Extraction of Natural Gas by Hydraulic Fracturing

EXTRACTION OF NATURAL GAS BY

HYDRAULIC FRACTURING

MICHAEL JOSEPH KNUDSEN

SUPERVISORY COMMITTEE:

DR. LOC VU-QUOC, MECHANICAL & AEROSPACE ENGINEERING

DR. WILLIAM E. LEAR, MECHANICAL & AEROSPACE ENGINEERING

DR. R. KEITH STANFILL, INDUSTRIAL & SYSTEMS ENGINEERING

A THESIS PRESENTED TO THE UNIVERSITY OF FLORIDA COLLEGE OF ENGINEERING IN

PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF

BACHELOR OF SCIENCE

MECHANICAL ENGINEERING

SUMMA CUM LAUDE

UNIVERSITY OF FLORIDA

2012

Extraction of Natural Gas by Hydraulic Fracturing Knudsen, Michael J. (2012)

2

2012 Michael Knudsen


3

Dedicated to

my parents for their undying love and support throughout my academic career and

my beautiful fianc for her patience and compassion


4

Acknowledgments

I would like to express my sincerest gratitude to Dr. Loc Vu-Quoc for his continuous guidance

throughout this year; his passion and excitement for engineering is inspiring, and I hope to have

that same fervor throughout my career.

I wish to thank Dr. R. Keith Stanfill for teaching me how to break down any given process in a

useful and informative way. The knowledge I have gained as one of his pupils will carry

forward into almost every aspect of my career as an engineer.

I would like to thank Dr. William E. Lear for his uncanny ability to explain many of the difficult

processes that engineers face every day. With influential mentors like Dr. Lear still in the

discipline, I am confident that I will be able to conquer anything with my engineering degrees.

Finally, I would like to thank the entire faculty and staff of the University of Floridas College of

Engineering for the education I have received. Without a doubt, I would not be the same person

today if I had never been a part of the Gator Nation.


5

Table of Contents

Acknowledgments........................................................................................................................... 4

Table of Figures .............................................................................................................................. 6

List of Tables .............................................................................................................................. 6

Abstract ........................................................................................................................................... 7

Introduction ..................................................................................................................................... 8

Horizontal Drilling .......................................................................................................................... 9

Hydraulic Fracture Theory ............................................................................................................ 11

Fracture Simulation and Discussion ............................................................................................. 23

Fracturing Fluids and Additives.................................................................................................... 26

Gas Locations and Environmental Concerns ................................................................................ 28

Future Presence of Hydraulic Fracturing ...................................................................................... 31

Conclusion .................................................................................................................................... 32

Works Cited .................................................................................................................................. 33

Appendix ....................................................................................................................................... 37


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Table of Figures

Figure 1: Horizontal Drilling ......................................................................................................... 9 Figure 2: Geosteering tool ........................................................................................................... 10 Figure 3: Crack propagation in an isotropic, linear elastic, impermeable body. ......................... 11 Figure 4: Fracture Modes I, II, and III ......................................................................................... 12

Figure 5: Tensile stress produced in a poroelastic material ......................................................... 13 Figure 6: PKN Model of Crack .................................................................................................... 16 Figure 7: KGD Model of a Crack ................................................................................................ 16

Figure 8: Radial Model of a Crack .............................................................................................. 16 Figure 9: In-Situ Stress vs. Depth ................................................................................................ 24 Figure 10: Minimum fracture extension pressure and maximum crack width as a function of

radius of fracture ........................................................................................................................... 25

Figure 10: US Shale Gas Resources ............................................................................................. 28 Figure 11: U.S. Natural Gas Production Projections, 1990-2035 ................................................ 31

List of Tables Table 1: Constant Propagation Parameters .................................................................................. 23

Table 2: Components in Fracturing Fluids .................................................................................. 27


