Hydraulic Fracturing

Parr I

Introduction ............................................................... 1

Damage Around the Wellbore ............................................1

Low Formation Permeability ............................................. 2

Non-Homogeneous Formations ...........................................2

Hydraulic Fracturing Definitions .......................................... 2

Parr 2

History of Fracturing ....................................................... 3

Early Work ............................................................ 3

Fracturing Today ....................................................... 3

Parr 3

Mechanics of Hydraulic Fracturing ........................................... 5

Fracture Initiation ...................................................... 5

Fracture Extension ...................................................... 6

Parr 4

Fracture Geometry ......................................................... 8

Fluid Injection into the Fracture .......................................... 8

Fluid Flow Along the Fracture Length ..................................... 9

Fluid Leak-Off ......................................................... 9

Parr _5

Particle Transport ......................................................... 10

Proppant Movement ................................................... 11

Proppant Settling ...................................................... 12

Proppant Bed ......................................................... 14

Tail-In Using Thin Fluids ............................................... 16

Suspended Proppants ...................................................16

Parr 6

Laboratory Tests for Selection of Base Fluids ................................17

Types of Base Fluids ................................................... 17

Structural and Chemical Analysis of Formation Samples ..................... 18

Evaluation of Fluid-Rock Interactions ..................................... 19

Evaluation of Fluid Properties ........................................... 20

Parr 7

Factors Influencing Hydrocarbon Production ................................. 21

Matrix Permeability .................................................... 21

Fracture Conductivity .................................................. 22

Summary ............................................................. 23

HESI303125
Part 8

Properties of Chemicals and Fracturing Fluids ................................ 23

Common Fracturing Chemicals .......................................... 23

Fracturing Polymers .................................................... 23

Crosslinking Agents .................................................... 28

pH Conu’ol Chemicals ..................................................29

Gel Breakers .......................................................... 29

Surfactants ........................................................... 29

Clay Stabilizers ........................................................

Alcohol .............................................................. 32

Biocides .............................................................. 32

Fluid Loss Additives ................................................... 32

Summary ............................................................. 32

Part 9

Proppants and Fracture Conductivity ........................................ 33

Types of Proppants .................................................... 33

Calculations for Production Rate ......................................... 34

Damage to Proppant Bed ............................................... 35

Selection of the Propping Agent .......................................... 38

Laboratory Tests for Conductivity ........................................ 38

Fracture Closure Stress ................................................. 40

Part 10

Production Increase ....................................................... 40

Calculations for Vertical Production Increase ............................... 41

Computer Simulations .................................................. 45

Part I I

Hydraulic Fracturing Equipment ............................................ 47

Fluid Storage ......................................................... 47

Proppant Storage ...................................................... 47

Blending Equipment ...............................................  ̄ .... 48

High Pressure Pumping Equipment ....................................... 49

Control Center ........................................................ 49

Surface Lines and Manifolding .......................................... 50

Part 12

Practical Design of Fracturing Treatments .................................... 50

Fracture Design Variables ...............................................50

Selection of Design Variables ............................................ 51

Part 13

Monitoring a Frac Treatment During Pumping ................................ 56

Analysis of Bottomhole Treating Pressure .................................. 56

Real-Time Treating Pressure Analysis in Field Operations .................... 57

Minifrac Process ....................................................... 58

Revised 6YH

HESI303126
Part i4

Post-Frac Analysis ......................................................... 60

Inadequate Initial Response ............................................. 60

Rapid Production Decline ............................................... 61

Refrac Treatments ..................................................... 62

References ............................................................... 63

Appendix A .............................................................. 67

Appendix B .............................................................. 74

Appendix C .............................................................. 80

Revised 6YH iii

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HESI303128
hydraulic fracturmR 1

INTRODUCTION

Part 1

After an oil or gas well has been drilled, the

wellbore pressure is reduced (lower than the reservoir pressure) which forces fluid to flow into the

wellbore. The oil an~or gas will be displaced toward the wellbore by methods such as fluid expansion, natural or artificial fluid displacement,

gravity drainage, capillary expulsion, etc. These

processes may work together or independently to

drive the hydrocarbon into the wellbore through

the permeability of the reservoir rock or, in some

wells, through a network of natural fractures.

In many instances, production of the well may

be commercially insufficient. Assuming the reservoir does contain commercial quantifies of producible hydrocarbons, then at least one of the

following conditions probably exists:

 ̄ damage around the wellbore

 ̄ low formation permeability

 ̄ non-homogeneous formation.

Damage Around the Wellbore

In this situation, the natural flow channels

within the reservoir (formation permeability or

natural fracture system) are sufficient to allow

commercial production rates, but these flow channels are severely plugged in the near-wellbore region. This plugging may have been caused by the

drilling fluid or completion fluids (i.e., cement

filtrate, perforating fluids, etc.). In some cases, the

damage may be a result of the formation reaction

with one or more of these fluids. The swelling of

formation clays, scale build-up and precipitation of

iron oxides are a few such possibilities.

The production problem then becomes one of

treating the reservoir in some manner which will

increase the flow of fluid into the wellbore (Fig.

1.1). This may be a simple acid wash or acid

breakdown of the perforations to remove or bypass the damage (restriction to flow) within the

formation. However, it is often necessary to overcome the effect of the damage through hydraulic

fracturing.

FILTRATE

Revised 6YH

HESI303129
hydraulic fracmrm~s

Low Formation Permeability

Most of the fracturing treatments being applied today are the result of low permeability of the

reservoir rock. We must keep in mind that the

most valid definition of "low permeability" is related to the economics of each individual well.

In many reservoirs, the original drilling proposal will include plans for a hydraulic fracturing

treatment as part of the completion program. Often, many details of the drilling or completion program will be dictated by factors which will help

enhance the effects of the hydraulic fracturing

treatment. Pre-planning for a fracturing treatment

can be the deciding factor in the success or failure

of obtaining commercial production rates.

Non-Homogeneous Formations

This category is probably the one where the

result of a fracturing treatment is the most unpredictable. Two of the more common examples of

the use of hydraulic fracturing in nonhomogeneous reservoirs are discontinuous lenticular sands and formations that produce primarily

through natural fracture systems. These reservoirs

are difficult to model. Often, the purpose of a fracturing treatment in a non-homogeneous formation

is to communicate with parts of the reservoir that

may have no hydraulic link to the wellbore.

Hydraulic Fracturing Def’mitions

Hydraulic fracturing may be defined as the

process in which fluid pressure is applied to the

exposed reservoir rock until failure or fracturing

occurs. After failure of the rock, generally referred

to as formation breakdown, a sustained application

of fluid pressure extends the fracture outward

from the point of failure. This fracture creates a

new and larger flow channel; it may connect existing natural fractures as well as provide additional

drainage area from the reservoir. The fluid used to

transmit the hydraulic pressure to the reservoir

rock is called the fracturing fluid.

At fracturing pressures, fluid will continue

penetrating the zone (Fig. 1.2) causing continued

fracturing of the formation rock, thus extending

the crack (fracture) farther into the formation. The

first fracturing fluid to enter the fracture is the pad

volume. It creates the fracture and begins to control fluid loss into the formation porosity along the

formation surfaces, which are the "walls" of the

fracture. To help prevent the fracture from closing

when pumping is stopped, propping agents (Fig.

1.3) are added to the fracturing fluid. Proppants

act as supports to hold the fracture open after the

treatment and to provide an improved ability of

the fracture to conduct oil or gas through the fracture to the wellbore.

UPPER LAYER

LOWER LAYER

Fig. 1.2 - Schematic of Hydraulic Fracturing

A. 20/40 Mesh

Ottawa Sand

lB. 20/40 Mesh Intermediate

Strength Bauxite Proppant

Fig. 1.3 - Typical Propping Agents (enlarged)

Revised 6YH

HESI303130
hydraulic fracturing 3

Since the beginning of hydraulic fracturing,

many different types of materials have been used

as propping agents: sand, walnut hulls, aluminum

pellets, plastic beads, steel shot, man-made glass

beads and sintered bauxite beads. Today’s propping agents are available in different size distributions and are used in varying quantities. Part 9 of

this text is an extensive review of propping agents

and their applications in hydraulic fracturing.

The ability of the fracture to conduct fluids to

the wellbore affects the ability of the well to produce. The fracture conductivity as well as the

length and the height of the fracture that is

propped open are all very important. High fracture

conductivity combined with a long propped fracture length may result in good increased production in old or new wells and may make a producer

from a noncommercial well. In Part 10 of this text,

we will discuss these production increases. The

effect of fracture conductivity, propped length and

propped height as they influence the stimulated

producing rates will be studied in detail.

HISTORY OF FRACTURING

Part 2

In 1948, Stanolind Oil & Gas Company (later

Pan American Petroleum Corporation and now

AMOCO) received a patent for its hydraulic fracturing process to stimulate well productivity. The

announcement culminated several years of extensive laboratory and field study. In March 1949,

Halliburton Oil Well Cementing Company (now

Halliburton Services), operating as an exclusive

licensee, performed the first two commercial fracturing treatments on the same day; one in Archer

County, Texas, and the other in Stephens County,

Oklahoma. Thus began one of the most outstanding well stimulation procedures that the petroleum

industry has ever known.

What has hydraulic fracturing meant to the oil

industry? Conservative estimates indicate that

three of every four wells fractured have resulted in

profitable production increases that in turn have

raised potential reserves tremendously.

Today, many fields exist because of these techniques. Without hydraulic fracturing, several producing horizons would have been bypassed as

either barren or commercially nonproductive. The

famous Spraberry formation of West Texas was

one of the first such zones. It was passed up in

several wells as not productive. Then fracturing

treatments indicated otherwise, and since that time

every well completed in that interval has been fractured.

Early Work

As in many new developments, changes in

hydraulic fracturing were destined to take place.

Early treatments were conservative. Volumes of

200 .to 400 gallons of fluid with 1/2-1b sand per gallon injected at rates of 2 to 4 bbl/min were considered average treatments. Twice that quantity was

considered a large job.

OccasionaLly some brave operator would perform a 1,500 to 2,000 gallon treatment which was

looked upon with critical speculation. In so doing,

more pumps were usually used, resulting in increased injection rates. These larger, higherinjection-rate type jobs began to show higher, more

sustained production increases. Gradually the job

sizes and injection rates began to increase. Higher

injection rates led to the belief that perhaps highly

viscous fluids were not necessary, as previously

had been believed. Experiments were conducted

with less expensive fluids of lower viscosity with

good results.

In the latter part of 1952, use of ref’med petroleum residuals and heavier crude oils became

popular in addition to the gelled hydrocarbons.

This permitted greater volume per dollar cost;

and, from that time on, aqueous base fluids became more popular and the treatment size increased steadily, as shown in Figures 2.1 and 2.2.

Figure 2.3 shows other historical trends of fracturing treatments. By 1982, the average job had increased to more than 60,000 gallons.

Fracturing Today

Present fracturing treatments are a far cry

from those performed over 30 years ago. Although

a great number of relatively small volume jobs are

still completed each day, it is now common to see

service equipment valued at several million dollars

surrounding a well (Fig. 2.4) and pumping

200,000 to 500,000 gallons of fracturing fluid and

500,000 to 2,000,000 pounds of proppant. Part 11

of this text discusses the fracturing field equipment presently in use.

Revised 6YH

HESI303131
Fig. 2.1

100

9O

8O

7O

60

5O

40

30

20

10

TREND OF FRACTURING BASE FLUIDS

AQUEOUS BASE FLUID_

49 ’53 ’57 ’61

OIL BASE FLUID

I I"-1"1

’65 ,69 ’73 ’77 ~81 ’85 ’89

YEAR

TREND OF AVERAGE

~FRACTURE TREATMENTS

IN THE UNITED STATES

32.0 100 ]100

-~ 1.6 80 (n-o~ 80

z ~ m, I 0 1.4 70’z-0 ~

~ 1.2 6o ~--: s~ /

~ 1.0 50

~o.8 4ogtl Ik /’/ ""

lso

go.6 ao ~ ~ rFLUIDiTREATMENT 30

~ 0.4 2o ~ ~ I I 2o

10

’49 ’53 ’57 ’61 ’65 ’69 ’73 ’77 ’81 ’85 ’89

YEAR

Fig. 2.2

IO00I

!500I

0001

EVOLUTION OF FRACTURING TECHNIQUES

INJECTION f ’-" ’--

RATE / J

/ -- .-~  ̄ HHPIJOB

’49 ’53 ’57 ’61 ’65 ’69 ’73 ’77 ’81 ’85 ’89

YEAR

Fig. 2.3

Revised 6YH

Fig. 2.4 - Massive HydrAulic Fracturing Treatment

HESI303132
hydraulic fracturing 5

MECHANICS OF

HYDRAULIC FRACTURING

Part 3

Since the hydraulic fractures of our interest

are created in reservoir rock, a discussion of the

mechanical behavior of rocks would be appropriate. Essentially all reservoir rock will have some

degree of elasticity and deformability. They will

vary from highly elastic, well cemented sandstones

to soft, weakly consolidated formations with very

little elasticity that will deform under pressure.

A very detailed theoretical discussion on rock

mechanics and the mechanics of hydraulic fracturing is given in Appendix A at the end of this text.

A brief overview of fracture mechanics will be provided here.

Fracture Initiation

In hydraulic fracturing we apply a force

against the reservoir rock. This is accomplished by

pumping a fluid into a wellbore that is in communication with the reservoir we wish to fracture.

The anticipated reaction is to overcome the tensile

strength of the rock and the minimum in situ

stress to create a tensile fracture in the formation.

Initiation of the fracture is commonly referred to

as "breakdown" of the formation.

In an open hole completion, the breakdown

pressure may be only slightly higher than the pressure needed to extend fracture growth. However,

in a perforated completion the breakdown pressure

may be significantly higher. This fact is related to

how efficiently the fluid is able to communicate its

hydraulic pressure to the reservoir rock. If there is

a very large number of clean, open perforations

and the fluid can easily penetrate the formation

matrix, then the perforated wellbore will be similar

to an open hole. But if only limited pressure communication exists, then breakdown pressure will be

higher. Once breakdown occurs and the fracture

has been initiated, the effect of rock tensile

strength will essentially disappear. Unless they

cause a severe restriction to fluid flow, the effect of

the perforations will also become negligible.

The fracture’s orientation and azimuth (i.e.,

compass orientation) will be dictated by the

stresses that exist in the rock. These stresses are

caused by the weight of the overburden and by

tectonic forces. As discussed in Appendix A, the

system of stresses can be represented mathematically by an equivalent set of in situ principal

stresses. In practical applications, one of these

three stresses will be the smallest; this fact will

dictate the orientation of the created hydraulic

fracture. Because the overburden stress (represented in Fig. 3.1 by "o’,") is very seldom the

smallest, nearly all hydraulic fractures in hydrocarbon reservoirs will be essentially vertical in orientation. In a normally pressured reservoir, the least

principal stress will be in the range of 0.6 to 0.9

psi per foot of depth. The least principal stress can

be measured in field practice by obtaining an "instant shut-in" measurement during a hydraulic

fracturing treatment. However, the magnitude of

the other two stresses cannot be determined accurately with current technology. Other methods of

determining the least in situ stress, as well as discussion on its importance, are given in Part 12 of

this text.

Lowest (least likely)

PRINCIPAL STRESS AND

FRACTURE ORIENTAr]ON

Fig. 3.1

L~Lowest 2

HESI303133
6 ~r~ulic fracturing

The azimuth of the fracture is not easily determined. However, extensive work is being done

using both laboratory tests and various field study

methods. Pierce, et. al. ~ discusses pulse testing as

one of the more reliable methods; however, this

method requires both the existence of and control

over several adjacent wells. Lacy2 gives the result

of a major operating company’s extensive field

investigation of five other techniques for determining the orientation of hydraulic fractures. He concludes that all five methods gave reliable results.

Figures 3.2 and 3.3 (taken from Lacy) are simple

but very accurately illustrate the value of knowing

the fracture orientation in both primary recovery

and when using secondary recovery techniques for

fractured wells.

Good Drainage

Incomplete Drainage

Fig. 3.2

Good Areal Sweep

Inject

Produce

Inefficient Areal Sweep

Produce

Inject

Produce

0

II

C

II

II

0

Fig. 3.3

Fracture Extension

Continuing to inject fluid into the fracture

after breakdown will result in extension of the fracture in the plane that is perpendicular to the least

in situ principal stress?" The fracture is simply

following the path of least resistance. In cased

boreholes, the location of the perforations may

affect the near-wellbore direction of fracture

growth, but probably only for a few feet. Both

laboratory and field observations have shown that

the presence of small natural fractures will not

alter the general direction of fracture growth.

However, the presence of multiple (parallel)

fracture strands were recently reported by WarpinskP in a mineback experiment.on a hydraulically fractured sandstone. He observed that these

multiple fracture strands, which were in addition

to the primary hydraulic fracture, usually extended

only a few feet. In a mineback experiment involving a shallow, naturally fractured coal seam (that

had been hydraulically fractured) only a very few

multiple fracture strands were observed.’

Revised 6YH

HESI303134
As the fracture extends from the wellbore the

growth will be in a radial pattern as long as there

are no significant changes in the magnitude of the

in situ stress or in rock properties. However, in

actual practice, the fracture will usually encounter

changing stresses and rock properties as it grows in

vertical height.

In recent years, several investigators have

shown that the minimum in situ stress in the various rock layers is the dominating feature.7-8 Earlier

theories that higher elastic moduli alone will stop

fracture growth at an interface have now largely

been discounted7s9 unless there is a very distinct

interface between the zones’°.

Boundary Rock

Pay Zone

U- - -B~u-ndary R-~ck

~r~Boundary Rock

F~YZOne

./]__

~J’~oundary Rock

Fig. 3.4

If the fracture grows vertically into the zone

with higher stress, this will arrest (or at least retard) the vertical growth and force most of the

fracture growth to be in length and/or width (Fig.

3.4). In some formations, such as massive chalks,

the rock properties are very uniform and the

stresses change so little that the hydraulic fracture

will continue to grow radially. In many formations,

the fracture may encounter a higher stress in only

one direction. That is, only the zone above or below the pay zone will have sufficient stress difference to inhibit fracture growth (Fig. 3.5).

¢, = 2500 psi

-L- ~ = 2000 psi

_

----

o’2 = 2000 psi .....

)

OR

2000 psi

Fig. 3.5

ReUsed

HESI303135
8 hydraulic fracturing

Unfortunately, there are also instances where either

the upper or lower boundary zone has a lower in

situ stress and most of the created fracture is outside the pay zone (Fig. 3.6). When this situation

exists, it will be very difficult to achieve commercially successful stimulation with hydraulic fracturing, unless very short propped fracture lengths are

acceptable. If the vertical fracture growth is into a

water bearing zone, the well may not be economical or, at best, will result in increased well costs

due to handling and disposal of the produced water. The high commercial success ratio of hydraulic

fracturing applications suggests the limited height

growth case (Fig. 3.4) is probably the most typical

result.

., [

~r. = 2500 psi

~ 1800 psi~

OR

Fig. 3.6

FRACTURE GEOMETRY

Part 4

The economic success or failure of a hydraulic

fracturing treatment usually depends on the geometry of the created fracture. For horizontal fractures, this includes its width (separation of the two

fracture faces) and radius. For vertical fractures

this means its width, length (lateral dimension)

and height (vertical dimension). Fracture shape

was discussed in Part 3 of this text.

