traces of fractures along trench walls, roughly coincidental with the major
axes, are commonly continuous. Continuous fractures represent over half (61%) of
the 18 fractures exposed along major-axis cross sections, including fractures EL3F1-
F2 (Figure 7.14), EUF1-F4 (Figure 7.17), EL6F1-F2 (Figure 7.12), and EL7F1
(Figure 7.13). The remaining 39% of fractures exhibit at least one discontinuity
along the major-axis cross section.
Discontinuities along fractures either step up or step down, in the direction
pointing away from the borehole (toward the fracture tip). Most discontinuous
fractures step up by 2 to 12 cm, at lateral intervals of 1 to 2 m. Up-stepping
fractures include EL2F1 (Figure 7.16), EL5F1-F2 (Figure 7.18), and EL7F2 (Figure
7.13), representing 22% of all fractures. Some fractures step downward by 4 to 8
cm, about 0.8 of the distance from the borehole to the fracture tip. Down-stepping
fractures include EL1F1 (Figure 7.15) and EL6F3 (Figure 7.12), representing 11%
of the fractures. Finally, one fracture, EL1F2 (Figure 7.15), steps up by 2 cm at a
distance of 1.5 m from the borehole, and steps back down again by 2 cm at a
distance of 1.7 m from the borehole. This up-down-stepping fracture represents 6%
of the total fracture count.
Fractures that are discontinuous on a trench wall are expected to be joined
somewhere out of the plane of the wall. Exposures were insufficient to verify this
expectation.
Fracture Margins
The cross sections exposed in the trenches do not afford a clear view of
fracture margins, since the terminations of fractures occur only as single points in
the cross sections. We did not excavate a fracture surface at its margin, due to time
constraints. Our assumption, hence, is that the fracture margins are generally
smooth, as shown in Figures 12-1 A.
Some evidence suggests that fracture margins may be lobate. Trench I,
which reveals the only cross section perpendicular to the direction of proppant flow
and at some distance away from the borehole, exposes the trace of merged fractures
EL4F2 and EL5F2 (Figure 7.19). Fracture EL4F2 contains weight #5 sand,
whereas fracture EL5F2 contains weight #7 sand (Table 73). The merged fractures
exhibit lenses of weight #5 sand, 10 to 20 cm wide in the horizontal direction,
separated by 10 to 40 cm long fracture segments dominated by weight #7 sand. In
some cases the lenses of #5 sand are separated by fracture segments occupied
exclusively by #7 sand, particularly in the north wall of Trench I (Figure 7.19).
These observations suggest that the proppant in fracture EL4F2 propagated along a
lobate front.
Coalescence of Fractures
Fractures created at equal depths in neighboring boreholes are prone to
merging. The topmost (first) fractures created at boreholes EL6 and EL7 - EL6F1
199
-------
TABLE 7.2: FRACTURE THICKNESS
Fracture
EL1F1
EL1F2
EL2F1
EL2F2
EL3F1
EL3F2
EWF1
EWF2
EMF3
EL4F4
EL5F1
EL5F2
EL5F3
EL5F4
EL5F5
EL6F1
EL6F2
EL6F3
EL7F1
EL7F2
GE1F1
GE1F2
GE2F1
GE2F2
GE3F1
Fracture
Thickness
(mm)
11.0
4.0
5.0
2.0
8.0
11.0
8.0
17.0
17.0
16.0
11.0
12,0
10.0
7.0
-~— .
14.0
13.0
13.0
20.0
10.0
— — .
— ..
— —
Max Thick.
Distance
(m)
5.0
1.5
3.5
0.5
3.5
2.5
1.0
2.5
2.5
1.5
2.0
2.0
1.5
0.5
......
2.0
2.0
2.5
2.5
U
Borehole
Uplift
(mm)
9.0
3.0
3.0
5.0
4.0
13.0
15.5
11.5
25.0
20.5
17.0
7.5
9:0
......
23.1
_. —
11.3
99.5
Ave
Notch
Radius
(cm)
15.2
14.0
10.2
10.2
11.4
17.8
17.8
17.8
11.4
15.2
15.2
19.1
25.4
20.3
19.1
12.7
19.1
15.2
17.8
8.9
Max
Notch
Radius
(cm)
17.8
14.0
12.7
11.4
12.7
22.9
203
27.9
12.7
19.1
15.2
20.3
38.1
26.7
22.9
15.2
38.1
17.8
40.6
10.2
— ..
200
-------
and EL7F1 (Figure 7.2) - may merge laterally to form a large, single fracture. The
two boreholes are spaced 4.5 m apart. Similarly, the topmost fractures at boreholes
ELI, EL2 and ELS - EL1F1, EL2F1 and EL3F1 - merge to form a 12 m long,
continuous fracture (Figure 73). There is a continuous fracture at the topmost (Fl)
horizon between boreholes ELI and EL2, which are only 3.25 m apart, but there is a
3 m gap between the tips of fractures EL1F1 and EL3F1 along the cross section
connecting the two boreholes, which are 6.25 m apart (Figure 7.3). The two
fractures, EL1F1 and EL3F1, merge at an unknown distance north of boreholes
ELI and EL3, indicated by the fact that they vent along the same horizon. The
topmost fractures at boreholes EL4 and ELS, spaced 4.25 m apart, also merge,
forming a single fracture (Figure 7.4). The fracture is 10 m long, with major axis
parallel to the line connecting the boreholes, and with an approximate area of 47
m2. (Figure 7.4).
The topmost fractures (Fl) were created at approximately the same depth (1
m) at all seven boreholes. The greatest distance between two boreholes with a
continuous fracture at the Fl horizon, along the cross section connecting the
boreholes, is 4.5 m (EL4F1 and EL5F1 in Figure 7.4). The smallest distance
between two boreholes (ELI and ELS) with a unfractured gap between the two Fl
fractures, along the cross section connecting the boreholes, is 6.25 m. Those two
fractures apparently merged north of the boreholes (EL1F1 and EL3F1 in Figure
7.3) because fluid vented during the formationof EL3F1 at the same location as
EL1F1. The smallest distance between two boreholes (ELS and EL7) with no
apparent merging of the Fl fractures is 6.5 m. This suggests that, for injection of the
volumes of gel and sand injected into till at the ELDA site, about 6 meters is the
maximum distance allowable between boreholes if connectivity of fractures at the
same horizon is desirable.
Only two cases of a fracture coalescing with an overlying fracture are
documented by the trench sections. The first is in the east wall of Trench C (Figure
7.13), where perlite-filled fracture EL7F2, created 30 cm below sand-filled fracture
EL7F1, merges with the overlying fracture at a distance of 2 m north of the
borehole. The relatively rapid rise of the perlite-filled fracture probably occurred
because the density of the perlite slurry was less than that of the sand slurries. The
only example of a rapidly rising, sand-filled fracture merging with an overlying
fracture occurs in the east wall of Trench G (Figure 7.17), where fracture EL4F3,
created 30 cm below fracture EL4F2, merges with the overlying fracture at a
distance of 2.5 m north of the borehole. The concentration of sand in EL4F3 is
similar to other, more flat-lying fractures (Table 7.3).
Coalescence of several other pairs of fractures, stacked closely together at
the borehole, is inferred from indirect evidence. The fracture EL2F2 was observed
to vent from the same horizon as the vent of EL2F1, which was 15 cm above EL2F2
at the borehole. It seems likely that EL2F2 coalesced at some point with EL2F1,
even though they appear to be separated in all trench exposures. The same
evidence indicates that EL3F2 merged with EL3F1.
In all those cases, the fractures coalesced several m away from the borehole.
Two fractures, EL5F3 and EL5F4, merged very close (<20 cm) to the borehole and
the two were indistinguishable except in the vicinity of the borehole. The fracture
EL5F4 was created 7 cm below EL5F3, the closest spacing we attempted. The
201
-------
TABLE 7.3: PROPPANT CONCENTRATION
Fracture
EL1F1
EL1F2
EL2F1
EL2F2
EL3F1
EL3F2
EL4F1
EL4F2
EIAF3
EL4F4
EL5F1
EL5F2
EL5F3
EL5F4
EL5F5
EL6F1
EL6F2
EL6F3
EL7F1
EL7F2
GE1F1
GE1F2
GE2F1
GE2F2
GE3F1
Sand
Size
#7
#7
#7
#7
#7
#7
#7
#5
#7
#7
#7
#7
#7
#5
#7
#7
#7
#7
#7
PERLTTE
#7
#7
#7
#7
#7
Total
Sand
(#)
300
200
200
500
200
200
200
100
300
250
300
300
400
300
300
600
600
600
1200
50
1200
1200
200
1100
3500
Total
Gel
(gal)
150
50
130
100
100
40
50
50
50
50
45
45
95
45
45
80
65
50
130
25
175
190
40
155
500
Injected
Cone
(#/gal)
2.0
4.0
1.5
5.0
2.0
5.0
4.0
2.0
6.0
5.0
6.7
6.7
4.2
6.7
6.7
7.5
9.2
12.0
9.2
2.0
6.9
6.3
5.0
7.1
7.0
202
-------
TABLE 7.4: FLOW PARAMETERS
Fracture
EL1F1
EL1F2
EL2F1
EL2F2
EL3F1
EL3F2
EL4F1
EL4F2
EL4F3
EL4F4
EL5F1
EL5F2
EL5F3
EL5F4
EL5F5
EL6F1
EL6F2
EL6F3
EL7F1
EL7F2
GE1F1
GE1F2
GE2F1
GE2F2
GE3F1
Pad
Size
(gal) (
5 H20
5 H20
5 H20
5 H20
5 H20
5 H20
15 H20
5 H20
5 H20
5 H20
15 H20
5 H20
5 H20
5 K20
5 H20
5 H20 10 GEL
5 H20 10 GEL
5 H20 10 GEL
5 H20 10 GEL
5 H20
5 H20 10 GEL
5 H20 10 GEL
5 H20 5 GEL
5 H20 10 GEL
5 H20 10 GEL
Flow
Rate
gal/min]
5
5
10
10
15
15
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
4
4
5
Peak
Pressure
I (psi)
28
21
49
29
40
13
36
31
11
26
32
27
18
7
24
35
46
44
26
38
85
29
115
85
Stress
Intensity
kPaCcnr5)
698
450
1090
582
920
«•_«•
1082
885
197
526
865
698
441
72
662
824
1355
1209
852
_____
_____
568
_____
_____
203
-------
trench cross section (Figure 7.18) does not show this coalescence, because of the
scale of the cross section.
