Understanding Permeability of Hydraulic Fracture Networks A Sandbox Analog Model-updated
1. 1
Understanding Permeability of Hydraulically Fracture Networks:
A Preliminary Sandbox Analog Model
Renee Heldman
West Chester University, M.S. Geoscience
Indiana University of Pennsylvania, B.S. Environmental Geology
Masters Research Project
Committee:
Howell Bosbyshell, Ph.D., Advisor
Martin Helmke Ph.D., Department Chair
Joby Hilliker, Ph.D., Graduate Coordinator
2. 2
Abstract
Considerable uncertainty exists in current scientific research on how the overall permeability
of a unit is affected by manmade hydraulic fracture networks. Studies by Wang and Park (2002)
showed how permeability of rocks decreased with increasing effective confining pressure; Walsh
(1981) found permeability of the fracture increases with increasing effective pressure; while finally Li
et al., (1994, 1997)found that permeability is a function of the confining pressure and pore pressure
only in units with very high permeability. With increased concern about the negative side effects
from hydraulic fracturing, including contaminant transport and induced seismic events like those
seen recently in Oklahoma, it is necessary to try to quantify and understand the fracture networks
overall impact on the permeability of these units.
By building an analog model, one can use fine grained silica powder to represent low
permeability organic shales. Under confined pressures, injection of similar viscosity material to that
of proprietary blends used in oil and natural gas sequestration was used to imitate hydraulic
fracturing processes. Taking ~1” cross sections across the injected material, one can see the
development of the fracture networks and apply a cubic mathematical approach to quantify the
fracture permeability. Additional parameters such as porosity, cohesion, and coefficient of internal
friction can be calculated to determine analogue appropriateness. From this laboratory modeling, it
was found that the development of the fracture network was highly dependent on the confining
pressure and viscosity of the injecting fluid. Generally, as the viscosity increased, so too did the
horizontal length of the fractures from increased forward propagation. Initial hydraulic conductivity
of the silica flour was 2.76 x 10-4
cm/s. After injection, these values were influenced by the aperture
of the fracture network, increasing the hydraulic conductivity of the system up to ~ 37 cm/s in
some cases and permeability to 0.032 cm2
from an original value of 2.7 x 10 -9
cm2
.
3. 3
Introduction
When direct experimentation or mathematical analysis are difficult or not possible, the best
remaining alternative is to utilize a scale model, as one does in the studies of aerodynamics,
hydraulics and mechanical and electrical engineering (Hubbert, 1937). Hubbert and Willis were the
first to model hydraulic fracturing processes (1957), utilizing gelatin to facilitate visual analysis of
their results. However, gelatin does not scale appropriately of model the behavior of brittle rocks.
When choosing to use a scale model, the testing materials must be geometrically and kinematically and
dynamically similar to the natural phenomena (Hubbert, 1937). To be geometrically similar, the two
objects in question, natural and experimental, must have proportional lengths and angles based on a
constant of proportionality (Hubbert, 1937). Kinematic similarity is defined for materials undergoing
some geometrical change as having proportional time intervals of which this change is inflicted,
based on the model ratio of time (Hubbert, 1937). The third type of similarity defined by Hubbert
(1937) is dynamic similarity, as having a ratio of mass, inertia, and force action upon the body in
proportional directions and magnitudes. This third type is the most difficult to model and is often
unattainable. Dynamic forces include gravity and inertia. While gravitational forces (g) are, for most
purposes, constant, inertia can vary independently. When the processes are slow, the inertial forces
become negligible (Hubbert, 1951; Rodrigues et al., 2009). For models that are under the same field
of gravity and have similar densities, the dimensions of stress may be scaled down linearly (Hubbert,
1937).
To apply these scaling relationships for brittle rocks that fail according to the Mohr-
Coulomb criterion only two parameters need to be described: cohesion (C) and the coefficient of
internal friction (μ) (Hubbert, 1937). Cohesion (C) is a property of the material and can be scaled
down linearly, while the coefficient of internal friction (μ), since it is unit less and dimensionless,
needs no scaling (Hubbert, 1937). Sand, and other fine grained dry materials, have small cohesion
4. 4
values and similar coefficients of internal friction to that of brittle crust and make good modeling
materials. Because of this, sand has become a standard use for modeling tectonics with sandbox
models. Sand, however, was not used in this model. For most dry granular testing materials in
“sandbox models” the cohesion of the materials is assumed to be negligible and the coefficient of
internal friction is ~0.58 (Schellart, 2000). Further studies by Krantz (1991) noticed that the
cohesion of sand is around 300-520 Pa, depending on handling procedures, and the coefficient of
internal friction is ~0.58 to 1.00 and therefore should not be neglected (Krantz, 1991). Because of
this, it is necessary to determine the shear strength of the material to establish the appropriateness of
the analogue. Cohesion values for intact natural rocks have yielded values of ~20-110 MPa
(Schellart, 2000). However, these intact rocks often have extensive fracture networks, faults and
joints that could greatly lower these values for the matrix as a whole.
Additional factors that can control fracture propagation are the effects of internal friction.
The amount of frictional sliding is controlled by the coefficient of internal friction (µ), based on the
cohesion properties of the material. Grains that are angular or readily interlock will display higher µ
values, while those that are rounded or have the ability to slide past one another with ease, will have
lower µ values, as seen in figure 1. The grains of the #325 silica flour are highly angular and have a
reasonable degree of “locking” ability. Byerlee (1978)notes that μ needs to be defined as the initial,
maximum or residual coefficient of internal friction since these values will differ and are not static
(figure 2). It was also found that there was no strong dependence of friction based on rock type;
where μ can vary from 0.3 to 10 based on surface roughness. Which raises the question “why is
friction at low pressure independent of rock type and initial surface roughness?” Byerlee
hypothesized that irregularities in the rock face that touch, deemed “asperities”, create zones of high
normal stress, so much so that they become fused and the shear force must overcome these fused
zones to shear the fault plane (figure 3). He however admits that while there must be some
5. 5
relationship between the shear strength and the compressive strength of the “asperities”, rocks that
fail in brittle failure involve far more complex physical processes than outline by this theory (Byerlee,
1978). His experimental data showed that at high pressure, friction behaves independently from rock
type and only plays a role in shear strength if large gouges of hydrated clay minerals, like
montmorillonite or vermiculite, are between fault blocks, increasing the pore fluid pressure within
the unit and reducing the overall effective pressure and friction (Byerlee, 1978). Here, the cohesion
and coefficient of internal friction will be determined for the fine grained silica flour, similar to that
used in previous research of magma intrusion modeling (Galland et al., 2006), as a more appropriate
analogue for low permeable shale.