The geometry of a hydraulic fracture depends

on many factors interrelated in a complex manner.

The physical events that simultaneously occur during fracture extension are:

 ̄ fluid injection into the fracture

 ̄ flow of fluid along the fracture length

 ̄ fluid leak-off into the fracture walls.

These factors must all be considered no matter what fracture shape, orientation or azimuth is

used in a calculation. For the purpose of simplifying the discussion in this part of the text, we have

assumed a vertical fracture that is either radial or

rectangular in shape. In field applications, horizontal fractures are uncommon. A more theoretical

and detailed discussion of fracture geometry calculation is given in Appendix B at the end of this

text.

Fluid Injection Into The Fracture

The volume of fluid injected into the fracture

(Vt) is the product of the injection rate (q) of the

surface pumps and pumping time (t):

V,= qt

The value of V, is one of the few numbers

accurately known during a fracturing treatment.

Of this volume, part stays inside the hydraulic

fracture (Vf) and part is lost to the formation as

leak-off (V~). Therefore:

V, = Vf + V~

The volume efficiency (El) of a hydraulic fracture is defined as:

(4-1)

Ef = V¢ / Vt

or

El= 1-Vt/Vf

(4-2)

((

Revised 6YH

HESI303136
The parameter Ef defines the fraction of the

injected volume which forms the actual fracture

volume. Thus, it is desirable to increase El, which

is usually done by decreasing V,.

In addition to the treatment volume, it is necessary to know the engineering properties of the

fluid itself. Laboratory experiments indicate that

most presently used treatment fluids have complex

behavior that cannot be precisely described by

simple models. Therefore, for mathematical simplicity, treatment fluids are either assumed to be

Newtonian, to behave like a power-law model, or

possibly tO behave like a Bingham Plastic, as some

authors have proposed for foam fluids. The powerlaw model is the most commonly used. For a

power law fluid, the engineering constants describing the treatment fluid behavior are its flow behavior index (n’) and absolute consistency (K’), which

are measured in the laboratory.

Fluid Flow Along the Fracture Length

The fluid being pumped is forced out of the

wellbore and into the fracture being extended. The

frictional losses due to fluid flow along the fracture

create a pressure drop between the fracture tip and

borehole, denoted by Ap~. The magnitude of this

pressure drop plays an important role in the computation of fracture geometry.

Kristianovich and Zheltov3 first pointed out

that the treatment fluid does not occupy the entire

length of the hydraulic fracture. The tip of the

fracture has a cusp shape and does not contain the

treatment fluid. According to Daneshy4, if x~ is the

wetted length of a vertical fracture, and q(x) and

w(x) denote the flow rate and fracture width respectively at a point along the fracture length,

then:

Apo = 2(2n’+l/n’-~-~-/ × K’f° [6q(x)]n’ dx

-’xo w(x)’"’÷’ (4-3)

Assuming that ~ry is the least in dtu principal

stress (Fig. 4.1), then the treatment pressure of a

hydraulic fracture (pf) can be calculated from:

p~ = (r~. + Ape (4-4)

In common oilfield terminology this pressure

(p~) is called the bottomhole treating pressure

(BHTP).

X

= -L P, = ,ry + ..Xp(x) x= L--/

~llbore

~g. 4.1 - Overhead View of a Vertical Fracture

If the frictional losses due to flow in the wellbore are denoted as A Ppi~ , frictional losses through

the perforations are A p~, and the hydrostatic

pressure induced by the weight of the treatment

fluid column down to the fracture depth is

then the wellhead pressure pw can be expressed as:

p, = pf + Ap~ + App~ - Ap~ (4-5)

The value of Ape as given by equation 4-3

does not include the influence of adding a propping agent to the treatment fluid. The Ape for a

fluid containing a propping agent can be computed

by replacing n’ and K’ of the fluid by that of the

slurry, if such data are available.

Fluid Leak-Off

As mentioned previously, part of the fluid in

contact with the fracture faces penetrates into the

formation pores and is lost as leak-off. This reduces the amount of fracture volume created per

unit volume of fluid injected. To decrease the rate

of leak-off, fluid-loss additives usually are added to

the treatment fluid to form a filter cake on the

fracture wall.

Figure 4.2 shows the results of a typical fluidloss test conducted in the laboratory using core

plugs from formation cores. The curve in this figure can be divided into two parts. In Part I, a f’flter

cake is in the process of forming. This fluid leakoff is mainly governed by the fracturing fluid viscosity, the formation fluid viscosity, pore pressure,

formation compressibility, the formation porosity

and permeability, etc. Fluid leak-off during this

time is called "spurt loss."

HESI303137
0 hydraulic fracturmg~

PURT VOLUME

m =2C,,,

°>b’-’"/

a ..

v’TIME

Fig. 4.2 - Plotted Data from Laboratory Fluid Loss Test

Point A in Figure 4.2 is identified by its ordinate, called spurt volume. This value is determined experimentally in the laboratory. The spurt

volume measured in the fluid-loss test is usually

dependent on the concentration and type of the

fluid-loss additives and the formation permeability.

It is quite common to measure a zero spurt loss on

low permeability formation cores, especially with

high viscosity fluids.

The slope of the line in Part I of the curve is

denoted by 2Cvo. The term C,o is a combined fluidloss coefficient where the leak-off rate is controlled

by fluid viscosity and compressibility but a filter

cake has not yet formed. This is explained by WilliamsY Since the Cv, value in an actual off or gas

reservoir may vary significantly from the laboratory test conditions, the C,, from the laboratory

test is seldom determined or used.

In Part II of the curve, a filter cake has now

been formed and is controlling fluid leak-off. This

part of the curve is identified by its slope, denoted

by m = 2Cw. The Cw is the fluid-loss coefficient

where the leak-off rate is controlled by the wall

building properties of the fluid and/or fluid loss

additives.

The fluid-loss test is usually run to determine

two parameters: the spurt volume and the fluid

loss coefficient. The magnitude of C,, is computed

from the reservoir as well as the treatment fluid

properties. With spurt volume and C,o known, one

can compute a spurt time.

The rate of fluid leak-off at any point in the

fracture depends on the time that the point has

been exposed to fracturing fluid. If this time is less

than the spurt time, then Part I of the curve determines the leak-off rate. For exposure times greater

than the spurt time, the rate of fluid leak-off is

measured from Part II of the curve. As long as the

fracture is extending through permeable rock,

some portion of the fracture will be in Part I, while

most of the exposed area will be in Part II.

Fluid leak-off has important effects on the

geometry of the created fracture. First, it decreases

the fracture volume, and consequently the size of

the fracture dimensions. It also affects the rate of

fluid flow down the fracture, q(x), which as shown

by equation 4-3, changes the fluid pressure inside

it.

PARTICLE TRANSPORT

Part 5

The effectiveness of any fracturing treatment

is strongly influenced by the conductivity of the

resultant propped fracture. Conductivity will depend on the size and strength of the propping

agent used, and the distribution of the proppant in

the fracture.

In the early days of fracturing, a common

assumption was that the proppant traveled with

the fluid with which it was mixed. This led to the

assumptions that the proppant’s distribution was

always the same as the fluid’s, and the fracture was

propped over 100 percent of its area.

These assumptions were not unrealistic when

the jobs were very small and the fluid was kerosene gelled with napalm. This was a very high

viscosity gel that could suspend the proppant partides during the treatment. However, as fracturing

fluid development moved toward lower viscosities

with such materials as water thickened with guar

gums or cellulose gels, or even ungelled water or

oil, the suspended proppant assumption became

less reasonable. Also, the treatment volumes increased significantly.

It is usually assumed that any part of the fracture surfaces that are not separated by proppant

particles will close back into their original position

under the influence of the in situ stresses. Thus,

only the propped portions of the fracture will be

available for fluid flow and will contribute to the

long term beneficial effects of the stimulation

treatment. The completeness of this fracture "healRevised 6YH

HESI303138
ing" has been argued for many years. It is generally believed that shallow, low stress wells may not

heal as completely as deeper wells where in

stresses are high.

It would seem reasonable that a fracture in a

producing formation would result in a higher producing rate if a large part of the fractured surface

were exposed than if only a small part of the fracture remained open. Therefore, the prediction of

the final distribution of the proppant is an important part of the design of fracturing treatments.

Present day fracturing fluids range across the

entire spectrum of physical properties. Viscosities

vary from that of water to materials that behave

like rubbery semi-solids. Densities may range from

that of gas-liquid foams ( = 1.6 lb/gal) to saturated

brines (= 12 Ib/gal). Thus, the proppantsuspending properties of fluids vary widely. There

has even been some recent application of compressed nitrogen gas using very low proppant concentrations (no liquid phase present).

Proppant Movement

Several steps are involved in the transport of

proppant particles in hydraulic fracturing:

1. Transport through the surface equipment

(pumps, etc.)

2. Transport down the wellbore tubulars

3. Movement and change of direction through the

perforation

4. Transport in the fracture itself and additional

settling that may occur while the fracture is

closing.

The fracture may be of two major forms:

 ̄ Horizontal fracture - a slot radiating away from

the wellbore in all directions in a plane perpendicular to the wellbore

 ̄ Vertical fracture - a slot extending in two directions from the wellbore.

These forms are illustrated in Figure 5.1. As

part B of this figure shows, the vertical fracture

may be radial or more nearly rectangular in shape.

The rectangular shape vertical fracture is usually

expected to be the most common form of hydraulic

fractures. Radial (either horizontal or vertical) fractures usually occur in a few select geographic areas.

A.Horizontal

Fracture

B. Vertical Fractures

Fig. 5.1

The shape of a vertical fracture created might

be visualized to be elliptical in both the horizontal

and vertical planes. Thus, each of the two fracture

wings might have a shape like Figure 5.2, which

shows only the right wing of the fracture. Of

course, the illustration in Figure 5.2 is distorted. If

the drawing were to a realistic scale, the length to

height ratio would be much greater and the width

would only appear to be a thin solid line.

Fig. 5.2

Predicting the movement of proppant particles

in the fracture mainly concerns determining the

fluid viscosities and velocities throughout the system."43 The fracture shown in Figure 5.2 has a

different cross-sectional area down its length (L)

and, hence, a different velocity for each position

Revised 6YH

HES1303139
2 hydraulic ,"rac!urmg

along its length. The real shape of any given fracture is unknown. To simplify velocity calculations,

a rectangular fracture such as one of the three

cases shown in Figure 5.3 usually is assumed for a

mathematical model. Which shape is selected is a

function of how accurate and sophisticated the

model will be.

Case 1 ~

Caseh~2 ~ ~

Rg. 5.3

This type of a fracture model would have a

constant height and, except in the most simple

models, a width that changes all along its length.

The most accurate model will be elliptical with the

most width variation occurring near the tips, as in

Case 3. Also, it usually is assumed that the entire

height is open to fluid entry and that the proppant

enters the fracture uniformly through its width at

the wellbore. These simplifications help greatly in

solving the mathematics of the proppant movement.

The movement of the proppant particles is "

affected by such parameters as:

 ̄ fluid velocity

 ̄ fluid viscosity

 ̄ fluid leak-off

 ̄ fluid density

 ̄ proppant size

 ̄ proppant density

 ̄ proppant shape

 ̄ proppant concentration.

Proppant Settling

The horizontal particle velocity and settling

rate (vertical velocity) will determine the distribution of particles in the fracture. When a proppant

particle enters the fracture with the moving stream

of fluid, the drag exerted on the particle will cause

it to move horizontally along the fracture. Assuming the particle did not contact the fracture walls

or other particles, it should travel horizontally with

the same velocity as the fluid. If the fluid were of

very low viscosity (a gas, for example) or the fluid~

particle density ratio is very great, there might be

slippage and the particle could lag behind the

fluid.

Simultaneously, the particle would be accelerated downward in the vertical direction by the

force of gravity. A particle settling in a static fluid

would reach a terminal velocity at which the force

due to gravity would balance the drag due to the

particle moving through the fluid. Assuming a

spherical particle, laminar flow, and Newtonian

fluid, the following equation would express the

settling velocity:

where:

= [ 4gdp(pp - p)~0.,

(12) 3pCD ]

v = setting velocity, ft/sec

d~ = particle diameter, in.

pp = particle density, lb/cu ft

p = fluid density, lb/cu ft

CD = drag coefficient

g = acceleration due to gravity, 32.2 ft/sec2

(5-1)

Revised 6YH

HESI303140
If the particle were very small or the viscosity

large enough that the Reynolds number (N~) is less

than 0.3 (Stokes Law region), the drag coefficient

would be:

24 cD -- ~ (5-2)

N~ denotes the Reynolds number and is defreed as:

where:

~ = fluid viscosity, cp

From equations 5-1, 5-2 and 5-3:

18.486dp’(p~- p).

In the Stokes Law region, the vertical velocity

reached by the fluid under these conditions would

depend upon the particle diameter, fluid viscosity

and the difference in density between the particle

and the fluid.

Figure 5.4 illustrates the vertical settling velocity for spherical particles falling in Newtonian

fluids. This figure is calculated using the specific

gravity of sand (2.65) and fluid density of water

(1.0).

(5-4)

SE13"LING VELOCITY vs SAND DIAMETER

0.1

0.01.

0.001 0.01 0.1

Free Sand Settling Velocity, O, Ft/Sec

8112 Mesh

12/20 Mesh

20140 Mesh

40/60 Mesh

1.0

Fig. 5.4 - Particle Settling Velocities

The horizontal fluid velocity depends upon

the fracture width and injection rate (assuming a

constant height). As the treatment progresses,

more fluid is pumped, and the fracture grows in

length and width. The relationship between the

fracture length, width and volume is logarithmic

and is illustrated in Figures 5.5 and 5.6. Thus, the

width is slowly increasing as the length increases.

LOG w

LOG VOLUME

Fig. 5.5

LOG L

LOG VOLUME

Fig. 5.6

If a constant input rate to the system is maintained, the velocity at any point along the fracture

length is slowly decreasing with time, due to the

increasing width. However, the velocity is greater

closer to the tip of the fracture, because the width

decreases .towards the tip.

In addition, all points on the fracture surface

are experiencing fluid loss to some degree. This is

caused by the high fluid pressure in the fracture.

The loss of fluid reduces the fluid velocity and

hence affects the particle velocity. Another factor

to consider is that fluid loss increases the proppant

concentration. This can affect settling rates, which

will be discussed later as "hindered settling."

A study of movement of a single particle in a

vertical fracture t-filed with a thin fluid is illustrated in Figure 5.7. If a particle M is introduced

into the frac.:ure from the wellbore, it will be accelerated to the bulk average fluid velocity .~ vertically. The resultant movement is the path MM’.

The distance along the fracture length the

particle travels before it reaches the bottom of the

HESI303141
4 hydraulic f~cturing

fracture will depend upon the magnitude of the

fluid velocity, the settling velocity v, and position

along the fracture height where the particle has

entered the fracture.

M

Fig. 5.7

The fluid velocity depends on the injection

rate, and the width and height of the fracture at

the time, and position along the fracture length

that is considered. The vertical settling velocity

will depend upon the fluid viscosity, particle diameter, particle shape, and the difference in density

between the particle and the fluid.

Proppant Bed

If a large number of particles carried in a thin

fluid is considered, such as in a fracturing treatment, the same situation exists as with a single

particle. As illustrated in Figure 5.8, the particles

entering the mouth of the fracture all begin to settie. The lower particles do not have as far to fall

and therefore reach the bottom of the fracture

sooner than those starting from the top. After a

longer period of time, more particles settle on top

of the previously introduced ones. A bed of particles begins to form on the bottom of the fracture

as more and more particles have time to reach the

particles resting on the bottom (Fig. 5.9). Model

studies conducted by Babcock" indicated that once

the particles reached the bottom of the fracture

they did not tend to move farther into the fracture

but formed a stable bed of proppant at the bottom.

Most fracturing treatments use a fluid that has

a significant viscosity. The thicker fluids will decrease the rate of proppant settling. Thus, there

will be only a small bed of settled proppant and

most of the fracture will contain a proppant slurry

(see Fig. 5.10). If the pumping time is long

enough, all the proppant in the leading edge of the

slurry may reach the bottom before the job is completed. This distance is often called the "carry distance," based on the specific job conditions. This

is essentially the greatest distance along the length

that proppant can travel under these conditions.

~g. 5.8

--g. 5,9

Fig. 5.10

Revised 6YH

HESI303142
After the carry distance is reached, the growth of

the bed is only in the vertical direction because the

particles entering the fracture at the wellbore will

settle to the top of the bed before they reach beyond this point (Fig. 5.11).

Carry D~stance

Fig. 5.11

Throughout the pumping time of the job a

number of factors are changing simultaneously,

each one of which affects the growth rate of the

bed:

 ̄ The fracture width is increasing; which tends to

decrease the fluid velocity, and thus to decrease

the distance the particles travel horizontally.

 ̄ The temperature of the proppant laden fluid

may be increasing as it moves down the fracture,

possibly making the fluid less viscous.

 ̄ The walls of the fracture are being cooled, so the

latter proppant stages are exposed to less heat

and maintain higher viscosity than early proppant stages.

 ̄ The fluid loss is increasing the proppant concentration which results in greater particle interference and a decrease in settling velocity in the

same manner that increasing fluid viscosity decreases particle settling rate. This is called "hindered settling."

Through the use of computer simulation of a

fracturing treatment, we can calculate the growth

of a hydraulic fracture. We can also model the

proppant transport to estimate the degree of settling during the pumping operation, t3 When we do

a computer simulation, we find that for most formation temperatures, gelled fluids will give an

end-of-pumping proppant distribution similar to

Figure 5.12. This figure is representative of a hydraulic fracturing treatment using a viscous fluid.

In this example treatment, a specific volume of

viscous fluid without proppant (pad fluid) was

pumped first, followed by stages containing 1.0,

2.0, 3.0 and 4.0 pounds of proppant per gallon of

fluid. A portion of the proppant has settled to the

bottom during the pumping operation, but most of

the proppant is still in a suspended slurry. Notice

that, due to fluid loss, the concentration of proppant in each stage has increased significantly. If the

fluid loss were more severe, the proppant concentrations would be even higher.

II Slurry I 1.8ppg

i ~ Slurry

Deposited Proppant Bed

Pad

Rg. 5.12

Figure 5.13 illustrates the propped fracture if

the suspended proppant could be trapped by fracture closure (healing) without any additional proppant settling having time to occur. Unfortunately,

this condition will not necessarily be the actual

result. The time needed for the fracture to close

sufficiently to trap the proppant may be quite

long. The settling velocity of the proppant will

depend on the proppant type and size, as well as

the fluid viscosity.

Unpropped Fracture

Fracture

Fig. 5.13

Figure 5.14 shows two other possibilities for

the final propped fracture that may result from the

treatment represented in Figure 5.12. In most reservoirs, it can be assumed that the unpropped fracture area will essentially heal back to such a degree

Revised 6YH

HES1303143
16 ,~vdraulic fracturing

that it will not significantly contribute to the stimulation of the well’s production. If a computer

simulation of a fracture stimulation is to be valid,

it will be necessary for the simulator to model the

fracture closure and the additional proppant settling that will occur during the closure time.

