HYDRAULIC FRACTURING · during a hydraulic fracture treatment. 11 (3-2). Distribution of the stress and the direction of the created fracture perpendicular to the minimum stress in

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Ministry of Higher Education and Scientific Research

University of Misan

Department of Petroleum Engineering

HYDRAULIC FRACTURING

Set by the Students

MOHAMMED KAREEM

SAJJAD RAHEEM

HAIDER MOHAMMAD

Under the supervision of

Dr. MOHAMMED ABDUL AMEER

II

Acknowledgment ______________________________ V

ABSTRACT __________________________________ 1

CHAPTER ONE ______________________________ 2

INTRODUCTION ___________________________ 2

CHAPTER TWO ______________________________ 4

LITERATURE REVIEW _____________________ 4

CHAPTER THREE ____________________________ 8

THEORETICAL BACKGROUND _____________ 8

3-1 Hydraulic Fracturing Process ________________ 8

1- Pre Pad Stage of Thin Fluids _________________ 8

2- Pad Stage of Viscous Fluid __________________ 9

3- Proppant Laden Stage_______________________ 9

4- Flush Stage _______________________________ 9

3-1-1 Candidate Selection ____________________ 10

3-1-2 The Physics of Fracturing ________________ 11

3-2 Fracture Geometry _______________________ 13

3-2-1 The KGD Model _______________________ 13

3-2-2 The PKN model _______________________ 15

3-3 Productivity of Fractured Wells _____________ 16

3-4 Hydraulic Fracturing Design _______________ 20

3-6 Selection of Proppant _____________________ 21

3-7 The maximum Treatment Pressure ___________ 24

3-8 Selection of Fracture Model ________________ 25

Index

III

3-9 Propped fracture width ____________________ 25

3-10 Proppant schedule ______________________ 27

CHAPTER FOUR ____________________________ 29

THEORETICAL WORK ____________________ 29

CHAPTER FIVE _____________________________ 35

CONCLUSIONS AND RECOMMENDATIONS _ 35

5-1: Conclusion: ____________________________ 35

5-2: Recommendation: _______________________ 37

REFERENCES ______________________________ 38

List of figures

IV

List of figures No. page (2-1). Chart for determination of the

particle bridging conditions

forPerforations.

6

(3-1). Expected pressure response

during a hydraulic fracture

treatment.

11

(3-2). Distribution of the stress and

the direction of the created fracture

perpendicular to the minimum stress

in horizontal well

12

(3-3). Borehole shape indicates stress

direction. 12

(3-4). Hydraulic fracture dimension

after propagation. 13

(3-5). The KGD fracture geometry. 15 (3-6).The PKN fracture geometry. 16 (3-7). Relationship between fracture

conductivity and equivalent skin

factor.

18

(3-8). Effect of fracture closure stress

on proppant pack permeability.

22

(3-9). Overburden formation of a

hydrocarbon. 22

(3-10).proppant profile development

during hydraulic fracture treatment. 28

(4-1). onset of proppant slurry and

continuous proppant addition. 34

List of figures

V

Acknowledgment

First and foremost, we would like to thank our research supervisor Dr.Mohammed

Abdul Ameerwhosewithout his assistance and dedicated involvement in every step

throughout the process, this research would have never been accomplished.

Getting through our dissertation required more than academic support, we have

many people to thankfor listening to and, at times, having to tolerate us over the

past four years, we cannot begin to express our gratitude and appreciation for their

friendship. They have been unwavering in their personal and professional support

during the time we spent at the university.

Most importantly, none of this could have happened without our families who

offered us encouragement, support and their unconditional love over the last

several years, that is why we are forever grateful.

Abstract

1

ABSTRACT

Hydraulic Fracturing consists of pumping a viscous fluid at a sufficiently high

pressure into the completion interval so that a two winged, hydraulic fracture is

formed. This fracture is then filled with a high conductivity, proppant which holds

the fracture open (maintains a high conductivity path to the wellbore) after the

treatment is finished.The propped fracture can have a width between 5mm and

35mmand a length of 100m or more, depending on the design technique employed

and thesize of the treatment.

The KGD and PKN are the most common models that describe the fracture

geometry (the KGD model assumes the height of the fracture is much greater than

its length while the PKN model assumes that the fracture length is at least three

times the height).

the productivity of fractured wellsdepends on two steps:

(1) Receiving fluids from formation.

(2) Transporting the received fluid to the wellbore.

Usually one of the steps is a limiting step that controlsthe well-production rate.

The concentration of proppant in fracturing fluid should not exceed certain value

(critical value) of concentration to prevent the phenomena of screen out (a

blocking of the fracture path caused by bridging the path or accumulation of the

proppant inside the fracture, clumping or lodging of the (solid particles) proppant

across the hydraulic fracture width).in addition to proppant concentration there are

another conditions that leads to screen out during the hydraulic fracturing job in a

well which are the ratio between the fracture widths to particle diameter that called

(β) and wall roughness.

Introduction Chapter One

2

CHAPTER ONE

INTRODUCTION

Hydraulic fracturing is a well stimulation method where a fluid is pumped into the

rock to create fractures that called hydraulic fracture. These fractures are intended

to function as high-conductivity fluid pathways enabling increased productivity of

a well

Ina hydraulic fracture is using a pressure to causehydraulic fracture, caused by

injecting of a fracturing fluid into a selected rock formation need to stimulate.

Fracturing fluid is pumped toward the selected formation need to stimulate using a

pressure that exceeds the formation fracture pressure.