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Abstract

Recent advancements in the controversial natural gas extraction method known as hydraulic

fracturing, or fracking, has been accompanied with an unparalleled wave of scrutiny over the

oil and gas industry. With the American energy industry shifting toward green initiatives,

environmental safety questions regarding fracking need to be answered quickly. Due to the

unconventional nature of this methodology, a sizeable amount of existing literature has

conflicting, overly technical views on the theory and dangers of hydraulic fracturing. The

purpose of this study is to familiarize scientists and engineers with the topic of hydraulic

fracturing at an introductory level by using a basic theoretical fracture model. For a Perkins-

Kern-Nordgren (PKN) fracture model, it was found that pressure drop controlled fracture width

and thus higher injection rates and more viscous fluids increased the maximum width of the

crack. Additionally, it was found that even with precautionary measures in place, ground water

pollution is not likely but possible if faulting of the rock formation occurs; this is a more

probable occurrence during horizontal rather than vertical drilling. Minor seismic activity was

discovered to be a consequence of fracking but the order of magnitude on the Richter scale made

this finding relatively insignificant.


8

Introduction

Nowhere is the promise of innovation greater than in American-made energyBut with only 2% of the worlds oil reserves, oil isnt enough. This country needs an all-out, all-of-the-above strategy that develops every

available source of American energy a strategy thats cleaner, cheaper, and full of new jobs. We have a supply of natural gas that can last America

nearly 100 yearsAmerica will develop this resource without putting the

health and safety of our citizens at risk.

President Barack Obama, 2012 State of the Union Address

With the American energy crisis rapidly growing, it is critical that the energy industry

turns to cleaner and cheaper domestic fuel resources to stop dependence on foreign oil. In 2009,

87% of natural gas consumed in the U.S. was produced in the United States. By 2035, the U.S.

Energy Information Administration (EIA) projects that 46% of domestically produced natural

gas will be obtained from shale rock formations, a 32% growth rate from shale gas produced in

2010. If the U.S. energy industry is able to harvest the domestic natural gas resources of

approximately 2,543 trillion cubic feet, American energy companies could supply up to 100

years of natural gas at the 2010 U.S. consumption rate (U.S. Department of Energy, 2012).

Hydraulic fracturing, colloquially referred to as fracking, has become a controversial

method of extracting natural gas reserves due to environmental concerns of groundwater

contamination. Fracking involves pumping high pressure fluids underground in order to crack

rock formations that contain natural gas. The high pressure fluids expand into pre-existing

fractures and forces crack growth underneath the surface. As the cracks continue to expand,

natural gas is released into the pipeline and is transported to the surface (Timmer, 2011).


9

Horizontal Drilling

A new type of oil and gas drilling technique is known as horizontal or directional drilling.

The well bore reaches depths of up to 10,000 feet in the rock formation before gradually turning

horizontal and through the porous rock reservoir where the natural gas is trapped. Figure 1

depicts the process of hydraulic fracturing and horizontal well drilling at such depths (U.S.

Department of Energy, 2012). The corner at which this gradual turn begins to take place in the

well is known as the kickoff point. Horizontal wells can extend up to five miles away from the

initial drill rig on the ground which makes this new technique extremely advantageous. As

hydraulic fracturing continues along the horizontal well, several pockets of natural gas are able

to be extracted that would have previously required new wells to be drilled. This has become

advantageous for natural gas wells with lower porosity because of the ability to obtain gas in

lateral shale rock (Union Town Energy).

Figure 1: Horizontal Drilling


10

In horizontal drilling, the reservoirs length works to the drilling companys advantage, as

the well provides the ability to produce more natural gas from one well. However, horizontal

wells are nearly 300% more costly than a standard vertical well. Therefore, horizontal drilling is

only employed when it becomes economically feasible; this could include higher production

rates, or lower permeability in the horizontal direction (Helms, 2008).