Unpropped Fracture

Unpropped Fracture

Fig. 5.14

Tail-In Using Thin Fluids

III

Another circumstance to consider is what

takes place when proppants of different sizes are

run, such as 20/40 mesh sand tailed-in by 12/20

mesh sand. The 12/20 sand will have a faster settling rate due to its larger grain size. If a low viscosity fracturing fluid is used, then where the

12/20 sand is deposited will depend upon where

the 20/40 sand is and what its deposition history

has been. If sufficient 20/40 sand were run to

reach an equilibrium bed height, and a considerable amount of 12/20 pumped, it may be predominantly deposited on the leading edge of the 20/40

bed as in Figure 5.15. Although the 12/20 might

be called tail-in, it really ended up at the leading

edge of the bed. If only a small quantity of 12/20

sand were run, it might all be on top of the 20/40

bed with no extension of the carry distance.

However, if the 20/40 sand had not been

pumped long enough to reach equilibrium height,

the 12/20 sand might be deposited as in Figure

5.16. In this case, the 12/20 sand only increased

the bed height without increasing the length. If a

very large quantity of 12/20 sand was pumped in

this example, it might reach equilibrium height

and then extend the carry distance.

Note: These illustrations ignore any entrance

effects at the wellbore.

Fig. 5,15

Fig. 5,16

Suspended Proppants

The deposition of proppant will be somewhat

different when fluids that have moderate to high

viscosities are considered.13 If the fluid has an apparent viscosity greater than about 100 centipoise,

there are several distributions that might occur.

A condition that might exist is where only the

first proppant remains in suspension in the fluid.

If the fluid viscosity were high or the first proppant were small, the terminal settling velocity

might be very slow and the particle settling would

be insignificant during the time of treatment.

If fluid of a few hundred centipoise viscosity

were used to carry 20/40 sand, the settling rate

might be about 0.001 ft/sec (i.e., during a 100 minute treatment, the particles would settle only 6

Revised 6YH

HES1303144
hydraulic fracturing 17

feet). If the fracture were 100 feet high, the deposited 20/40 sand bed would be very small and most

of the particles would still be suspended at the end

of the job. Tail-in of larger proppant introduced

after the 20/40 could displace the 20/40 sand slurry

and could form a bed configuration as in Figure

5.17.

Fig. 5.17

Suspenc~eO 12/20 ISuspended~

I 20/40 II

-~x__. [~eposite~t 12/20

~ Deposite6 20/40

If, after pumping ceases, the fracture remains

open for a very long period of time, and/or the

fluid viscosity thins enough for the proppant to

settle, a final bed configuration like that shown in

Figure 5.18 might result.

a fracturing fluid with an apparent viscosity

greater than 200 centipoise in the fracture probably

will transport the proppant with little settling.

tad

Fig. 5.19

Obviously many possible situations might be

imagined, but the cases shown serve to illustrate

some of the complexities of proppant distribution.

The result of the consideration of proppant

settling is that the propped length (xr) will be less

than the created fracture length (L) and only part

of the created height may be propped. The resulting production increase will depend upon both the

propped length and the propped height, as will be

discussed in Part 10.

Fig. 5.18

If the proppant is in suspension due to a high

viscosity fluid and the fracture closed before settling takes place, a low concentration distribution

may result (Fig. 5.19). This condition would not

be uncommon with modern, complexed gelled

fracturing fluids. The proppant distribution would

be at a much smaller concentration (lb/sq ft of surface area) than when a bed was formed. In general,

LABORATORY TESTS FOR

SELECTION OF BASE FLUIDS

Part 6

Types of Base Fluids

Two basic types of fluids are used in hydraulic

fracturing: hydrocarbon (or oil) base and aqueous

(or water) base fluids. Hydrocarbon base fluids

may be crude oils or refined liquid hydrocarbons.

The advantages of this type of fluid are that they:

 ̄ are non-damaging to clays

 ̄ have low fluid-rock interfacial tension

 ̄ are generally compatible with most formations

and formation fluids.

The economics of hydrocarbon fluids may be

advantageous, depending upon whether the fluid is

Revited

HESI303145
8 hT,~raulic fracturing~

recovered and either reused or sold. Of course

there are disadvantages to the use of liquid hydrocarbons. The primary disadvantage is that they can

be hazardous to handle under certain conditions.

The use of water base fluids has continually

increased. This type of fluid includes low strength

salt solutions, water-alcohol mixtures and low

strength acids using 3 to 5 percent hydrochloric

acid as an aqueous base. Water from various

sources may be used as a base fluid. The most

common sources are city and well water. Occasionally, water from streams, lakes or sea water is used

as a base fracturing fluid. However, water from

these sources should be checked for suspended

solids or other contaminants which should be removed before the fluid is used.

There are a number of advantages to water

base fluids:

 ̄ these fluids are safe to handle

 ̄ water sources are usually readily available

 ̄ gelling agents and other chemicals can be

batch mixed (premixing)

 ̄ chemicals can be mixed continuously as the

fluid is being pumped into the wellbore

 ̄ it is possible to obtain much higher temperature stability than with oil base fluids.

The primary disadvantage is that water base

fluids could have some detrimental effect on formations which tend to be water sensitive, i.e.,

those with clay minerals and/or fluid retention

problems.

There are several laboratory tests which can

be conducted to determine the compatibility of the

fracturing fluid with a given formation. These tests

include petrographic analysis, X-ray diffraction

analysis, and basic fluid-rock compatibility testing.

Fluid-rock compatibility is evaluated through immersion tests, porosity and permeability testing,

fluid flow tests through the core samples using

various potential base fracturing fluids, and regained gas permeability testing. Other tests can

help predict potential emulsion problems and how

to reduce them, the compatibility of formation oil

with fracturing fluid oil (if an oil base fluid has

been selected), how best to destroy the gelling

agent which has been used in a fracturing treatment (gel break), fluid loss control, and fracture

conductivity measurements. These tests will be

discussed in more detail during the remainder of

this section.

Structural and Chemical Analysis of Formation Samples

Selection of base fracturing fluid is one of the

most important parameters in the successful application of hydraulic fracturing. Several laboratory

tests can be conducted on formation samples to

help us select the most appropriate base fracturing

fluid.

Petrographic Analysis

Using thin sections and the scanning electron

microscope (SEM), it is possible to determine the

type of formation with which we are dealing. Using thin sections, the type of minerals present and

the general relationship between the formation

matrix, the cementing materials and pore space can

be observed. This gives an indication of the type of

minerals that the fracturing fluid will contact when

fluid loss occurs. With knowledge of basic fluidrock interactions, thin section petrographic analysis gives some insight into potential compatibility

problems.

Another type of petrographic analysis uses the

SEM to observe the pore space and pore configuration of formation samples. The effects of various

fluids when placed on the core samples can also be

observed.1~-1~ The use of the Energy Dispersive Xray (EDX) analysis with the SEM allows better

identification of the samples being obse .ry~l-,~--~ ’ ..

 ̄  ̄

.~.¢J ’~£ ~L:r3’,.~ , X-Ray Diffraction Analysis ~ ...... ;,, ; "

This analysis is commonly use~l in bur indits--’"-

try to determine the type of crystalline formation

minerals present. X-ray diffraction, coupled with

the petrographic analyses described earlier, allows

us to determine the chemical and mineralogical

make-up of the formation.

The X-ray diffraction analysis is normally

done in two steps. The bulk sample is ground and

X-rayed to determine the non-clay fraction. The

minerals normally detected in the non-clay fraction

are quartz, feldspar, calcite, dolomite, anhydrite,

and other minerals in lesser quantities. The clay

fraction is separated by mixing the ground bulk

sample with water. The smaller particles are suspended in the fluid and are poured off onto a glass

slide. The water is allowed to evaporate, allowing

settling and orientation of the small particles. An

X-ray diffraction analysis is then made of this sepRevi~ed 6YH

HESI303146
arated, small particle fraction of the bulk sample.

By separating the fine, small particles, the clays

are concentrated and a better analysis is made. In

the clay fraction, clays of the kaolinite, chlorite,

illite, smectite and mixed-layer types may normally

be detected.

Evaluation of Fluid-Rock Interactions

Immersion Tests

These are basic and qualitative tests. However, immersion tests do allow a relative determination of the amount of fines which may be released

from the reaction between a fluid and rock sample.

By comparing the quantity of fines released from

the rock samples when subjected to various fluids,

relative compatibility is obtained.

For the immersion test, formation core pieces

are placed in various test fluids: fresh water, 2%

calcium chloride water, 10% sodium chloride, 2%

potassium chloride, various acid base fluids, and

kerosene. The acid base fluids allow evaluation of

the effects of low pH fluids. If the formation sample contains significant quantities of swelling clays

(smectite, mixed-layer, etc.), release of f’mes may

be partially controlled by the low pH or acidic base

fluids. Previous work has shown that aqueous fluids with pH less than 7 are more compatible with

clay containing formations than those with pH

greater than 7. ~16-~8 For this reason, ff at all possible, the aqueous base fracturing fluids are designed

with pH less than 7. However, because of other

fluid properties related to pH, a pH greater than 7

may be necessary in some cases to obtain the most

desirable fracturing fluid properties. This subject

will be discussed in more detail later in this text

(Part 7).

Porosity and Permeability Tests

Tests on formation samples cannot always be

made with the greatest degree of confidence. When

a core is removed from a well, it may be contaminated with drilling fluid. In addition, there is a

significant pressure change which could cause alteration of the physical condition of the clays. In

many instances, the cores have not been preserved

and are completely dry before any test is initiated.

This condition can develop a strain in the clay

packets which is rapidly released when the rock is

rewet. The drying-wetting procedure is certainly

one that would enhance the migration of clays,

resulting in an indicated permeability damage

more severe than would occur in the formation.

On the other hand, permeabilities normally

determined in the laboratory may be significandy

greater than those that exist in the formation.

Thomas and Ward’9 found that with cores that

contained very little clay, an overburden pressure

of 3,000 psi reduced surface gas permeability values by 62 to 90%. At 6,000 psi, permeability reduction was in the range of 73 to 99%. Thus,

permeability damage determined in the laboratory

with formation samples does not necessarily reflect

the same degree of damage that could occur in the

formation.

Porosity and permeability testing help us to

determine:

 ̄ how much fluid might be lost to the formation

under various conditions during a fracturing

treatment

 ̄ the levels of porosity and permeability which

may be related to potential fluid retention

problems

 ̄ which core samples should be used in various

types of laboratory testing.

Fluid Flow Tests

Fluid flow tests are normally used in our industry to evaluate the effects of fluid which may

be lost and forced to flow through the formation.

Of concern here is the movement of f’me particles

through the formation.

Fluid flow tests are normally conducted on

formation core samples having liquid permeabilities of at least 0.1 millidarcy. Lower permeabilities

tend to yield results which are somewhat erratic

due to low flow rates. Flow tests are conducted by

obtaining an initial flow rate with some compatible

fluid such as formation water, oil, etc. through a

core plug. Then a second flow is normally made in

the reverse direction through the core plug with a

test fluid. Following the second flow, the final flow

in the same flow direction as the original flow is

made with the original flowing fluid. By comparing the initial flow to the f’mal flow, it is possible to

determine the effects of the test fluid on the core

sample. There is an API standard test procedure,

discussed in API RP 39, for conducting these tests;

however, there are many variations of this basic

procedure used in our industry.

HESI303147
Regained Gas Permeability Tests

In the case of extremely low permeability and

where it would be anticipated that the produced

hydrocarbon would be a gas, the concern is not so

much from fluid flow through the formation as it

is in fluid retention. Small amounts of fluid which

are lost to the formation may be retained by the

formation due to capillary effects. Regained gas

permeability may be low or nonexistent. Several

papers have dealt with the effects of damage along

the fracture face.2°’2 Fluid retention in very low

permeability formations can be aggravated by

small capillaries, fluid-rock incompatibility, and

low reservoir pressure. The laboratory test

used to determine the relative fluid retention effects of various fluids on low permeability gas

sands is a basic regained gas permeability test. The

core samples are saturated with a test fluid to as

near 100% saturation as possible. Then the core

sample is contacted with a gas, normally methane

or nitrogen, at a given pressure. The permeability

to gas is then measured versus time. The time required to obtain some fraction of the original gas

permeability, normally 70%, is recorded for some

fluid. Various fluids are tested, and by comparing

the relative times (T-l, T-2, etc.), it is possible to

determine which fluids would allow faster regained

gas permeability and well clean-up after fracturing

(Fig. 6.1).

When fluid retention or slow clean-up following fracturing is thought to be a problem, energized fracturing fluids may be advantageous.

Nitrogen and carbon dioxide gases are often used

for this purpose.

100%

Fluid 1

~

Fluid 2

~ Fluid 3 ,.

T1 Time T2

Fig. 6.1

Evaluation of Fluid Properties

At least five other tests can be conducted in

the laboratory for information about fluid compatibilities.

Emulsion Tests

Once a base fracturing fluid has been selected

which is compatible with the formation, it is important to select the right non-emulsifying agent to

be added to that fluid. The purpose of the nonemulsifying agent is to prevent down.hole emulsions from occurring if liquid hydrocarbons are

present and aqueous base treating fluids are used.

These tests are normally conducted in the laboratory by mixing equal volumes of the base fracturing fluid and the liquid hydrocarbon under

agitation to see if an emulsion is formed. If so,

through additional testing the proper quantity and

type of non-emulsifying agent is determined.

Oil Compatibility Tests

If the laboratory testing has indicated that an

oil base fluid should be used in an oil producing

formation, then it is important to determine if the

two fluids (the fracturing fluid and the formation

fluid) are compatible. This is normally done by

mixing equal volumes of the two hydrocarbons and

observing any formation of precipitates, sludge,

etc.

Gel Break Tests

Since viscosifiers (gelling agents) are used in

the majority of fracturing fluids, it is important to

incorporate the proper breakers to assure a gel

break after the gelling agent has served its purpose. In many cases, standard gel break curves are

given by the various service companies for the different gelling agents. If long pumping times, at

possibly high bottom hole temperatures, are to be

encountered, special gel break tests may have to be

conducted to find out if the gelling agent will withstand the extreme conditions for the desired pumping time and break within the desired gel break

time.

Fluid Loss Tests

Fluid loss tests are usually conducted with the

base fracturing fluid that had been selected

through previous tests. Fluid used in fluid loss

R¢,dsed 6YH

HES1303148
testing would normally contain gelling agents and

solid particulate or liquid fluid loss additives when

necessary.

Fracture Conductivity Tests

If there is concern about the selected base

fracturing fluid softening the formation face so

that proppant embedment may become a problem,

core samples can be subjected to the base fluid

prior to fracture conductivity testing. Then the

effects of the wetted core on fracture conductivity

can be determined. The type of testing will be

discussed further in Part 9 of this text.

FACTORS INFLUENCING

HYDROCARBON

PRODUCTION

Part 7

Several factors can influence the results of

treating hydrocarbon reservoirs by hydraulic fracturing using proppants to maintain conductivity in

the created fracture. These factors can be divided

into two areas where the effects of fracturing fluids

and additives are observed:

 ̄ matrix permeability in the vicinity of the fracture face

 ̄ fracture conductivity of the proppant bed.

Matrix Permeability

Cementing Materials in Sandstones

When dealing with the hydraulic fracturing of

sandstone reservoirs, there are three basic types of

sandstone to consider. These types are categorized

by their cementing material: silicate, clay, or carbonate.

With silicate cemented sandstone, there is

little concern about fluid reaction with the rock

since the silicate is basically inert to any of the base

fracturing fluids. The second type is a clay cemented sandstone in which clay is exposed at the

pore space. Any fluid which leaks off to the pore

space may contact a potentially very reactive material which can cause formation damage by swelling

or dislodging the clays and/or fines so that migration can occur. In carbonate cemented sandstone,

the cementing material in contact with the pore

space is acid soluble. Here we can expect low pH

or acidic fracturing fluids to react with the carbonate, which could have either advantageous or detrimental results. In may cases, there may be more

than one cementing material in a given interval,

and multiple reactions must be considered.

There are also those formations which are

almost entirely carbonate (limestones and dolomites) which may respond to hydraulic fracturing

using either propping agents or acids to generate

fracture conductivity.

Fluid Retention

The result of fracturing fluid retention near

the fracture face can decrease the rate of hydrocarbon production. Fluid retention is a common

problem encountered in the fracturing of low permeability sandstone formations using aqueous base

fluids. This problem can be minimized by using

various chemicals such as surfactants and alcohols

to reduce surface and/or interfacial tension, and

energizing gases such as nitrogen and carbon dioxide.

Iron Compounds

Another common problem can be encountered

in formations which have high concentrations of

iron containing clays and minerals in the matrix

rock. These iron compounds can result in matrix

permeability reduction either as migrating fines or

as precipitation of dissolved iron compounds. The

precipitation of gelatinous iron compounds can be

minimized by controlling pH below 3.5, preventing oxidation of ferrous to ferric iron, and/or using

chelating agents to maintain the iron in a soluble

form. 23

Fluid Residue

Other sources of potential reduction in matrix

permeability near the fracture face are the solids

introduced in the fracturing fluid. These solids can

arise from gelling agent residue, fluid loss addifives, and impurities in the water used for the fracturing fluid.

Clays

The presence of clays in the matrix can have a

major influence on the production of hydrocarRevised 6YH

HESI303149
bons. The problems presented by clays are complicated by the fact that clay composition and its

location in the rock permeability can vary extensively. In reality, clays along any part of the drilled

hole can present a variety of problems in all phases

of the life of the well. There are shales that show a

high degree of deterioration when contacted by the

common types of water base drilling fluids. Fluid

loss from cement slurries and certain water base

stimulation fluids are other sources of potential

damage to permeability.

Clays may be found in almost all types of

rock. Some rocks may be defined as a "water sensitive" formation if a reduction in effective permeability is noted when a foreign water invades the

formation. Normally, sandstone formations exhibit

the greatest degree of water sensitivity. Clays may

also be present in carbonate rocks, but are frequently encapsulated in the rock matrix. Thus,

they are not in a position to be contacted by the

invading fluids.

In addition to the problems caused by swelling clays, permeability damage may be caused by

migration of clays and other fines with fluid flow.

Subsequent bridging of particles at flow restrictions in the rock flow channels causes a plugging

action which results in a permeability reduction.

This overall effect primarily occurs during the flow

of water. (Clays are discussed further in Appendix

C.)

Fracture Conductivity.

Since one of the primary goals of a successful

stimulation treatment is to place a high permeability proppant bed in the created fracture, any factors which tend to reduce the conductivity should

be minimized. Some of these factors are discussed

below.

Embedment

Proppant embedment in the fracture face as

closure occurs will reduce the proppant bed conductivity. Fracturing fluids should be carefully

selected to minimize softening of the formation

due to incompatibility of the rock and fracturing

fluid.

As leak-off occurs during the fracturing treatment, the filter cake deposited by the various

chemicals used can also lead to a potential source

of conductivity reduction. This reduction can

RevVed 6YH

result due to embedment of proppant in the filter

cake which forms along the fracture face. This

problem would be most prevalent in formations

with high rates of fluid leak-off.