Hydraulic fracturing deals with injection high viscosity fluid called (fracturing

fluid), down to the wellbore at a flow rate, which isgreater than the fluid leak-off

rate into the both sides of the hydraulic fracture so that it builds-up pressure to

overcome the tensile strength of the formation rock and create an effective

communication between the stimulated formation and the wellbore. The effect is

the initiation and propagation of crack or fractures on a plane perpendicular on the

least principal stress.

The success of hydraulic fracturing job depends on a large extent on the hydraulic

fracture dimensions: half length, width and height of the hydraulic fractures, as

well as the proppants, fracturing fluids, treatment schedule etc. The mechanical

properties that control fracture geometry are Young's model, which is primary

control of the fracture width, where the fracture height is primarily controlled by

minimum closure stress contrasts.

After fracturing the reservoir, a propping agent which is non compressible solid

particle material, such as sand or ceramic beads that are added to the fracturing

Introduction Chapter One

3

fluid to form a slurry that is pumped into the new generated fracture in the

formation, in order to prevent the fracture from fully closing again when the

pumping pressure is released. This causesboth sides or walls of the hydraulic

fracture to compress onto the proppant, i.e. the proppantis trapped between the

fractures faces,generating a high-permeable path way or high conductivity, that

allows the oil and/ or natural gas to flow into the well and then to the surface.

Theproppant transportability of a base fluid depends on the type of additives which

control the viscosity, added to the water base.

The main principal physical properties of the proppants affecting the hydraulic

fractures conductivity are proppant grain sizedistribution, strength, roundness,

quantities of fines (proppant), density, and sphericity.

During hydraulic fracturing job, engineers need to maintain a constant rate of

fracturing fluid injection.

Chapter Two Literature Review

4

CHAPTER TWO

LITERATURE REVIEW

Howard, 1970(1), defined the Hydraulic fracturing as the process of creating a

fracture, or hydraulic fracture system, in a permeable and porous medium by

injecting a fluid under pressure through a wellbore in order to overcome in situ

stresses and cause the material to fall and create hydraulic fracture.

Pai et al, 1983(2),Investigated that the Injection rate during the hydraulic fracturing

job, affect hydraulic fracture height and fluid distribution in the fracture is critical

to the success of the fracture job. Decreasing in injection rate during later treatment

stages, reduces the fracture height, further growth chance and also prevent

equipment overload pressure during high solid particles (proppant) concentration

pumping. But, high injection rates during the fracturing job is necessary to carry

the proppant in the fracturing fluid and to reduce the probability of premature

screen out during treatment. The same results obtained by the researchers Pai et al

1983(3).DeltefMader 1989(4).

P.J.Hudson 1992(5).investigated when hydraulic fracture reorientation occurs, the

fluid flow limitation can be happened or created because of tortuosity and reduce

in the width of the fracture in the region affected. Because of this unwanted effect

on the pressure of injection and production. Without controlling of this

phenomenon, by orienting the wellbore, selectively with the field of stress,

propagation the size of the hydraulic fracture can be described by abnormally high

pressures treating because of increasing in friction happened by roughness of the

fracture wall, flow restriction, and tortuosity.


5

Plugging or bridge of pores of porous formation and perforation in oil wells occur

a lot during various operation in gas and oil industry, including perforation, water

flooding, drilling, work over, and hydraulic fracturing. Solid Particles migrate and

moves at high concentration with solid particles to hole size ratio, that may lead to

form plug or bridge narrow down and across perforation and pore throat, cause

reduction of flow rate through the formation. This may lead to sever damage and

reduction in the productivity of the gas and oil wells. The operators in that case

need to adjust the conditions for avoiding the plugging of pore and perforation by

suspended particles. Pai 1992 (5).found the same results.

King, 1997(6),showed that the values of β are very close to the values of 2 and 6

indicated by Figure (2-1) given by Gruesbeck and Collins (1982) (7).for bridging of

particles in perforations.

Civan2000(8).studied the value of the parameter β, and he indicated that the flow of

a particulate suspension into porous media may lead to one of the following

phenomena.

a. β <3, external filter cake formation

b. 3< β <7, internal filter cake formation

c. β >7, negligible filter cake involvement

β = DT/DP is the pore – to - particles dimension less β.


6

Richard 2013(9), presented that during hydraulic fracturing job, engineers need to

maintain a constant rate of fracturing fluid injection. The volume that inject

includes the additional volume created during stimulation and the fluid loss to the

formation because of leak off through the permeable wall of the two sides of the

fracture. However, the rate of leak off during the growing fracture tip is extremely

high. Therefore, it is not possible to initiate a hydraulic fracture with proppant in

the fracturing fluid because the high fluid loss (leak off) would cause the proppant

at the fracture tip to reach the consistency of a dry solid, which lead to bridge and

screen out conditions. For that, some volume of clean fluid—a pad—must be

pumped before any proppant is pumped.

Fig (2-1). Chart for determination of the particle bridging conditions for

Perforations.


7

Brekke 2014(10)., presented a problem, that called screen out, can occur during the

fracturing job. Screen outs, happen when a continued injection of fluid into the

fracture requires pressure above the safe limitations of the wellbore and surface

equipment.

These conditions occur because of the high fluid leakage to the formation, high

concentration of proppants, and an insufficient pad size that blocks the flow of

proppants. For that, pressure rapidly builds up. Screen out can disrupt a hydraulic

fracturing operation and need to clean of the wellbore before take back the fracture

job. A delay in one hydraulic fracturing job can cause disruption on the completion

and production of subsequent fractures.