A horizontal well is drilled by adding a hydraulic motor or geosteering tool above the

drill bit as shown in Figure 2. This allows the drilling engineer to have steering control over the

well without having to explicitly alter the orientation of the main drill. Sensors on the

geosteering tool allow the user to find current position, as well as calculate the probable drill

path. These sensors also give the drilling engineer environmental information such as pressures,

temperatures, and forces that the bit is seeing. These readings are what drive the drilling fluid

and ultimately controls the hydraulic motor.

Figure 2: Geosteering tool (Helms, 2008)

Several improvements have been and will continue to be seen in the methodology used in

horizontal fracturing. Distances achieved in horizontal drilling have grown from 400 to 8,000

feet over the last 50 years. Further improvements continue to be made by casing the well into

the rock formation which allows the operators to use a lower density drilling mud. Once the

desired horizontal displacement is reached, fracking is completed in intervals from the end of the

well back toward the vertical borehole to extract natural gas from the reservoir (Helms, 2008).


11

Hydraulic Fracture Theory

The theory behind fracking is simply that natural gas can be extracted through porous

rock mass by creating enough pressure to stimulate crack growth. This crack growth is created

by sending pressurized pumping fluid through the well to average depths of 3000 meters at high

flow rates to expand into existing fractures (J. Daniel Arthur, 2008). When the drilling fluid

pressure is greater than the in-situ stress of the rock mass, fracture occurs which allows the fluid

to continue expanding further into the material.

Some simplifying assumptions are necessary in order to create a solvable model of the

hydraulic fracturing theory. As exemplified in Figure 3, the material in which the steady-state

crack growth is assumed to occur in an isotropic, homogeneous, linear elastic, impermeable

body. The pressurized fluid is assumed to be an incompressible fluid acting with power-law

shear thinning flow.

Figure 3: Crack propagation in an isotropic, linear elastic, impermeable body.


12

As the pressure from the fluid rises above the combination of the lowest principal stress

and the tensile strength of the soil material, tensile failure occurs. While this can happen

naturally, human-controlled fractures are caused by continual pumping of the fluid into the

borehole of the well. As the fluid is pumped, the pressure increases and will first fracture normal

to the location and direction of smallest resistance.

In general, a fracture typically comprises of some form of mechanical discontinuity in or

on a material. In crack growth, materials can experience three different modes of fracture during

failure which can occur on an individual or combined basis as shown in Figure 4. Mode I

fracture occurs when the walls of a crack propagate in a normal direction away from one another.

Mode II fracture occurs in shear where the crack walls propagate in a sliding away from one

another. Mode III fracture occurs in shear where the crack walls propagate in a tearing direction

away from one another (Lacazette, 2000). Any of these three modes of fracture may occur

during hydraulic fracturing depending on the orientation of existing cracks in relation to the well

borehole that has been drilled. Mode I fracture is the most common type of fracture mode that

occurs in hydraulic fracturing and will be assumed through the remainder of this investigation.

Figure 4: Fracture Modes I, II, and III


13

Figure 5: Tensile stress produced in a poroelastic material (Fjar, Holt, Horsrud, Raaen, & Risnes, 2008)

The pressure required to propagate the fracture is the result of three different

components: the pressure that maintains the crack opening in the direction of the smallest

principal stress, the pressure seen while pumping fracking fluid into the wellbore, and the

pressure required to overcome the tensile strength at the actual fracture tip (Fjar, Holt, Horsrud,

Raaen, & Risnes, 2008). Figure 5 represents a poroelastic structure in which pressure that occurs

between the pores is controlled at the valve, and the overall effective stress is the difference

between the in-situ stress and the pore pressure as in (1).

(1)

The in-situ vertical stress will change with depth due in large part to changes in density of

the rock formations along with the effects of the gravitational force. Assuming a constant

gravitational acceleration and a depth, h, the vertical stress can be found in (2) where the z is


14

along the zenith axis which points radially inward to the center of the earth and z = 0 lies at the

start of the well.