Permeability (K) is defined as the ease with which water or other material can flow through
rock or aquifer media. It is generally measured as the rate of fluid flow through the media as
hydraulic conductivity (k), a function of hydraulic gradient, as defined by Darcy’s Law (Fetter, 2001).
Silica flour Silica flour
Figure 1 A (left) and B (right): Micrographs of Silica Flour #325 taken with a scanning electron microscope (SEM), A at
50 microns and B at 10 microns. High power magnification shows the highly angular shape of the silica flour, similar to that
of the SI-CYSTAL of the Galland et al. (2006) research (Heldman, 2016).
6. 6
Permeability can vary depending on the geologic media from highly permeable units like well-sorted
sands at 10 -3
– 10 -1
cm/s to very low permeable units such as silt at 10 -6
– 10 -4
cm/s (Fetter,
2001). Not only is permeability affected by the inherent characteristics of the media, but also other
secondary porosity processes. Secondary porosity features are a result of any process that changes
the porosity of the unit after the formation of the rock such as the chemical reaction of dissolution
and cementation, or physical alterations from stress and strain processes. Fractures in rocks are an
important source of secondary porosity. These fractures affect the connectivity of the pores within
the media, enlarging or impeding the flow and increasing or decreasing the permeability of the unit
accordingly. The aperture of the fractures directly affects permeability. Fracture aperture defines the
parameters of flow and transportation processes and can range from small to large scale. Hydro-
mechanical processes and overall matrix permeability are hard to predict in highly fractured rock
units (Rutqvist, 2015). This is partially due to the fact that matrix permeability is highly dependent
on site characteristics and the hydraulic and mechanical interactions within largely heterogeneous
fracture networks (Rutqvist, 2015). Therefore, without field observation and site reconnaissance, it is
Fig 3: Close up schematic of proposed rough surface of
material creating a small number of zones that touch, known
as “asperities” that under higher normal stress (outline by red
boxes) than surrounding surfaces become fused resulting in
high shear values (Heldman, 2016).
Figure 2: Graph of Force vs. displacement taken from
Byerlee (1978); points C, D, and G are value of initial,
maximum and residual friction illustrating that friction (µ)
is variable throughout testing resulting in “jerky” motion
described in shear failure.
7. 7
difficult to confidently predict matrix permeability. We often generate “artificial fracture walls” from
numerical simulations and models (Berkowitz, 2002). It is also difficult since the fractures are not at
static state. Processes of uplift, erosion, pressure and time constantly change the fracture, potentially
increasing it in size, but also making it susceptible to infilling and dissolution processes that change
the permeability of the fracture. In general, the larger the fracture aperture, the more fluid transport
can occur.
The goal of this model is to try to quantify a change in the permeability of a unit pre and
post fracture. A plastic storage container was filled with silica flour to represent a low permeability
shale matrix. Fluid was then injected into the matrix to model hydraulic fracturing processes. After
the fluid solidified, ~1” cross sections were carefully removed to locate any fractures trapped within
them. The aperture of the fractures were measured for analysis. From these measurements we can
apply a cube law relationship to calculate the hydraulic conductivity of the fracture and determine
how this changes the overall permeability of the matrix.
9. 9
to remain fluid during injection, to model fracturing fluid, but later solidify, as not to disturb the
fracture network created after injection. For testing purposes, thick sections of the material will be
removed from the plastic storage box and measured for calculated hydraulic properties such as
permeability and therefore the vegetable shortening fracture network needs to maintain its shape
once moved. Additionally, viscosity measurements of the fluid must be calculated to further material
appropriateness and are discussed in later sections.
Low Permeable Shale Analogue:
Shale, while generally having low permeability, can have a wide range in porosity. The pores
within the shale may range from nanometer to micrometer in size (Sang et al., 2016). When this
shale is in the presence of organic matter it often changes the characteristics of the host rock. When
large amounts of oil or natural gas are trapped within the pores of the shale, the overall density of
the rock decreases, increasing overall porosity, altering wettability and assisting in adsorption (Sang
et al., 2016). Gas stored in shale may exist in one of three forms: as free gas in the matrix; adsorbed
to the surface of the pores; or dissolved within kerogen (Sang et al., 2016). While all three types are
chemically the same (methane), how they are removed from the shale matrix is very different. Free
gas is produced first, accounting for 60% of all the gas retrieved through sequestration (Sang et al.,
2016). Once pore spaces are voided of the free gas, the adsorbed gas, once clung to the pore spaces
within the matrix, desorbs and fills in the voids and is next for production. Finally, as the
concentration gradient between the pore spaces and kerogen increases, the dissolved gas diffuses
into the voided pore spaces and is the last produced (Sang et al., 2016). When shale has a high
porosity, the total gas flow is highly dependent on the surface area of the pores and processes of
adsorption and diffusion gain greater importance (Sang et al., 2016).
An analogue is needed to represent low permeable shales that are consistently hydraulically
fractured to obtain their oil and natural gas contents. This analogue must behave similar to and have
10. 10
hydraulic conductivity properties like that of a shale. For this model, small grain size is also
necessary to prevent percolation of injected material, since permeability is proportional to the square
of the grain size (Sang et al., 2016). Since hydraulic fracturing fluids travel through preferential
fracture networks, the material being injected must be susceptible to fracture and have a low
intrinsic permeability. Secondly, the material must also be incompatible with the injection material to
prevent further percolation and adhesion (wettability). Choosing a matrix material that is hydrophilic
will allow us to use the hydrophobic vegetable shortening mixture as the injection material. The
AGSCO Silica Flour #325 was chosen since it had similar grain size and density parameters to that
of the SI-SPHERE and SI-CRYSTAL used in the Galland et al. (2006) research. Their hydrophilic
property and small grain size makes them a good candidate for the sedimentary rock analogue to be
used with the vegetable shortening. This flour was produced by grinding rounded Midwest sands to
a finer particle size (mean volume 17.8 microns, see Appendix 1 for grain size distribution) small
enough to fit through a #325 mesh (AGSCO #325 Technical Sheet). These flours are traditionally
used in concrete, refractory mixes and grouting compounds.