We conclude that, for the conditions of the ELD A site, vertical fracture
spacings of 30 cm will typically result in distinct fractures. Vertical spacings of IS
cm will result in fractures that merge locally but remain distinct elsewhere, whereas
vertical spacings of 7 cm will result in fractures that rapidly merge. Spacings
between 15 and 30 cm probably would be a reasonable lower limit.
Surface Texture of Fractures
Cross sections of the fractures (Figures 7.12-7.19) exhibit few undulations or
other signs of roughness along the fractures. Borehole EL6 (Figure 7.12) contains
good examples of both a typical, smooth fracture - EL6F2 - and an exceptionally
rough, undulose fracture - EL6F3. There is no significant difference between the
injected sand concentration of the two fractures, so the difference in surface texture,
as expressed in the fracture traces, is assumed to be due to inhomogeneities of the
soil profile.
DIMENSIONS OF THE HYDRAULIC FRACTURES
Surface areas of the fractures created at the ELDA site, estimated from
fracture outlines shown in Figures 72-7A, range from less than one square meter to
over sixty square meters (Table 7.1). Data shown in Tables 7.1 and 73 reveal no
statistically significant correlations between surface areas of fractures on one hand,
and injected proppant volumes or injected sand concentrations on the other hand.
Comparison of the relationship between total injected volume of gel and
PVI m m mm « * J» f >rw^ IV W m\. f 1 * ..1 1 * • 1
cture surface an
o 750 kg of sand
,, i by 0.14 square i
proppant. For lower sand concentrations 400 to 500 kg/nr (4.0^5.0 Ibs/gal), tie
data indicate a decrease of area by 0.07 square meters per additional 0.004 rrr (gal).
These data suggest that factors other than proppant volume influence the surface
area of hydraulic fractures. A fracture tip screen-out could inhibit propagation,
thereby limiting their surface area.
Comparison of the relationship between the concentration of sand in the
injected proppant, measured as pounds of sand per gallon of gel (Table 73), versus
fracture surface area (Table 7.1), for fractures within narrow ranges of total volume
of injected proppant, indicates an increase of area by two to seven square meters
per additional pound of sand per gallon of gel. Assuming that sanding-out at
fracture tips influences fracture surface area, as suggested above, these data indicate
that the likelihood of early "sand-out," and, consequently, of small surface area, is
not directly related to the sand concentration, as intuition might suggest. Clearly,
more work is needed toward an understanding of hydraulic fracture propagation.
204
-------
THICKNESS PROFILES OF THE HYDRAULIC FRACTURES
Trenches B through H provide an excellent opportunity to measure the
thickness of proppant sand along the major axes of fractures (Figures 7.20-7.26).
Although thickness commonly varies by two to five mm over distances of 20 cm or
less, third order regression yields asymmetric curves with maximum thickness close
to the center of the fracture, and hence, northeast of the borehole. Thirteen
fractures (72%) are skewed away from the borehole, so that the midpoint along the
fracture trace is located between the point of maximum thickness and the borehole.
Four fractures (22%) are skewed toward the borehole, so that the point of
maximum thickness is located between the fracture midpoint and the borehole
(EL2F2, EL3F2, EL4F4 and EL6F2). Only one fracture (EL4F1) exhibited a
symmetrical thickness profile, in which the distance between the fracture midpoint
and the point of maximum thickness is less than 10% of the distance between the
fracture midpoint and the edge of the fracture.
DIRECTION OF PROPAGATION
Most of the fractures propagated preferentially in the downslope direction,
as shown in Figures 7.5-7.11. Maps of fracture outlines (Figures 7.2-7.4), as well as
measurements of major axis lengths and maximum distances from boreholes (Table
7.1), indicate that the distance from the borehole to the downslope edge of a
fracture may be as much as seven times longer than the distance from the borehole
to the upslope end of the fracture. Clearly, the additional overburden pressure on
the upslope side prevented fracture propagation under the steep bank bounding the
southwest edge of the bench (Figures 7.1,7.5-7.11).
Contours of the uplift of ground surface during fracturing, discussed in the
next section, indicate slightly different orientations of major and minor semi-axes of
the elliptical fracture outlines defined by uplift contours than the orientations
indicated by trench cross sections. In both cases, though, the direction of
propagation is clearly downhill.
DISCUSSION
In some respects, hydraulic fractures created during the 1989 tests are
remarkably similar to the ones created during 1988; in plan, both are elongate with
aspect ratios of 2:3, and they are highly asymmetric with respect to their parent
boreholes. In other respects, fractures created during the two years are much
different. Those created during 1989 are nearly flat-lying, and none climbed to the
ground surface to vent. Where they did vent, the fractures grew horizontally until
they intersected a downwardly sloping ground surface, much like HF13 from the
1988 tests.
The fractures created in 1989 were slightly smaller in area than those of the
previous year; however, the sizes of the all the 1988 fractures were limited by
venting, whereas most of the 1989 fractures did not vent and they could have been
larger if more fluid was pumped into them. Sand filled all the fractures created in
1989, whereas it only filled a few during the 1988 tests. The average thickness of
205
-------
TRENCH B
-3-2-101234567
^ ^
6
6
OT
VI
QJ
15
10
O
H 5
F2
EL 6
O -3-2-101234667
-------
TRENCH C
r -»
6
6
CO
w
0)
C
^}
o
-3 -2 -
0)
cd
30
25
20
15
10
5
0
EL7
Trench t
-3 -2 -1
Fracture Length (m)
Figure 751. Graph of fracture thickness (mm) as a function of the distance away
from the borehole (m), for fractures EL7F1 (top), and EL7F2
(bottom). Thicknesses were measured along east and west walls of
trench C
207
-------
r- ->
6
g
W
OT
CD
fi
TRENCH D
456
O
(D
O
12
10
8
6
4
2
F2
EL3i
Fracture Length (m)
Figure 7.22. Graph of fracture thickness (mm) as a function of the distance away
from the borehole (m), for fractures EL3F1 (top), and EL3F2
(bottom). Thicknesses were measured along east and west walls of
trench D.
208
-------
TRENCH E
01
If}
CD
PI
X
O
-2-1012345678
O
(0
8
Fracture Length (m)
Figure 723. Graph of fracture thickness (mm) as a function of the distance away
from the borehole (m), for fractures EL1F1 (top), and EL1F2
(bottom). Thicknesses were measured along east and west walls of
trench E.
209
-------
r -^
6
a
W
w
Q)
CJ
44
O
£-•
0)
JH
3
-*J
o
CO
JH
6
6
TRENCH F
Fl
EL 2
Trench
A
-2 -1
Fracture Length (m)
Figure 7.24. Graph of fracture thickness (mm) as a function of the distance away
from the borehole (m), for fractures EL2F1 (top), and EL2F2
(bottom). Thicknesses were measured along east and west walls of
trench F.
210
-------
Fracture Length (m)
Figure 7.25. Graph of fracture thickness (mm) as a function of the distance away
from the borehole (m), for fractures EMF1, EL4F2, EL4F3 and
EL4F4. Thicknesses were measured along east and west walls of
trench G.
211
-------
TRENCH H
10
8
6
4
2
F3
ELS
Trench
A
-3 -2-10 1
Fracture Length (m)
Figure 726. Graph of fracture thickness (mm) as a function of the distance away
from the borehole (m), for fractures EL5F1 (top), EL5F2 (middle)
and EL5F3 (bottom). Thicknesses were measured along east and
west walls of trench H.
212
-------
sand in the 1989 fractures (11 mm) exceeded the maximum thickness (9 mm) from
the previous year.
Hydraulic fractures created during the 1989 test increased the steady-state
rate of inflow into boreholes in unsaturated ground (data are in Section 1) by factors
between 3.1 and 9.0. That amount of increase in flow rate could significantly
improve the rate of remediation of a contaminated site. There are certainly aspects
of the technology that can be improved - most of which we are currently pursuing -
but the technology used during the 1989 tests appears to be capable of providing
important improvements in remediation. We conclude that the technique of
hydraulic fracturing is ready to be tested during remediation.
