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

1

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

2

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.

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

3

(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 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

4

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

5

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 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

6

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).

7

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

8

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

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).

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 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

Determining Analogue Material Appropriateness

Hydraulic Fracturing Fluid Analogue:

Hydraulic fracturing fluid normally consists of water mixed with other

chemicals and proppants to increase the efficiency of the fracturing

process. For example, a proppant that is typically used is sand, which is

required to create a void space and hold open the fracture after pumping

has ceased (Vidic et al., 2013). Chemical additives, such as acids, friction

reducers, and gelling agents are determined based on the geological

characteristics of the site. Acids may be used to clean the well bore and

dissolve minerals to minimize the buildup of metal oxides in the well.

Friction reducers, like petroleum and other alcohols, help minimize the

friction between the fracking fluid and the pipe (Vidic et al., 2013). Gelling

agents, like guar gum or xantham gum, increase the viscosity of the water,

giving it the ability to hold larger amounts of sand in suspension (Vidic et

al., 2013). When several additives are used together, the fluid is deemed

crosslinked gel (“Fracturing Fluids 101”, 2012). Due to the increased

additives, these fluids have a high viscosity (100-1000 cP or 0.1-1 Pas) and

produce wider fractures (“Fracturing Fluids 101”, 2012). Consequently,

they are also more damaging to the proppant pack are frequently used in oil

and high liquid wells (“Fracturing Fluids 101”, 2012). While some states

require chemical additives to be listed for public access, most of the over

750 chemicals that are used are not regulated by the U.S. Safe Drinking

Water Act, which raises concerns about possible sources of ground water

contamination (Vidic et al., 2013). For operation of a single well, 2 to 7

million gallons of water are needed for the hydraulic fracturing process, not

only serving as a potential source of contamination, but also posing a threat

on water quantity during periods of drought (Vidic et al., 2013).

For this investigation, Crisco © vegetable shortening will be used as

the analogue for the hydraulic fracturing fluid. The benefits of using this

testing material are its low melting point and its ability to remain solid at

room temperature. When choosing an injection fluid it was necessary for it

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

11

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 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 12

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.

13

These materials were also chosen because they are chemically and

physically incompatible with the injection material, that is to say, if the

injection fluid is hydrophobic, a hydrophilic granular material is needed.

These materials have a calculated bulk density of 1.34 g/cm 3 and were

mixed to create a homogenous mixture (grain sizes were similar enough

that the mixture was deemed homogenous) (Galland et al., 2006). Since

both materials showed a Mohr-Coulomb failure envelope, they were suitable

to model brittle upper crust. They chose to use vegetable oil at 50 °C

(viscosity of 0.02 Pas) to represent the magma, which was allowed to cool to

room temperature and solidify after the fracturing process. The procedure

outlined in this paper follows several of the parameters of the Galland et al.

(2006) research.

Materials used in Experimentation

AGSCO Silica Flour #325 Crisco © All-Vegetable Shortening

Plastic Storage Container (42.9cm x 29.2cm x 23.5cm)

2 oz. plastic syringe 4 PVC coupling (6.2mm x 4.2 mm)

Rind Stand 4”x6” base, 18” rod

Ring Support Stainless Steel Fishing line

Everbuilt Clothesline Separator

2 oz. Plastic Drinking Cups Digital Scale Thunder Group SCSL005 GT-40 48 lb. Portion Control Scale

Hot Plate Thermometer 100 ml Graduated cylinder250 ml beakers Plastic tubing All American © Black Oil

Paint“Magic Coasters” Modeling Clay TimerFalling Head Permeameter Housing Chamber Collection Container“Straight Edge” and “L” shaped Sheet Metal Extraction Tools

36cm x 28 cm piece of cardboard

Computer with Microsoft Excel and PowerPoint

Green Cleaning Scrubbers Camera Tablespoon scoopula14

Table 1: List of testing materials (Heldman, 2016).

15

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 calculate initial

hydraulic 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 = dr2 •L • ln Ho dc2•t Ht

16

(1)

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)

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 17

Vertical

LeverTubing

Tubing

Entering Port and Filter

Exit Port and Filter

Housing Chamber

Ho

Measuring tool

SampleCollection

Container

Figure 4: Schematic of Falling Head Permeameter Testing Apparatus (Heldman, 2016).

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 Steel Fishing 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 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 18

τσnSilica FlourDHMobile Upper

CylinderStationary Lower

CylinderHanging WiresRing Stand

M

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)

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

19

(2)

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 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

20

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).