Background on Galland et al. (2006) Research
Previous research was conducted by Galland et al. (2006) in order to understand the
complexities of low viscosity magma intrusion. Researchers created a “sandbox” model using low
permeable sediments and vegetable oil as and analogue for brittle crust and low viscosity magma
respectively. To model the crust, researchers used a mixture of crystalline silica powder (SI-
CRYSTAL) and siliceous microspheres (SI-SPHERE) of grain sizes less than 30 micrometers to
represent competent (SI- CRYSTAL) and incompetent (SI-SPHERE) rock (Galland et al., 2006). In
previous studies, sandbox model analogs have not been representative of sedimentary rocks such as
low permeable shales. To counteract percolation and seepage of the fluid into the pore spaces, small
pore size granular material must be used. These materials were also chosen because they are
12. 12
Preliminary Testing Procedures and Methods
In order to quantify a change in the permeability of a unit, pre and post fracture hydraulic
conductivity must be measured. To calculateinitialhydraulic conductivity (k) of a sample in the lab,
common practice is to use a falling head permeameter. This consists of housing the sediment, in
this case silica flour, in some kind of chamber with a port into and out of the chamber. Filters are
used on both ports to keep the sediment from leaving the chamber (see figure 4). Before testing can
begin, it is necessary to make sure the sediment is fully saturated or flushed. Water was placed into a
vertical column with an on-off lever, normally coupled with a meter stick or other measuring device,
and will hereby be referred to as a falling head permeameter. The falling head permeameter is
connected by tubing to the bottom or entering port on the housing chamber and tubing is also
attached to the top or exit port of the chamber. Initial water height in the permeameter is recorded,
deemed the initial head, or Ho. Once the lever on the permeameter is open, allowing the flow of
water from the permeameter to the housing chamber, a timer was started. As the water flows from
the permeameter to the housing chamber, the head, or level of water in the permeameter, will drop.
At intermittent times (s) during the flow, the time and head value (cm), was recorded. Hydraulic
conductivity was then calculated based on the following equation and results are listed in appendix 2
(Fetter, 2001):
k = dr
2
•L • ln Ho
dc
2
•t Ht
dr – diameter of the vertical column (cm)
L – length of the sample in the housing chamber (cm)
dc – diameter of the sample in the housing chamber (cm)
t – time between Ho and Ht (s)
Ho – initial “head” (cm)
Ht – final “head” (cm)
(1)
13. 13
Ho, Ht, and time are determined by
applying a linear line through the
early time data on a graph of Ht
(cm) vs. Time (s) (see appendix 2).
The early time data is used because
it displays the most accurate
behavior of the flow in the system.
Where the line crosses the y axis
becomes the Ho value and y
component of where the line crosses
the x axis becomes the Ht value,
while time (t) is the coupled x
component. For simplicity in this
study, Ht was kept constant at 10
cm.
Next, we must establish the cohesion (C) and coefficient of internal friction (µ) through
shear testing of the material. To measure the shear stress of the silica flour, the apparatus in figure 5
was used based on experiments from Hubbert (1951), Krantz (1991), Schellart (2000), and Galland
et al (2006). This apparatus, as noted in the figure, consists of an upper and lower cylinder (PVC
coupling 6.2cm x 4.2 cm) which houses the silica flour (use of a small diameter allows testing
procedure to keep sediment thickness as small and as constant as possible). The lower cylinder is
mounted to the base of the ring stand to restrict its movement. The upper cylinder is suspended
from 4 fixed wires (Stainless SteelFishing line) at a length of 47.5cm mounted by eye hooks attached
to the arm of the ring stand (length of wire was ~8x the diameter of the cylinder to reduced friction
from testing apparatus) (Schellart, 2000). A small amount of space (6mm) exists between the two
Collection
Container
Sample
Measuringtool
Ho
Housing
Chamber
Exit Port
and Filter
Entering Port
and Filter
Tubing
Tubing
Lever
Vertical Column
Falling Head
Permeameter
Figure 4: Schematic of Falling Head Permeameter Testing Apparatus
(Heldman, 2016).
14. 14
cylinders to prevent any interaction between the two cylinders. The upper cylinder is also fixed to a
mass (M) (at a 90° angle) hanging over a pulley (Everbuilt Clothesline Separator) that is mounted to
the ring stand. This will allow for lateral movement (failure) to occur when the mass (M) overcomes
the shear strength of the silica flour. Strength is a dependent variable and is a function of the three
principal stresses and inversely related to temperature (Hubbert, 1937). Also, as noted by Krantz, the
density and the coefficient of internal friction (µ) vary more with the handling technique than the
composition of the material itself. Therefore, it is necessary to maintain consistent pouring methods
when testing.
Before testing, it is necessary to determine any friction introduced by the pulley. To establish
this, the apparatus (figure 5) was set up as normal without the silica flour, and small amount of silica
flour were poured into the hanging bucket with a scoopula until the mass (M) was significant
enough to displace the empty upper cylinder a few millimeters (≥3mm). Testing showed shear
values averaging around 15 Pa were enough to lead to failure. However, since the shear forces tested
during the experiments ranged from averages of 240 – 320 Pa (non-compacted and compacted)
M
Ring Stand
Hanging Wires
Stationary Lower
Cylinder
Mobile Upper
Cylinder
H
D
Silica Flour
σ
n
τ
Figure 5: Schematic of Shear testing apparatus. Silica flour was slowly poured into upper and lower cylinders using a 1 tablespoon
scoopula and then packed systematically for compacted silica test trials. Solid arrows indicate direction of motion (Heldman, 2016).
15. 15
shear stress induced by friction would lead to only a small percentage of error. Additionally,
frictional forces between the silica flour and the upper cylinder must be checked. To do this, silica
flour with and without the upper cylinder was weighed, which resulted in a less than 1% difference is
mass, illustrating that this force is negligible for these testing purposes.
The normal load on the shear plane is determined by the height of the material (H) above
the gap between the two cylinders. It can be calculated based on the following equation:
σn = ρ g Η
where σn is the normal force, ρ is the density, g is the acceleration due to gravity, and H is the height
of the material above the shear plane (gap) (Galland et al., 2006). This experimental apparatus will
allow us to test normal stresses in the range of ~50-900 Pa (Schellart, 2000).