Yongping Li2015(11), presented that the fracture system geometry becomes

complicated, because of the dense natural fracture distribution in the treated

formation and around wellbore fracture tortuosity appears. More over the natural

fracture increase the fracturing leak off rate to the treated formation, which can

hardly be made up with high pumping rate because of high treatment pressure

limit. Because of these factors make the screen out be prone to happen during the

fracturing treatment.

https://www.onepetro.org/search?q=dc_creator%3A%28%22Li%2C+Yongping%22%29

Chapter Three Theoretical Background

8

CHAPTER THREE

THEORETICAL BACKGROUND

3-1 Hydraulic Fracturing Process

Hydraulic Fracturing Process consist of four stages (Job sequence), Shah 2008(12).

1. Pre-pad Stage or pre-pad volume.

2. Pad Stage or pad volume.

3. Proppant-laden stage or proppant-laden volume.

4. Flush stage or displacement volume.

The hydraulic fracturing sequence shown in fig (3-1)

Fracture propagates in a plane perpendicular to the least principal normal stress.

The least principal stress normal to the plane of the fracture is shut-in pressure Ps

fig (3-2 and 3-3). Once the fracture is created then it can be closed by reducing the

borehole pressure and raising it again above the value Ps. However, the pack

pressure required to reopen the fracture is less than Pc1 (fig (3-1)) since the tensile

strength of the rock has already been overcome.

1- Pre Pad Stage of Thin Fluids

function is to initiate a fracture and to cool down formation in hot wells

( T > 250 oF)

pre pad stage requires about 10% of the total volume

Water & friction reducer (low concentration polymer solution, under

turbulent flow)

low concentrations - liquid : 1/4 gal or 1/2 gal per 1000 gal

Solid: 1/2 lb to 4 lb/Mgal


9

quality of water is important

clay stabilizers : 2% KCl or 2% CaCl2

fluid loss additives : 10 to 20 lb/Mgal polymeric solution

2- Pad Stage of Viscous Fluid

function is to aid in conditioning the created fracture and to Insure

fracture width, length and height

Pad stage requires about 40% of the total volume

Fluid type

Uncross linked or cross linked water based fluid

oil based fluid

foam based fluid

emulsions

3- Proppant Laden Stage

function is to help transport and distribute proppant into

fracture

Stage requires about 40% of the total volume

contains viscous fluid and proppant

4- Flush Stage

function is to displace proppant laden fluid into the fracture

stage requires about 10% of the total volume

contains thin fluid; same as in the pre-pad stage

avoid over displacement- so fracture won’t close


10

3-1-1 Candidate Selection, Shah 2008 (12),Andreas Reinicke 2010(13)

success in a fracturing treatment depends on proper selection of

candidate

consider permeability, skin factor, gas-in-place, mechanical

conditions

parameters used to select a candidate are

Parameter Symbol Parameter weighing factor

Permeability/ viscosity K/ 0.25

Porosity 0.05

Skin s 0.2

Net pay thickness h 0.1

Water saturation Sw 0.1

Formation depth D 0.05

Formation pressure

gradient Gp 0.1

Drainage area A 0.05

Wellbore condition Wd 0.1


11

Pre

ssure

Time

Pc2

Breakdown pressure

Shut

in

Fracture

extension Pressure (propagation)

Resuming Pumping

Ps

Pc1

3-1-2 The Physics of Fracturing

Richard Nolen 2013 (14), stated that the size and orientation of a fracture, and the

magnitude of the pressure needed to create it, are dictated by the formation’s in situ

stress field.

Hydraulic fractures open in the direction of the least principal stress and propagate

in the plane of the greatest and intermediate stresses.

Fig (3-1) Expected pressure response during a hydraulic fracture

treatment. Shah 2008(12).


12

Fig (3-3) Borehole shape indicates stress direction(14)

Fig (3-2) Distribution of the stress and the direction of the created

fracture perpendicular to the minimum stress in horizontal well(14)


13

The fracture shape after propagation will appear as shown in fig (3-4). The

dimension of the hydraulic fracture denoted as (h) for fracture height, (L) for

fracture half-length and (w) for fracture width.

3-2 Fracture Geometry

It is still controversial about whether a single fracture or multiple fractures are

created in a hydraulic fracturing job. Whereas both cases have been evidenced

based on the information collected from tiltmeters and micro seismic data, it is

commonly accepted that each individual fracture is sheet-like. However, the shape

of the fracture varies as predicted by different models.

3-2-1 The KGD Model

Assuming that a fixed-height vertical fracture is propagated in a well-confined pay

zone (i.e., the stresses in the layers above and below the pay zone are large enough

to prevent fracture growth out of the pay zone), Khristianovich and Zheltov (1955)

Fig (3-4). Hydraulic fracture dimension after propagation.

h


14

presented a fracture model as shown in Fig (3-5). The model assumes that the

width of the crack at any distance from the well is independent of vertical position,

which is a reasonable approximation for a fracture with height much greater than

its length. Their solution included the fracture mechanics aspects of the fracture

tip.

They assumed that the flow rate in the fracture was constant, and that the pressure

in the fracture could be approximated by a constant pressure in the majority of the

fracture body, except for a small region near the tip with no fluid penetration, and

hence, no fluid pressure. This concept of fluid lag has remained an element of the

mechanics of the fracture tip. Geertsma and de Klerk (1969) gave a much simpler

solution to the same problem. The solution is now referred to as the KGD model.

The average width of the KGD fracture is expressed as

�̅� = 0.29 [𝑞𝑖𝜇(1−𝑣)𝑥𝑓

2

𝐺ℎ𝑓]

14⁄ (

𝜋

4) ……….(3-1)

Where

�̅� : average width, in.