( )

(2)

Assuming a constant density gradient, this reduces to (3). Note that this is an

oversimplification, as rock layers are bound to have varying rock densities. For the purpose of

roughly estimating the vertical in-situ stress, , the constant density gradient approximation is

appropriate.

(3)

The in-situ stresses and are taken to be the three principal stresses acting in the

rock material and therefore are the eigenvalues of the stress tensor at that location. The vertical

stress, , is represented by (3) while the horizontal stresses and represent the maximum

and minimum horizontal stresses respectively. The maximum horizontal stress is orthogonal to

the minimum horizontal stress and is larger due to additional external tectonic stresses that exist

in the rock. The minimum horizontal stress can be related to the vertical in-situ stress by (4)

(Environmental Protection Agency, 2011).

( ) (4)


15

where is the Poissons ratio of the rock material, is the pore pressure, and are

Biots parameters for the vertical and horizontal directions, and is the external tectonic

stress. For simplification purposes, the Biots parameters are taken to be and

Thus, the minimum horizontal in-situ stress reduces to (5).

( ) (5)

There are many models that have been employed in the study of hydraulic fracturing

mechanics. In this study, a simplified linear elastic hydraulic fracture (LEHF) model is

developed to determine how fracturing fluid viscosity and injection flow rate affect the overall

growth of fractures. The Perkins-Kern-Nordgren (PKN) fracture model is shown in Figure 6 and

is typically accepted for fractures where

where H/2 is the semi-major axis of an ellipse

and L is the length of the crack which propagates in the direction of L. The PKN model assumes

plane strain in the vertical plane with a constant elastic modulus. Similarly, the Khristianovic-

Geertsma-de Klerk (KGD) fracture model is represented in Figure 7 and is applicable for short

fractures. The KGD model assumes a plane-strain condition in the horizontal plane and thus the

fracture propagation is independent of height. The radial fracture model is shown in Figure 8

and assumes the crack propagation is radially outward from the well borehole (Valencia, 2005).


16

Figure 6: PKN Model of Crack (J. Adachi, 2007)

Figure 7: KGD Model of a Crack (J. Adachi, 2007)

Figure 8: Radial Model of a Crack (J. Adachi, 2007)


17

The following analysis of a hydraulic fracture implements the PKN fracture model for

crack widths resulting from Newtonian fluids in laminar flow for vertical fractures (Perkins,

1961). The fluid dynamics of the fracking fluid that occurs inside a crack is governed by

Poiseuille flow (Yuan, 1997). In general, fracture mechanics follow three governing equations:

the elasticity equation, the lubrication equation, and the continuity equation. For the purposes of

this study, the following assumptions were made (Perkins, 1961):

Assumptions:

2-Dimensional

Laminar flow

Vertical fracture

Elliptical crack

Brittle, elastic rock material

Isotropic

Constant rock material properties

Incompressible Newtonian fluid

No leak-off in the fracking fluid

Constant fluid injection rate, Q (implies negligible leak-off and accumulation)

Constant fluid viscosity,

Thin film lubrication theory, h/L


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Perkins and Kern have found that the propagation of a crack is completely driven by the fluid

pressure drop through the aperture. Beginning with the Fanning equation yields (6):

(6)

where f is the friction factor, v is the velocity of the fluid, is the density of the fluid, and De is

the equivalent diameter. For laminar flow, the friction factor is defined as in (7):

(7)

According to Perry, for an ellipse with an eccentricity of approximately zero (Perry, 1950),

(

) (8)

where RH is the hydraulic radius (which can be computed as the area divided by the wetted

perimeter), and is a proportionality constant. The velocity of the fluid in the fracture can be

expressed as the flow rate per unit area in the elliptical crack as shown in (9) for laminar flow:

(9)

Using laminar flow on the same ellipse, the pressure gradient can be written as in (10):

(10)

By equating (6) and (10) and substituting (7), (8) and (9), one can solve for the proportionality

constant as in (11)-(16).