During testing, the silica flour is slowly poured into the hanging bucket using a tablespoon
scoopula until mass (M) is sufficient to cause a few millimeters of lateral movement in the upper
cylinder (≥3mm), representing shear failure. This was repeated for several trials, with silica flour
(2)
y = 0.5922x + 105.63
R2
= 0.7346
0
50
100
150
200
250
300
350
400
450
500
-50 50 150 250 350 450 550
ShearStres(Pa)
Normal Stress (Pa)
Shear Vs. Normal Stress (Pa)
Shear Stress (Pa)
Tensil Stress (Pa)
Figure 6: Shear vs Normal Stress Mohr diagram for Compacted Silica flour. The linear relationship (τ=µ●σn + C)
between shear stress and normal stress was forecasted backward to find the point of intersection when normal stress
equals zero, the value of cohesion (105.63 Pa) (Heldman, 2016).
16. 16
replaced in the both upper and lower cylinders (see appendix 3A). The average mass necessary for
shear failure was calculated as 75 g for the non-compacted silica flour when column height was
4.2cm. Understanding that the silica flour, when poured into the final testing apparatus (plastic
storage container) will be compacted, shear testing of compacted silica flour was also tested. The
average mass necessary for shear failure was calculated as ~100 g for the compacted silica flour with
variable column height (see appendix 3B) and average shear stress of ~ 320 Pa. As outlined by
Krantz (1991), density, cohesion and coefficient of internal friction are highly dependent on the
pouring methods of granular materials and is necessary to keep these consistent throughout testing.
For the compacted silica flour, material was poured using the tablespoon scoopula from a height of
~ 9 cm and tampered with the scoopula until a clear horizontal shear plane was established within
the upper cylinder. With these trails, several heights were tested to understand the relationship
between normal stress (σn) and shear stress (τ) and graphed in Figure 6.
Next, we must establish tensile strengths. The apparatus used to measure this is depicted in
Figure 7 (or original on pg. 795 from the study by Galland et al., 2006). Modifications in this
experiment included the use of “Magic Coasters” (acting as a low friction surface) as the mobile and
fixed plates and an eye hook attached to the mobile half of the PVC coupling allowing orientation of
the pulley and hanging mass always at angle α=90° for tensile strength testing. The two vertical
PVC coupling pieces were attached to the “magic coasters”, separated by a small vertical gap (2
mm). Compacted silica flour of known height (H) is added to the two vertical half cylinders,
supported through its cohesion properties to maintain shape and not collapse through the vertical
gap in the cylinder. The free half of the cylinder is attached to a mass (M) using the hanging wire.
This mass is allowed to freely hang over the pulley at angle (α) to the vertical fracture surface. When
the mass (M) is oriented at α=90° (Galland et al., 2006). Results are shown in table 2 and figure 6,
and data is in appendix 4. Shear (τ) and tensile force (T) can be calculated as mass (M) multiplied by
17. 17
the sine or cosine of angle (α) per height and diameter of the fault plane (Η x D) as outlined by
Galland et al. (2006):
σn =σ sin(α) = M sin (α) / Η D
τ = σ cos(α) = M cos(α) / H D
When α =0 and σn = 0 Pa, the failure equals the cohesion of the material, and when α= 90° and τ =
0 Pa, the failure equals the tensile strength of the material. When graphing the shear and tensile
strength vs. the normal stress (figure 6), we developed a Mohr-Coulomb failure envelope
represented by the equation τ = µ ● σn + C graphed as the linear line of best fit (Galland et al., 2006).
Source Particle d (microns) ρ (g/cm3) C (Pa) T (Pa) µ
Galland et al.
(2006)
SI-CRYSTAL ~10-20
SI-SPHERE ~30
1.33 + 0.2%
1.56 + 0.18%
288 + 26
1.5
88 + 17
Negligible
0.840+ 0.042
Experiment #325 Si Flour ~17.8 1.25 105.63 40.32 0.5992
(3)
(4)
Table 2: Compared values from experiment with Galland et al. (2006) study, d is the diameter of the particle size, ρ is
the density of the particles in g/cm3 , C is the cohesion, T is the tensile strength, and µ is the coeff. of internal friction
(Heldman, 2016).
Figure 7: Top view of tensile strength testing apparatus. Silica flour was poured into the two vertical halves of the PVC coupling
using the same pouring and packing procedures as the shear strength testing. Black arrows indicate motion (Heldman, 2016).
VerticalGap:2mm
Top View of Tensile Schematics
Eyehook
Pulley
Silica flour
Silica flour
“MagicCoasters”
HalfPVC
Coupling
Fixed Plate
Mobile
Plate
20. 20
Permeability (K), the ease with which water or other material can flow through rock or
aquifer media, is generally measured as the rate of fluid flow through the media as hydraulic
conductivity (k), a function of hydraulic gradient, as defined by Darcy’s Law (Fetter, 2001).
k = Q / (i • A)
k - hydraulic conductivity (cm/s)
Q - discharge (cm3
/s)
i -hydraulic gradient
A - cross sectional area (cm2
)
Using the cube law, fracture permeability can be calculated by the following (Snow, 1965):
kf = b3
ρ g N
12 ν B
b – fracture aperture (cm)
ρ – density in (g/cm3
)
ν - viscosity of fracturing fluid (g/cms)
g – gravity (cm/s2
)
N – number of fractures (assumed 1)
B – fracture spacing (assumed 1)
From which permeability can be calculated using the equation (Fetter, 2001):
K = k ● (ν / (ρ ● g)
K – permeability if unit (cm2
)
k – hydraulic conductivity(cm/s)
ρ – density (g/cm3
)
ν - viscosity (g/cms)
g- gravity (cm/s2
)
Results
In this model, the cube law equation (8) is used to calculate the hydraulic conductivity of the
fracture. Results are listed in appendix 10. The hydraulic conductivity of the fracture is proportional
to the cube of the aperture. Because of this, it is highly dependent on the fracture geometry, which
was not consistent between trials. Furthermore, several trails (1, 4, and 13) did not display fractures
at all. Rather, the injection fluid back-filled the space around the injection tube and created a pooled
(7)
(8)
(9)
21. 21
plume of fluid near the injection port
(see figure 9). These trails were not
used for hydraulic conductivity and
permeability calculations. For those
that did display fractures, the largest
single fracture within the matrix was
used for calculations (see appendix 6
for fracture images). From the images,
the fracture aperture can be determined
using the scale within the picture (see
figure 10). This measurement is then
applied to the cube law to find the
hydraulic conductivity (appendix 10). Then, using equation 9, we can determine the permeability and
compare it to the initial value found from the falling head permeameter testing and equation 1,
yielding a value of 2.7 x 10 -9
cm2
, using the viscosity and density of water at room temperature
(~22°C). The average permeability of the
fractured unit was 0.032 cm2
. That’s a significant
increase. The fractured unit permeability
calculations were highly variable and largely
dependent on the fracture geometry. The first
few trails all displayed the back filling and
pooling effect as described from trials 1, 4, and
13. Additionally, most of the trials resulted in
surface rupture, feed from vertical dikes that
Figure 9: Back-filling of the injection fluid pooled near the
injection port. These trials were not used in calculations (Heldman,
2016).