𝑞𝑖 : pumping rate, bpm

𝜇 : fluid viscosity, cp

G: E/2(1 + v), shear modulus, psia

ℎ𝑓 : fracture height, ft


15

3-2-2 The PKN model

Perkins and Kern (1961) also derived a solution for a fixed height vertical fracture

as illustrated in Fig. (3-6). Nordgren (1972) added leakoff and storage within the

fracture (due to increasing width) to the Perkins and Kern model, deriving what is

now known as the PKN model. The average width of the PKN fracture is

expressed as:

�̅� = 0.3 [𝑞𝑖𝜇(1−𝑣)𝑥𝑓

𝐺]

14⁄ (

𝜋

4𝛾)……… (3-2)

Where ƴ = 0.75.

The PKN model has an elliptical shape at the wellbore, the maximum is at the

centerline of this ellipse, with zero width at the top and the bottom.

(3-5). The KGD fracture geometry.


16

For Newtonian fluid the maximum width when the fracture half-length is equal to

xf, is given by:

ωmax = 0.3 [qi μ (1−v )xf

G]

14⁄ ……… (3-3)

It is important to emphasize that even for contained fractures, the PKN solution is

only valid when the fracture length is at least three times the height.

3-3 Productivity of Fractured Wells

Hydraulically created fractures gather fluids from reservoir matrix and provide

channels for the fluid to flow into wellbores. Apparently, the productivity of

fractured wells depends on two steps: (1) receiving fluids from formation and (2)

transporting the received fluid to the wellbore. Usually one of the steps is a

limiting step that controls the well-production rate. The efficiency of the first step

Fig(3-6) The PKN fracture geometry (15).


17

depends on fracture dimension (length and height), and the efficiency of the second

step depends on fracture permeability. The relative importance of each of the steps

can be analyzed using the concept of fracture conductivity defined as (Argawal et

al., 1979; Cinco-Ley and Samaniego,1981):

𝐹𝐶𝐷 = 𝐾𝑓𝑤

𝐾𝑥𝑓 ……… (3-4)

where

𝐹𝐶𝐷: fracture conductivity, dimensionless

𝑘𝑓 : fracture permeability, md

w: fracture width, ft

𝑥𝑓: fracture half-length, ft.

In the situations in which the fracture dimension is much less than the drainage

area of the well, the long-term productivity of the fractured well can be estimated

assuming pseudo-radial flow in the reservoir. Then the inflow equation can be

written as:

𝑞 = 𝑘ℎ (𝑝𝑒− 𝑝𝑤𝑓)

141.2 𝐵𝜇 (ln𝑟𝑒𝑟𝑤

+𝑆𝑓) ……… (3-5)

Where 𝑆𝑓is the equivalent skin factor. The fold of increase can be expressed as:

𝐽

𝐽𝑜=

𝑙𝑛𝑟𝑒𝑟𝑤

ln𝑟𝑒𝑟𝑤

+ 𝑆𝑓……… (3-6)

Where

J: productivity of fractured well, STB/day-psi

𝐽𝑜: productivity of non-fractured well, STB/day-psi.

The effective skin factor 𝑆𝑓can be determined based on fracture conductivity and

Fig(3-7).


18

It is seen from Fig. that the parameter 𝑆𝑓+ ln (𝑥𝑓/𝑟𝑤) approaches a constant value

in the range

Of 𝐹𝐶𝐷> 100, that is, which gives:

𝑆𝑓 ≈ 0.7 – ln (𝑥𝑓/𝑟𝑤) ……… (3-7)

Meaning that the equivalent skin factor of fractured wells depends only on fracture

length for high-conductivity fractures, not fracture permeability and width. This is

the situation in which the first step is the limiting step. On the other hand,

Fig(3-7)indicates that the parameter

Sf + ln (𝑥𝑓/𝑟𝑤) declines linearly with log (𝐹𝐶𝐷) in the range of 𝐹𝐶𝐷< 1, that is,

𝑆𝑓 ≈ 1.52 + 2.31 log (𝑟𝑤)-1.545 log (𝑘𝑓w

𝑘⁄ ) - 0.765 log (𝑥𝑓) …… (3-8)

Fig (3-7) Relationship between fracture conductivity and equivalent

skin factor (Cinco-Ley and Samaniego, (1981)(15).


19

Comparing the coefficients of the last two terms in this relation indicates that the

equivalent skin factor of fractured well is more sensitive to the fracture

permeability and width than to fracture length for low-conductivity fractures. This

is the situation in which the second step is the limiting step.

The previous analyses reveal that low-permeability reservoirs, leading to high-

conductivity fractures, would benefit greatly from fracture length, whereas high-

permeability reservoirs, naturally leading to low-conductivity fractures, require

good fracture permeability and width. Valko et al. (1997) converted the data in Fig

(3-7) into the following correlation:

𝑠𝑓 + ln(𝑥𝑓

𝑟𝑤) =

1.65 0.328 𝑢+0.116𝑢2

1+0.180𝑢+0.064𝑢2+0.05𝑢3……… (3.9)

Where

𝑢 = ln(𝐹𝐶𝐷)……… (3-10)

In the situations in which the fracture dimension is comparable to the drainage area

of the well, significant error may result from using Eq. (3-6), which was derived

based on radial flow. In these cases, the long-term productivity of the well may be

estimated assuming bilinear flow in the reservoir.