F’mes in Fracture

Several sources of potential flow restrictions in

fracture proppant beds originate from the chemical

additives in the fracturing fluids. Nondegradable

fluid loss additives such as silica flour can lead to

significant reductions in fracture conductivity if

the material migrates into the proppant bed. Solids

originating from the gelling agents used in fracturing fluids are also a source of potential damage to

proppant bed conductivity. As the polymers degrade, many leave an insoluble residue which can

reduce flow through the proppant bed.

Clays along the fracture face can contribute to

conductivity reduction especially if the fracturing

fluid is not selected carefully for compatibility with

the formation rock. Fines can be released into the

proppant system. These fines may drastically reduce the conductivity of the proppant bed.2’

As illustrated in Figure 7.1, greater than 65%

reduction in fracture conductivity can result with

as little as 5% fines (60 to 140 mesh) added to a

1.0 lb/ft2 sand proppant system. These fines can

result from fluid-rock interaction along a fracture

face.

FINES VS. FRACTURE CONDUCTIVI’~

5 10 15 20 25

% Rnes Added

Fig. 7.1

Fines associated with the propping agent can

also cause significant reduction in fracture conductivity. These f’mes can originate from impurities

present in the propping agent or can be generated

due to crushing of the proppant.

HESI303150
Solids in the proppant bed may arise from

drilling fluids that have been lost in the hydrocarbon bearing zone that is fractured. These drilling

fluid solids can cause significant production problems as the fines migrate into the propped fracture.

Summary

The result of a successful fracturing treatment

is a highly conductive fracture. Many factors have

to be considered in selecting a fluid to minimize

the fluid-rock and fluid-fluid interactions. Careful

selection of the base fluid and additives will result

in designing a hydraulic fracturing treatment with

optimum results.

PROPERTIES OF CHEMICALS

AND FRACTURING FLUIDS

Part 8

Many factors should be considered when selecting a base fluid for hydraulic fracturing. In

addition to the formation properties discussed in

Part 7, other conditions that influence the selection

of base fluid include:

 ̄ fluid temperatures encountered

 ̄ treating pressures

 ̄ well completion (tubing vs. casing)

 ̄ economics

 ̄ safety.

As noted earlier in this section (Fig. 2.1), the

trend of base fluid selection has resulted in more

than 90% of the current usage being water base

fluids.

Common Fractttdng Chemicals

There are a number of chemical additives being used in fracturing fluids. These chemicals give

the fluids certain desired properties to assist in

successful hydraulic fracturing treatments. The

following general classes of chemicals and their

properties are discussed in the remainder of this

part of the discussion on hydraulic fracturing:

 ̄ polymers

 ̄ crosslinkers

 ̄ pH control chemicals

 ̄ gel breakers

 ̄ surfactants

 ̄ clay stabilizers

 ̄ alcohol

 ̄ biocides

 ̄ fluid loss additives

 ̄ friction reducers.

Fracturing Polymers

A polymer is defined as a substance composed

of giant molecules that have been formed by a

chemical combination of specific small molecules.

The polymers used in fracturing are used primarily

as gelling agents to increase viscosity of the fracturing fluid for the development of fracture width

and proppant transport. The gelling agent also

gives some reduction in pipe friction from the base

fluid while treating down the tubular goods. Polymers are also often used in low concentrations

solely for the purpose of reduction in pipe friction.

With oil base fluid., a polymer is formed i.n

dtu in the oil through the formation of an "association polymer." An organic acid or organicphosphoric acid and a base are reacted in the

liquid hydrocarbon to form association polymers

(Figs. 8.1 and 8.2). Currently, the most common

chemicals being used for the gelation of oils for

fracturing fluids are the aluminum phosphate type

products. In addition to the primary association

polymer being formed, there have been recent developments which allow the addition of a solid

aluminum phosphate to the pre-gelled oil. This

solid material acts as a secondary gelling agent

which yields viscosity downhole for better temperature stability than has been available in the past. ~

The use of polymers in aqueous base fluids is

somewhat less complex and more controllable than

those formed in oil base fluids. In aqueous base

fluids, polymers as free flowing solids are normally

added to the water and hydrate, yielding an increase in fluid viscosity. As illustrated in Figure

8.3, this tightly coiled, dry polymer uncoils as it

reacts with water and hydrates to become more

linear. This long chain, linear polymer occupies

more volume as it hydrates and tends to reduce the

levied 6YH

HESI303151
4 hydraulic fracturing

mobility of the water molecules. This’decreased

mobility results in an increase in fluid viscosity.

The base fluids, water and oil, usually exhibit

Newtonian fluid behavior in viscosity characteristics. In any of the base fluids in which a polymer

or an association polymer is formed, the shear rate

- shear stress relationship is changed, and we are

no longer dealing with a Newtonian fluid. As

shown in Figure 8.4, in addition to Newtonian

fluids, there can be several types of nonNewtonian fluids with different rheological properties. The Bingham plastic fluids are those which

can be characterized by a straight line curve which

as an intercept on a shear stress axis, have a yield

stress value.

CHEMISTRY OF OIL GELS

CHa(CH2)mCO2H

Acid

+

NaOH

Base

CHa

I

Association Polymer

F~g. 8.1

ALUMINUM PHOSPHATE

ASSOCIATION POLYMER

RN /R /R

ON /O

RNON /O

...o, ,.O ::,,:::o. "" "’" "" 0% p ok p

o/ NO

o/ NO

H/ NR H/ NR

Fig. 8.2

COILED

POLYMER

(DRY)

WATER BASE

LINEAR POLYMER

(HYDRATED)

Fig. 8.3

The pseudo-plastic fluids are those which

exhibit no yield stress value and are characteristic

of most of the fracturing fluids used in our industry today. In Figure 8.4, a rectilinear plot of shear

stress versus shear rate, these pseudo-plastic fluids

are represented by a curve. However, where a loglog plot of the same data is made, a straight line,

Linear relationship with a slope between 0 and 1 is

obtained. An empirical relationship known as the

"power law" is widely used to describe these fluids. As shown in Figure 8.5, the slope of the

straight line is denoted as n’ and the intercept at

unity shear as K’. The n’, a measure of the degree

of the non-Newtonian behavior of the fluid, is a

constant. By knowing the n’ and K’ values for a

given non-Newtonian, power law fluid, the apparent viscosity can be calculated using the following

equation:

47,879 K’

P" - (SR) "°’

where:

Ix. = apparent viscosity, cp

K’ = consistency index, lbf (sec)*’

ft2

n’ = flow behavior index

SR = shear rate, sec .1

Shear stress is expressed in units of lb/ft2.

(8-1)

Revised 6YH

HESI303152
The shear rate in the fracture can be calculated with the following equation:

40.464 q SR - w~ h

(8-2)

where:

q = injection rate, bpm

w = fracture width, inches

h = fracture height, feet

There are many ways of reporting viscosity of

the various fracturing fluids in our industry today.

However, through the use of the power law concept, an apparent viscosity can be calculated at a

specified shear rate. The shear rate used in calculating the apparent viscosity should always be reported. As an example, a fluid having an an n’ of

0.5 and K’ of 0.025 would have a calculated apparent viscosity of 53 cp at 511 sec-~ and 120 cp at 100

seC4.

There are several polymers used in aqueous

base fracturing in our industry including:

 ̄ guar

 ̄ refined guar

 ̄ hydroxypropyl guar (HPG)

 ̄ carboxymethylhydroxypropyl guar (CMHPG)

 ̄ hydroxyethyl cellulose (HEC)

 ̄ carboxymethyl cellulose (CMC)

 ̄ carboxymethylhydroxyethyl cellulose

(CMHEC)

 ̄ polyacrylamide (PAM)

 ̄ xanthan (XC).

Shear

Stress,

Pressure

Drop, or

Torque

Laminar Flow

Shear Rate, Rate of Flow or Rpm

Fig. 8.4

NON-NEWTONIAN

POWER LAW FLUIDS

47879 K’ IJ, a = (SR)I -n’ ,cp

Fig. 8.5

log SR, sec-1

The requirements for fracturing fluids are

quite variable. Because of the wide variation in

requirements and applications of fracturing fluids,

a large number of fracturing chemicals have been

developed. The gelling agents for aqueous base

fluids are polymeric, hydrophilic chemicals. ~z7

These chemicals are polymers, and as such are

distinguished from non-polymers on the basis of

their molecular size. This large molecular size

leads to their ability to alter the viscosityrheological properties of the fluids. The structure

for each repeating unit for the guar, guar derivative

and cellulose derivative is shown in Figures 8.6,

8.7, and 8.8.

All of the polymers possess quite different

chemical characteristics, and each imparts different

properties to a fracturing fluid. Polyacrylamides

and the xanthan polymers are used only occasionally as gelling agents. Guar and guar derivatives are

most commonly used.

Guar

Guar is a naturally occurring polymer. It

comes from the guar bean, which is grown primarily in India. The bean’s hull is removed and the

inside portion (or endosperm) is ground into a fine

powder giving us the basic guar polymer used as a

viscosifier. This polymer is used in many industries, and several million pounds of guar are used

in the hydraulic fracturing industry each year. The

general properties of guar include:

 ̄ May be used in brines

 ̄ 8 - 10% residue

 ̄ Easy to crosslink

 ̄ 50 lb -- 48 cp ~ 511 sec~

 ̄ Cost factor -- 1.0

HESI303153
One of the concerns in the use of guar has

been the residue which remains upon its degradation following a fracturing treatment. Several studies have been conducted on the effect of inherent

solids present in the guar and fracturing fluids.

These studies indicate that damage can be expected from the solids in some cases. 28.~9 However,

the solids associated with such fracturing fluids

should not always be looked upon as detrimental

since fluid loss to the formation is a very important fracturing treatment parameter. Fluid loss to

the formation can be controlled in some cases with

fracturing fluid viscosity, as discussed earlier.

However, in many cases solid particles are required

to control fluid loss. If a gelling agent contains

solid particles, it obviously possesses better fluid

loss properties than one which is solids free. For

this reason, in selecting a gelling agent, potential

damage from solids should be considered in conjunction with the fluid loss and successful proppant placement during the treatment.

REPEATING UNIT FOR GUAR

POLYMER

n ~ 400-600

CH±OH

H N

Fig. 8.6

REPEATING UNIT FOR GUAR

DERIVATIVE R = H OR

HYDROXYALKYL GROUP

I n-’~o4o~

RO H

CH:OR

REPEATING UNIT FOR CELLULOSE

DERIVATIVE R = H,

HYDROXYALKYL, OR

CARBOXYMETHYL

n 5 3000-4000

CH=OR

Fig. 8.8

The popularity of guar as a gelling agent for

fracturing fluids is primarily due to its ability to

produce substantial viscosity per unit cost, compared with other gelling agents. A refined guar has

been introduced recently that has a reduced

amount of residue compared to guar, but similar

properties otherwise.

Guar Derivatives

Derivatized guars, such as hydroxypropyl

guar (HPG) and carboxymethylhydroxypropyl guar

(CMHPG) have most of the advantages of the regular guar with the additional advantage of a reduction in residue after break. Current usage trends

show that HPG is now being favored over the underivatized guar. It should be pointed out that not

all hydroxypropyl guar polymers are the same.

They can vary depending upon the degree of derivatization. For example, when there is a high

degree of substitution with hydroxypropyl groups

on the guar molecule, the HPG becomes more soluble in alcohol. Various HPGs are available for

different applications. The general properties of

HPG include:

 ̄ May be used in brines

 ̄ 1 - 2% residue

 ̄ Easy to crosslink

 ̄ 50 lb -- 51 cp @ 511 sec~

 ̄ Cost factor -- 1.4

Another guar derivative, carboxymethylhydroxypropyl (CMHPG) has properties similar to

HPG with additional versatility in crosslinking

properties. Its properties include:

Fig. 8.7

Revised 6YH

HESI303154
 ̄ May be used in brines

 ̄ 1 - 2% residue

 ̄ Easy to crosslink

.1

 ̄ 50 lb-- 42 cp @ 511 sec

 ̄ Cost factor -- 1.4

Cellulose Derivatives

Cellulose derivatives have been used in our

industry for several years. The most popular cellulose derivative used in hydraulic fracturing operations has been hydroxyethyl cellulose (HEC). The

general properties of HEC include:

 ̄ May be used in brines

 ̄ Residue free

 ̄ Not usually crosslinked

 ̄ 50 lb -- 68 cp @ 5 I1 sec~

 ̄ Cost factor -- 1.7

One of the primary advantages of HEC is that

it is residue free after degradation. If formation or

proppant system damage from residue is anticipated, HEC is preferred. (See Figs. 8.9, 8.10, and

8.11 to compare amountS of residue from guar,

guar derivatives and cellulose derivatives.) The

HEC is not usually used as a crosslinked fluid for

most fracturing applications.

Carboxymethyl cellulose (CMC) is used as a

residue-free polymer which can be crosslinked.

One disadvantage of CMC is its limited use in

brines due to its salt sensitivity; the higher the

percentage of salt in an aqueous solution, the less

viscosity yield per pound. The maximum acceptable salt (NaC1 or KCI) content is normally 2% or

less. It is extremely sensitive to calcium salts. CMC

is being used in a number of areas to prepare a

crosslinked, residue-free fracturing fluid. The general properties of CMC include:

 ̄ Limited use in brines

 ̄ Residue free

 ̄ Easy to crosslink

 ̄ 50 lb -- 43 cp @ 511 sec~

 ̄ Cost factor -- 1.6

More recently, a double derivatized cellulose,

carboxymethyl-hydroxyethyl cellulose (CMHEC) is

f’mding wide usage in a number of applications.

CMHEC has the advantages, but not the disadvantages of HEC and CMC. Its properties include:

 ̄ May be used in brines

 ̄ Residue free

 ̄ Easy to crossllnk

.!

 ̄ 501b--55cp(~z 511sec

 ̄ Cost factor -- 1.7

Polyacrylamides

As mentioned earlier, polyacrylamides (PAM)

are very rarely used as a fracturing fluid gelling

agent. Those polyacrylamides and copolymers that

are being used primarily function as friction reducers at concentrations in the dry form of 2 to 4 lbs

per 1000 gallons fluid. They would normally be

used in a prepad and/or flush volume of the fracturing treatment. PAM can be degraded, is residue

free and usually ionic in nature. Cationic and anionic (as well as nonionic) forms are available for

various applications. The properties of polyacrylamide and copolymers include:

 ̄ Friction reduction

 ̄ Residue free

 ̄ Used in low concentrations

 ̄ Cost factor -- 1.8

Fig. 8.9

Fig. 8.10

HESI303155
Fig. 8.11

Xanthan

The xanthan polymer has been used for a

number of years in the drilling industry. However,

within the last few years it has been introduced

into the fracturing fluid industry, and there are

some areas which are using the xanthan gum as a

viscosifier. Xanthan properties include:

 ̄ May be used in brines

 ̄ 3% residue (using hypochlorite, oxidizing

breaker)

 ̄ Can crosslink

 ̄ 50 lb -- 28 cp @ 511 sec"1

 ̄ Cost factor 2.0

Although xanthan polymers do not yield as

much viscosity per pound as other viscosifying

polymers, they do have very good proppant transport characteristics. This has been one of their

main advantages of use in hydraulic fracturing

work. One of the primary disadvantages is the

inability to obtain a controlled break of the gelled

fluid.

Crosslinking Agents

A large percentage of fracturing fluids are

being crosslinked with chemical agents. Used in

very small amounts, these agents can give very

large increases in apparent viscosity of the base

gel. The crosslinkers work by chemically linking

the linear polymers in the fluid together, further

restricting the ability of the water molecules to

move as shown in Figure 8.12. Some common

crossLinking agents are:

 ̄ borates

 ̄ aluminum

 ̄ titanium

 ̄ zirconium

 ̄ antimony.

The selection of the proper crosslinking agent

is based upon the type of gelling agent being used,

the pH of the gel system, predicted fluid temperatures, as well as other factors. In the case of borates, the pH of the base fluid needs to be in the

range of 9 to 10 for crosslinking. With most of the

other crosslinkers, metallic ions, the pH will usually be in the range of 2 to 8 depending on the

polymer used.

Of concern with these crosshnked fluids is the

shear stability while pumping down the tubular

goods and through the perforations. The shear

stability can be evaluated in the laboratory by

shearing the crosslinked gel with a gear pump or

other shearing device and determining the time

required for the crosslinked gel structure to reappear or reheal. This may be related to the fluid

going through the surface pumping equipment, the

tubular goods, and perforations. Following shear,

the crosslinked fluids should reheal rapidly under

downhole conditions so the propping agents will be

transported and not dropped from the fluid inside

the fracture near the wellbore. This is an important consideration in the choice of any of the gelling agents and crosslinkers available.3°31

CROSSLINKED POLYMERS

I~g. 8.12

Revised 6YH

HESI303156
The use of delayed reacting crosslinkers to

minimize the effect of shear in surface equipment

and tubular goods is a recent development. The

reaction of the crosslinker can be controlled so that

crosslinking occurs near the perforations or after

the fluid enters the fracture. The resulting fluid

has considerably more viscosity in the fracture

than a fluid that experiences high shear while

crosslinking (Fig. 8.13).

CROSSLINKED FLUID VISCOSITY AS RELATED

TO CROSSLINK TIME

D+R

Temperature

Fig. 8.13

These chemicals may be preblended with the

gelling agent or added separately as required during a hydraulic fracturing treatment.

Gel Breakers

Gel breakers are important chemicals which

are used in most fracturing treatments. The breakers for oil gels work by interfering with association

polymers. Normally an acid or a base is used for

the oil systems.

In water base fluids where a polymer has been

used, the breaker will chemically degrade the polymer into several short chains with reduced viscosity. This change from high to low viscosity is

necessary to minimize flowback of any proppant

from the fracture and to maximize the amount of

treatment fluid returning after the fracturing treatment. There are three classes of chemicals norreally used by the service industry as gel breakers

in water base fluids: enzymes, oxidizers, and acids

(see Fig. 8.14).

pH Control Chemicals

The pH of the fracturing fluid has been mentioned several times throughout this discussion.

The control of pH is very important to the total

fracturing operation. The pH control chemicals

allow buffering of aqueous base fracturing fluids in

the desired pH range. By proper pH control, polymer hydration rate, polymer temperature stability,

crosslinking characteristics, gel break and clay

control may be obtained. A pH less than 7 is preferred from a formation-fluid compatibility standpoint. However, because of the many factors

involved, it may be necessary to override this to

obtain other desired properties of the fracturing

fluid.

Common pH control chemicals used in our

industry include:

 ̄ monosodium phosphate

 ̄ sodium acetate (acetic acid)

 ̄ fumaric acid

 ̄ citric acid

 ̄ formic acid

 ̄ sodium bicarbonate

 ̄ sodium carbonate

 ̄ magnesium oxide.

GEL BREAKERS IN WATER BASE FLUIDS

Temperature pH

Enzymes 80 - 140°F 4 - 7.0

Oxidizers 140 - 260°F -

Acids 200°F <7.0

Fig. 8.14

Surfactants

Most fracturing fluids include surfactants

(surface active agents) for one purpose or another.

Surfactants are used to reduce surface tension and

capillary pressure in pore spaces. They are also

used to form emulsions, to prevent or break emulsions, to create or break foam, or to alter wetting

properties of capillary surfaces. (Surfactants are

discussed in more detail in Section 10 of this manual, Chemical Stimulation.)