b
Figure 10: Measurements taken for calculating the
hydraulic conductivity of the fracture using the cube law,
b is fracture aperture (Heldman, 2016).
22. 22
developed. Only one trial, trial number 10, displayed somewhat traditional horizontal hydraulic
fractures. To counteract the negative effect of percolation, extensive surface rupture, and large
vertical dike development, compaction of the silica flour after the injection tube was inserted into
the plastic storage container was crucial. This reduced the amount of back-filling and fueled forward
propagation of the injection fluid. Higher viscosity injection fluid also hindered the development of
large vertical dikes. By bringing the injection fluid temperature down to 40 ºC and increasing the
amount of oil paint in the mixture, this increased the mixtures viscosity to 0.44 Pa from that of 0.11
Pa at 50 ºC.
Discussion of Results
Several factors may account for the highly variable fracture geometry displayed between
trials. One, the confining pressure and density of the silica flour varied for each trial. Two, the
temperature of the injection fluid was a rough estimate. Temperature of the oil reservoir was taken
prior to loading of the injection tube and the syringe, and for some trials, up to 2 minutes of time
would lapse before the fluid was injected, resulting in some cooling and increased viscosity. Third,
some silica flour was reused between trials. The portion of the silica flour that came into contact
with the injection fluid was discarded after each trial, however, all other flour was reused. While
packing procedures were kept constant, the reuse of the flour may have caused some clumping to
occur, creating zones of variable density and fracture preferential pathways. Four, injection rate was
not accounted for. While injection rate was kept slow to negate any inertial effects and turbulence
within the injection tube, since the flow rate was not measured it was not perfectly consistent
between trials. Five, trials were conducted over several days and some silica samples were left open
in the ambient laboratory. Moisture could have accumulated within the pores of the silica resulting
in clumping and furthering any error already addressed by number three.
23. 23
In previous studies, fracture aperture and permeability are highly dependent on the sample
size and normal stress (hereby referred to as confining pressure). For rocks that are undergoing
confining pressures larger than 5 MPa, fracture permeability essentially becomes zero (Rutqvist,
2015). This is partially due to the soft fracture infilling of minerals that solidify and clog the fracture
at high confining pressure. While our normal stress did not reach the magnitude of MPa, a
relationship between the confining pressure and fracture development was established. This was
primarily due to the proportional relationship between the confining pressure and the fracture
aperture and fracture propagation. Because the cube law equation (8) is so heavily dependent on the
fracture aperture, confining pressure is then positively related to the hydraulic conductivity of the
fracture and the unit permeability. Some problems noted by Rutqvist with small scale models is that
they are normally isotropic and lack the heterogeneities of the complex fracture systems they are
attempting to quantify. This makes it hard to utilize these models when predicting in-situ
permeability (Rutqvist, 2015). This is true for our model. It is near impossible to model stress-
permeability relationships for every point within the matrix of a rock body since so much internal
variability exists. Models can be used to estimate the overall rock stress-permeability relationship and
possible maximum and minimum values. Other factors that may affect permeability are fracture
frequency, mineral infilling, and temperature. Permeability generally displays an inverse relationship
with depth, however, local variations may make this relationship highly variable. Permeability is also
inversely related to temperature up to 150ºC under constant stress, due to mineralization of fractures
(Rutqvist, 2015), as was the case for this study. As noted by Domenico and Schwartz (1998), in
“fractured rocks, the interconnected discontinuities are … the main passage for fluid flow, with the
solid rock blocks considered impermeable”. While this is generally the case for low permeable units,
and our silica flour, we cannot say that this applies to all fluid media. In general, the static state
permeability of the modeled unit increased after fracture, though additional forces of stress my
change this fracture network, enhancing or impeding the flow.
24. 24
Comparing Results to Previous Research Studies of Stress-Strain Effects on Permeability
Not only is understanding how stress and strain processes effect the hydrogeology of a unit
important, but it is also necessary for geological engineers and safety personal, particularly in the
mining industry. While Darcy’s law defines permeability (K) as function of discharge (Q) over
hydraulic gradient and cross sectional area (i and A), it doesn’t take into account pressure and stress
affects that commonly occur in aquifers of different geologic media. As discharge velocity of a fluid
increases, so does the intrinsic permeability of the medium in which it is flowing (Rodrigues et al.,
2009). To understand these relationships, Wang and Park (2002) conducted lab experiments on
several types of geologic clastic media, ranging from mudstone to medium sandstone, to predict
behavior of groundwater in underground mines under confining pressures ranging from 25 to 444
MPa. During the testing, the researchers noted that the rock specimens underwent three stages of
deformation: linear elastic deformation, elasto-plastic deformation, and peak and post peak
deformation. They found that the fluid permeability for the specimen was directly related to the
evolution of the micro-fractures in the rock sample over the course of several stages (Wang & Park,
2002). While mineralogy and primary features of the rock determine the basic parameters of
permeability, as noted above, secondary features and changes to porosity and fracture aperture from
stress or strain can play a significant role in the overall permeability of the unit, as expressed by the
cube law. The researchers concluded that, in general, permeability was proportional to the pore
pressure and inversely proportional to the confining pressure (Wang & Park, 2002). Our results
showed that the fractures increased the hydraulic conductivity of the unit, ranging from 0.065 ~ 37
cm/s and was highly dependent on the fault geometry. Our results however yielded a more positive
relationship between confining pressure (normal stress) and fracture permeability as illustrated in
figure 11 A and B. Figure 11 A was graphed on linear axes with all data points. A clear outlier can be
25. 25
seen at ~1200 Pa of normal stress. This point was removed and then a semi-log scale for the
fracture permeability was graphed versus normal stress. By using a semi-log scale (figure 11 B), a
better relationship can be seen between the parameters of fracture length for high viscosity trials,
permeability and normal stress.