213
-------
SECTION EIGHT
MONITORING HYDRAULIC FRACTURES
Monitoring the geometry of hydraulic fractures created to improve
remediation should be done for two purposes. On one hand, the performance of a
fracture in delivery or recovery is sensitive to its geometry, so monitoring will yield
information that will improve the design of delivery or recovery systems. On the
other hand, some sites will require that hydraulic fractures do not interfere with
features, such as sewers, foundations, or electric cables, so monitoring will yield
information that could suppress the growth of errant fractures.
A wide range of methods is available to predict and monitor the geometry of
hydraulic fractures. The majority of them were developed within the petroleum
industry and they are typically used where hydraulic fractures cut rock at depths of
hundreds or thousands of meters; the conditions typical of oil wells. To our
knowledge, none of those methods has been evaluated where hydraulic fractures cut
soils at depths of a few to several tens of meters; the conditions typical of many
remedial applications.
During field tests described in previous chapters we examined four
techniques of monitoring processes related to hydraulic fracturing. Those
techniques include measuring 1) the pressure of fracturing fluid; 2) tilting of the
ground surface over a fracture; 3) uplift of the ground surface; 4) electrical
resistivity of ground containing a hydraulic fracture. The objectives of our study
were to examine the level of effort required to implement and reduce data from
each technique, and to evaluate the potential that it could have in future
applications.
INJECTION PRESSURE
The pressure of fracturing fluid varies with time during creation of a
hydraulic fracture, and the pressure record is a basic tool of monitoring. The form
of the pressure record can be used to infer when propagation starts, as well as
various aspects of fracture geometry. Problems such as plugging of the fracture with
sand result in large pressure surges that are readily identified on the pressure
record.
Method
Injection pressure was recorded during a few of the tests in 1988 and all of
the tests in 1989. Pressure was measured at the ground surface using a Druck
transducer interfaced with a data acquisition system and lap-top computer.
Measurements were taken every second and both written to a disk file and displayed
as a plot on the video screen. The pressure records for the tests are shown in Figure
8.1.
Results
Most of the records obtained during the 1989 tests are similar in general
form, and consist of the following four basic periods:
214
-------
EL1F1
30.0
24.0
n MA
OJ
en
in
-------
EL2F1
60.0
to.o
»
t-l
n
n
ZS.O
OH
10.0
HA
~ ( 1 I
•
-1 1 1
-
-
•fk
•3
I ^
-Ar-^_ M -
aj-1*!" 1 i i i 1 i i A'H i i 1 i t i 1 i r i 1 i L
0.0 2.0 4JO tJ> B.O 10.0 12.0 l*.0
time (min)
EL2F2
M-O
n
in
v
P4 ""t
| i—i i j T—I r-j--!—r i 7
I "I
I q
i i i [ r i i I i i i
0-0 U 4J) IJ BJ) 10J lifl
time (min)
Figure 8.1, continued. Pressure records from fracturing tests during 1989.
216
-------
EL3F1
I
V
e.o (.0 10.0
time (min)
12.0 14.0
EL3F2
time (min)
Figure 8.1, continued. Pressure records from fracturing tests during 1989.
217
-------
EL4F1
0)
«- 200
w
0)
i i i t i 1*1 iiiiiiiiiiitiiiiiiiiiiii
z.o «.o
tio WLO
time (mln)
14.0 it.c
EL4F2
ra
O.
tQ
u
1E.D
tt i I i i i 1
to u>
fill L
I , 1 , I , 1 , t
•J U 1OO
time (min)
Figure 8.1, continued. Pressure records from fracturing tests during 1989.
218
-------
EL4F3
1ZJ>
10.0 16.0
time (min)
EL4F4
25.0 -
0.0 to 4.0 e.o
10.0 12.0 14.C
time (min)
Figure 8.1, continued. Pressure records from fracturing tests during 1989.
219
-------
EL5F1
88.0
n
a,
v
u
n.
I . I I I 1
0.0
B.O
10.0
time (min)
EL5F2
time (min)
Figure 8.1, continued. Pressure records from fracturing tests during 1989.
220
-------
EL5F3
tO 2.0
time (min)
EL5F4
10 U 100 liO
time (min)
Figure 8.1, continued. Pressure records from fracturing tests during 1989.
221
-------
EL6F1
110.0
ra TO.O
en
n
0)
1(IiII
' • ' i
m.lt i r i I i t i
u
wl r i i i
4.0
fl.0
time (min)
EL6F1A
28.0
ICLO U.O
time (min)
taj)
2flJ
Figure 8.1, continued. Pressure records from fracturing tests during 1989.
222
-------
EL6F2
n
a
3 no -
w
0)
S.D
10.0 18.0 200
time (tnin)
29.0
EL6F3
IB.O
time (min)
80.C
23.0
Figure 8.1, continued. Pressure records from fracturing tests during 1989.
223
-------
EL7F1
. i i i i ; i i i i
to
CO 30.0
J-!
P,
0.0
0.0
f -I
1 • ••-•'- I • • • • I ' '
20.0 30.0
time (min)
EL7F2
ZBJJ
en
CO
a
«•
i i i 1 i i
fit
o-
l
I i i i t i i i I .1 i i I i i i t t i i.
2J 10 14 U 1IU 124
time (min)
Figure 8.1, continued. Pressure records from fracturing tests during 1989.
224
-------
GE1F1
90.0
20.0
3
CO
g 10.0
O.
-
a-
«
: rt-
-10.D
0.0
?;
ir
\
J? *{,'
,5 s (*2 «'
l°-° ZO.O 30.0 «0.0 SO.O
time (min)
GE1F2A
3
CO
(0
V
L,
time (rain)
Figure 8.1, continued. Pressure records from fracturing tests during 1989.
225
-------
GE1F2B
ISOJ
g ""
-------
GE2F1
300 -
0.0 2.0 4.0 6.0 8.0 10.0 12.0 110 16.0 18.0
GE2F2
120.0
OJ
t-l
3
m
m
0)
OLD 10J) Z04> SOU) 4041 60.0
Figure 8.1, continued. Pressure records from fracturing tests during 1989.
227
-------
Period I: Pressure increases rapidly for several seconds and reaches a peak
between 70 and 275 kPa (10 and 40 psi)1.
Period II: Pressure decreases over one to several minutes and reaches a
minimum between 20 and 70 kPa (3 and 10 psi).
Period HI: Pressure increases to between 35 and 70 kPa (5 and 10 psi), and then
decreases gradually. This is the longest of the periods and lasts from
several minutes to more than an hour, depending on the volume of fluid
pumped into the ground.
Period IV: Pressure decreases abruptly and is followed by a gradual flattening
of the slope.
The fracturing periods are associated with various events during the
fracturing procedure. Typically, a change in flow rate causes an instantaneous
change in pressure, whereas a change in fluid properties results in a change in
pressure roughly 30 seconds later. This lag is the same length of time it took fluid to
traverse the injection hose and reach the transducer.
Inflation of the pumping system prior to fracturing occurs during Period I.
We infer that the abrupt decrease in pressure marking the beginning of Period n
marks the onset of fracture propagation. The increase in pressure marking the
beginning of Period III typically occurs roughly 30 seconds after we began to pump
gefand sand, and it is due to the increase in viscosity of that fluid compared with
fluid that was injected initially. As the fracture increases in size, we expect a gentle
decrease in pressure and this behavior is seen during Period III of most tests.
Pressure fluctuations within Period III are typically associated with changing from
one batch of gel to another. Increasing the sand concentration, for example, is
commonly followed by an increase in pressure within Period in (e.g. EL6F3). Other
fluctuations in pressure during Period HI are associated with minor adjustments in
pumping rate. The decrease in pressure during the beginning of Period IV is
associated with a reduction in fluid viscosity when we'changed from pumping sand-
laden gel to water at the end of a test. A sharp drop in pressure, marked by a nearly
vertical slope on the record, corresponds to the time when the pump stopped.
Pressures were not recorded after the pump was turned off, so we are unable to
evaluate the methods of Nolte and Smith (1981), who use the record of pressure
after shut-in to determine leakoff parameters.
The pressure record can be used to diagnose problems associated with the
fracturing equipment When the fracture is growing during Period HI, a major
increase in pressure (EL6F1, GE1F2A, GE1F2B) typically indicated a blockage
downstream of the transducer, whereas a major decrease (e.g. EL54F4) indicates an
upstream blockage. Downstream blockages were caused when plugs of sand formed
at the entrance to the fracture. This problem is caused either by excessive early
leakoff, or by an early concentration of sand that was too great. Therefore, when
the pressure record indicated a downstream blockage, we recut the starter notch,
increased the volume and viscosity of the pad, decreased the initial sand
1 Cited pressures are for tests at the ELDA site. Pressures at the Goettle site were
typically greater, as seen on the records.
228
-------
concentration and tried again to create the fracture. This strategy was successful.
Unexpected pressure drops indicating upstream blockages were caused, at least
during our tests, by clogging of the pump usually because of inadequate crosslinking.
Venting of the fracture to the ground surface occurred during the creation of
five fractures (EL1F1, EL2F1, EL2F2, EL3F1, EL3F2), and in most cases venting
has negligible effect on the form of the pressure record. One explanation is that the
pressure of the injection fluid at the tip of the fracture is essentially zero, so that
pressure at the tip would be unaffected by venting. All of those fractures, except
EL1F1, merged with another earlier fracture, but we were unable to identify a
feature of the records that indicates merging.