19

(

) (

)

(11)

( )

(12)

(13)

[ ( )]

(14)

(15)

As , the proportionality constant can be solved for and is assumed to remain constant

throughout the crack propagation.

(16)

The Reynolds number for laminar flows (Re < 2500) is defined in (17). By substituting (8) and

(9), and expressing the fluid density in terms of the specific gravity, (17) can be simplified into

(20) as shown below. A condition exists for laminar flow, ( )

so that the Reynolds

number does not exceed 2500; these equations are only valid for this criterion (Perkins, 1961).

(17)

(

) (

)

(18)

( )

(19)

( )

(20)


20

Substituting (7), (8) and (9) into (6), we see that:

(

( )

)( )

( )

( )

( )

(21)

This crack width is a function of the pressure, so a separation of variables is performed in

equation (21) to solve for the effective pressure distribution by substituting the Sneddon equation

in (23); the Sneddon equation is used to solve for the crack width at any point along the fracture.

Assuming Qx is a constant, in other words there is no leakoff and no accumulation that takes

place, equations (22) and (23) are combined with known initial conditions and integrated to yield

the pressure distribution in (29).

( )

( )

(22)

( )( )

(23)

( )

( ( )( )

)

(24)

( ) ( )

( )

(25)

( )| (26)

( ) ( )

( )

( )

(27)


21

( )

( )

(28)

( ) [

( ) ]

(29)

Plugging (29) back into (23) yields the following:

( )

[

( ) ]

(30)

[ ( )

]

(31)

Assuming a constant Poissons ratio of v = 0.15, equation (31) becomes:

[

]

(32)

Where Q is expressed in (bbl/min), is expressed in (cP), L is expressed in (ft), and E is

expressed in (psi). By applying the dimensional analysis in (33), the width equation becomes

equation (34) as derived by Perkins and Kern.

(

)(

) (

) (

) (

)

(33)

[

]

[

]

(34)

R.A. Sack derived Eq. (35) by means of an energy balance. This is the minimum pressure that is

required to overcome the pressure difference due to the in-situ stress and extend the fracture

(Perkins, 1961).

( ) [

( ) ]

(35)


22

Where is the specific surface energy of the rock and C is the fracture radius. Equation (35)

yields that the minimum pressure required to extend the fracture varies inversely as in the square

root of fracture radius given a constant specific surface energy, modulus of elasticity, and

Poissons ratio (Perkins, 1961). The total crack width for a uniform pressure acting over the

surface of the crack in a plane perpendicular to total earth stress yields (36):

( )( )

(

)

(36)

where C is the maximum fracture radius and r is a variable along the direction of C. The

maximum crack width occurs when r = 0 (Perkins, 1961).

( )( )

(37)


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Fracture Simulation and Discussion

In this study, a MATLAB model for hydraulic fracturing crack growth was developed

using the Perkins-Kern-Nordgren (PKN) model geometry and the hydraulic fracture theory

previously described. The model was meant to show how minimum fracture pressure and

maximum aperture width varied with radius of fracture. A set of parameters displayed in Table 1

were used as constants throughout the fracture simulation. These values were taken from

averages found in the literature (Hydraulic Fracturing Analysis). The simulation was performed

for up to a fracture radius of 200 ft away from the wellbore. The MATLAB code for this

simulation can be found in the Appendix.

Table 1: Constant Propagation Parameters

Constant Propagation Parameters

Poissons Ratio

Crack Height

Youngs Modulus

Specific Surface Energy

Specific Gravity

Max Radius of Fracture


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Figure 9: In-Situ Stress vs. Depth

Figure 9 shows how the in-situ stress varies as a function of depth in the horizontal and

vertical directions. As natural gas well depths are reached, the vertical in-situ stress begins to

greatly out-weigh the minimum-horizontal stress. This means when pressurized fluid is pumped

into the wellbore, the pressure will cause fracture in the horizontal direction since the horizontal

in-situ stress will be overcome more easily. If the tectonic stresses are high enough however, the

horizontal stress can be larger than the vertical in-situ stress. In this scenario, the fracture would

propagate in the vertical direction.