y = -3E-06x + 0.0349
R² = 0.0001
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800
FracturePermeability(cm2)
Normal Stress (Pa)
Fractured Permeability vs. NormalStress
y = 4E-05e0.0039x
R² = 0.2605
0
2
4
6
8
10
12
14
16
18
20
0.0001
0.001
0.01
0.1
1
800 1000 1200 1400 1600 1800
FractureLength(cm)
LogofFracturePermeability(cm2)
Normal Stress (Pa)
Log of FracturedPermeability andFracture Lengthvs. Normal
Stress
Fractured Permeability (cm2)
High Viscosity Fracture Length
Expon. (Fractured Permeability
(cm2))
Figure 11 A and B (top and bottom): (A) is graphed with linear axes and illustrates an outlier at ~1200 Pa which
was removed and then graphed on a semi-log scale to illustrate the positive relationship between confining pressure
(normal stress) and fracture permeability (B) and also illustrating a general positive relationship between fracture
length and normal stress (Heldman, 2016).
26. 26
Studies later by Gangi (1978) provided models to relate permeability to confining pressure, p,
of different porous materials. These too showed that generally permeability decreases with
increasing normalized confining pressure (Wang & Park, 2002). Further complicating these
scenarios, Li et al. (1994, 1997) investigated the permeability of the Yinzhuang sandstones under
several stress and strain parameters and found that the confining pressure has the greatest influence
on permeability in the strain-softening region and pore pressure only played a role under units with
very high permeability (Wang & Park, 2002). It seems that the literature that is available on this topic
is very controversial and inconclusive. With the addition of the results of this study, we gain better
understanding of these concepts, modeled by the general increase in the hydraulic conductivity of
the matrix when fractures are introduced into the system.
Critical Fracture Pressure needed for Hydraulic Fracturing
Natural gas, or shale gas, has become an important resource in the modern energy sector.
This shale gas, also referred to as “unconventional gas”, accumulates in tightly bound aquifers
(usually low permeable shales) and has become a profitable modern energy resource with the use of
hydraulic fracturing technology and horizontal drilling. Limiting the number of drilling pads and
allowing natural gas extraction to be conducted in regions not favorable to vertical drilling, are some
of the benefits from the use of horizontal drilling technology (Vidic, et al. 2013). Oklahoma, utilizing
this extraction process, has become an emerging center for natural gas production accounting for 7.1
percent of the total gross production for the United States producing 2,143,999 million ft.3
in 2013
("Oklahoma State Profile and Energy Estimates"). Hydraulic fracturing is the process by which a
high-pressure fluid is injected into the low permeable rock layers to create fractures and fracture
networks, modeled by the vegetable shortening mixture and silica flour (Domenico & Schwartz,
1998). These fractures serve as secondary porosity pathways that allow for the sequestration of the
27. 27
natural gas. When the fluid pressure exceeds the tensile strength of the rock, rupture will occur. It
was later, through experimental observation by Handlin (1969), that the pressure (Pcritical) needed for
critical failure of sedimentary rocks is 80% of the normal stress (σ) shown by the following equation:
P critical = 0.8 σ
Unlike Handlin, the average ratio of the critical pressure to confining pressure necessary
for rupture in this model was ~24 (see appendix 7). In this model, the critical fracture pressure was
much higher than the confining pressure. This could be explained by the misrepresentation of the
force. Force (P critical) was calculated by multiplying the mass (M) read from the scale during testing
by gravity (g) and divided by the cross sectional area (A2
) of the plunger of the syringe:
P critical = (M ● g)/ A
P critical – critical pressure (Pa)
M – mass (kg)
g – gravity (m/s2)
A – cross sectional area of plunger
Our results were too large, roughly by a factor of 10 when graphing the Mohr-Coulomb failure
envelope based on the line of best fit from figure 6 with the critical injection data from appendix 7
(see figure 12 A). If the critical fracture pressure values (kg/m2
) already accounted for the force of
gravity (since the values read from the scale might be measurements of weight and not mass), then
when calculating the criticalpressure force we would not need to multiple by gravity. If this was the
case, then the actual critical fracture pressure values would be those found in the “Critical Fracture
Pressure (kg/m2
)” column of appendix 7, reducing the ratio to ~2.4 and would fit the Mohr-
Coulomb failure envelope in figure 12 B.
Fluid pressure, usually created by water, has the ability to reduce the sliding frictional
resistance (shear resistance) between rock bodies so that displacement is possible (Domenico &
Schwartz, 1998). Attainment of sufficient fluid pressure depends a variety of factors including: 1)
presence of clay rocks, 2) interbedded sandstones, 3) large total thickness of rock beds, and 4) rapid
(10)
(11)
28. 28
-1400
-900
-400
100
600
1100
0 500 1000 1500 2000 2500 3000 3500 4000
ShearStress(Pa)
Normal Stress (Pa)
Mohr-Coulmb FailureEnvolpefor Critical FracturePressure
(kg/m2)
-1400
-900
-400
100
600
1100
0 500 1000 1500 2000 2500 3000 3500 4000
ShearStress(Pa)
Normal Stress (Pa)
Mohr-Coulmb FailureEnvolpefor Critical FracturePressure
(kg/m2)
Figure 12 A and B (top and bottom): Mohr-Coulomb failure envelope of critical pressure for failure within the
“sandbox” model. (A) Orange circle indicates Mohr circle of “Critical Fracture Pressure (Pa)” and (B) Mohr circle of
“Critical Fracture Pressure (kg/m2) blue line for both figures is the (τ=µ●σn + C) line established from figure 6
(Heldman, 2016).