Surfactants are polar chemicals and can be

adsorbed on all rock surfaces. Silicates (sand, feldspar, and clays) carry a negative charge and would

naturally attract any organic chemical that carries a

positive charge. In addition, relatively large anionic

(negatively charged) and nonionic organic molecules are adsorbed by silicates through hydrogen

Revised 6YH

HESI303157
bonding and Van der Waal’s forces. The amount of

chemical that will be adsorbed by a silicate surface

is directly proportional to the available surface

area. Dispersed smectite may have a surface area

as great as 750 square meters per gram. However,

where the clay crystals are in packets and not thoroughly dispersed, only a small portion of this area

is available for adsorption. The adsorption of surfactants on clay would be significantly greater than

on sand (150 to 200 square centimeters per gram).

Wetting Properties

Surfactants are frequently used with stimulation fluids to help prevent emulsions and aid in the

recovery of water from the rock. With smectite, it

has been shown that up to 0.55 grams of some

surfactants can be adsorbed by one gram of this

clay.32 Cationic surfactants are very strongly adsorbed and are essentially impossible to remove

with water. Nonionlc surfactants are also strongly

adsorbed but can be partially removed by water.

Anionic surfactants are adsorbed but are readily

removed by water. The degree of surfactant ad- -

sorption by illite and kaolinite is, on the average,

about 5% of that adsorbed by smectite while adsorption by sand is even less.

The wettability of the rock can be altered

from water wet to oil wet by the adsorption of cationic surfactants and by certain nonionic surfactants. This change in wettability can cause a severe

decrease in the permeability of the rock to oil.

Flow tests with cores having a wide range in permeability have indicated the greatest percentage

decrease in flow due to oil wetting to occur where

the original permeability was quite low.

The use of cationic surfactant in water fracturing procedures can present problems in more

than one area. Water lost to rock may become

trapped in the small flow channels due to oil wetring, thus limiting the production of hydrocarbons.

It has also been reported that oil-wet sand used as

the propping agent reduced fracture conductivity a

significant amount."

An oil-wetting surfactant had been used with

water to fracture several wells in a certain area.

Water recovery was almost nil, and the resulting

oil production was very disappointing. A change to

a water-wetting anionic surfactant resulted in a fast

water recovery and a good increase in oil production.

Reused 6YH

Some oil-base and invert emulsion muds contain surfactants that oil wet sandstone formations.

The resulting permeability damage frequently

masks the true potential of the well during initial

testing. This condition can be, at best, partially

remedied by treating the formation with a fluid

containing a strong water-wetting surfactant. However, complete contact of all the damage area with

this treatment cannot always be assured.

In recent years, a new technique in treating

sandstone formations to enhance aqueous fracturing fluid recovery was introduced. ~’ A special surfactant leaves the sandstone matrix and proppant

bed in a non-wet condition. The percent recovery

of the aqueous fracturing fluid following the fracturing treatment has been significantly improved

over conventional surfactants. The results of enhanced fluid recovery are shorter clean-up times

and larger production increases.

Emulsions

Surfactants are used in the preparation of

emulsions for use as fracturing fluids. The most

common emulsion" contains approximately 33%

water as the external phase and approximately 67%

as the internal phase of the emulsion. Emulsifying

surfactants are used at approximately 0.3 to 0.8%

by volume of the water phase. The water phase is

normally gelled with 20 to 50 lbs of gelling agent

per 1,000 gallons. This emulsion fracturing fluid

has several desirable properties. It has very good

viscosity and fluid loss properties as well as good

temperature stability and proppant transport. If

the oil is recovered and sold or reused, the total

cost of the emulsion per gallon is low. There is less

water to contact the formation than in a 100% water base fluid treatment.

A disadvantage of the emulsion is high pipe

friction. However, in areas where it has been used

on a large scale, completion strings have been designed around the use of an emulsion as a fracturing fluid. As a result, the friction property

disadvantage is overcome.

Foams

Surfactants are also used in the fracturing

industry to prepare foam fracturing fluids. The

surfactant concentration usually ranges from 0.5 to

1.0% (based upon volume of liquid). Normally, 20

to 40% water, acid or oil and 80 to 60% nitrogen or

carbon dioxide gas is used.

HESI303158
Foams used as fracturing fluids are dispersions of carbon dioxide or nitrogen gas in a liquid

with a small amount of surfactant. They have been

proven to be very effective, particularly in low

permeability, low pressure gas and oil zones. The

external liquid phase may be water, alcohol, acid or

oil. In most cases, the liquid phase is gelled to assist in transporting propping agents through the

surface equipment and to add viscosity to the

foam.

The apparent viscosity of foam is directly related to the volumetric percentage of gas phase and

liquid phase (Fig. 8.15). The volumetric gas percentage is referred to as the foam quality. For example, a 70 quality foam would consist of 70% by

volume gas and 30% liquid under the temperature

and pressure conditions to which it is being subjected.

APPARENT VISCOSITY OF CO,WATER

TWO PHASE FLUID AS A FUNCTION OF

300 CO2 QUALITY

.

o io ~ ~ ~o

P~e:~et CO~

F~g. 8.15

A normal foam fracturing treatment would

consist of passing the gelled liquid phase containing a surfactant through a blender where it is

mixed with propping agent and is then passed

through a pressurizing pump. Gaseous nitrogen or

liquid carbon dioxide is injected downstream from

the pressuring pump. A foam is formed at the

point of gas injection into the liquid-propping

agent stream. In some cases, foam generators are

used at the point of gas injection to assure a more

homogeneous foam. A maior concern in early foam

fracturing treatments using proppant was the relatively low concentration of proppant in the foam.

Since propping agent is added only to the liquid

portion of the foam, the proppant concentration is

reduced when the foam is made. However, this

potential disadvantage has been overcome through

the use of proppant concentrators, changes in

pumping equipment valves, etc., and proppant

concentrations of 1 to 10 lbs per gallon of foam are

now being used.

The advantages of foam are:

 ̄ excellent fluid loss characteristics

 ̄ good viscosity development

 ̄ sand carrying capability

 ̄ less liquid on formation

 ̄ rapid clean-up following treatment.

Fluid loss characteristics for foam have been

evaluated and reported by Blauer~, KingsT, and

Harris.3s These results indicate the fluid loss to the

formation is very low and superior to conventional

treatment fluids.

Foam viscosity has been described by Mitchell" as a Bingham plastic fluid, and by Reidenbach, et. al.~ as a yield pseudoplastic fluid. The

foam viscosity is related to the foam quality and

liquid phase viscosity.

Sand carrying capability has been measured in

static foams, which have been found to be very

good for. this purpose. Blauer reports that measured settling velocities in foams are much less

than settling velocities in water or gelled water.

Foam is sensitive to injection pressure since

the internal phase is compressible. Higher pressure

during a treatment would require more of the gas

phase to maintain the volumetric ratio for a given

quality foam. (For further information about the

applications of nitrogen, see Section 15 in this

manual.)

Computer programs are available~41 to calculate wellhead pressure, friction pressure, bottom

hole treating pressure, etc. for foam frac treatments.. Computer programs are also available for

frac design calculations where foam is being used.

Clay Stabilizers

Clay migration can be effectively controlled

by two processes. One uses the hydroxyaluminum

ion which is strongly adsorbed by clay. Subsequent

polymerization of this ion develops an inorganic

coating on the clay surfaces which minimizes clay

migration. Its use is well established in several

types of field applications. However, a treated formarion should not be acidized since this will remove the polymer from the clay.

RevVed 6YH

HESI303159
The other process uses a cationic organic polymer that is effectively adsorbed by clay. Again, the

polymer coating minimizes the possibility of clay

migration. Its use has been field proven in acid

treatments to help maintain a high level of production for a longer period of time and in preflushes

in fracturing. In addition, the organic polymer

coating appears to be stable to most hydrochloric

acid solutions and other well fluids.

Alcohol

Alcohol, a common fracturing chemical, is

used in two ways. In one use, alcohol is mixed

with water base fluid to make the fluid more compatible with the formation. With alcohol present in

a water base fluid at normally 20 to 40%, lower

surface and interracial tension between the fluid

and the rock is anticipated. It will also increase the

vapor pressure of the fluid. These factors will help

in the clean-up following treatment. Alcohol has

the disadvantage of being somewhat expensive and

can be hazardous to handle on location.

In other cases, alcohol is used in the range of

5 to 10% primarily to add temperature stability to

the gel system. In addition to alcohol for gel stabilization, other types of gel stabilizers are also used.

Biocides

Biocides are used in many fracturing fluids to

protect the polymer from attack by bacteria. Bactericides, or biocides, are chemicals that destroy

bacteria or microorganisms and prevent their further growth. Two types of microorganisms may be

found in water base fluids: aerobic (which consume water) and anaerobic. The anaerobic type are

sulfate reducing microorganisms which destroy the

polymer and produce hydrogen sulfide downhole.

Bactericides such as formaldehyde, amines and

amides are used to control growth of bacteria in

solutions containing polymers. The cycle for polymer degradation by microorganisms is illustrated

in Figure 8.16.

DEGRADATION OF POLYMER

BY MICROORGANISMS

Rg, 8.16

Microorganism Polymer

~Sugar/

Fluid Loss Additives

Fluid loss additives are a necessary part of

many fracturing fluids to assist in the control of

leak-off of the fracturing fluid to the formation

during treatment. Commonly used fluid loss agents

 ̄ silica flour

 ̄ silica flour and polymer

 ̄ oil soluble resin

 ̄ oil soluble resin and natural polymer

 ̄ emulsions

 ̄ insoluble gases

 ̄ hydrocarbon phase.

Both oil base and water base fracturing fluids

are being used in the fracturing industry. Water

base, which includes alcohol-water mixtures and

low strength acids, make up the majority of treating fluids.

The common chemicals added to these fluids

are polymers for viscosity development,

crosslinkers for viscosity enhancement, pH control

chemicals, gel breakers for polymer degradation

following the treatment, surfactants, clay stabilizers, alcohol, bactericides, fluid loss additives and

friction reducers. By using surfactants, emulsions

and foams can be made.

By proper analysis of the formation and treatment parameters, the proper chemicals may be

selected.

Revised 6YH

HES1303160
PROPPANTS AND

FRACTURE CONDUCTIVITY

Part 9

A main factor affecting the outcome of a hydraulic fracturing treatment is obtaining an adequate propped fracture. The propping agent

should provide and maintain a highly permeable

path for fluid flow toward the wellbore. The need

for a propping agent to help provide that path has

been verified by numerous field experiments.

When proppants are used, production is usually

higher and the production decline rate is much

slower. This suggests that an unpropped fracture is

subjected to a combination of forces that tend to

close the fracture which reduces its conductivity.

Fracture conductivity (or fracture flow capacity) is the ability of the fracture to convey the reservoir fluid to the wellbore. It is generally

expressed as the product of fracture permeability

and the fracture width.

Proppant particles must support the closure

stress to prevent fracture closure. In so doing,

some of the particles may crush, or in a soft formation, embed into the rock. The degree of crushing

or embedment depends on:

 ̄ proppant strength and size

 ̄ hardness of the formation being propped

 ̄ closure stress being applied to the proppant

bed.

If the particle either crushes or embeds, the

fracture conductivity will decrease markedly. If

severe crushing or embedment occurs, the fracture

conductivity may decrease so low that not enough

contrast exists between the conductivity of the

proppant bed and the permeability of the reservoir

rock. If this were to happen, results from the fracturing treatment may not be satisfactory because of

the loss of fracture conductivity.’2’ ~,.,~ ~ ,3

Types of Proppants

One of the ~st propping agents used in fracturing treatments was screened river sand. However, such angular, poorly screened sand contained

some particles that were too large to enter the fracture. Also, bridges sometimes would form in the

wellbore, on subsurface tools, or within the fracture itself. If the proppant is too large or if bridghag occurs, then a "screen out" will result and the

treatment will have to be ended prematurely. This

may result in a smaller propped fracture than had

been designed and addltionai expense for cleaning

out the proppant in the wellbore. Sands and other

types of selected propping agents now employed

are less angular and more uniformly graded ha size

than the early sands.

There is a long list of materials that have been

tested as potential propping agents. Many have

been tried in various types of formations but most

have been rejected from excessive cost or failure to

significantly outperform sand. Plastic beads, aluminum pellets, rounded walnut hulls and glass

beads of various sieve size ranges are found in the

"graveyard" of experimental propping agents.

High strength glass beads experienced possibly the

longest life of the earlier proppants.

Six proppants are commonly used in fracturhag today:

 ̄ sand

 ̄ high strength sintered bauxite

 ̄ intermediate strength sintered bauxite (or

other aluminum oxide ceramics)

 ̄ calcined bauxite

 ̄ resin coated sand

 ̄ zirconium oxide.

Today, graded silica sand (SiO2) is the predominant propping agent used in hydraulic fracturing operations. It is the most economical

proppant to use. However, it may be somewhat

limited in its effectiveness because of lower resistance to crushing. In deep formations with high

stresses, a higher strength proppant is usually substituted for sand. In the late 1970’s sintered bauxite particles were introduced which were able to

maintain high conductivity to very high closure

stressesJ5 "" In the 1980’s, we have seen a proliferation of intermediate strength and high strength

proppants intended for closure stress applications

above 6000 psi.’5~

Figure 9.1 gives the specific gravities and absolute volumes of sand and other types of proppants.

The shape of a proppant particle is a significant factor in its ability to provide conductivity.

Particles should be smooth and spherical so they

will pack with large pore spaces. In some select

cases, angularity may be advantageous because the

proppant will tend to bridge in the fracture and be

HESI303161
4 hydraulic fracturing

less likely to flow back into the wellbore. This is

especially true in a formation where the fracture is

very slow to close back completely.

The range of the mesh sizes recognized by the

API’748 is provided in Figure 9.2. This figure also

gives the maximum and average proppant diameters for each of the sizes.

Specific Absolute Volume

Proppant Gravity gaFlb

Sand 2.65 0.0453

Super Prop~R’ 3.55 - 3.73 0.0338 - 0.0322

Resin Coated Sand 2.57 - 2.61 0.0467- 0.0460

Z-Prop 126’ 3.1 70.0379

ISB~ 3.1 - 3.2 0.0387 - 0.0375

ISC’ 2.7 ~ 2.8 0.0445 - 0.0429

High strength sintered bauxite proppant

Zircorfium oxide proppant

Intermediate strength sintered bauxite proppant

Intermediate strength cera~c proppant

Fig. 9.1

Proppant Maximum Average Proppant

Size Diameter Diameter (PD)

--mesh --in. --in.

4/8 0.187 0.173

6/12"* 0.132 0.099

8/12 0.093 0.087

8/16"* 0.093 0.082

10/20 0.079 0.061

10/30 0.079 0.056

12/20" 0.067 0.054

16/20"* 0.047 0.041

16/30"* 0.047 0.039

18/20"* 0.039 0.036

18"35 0.039 0.032

20/40" 0.0336 0.0272

20/50 0.0336 0.0218

30/50"* 0.0237 0.0185

30/60 0.0237 0.0180

40/60 0.0168 0.014

40/70" 0.016 0.013

70/140"* 0.0084 0.0099

(100 mesh)

* Recognized by API as a primary proppant size

** Recognized by API as a alternate proppant size

NOTE: Average proppant diameters shown are based on

typical size distribution from screen analysis data, not

the average of large and small sieve openings.

Fig. 9.2

Revised 6YH

Sand is available in both round and sub-round

shapes. Based on the API guidelines, at least 90%

by weight of the proppant’s grains should fall between the range of screen sizes specified. Generally, the larger sizes of sand are more angular than

those available in 20/40 mesh or smaller sizes. Figure 9.3 is a photograph of a round 20/40 mesh

sand and a typical 20/40 mesh sintered bauxite

proppant.

20/40 Mesh 20/40 Mesh

Sand Sintered Bauxite

Fig. 9.3

Calculations for Production Rate

From Darcy’s law, the production rate for

radial flow may be calculated from this formula:

2 w(kh) Ap

q - I~ In (rdr,,) (9-1)

where:

q = production rate

(kh) = formation flow capacity

Ap = pressure drop

~ = fluid viscosity

In r,/r. = ratio of drainage radius to wellbore radius

This equation shows that the production rate

is a direct function of the formation flow capacity

if you assume a constant pressure drop, fluid viscosity, and ratio of drainage radius to wellbore

radius. Figure 9.4 illustrates a formation of thickness h~ feet, having an average permeability of k

millidarcies. The formation conductivity is k times

hi or (kh) millidarcy-feet.

HESI303162
If a vertical fracture is created in the formation and propped open, it will have an ability to

conduct fluid measured by the fracture conductivity of the proppant bed within the fracture. This is

expressed as the product of fracture permeability

and the fracture width, (kw)f.

The fracture conductivity is a property that is

measurable in the laboratory. Rather than measure

the fracture permeability (kf), the term (kw)f is

used. If the width were measured, the kf could be

determined. However, laboratory measurements

show that, for most proppants, the fracture permeability (kf) will vary with width (wf) for very narrow bed widths. For example, k~ at a fracture

width of 0.1 inch is not usually equal to kf at a

fracture width of 0.25 inch. This phenomenon is

mostly caused by "wall effects" since most

propped fractures are relatively narrow. This behavior is also partly caused by particle size distribution, particle shape, embedment, and grain

strength of the proppant. If proppants were perfect spheres with a single grain size and neither

crushing nor embedment were to occur, then we

would be more likely to find k~ to be constant with

varying widths, once the proppant pack thickness

exceeded three to four layers of proppant. Formnately, this problem of k~ varying with width can

be overcome by conducting multiple laboratory

tests with different proppant bed widths (w~) for

each proppant used.

Figure 9.4 shows a fracture that has been

placed in a formation and is being held open by

propping agents to a width w. The fracture conductivity of this propped fracture is k~ times w or

(kw)~.

Consider a formation 20 feet thick with an

average permeability (k) of 5 md. The original

formation flow capacity is 100 md-ft. A fracture

filled with a three layer pack of 20/40 mesh sand

would have a width of about 0.082 inch (or 0.0068

feet) with a fracture conductivity of approximately

2000 rod-ft. This assumes insignificant crushing or

embedding of particles. The fracture permeability

would be 2000 md-ft divided by 0.0068 ft, which

is 294,000 md. In this example, the propped fracture has a flow capacity 20 times that of the formation and the permeability contrast (k/k) is a factor

of 58,800. Therefore, it would appear that fracture

conductivity is a significant factor in the successful

application of hydraulic fracturing stimulation.

The fracture must be able to easily conduct fluid

delivered to it by the formation. (Part 10 of this

text will discuss theoretical production increase.)

For the purpose of calculation, consider a case

where the fracture permeability is much higher

than that of the formation (k~>>k). The production increase created by the fracture can be approximated by replacing the fracture with a borehole.

The radius of this borehole would be approximately haft the fracture lengthy Using Darcy’s

Law to approximate the production increase:

k/q- ro kl r’\ +

where:

(9-2)

r’ = effective wellbore radius (1/2 fracture

length)

k~ = fracture permeability

k = formation permeability

In the previous illustration, if r. = 660 ft, L

= 500 ft and r, = .5 ft, then r’ = 500/2 = 250 ft:

~/q =

In 2-~ + 294,000 In

The production increase is 7.40.

I

Damage to Proppant Bed III

The crushing or embedment of proppant particles may cause a fast decline in productivity because of the reduction in fracture conductivity.