20

3-4 Hydraulic Fracturing Design

Hydraulic fracturing designs are performed on the basis of parametric studies to

maximize net present values (NPVs)of the fractured wells. A hydraulic fracturing

design should follow the following procedure:

1. Select a fracturing fluid

2. Select a proppant

3. Determine the maximum allowable treatment pressure

4. Select a fracture propagation model

5. Select treatment size (fracture length and proppant

Concentration)

6. Perform production forecast analyses

7. Perform NPV analysis

A complete design must include the following components to direct field

operations:

. Specifications of fracturing fluid and proppant.

. Fluid volume and proppant weight requirements.

. Fluid injection schedule and proppant mixing schedule.

. Predicted injection pressure profile.

3-5 Selection of Fracturing Fluid

Fracturing fluid plays a vital role in hydraulic fracture treatment because it controls

the efficiencies of carrying proppant and filling in the fracture pad. Fluid loss is a

major fracture design variable characterized by a fluid-loss coefficient CL and a

spurt-loss coefficient Sp. Spurt loss occurs only for wall-building fluids and only

until the filter cake is established. Fluid loss into the formation is amore steady


21

process than spurt loss. It occurs after the filter cake is developed. Excessive fluid

loss prevents fracture propagation because of insufficient fluid volume

accumulation in the fracture. Therefore, a fracture fluid with the lowest possible

value of fluid-loss (leak-off) coefficient CL should be selected. The second major

variable is fluid viscosity. It affects transporting, suspending, and deposition of

proppants, as well as back-flowing after treatment. The viscosity should be

controlled in a range suitable for the treatment. A fluid viscosity being too high can

result in excessive injection pressure during the treatment. However, other

considerations may also be major for particular cases. They are compatibility with

reservoir fluids and rock, compatibility with other materials (e.g., resin-coated

proppant), compatibility with operating pressure and temperature, and safety and

environmental concerns.

3-6 Selection of Proppant

Proppant must be selected on the basis of in situ stress conditions. Major concerns

are compressive strength and the effect of stress on proppant permeability. For a

vertical fracture, the compressive strength of the proppant should be greater than

the effective horizontal stress. In general, bigger proppant yields better

permeability, but proppant size must be checked against proppant admittance

criteria through the perforations and inside the fracture. Figure (3-8) shows

permeabilities of various types of proppants under fracture closure stress.


22

Consider a reservoir rock at depth H as shown in Fig.

Fig (3-8) Effect of fracture closure stress on proppant pack permeability

(Economides and Nolte, (2000)(15).

Fig (3-9) Overburden formation of a hydrocarbon reservoir

(15).(1hydrocarbon reservoir


23

The in situ stress caused by the weight of the overburden formation in the vertical

direction is expressed as:

𝜎𝑣 = 𝜌𝐻

144 ……… (3-13)

Where

𝜎𝑣 ∶overburden stress, psi

𝜌 ∶the average density of overburden formation, lb/ft3

H: depth, ft.

The overburden stress is carried by both the rock grains and the fluid within the

pore space between the grains. The contact stress between grains is called effective

stress.

𝜎𝑣′ = 𝜎𝑣 − 𝛼𝑝𝑝 ……… (3-14)

Yield

𝜎𝑣′ =

𝜌𝐻

144− 𝛼𝑝𝑝 ……… (3-15)

Where

𝜎𝑣′ :effective vertical stress, psi

𝛼 :Biot’s poro-elastic constant, approximately 0.7

𝑝𝑝:pore pressure, psi.

The effective horizontal stress is expressed as:

𝜎ℎ′ =

𝑣

1−𝑣𝜎𝑣

′ ……… (3-16)

Yield

𝜎ℎ′ =

𝑣

1−𝑣(

𝜌𝐻

144− 𝛼𝑝𝑝) ……… (3-17)


24

3-7 The maximum Treatment Pressure

The maximum treatment pressure is expected to occur when the formation is

broken down. The bottom-hole pressure is equal to the formation breakdown

pressure 𝑝𝑏𝑑 and the expected surface pressure can be calculated by:

𝑝𝑠𝑖 = 𝑝𝑏𝑑 − 𝑝𝑝ℎ + ∆𝑝𝑓 ……… (3-18)

Where

𝑝𝑠𝑖 =surface injection pressure, psia

𝑝𝑏𝑑=formation breakdown pressure, psia

𝑝𝑝ℎ=hydrostatic pressure drop, psia

∆𝑝𝑓 =frictional pressure drop, psia.

To avert the procedure of friction factor determination, the following

approximation may be used for the frictional pressure drop calculation

(Economides and Nolte, 2000):

∆𝑝𝑓=518ρ0.79q1.79μ0.202

1000 D4.79 𝐿 ……… (3-19)

Where

ρ=density of fluid, g/cm3

q =injection rate, bbl/min

μ=fluid viscosity, cp

D =tubing diameter, in.

L =tubing length, ft

The above equation is relatively accurate for estimating frictional pressures for

newtonian fluids at low flow rates.


25

3-8 Selection of Fracture Model

An appropriate fracture propagation model is selected for the formation

characteristics and pressure behavior on the basis of in situ stresses and laboratory

tests. Generally, the model should be selected to match the level of complexity

required for the specific application, quality and quantity of data, allocated time to

perform a design, and desired level of output. Modeling with a planar 3D model

can be time consuming, whereas the results from a 2D model can be simplistic.

Pseudo-3D models provide a compromise and are most often used in the industry.

However, 2D models are still attractive in situations in which the reservoir

conditions are simple and well understood. For instance, to simulate a short

fracture to be created in a thick sandstone, the KGD model maybe beneficial. To

simulate a long fracture to be created in a sandstone tightly bonded by strong

overlaying and underlaying shales, the PKN model is more appropriate.