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 21

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

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

Source Particle d (microns)

ρ (g/cm3) C (Pa) T (Pa) µ

Galland et al. (2006)

SI-CRYSTAL ~10-20SI-SPHERE ~30

1.33 + 0.2%1.56 + 0.18%

288 + 261.5

88 + 17Negligible

0.840+ 0.042

Experiment #325 Si Flour ~17.8 1.25 105.63 40.32 0.5992When 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 22

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).

Mobile Plate

Fixed PlateHalf PVC Coupling

“Magic Coasters”

M

Silica flour

Silica flour

Pulley

Eye hook

Top View of Tensile Schematics

Vertical Gap: 2mm

represented by the equation τ = µ ● σn + C graphed as the linear line of best

fit (Galland et al., 2006).

Next, we determined if the vegetable shortening has a similar

viscosity as the hydraulic fracturing fluid to determine its appropriateness

as an analogue. The temperature at which the Crisco © All-Vegetable

shortening melts is ~ 33°C, similar to the Vegetaline produced by ASTRA

used in Galland et al. study (2006). This was established by placing a 50 mL

sample into a 250 mL beaker and heated over a hot plate. The sample was

then allowed to cool back to room temperature, ~22 ºC, taking about 5

minutes to transitioning from a liquid to solid. The time and temperature at

which the vegetable shortening solidifies is appropriate for this experiment

and will allow extensive fracture networks to develop prior to the fluid

solidifying. The density of the oil was then calculated (Table 3) as

23

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).

0.901g/mL at ~33ºC (liquid) and as 0.902 g/ml ~31ºC (solid). As the oil

solidified, the volume decreased by less than 0.1%, negligible for the

purposes of this experiment. Because the vegetable shortening becomes

white when cooled, and would become indistinguishable from the silica

flour, so black oil paint was added to the shortening to tint the mixture. This

did not greatly affect its density.

To determine viscosity (ν), the vegetable shortening mixture was

heated to 50 °C and poured into a 100 mL graduated cylinder to the 100 mL

mark. Next, spheres of modeling clay with a diameter of 0.6 cm were

dropped into the vegetable oil. The time required for the clay sphere to fall

18 cm on average was ~1 second at 50 °C over 6 trails. Additional testing

of viscosity of the vegetable shortening mixture were conducted at 40 °C.

The average time it took the modeling clay to fall 18 cm for these trails was

4.9 seconds over 4 trails. Viscosity was then calculated by the following

equation and results are noted in table 3 (Stokes Law, 1851):

ν = 2 (ρ sphere – ρ liq) g r2 / (9 V)

ρ sphere – density of clay sphere (g/mL)ρ liq – density of liquid at 50°C (g/mL)g – gravity (cm/s2)r –radius (cm)V- velocity (cm/s)

Temperature (°C)

Density (g/mL)

Viscosity (g/cm• s)

Viscosity (Pa•s)

Solid Vegetable Shortening

31 0.9018 - -

Liquid Vegetable Shortening

50 0.9009 1.126 0.1126

24

(5)

MixtureLiquid Vegetable Shortening Mixture

40 0.8595 4.381 0.4381

Principal Testing Procedures and Methods

The principal testing procedures were carried out for a total of 14

trials, using the apparatus outlined in figure 8. These steps are outline in

appendix 5. Results and images from testing procedure can be found in

appendix 6 and 7. It was found that better results were achieved when the

viscosity of the injection fluid was increased. This was done by lowering the

injection temperature to 40 °C. These trails are deemed “high viscosity

trials” (trials 6-14) and conversely, the “low viscosity trials” at 50 °C (trials

25

Table 3: Properties of the Crisco © All-Vegetable shortening, density and viscosity were calculated based on methods mentioned below (Heldman, 2016).

48 lb. Scale

Sheet Metal Extraction Tools

Injection Tubing

Plastic Syringe

Hot Plate

Heated Oil Reservoir

Plastic Storage Container

Silica Flour

Figure 8: Principal Testing Apparatus. Oil is extracted from the reservoir using injection tubing connected to the plastic syringe and injected into the silica flour housed in the plastic storage container. Pressure of injection are read from the scale as the tester pushed down on the plunger during injection. Once solidified, the samples are then extracted using the sheet metal extraction tools in ~1” cross sections (Heldman, 2016).

1-5). Each trial resulted in highly variable fracture geometry and trials 1, 4,

and 13 displayed no fracturing.

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 gradientA - cross sectional area (cm2)

Using the cube law, fracture permeability can be calculated by the following

(Snow, 1965):

kf = b 3 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

26

(7)

(8)

(9)

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 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.