Re~i~l 6YH

HESI303163
Figure 9.5 illustrates what may happen in a thxn,

multilayer system of rigid particles when there is

significant embedment. The flow capacity may be

partially or entirely lost because of the closure. In

many cases, the closure may crush the formation

instead of the proppant. The formation may then

release debris that partially plugs the proppant

bed. When you have a wide, multilayer proppant

system, the effect of the plugging caused by formation fines is usually much more significant that the

loss in fracture width caused by embedment.

Proppant Not Embedded

Proppant Partially Embedded

Fig. 9.5

Figure 9.6 illustrates severe crushing of rigid

particles. Sand may be crushed by the action of the

formation stresses in hard rocks; however, it does

not usually crush to a very fine powder. Sand may

shatter into smaller grains and, eventually, produce

enough small particles to give some support. The

result may be a propped fracture of a slightly narrower width and a poorer range of proppant sizes

than expected. Therefore, the proppant bed would

have less conductivity.

Proppant Not Crushed

Proppant Severely Crushed

Fig. 9.6

Silica sand (SiO:) has been employed as a

proppant since commercial fracturing began. It is

still the most economical and the most widely used

proppant. However, it may be somewhat limited in

its effectiveness because of lower resistance to

crushing. In deep formations with high stresses, a

higher strength proppant is usually substituted for

sand.

The conductivity of a propping agent will

depend on, among other factors, the concentration

of the proppant in the fracture. For low viscosity

fluids (or for other conditions that develop a bed of

proppant because of settling), the propped fracture

width is equal to the pumping fracture width less

some shrinkage caused by compaction, embedment, and crushing. You can use Figure 9.7 to

estimate the proppant concentration if you know

the propped width.

10000

5000

z

1000 0

PROPPANT CONCENTRATION

IN FRACTURE

vs

FRACTURE WIDTH (w)

/

0.05 0.1

10o

0.01 0.5 1.0

w in.

Fig. 9.7

In the case of more viscous fluids which are

capable of suspending the proppant, the slurry

concentration can be used to estimate the proppant

concentration in units of pounds per square foot of

fracture area. Once you obtain the concentration,

you can estimate the propped width using Figure

9.7. Using sophisticated computer design simulators, a very detailed calculation of the final proppant bed can be modeled.

HES1303164
The fracture conductivity of a particular type

of proppant also will depend upon the characteristics of the rock being propped. Typical conductivity curves for 20/40 mesh sand and 8/12 mesh sand

are shown in Figures 9.8 and 9.9, respectively.

Figure 9.10 is a comparison of several different

proppants under identical test conditions. These

curves were based on tests of proppant packs between steel plates for Figures 9.8 and 9.10, and

between cores of Berea sandstone (with moderate

hardness) for Figure 9.9.

3

2

lO’

z

0

5

3

2

FRACTURE CONDUCTIVITY

VS.

PROPPANT CONCENTRATION IN FRACTURE

20,’40 OTTAWA SAND

STEEL PLATES

CLOSURE STRESS (PSI)

6000

101

0.1 0~ 0.3 0,4 0.5 1.0 2. 3. 4. S, 10

CONCENTRATION - LB/SQ. FT.

Fig. 9.8

A close examination of the data for low proppant concentrations in Figure 9.9 indicates some

abnormal shapes in the curves. In this graph, the

abnormalities begin to occur as the proppant concent.ration is decreasing from a full 2 + layer pack

down to a monolayer (at 0.7 lbs/sq ft in Fig. 9.9).

As the proppant concentration decreases below a

monolayer pack, the conductivity will increase if

the particles can support the load without being

severely crushed (see Fig. 9.10 at the lower

stresses). However, if the grains are too weak to

support the load in a partial monolayer system,

then the conductivity will drop as shown in Figure

9.9 for the higher stresses.

FRACTURE CONDUCTIVITY

VS.

SAND CONCENTRATION IN FRACTURE

~12 BRADY SAND

ON BEREA SANDSTONE CORES

0.1 0.2 0.3 0.4 0.5 1.0 2.

CONCENTRATION - LB/SQ. FT.

Fig. 9.9

Fig. 9.10

FLOW CAPACITY DATA FOR VARIOUS PROPPANTS

2000 4~O0 6000 ~ 10000 12000 14000 1~000

CLOSURE STRESS (PSi)

Rcvi~d 6".£H

HESI303165
3 8 hydraulic fracmrm~g’

In a realistic application, it would be highly

unlikely to obtain proppant beds of less than a 2-

layer thickness in a vertical fracture. Many field

studies in the past have attempted to use partial

monolayers for various reasons, but very few were

a commercial success. Some were such complete

failures that many wells had to be refractured using higher proppant concentrations to increase

production.

Selection of the Propping Agent

One of the most important factors in the design of hydraulic fracturing treatments is the selection of a propping agent that can effectively

provide the fracture conductivity needed for stimulation of a well.

Examination of Figures 9.9 and 9.10 shows a

marked difference in the conductivities of 20/40

mesh sand and 8/12 mesh sand. The tests for Figure 9.10 were conducted using a medium hardness

sandstone outcrop (Berea) as the fracture faces.

Only slight embedment (1/3 grain diameter or less)

was observed even at the highest stress (6000 psi).

Therefore, this data is not representative of soft

formations where embedment could be a problem,

nor is the data in Figures 9.8 or 9.10 which were

measured on steel plates.

Several interesting points should be noted

during a comparison of Figures 9.8, 9.9, and 9.10:

 ̄ The larger particles (8/12 mesh sand) have a

much higher conductivity that the 20/40 sand

for the same concentration at the lower closure

stresses.

 ̄ The 8/12 mesh sand is much more affected by

changes in closure stress (i.e., it is more easily

crushed).

 ̄ At stresses above 4500 psi and concentrations

above 1 lb/sq ft, 20/40 mesh sand has more

conductivity than 8/12 mesh sand.

 ̄ The data in Figure 9.10 shows that different

proppants resist crushing to different degrees

although all these are 20/40 mesh size proppants.

Selecting the proper type and size of proppant

to use in a particular formation requires the gathering of laboratory data such as the information

provided in these figures.

Three factors previously discussed may influence the conductivity resulting from a bed of proppant under load:

 ̄ The particles may embed in the rock surface

if they are stronger than the rock and the closure stress is sufficient to cause embedment.

 ̄ A large percentage of the grains may crush if

the rock is strong and the stress is greater than

the grains can withstand.

 ̄ The proppant bed may become plugged because of the invasion of formation fines.

Of these three, only proppant crushing can

easily be modeled in the laboratory.

Laboratory Tests for Conductivity

One of the best methods for determining the

applicability of a proppant is the test for conductivity. This test was used to obtain the data listed

in Figures 9.8, 9.9 and 9.10. Conductivity tests are

routinely performed by service company laboratories to aid in choosing the proper proppant for

various formation conditions.

Figure 9.11 shows two methods which use

actual cores in the flow capacity test. The samples

in the lower part of the figure show a core sample

cast in a lead mold with a stainless steel screenwire molded in place to retain the particles on the

core face. A second core is also mounted in lead

with part of the core projecting above the lead.

Fig. 9.11

Revised 6YH

HESI303166
This part of the core is the "head" and will be inverted onto the proppant bed after the desired

quantity of proppant has been placed inside the

screen. The test cell shown in the upper part of

Figure 9.11 is a steel cell which uses thin core wafers to provide the same final type of test set-up

(i.e., the proppant bed is "sandwiched" between

core wafers). Figure 9.12 illustrates two of the

metal cells being tested simultaneously in a loading

frame. The closure stress is increased and conductivity (fracture flow capacity) measurements can be

made at any stress level up to the limit of the loading frame.

Fig. 9.12

Typically, conductivity of the proppant pack

being tested will be measured at different closure

stress values. Test fluid flows through the central

weilbore and radially out through the bed of proppant. By knowing the flow rate, pressure drop, and

the geometry of the system, you can calculate a

conductivity value using Darcy’s Law at each closure stress:

(kw)f =

where:

5.22 ql~ In

Ap (%3)

(kw)f

q

ro

rw

Ap

= conductivity, md-ft

= flow rate, cc/sec

= outer radius, cm

= weilbore radius, cm

= pressure drop, arm

= fluid viscosity, cp

Conductivity tests are used to evaluate the

relationship between the hardness of the actual

formation rock and the strength of the proppant

grains.

The values from the conductivity tests are

usually applied directly to design calculations that

use production increase ratios. However, the crushing of proppant grains may not have the same influence on the results of the test as it might have in

a full size fracture. The short flow path of the test

may allow the fines produced by crushing to wash

out of the bed and cause a conductivity value that

is too high. Also, in actual downhole conditions,

the proppant bed may have two or more fluid

phases present during the producing life of the

well. Formation fines that may invade the proppant pack are also difficult to simulate in the laboratory.

Because of these and many other factors, some

of the more experienced design engineers will discount the conductivity data measured in the laboratory before they calculate production increase.

Unfortunately, no single discount factor can be

used because so many factors are involved in each

separate case. The appropriate value may vary

from 1 (no discount) to 0.1 or lower. Typically,

values from 0.5 to 0.1 will be used?° In recent laboratory studies, McDaniel ~1.s, identified that much

lower conductivities exist with extended test times

and elevated temperatures. These tests used an

API linear test ceil $3 like the drawing in Figure

9.13 and the photograph in Figure 9.14, where the

ceil is inside a load frame.

LINEAR FLOW PROPPANT CONDUCTIVITY TEST CELL

Fig. 9.13

Re~sed6YH

HESI303167
40 hydrouS frat:turini’

Fig. 9.14

The calculation of effective fracture conductivity for an actual treatment depends upon the

proppant distribution in the fracture. Computerized simulations of hydraulic fracturing are widely

available to make. such calculations.

Fracture Closure Stress

The fracture closure stress is the amount of

stress the propping agent must withstand inside

the fracture. Closure stress affects treatment parameters such as the type and amount of proppant,

the fracture conductivity, and the amount of production increase.

The magnitude of the closure stress depends

on the least in situ principal stress, the reservoir

pressure and the flowing bottomhole pressure

while the well is producing. The least in situ principle stress can be determined if an instant shut-in

pressure is measured while fracturing a formation.

If possible, record the magnitude of the instant

shut-in pressure during the very early stages of the

treatment, since the instant shut-in pressure at the

end of a treatment may be falsely high due to "supercharge" of the reservoir caused by frac fluid

leak-off.

The closure stress applied to a proppant bed

will vary with the producing condition of the well.

When the fracture has first healed on the proppant

bed, but prior to opening the well for cleanup and

production, the closure stress will be at a minimum. This value for minimum closure stress can

be calculated:

Revised 6YH

Minimum closure stress = P,si + APh - Po

where:

(9-4)

= instant shut-in pressure at the wellhead, psi

=hydrostatic pressure of fluid in the

wellbore, psi

Po = static reservoir pressure (pore pressure), psi

When the well is opened to flow (or is

pumped), the closure stress on the proppant bed

will increase. This is because the pore pressure in

the proppant bed is now considerably lower than

the formation pore pressure. Probably the best

estimate of the closure stress for the producing

well is to substitute the bottomhole flowing pressure for the reservoir pressure in equation 9-4.

Since this is often the value used in selecting a

proppant for a treatment design, we will referto

this as the "design closure stress." It can be calculated as follows:

Design closure stress = P,., + APh - P~,, (9-5)

where:

P~o. = bottomhole flowing pressure from producing well, psi

The closure stress does not stay constant during the life of a fracture. The reservoir pressure

will decrease as fluid is withdrawn from the reservoir, and the Pnow usually decreases even faster..

PRODUCTION INCREASE

Part 10

The use of hydraulic fracturing methods for

production stimulation has become a common procedure in the oil and gas industry. Fracturing treatments are performed on wells of various potentials

to help increase the production rate. Along with

the desire for increased production is the need to

predict what increase might be expected. This

knowledge is useful in planning economical treatments that accomplish the desired production goals

for the well.

Production increase may be defined as the

ratio of production rate after fracturing to the production rate before fracturing at the same pressure

differential (that is, the ratio of productivity indices).

HESI303168
Production increases from horizontal radial

fractures may be calculated in theory by using

equations developed from mathematical analyses

and electrical models.’3 Theoretical production

increases due to vertical fractures may also be predicted using curves developed from electrical and

mathematical models.’"" ~’~’

Early studies usually assumed that the vertical

fracture height and the formation height were

equalfl However, the final fracture height through

which fluid is produced may not be equal to the

created height because of the propped bed configuration. This is based on the study of proppant

transport relationships in vertical fractures. ~2  ̄ ~

Modern fracture design simulators are capable

of calculating the proppant suspension and settLing

during pumping. Some of the more sophisticated

simulators will also model the changes in proppant

location during the time that the fracture is closing

following shut-in.l~ If increased hydrocarbon flow

occurs only through the propped portion of the

fracture, it becomes essential to know how production increase varies with the ratio of propped fracture height to formation height. Future

investigation may determine that the fracture does

not heal completely and that a highly permeable

channel exists over the deposited bed of proppant.

The effect of such a channel is not considered in

this discussion.

We need to consider a number of variables

when designing a fracturing stimulation treatment.

The dimensions and conductivity of the fracture

are affected by factors including:

 ̄ volume of the treatment

 ̄ type of proppant

 ̄ size of proppant

 ̄ concentration of proppant

 ̄ treatment fluid properties

 ̄ well conditions.

Production increase from a vertical fracture is

affected by propped length, height, width, and the

conductivity of the fracture for a given set of formarion conditions.

Calculations for Vertical Fracture Production

Increase

The parameters used in the calculation of production increase must be either measured or reasonably estimated. For example, the conductivity

of the fracture may be measured in the laboratory

using layers of proppant placed between formation

core surfaces as described previously in this section

(Part 9). The reservoir pressure must be known,

and the properties of the reservoir fluid must be

measured or estimated. When such parameters are

used to determine production increase ratios using

analog models, some assumptions are usually

made:

 ̄ The formation is a homogeneous, isotropic,

porous medium.

 ̄ The reservoir fluid is incompressible.

 ̄ The fracture width is constant.

 ̄ The fracture is constant in height and extends

equal distances in two opposite directions

from the wellbore.

 ̄ The conditions that exist in the reservoir are

steady state.

 ̄ The effects of gravity on the fluid may be

ignored.

 ̄ The flow that exists is single phase.

One of the ftrst papers published concerning

fracturing and its effect on production stimulation

was by McGuire and Sikora.‘3 Their study was

accomplished using an electrical model composed

of a network of capacitors and resistors. The

results of this work are shown in Figure 10.1. This

work has several limitations that, in some cases,

lessen its usefulness in particular field applications:

Fig. 10.1

14

12

4

2

ol

x._!

.5

.4

.3

.2

.1

10s 10~ 10s 10s

RELATIVE CONDUCTIVITY, (kw)~, ~

k " S

 ̄ Because of the way the reservoir was modeled,

the resulting production increases are indicative of an unknown time. The curves do not

Reviled 6YH

HESI303169
2 ,hydraulic frac:urmg

apply to a steady-state production rate that

would exist at later times. (However, in the

case of gas wells in fight formations, steadystate conditions may not apply until an appreciable period of the producing time has

passed.) The authors call the model a semisteady-state case.

The data assume that the propped fracture

extends throughout the entire vertical interval

of the producing section. It does not consider

the propped fracture height being different

from the thickness of the interval.

The data assume an incompressible fluid.

The resulting values may be too high for

steady-state production increase ratios. They differ

from work done by others in this field of study,

including that by Prats,° Smith,s* and Tinsley, et.

al?~ Wtfile the shapes of these curves agree, the

magnitudes of the values do not.

Calculations for Increase Ratio

The paper by Prats may be used to obtain a

measure of the effectiveness of the vertical fracture. For values of (r=/xf) > 2, the improvement in

production rate for infinite fracture conductivity is

given by equation 10-1:

where:

qgq = increase ratio

ro = drainage radius, ft

x~ = fracture length, wellbore to tip, ft

r, = wellbore radius, ft

r’,, = effective well radius - may be found

from Figure 10.2 using a value for "a"

as follows:

(10-1)

k = formation permeability, md

(kw)f = fracture conductivity, md-in.

Prat’s work is valid for these conditions:

 ̄ short fractures, xf < r)2

 ̄ incompressible fluids

 ̄ single plane vertical fracture

 ̄ when a ~< 1; if a > 1, a well pressure correction should be made using Figure 10.3

 ̄ equal fracture and formation height.

If the fracture conductivity is less than infinite, a correction for fracture pressure drop is introduced using Figure 10.3 and the value of a to

Fred p.,o(a,r.D):

In r. q~_

q

In 77- -2

where:

(10-2)

pressure drop as a function of a

dimensionless well radius r.t, =

r~/xf

Another method for estimating an effective

wellbore radius (r’.) uses the skin factor and the

following relationship:

’r ~ = r.e" (10-3)

~

1.0

",-- 0.5

<w 0,7

WUJ ~o.o~

,uJ, 0.001

WELL RADIUS OF THE

FRACTURE AND L IS THE HALF

LENGTH OF THE FRACTURE

0.01 0.1 1.0 10 100 1000

RELATIVE CAPACITY PARAMETER, a

Fig. 10.2 - Effective Well Radius

o. 0.8

z .,~ W

-- tr 0.4

°8~ o.~

a = 100

1⁄2

~

a=10’

la = 1!

0.01 0.02 0.03 0.04 0.05

DIMENSIONLESS WELL RADIUS, r,.,/xf

Fig. 10.3 - Pressure Correction at Well

In an unfractured formation, the production

rate is affected by the formation height. The production rate in a hydraulically fractured formation

Revised 6YH

HESI303170
is affected by the propped fracture height which

can be significantly less than the formation height.

Therefore, the production increase ratio is a function of the ratio of propped fracture height to formarion height.

For a truly meaningful prediction, the production increase should be affected by the degree to

which the producing zone is propped. Assuming

that the unpropped portion of the fracture closes,

then the production increase ratio should be a

function of the propped height to formation height

ratio. In one study", an electrolytic model was

used to study this relationship. Production increase

was related to the model parameters. In a subsequent paper$6, the mathematical analysis was corrected and modified to dimensionless form. It was

also generalized to any r Jr, ratio. Examples of new

graphs are presented in Figures 10.4 and 10.5.

These plots are similar to the earlier work of

McGulre and Sikora (Fig. 10.1), except the x-axis

is dimensionless and the propped fracture height is

considered as a variable.

Calculations for Dimensionless Fracture Capaco

The x-axes of Figures 10.4 and 10.5 represent

"dimensionless capacity." This term is def’med as:

C,hf r(~._~

C - 2 K- in (10-4)

This term uses the C, definition of Cinco, et.

(kw), C, = ~kx, (10-5)

where:

(kw)~

k

h~

r,

r=

= fracture conductivity, md-ft

= propped fracture length, ft

= formation permeability, md

= propped fracture height, ff

= formation thickness, ff

= radius of drainage, ff

= wellbore radius, ft

The curves for x]ro ratios of 0.9 and 1.0 are

not included because the data were not considered

to be applicable to field conditions. In the model

that was used, a fracture that extends to or near

the boundary of the model would have an infinite

supply of fluid. In reMity, the boundary of the

prototy.pe is not an infinite source of fluid and

would also be affected by surrounding wells.