The form of the pressure record, after removing fluctuations due to changes
in fluid properties or pumping rate, is related to the geometry of the fracture and
rate of leakoff. Methods are currently available for inferring the geometry of
vertical fractures from the forms of records during Period III (Nolle and Smith, 1981
and 1987). Some of those methods are applicable to shallow, flat-lying, asymmetric
fractures such as the ones we created, but most of the methods of interpretation
have been developed for oil-field applications where fractures are vertical.
Leakoff characteristics can be determined from pressure records made
during pumping and after the pump has been shut off (Nolle, 1979; Nolte and
Smith, 1987). Records made during this work were terminated too early to make
reliable measurements of leakoff characteristics, however. Future work should
focus on obtaining the leakoff characteristics, and using that information to
anticipate tip screen-out (Smith and others, 1987; Nolte, 1984).
SURFACE TILT
The ground surface overlying a hydraulic fracture is deformed as the fracture
inflates. Characteristics of the fracture can be inferred by measuring the
deformation and then using various theoretical analyses. In this study, deformation
was determined either by measuring changes in slope of the ground surface with
tiltmeters, or by measuring changes in altitude with a leveling device. The work
with tiltmeters was conducted during the 1988 tests and is described in the following
section.
Method
Surface tilt was measured as a function of time using Model 722 tiltmeters
rented from Applied Geomechanics Inc., Santa Cruz, California. That model is
cylindrical in shape and designed to be placed below the ground surface in a boring.
It is accurate to within 0.1 microradian.
229
-------
The tiltmeters were installed slightly below the ground surface in vertical
boreholes. Sand was placed around the tiltmeters and the orientation of their major
axis was adjusted to vertical. Signals from the tiltmeters were conditioned using
electronic equipment rented from Applied Geomechanics Inc. and then recorded on
our data acquisition system.
A total of eight tiltmeters were installed around the cluster of boreholes 4,5,
6, and 7 (Fig. 8.2). Three of those boreholes are at the vertices of an equilateral
triangle, and the other is at the center of the triangle. Six of the tiltmeters were
arranged in a hexagonal pattern around the three boreholes, and the other two
tiltmeters were near the central borehole (Fig. 8.2). The arrangement placed three
tiltmeters at roughly equal distances from each borehole, and placed the others at
greater distances. A single layout of tiltmeters was necessary because installation
required several hours and we were unable to move them on the day of the 1988
test. One of the tiltmeters, tiltmeter F, yielded erratic data and was omitted from
the interpretations.
Results
Creating hydraulic fractures caused tilts of as much as 2000 microradians
(Appendix A), a strong signal for the instruments we used. Tilt signals varied widely
as functions of time and location (Fig. 8.3), and a meaningful interpretation of this
information is only possible after data reduction. Qualitative information about the
location and orientation of the fracture can be obtained by plotting tilts as vectors in
plan view. Suchplots can be created in real time and interpreted as the fracture is
being created. This procedure was not attempted during field tests.
Tilt data can also be used to obtain quantitative estimates of fracture
geometry. This procedure involves inverting the tilt measurements using a
mathematical solution for surface displacement over a fracture at depth. The
solution used in this work assumes that the fracture is planar and shaped like a
rectangle. A total of eight parameters, which specify tne size, location, aspect ratio,
and aperture of the fracture, are obtained from a nonlinear inversion of that
solution (Davis, 1983). Engineers at Applied Geomechanics Inc. developed the
inversion technique, and analyzed the data from the tiltmeters. They estimated the
geometry of each fracture at several times during its creation, and their results are
compared with maps of the fractures in Figures 8.4 through 8.6.
Each of Figures 8.4 through 8.6 consists of a series of two or three contour
maps illustrating the change of fracture geometry during the fracturing process.
Figure 8.4 shows three stages in the development of fracture HF5 (created from
borehole #5); Figure 8.5 shows three stages in the development of fracture HF6
(borehole #6); and Figure 8.6 shows two stages in the development of fracture HF7
(borehole #7).
Table 8.1 compares orientations (strikes and dips) of fractures determined
from tiltmeter data to those determined from excavation of the fractures. Following
the convention used by Applied Geomechanics Inc., the subcontractor responsible
for tiltmeter data, the direction of fracture dip represents a clockwise, 90° rotation
from the azimuth of the fracture strike. Coordinates of the center of the fracture
relative to the borehole, calculated from tiltmeter data, along with fracture aperture
230
-------
CD
B
©
#6
l.69m
G
CD
#4©
3.84m
©
H
Borehole
1. 83m
0 1
meter
F Tlltmeter
©« -- '
C
©
#5
1.04m
©
E
©
Boreholes and Tlltmeters, ELDA Landfill
Figure 8.2. TDtmeter array from 1988 tests.
231
-------
788. .-r
"79B-.B
-1988
.8BB
(*to>
xE a
Figure 8.3. Tilt as a function of time.
232
-------
2298 -T"•XC--B
1698 -••
189B
40B.
-2BB.
-888.
-14BB
xE 0
693. -r
-BBB.
.aaa
SB.B188.13B.20B.
Tin* <«to)
Figure 8.3, continued. Tilt as a function of time.
233
-------
(thickness), are also given in Table 8.1. Coordinates are measured in ft, with the
positive* direction pointing eastward, and the positivey direction pointing
northward. Fracture aperture is measured in inches.
TABLE: 8.1. ACTUAL AND PREDICTED ORIENTATIONS OF FRACTURES
Era Actual Strike Tilt-meter Actual Dip Tilt-meter
Strike Dip
HF5a 80 98 22 8
HF5b 84 143 26 37
HF5c 40 359 17 37
HF6a 359 332 9 11
HF6b 359 334 9 23
HF6c 349 4 14 29
HF7a 228 242 27 1
HFTb 228 213 27 27
Borehole 5
Inversion of data from borehole 5 indicates that a very thin (0.03 cm; 0.01 in),
nearly horizontal fracture, striking 98° and dipping 8° SW, formed 1 minute after
fracturing commenced (Figure 8.4a). The "tiltmeter strike" is fairly close to the
strike based on excavation (80°), although the "tiltmeter dip" is considerably
shallower than the "excavation dip" (23°). One minute later (Figure 8.4b), tiltmeter
data indicate a somewhat thicker fracture (0.03 cm; 0.01 in), with strike rotated
clockwise to 143°, and dip increased to 37° SW. Although the tiltmeter strike at this
stage is less consistent with the excavated strike than it was a minute earlier (Figure
8.4a), the tiltmeter dip is closer to the excavated dip. Tiltmeter data shown in
Figures 8.4a and 8.4b suggest that the smaller, eastern lobe of the fracture formed
during the first two minutes of fracturing. Tiltmeter data for the final phase of
fracturing (Figure 8.4c), 3 minutes and 20 seconds after fracturing commenced,
indicate Formation of a fracture twice as thick (0.61 cm; 0.24 in) as a minute earlier,
striking 359° and dipping 37° NE. Fracture propagation during this phase occurred
several ft west of the borehole. The location and orientation of the fracture based
on tiltmeter data strongly suggests that the larger, western lobe of the fracture (as
mapped from excavation) formed late during the fracturing process (after 3
minutes).
234
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HF5
a
0 1 Z
meters
HF5
Z.O'O.E
0 1 Z
met era
HF5
0 1 Z
Betera
Figure 8.4. Hydraulic fracture HF5 and interpretation of surface tilts at three
times during the test.
235
-------
The fracture inferred from early tiltmeter data at borehole 5 is inconsistent
with excavation data, but the later two fractures are consistent with field
observations. The second frame in the interpretation indicates that the eastern lobe
of HF5 formed first and was followed by growth of the western lobe. Apparently,
propagation of the eastern lobe was arrested before it could vent. Continued
injection resulted in growth of the western lobe, which vented in two locations west
and northwest of the borehole. The tiltmeter inversion underestimates the area of
the fracture, but overestimates its dip, based on excavation of the fractures.
Borehole 6
Comparison of tiltmeter inversion data with the fracture map based on
excavation around borehole 6, shown in Figure 8.5, indicates that comparatively
steeper-dipping (23°) but still NW-striking (334°) portions of the fracture formed up
to 2 m away from the borehole, as late as 7 minutes and 40 seconds after fracturing
commenced (Figure 8.5b). Finally, distal portions of the fracture, dipping as much
as 29° SE and striking NNE (4°), formed over 8 minutes after fracturing
commenced.
Tiltmeter and excavation data for fracture HF6 clearly illustrate the ability to
trace the dynamic development of a fracture using tiltmeter inversion data.
Borehole 7
Development of a relatively small fracture is documented in Figure 8.6,
showing tiltmeter inversion data and excavation data for fracture HF7,2 minutes
(Figure 8.6a) and 3 minutes (Figure 8.6b) after commencement of fracturing.
Comparison of the first frame (Figure 8.6a) with other frames representing 2
minutes after commencement of fracturing (Figures 8.4b and 8.5a) reveals
comparatively low fracture dip (1° NW). Tiltmeter-generated strike and dip of the
fracture 3 minutes after commencement, shown in Figure 8.6b, is in fairly good
agreement with excavation data (Table 8.1).