27

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 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

28

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.

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 29

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

30

permeability of the modeled unit increased after fracture, though additional

forces of stress my change this fracture network, enhancing or impeding

the flow.

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

31

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 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.

32

800 900 1000 1100 1200 1300 1400 1500 1600 1700 18000

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

f(x) = − 2.60936733181305E-06 x + 0.0348691010088018R² = 0.000116347056058896

Fractured Permeability vs. Normal Stress

Normal Stress (Pa)

Frac

ture

Per

mea

bilit

y (c

m2)

800 1000 1200 1400 1600 18000.0001

0.001

0.01

0.1

02468101214161820

f(x) = 3.96875635937012E-05 exp( 0.00394976388651321 x )R² = 0.260538949349272

Log of Fractured Permeability and Fracture Length vs. Normal Stress

Fractured Permeability (cm2)Exponential (Fractured Permeability (cm2))High Viscosity Fracture Length

Normal Stress (Pa)

Log

of F

ract

ure

Perm

eabi

lity

(cm

2)

Fracture Length (cm)

33

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

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

34

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 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)/ AP critical – critical pressure (Pa)M – mass (kg)g – gravity (m/s2)A – cross sectional area of plunger

35

(11

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 critical pressure 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

36

0 500 1000 1500 2000 2500 3000 3500 4000

-1400

-900

-400

100

600

1100

Mohr-Coulmb Failure Envolpe for Critical Fracture Pressure (kg/m2)

Normal Stress (Pa)

Shea

r Str

ess (

Pa)

37

sed

imentation (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 38

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).

 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, seismic activity within the north and central portion of the state

39

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 systematically shut 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

40

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 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 41

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).

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 42

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.

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 43

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.

44

Resources:

Asher, S. (2015, September 13). Who’s at fault? High injection rates add pressure to Oklahoma’s basement rock. Retrieved November 11, 2016, from http://www.enidnews.com/news/earthquakes/who-s-at-fault-high-injection-rates-add-pressure-to/article_dc81b0fe-59bb-11e5-92ba-af22acecf4c8.html

Berkowitz, B. (2002). Characterizing flow and transport in fractured geological media: A review. Advances in Water Resources, 25, 861-884. Domenico, P., & Schwartz, F. (1998). Hydraulic Conductivity and Permeability of Geologic Materials. In Physical and chemical hydrogeology (2nd ed.). New York: Wiley.

Byerlee, J. (1978). Friction of rocks. Pure and applied geophysics, 116(4-5), 615-626.

Domenico, P., & Schwartz, F. (1998). Hydraulic Conductivity and Permeability of Geologic Materials. In Physical and chemical hydrogeology (2nd ed.). New York: Wiley.

Domenico, P., & Schwartz, F. (1998). Stress, Strain and Pore Fluids. In Physical and chemical hydrogeology (2nd ed.). New York: Wiley.

“Dozens of Wastewater Wells Directed to Shut Down in OK. (2016, September 3). Retrieved September 6, 2016, from http://www.news9.com/story/33009543/dozens-of-wastewater-wells-directed-to-shut-down-in-ok

Ellsworth, William. Injection-Induced Earthquakes, 2013. Science, vol. 341, no. 6142, July 12, 2013.http://www/sciencemag.org.proxy-wcupa.kinpa.org.

Ellsworth, William. “Overview of Induced Seismicity”  Keynote Speech, Induced Seismicity in the Midcontinent from American Geoscience Institute, April 7, 2015.

Fetter, C. (2001). Properties of Aquifers. In Applied Hydrogeology (4th ed.). Upper Saddle River, New Jersey: Prentice Hall.

“Fracturing Fluids 101”. (2012). Retrieved June 7, 2016, from http://www.hexionfracline.com/fracturing-fluids-101

Galland, O., Cobbold, P. R., Hallot, E., de Bremond d’Ars, J., & Delavaud, G. (2006). Use of vegetable oil and silica powder for scale modelling of magmatic intrusion in a deforming brittle crust. Earth and Planetary Science Letters, 243(3), 786-804.

Handin,J. (1969). On the Coulomb–Mohr failure criterion. Journal of Geophysical Research, 74 (1969), pp. 5343–5348

Healy J.H., Rubey W.W., Griggs D.T., 1968, The Denver earthquakes: Science, v. 161, p. 1301–1310, doi:10.1126/science.161.3848.1301.