0 10 20 30 40 50 60

0

500

1000

1500

2000

2500

3000

Stress ( [MPa])

Depth

(h [

m])

In-Situ Stress vs. Depth

v

h


25

Figure 10: Minimum fracture extension pressure and maximum crack width as a function of radius of fracture

Figure 11 shows the plots of minimum fracture extension pressure (35) and maximum

crack width at the wellbore (37) as a function of radius fracture. It can be seen that crack widths

are controlled by the pressure drop in the fluid for static conditions with no fluid leak-off. For

very small fracture radii, extremely high injection pressures are necessary to fracture the walls.

The higher pressures, however, would widen the crack faster, allowing the injection pressure

required to drop even further. The fluid pressure at the crack tip asymptotically decreases toward

the in-situ stresses in the ground due to tectonic stress. As seen here, the pressure drop in the

fluid drives the crack width propagation; the larger the pressure drop, the larger the crack width.

By association, high fluid injection rates, Q, and fluids with larger viscosities (more proppant

slurry), , tend to produce larger crack widths while low Q and will result in slender cracks

(Perkins, 1961).

0 20 40 60 80 100 120 140 160 180 2000

20

40

60

80

100

120

140

(P-

), m

in f

ractu

re e

xte

nsio

n p

ressure

(psi)

c, radius of fracture (ft)

0 20 40 60 80 100 120 140 160 180 2000

0.005

0.01

0.015

0.02

0.025

0.03

Max C

rack W

idth

at

Well

Bore

(in

)

Min Fracture Extension Pressure

Max Crack Width


26

Fracturing Fluids and Additives

Hydraulic fracturing can be performed using a multitude of various fracking fluids.

These fracking fluids may be selected depending on the type of rock and depths at which

fracturing is desired. A typical fracture process involves four stages in which the following types

of fracking fluids are used: a prepad, a pad, a proppant, and a flush. A prepad is a low-viscosity

saline solution pumped down into the borehole to prevent rock formation damage and typically

contains some form of fluid loss prevention additives and surfactants. Subsequently, a viscous

pad fluid is initially pumped into the borehole and pressurized to actually produce the fractures.

Proppants are particles that are then added to lower viscosity fracking fluids to sustain fractures

because closure can occur pretty quickly due to the high underground pressures. Finally, flush

fluids are used to clean out the fracture fluid from underground (Fink, 2003).

Fracking fluids are often considered to be a water-based, oil-based, multiphase, or

surfactant-based gel that may or may not contain a proppant pack. In the majority of cases,

water-based gels are used but are becoming more controversial due to the residue they leave in

rock formations after fracking is completed (Hydraulic Gel Fracturing, 2005). These water-

based solutions contain additives that precipitate proppant delivery and stimulate crack growth.

There are certainly pros and cons to each type of fracking fluid. Oil-based fluids tend to have a

higher risk of explosion or fire than do water-based fluids. Multiphase fluids are fracturing

fluids that contain a second phase and are typically categorized as foams and emulsions. These

fluids can be obtained by adding various gases or hydrocarbons to change fluid properties such

as viscosity and temperature sensitivity. Foams tend to be lower pressure while emulsions tend

to be higher pressure and both are low temperature fluids that lose viscosity with increasing


27

temperature. Due to the additional phase that is added to the fracturing gels, multiphase fluids

are often more expensive than water-based and oil-based fluids. Surfactant-based fluids are

newly developed fluids that significantly improve leak-off control and proppant delivery. Other

surfactant-based fracking gels are currently being developed to reduce the damage seen in

individual fractures which will ultimately diminish the overall reservoir damage. Table 2,

reproduced from Oil Field Chemicals, displays various components and functions of additives

and fracturing fluids (Fink, 2003).