Examination of Figures 10.4 and 10.5 shows

the effect propped fracture height has on steadystate production increase. Lowering the proppant

bed height decreases the C value, thus decreasing

the JdJi term. In addition, lower h/h~- results in

shifting to a different graph where the range of Jd

Ji values is lower.

h!

--= 1.0

I

0.1 1 10 100

h~ C= [0.5C,~lnrdr~,]

Fig. 10.4 - Productivity Index Ratio (h/h=) = 1.0

0.25 Xtire

(~)f

0.1 1 10 100

C = 0.5 C, ~ In rdrw

Fig. 10.5 - Productivity Index Ratio (hCh3 = 0.25

For example, if C = 10 at hflni = 1, and x~rc

= 0.6, the JdJi term - 4.6. If the bed height were

lowered and h/hi = 0.25, C would become 2.5 and

Jf,/Ji term - 3.0. This effect is quite significant if

the C term is in the range of 1 to 10.

Revised ~YH

HESI303171
Note that the C~ term is inversely proportional

to fracture length xf. This indicates that longer

fractures require higher fracture conductivity to

result in the same production increase.

When an x~/ro curve approaches its asymptote

(becomes horizontal), this implies that the fracture

is conducting fluid as fast as the formation can

deliver and that no improvement can be realized

for C values above a certain point. If h~/h~ -- 1.0

and an 8 inch diameter well is drilled in an 80 acre

pattern where k = 0.1 md, then for xf = 500 ft,

the (kw)f term need be not greater than 3,820 mdft. That conductivity value would yield essentially

an infinitely conductive fracture, having a C, value

of 24. Cinco’s results imply that for C, > 100,

there is almost no difference between finite and

infinite conductivity fracture cases. His figures

indicate very small differences above Cr -- 10.

Figures 10.4 and 10.5 agree with his conclusion.

An example of the effect of height ratio (h/hi)

on the steady-state production increase is shown in

Figure 10.6. The effect is pronounced for low values of h,dai. For practical purposes, a fracture

height ratio > 0.5 is suitable.

1 O0

~ 80

~ 60

"

~’~ 2o/

.1 .2

INFLUENCE OF h#hi ON Jfs/Ji

.3 .4 .5 .6 .7 .8

hjhi VALUE

.9 1,0

Fqg. 10.6 - Height Ratio Effect

Production increase ratio, JdJ,, assumes no

wellbore damage. In practice, wellbore damage

may be common and the effect of damage usually

is eliminated by the fracturing operation. Prior to

the treatment, production is restricted due to the

damage around the wellbore. However, following

the treatment the majority of the production is

through the fracture and the damage around the

wellbore offers no appreciable restriction.

Revised 6YH

The damage, as calculated by drill stem tests

or pressure build-up data, can express the restriction in production as a damage ratio or skin(s).

The former is the ratio of theoretical production

capacity with no damage to the present production

(i.e., the inverse of flow efficiency). Therefore, if a

well were making 10 BOPD with a damage ratio of

4.0, the production without damage should be 40

BOPD.

If the well were to be fractured and the results

of a design calculation indicate Jf,/Ji ratio of 3.0,

the total expected steady state production ratio

would be 10.0 x 4.0 (damage ratio) x 3.0 (Jf,/Ji) or

120 BOPD. As can be seen, the damage ratio is a

very important consideration and cannot be ignored. Keep in mind that caution should be exercised in predicting exact production values from

production increase curves because of the assumptions inherent in the development of these curves.

An important factor in the use of the production increase curves is the selection of values for

well spacing and drainage radius. It should not be

assumed that since wells are drilled on some assigned surface spacing that they are actually draining this area. It might be years before the effects of

withdrawing fluid from the wellbore are felt at the

spacing boundary. Well spacings used in frac design should be realistic values, not necessarily government specifications.

The production increase curves in Figures

10.4 and 10.5 have limitations as mentioned, but

are useful in fracture treatment design. Curves

such as these represent a way that the treatment

variables may be related to each other to compare

their effect on the treatment results.

A typical curve (for example, Fig. 10.4) shows

that there are only three variables under the control of the treatment designer. These are the parameters that may be modified by selection of

fluids, proppant types, and treatment conditions:

 ̄ height ratio, h/hl

 ̄ fracture conductivity, (kw)f

 ̄ propped length, xf.

An example of the use of curves would be the

case in which a choice of a proppant in a particular

permeability formation resulted in a low value of

the C, term. If the proppant is in suspension in the

fluid, a height ratio of 1.0 may be assumed. The

low C, would also imply a low dimensionless capacity (C). At very low C values, the Jf,/Ji would be

HESI303172
affected very little by fracture length xf. One

would not consider increasing length as a means of

increasing J,/J~ without making a corresponding

increase in C, through a higher conductivity value,

(kw)f. As x, is increased, its effect on Cr must be

considered and the (kw)~ adjusted. ACr value of >

10 would be a suitable goal in most designs.

Computer Simulations

All of the above discussions on production

increase prediction methods assume essentially

steady-state flow of incompressible fluids. Predictions become more involved ff transient flow prevails for the time in question or a compressible

fluid is flowing. Usually this type of problem is

simulated by using a computer to solve the differential equations describing the pressure behavior.

These equations may not be solved analytically

except for specific simplified cases, so the pressure

must be approximated by numerical methods. The

use of the steady-state methods is generally accepted for oil wells, but will be pessimistic in gas

reservoirs in which the fluids are very compressible.

Production Simulators

The most recent method for predicting the

increase in production involves the use of a "production simulator" computer model. These models

are based on predicting the transient pressure response of a reservoir.

The modeling of oil or gas production from a

radial flow (unfractured) reservoir has been available for a long timefl Later, methods for modeling

flow through an infinitely conductive fracture in a

reservoir were developed." However, it has only

been since the late 1970’s that usable models have

become available to simulate production of a hydraulically fractured reservoir where the fracture

conductivity could be variedf143 Continued refinement of this technique has made production simulators an important tool for predicting the

production increase resulting from hydraulic fracturing.~

When a solution of a model is plotted in a

dimensionless form, it is usually called a type

curve. Because of the generality of the type curve,

it can be used for either analysis of well tests"*~

or predicting future performancefl In the following few pages, the model for predicting production

increase using type curves is presented.

Type Curve Analysis Method

The "Fractured Reservoir" type curves are

used to model production following a hydraulic

fracturing treatment. The earliest type curves were

based on infinite fracture conductivity and had

limited practical applications. However, the more

recent development of type curves for finite conductivity fractures has resulted in production simulators that have definite practical application to

help design hydraulic fracturing treatments.

Mathematical Model for Type Curves

The mathematical model has several assumptions. The well is assumed to be vertically fractured in the center of a square reservoir and

producing at a constant bottomhole pressure under

unsteady state conditions. The formation has a

constant height. The outer boundaries of the reservoir are no-flow boundaries. The fracture extends

an equal distance on each side of the wellbore. The

fracture is propped and has a finite conductivity

(wfkf). It completely penetrates the formation in

height.

Other assumptions are used in developing the

model. Foremost among these are:

 ̄ The porous medium is homogeneous and isotropic.

 ̄ Gravitational effects are negligible and the

reservoir is bounded above and below by impermeable strata. The problem is therefore

two-dimensional.

 ̄ The working fluid is a single phase and compressible. Fluid density is described by the

equation:

p = po exp [c(p- po)] (10-6)

 ̄ The flow in both the formation and the fracture is laminar and described by Darcy’s Law.

A finite element simulator may be used to

solve the partial differential equations that describe

the initial and boundary conditions. An example of

this solution is shown in Figure 10.7. Series of

these type curves have been developed. Each of

these curves gives the dimensionless flow rate versus dimensionless time for various x,Jxf ratios. Each

of these graphs represents a specific dimensionless

fracture conductivity. These type curves can be

Revised

HESI303173
6 hydraulic fracturing

used in analysis of drawdown tests by applying the

conventional and frequently discussed type curve

matching technique. If the graphs are to be used

for that purpose, they should be applied for a well

producing at a constant flowing pressure.

Fig. 10.7

The type curve can be used to:

 ̄ predict flow decline with time

 ̄ help design a fracture treatment

 ̄ evaluate a fracturing treatment using a history

match technique.

To use the type curve for prediction or history

match, curves are first stored into a computer.

Because the original solution is obtained numerically, only data points were available. The data

were stored as continuous functions rather than

discrete points, eliminating the need for numerical

interpolation. The data points of each curve were

fitted by a polynomial of seventh order. The coefficient of these polynomials are stored in the computer memory. The deviation of the calculated

points using these polynomials from the original

data points was always less than 1% and in most

points within 0.3%.

Because of the nature of the inner boundary

condition, wellbore storage would not affect the

type curves. However, a few aspects regarding actual well performance have to be considered to

obtain a reliable prediction and/or history match.

These aspects are:

 ̄ Change in flowing pressure - In history

matching, it is obvious that well flowing pressure does not remain constant for the long

time considered in such a study. Thus, it is

Re~ed 6YH

important to consider the change in flowing

pressure using superposition. EhlegEconomides and Ramey~’ discussed superposition for wells producing under constant

pressure. Their equation for step pressure

testing is used to accommodate the effect of

changing flowing pressure.

 ̄ Reduction in fracture conductivity - With

increasing closure stress, there is a reduction

in fracture conductivity. When a fractured

well begins production, the pressure in the

fracture is reduced significantly. The closure

stress is approximated as the difference between bottom_hole treating pressure and the

average pore pressure in the fracture. The

fracture conductivity of the proppant bed will

decrease as the closure stress increases. As a

result, the fracture conductivity will decrease

with time. Laboratory data on fracture conductivity as a function of proppant concentration and fracture closure stress are available in

the literature. Examples of these graphs were

presented in Figures 9.8 through 9.10. Using

these data, the effect of changing closure

stress can be considered in calculating the

predicted fracture conductivity. Because the

type curves neglect the effect closure stress

has on fracture conductivity, this effect is considered in an approximate way. For a given

time step, an average closure stress value for

the fracture is estimated.

 ̄ Turbulent flow - Using a numerical simulator

(finite difference simulator) and calculating

the fluid velocity inside a fracture, it has been

found that the apparent fracture conductivity

can be significantly affected by turbulent flow

inside the fracture. This effect is especially

pronounced in early time when the flow rate is

high. The effect of turbulent flow is considered in a similar fashion to the closure stress

effect. First, a turbulent factor ~ is calculated:

~ - kf - 2.97 x 10 ~°[3vl~ (10-7)

1 +

This equation is based on work done by Forcheimer.67 Because the fluid velocity inside the

fracture changes with time, this turbulent factor

starts at a low value and increases with time. Eventually this factor approaches one for laminar flow.

This approach, which has been used before,62 ~’ ~

can be incorporated into a computer program that

HESI303174
uses the presented type curves with these discussed

features. The program can predict a well performance with an accuracy comparable to a numerical

simulator but it has the advantage of taking much

less computation time.

ever, the rate of improvement declines. The increase in cumulative production after three years as

the fracture length changes from 200 to 600 md-ft

is only about 17%. This shows that for the longer

fracture length, a fracture conductivity of 1000

md-ft may not be sufficient; the dimensionless

fracture conductivity (Cr) for the 600 ft length is

too low. As discussed earlier, experience has shown

that a dimensionless fracture conductivity of about

10 is usually desired to produce a particular formation efficiently.

Fig. 10.8

HYDRAULIC

FRACTURING EQUIPMENT

Part 11

The equipment used to perform hydraulic

fracturing treatments has evolved from simple

modified cementing units to become some of the

most powerful and specialized equipment in the

service sector of the oilfield. A brief overview of

the types of equipment currently used is provided

in this part.

0.9

The type curves may be used to estimate fracture parameters. This may be achieved by changing fracture length and conductivity and plotting

the production as a function of time. Example well

data were used to demonstrate this procedure. The

fracture length was chosen at varying percentages

of the drainage radius, and the type curve simulator was run using fracture lengths of 200, 400, and

600 ft. A formation permeability of 0.1 and a fracture conductivity of 1000 md-ft were assumed.

Results of this simulation are shown in Figures

10.8 and 10.9. The well performance can be seen

to improve as the fracture length increases. HowFluid Storage

On very small jobs, fluid is frequently used

directly from transport trucks of 50 to 150 bbl

capacity. Portable lay down tanks (frac tanks) of

about 500 bbl capacity are used on a majority of

frac jobs. On some jobs using fresh water, lined

earthen pits are used to store volumes of over a

million gallons of water. In offshore operations, the

fluid may be stored in tanks on the rig or on a

stimulation vessel. Sometimes, £fltered sea water

may be used without any storage.

Proppant Storage

On small to moderate size jobs, proppant is

usually fed to the blending equipment directly

from the trucks used to transport the proppant to

location. Larger quantities of proppant or high

concentrations at high rates are usually stored in

portable field storage facilities (Fig. 11.1). This

type of storage unit usually uses gravity feed onto a

hydraulic driven conveyor belt system to supply

the proppant to the blending equipment.

HESI303175
Fig. 11.1 - Proppant storage unit with integral unloading belt.

Capacity = 222,000 Ibs sand.

Blending Equipment

The success of a fracturing treatment also

depends on the reliability of pumping and blending equipment. A blender (or proportioner) transfers the fracturing fluid from the storage area (such

as 500 barrel frac tanks) to the high pressure

pumping equipment. As the fluid passes through

the blender, a uniform mixture of chemicals and

propping agent is added to the fluid. The blender

must be capable of maintaining a uniform mixture

regardless of injection rates and volumes.

Fracturing fluids containing gelling agents to

increase viscosity may be mixed either in a batch

or in a continuous process; the choice depends on

conditions at the well location. Regardless of the

mixing process used, the fracturing fluid should be

smooth and lump-free to obtain maximum efflFRACTURING

SUPPLY PUMP

BASIC FLUID -~

CHEMICAL METERING

PUMP A --

ciency from a particular chemical.

Mechanical mixers that provide excellent mixing have been developed and are used extensively

in field operations. Fast hydrating chemicals can

be used which provide better yield at lower concentrations and make continuous application more

efficient. Dry chemical proportioners permit accurate addition of fluid loss agents, propping agents,

and~or other additives.

A typical blender (Fig. 11.2) may consist of

one or more chemical metering pumps and proppant proportioners, all metering materials at various ratios into the fluid. The fluid is pulled into

the blender by a centrifugal pump and goes into

the agitator tank (blender tub). After addition of

the chemicals and propping agent, the pressurizer

pump moves the sand-fluid mixture to high pressure pumping equipment. Present proportioning equipment can alter the concentration of either

chemicals or propping agent during the job as dictated by treatment conditions. It may be desirable

to increase or decrease the concentration of gelling

agents, fluid loss additives, or breakers during the

treatment or in the flush at the end of the job. The

concentration of propping agent in the fluid normally is started at 0.5 to 1.0 pound per gallon and

increased, as the job progresses, to as high as 20 +

pounds per gallon in some cases. However, should

excessive pressure or reduced rate be encountered

during the treatment, the blender must be able to

immediately stop adding the propping agent.

DRY CHEMICAL

PROPORTIONER

y

SAND

PROPORTIONING

CONTROL

~ SAND

BULK OR SACK

CHEMICAL METERING

PUMP B

AGITATOR TANK

OR TUB

STABILIZER

PRESSURIZER P~

S

FLOWMETER

~ SAND-FLUID

MIXTURE TO

PUMP TRUCK

Fig. 11.2 - Schematic diagram of sand proportioner which permits (a) continuous operation (b) maintenance of constant ratio of materials

within narrow limits regardless of injection rates (c) instantaneous variation of the sand to fluid ratio

Re~$¢,~ 6¥H

HESI303176
Use of an accurate, flexible and continuous

type of blender (Fig. 11.3) has been shown to be

the most efficient method of mixing and metering

fluid and additives. Development of this type

equipment has made it possible to conduct the

large volume, high iniection rate treatments now

being performed.

Intensifier pumps (Fig. 11.5) use either conventional pumps or special dedicated primary

pumps as their power source. Intensifier pumps

provide more reliable pumping at high pressures

and high proppant concentrations for long pumphag times due to their long stroke (typically about

5 feet) and high volume per stroke.

Fig. 11.3 - Trailer mounted 100 barrel per minute blender

High Pressure Pumping Equipment

The primary high pressure pumps used in

fracturing are truck mounted (or air transportable

skid mounted), predominantly diesel powered,

crankshaft driven plunger pumps (Fig. 11.4). The

size and weight limitations imposed to comply with

state load 1Lrnits have resulted in a total delivered

hydraulic horsepower of 1,000 to 1,500 hydraulic

horsepower (HHp) per truck, whether delivered by

one pump or two. Recent advances in engine,

transmission, and pump design should result in an

increase in maximum HHp per truck unit to 2,000

HHp by the late 1980’s.

Fig. 11.4 - Body load truck mounted high pressure pumps. The

two pumps can deliver a total of 1200 hydraulic

horsepower.

Fig. 11.5 - Intensifier pump with 5-foot stroke. Rated at 15 BPM to

15,000 psi or I0 BPM to 20,000 psi.

Control Center

The operational control center for a frac job is

generally mounted on its own van or truck. It conrains the readouts and recording devices for the

instruments used to monitor the job and the necessary communications equipment to control the job.

Pressure transducers usually monitor pressure

in the treating line near the wellhead. If the job is

through tubing, the annulus pressure is also monitored. Flow meters (usually turbine type) are used

to monitor fluid flow rates while radioactive densometers are frequently used to measure fluid density, from which proppant concentration is

calculated.

Computers have recently been introduced as

part of the control center equipment. This results

in improved recording and data handling capabilities and can provide "real-time" calculation of information such as a calculated bottom-hole treating

pressure and, on foam jobs, a calculated foam

quality both at the surface and at bottom-hole conditions. For foam treatments using N~ and CO~

gas, special flow meters that use both temperature

and pressure inputs are required to obtain accurate

gas flow rates.

HES1303177
Surface Lines and Manifolding

Low pressure and high pressure flow lines

used in fracturing have been developed and

adapted from other uses to allow rapid and reliable

assembly and disassembly in a wide variety of configurations. Low pressure manifolding will usually

use multiple flexible hoses coupled to large (8 to 12

inch) diameter steel lines used for long runs. The

high pressure discharge lines use either a WECO®

type hammer union or a GRAYLOC® type clamp

union. In normal operations, the high pressure

discharge line will be rated at working pressures

up to 10,000 psi. However, discharge lines rated to

15,000 psi are common, and 20,000 psi rated lines

are available in most areas where they might be

needed. On offshore stimulation vessels, a reel of

steel jacketed flexible hose (rated to 15,000 psi) is

normally used to make connections from the

pumps on the boat to the wellhead on a platform

(Fig. 11.6).

Fig. 11.6 - Flexible steel-jack hose which provides connection

between stimulation vessel and jack-up rig

Wellhead isolation tools are available that isolate the wellhead tree from fracturing treating pressure by inserting a mandrel through the tree and

sealing it into the top of the tubing. This will isolate the wellhead from both pressure and proppant

during the treatment.

PRACTICAL DESIGN OF

FRACTURING TREATMENTS

Part 12

The practical application of hydraulic fracturing to oil and gas wells incorporates the use of

many "technological tools" such as:

 ̄ electric logs

 ̄ pre-frac and post-frac wellbore surveys

 ̄ laboratory studies on formation samples, fluid

theology, propping agents, etc.