Holland, Austin. “Potential for Induced Seismicity and Current Mitigation Efforts within Oklahoma.” Keynote Speech, Induced Seismicity in the Midcontinent from American Geoscience Institute, April 7, 2015.

Hubbert, M. K. (1937). Theory of scale models as applied to the study of geologic structures. Geological Society of America Bulletin, 48(10), 1459-1520.

Hubbert, M. K. (1951). Mechanical basis for certain familiar geologic structures. Geological Society of America Bulletin, 62(4), 355-372.

Hubbert, M.K., Willis, D.G., (1957). Mechanics of Hydraulic Fracturing. Petroleum Transactions of the American Institute of Mining Engineers, 210, (153-168).

45

Hydraulic Fracturing: The Process. (2010, July 20). Retrieved November 8, 2016, from http://fracfocus.org/hydraulic-fracturing-how-it-works/hydraulic-fracturing-process.

Krantz, R. W. (1991). Measurements of friction coefficients and cohesion for faulting and fault reactivation in laboratory models using sand and sand mixtures. Tectonophysics, 188(1-2), 203-207.

Kress, R. (2016, January 25). Separating Fact From Fiction On Oklahoma Earthquakes. Retrieved October 18, 2016, from http://energyfuse.org/separating-fact-from-fiction-on-oklahoma-earthquakes.

Miller, I., & Brodsky. (2012). United States Well Data Resource Links. Retrieved December 2, 2015, from http://www.pmc.ucsc.edu/~ivmiller/

Morley, C. K. (1999). How successful are analogue models in addressing the influence of pre-existing fabrics on rift structure?. Journal of Structural Geology, 21(8), 1267-1274.

“Oklahoma State Profile and Energy Estimates.” Rankings: Natural Gas Marketed Production, 2013. U.S. Energy Information Administration (EIA), 2013. Web. 12 Oct. 2015.http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd

Powers, S. (1931). Structural geology of northeastern Oklahoma. The Journal of Geology, 117-132.

“Record Number of Oklahoma Tremors Raises Possibility of Damaging Earthquakes”, Joint Statement on Oklahoma Earthquakes, May 2, 2014, http://earthquake.usgs.gov/regional/ceus/products/newsrelease_05022014.php

Rodrigues, N., Cobbold, P. R., & Løseth, H. (2009). Physical modelling of sand injectites. Tectonophysics, 474(3), 610-632.

Rutqvist, J. (2015). Fractured rock stress‐permeability relationships from in situ data and effects of temperature and chemical‐mechanical couplings. Geofluids, 15(1-2), 48-66.

Sang, Q., Li, Y., Zhu, C., Zhang, S., & Dong, M. (2016). Experimental investigation of shale gas production with different pressure depletion schemes. Fuel, 186, 293-304.

Seismic Monitoring Program. (2010). Oklahoma Geological Survey, Retrieved December 2, 2015, fromhttp://www.okgeosurvey1.gov/pages/earthquakes/catalogs.php

Schellart, W. P. (2000). Shear test results for cohesion and friction coefficients for different granular materials: scaling implications for their usage in analogue modelling. Tectonophysics, 324(1), 1-16.

Snow, D.T. (1965) A parallel plate model of fractured permeable media. PhD Thesis Univ. of Calif., Berkeley.Than, B. K. (2015, June 18). Oklahoma earthquakes linked to oil and gas wastewater

disposal wells, say Stanford researchers. Retrieved November 8, 2016, from http://news.stanford.edu/2015/06/18/okla-quake-drilling-061815/

USGS, “Magnitude 5.6 – OKLAHOMA.” Earthquake Hazards Program, 2015. Accessed April 28, 2015. http://earthquake.usgs.gov/earthquakes/eqinthenews/2011/usb0006klz/#sum .

46

Wang, J., & Park, H. (2002). Fluid permeability of sedimentary rocks in a complete stress–strain process. Engineering Geology, 63(3-4), 291-300. Retrieved December 2, 2015, from http://www.sciencedirect.com/science/article/pii/S0013795201000886

 Wines, Michael. “Oklahoma Recognizes Role of Drilling in Earthquakes.” New York Times, 21 Apr. 2015. Accessed April, 27 2015. http://www.nytimes.com/2015/04/22/us/klahoma-acknowledges-wastewater-from-oil-and-gas-wells-as-major-cause-of-quakes.html?_r=0.

Vidic, R. et al (2013, May 17). Impact of Shale Gas Development on Regional Water Quality. SCIENCE, 826-836.