Discussion
Propagation direction and strike are predicted within roughly 45° and dip is
generally within 15°-mostly dip is overestimated. Sizes of fractures are generally
underestimated, except in the case of HF7 where it is markedly overestimated. The
general locations of the fractures is predicted with reasonable accuracy, however.
The results of the inversions of tiltmeter data are remarkably consistent with
field mapping, considering that the inversion scheme must reconcile the tilt field
resulting from a fracture whose geometry is much more complex than the simple
rectangular model it uses. The inversions of tilt data taken during the 1989 tests,
where the fracture forms were quite simple, certainly would have yielded more
accurate results. Moreover, some of the error in the tilt data results from
236
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HF6
a.
HF6
b.
0 1 t
•at era
HF6
•0.6
0 1 £
metera
Figure 8.5. Hydraulic fracture HF6 and interpretation of surface tilts at three
times during the test.
-------
oo
HF7
a.
0 t Z
meters
X
HF7
0 1 Z
meters
Figure 8.6. Hydraulic fracture HF7 and interpretation of surface tilts at three
times during the test.
-------
placement of the tiltmeters. For example, the inversion of data from HF7
overestimates the extent of the southern boundary of the fracture, but there are no
tilt data from the southern side so the inversion must resort to extrapolation.
Inversion of tiltmeter data should provide estimates of location during
propagation. Application of this technique to real-time monitoring — inversion in
the field during fracturing - should provide a safeguard against the growth of errant
fractures, and it may allow for small adjustments in the fracturing process to
optimize fracture performance.
SURFACE UPLIFT
Design
Standard surveying techniques were employed to measure surface uplift
incurred during fracturing. Elevations of points distributed radially around each
borehole were measured before and after individual fracturing episodes. Values of
the difference between elevations before and after fracturing, measured in mm at
each surveying point, are contoured for several fractures in Figures 8.7 • 8.10.
Superimposed on the uplift contours are contours representing the thickness
of the fracture associated with the measured uplift. Thicknesses of fractures were
measured directly on trench walls exposing traces of the fractures.
Uplift contours shown in Figures 8.7 and 8.10 represent total uplift incurred
during the creation of a chronological series of fractures. Accordingly, the
superimposed thickness contours indicate the combined thickness of all fractures
involved in the uplift.
Results
Surface uplift and fracture thickness contours combined for fractures EL6F2
and EL6F3 are shown in Figure 8.7. Contours for fractures EL7F1 and EL7F2 are
shown in Figures 8.8 and 8.9, respectively. Combined contours for fractures EL5F1
through EL5F4 are shown in Figure 8.10. Fracture thickness contours are bold, and
surface uplift contours are medium weight in the figures.
Several characteristic features were used to compare the uplift and thickness
contours for each fracture or group of fractures. These include the strike of the
major axis of the ellipse roughly defined by the contours; the ratio of major to minor
axis (aspect ratio); the maximum values of uplift and thickness; the distances from
the borehole to the points of maximum value (the tops of the domes defined by the
contour sets); and the distances from the points of maximum value to the points of
zero uplift or thickness, measured along the major axes.
239
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EL6FE-F3
•- C \
B -.
Uplift Contour
Thickness Contour
Trench Out 11ne
— — Uplift Grid
Figure 8.7. Thickness and uplift contours, combined for fractures EL6F2 and
EL6F3.
-------
EL7F1
C \
Uplift Contour
Thickness Contour
Trench Outline
Uplift Grid
0 j
meter
EL6
Figure 8.8. Thickness and uplift contours for fracture EL7F1.
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Borehole 6
Total surface uplift and total fracture thickness associated with fracturing
episodes EL6F2 and EL6F3 are shown in Figure 8.7. Both contour sets are roughly
elliptical in shape, with aspect ratios of about 1.5 to 1.6. The major axis of uplift
contours generally trends to the northwest, whereas that of thickness contours
trends roughly to the north. The distance between the maximum and zero values
along the major axes is about 5 to 5.5 m in both contour sets. The distances between
the borehole and the points of maximum value are 3.5 m for the uplift contours, and
2.5 m for the thickness contours. Maximum uplift is 20 mm and maximum thickness
is 14 mm, indicating 30% deflation.
It appears that the general shape and size of the contour domes defined by
uplift and thickness contours for fractures EL6F2 and EL6F3 are roughly
equivalent, whereas the major axis trends differ by about 45°. The major axis trend
for the thickness contours coincides more closely with the downslope direction than
that for the uplift contours. The downslope direction is approximately parallel to
the trends of trenches B and C.
A noteworthy feature of the surface deformation is the zone of subsidence
beyond the zone of uplift. Subsidence appears to have occurred along or beyond the
outer margins of the fractures, a result predicted by theoretical analyses (Pollard
and Holzhausen, 1979).
Borehole 7
Uplift and thickness contours are plotted separately for two fractures created
at borehole 7 - EL7F1 and EL7F2. Shapes and degrees of consistency between
uplift and thickness data are quite different for the two fractures.
Contours of fracture EL7F1, shown in Figure 8.8, are fairly circular, with
radial distances of approximately 3.5 meters between the maximum value (center of
the circle) to values of zero, in both the uplift and thickness contour sets. The
maximum uplift is 30 mm, and maximum thickness is about half of maximum uplift,
indicating 50% deflation. Distances from the borehole to points of maximum uplift
and thickness are 1.5 m and 2 m, respectively. Subsidence was observed on two of
the lines of data, but the other lines recorded only uplift (Fig. 8.8).
The two contour sets reflect good general agreement over the shape and
areal extent of fracture EL7F1. Doubling of surface uplift, measured immediately
after creation of the fracture, compared to fracture thickness reflects significant
settling, or deflation, of the fracture and its overburden following the creation of the
fracture.
The main difference between the contour sets lies in the orientations of the
elliptical, inner contours of both sets. Inner contours of uplift trend northeastward,
whereas those of thickness trend northward. These trends reflect bias due to the
distribution of data points, which is limited to two orthogonal axes for uplift, and the
trench walls for thickness.
242
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The surface deformation over EL7F2 (Figure 8.9) is unusual; there is a zone
of subsidence containing the borehole and the maximum uplift (5 mm) is located
about 5 m north of the borehole. The thickest part of EL7F2 is 5 m north of the
borehole, and that location is coincident with the point of maximum uplift. The
basin-like zone of subsidence, however, is difficult to explain. The fracture EL7F2
dips slightly 5° to the south, and Pollard and Holzhausen (1979) show that a dipping
fracture will produce an asymmetric deformation field. The sense of asymmetry
predicted theoretically, however, is opposite that which is observed; it predicts a
zone of subsidence centered north of the well. The zone of subsidence is difficult to
explain.
Differences in the trends of major axes of the two contour sets are that same
as those exhibited by contours of the overlying fracture (EL7F1). The differences
are due to the distribution of data points, which was dictated by trench location for
thickness contours, and by the surveying grid configuration for uplift contours. Time
constraints prevented the use of more surveying data points.
Borehole 5
The clearest correlation between uplift and thickness contours is exhibited by
the combined contours for fractures EL5F1, EL5F2, EL5F3, and EL5F4, shown in
Figure 8.10. Both contour sets are roughly circular, with maxima (center of circle)
at or near the borehole. Maximum uplift, located approximately 1 m east of the
borehole, is almost 30 mm, and maximum thickness, located at the borehole, is 20
mm, so thickness is 33% less than uplift. The average distance from the maximum
value to the zero contour is 4 m for uplift, and 3 m for thickness, so the area
enclosed by the zero uplift contour is 33% larger than the area enclosed by the zero
thickness contour.
The shapes of the uplift and thickness contour sets are similar. Both contour
sets exhibit a conspicuous, localized disturbance in the northeastern hemisphere,
about midway between the borehole and the periphery (zero contour). The
irregularity seems to reflect a discontinuity in one of the fractures. This is not
surprising, since the trace of fracture EL5F1, shown in Figure 7.18, is markedly
discontinuous.
The areal distributions of the two contour sets, however, are different, as
manifested by the distances from the borehole to the maxima, and by the areas
enclosed within the zero contours. Compared to the area underlain by fractures, the
area of surface uplift is 33% larger, and shifted approximately 2 m eastward, or
downslope (see Figure 7.1 for topography).
ELECTRICAL RESISTIVITY
Electrical resistivity is another method of sensing hydraulic fractures without
disturbing the subsurface. Adding an electrolyte to the fracturing fluid will result in
a highly conductive fracture that is embedded in poorly conductive till. Three
geophysical techniques of monitoring fracture location by sensing the conductivity
contrast were employed at the ELDA site during the 1988 fracturing test. These
243
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EL7FE
. C
. B
Uplift Contour
Thickness Contour
Trench Out 11ne
Uplift Grid
0 1
meter
EL6
Figure 8.9. Thickness and uplift contours for fracture EL7F2.
-------
EL5F1-F4
Uplift Contour
Thickness Contour
Trenoh Out line .
— Uplift Grid
0 1
I 1
meter
Figure 8.10. Thickness and uplift contours, combined for fractures EL5F1,
EL5F2, EL5F3 and EL5F4.