29. 29
sedimentation (Domenico & Schwartz, 1998). Since high fluid pressure cannot be sustained
indefinitely, a fracture may occur, but without a large sudden displacement, pressure will build up
again and repeat the process (Domenico & Schwartz, 1998). Fluid pressure builds up between the
rock layers until it overcomes the shear friction between the units and allows for slippage, which acts
to temporarily relieve the stress (Domenico & Schwartz, 1998). So long that the system remains
under pressure, the process will repeat; where critical failure pressure is met, fracture occurs to
relieve pressure, and as soon as fracture ends, pressure builds up again to repeat the cycle. Gretener
(1972) noted that the movement of the rock bodies is “caterpillar” like, only moving inches and
centimeters at a time (Domenico & Schwartz, 1998). In this model, the “caterpillar” like movement
was indistinguishable, and in general, the initial critical pressure yielded the highest pressure value,
followed by a lower semi-constant injection pressure. This pattern of pressure spike, fracture,
pressure spike, fracture went unnoticed at this small a scale.
Hydraulic Fracturing and Induced Seismicity
Since the 1960s, scientists have been suspicious about the role of human interaction in
seismicity. One of the first examples of this was Rocky Mountain Arsenal in Denver, Colorado.
Here, deep-water injection wells were drilled to dispose of hazardous chemical weapons, which were
produced from the weapons plant on site (Healy et al., 1968). Injection began in 1962 and ended in
1966, coinciding with seismic activity beginning within months of the industrial activity and lasted
up to two decades after completion (Ellsworth, 2013). Several other factors can affect failure, as
noted by Dimenico and Schwartz, including 1) rate and duration of pressurization mechanisms, 2)
permeability and compressibility of the rock, 3) the degree to which the process is isolated from the
surface, 4) the orientation of the fault plane relative to principal stress and finally 5) the degree of
difference between the greatest and least principal stress (Domenico & Schwartz, 1998).
30. 30
In the United States, we see the most earthquake activity along the western plate boundary
on the Pacific coast. However, recently we have seen more and more seismic activity within the
interior of the United States, where faults are no longer tectonically active, as in the case of
Oklahoma. Recently, seismicactivity within the north and central portion of the state has become a
weekly phenomenon. The largest events to date occurred on November 6, 2011, and September 3,
2016, both a 5.6 magnitude earthquake struck central and north-central Oklahoma. The 2011 event
injured two people and 14 homes were destroyed (USGS, 2015). In fact, several tremors were
experience during 2011, resulting in millions of dollars in damage. The U.S. Geological Survey and
Oklahoma Geological Survey analysis found that 145 earthquakes of M≥ 3.0 occurred in Oklahoma
from January 2014 to May 2, 2014 (“Record Number of Oklahoma Tremors Raises Possibility of
Damaging Earthquakes”, 2014). During the previous year (2013), 109 earthquakes of this magnitude
were experienced in the state, and just merely two events of M≥ 3.0 from 1978 to 2008 (“Record
Number of Oklahoma Tremors Raises Possibility of Damaging Earthquakes”, 2014). Fortunately,
the 2016 event resulted in less structural damaged and only one injury (“Dozens of Wastewater
Wells Directed to Shut Down in OK”, 2016). In response to the 2016 event, the Oklahoma
Corporation Commission directed dozens of wastewater wells within 725 square miles of the 2016
epicenter to be systematicallyshut down. Because this event occurred within a historic fault line, the
commission decided that the wells must be shut down over the course of a few days after the event,
noting that a “sudden” shutdown would likely trigger another seismic event (“Dozens of Wastewater
Wells Directed to Shut Down in OK”, 2016).
The challenge with hydraulic fracturing is that anytime you drill for oil, you don’t just get oil.
Mixtures usually contain oil and connate water, originating from the bedrock. . The injected water
normally contains sand and other chemicals used to break up rock formations. Produced water is old
connate seawater that has dissolved oil and gas components within the matrix. Only about “5
percent of the total water is actually frack water… most of the water that comes back up was already
31. 31
there” (Asher, 2015). As noted by Bill Ellsworth, a geologist with the U.S. Geological Survey, “Even
in conventional oil fields, you might be five barrels of water and one barrel of oil” (Asher, 2015). In
Oklahoma, oil and gas that is extracted commonly has a high water to hydrocarbon ratio (Kress,
2016). For ever barrel of oil that is produced, companies are left with 10 to 15 barrels of wastewater
(Kress, 2016). With more and more production, companies need to find places to store the
produced water. Due to the difficulty and expense of treating produced waters, they are often re-
injected into the formation or nearby formations, making sure to inject these contaminated waters
deep enough so that they do not risk groundwater or farmland (Asher, 2015). Previously, companies
just re-injected it into the same formation, now they are injecting the production waters in
formations below the production fields (Asher, 2015).
A large majority of these fluids are being injected into the Arbuckle formation, ranging in
thickness up to 6,000 feet (Holland, 2015). This group, which is Cambrian to Ordovician in age, sits
directly above the crystalline basement, were most of induced seismicity is occurring (Holland,
2015). Disposal of wastewater into the Arbuckle formation has increased from about 20 million
barrels per year in 1997 to about 400 million barrels per year in 2013 (Than, 2015). With the increase
in fluid injection, faults have become pressurized, reducing the amount of time needed for pressure
build up to lead to a failure. Additionally, because pressure from the wastewater injection is
spreading throughout the Arbuckle formation, its effects can be felt hundreds of miles from the
injection site, leading to widespread seismicity and natural delayed effects from the pressure
propagation (Than, 2015). Solutions to the number and severity of the seismic events may be to
cease injection of produced water into the Arbuckle formation entirely (Than, 2015). Alternative
injection cites that have been considered are the Mississippian Lime, an oil-rich limestone layer, the
principal source of produced water in Oklahoma (Than, 2015). In other states like Colorado and
Wyoming, evaporation pits are used to dispose of wastewater, which are banned for use in
Oklahoma (Asher, 2015).
32. 32
Conclusion and Future Investigations
In this study, an analogue hydraulic fracturing fluid was injected into fine grained silica flour,
serving as an analogue for low permeable sedimentary rock. It was found that the development of
the fracture network was highly dependent on the confining pressure and viscosity of the injection
fluid. A general positive relationship was illustrated between the confining pressure, the viscosity and
the fracture length geometry (figure 11). Using the cube law, the fracture hydraulic conductivity was
calculated and used to determine the overall matrix permeability. The average permeability of the
fracture was 0.032 cm2
; increased from 2.7 x 10 -9
cm2
of the pre-fractured matrix. However, fracture
geometry was highly variable, where vertical dikes and surface rupture occurred within several trials.