Table 2: Components in Fracturing Fluids


28

Gas Locations and Environmental Concerns

According to the United States Energy Information Administration (EIA), shale gas

makes up 60.64 trillion cubic feet (tcf) of total natural gas production each year which is nearly a

quarter of annual U.S. natural gas production. Figure 11 shows the shale gas map of the U.S. as

of 2011, with the largest reservoirs, the Marcellus, Haynesville, and Barnett shale formations

comprising of over 500 trillion cubic feet of natural gas resources. Another notable player is the

Bakken formation in North Dakota, which is primarily a shale oil reservoir (U.S. Energy

Information Administration, 2011).

Figure 11: US Shale Gas Resources (U.S. Energy Information Administration, 2011)


29

With the American energy industry trending toward green energy, profitable natural gas

production is becoming a critical source of revenue for successful oil and gas companies.

Natural gas is considered a cleaner form of energy due to its lower levels of carbon emissions

during combustion when compared to other natural resources. With new approaches like

hydraulic fracturing making its way into industry, catastrophic events such as the 2010

Deepwater Horizon oil spill have caused environmental concerns regarding oil and gas

technology to be at an all-time high. Among other concerns, environmentalists are worried about

the effect hydraulic fracturing is having on contaminating drinking water, causing earthquakes or

other seismic activity, and ruining the land by introducing foreign chemicals into the soil (U.S.

Department of Energy, 2012).

With water-based fracking fluids constantly being used, some environmentalists are not

only concerned about contaminating groundwater but also with the amount of water used to

perform hydraulic fracturing. For a typical natural gas well, approximately 4.5 million gallons of

water are used during the hydraulic fracturing process; this number is only expected to increase

with the growing production of natural gas. However, many companies currently drilling for

natural gas use resources other than fresh drinking water to achieve these amounts including

municipal wastewater, groundwater, and reusing fracking water (Chesapeake Energy). Another

concern is the contamination of the ground water in aquifers surrounding gas wells. Several laws

have been implemented into industry by the Ground Water Protection Council (GWPC) in order

to regulate the environmental consequences of hydraulic fracturing on groundwater sustainability

and quality. According to the GWPC, the potential for hydraulic fracturing to adversely affect

ground water aquifers is as low as one in 200 million (Chesapeake Energy). This is because


30

most underground aquifers are less than 1,000 feet deep, while hydraulic fracturing occurs up to

10,000 feet deep, i.e., significantly below the water table (Baker Hughes, 2011).

However, since most fracking fluids are water-based, other oily chemical additives tend

to have lower densities than water and at high pressures underground can start to separate out of

the fracking water. This separation ultimately allows for the fracking chemicals to become

pollutants in naturally occurring groundwater formations by making their way through the shale

rock. More often than not, pollution due to hydraulic fracturing is caused by a failure in the well

casing or by geological faulting due to high fracking pressures. According to a study done by

Otsego 2000, from a pressure standpoint, the horizontal hydrofracturing of shale is effectively

the explosion of a massive pipe bomb underground (Northrup, 2010). During these effective

explosions, faulting may occur that creates a path for natural gas or fracking fluid to escape to

the underwater aquifers. The Environmental Protection Agency has not released an official

statement regarding the effects hydraulic fracturing has on drinking water and is currently

investigating in a 3-year study (United States Environmental Protection Agency, 2012).

Another growing concern of environmentalists is seismic activity induced by hydraulic

fracturing. In multiple studies, it has been found that hydraulic fracturing does cause an increase

in seismic activity, however, on the Richter scale, these minor tremors typically rank somewhere

between -4.5 to -1 which are not felt above ground. According to Oklahoma seismologist Austin

Holland, the seismic activity caused by hydraulic fracturing is really quite inconsequential

(America's Natural Gas Alliance). In accordance with Holland, the U.S. Department of Energy

officially stated that hydrofracturing to intentionally create permeability rarely creates unwanted

induced seismicity large enough to be detected on the surface even with very sensitive sensors,

let alone be a hazard or an annoyance (Colorado Oil & Gas Association, 2012).