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Appendix 1

48

Appendix 2

Falling Head Permeameter Testing

49

Permeability of Silica flour testing

K=dr^2*L /(dc^2*t)*ln(Ho/Ht)

Trail 1 Trail 2 Trail 3dr= 0.5cm 0.45 0.45 0.45L= 15.24cm 4.2 4.2 4.2dc= 7.62cm 3.3 3.3 3.3t= 12.8s 250 120 700Ho= 75cm 38 36 36Ht= 10cm 10 10 10

K= 0.0103cm/s2.34E-

04 5.08E-04 8.71E-05

Average:

0.0002764

Trial 1

Head (cm) Time (s) Trial 2

Head (cm) Time (s) Trial 3

Head (cm) Time (s)

80.6 0 85.4 0 87.9 0

37.5 2 45 1 55 0.5

35.5 11 36 2 36 6

35 15 35.5 3 35.5 13

34.5 19 34.5 6 35 20

34 28 34 8 34.5 37

33.5 39 33.5 13 34 75

33 54 33 18 33.8 112

32.5 107 32.5 26 33.5 185

32 168 32 36

31.5 313 31.5 60

31 94

30.7 125

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Appendix 3 A and BDetermining Shear Stress of Noncompacted Flour

Mass to Displace ≥3mm (g)

Shear Stress (Pa)

76.96 250.07

ρ (kg/m^3)981.622405

7 75.55 245.49g (m/s^2) 9.81 83.82 272.36H (m) 0.042 71.4 232.00

σn (Pa)404.448063

6 62.44 202.8972.25 234.7780.76 262.42

Displacement is defined by a movement of at least 3 mm 72.4 235.25

72.75 236.3987.49 284.2972.5 235.58

82.09 266.7473.92 240.1979.69 258.9484.11 273.3073.73 239.5770.13 227.8857.74 187.6275.42 245.0778.04 253.58

Avg 75.1595 244.22Determining Shear Stress of Compacted Flour

Mass to Displace ≥3mm (g)

Shear Stress (Pa)

117.22 380.89ρ (kg/m^3) 1248.00024 133.61 434.14g (m/s^2) 9.81 138.39 449.68D (cm) 6.2 119.76 389.14A (cm^2) 30.1906991 97.07 315.41A (m^2) 0.00301907 88.41 287.27

108.83 353.63Displacement is defined by a movement of at least 3 mm 107.96 350.80

84.14 273.40104.16 338.45

88.52 287.63118.4 384.72

115.57 375.5398.3 319.41

57.21 185.9080.6 261.90

49.32 160.2677.63 252.2582.59 268.36

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101.19 328.80Avg 98.444 319.88

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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)1248.000

24 37.6173 -40.45 1.5 0g (m/s^2) 9.81 34.38 -29.19 1.9 0D (cm) 6.2 71.9033 -39.99 2.9 0

A (cm^2)30.19069

91 76.4626 -53.62 2.3 0

A (m^2)0.003019

07 56.4958 -35.05 2.6 060.3345 -42.31 2.3 0

77.079 -51.80 2.4 0Avg -40.32

The normal stress is zero since the alpha angle is always 90, only forces acting on apparatus is tension (which is negative)

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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 take about 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

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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.

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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

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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.

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Appendix 6

58

Appendix 7

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Principal Testing Data

Appendix 8

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Appendix 9

61

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Appendix 10

Trial number

Fracture

aperture (cm)

Number of

Fractures

Fracture Spacing

(cm)

Hydraulic Conductivity of Fracture (cm/s)

Permeability of Fractured unit

(cm2)

Increase in

Permeability (cm2)

1* * * * * *2 0.4 1 1 4.1818 0.0053 0.00533 0.2 1 1 0.5227 0.0007 0.00074* * * * * *5 0.1 1 1 0.0653 0.0003 0.00036 0.3 1 1 0.4534 0.0023 0.00227 0.5 1 1 2.0992 0.0104 0.01048 1.3 1 1 36.8961 0.1831 0.18319 0.7 1 1 5.7603 0.0286 0.0286

10 0.3 1 1 0.4534 0.0023 0.002211 0.8 1 1 8.5984 0.0427 0.042712 0.8 1 1 8.5984 0.0427 0.042713* * * * * *14 0.7 1 1 5.7603 0.0286 0.0286

* percolation around injection tube occurred- no fractures present

ρ fluid 0.9009g/cm3

g 980cm/s2Average: 0.0315 0.0315

ν low (trials 1-5) 1.1260g/cmsν high (trials 6-14) 4.3810g/cms

k silica flour 0.0003cm/sK unfractured unit with H2O

2.7240E-09cm2

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