3-9 Propped fracture width

The propped width of the fracture describes the fracture geometry that controls

posttreatment production.

The fracture conductivity is simply the product of the propped width and the

proppant pack permeability.

Assuming that a mass of proppant𝑀𝑝has been injected into a fracture of half-length

𝑥𝑓 and hight ℎ𝑓 and the proppant uniformly distributed, then

𝑀𝑝 = 2𝑥𝑓ℎ𝑓𝑤𝑝(1 − ∅)𝜌𝑝……… (3-20)

Where the product 2𝑥𝑓ℎ𝑓𝑤𝑝(1 − ∅) represents the volume of the proppant pack in

𝑓𝑡3 and is characteristic of the propant type and size. The density 𝜌𝑝 is also a

characteristic property of the proppant.

A frequently used quantity is the proppant concentration in the fracture 𝑐𝑝 defined

by:

𝑐𝑝 =𝑀𝑝

2𝑥𝑓ℎ𝑓……… (3-21)


26

And the units are 𝑖𝑏/𝑓𝑡2. Traditionally a good proppant pack concentration in a

fracture would be 2𝑖𝑏/𝑓𝑡2. Therefore Eq. (3-21) rearranged for the propped width

𝑤𝑝 leads to:

𝑤𝑝 =𝑐𝑝

(1−∅)𝜌𝑝 ……… (3-22)

The average slurry concentration is given by:

𝑐𝑝′ =

𝑐𝑓

𝜖+1……… (3-23)

Where

𝑐𝑝′ : average slurry concentration in ppg.

𝑐𝑓: end-of-job slurry concentration in ppg.

𝜖: variable depend on fluid efficiency.

The mass of proppant then would be:

𝑀𝑝 = 𝑐𝑝′ (𝑉𝑖 − 𝑉𝑝𝑎𝑑)……… (3-24)

Where

𝑉𝑖: total fluid volume required in gal.

𝑉𝑝𝑎𝑑:pad volume in gal.

Equations (3-20) through (3-24) are sufficient to calculate the propped width of a

fracture.


27

3-10 Proppant schedule

Proppant addition, its starting point, and at what concentration it is added verses

time depend on fluid efficiency(η).

Nolt(1986) has shown that, based on material balance, the continuous proppant

addition verses time should follow a relationship expressed by:

𝑐𝑝(𝑡) = 𝑐𝑓 (𝑡−𝑡𝑝𝑎𝑑

𝑡𝑖−𝑡𝑝𝑎𝑑)

∈

……… (3-25)

Where

𝑐𝑝(t): slurry concentration in ppg.

𝑐𝑓: end-of-job slurry concentration in ppg.

𝑡𝑝𝑎𝑑: pad stage time.

𝑡𝑖: total time.

The variable ( 𝜖) depend on the fluid efficincy and is given by:

𝜖 =1−ɳ

1+ɳ……… (3-26)

Equation (3-25) and (3-26) simply denote the appropriate proppant addition mode

so that the entire hydraulic length coincides with the propped length. This is not

entirely realistic, since the fracture length, beyond the point where the hydraulic

width is smaller than three proppantdiameters, cannot accept proppant; it will

bridge (note: bridging can also occur at widths larger than three proppant

diameters, which is the absolute minimum.) Hence, in designing hydraulic fracture

treatment, this type of criterion may be used as a check for total mass of proppant

that can be placed. Another consideration for the end of job slurry concentration

(𝑐𝑓) is the proppant transporting ability of fracture fluid. Certainly, in all cases the

calculated average propped width cannot exceed the average hydraulic width.


28

FIG (3-10) proppant profile development during hydraulic fracture treatment(16).


29

CHAPTER FOUR

THEORETICAL WORK

A gasreservoir has a permeabilityof 1 md. A vertical well of 0.328-ft radius draws

thereservoir from the center of an area of 160 acres. If thewell is hydraulically

fractured to create a 2,000-ft long,0.12-in. wide fracture of 200,000 md

permeability aroundthe center of the drainage area.

1-Calculate the fold of increase in well productivity (15).

Solution: Radius of the drainage area

𝑟𝑒 = √𝐴

𝜋= √

(43560 )(160)

𝜋 =1,490ft

Fracture conductivity:

𝐹𝐶𝐷 = 𝐾𝑓𝑤

𝑘𝑥𝑓=

(200.000 )(0.1212⁄ )

(1)(2.000)2⁄

= 2 From figure Fig(3-7)

Chapter four Theoretical work

30

Reads𝑆𝑓 + ln(𝑥𝑓

𝑟𝑤)⁄ ≈ 1.2

which gives

𝑆𝑓 ≈ 1.2 − ln (𝑥𝑓

𝑟𝑤⁄ ) = 1.2 − ln(1.000

0.328⁄ ) = −6.82

The fold of increase is

𝐽

𝐽𝑜=



+ 𝑆𝑓=

𝑙𝑛1.490

0.328

𝑙𝑛1.490

0.328−6.82

= 5.27

2-estimate the minimum required compressive strength of 20/40 proppant. If

intermediate-strength proppant is used, estimate the permeability of the proppant

pack. Additional information are:

Formation depth=10,000 ft, overburden density=165 lbm/ft3, poison’s ratio=0.25,

biot constant=0.7, reservoir pressure=6,500 psi, production drawdown=2000 and

4000 psi (15).