Additionally, a general positive relationship was found between the confining pressure and
permeability of the fractured matrix when outlying data points were discarded.
Contamination that enters the system at the central Oklahoma aquifer has the potential to
discharge into the tributaries of the Mississippi River Basin. With an increase is seismicity in this
region, government and planning officials should be concerned about a result of increased
permeability and increased potential of extended contamination. It would be interesting for future
investigations to use the data presented in this paper to address this issue. With the average
permeability calculations, one could attempt to track potential contamination of the fracturing fluid
if released into the central Oklahoma formation. Using some mathematical analysis and 3D
modeling, one could attempt to calculate how long it would take the substance to reach nearby
groundwater aquifers and quantify any potential of increased contamination from the increased
permeability of highly fractured formations.
33. 33
Acknowledgements
I would like to thank Dale Lynch for his assistance in preliminary and primary testing
procedures and Peter Hornbach for his assistance in the collection of SEM images. I would also like
to thank Dr. Martin Helmke for his assistance in hydraulic conductivity and permeability calculations
and my advisor Dr. Howell Bosbyshell for his assistance in the creation of testing materials, testing
procedures and continued guidance throughout the preparation of this study.
34. 34
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39. 39
Appendix 3 A and B
Determining Shear Stress of Noncompacted Flour Mass to Displace ≥3mm (g) Shear Stress (Pa)
76.96 250.07
ρ (kg/m^3) 981.6224057 75.55 245.49
g (m/s^2) 9.81 83.82 272.36
H (m) 0.042 71.4 232.00
σn (Pa) 404.4480636 62.44 202.89
72.25 234.77
80.76 262.42
Displacement is defined by a movement of at least 3 mm 72.4 235.25
72.75 236.39
87.49 284.29
72.5 235.58
82.09 266.74
73.92 240.19
79.69 258.94
84.11 273.30
73.73 239.57
70.13 227.88
57.74 187.62
75.42 245.07
78.04 253.58
Avg 75.1595 244.22
Determining Shear Stress of Compacted Flour
Mass to Displace ≥3mm
(g) Shear Stress (Pa)
117.22 380.89
ρ (kg/m^3) 1248.00024 133.61 434.14
g (m/s^2) 9.81 138.39 449.68
D (cm) 6.2 119.76 389.14
A (cm^2) 30.1906991 97.07 315.41
A (m^2) 0.00301907 88.41 287.27
108.83 353.63
Displacement is defined by a movement of at least 3 mm 107.96 350.80
84.14 273.40
104.16 338.45
88.52 287.63
118.4 384.72
115.57 375.53
98.3 319.41
57.21 185.90
80.6 261.90
49.32 160.26
77.63 252.25
82.59 268.36
101.19 328.80
Avg 98.444 319.88
40. 40
Appendix 4
Determining Tensile Strength of Silica
Flour
Mass to Displace ≥3mm
(g)
Tensile Stress
(Pa)
Height
(cm)
Normal Stress σn
(Pa)
35.5347 -30.17 1.9 0
ρ (kg/m^3) 1248.00024 37.6173 -40.45 1.5 0
g (m/s^2) 9.81 34.38 -29.19 1.9 0
D (cm) 6.2 71.9033 -39.99 2.9 0
A (cm^2) 30.1906991 76.4626 -53.62 2.3 0
A (m^2) 0.00301907 56.4958 -35.05 2.6 0
60.3345 -42.31 2.3 0
77.079 -51.80 2.4 0
Avg -40.32
The normal stress is zero since the alpha angle is always 90, only forces acting on apparatus is tension
(which is negative)
41. 41
Appendix 5
Procedural Steps for Primary Testing
1) Set up the testing apparatus by adding 20 to 40 lbs. of silica flour to
the plastic storage container. Using the 48 lb. scale, measure and record
the weight of the material. Then pack the silica flour down using the
cardboard and measure and record the height of the compacted silica
flour. Insert a piece of straight plastic tubing (17 cm in length) into the
injection port on the plastic storage container to open a pathway for
the injection tube. Heat the vegetable shortening mixed with oil paint
in a 250 mL beaker to 40 °C over a hot plate. Using the syringe and
plastic tubing (38 cm) suction the injection fluid from the heated
reservoir, making sure not to trap any air. Insert the end of the
injection tube into the injection port a full 17cm. Stand the plunger of
the syringe on the 48 lb. scale and slowly press down on the syringe to
compress the plunger and inject the fluid. Measure and record the
highest weight value and lower constant weight value from the scale as
the “critical injection pressure” and “injection pressure” respectively.
2) After the injection process, allow the vegetable shortening mixture
to solidify, this typically takeabout 5 minutes at a room temperature of
~22 °C. Remove the injection tubing and syringe. Both the syringe and
injection tubing will need to be cleared of any leftover injection fluid.
If the fluid has become solid they will need to be heated in the 250 mL
beaker of vegetable shortening. Do not flush out the syringe or
injection tubing with water. Using the straight edge piece of sheet
metal, cut into the silica flour a few inches from the side opposite the
injection port on the plastic storage container.
3) Clear out all silica flour between the straight piece of sheet metal
and the end of the plastic storage container opposite the injection port.
Clearly away this material will allow for better extraction of the cross
sections. Remove the straight edge piece of sheet metal and replace it
with the “L” shaped edge sheet metal, making sure not to disturb the
silica flour in the process.
42. 42
4) Replace the straight edge piece of sheet metal fully into the silica
flour ~ 1” from the “L” shaped edge sheet metal. Then slowly lift up
both piece of sheet metal, trying not to disturb the silica flour trapped
between the two pieces of sheet metal and the remaining silica flour
left in the plastic storage container.
5) Once removed, lay both pieces of sheet metal horizontally or place
on a flat horizontal surface. Slowly lift the straight edge sheet metal
away from the “L” shaped edge sheet metal to reveal the silica flour in
the ~ 1” cross section.
6) Measure and record the height and width (in cm) of any fractures
that are found within the ~ 1” cross section.
7) Measure and record the distance from the injection port of any
fractures found within the ~1” cross section. Repeat steps 4 through 7
every ~1” working towards the injection port. Discard any silica flour
contaminated by the injection fluid. Then repeat all steps 1 through 7
for a total of 14 trails.