31

Future Presence of Hydraulic Fracturing

According to the EIA as of 2012, the United States has approximately 2,214 tcf of

technically recoverable gas. With lower drilling costs and a shift toward green energy, it is

plausible that natural gas production will significantly increase over the next twenty years.

Figure 12 shows the EIAs natural gas projections through 2035. President Obamas 2012 State

of the Union Address statement that the U.S. has enough natural gas to provide power over the

next 100 years is true based only on the 2010 production rate. With the growth projections seen

in Figure 12 comes higher demand, and thus higher production rates would be required for

natural gas drilling agencies. Although natural gas production is still in its early stages of

economic feasibility, natural gas certainly appears to be quickly making its way to the global

energy market.

Figure 12: U.S. Natural Gas Production Projections, 1990-2035 (U.S. Energy Information Administration, 2011)


32

Conclusion

In conclusion, the controversial method of hydraulic fracturing is going to be a critical

component of the oil and gas industry over the next 30 years. There are many tools available to

engineers today that can be help model hydraulic fracturing, but the fundamental models stem

from crack propagation governed by the elasticity, lubrication, and continuity equations. As

outlined by Perkins and Kern, it was found that crack widths are controlled by the pressure drop

in the fluid for static conditions in laminar flow. In general, high fluid injection rates and highly

viscous fluids are more advantageous in expanding an aperture. Some of these highly viscous

fluids begin to behave like a non-Newtonian fluid which changes the analysis quite a bit.

Fracking fluids are delivered in three main stages: a prepad (surface protection and preparation),

a frac pack (which includes a pad such as water and proppant such as sand), and a flush which

cleans out the fracture fluid after the natural gas has been extracted. Proppants are necessary

additives to fluids because the particles are used to prevent closure in the fractures due to the

highly compressive stresses seen underground. Although no official statement has been released

by the EPA regarding the safety of fracking, there have been some observations where fracking

has caused an increase in pollutants in the groundwater around drilling sites as well as an

increase in seismic activity. However, fracking has been performed for well over 50 years and is

often employed in natural gas and oil wells today. With the surge in green initiatives in the

American energy industry, the U.S. will more than likely experience a large growth as predicted

by the EIA. This recent boom in natural gas means perfecting the understanding of this

technology is pertinent to the future profitability of the energy industry as well as the safety of

the environment.


33

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37

Appendix

MATLAB CODE:

%This MATLAB simulation is based on the PKN crack model %Perkins, T.K., Kern (1961). Widths of Hydraulic Fractures. %Journal of Petroleum Technology, 937-949.

%Constant parameters H = 40; %ft Q = 30; %bbl/min mu = 4; %cP SpGr = 0.9; %dimensionless parameter E = 4e6; %psi nu = 0.15; c = 0:1:200; %fracture radius, ft alpha = 0.01; %specific surface energy Pm_sig = sqrt(pi*alpha*E./(2*(1-nu^2).*c)); %minimum pressure difference W = 8.*(Pm_sig).*c*12/(pi*E); %max crack width [ax,h1,h2] = plotyy(c,Pm_sig,c,W) %double plot

%figure properties axis(ax(1),[0 200 0 140]) set(ax(1),'YTick',[0 20 40 60 80 100 120 140]) set(get(ax(1),'Ylabel'),'String','(P-\sigma), min fracture extension pressure

(psi)') axis(ax(2),[0 200 0 0.03]) set(ax(2),'YTick',0:.03/6:.03) set(get(ax(2),'Ylabel'),'String','Max Crack Width at Well Bore (in)') set(h1,'LineStyle','-','linewidth',1.5) set(h2,'LineStyle','--','linewidth',1.5) xlabel('c, radius of fracture (ft)') legend('Min Fracture Extension Pressure','Max Crack Width')

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Extraction of Natural Gas by Hydraulic Fracturing