Solution:

the initial effective horizontal stress:

σh =v

1 − v(

ρH

144− αPp)

= 0.25

1 − 0.25[(165)(10.0000)

144− (0.7)(6500)] = 2303 psi

The effective horizontal stress under 2,000 psi pressure drawdown

σh =v

1 − v(

ρH

144− αPp)


31

= 0.25

1 − 0.25[(165)(10.0000)

144− (0.7)(4500)] = 2770 psi

The effective horizontal stress under 4,000 psi pressure drawdown

σh =v

1 − v(

ρH

144− αPp)

= 0.25

1 − 0.25[(165)(10,0000)

144− (0.7)(2500)] = 3236 psi

3-predict the maximum expected surface injection pressure using the following

additional data:

Specific gravity of fracturing fluid =1.2, viscosity of fracturing fluid=20 cp, tubing

inner diameter= 3.0 in, Fluid injection rate=10 bpm, Pbd= 6600 psi (15).

Solution:

Hydrostatic pressure drop:

∆ph = (0.4330 (1.2)(10.000) = 5196 psi

Frictional pressure drop:

∆pf = 518 ρ0.79q1.79μ0.207

1,000 D4.79 L

=518 (1.2)0.79(10)1.79(20)0.207

1.000 (3)4.79 (10,000) =3,555 psi

Expected surface pressure:

psi = pbd − ∆ph + ∆pf = 6600 − 5196 + 3555

= 4,959psi


32

4-What would be the maximum and average fracture widths when the fracture

half-length is 1000 ft, the apparent viscosity of the fluid is 100 cp, and the injection

rate is 40 bpm? Assume that ѵ=0.25 and E=4 *106𝑝𝑠𝑖. What would be the average

width when 𝑥𝑓 = 2000 𝑓𝑡?calculate the volume of the created fracture if ℎ𝑓=100 ft

when 𝑥𝑓=1000ft assuming PKN model (17).

Solution:

From the shear modulus equation,

G=4 𝑥106

2(1+0∙25)=1.6 x 106𝑝𝑠𝑖

And from Eq. (3-2) in previous chapter, when 𝑥𝑓 = 1000 𝑓𝑡,

ώ = 0 ∙ 3 [(40)(100)(1 − 0 ∙ 25)(1000)

1 ∙ 6 x 106]

14⁄

(𝜋

4 0 ∙ 75)

= (0.35) (0.59) =0.21 in

And from Eq. (3-3) in previous chapter.

𝜔𝑚𝑎𝑥 = 0 ∙ 3 [(40)(100)(1−0∙25)(1000)

1∙6 x 106 ]1

4⁄=0.35 in

When xf=2000 ft the ωmax and ώare 0.42 and 0.25 inch respectively (simply the

previous results multiplied by 21/4).

The volume of the 1000 ft (half-length) fracture is:

V=2 𝑥𝑓ℎ𝑓ώ= (2) (1000) (100) (0∙21

12)=3500 𝑓𝑡3


33

5-Suppose that 20/40 mesh sintered bauxite is injected (ø𝑝 = 0.42 and 𝜌𝑝 =

230𝐼𝑏

𝑓𝑡3 )Into a fracture designed to have 𝑥𝑓 = 1000 𝑓𝑡 and ℎ𝑓 = 150 𝑓𝑡,If 𝑐𝑓 =

3𝑝𝑝𝑔𝑎𝑛𝑑 𝜖 = 0 ∙ 43 .calculate the total mass of proppant, the propped width, and

the proppant concentration in the fracture. The volume of pad

is 1.76*105 gal and total fluid volume required is 4.12*105gal (17).

Solution:

The average slurry concentration can be calculated from Eq. (3-23).

Ć(𝑡)𝑝 =𝑐𝑓

1+ϵ=

3

1∙43=2.1ppg

The mass of proppant can be determined:

𝑀𝑝=(2.1)(4.12*105-1.76*105)= 4.9 x 105Ib

The proppant concentration in the fracture, 𝑐𝑝, can be calculated from Eq. (3-21).

𝑐𝑝= 4∙9 x 105

(2)(1000)(150) = 1.63 Ib/𝑓𝑡2

Finally, using Propped fracture width equation:

𝜔𝑝= 1∙63

(1−0∙42)(230) = 0.012 ft = 0.15 in

6-assume that the total injection time, 𝑡𝑖, is 245 min, and for efficiency ɳ = 0.4, the

pad injection time 𝑡𝑝𝑎𝑑 is 105 min. if the end of job slurry concentration 𝑐𝑓 is

3ppg, plot the continuous proppant addition schedule (17).

Solution:

from eq. (3-26) in previous chapter and ɳ= 0.4,

ϵ =1 − 0.4

1 + 0.4= 0.43


34

And from eq. (3-25) and cf=3 ppg,

cp(t) = 3 (t − 105

245 + 105)

0.43

For example, at t= 150min cp(t)=1.84 ppg. Of course, at t= 105 min, cp(t) = 0,

And at t=245 min, cp(t)=3 ppg.

Figure (4-1) is a plot of the injection with the onset of proppant addition and

proppant schedule.

Fig (4-1) onset of proppant slurry and continuous proppant

addition (17).Fig (3-5) The KGD fracture geometry (15).

Chapter five Conclusion and Recommendation

35

CHAPTER FIVE

CONCLUSIONS AND RECOMMENDATIONS

5-1:Conclusion:

The following conclusions have been drawn from the present study:

1- Through the theoretical work of fold of increase in well productivity, It can

be seen that the productivity index for fractured well is increased five times

from the original productivity, so if the original well produce one barrel per

day for 1 psi pressure drop, after hydraulic fracturing the well will produce

five barrels per day for 1 psi pressure drop.