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were, the mise-a-la-masse, Wenner, and dipole-dipole methods. The mise-a-la-
masse method was the most successful, yielding encouraging results for static and
dynamic tests during the 1988 field test. It revealed fields of well-developed changes
in apparent resistivity following fracturing. In addition, mise-a-la-masse showed
abrupt changes in apparent resistivity as a function of time during a test, probably
indicating the fracture had reached a critical location with respect to the sensing
electrodes. The resistivity measurements were made in collaboration with Dr.
Donald Stierman, who is a specialist in applying geophysical techniques to waste
sites (Stierman, 1988). The following two sections are based on Stierman's findings.
Design
All resistivity measurements were made using a SoilTest R-60 resistivity
system and a digital ammeter. The R-60 transmitter consists of 6 batteries wired
such that output voltages can be varied between 45 and 840 volts in 6 dial-selected
steps. Porous pots containing saturated copper sulfate solution as electrolyte served
as electrodes. Distances were measured with a fiberglass surveyor's tape.
Slurry injected into the hydraulic fractures was spiked with about 3% KC1 to
ensure strong contrast between the electrical resistivities of the fluid and the
formation. Samples collected were tested in the laboratory and found to exhibit
electrical resistivities of about 0.3 ohm-meters at 25° C, consistent with a
concentration of between 20 and 30 ppb of total dissolved solids. The fluid was
about 120 to 400 times more conductive (less resistive) than the till in which the new
fractures were developed.
Electromagnetic ground conductivity measurements were also made using a
Geonics EM34-3XL in the horizontal dipole mode. Results were convened to
apparent resistivity so that they could be compared directly with DC resistivity
measurements.
The mise-a-la-masse method uses a conductive rock or soil body as one
current electrode, with a second current electrode set at some distance away. A
roving potential electrode maps the electrical field resulting from injecting current
into the rock or soil body. If the ground is homogeneous, the current electrode acts
as an electrical monopole at the center of a series of concentric circular
equipotential contours. This field is distorted in the presence of subsurface
conductors and the equipotentials tend to outline any buried conductive structures.
This technique has been applied to mapping leaks from waste disposal lagoons
(Stierman, 1988).
During the 1988 ELDA fracturing test, one current electrode was planted
over 200 m to the east, effectively at infinity over the 20-m diameter array.
Boreholes H4, H5, H6, or H7 served as the second current electrode. Potential was
measured with respect to a porous pot planted over 200 m to the west. Colinear
electrodes were planted along lines connecting boreholes. The total number of
electrodes is 18.
246
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Results
Following the creation of fracture H4, mise-a-la-masse measurements were
made for boreholes 4 and 6. Results were dramatic at borehole 4, shown in Figure
8.11, which is a contour map of apparent resistivity at borehole 4 after fracture H4.
Results were unimpressive at borehole 6 during creation of fracture H4. Post-
fracture measurements show resistivity decreased 10 to 15% for electrodes nearest
borehole 4, but increased slightly for borehole 6 (Figure 8.12). There is a strong
correlation between the resistivity decrease and distance from borehole 4, with an
elongation of this trend southeastward, toward borehole 5. This elongation suggests
that fracture H4 propagated preferentially toward the southeast. The generally
elliptical shape of the resistivity change contours suggests a largely horizontal
fracture.
Boreholes 5,6 and 7 were shallower than borehole 4, and the shallower
fractures created at these boreholes were expected to obscure deeper fractures.
Due to time constraints, results shown in Figure 8.13 represent the composite effect
of fractures H4 and H5. Again, there is a clear correlation between a decrease in
resistivity and the distance from borehole 5 for mise-a-la-masse using borehole 5 as
a current electrode. Resistivity on borehole 4 following fracture 5 (Figure 8.14)
shows a resistivity increase at most electrodes. The "bulls-eye" patterns of opposite
polarities suggests a horizontal fracture extending some 3 to 5 m in each direction
from the borehole.
Following the creation of fracture H7, mise-a-la-masse measurements on
borehple 4, contoured in Figure 8.15, show complex distortion of the electrical field.
Resistivity decreases at most electrodes with a maximum decrease of 13.5% on a
corner of the array opposite from the fractured borehole. Resistivity increases at
one of the electrodes nearest boreholes 4 and 7. This pattern suggests a single
vertical fracture extending from borehole 7 nearly to borehole 6.
Changes for mise-a-la-masse measurements on borehole 7 (Figure 8.16)
represent a composite of the effects of fractures H4, H5 and H7. The composite
result is a decrease in resistivity of about 10%, extending north and south
approximately 6 m (20 ft), with less distortion of the electrical field east or west.
This suggests the fracture from borehole 7 trends north-south rather than east-west.
The fracture vented into the shallow hole dug for one of the electrodes (E4). It is
interesting that the change in resistivity measured by this electrode, directly in the
new fracture, is less than that observed at other electrodes.
Following fracturing of borehole 6, mise-a-la-masse measurements of
fracture H4 showed an increase in apparent resistivity of 6 to 10% in the vicinity of
the borehole (Figure 8.17). A region of low apparent resistivity extends west from
borehole 4 toward boreholes 7 and 6, suggesting that fractures have intersected.
Mise-a-la-masse measurements of composite of the effects of fractures H5, H7 and
H6 on borehole 6, contoured in Figure 8.18, yield a more complex pattern. It is
interesting that the largest decrease in apparent resistivity for this final mise-a-la-
masse measurement on borehole 6 is nearer borehole 4 than 6. Because these
calculations reflect only changes after measurements made subsequent to fracture
H4 (Figure 8.12), the interpretation that fractures H6, H4, and possibly H7 are
interconnected must be checked against direct observations.
247
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10ft
Figure 8.11. Apparent resistivity contour map (mise-a-la-masse) on borehole 4,
following fracture H4. Contour interval is 1 ohm-meter.
248
-------
10ft
Figure 8.12. Apparent resistivity contour map (mise-a-la-masse) on borehole 6,
following fracture H4. Contour interval is 1 ohm-meter.
249
-------
10ft
Figure 8.13. Apparent resistivity contour map (mise-a-la-masse) on borehole 5,
following fractures H4 and H5. Contour interval is 1 ohm-meter.
250
-------
10ft
Figure 8.14. Apparent resistivity contour map (mise-a-la-masse) on borehole 4,
following fracture H5. Contour interval is 1 ohm-meter.
251
-------
10ft
Figure 8.15. Apparent resistivity contour map (mise-a-la-masse) on borehole 4,
following fractures H4, H5 and H7. Contour interval is 1 ohm-
meter.
252
-------
10ft
Figure 8.16. Apparent resistivity contour map (mise-a-la-masse) on borehole 7,
following fractures H4, H5 and H7. Contour interval is 1 ohm-
meter.
253
-------
10ft
Figure 8.17. Apparent resistivity contour map (mise-a-la-masse) on borehole 4,
following fracture H6. Contour interval is 1 ohm-meter.
254
-------
10ft
Figure 8.18. Apparent resistivity contour map (mise-a-la-masse) on borehole 6,
following fracture H6. Contour interval is 1 ohm-meter.
255
-------
X DECREASE. FRAC 4
X DECREASE. FRAC 5
» DECREASE. FRAC 7
* DECREASE U4 FRAC 6
Figure 8.19. Summary of mise-a-la-masse apparent resistivity changes relative to
borehole 4 resulting from fractures H4, H5, H6 and H7. Cross-
hatching indicates locations of fractures.
256
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borehole 7 toward borehole 6, representing a unilateral rupture, which is probably
vertical. Figure 8.19d shows a decrease in apparent resistivity toward the midpoint
between boreholes 6 and 7, with a decrease in apparent resistivity over much of the
remaining array. This means electrical current density has decreased over most of
the array, so current must have been diverted through a new conductor developed
during the creation of fracture H6.
In conclusion, it is clear that hydraulic fracturing with a conductive fluid in a
relatively resistive formation causes observable, but complex changes in die
electrical properties of the formation. The mise-a-la-masse method yields valuable
results, but further research is needed before its use could become commonplace.
Specifically, measurements made as fractures are being propagated may help
understand and interpret the sometimes complex results.
DISCUSSION
Pressure records, surface uplift, and surface tilt all are available methods of
monitoring hydraulic fractures at shallow depths. Pressure records require simple
equipment (a transducer and a data recorder), and indicate the onset of fracturing,
show various fluctuations in pumping schedule and provide a rapid indicator of
various problems. Methods of estimating orientation, asymmetry, and tip screenout
(e.g. Nolle and Smith, 1981; Smith and others, 1987) from the pressure records of
shallow fractures seems feasible.
Surface uplifts of a cm or more over hydraulic fractures were readily
measured with a standard engineer's leveling telescope. Contour plots of uplift
correlated with shallow hydraulic fractures, providing estimates of the leading edge
and point of maximum thickness. Numerical inversion of uplift data should improve
the qualitative correlations attempted in this work, providing estimates of the size,
thickness, orientation and location of hydraulic fractures at depth.
During the 1988 tests, surface tilts were measured in real time with
sophisticated tiltmeters and a datalogger. Inversion of those data after the tests
provided estimates of how the fractures developed as a function of time.
Comparison with maps indicates that the inversion provides crude simplifications of
the actual fracture forms. In future applications, real time inversion or the tiltmeter
data could yield estimates of fracture form as it is being created.
Electrical resistivity measurements, particularly those using the mise-a-la-
masse technique, are able to sense the shallow fractures created during these tests.