2- From the theoretical results, for the intermediate-strength proppantthe

minimum required compressive strength is 3236 psi, so if the proppant have

compressive strength less than this value the proppant will be crushed and

the fracture job will be field, so the Proppant must be selected on the basis of

in situ stress conditions.

3- From the theoretical work we can calculate the maximum surface pressure

that we need it to inject the fluid inside the wellbore depending on the break

down pressure for the formation and the frictional, hydrostatic pressure drop.

4- Through the theoretical work of PKN model, when the injection pressure of

fluid increase the dimensions of the fracture will increase (proportional

relationship).

5- From the calculation of propped width, we conclude that the propped width

will be always less than the average width of the fracture because the effect

of the closure pressure of the fracture wall after releasing the fluid from the

fracture and the proppant will settle inside the fracture.


36

6- From fig (4-1) in the previous chapter we observe that after ending of the

pad stage (after 105 min) the proppant addition will start and continue until

the time reaches 245 min, through this time the proppant concentration

increases from 0 to 3 ppg.

NOTE: we should concern that the proppant concentration will not exceed a

certain value(critical value) of concentration to prevent the screen out

phenomena.


37

5-2:Recommendation:

The following points should be taken into considerations for future works:

1- Instead of PKN model, use KGD model to calculate the maximum and

average fracture width and study the differences between obtained results

of these two models, and show the effect of injection pressure on the

dimensions of the above models.

2- Calculate the minimum required compressive strength for different types

of proppant such as (high strength proppant and resin coated sand,…etc)

and study the effect of fracture closure stress on proppant pack

permeability.

3- Study the screen out phenomena by calculating the critical value of

proppant concentration that screen out will occurs after this value of

concentration.

4- Using different values of pressure to study the effect of it on screen out.

REFERENCES

38

REFERENCES

No. Title

1 Howard, G. C. and Fast, C. R.: Hydraulic Fracturing, Society of

Petroleum Engineers of AIME, Monograph 2, New York City

1970.

2 Pai et al., “Tight Sands Require Detailed Planning”, Oil and Gas

Journal, Jul. 25, 1983, pp. 135-139.

3 Pai et al., “Formation Needs Are Key to Fluid and Proppant

Selection”, Oil and Gas Journal, Aug. 8, 1983, pp. l26—128.

4 DeltefMader, “Hydraulic proppant fracturing and gravel packing”,

1st Edition Elsevier, 1st March, 1989.

5 P.J. Hudson and R.P. Matson,” Hydraulic Fracturing in Horizontal

Wellbores”, 1992, SPE 23950.

6 King, R. W., and Adegbesan, K. O., "Resolution of the Principal

Formation Damage Mechanisms Causing Injectivity and

Productivity Impairment in the Pembina Cardium Reservoir," SPE

Paper 38870, Proceedings of the 1997 Annual Technical

Conference and Exhibition held in San Antonio, Texas, October 5-

8, 1997, pp. 277-288.

7 Gruesbeck C and Collins RE:” particle transport through

perforation”, paper SPE 8006, presented at 3rd symposium on

formation damage control of the SPE of AIME Lafayette,

Louisiana, USA February 15-16, 1982.

8 FarukCivan, “Reservoir formation damage”, Gulf Publishing

REFERENCES

39

Company Houston, Texas 2000.

9 Richard Nolen-Hoeksema, Oilfield Review Summer 2013: 25, no.

2. Copyright © 2013 Schlumberger.

10 Kristian Brekke, Bellaire, Tx (U S) "System and Method for

Detecting Screen-Out Usinga Fracturing Valve for Mitigation",

Patent Application Publication Pub. N0. US 2014/0083680 A1,

Date: Mar. 27, 2014.

11 Yongping Li,Jianhua Xu,Fei Yan,Siyun Zeng,Xingsheng

Cheng,Fuxiang Zhang, “Hydraulic Fracturing in HPHT Deep

Naturally Fractured Reservoir in China”, SPE-176070-MS 2015.

12 Shah, S. “PE – 5423 Advanced Stimulation Class Notes”. MPGE,

University of Oklahoma, fall 2008, Norman, Ok.

13 Andreas Reinicke , Erik Rybacki, Sergei Stanchits, Ernst

Huenges, Georg Dresen, “Hydraulic fracturing stimulation

technique sand formation damage mechanisms—Implications

from laboratory testing of tight sandstone–proppant systems”,

2010 Elsevier

14 Richard Nolen –Hoeksema, “Elements of Hydraulic Fracturing”,

Oilfield Review Summer 2013: 25, no. 2.

15 Petroleum_Production_Engineering,_Elsevier_(2007).

16 Hydraulic Fracturing6.

17 Micheal_Economides_-_Petroleum_Production_System.

https://www.onepetro.org/search?q=dc_creator%3A%28%22Li%2C+Yongping%22%29

https://www.onepetro.org/search?q=dc_creator%3A%28%22Xu%2C+Jianhua%22%29

https://www.onepetro.org/search?q=dc_creator%3A%28%22Yan%2C+Fei%22%29

https://www.onepetro.org/search?q=dc_creator%3A%28%22Zeng%2C+Siyun%22%29

https://www.onepetro.org/search?q=dc_creator%3A%28%22Cheng%2C+Xingsheng%22%29

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HYDRAULIC FRACTURING · during a hydraulic fracture treatment. 11 (3-2). Distribution of the stress and the direction of the created fracture perpendicular to the minimum stress in