Methods of inverting electrical signals to obtain estimates of fracture geometry,
which are currently being developed, will be required before the mise-a-la-masse
method is practical for monitoring hydraulic fractures.
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SECTION NINE
SUMMARY AND CONCLUSIONS
The objective of this study was to evaluate the feasibility of using hydraulic
fracturing under conditions of contaminated regions. Most current applications of
hydraulic fracturing are in oil reservoirs, and available techniques are designed for
that application. Oil reservoirs are typically deeper and composed of different
materials than contaminated regions, so the suitability of reservoir fracturing
methods for contaminated soil use is unknown. Contaminants commonly occur in
soils, or unlithified sediments, that are weaker and more compliant than the
limestone or sandstone typical of reservoirs. Previous studies of hydraulic fracturing
of soil have focused on methods of preventing fracture initiation during various
geotechnical practices, so little is known about the details of the propagation of a
hydraulic fracture in soil. Moreover, most contaminants occur at relatively shallow
depths, so that hydraulic fractures could vent to the ground surface before they grow
any appreciable distance from a well. The technique will be of limited value if
venting limits fracture lengths to, say, a few well diameters.
The project consisted of studies in the laboratory and in the field, as well as
an investigation of possible applications and a review of previous work. Laboratory
studies were intended to reveal details of the process of hydraulic fracturing of soil,
and to assess the ability of linear elastic fracture mechanics to predict the essential
details. Field studies were intended to show whether fractures of useful size could
be created and propped with sand at shallow depths in soil.
POTENTIAL APPLICATIONS
Most remedial systems requiring fluid flow either into or out of the
subsurface could benefit from hydraulic fracturing. Pump and treat systems are
obvious candidates because they employ procedures resembling those used in
petroleum recovery, where the benefits of hydraulic fractures are without question.
A review of data from oil wells, gas wells, and water wells that have been
hydraulically fractured indicate a consistent increase in yield. Preliminary data from
this research indicate that steady-state rates of inflow into unsaturated ground are
greater, by factors of 3.1 to 9.0, into wells intersecting hydraulic fractures as
compared with those in unfractured ground. Magnitudes of increase in observed
yields, in general, are similar to magnitudes calculated using simple theoretical
analyses. Based on a review of published data and simple analyses, we expect that
hydraulic fracturing could increase yields of contaminant recovery wells consistently
by as much as five times, commonly by as much as 10 times, and in some cases it
could increase yields by factors much more than 10 times. The magnitude of the
effect will depend on sue conditions, the methods used to create hydraulic fractures,
and the methods used to complete and develop associated wells.
Pump and treat systems are by no means the only remedial methods that
might benefit from hydraulic fracturing. The yields of vapor-producing wells, such
as those recovering natural gas or steam, are unproved by hydraulic fracturing, so by
analogy we expect that vapor extraction systems could benefit from this technology.
Similarly, hydraulic fracturing could be used in conjunction with steam stripping - a
process developed to improve yields of oil wells and currently being tested under
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remedial conditions. Horizontal, sheet-like hydraulic fractures placed below a
contaminated region could be used as gravity drains to intercept the leachate from
soil flushing systems (Murdoch and others, 1987), improving the effectiveness of that
remedial action.
The novel application of delivering solid material, as granules pumped into
hydraulic fractures, is noteworthy. Bio-remediation systems stand to benefit in
particular because either nutrients for microorganisms, or the microorganisms
themselves, could potentially be delivered as fine-grained solids in hydraulic
fractures. Air sparging-pumping air into the ground to encourage the growth of
aerobic bacteria-could be more effective in ground containing hydraulic fractures.
LABORATORY STUDIES: SUMMARY OF RESULTS
1. Hydraulic fracturing in the Center Hill clay can be predicted and analyzed
using methods of linear elastic fracture mechanics, similar to those used to predict
hydraulic fracturing in rock. The large body of published papers analyzing hydraulic
fracturing in rock can be used to predict field applications in soil, with appropriate
modifications for boundary conditions (e.g. ground surface), material properties
(e.g. elastic constants, leakoff parameters), and state of stress encountered at
shallow depths.
2. Hydraulic fractures created in the laboratory consist of the following
zones, which are arranged in order from the point of injection to the leading edge:
1) Starter slot This feature was created during sample preparation;
2) Parent fracture A continuous fracture surface marked by slight steps, ridges, or
grooves.
3) Lobes The parent fracture twists or curves slightly, breaking into a family of
discontinuous fracture lobes.
4) Unwetted tip Leading edge of the fracture is unstained by dye in the injection
fluid.
Those zones were identified on almost all fracture surfaces. The only
exception is that the unwetted tip zone was absent from fractures created in samples
of less than 21% moisture; the entire fracture surface was stained. Published
descriptions of the appearance of hydraulic fractures created in rock are similar to
those produced in soil during this study.
3. Records of injection pressure as a function of time show three
characteristic periods, which are interpreted as follows:
Period I: Injection pressure increases linearly with time, slope constant. Indicates
inflation of the starter slot.
259
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Period II: Slope of pressure record decreases but remains positive. Change in slope
indicates onset of fracturing, positive slope indicates stable
propagation.
Period III: Pressure reaches a maximum and slope becomes negative. Indicates
unstable propagation.
In some samples, particularly the wetter ones, propagation begins slightly
before the change in slope of the record, and the onset of propagation may have
been overestimated by methods used in the study.
4. Moisture content and length of starter slot strongly affect the pressure
record. As moisture content decreases, the duration of stable propagation (Period
n) diminishes and the slope steepens during unstable propagation (Period III).
Moreover, the pressure required to initiate fracturing increases as moisture content
decreases. Similar trends occur when the length of the starter slot decrease; the
duration of stable propagation diminishes and the pressure required to initiate
fracturing increases.
5. The critical stress intensity factor can adequately predict the pressure
required to initiate hydraulic fracturing of soil. It is independent of the length of the
starter slot, for the slot lengths used in this study, and it predicts the driving pressure
at the onset of fracturing to within 10 percent, on average. It was more accurate for
samples wetter than the plastic limit (20% moisture by weight) and less accurate for
samples drier than that value.
6. Under the confining stress used in the laboratory experiments, the size of
the crack-tip process zone is estimated to increase from 0.13 to 0.47 cm as moisture
decreases from 27 to 20%, according to preliminary measurements. The accuracy of
the critical stress intensity method diminishes as the size of the process zone
increases, which is consistent with the findings that accuracy of the laboratory tests
decreased as samples became drier. Ouchterlony (1982) suggests that the starter
slot should be at least 93 times longer than the process zone to ensure small scale
yielding and maintain sufficient accuracy. Slot lengths ranged from 1.22 cm to 5.08
cm in the experiments, suggesting that the criteria of Ouchterlony are satisfied when
using samples moister than the plastic limit. Those criteria are not met for the
shorter slot lengths used in the drier samples, suggesting that slots at least 5 cm long
should be used in samples drier than the plastic limit.
7. The value of the critical stress intensity is highly sensitive to moisture
content, decreasing sharply from roughly 200 kPa cm1* to 30 kPa cm1/2 as moisture
content increased by a few percent (from 20 to 22%). The sharp change in critical
stress intensity corresponds to the plastic limit of the Center Hill clay.
8. Critical stress intensity goes to zero for samples of Center Hill clay greater
than 32% moisture, although hydraulic fractures are readily created under those
moisture conditions. Critical stress intensity fails as apredictor of moisture
conditions that preclude the formation of a hydraulic fracture. Presumably,
hydraulic fracturing will be impossible at extremely high moisture contents when the
soil approaches a slurry in composition, but the moisture content at which this
260
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occurs exceeds those used in this study and cannot be predicted using critical stress
intensity.
9. Theoretical analyses based on linear elastic fracture mechanics and linear
viscous fluid mechanics explain many of the details of the laboratory experiments,
including the development of an unwetted tip, the average propagation velocity,
changes in the form of the pressure record with changes in slot length or moisture
content. Analyses used to predict field applications should include the effects of
leakoff, which were omitted from the analyses presented here.
FIELD STUDIES: SUMMARY OF CONCLUSIONS
1. Hydraulic fractures of useful size can be created and propped with sand at
shallow depths in glacial till.
2. Pumps and blenders used by the oil industry will successfully create
hydraulic fractures at shallow depths. Blenders and pumps used for the 1988 test
were designed for pumping rates, pressures and volumes that greatly exceed the
specifications required for shallow depths. Several shortcomings, including sparse
proppant density in the fractures created, during the 1988 test, appear to be related
to lack of control of the oversized equipment.
A blender and pump unit which is readily available for injection grouting and
was used in the 1989 tests consistently resulted in hydraulic fractures propped with
sand. That equipment is inexpensive and simple to operate relative to the oil-field
equipment, but it too has drawbacks. The blenders were underpowered, resulting in
long mixing times that limited the rate of injection. A progressive cavity pump used
to inject slurry suffered excessive wear, and as a result the rotor and stator had to be
replaced at the end of the project.
3. Vertical fractures nucleated at the walls of open cylindrical boreholes,
even when the far-field state of stress favored horizontal fractures. Shallow
horizontal notches, cut 3.75 cm into the walls of the open boreholes, failed to
nucleate a horizontal fracture in most cases. The vertical fractures extend several
cm to several dm away from the open borehole, and then abruptly (typically within a
few cm) roll over and become flat-lying. Vertical fractures at the borehole reduced
the maximum lengths fractures achieved before venting, and they may have
restricted the transport of proppant.
Vertical fractures created during the 1988 test were a consequence of the
borehole design because they were eliminated by decreasing the length of the
cylindrical hole and increasing the size of the notch. Hydraulic fractures adjacent to
boreholes in till were always horizontal when they were nucleated from notches cut
10 to 20 cm in till with a water jet, as in the 1989 tests.
4. The form of the fractures created during the 1988 test is characterized by
the following four zones arranged in increasing distance from the parent borehole:
Zone 1: a sub-vertical orientation adjacent to the borehole.
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Zone 2: a flat-lying orientation in the vicinity of the borehole.
Zone 3: a planar to trough-like fracture dipping gently (15° to 25°) toward the
borehole. This zone extends in one direction away from the borehole
and composes most of the fracture.
Zone 4: a steeply-dipping orientation that vents to the ground surface
In plan the fractures are crudely elliptical, with aspect ratios of roughly 2:3.
The parent borehole is typically near one end of the major axis and the vent is at the
other end.
The form of the fractures created during the 1989 test was simpler than that
of the previous year; the fractures were nearly flat-lying from their parent borehole
to then- leading edge. Some fractures dipped gently toward the borehole, but even
the steepest dip was only 5°. In plan, the fractures created during 1989 were slightly
elongate (aspect of 2:3) and they were highly assymetric with respect to the
borehole; in plan they are similar to the results of the previous year.
5. Fractures created during the 1988 dipped more steeply than those of the
1989 test. The dip is important because it defines how far the fracture can extend
before venting. Three differences between the 1988 and 1989 tests are recognized
that could have affected the average dip.
a) Rate of injection during the 1989 test was less than that of the 1988 test.
Pollard and Holzhausen (1979) show that decreasing the pressure gradient within
the fracture (say, by decreasing pumping rate) will inhibit growth toward the ground
surface.
b) Sand concentration, and thus slurry density, was greater during the 1989
test Increasing fluid density will decrease the static drivr —-——•"«—*'- -
Secor and Pollard, 1975; Abou-Sayed and others, 1984),
c) The topographic surface overlying fractures during the 1989 test was
benched, whereas it was nearly flat over the dipping fractures created in 1988. It
appears that topography may contribute to the orientation of shallow hydraulic
fractures (perhaps by inducing horizontal variations in vertical stress), but
mechanisms controlling this suggestion must be investigated in more detail.
6. The major axes of hydraulic fractures created during both tests extended
away from parent boreholes in directions that minimize the vertical stress. During
the 1988 tests, fractures either propagated away from a backhoe parked next to the
borehole, or they propagated in the same direction as the overlying slope. During
the 1989 tests, all fractures grew away from a steep embankment.
Those observations suggest that preferred propagation directions of
horizontal fractures can be crudely predicted based on topography; they will
grow in
262
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the downslope direction. This raises the possibility that the direction of propagation
could be influenced by artificially loading the ground surface, which could be
important at sites underlain by regions that should not be fractured. It also indicates
that a horizontal hydraulic fracture created next to a building will tend to grow away
from the building.
7. Fractures were created and filled with sand at depths ranging from 1 to 4
m. Dimensions of fractures created between 1 and 2 m are known in detail from
excavations. They are as follows: during the 1988 tests, the maximum length, from
borehole to the leading edge, ranged from 1.8 to 13.5 m and it averaged 578 m.
Areas covered by those fractures ranged from 2.2 to 90 m2, and averaged 25 m2.
The thickest part of a fracture created in 1988 was 9mm, and many of the fractures
created that year were nearly devoid of sand.
i
During the 1989 tests, the maximum lengths ranged from 0.8 to 7.2 m, and
averaged 4.0 m. Areas covered by the fractures ranged from 0.8 to 36.7 m2, and they
averaged 19.2 m2. All the fractures contained sand, ranging in maximum thickness
from 2 to 20 mm, and averaging 11 mm.
The fractures created in 1989 were slightly smaller in area than those of the
previous year; however, the sizes of all the 1988 fractures were limited by venting,
whereas most of the 1989 fractures did not vent and they could have been larger if
more fluid had been pumped into them. The average thickness of sand in the 1989
fractures exceeded the maximum thickness from the previous year.
The increase in thickness of sand, from the 1988 to the 1989 tests, apparently
results from changes in the above-ground mixers and pumps. The above-ground
equipment used in 1988 was designed for flow rates and pressures required to create
hydraulic fractures in oil wells, which are as much as several orders or magnitude
more than the flow rates and pressures required for our applications. The oil-field
equipment lacked the control required to mix and pump the relatively small
applications that we required. This simply indicates that filling hydraulic fractures
with sand will be facilitated by using above-ground equipment that is designed for
the conditions of the application.
8. A method of creating fractures from a device driven into the ground was
developed to facilitate the creation of multiple fractures in soil. As many as four,
fiat-lying hydraulic fractures were stacked at spacings of 30 cm without intersecting
their neighbors. When one fracture was created 15 cm below another, the lower
fracture would commonly climb upward and intersect the overlying fracture several
meters from the borehole. One spacing of 7 cm was attempted; the lower fracture
intersected the upper one several dm from the borehole.
It would be possible to stack flat-lying fractures at spacings between 15 and
30 cm throughout a contaminated region at the ELDA site, and similar spacings
should be possible under similar site conditions.
9. Pressure records, surface uplift, and surface tilt all are available methods
of monitoring hydraulic fractures at shallow depths. Pressure records require simple
equipment (a transducer and a data recorder), and indicate the onset of fracturing,
show various floatations in pumping schedule and provide a rapid indicator of
263
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various problems. Methods of estimating orientation, assymetry, and tip screenout
(e.g. Nolte and Smith, 1981; Smith and others, 1987) from the pressure records of
shallow fractures seems feasible.
Electric resistivity measurements, particularly those using the mise-a-la-
masse technique, were able to detect the hydraulic fractures created during the 1988
tests. Methods of inverting electrical signals to obtain estimates of fractures
geometry will be required, however, before this method yield quantitative estimates
of fracture geometry.
Surface uplifts of a cm or more over hydraulic fractures were readily
measured with a standard engineer's leveling telescope. Contour plots of uplift
correlated with shallow hydraulic fractures, providing estimates of the leading edge
and point of maximum thickness. Numerical inversion of uplift data should provide
valuable estimates of the size, thickness and location of hydraulic fractures at depth.
During the 1988 tests, surface tilts were measured in real time with tiltmeters
and a datalogger. Inversion of those data after the tests provided estimates of how
the fractures developed as a function of time. Comparison with maps indicates that
the inversion provides crude simplifications of the actual fracture forms. In future
applications, real time inversion of the tiltmeter data could yield estimates of
fracture form as it is being created.
Electrical resistivity measurements, particularly those using the mise-a-la-
masse technique, are able to sense the shallow fractures created during these tests.
Methods of inverting electrical signals to obtain estimates of fracture geometry,
which are currently being developed, will be required before the mise-a-la-masse
method is practical for monitoring hydraulic fractures.
264
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281
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APPENDIX
RECORDS OF PRESSURE, INJECTED VOLUME, SURFACE UPLIFT AND
SURFACE TILT AS FUNCTIONS OF TIME.
282
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350
300
250
200
150
100
50'
0<
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: Well #8 A, -
• Begin 17:07 / A-
/ ,
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1
Pressure L i
/^ i
/ j
A ._— ._ A. -
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550
500
450
400
350
300
250
200
150
100
50
n
O
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Q.
.2
^^
0 -2
3
Well #8
• Begin 17:12
AAA— A— — AAA— A— AAA A— A 0Wh
_^_ M — i • M i u &* KJU
o 6' east of well
* at well
0 5 10 15 20 25 30 35 40 45
Time (minutes)
291
-------
150
'55 125
Q.
100
Well #10
Begin 14:44
5)150
- 125
10
Time (minutes)
T
t,
-M
q>
o
o
*0
0)
0
J
2
1
Di
Ul
-1
-2
3
Well #10
Begin 14:46
K
/\
^v
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N.
o 6' west of well >.
^ at well \
A
5 10
Time (minutes)
15
292
-------
200 -
Well #9
Begin 16:12
5 10
Time (minutes)
KM
"c
Q>
E
0)
o
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Q.
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5
7
6
5
4
3
2
1
Oi
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• Well #9
Begin 16:12
; o 6' west of well
L * at well
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b o
if
I/
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1
1
f
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^7
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10
Time (minutes)
293
15
-------
CD
Q.
3
m
m
Q)
c
o
tp
a
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90
80
70
60
50
40
30
20
10
Well
Begin 11:16
' Estimated
Volume
Pressure
90
80
70
60
50
40
30
20
10
0
Time (minutes)
294
-------
400
« 350
o.
^ 300
| 250
Q. 200
c •
S 150
I 100
50
Well #13
Begin 10:15
Pressure
Volume
10 15
Time (minutes)
u
4
1* ^
1 2
"c 1
Q)
E Oc
§ u<
1-1
Q
-3
-4
-5
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1
7
/
Well #13
Begin 10:15
\ :
\
o
\
\
0
\ •
\ :
0 -
,
10 15
Time (minutes)
295
20
-------
------- |