 ̄ reservoir transient pressure analysis

 ̄ computerized reservoir production simulators

 ̄ computerized hydraulic fracturing design simulators

 ̄ "microfrac" tests and analyses

 ̄ "mini£rac" tests and analyses.

Long term post-frac production analysis of a

well will also influence the type of stimulation

treatments used on other wells in the same field.

This will be discussed in Part 14 of this text.

Fracture Design Variables

There are many parameters that can be varied

in designing a hydraulic fracturing treatment. The

type of fluid used could be water based, oil based,

an emulsion, or a foam. The fluid viscosity can be

adjusted by using various types of gel systems.

Typically, the volume to be pumped will be specified as part of the design, and the injection rate is

also predetermined for most treatments. The type

of proppant and the sieve size must be selected.

The proppant addition schedule will usually be

specified and the specified volume of proppant will

be on location before the job starts. In most applications, the sequence will be:

 ̄ pre-pad volume

 ̄ pad volume

 ̄ proppant-laden volume

 ̄ displacement volume.

Revised 6YH

HESI303178
The "pre-pad fluid" is ungelled or lighdy gelled fluid that is pumped prior to starting the gelled

fluid. If using an ungelled frac fluid, then this

stage is not considered. Many treatments start the

pumping with the viscous frac fluid. However, if

the wellbore tubulars contain fluid when the job

starts, this would be considered as pre-pad. A

small volume of hydrochloric acid is occasionally

used as a "spearhead" to remove scale or otherwise

improve the perforation tunnels to promote adequate fluid penetration and lower breakdown pressure.

The "pad" is the viscous fluid pumped prior

to starting the proppant. If the fracture width is

too small, then the proppant grains will bridge

instead of moving down the fracture as a slurry.

After the specified proppant schedule has been

completed, a calculated volume of displacement is

pumped before the pumping is terminated. This

removes essentially all of the proppant slurry from

the wellbore tubulars.

The variables that must be considered in a

specific fracturing treatment design are:

 ̄ base fluid type

 ̄ fluid viscosity, fluid loss properties and pipe

friction

 ̄ fluid volume

 ̄ injection rate

 ̄ proppant type

 ̄ proppant concentration

 ̄ physical properties of the formation

 ̄ fluid temperature in the fracture.

Fluid Loss~ WIDTH

~-~ ’nj~c, ttie°n 4 ....

In Situ Stress’

Young’s

of Elasticit,~

Fluid

Viscosity

Treatment

Volume

~ Fluid Loss

In Situ Stress

Young’s Modulus

i of Elasticity

F]g. 12.1 - Factors Affecting Fracture Width

The limitations on many of the above factors

are related to the crack width. In simplified terms,

Figure 12.1 illustrates the effect of these factors on

creating width. A more detailed discussion of this

effect on crack width was presented in Part 4 and

Appendix B of tiffs text.

Selection of Design Variables

Like nearly all facets of the oilfield, experience is the best teacher when it comes to designing

a fracturing treatment for a specific well. However,

none of us gets to start with experience, and even

the very experienced are often faced with reservoir

and well-site conditions that are drastically different than any previously encountered. For these

reasons, we will outline a step-by-step decisionmaking process that will help select the fluid, injection rate, proppant, and pumping schedule to

use in a hydraulic fracturing treatment. The sequence given here is only a suggested order; the

sequence will often be altered by various surface or

reservoir conditions or possibly for economic’~ or

political reasons.

Step 1 - Selection of Acceptable Fracturing Fluids

It is not necessary to choose the exact fluid

composition and volume during this first phase.

This step should be used to narrow the choice to

no more than three possibilities. Appropriate fluid

volumes will be determined later.

The fluid selection process is usually based on

three considerations, or some combination of the

 ̄ availability

 ̄ cost

 ̄ technical superiority.

For the purpose of our discussion, we will

assume any desired fluid would be available, although in many situations this is not true. The

logistics of some wells may limit the types of fluids

available. This is especially true in underdeveloped

regions and offshore operations. For example, the

use of nitrogen and CO2 requires pressurized transport and storage as well as the specialized equipment that may not be be available without

advanced planning and]or additional mobilization

or set-up charges.

HESI303179
The relative cost of two different fracturing

treatments .will vary with the type and concentration of gelling agents and their chemical additives.

The volume of the fluid used, the type and volume

of propping agent and the service company equipment pumping charges are also variables. In some

cases, process license fees must also be added to

the cost of a treatment. Most of these costs are

relatively consistent from coast to coast in the

United States. However, international prices will

vary drastically due to transportation costs, import

fees, and the local availability of some products.

Pumping and equipment costs will also vary widely

throughout the world. To compare costs between

two proposed fracturing designs, it will be necessary to obtain estimates from a service company

that operates in the geographical area of the

well(s).

The technical superiority of one fluid versus

another is related to the specific conditions of the

well under consideration. In some instances, it

may be that the least sophisticated and lowest cost

frac fluid best fulfills the technical requirements.

Unfortunately, this is usually not the case. The

purposes of the fracturing fluid can be identified

as:

 ̄ to transmit hydraulic pressure into the fracture

 ̄ to extend the fracture penetration into the

producing formation

 ̄ to create sufficient width for the fracture to

accept the size and concentration of proppant

used

 ̄ to transport the proppant into the fracture and

control proppant deposition.

The selection of fluid type may be dependent

on compatibility with the reservoir fluids or the

rock itseff. The fluid loss properties and the fluid

viscosity (as a function of temperature and time)

are also factors to be considered. (Part 6 of this

text presented extensive discussion of these topics.)

For specific fluid systems being considered, the

service companies will have extensive data on the

fluids they offer. In a later step, this data will be

used with a computer frac design simulator for

more specific comparisons.

Step 2 - Selection of Propped Length(s)

There are basically three values that describe a

propped fracture:

 ̄ propped length

 ̄ propped height

 ̄ fracture conductivity.

Unfortunately, it is nearly impossible to pro°

pose a step-by-step design procedure where you

can make all the comparisons desired without specifying one of the above three values as a "target."

It will later be necessary to loop back to this step

and choose another "target" for comparative purposes. The most commonly used "target" in current design technology is the propped fracture

length,4s so that is what will be used here.

Step 3 - Selection of Created Fracture Height

The design procedure common for many years

has been to assume the created height will be the

same as the perforated interval or the productive

pay interval. This can be a major flaw in the design process. Prior to the 1980’s, only a few in the

industry recognized the importance of accurate

fracture height predictions,ss Previously, most computer simulators would only indicate shorter

propped lengths when excess height growth occurred. Very few could accurately model proppant

transport and even fewer would model fracture

closure. The industry now realizes that the loss of

length is not the only concern.’s ~ a The most important question is "Do we prop the pay interval?"

or "Does most of the proppant go to some nonproductive zone above or below the pay interval?"

It has always been obvious when an operator

would frac into a water zone, but for some reason

this was the only situation where fracture height

growth was a major concern. Before using a computer design simulator, we need some understanding of possible fracture height growth. The major

factors that affect height growth are listed here in

their approximate order of importance:

 ̄ in situ stress variations

 ̄ pressure in the fracture

 ̄ size of perforated interval

 ̄ variations in elastic modulus.

For many years, the only valid analysis for

height was to use post-frac surveys. Using these

surveys (which are sometimes difficult to interpret)

Revised 6YH

HESI303180
in conjunction with standard electric logs, an engineer may find an apparent correlation between

logged features that would help predict what type

of rock may impede fracture height growth and

when excessive growth was Likely. As a result of

extensive research work in many laboratory and

field studies in recent years, the industry has accepted the concept that fracture height is primarily

controlled by the in siru stress variations in the

reservoir. "" ,0. ,  ̄ 70

There are now a number of pseudo-threedimensional (3-D) fracture simulators throughout

the industry that use in situ stress variations to.

predict fracture growth in all three dimensions.

Figure 12.2 shows illustrations of optimistic and

conservative two-dimensional (2-D) model predictions for created length (Case 1). In addition, Figure 12.2 shows 3-D simulations for good stress

contrast of400 psi (Case 2) and a low stress contrast of only 50 psi (Case 3). It is apparent that the

2-D simulator could easily model the Case 2 situation. If a valid fracture height was used in the 2-D

Case 1 : 2-Dimensional fracture simulator prediction

Model

; Stress = 4300 ., .:.;,,:;’. ~

Stress = 4700 psi

Case 2: High stress contrast 3-D simulation

~..,~/--- 3-D Model

Stressy

Case 3: Low stress contrast 3-D simulation

Fig. 12.2 - Comparison of 2-D Design with 3-D Simulator where

Pay Zone has Lowest Stress

simulator, Case 3 could also be approximated with

a 2-D model.

Figure 12.3 gives a better comparison of Case

2 and Case 3 with the 2-D examples. Case 3 shows

that frac lengths will be considerably shorter when

the stress contrast is low. Also, if the proppant is

not well suspended, the fracture within the pay

zone may not be adequately propped open.

:~:: .’.:: ":.’t2.: .": ....." :.:::: ::~ .":  ̄ ". 

Case 2

Case 3

Fig. !2.3 - Comparison of 3-D Simulations for Case 2 and Case 3

with 2oD Predictions

If a lower in situ stress exists in the reservoir

immediately above the pay zone, the Case 4 result

will occur (Fig. 12.4). The resultant length will be

much less than desired. There should be no problem in being sure proppant remains in the fractured portion of the pay zone. However, the

fracture width in the low stress zone will be greater

than down in the pay interval, and the fracture will

close first in the higher stressed portion at the

completion of the job. A larger treatment size will

have only a limited effect on obtaining more length

within the pay zone.

Case 5 in Figure 12.5 illustrates the result of a

lower in situ stress existing in the reservoir immediately below the productive interval. This is usually the worst situation which could occur.

Fracture length in the productive zone will be limited and proppant settling must be avoided during

the pumping operation as well as during fracture

closure. The fracture will close fast in the productive interval, since it has the higher stress.

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Model

= 4300 psi .~,

Stress = 4300 psi

Case 4: Lower stress above pay zone

Fig. 12.4 - Compare these with the 2-D simulations - note upward

growth.

Stress = 4300 psi

Stress = 4150 psi

4300 psi

3-D Model

Case 5: Lower stress below pay zone

Fig. 12.5 - Fracture grows downward to lower stress, quite different

than 2-D simulations

The determination of in situ stress in the productive zone and adjacent rock is critical for the

valid modelling of a treatment design. Even if only

a 2-D simulator is used, the accuracy of the prediction is dependent on the validity of the assumed

fracture height. The in situ stress data are required

input for using most of the pseudo-3-D simulation

models. The only accurate way to measure these

stress values is by creating a hydraulic fracture,

then taking an instant shut-in pressure measurement. The created fracture should have a very

limited height, since the pressure response observed will be for the lowest stress value within the

created fracture. A process called "microfracing"

has been developed where very small volumes

(typically 20 to 100 gallons of fluid) are used in a

small fracturing operation to measure in situ stress.

Fracture heights will be small with these volumes.

Microfracs can be performed during the drilling or

after the well has been cased. Cased hole microfracs may required squeeze cementing, since stress

measurements are often needed for zones that an

operator does not want perforated during the stimulation treatment.

Revised 6YH

In the mid-1980’s, a logging technique was

introduced to estimate in situ stresses in the reservoir using a long spaced acoustic tool which gives a

more accurate value for the At of the shear wave.71

The tool itself was first developed in the mid

1960’s. There was little demand for the data, and

computer technology at that time required significant "hand analysis" to separate the second shear

wave response. The logging service itself is only a

sophisticated mechanical properties log and a fracture toughness log. The data is digitized and the

logging service company makes several assumptions including linear elasticity, isotrophy and homogeneous composition to predict in situ stress

values throughout the logged interval. Some companies also link this data into a pseudo-3-D frac

design simulator to present the results in a very

simple, neat format as a "fracture height log."

Many operators have used this service prior to a

frac treatment and followed with conventional

post-frac survey methods for comparison. The

agreement has varied from excellent to poor. However, within a single field, the results have been

more consistent (good or poor agreement within

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the field). Comparison of in siru stress predictions

of the fracture height log and by microfrac measurements have also shown inconsistent results.

Step 4 - Selection of Range of Injection Rates

At this point, it is necessary to consider the

pump rate for the fracturing treatment. In most

instances, this step is actually used to determine

the range of injection rates to be considered. Here

are four important factors to consider:

 ̄ maximum allowable treating pressure

 ̄ equipment limitations

 ̄ proppant placement

 ̄ created fracture height.

After the maximum treating pressure has been

determined for the subject well, the predicted friction pressure of the fracturing fluid system(s) will

usually establish an upper limit on the possible

rate. In some instances, a certain fluid system may

be chosen because it has the lowest friction loss of

the fluids being considered. Other times, all fluids

being considered will allow more rate than desired.

There are several equipment limitations that

could exist. The most obvious would be the horsepower availability of the service companies. In

some instances, deliverability of the fluid (or one

component of the fluid system) or of the proppant

may set the minimum or maximum injection rate.

Erosional effects of the proppant on the surface

iron or the tree on the wellhead may dictate a maximum rate.

The effect of injection rate on the ability to

successfully place the desired proppant is a difficult analogy. In fact, until there is some previous

experience in the reservoir with the selected fluid

system and specific proppant to be used, it may be

necessary to ignore this consideration until experience indicates problems with proppant placement.

Experience with the selected fluid system in similar reservoirs is helpful. Proppant size, proppant

density, proppant concentration, fluid viscosity,

and injection rate all are factors in the transport of

the proppant. The width of the fracture, proppant

size, and proppant concentration are all factors in

whether bridging of the proppant occurs somewhere inside the fracture. There are instances

when the "proppant placement" problem is in the

weLlbore, slowly filling the wellbore with proppant

as the job progresses. The factors involved are the

size of the casing, the length of the perforated interval, the number of perforations accepting fluid,

fluid viscosity (in the wellbore) and the injection

rate.

One of the most important effects of injection

rate is its influence on fracture height. Numerous

field studies related to excess height growth have

shown injection rate to be the most important single factor that can be controlled (in situ stress variations are the major factor). Conversely, when

attempting to treat large perforated intervals, it is

important to use the maximum injection rate feasible. Decreasing the rate to avoid excess height will

lengthen the job time and increase proppant placement problems.

Step 5 - Selection of Proppant Type(s), Size(s)

and Concentration(s)

In many fields, previous experience may have

identified a suitable proppant type, size, and

pumping schedule. However, even in these instances it is wise to re-examine the "status quo" for

improvements. Since the whole purpose of a hydraulic fracturing treatment is to place the proppant, this step should not be slighted. In most

applications, cost considerations limit the proppant

type to the common quartz sands being marketed

as proppants. Frac sand and manufactured proppants are available in many different sieve sizes.

(Part 9 of this text discussed proppants in detail.)

The size and density of the proppant will affect

proppant settling and also the maximum proppant

concentration that can be placed without a screenout from bridging of the proppants in the narrow

crack. Field experience usually shows higher concentrations will give better production results.n73

.In some instances, this is judged to be the effect of

higher fracture conductivity, while other times the

improvement is attributed to more propped fracture height.

Step 6 - Use of Fracture Design Simulator

Now it is time to put all the parameters into a

fracture design simulator. Hopefully, a computerized simulator is available, since several "iterations" will usually be required to make

comparisons between designs. There are hundreds

of computer frac design simulators in existence,

from very simple 2-D single-viscosity models without proppant transport correlations to the most

HESI303183
sophisticated pseudo-3-D models which calculate

the varying fluid viscosities as a function of temperature and time. Most 2-D simulators are based

on one of the two classical geometry theories described in Appendix B as Group 1 or Group 2.

However, even when two different simulators were

written using the same geometry theory, the resultant design calculations can vary significantly.

Three other important factors in a simulator are

the fluid loss model, the fluid viscosity model, and

the proppant transport model.

If there is more than one simulator available

to an operator for designing treatments, the most

practical approach is to determine which of the

simulators has the features most important to the

field application and use that simulator exclusively

for designing fracturing treatments. If, for example, the primary design criteria is propped length,

then three different simulators may give conflicting calculations for fluid and/or proppant volumes

required for a specific propped length. If the operator is considering propped lengths of 500, 800,

and 1000 feet for a specific well, then the results

for 500 feet on simulator "A" should not be compared to results for 800 feet on simulator "B;’ etc.

It is best to compare simulator "A" and "B" on

their technical merits, then use only the selected

simulator for comparisons of job designs for a specific well.

Step 7 - Post-Treatment Check of Simulator Calculations

It is very difficult to accurately predict all the

data input to the simulator. When field results

vary significantly from the simulator prediction,

the most likely problem is inaccurate data given to

the simulator. Erroneous data for fluid viscosity or

an incorrect fluid loss coefficient will force the

design simulator to make poor predictions. In

some cases, the simulator may use models that are

too simple. This will be the case for a graphical

hand-calculated solution, as well as for some computerized models. Highly sophisticated 3-D models

will also give unreliable results when much of the

input data was "assumed." This is especially true

for the in situ stress values.

If field results appear to differ significantly

from design simulator predictions, the first step is

to validate the input data to the simulator. If this is

not successful, the operator should try to obtain

the use of a better simulator.

MONITORING A

FRAC TREATMENT

DURING PUMPING

Part 13

Analysis of Bottomhole Treating Pressure

During the late 1970’s, an Amoco Research

project gathered detailed pressure data during hydraulic fracturing treatments in several reservoirs.

In 1979, using part of this data base, Nolte introduced a new method for analysis of treating pressures observed during fracturing propagation.7’-7~

The pressure data was obtained by using an openended tubing/annulus configuration that enabled

the real-time measurement of bottomhole treating

pressure. This work predicted new relationships

between the observed pressure response and the

corresponding fracture growth behavior. The researchers observed that a large number of the wells

that were monitored followed one (or more) of four

identifiable modes of pressure behavior (Fig.

13.1). The log of the net pressure (y-axis) versus

the log of the pump time (x-axis) was plotted. The

type of formation pressure response that may

result was later expanded by Conway, et.al?6 The

net pressure was defined as the pressure acting to

open and propagate the fracture. Nolte and Smith

presented a separate work which detailed methods

for obtaining accurate values of the fracture closure

pressure.~7 This method will be detailed later in the

"minifrac" discussion.

Mode I Mode II

Mode III

~,~ Mode IV

Log (Pump Time)

 ̄ Fracture closure pressure as determined by mini-frac

and pressure decline

Fig. 131 - Plot of Treating Pressure vs. Time

Revised 6YH

HES1303184
To explain their observations, Nolte and

Smith used the fracture model of Perkins and

Kern" to describe the fluid pressure required to

extend a fracture with time.

Nolte’s assumptions lead to the conclusion

that the fluid pressure would slowly increase with

time if the fracture height is relatively constant.

This concept predicts that for a Newtonian fluid

extending a confined height fracture at constant

injection rate, the wellbore pressure will increase

proportionally to time raised to a power:

p(t) = k * t% I/s < e < 1/5 (13-1)

The larger value is for the assumption of a

relatively small fluid loss rate (relative to the injection rate) while the smaller value of the exponent is

for a relatively large fluid loss rate. The bounds of

the time exponent of equation 13-1 are for a Newtonian fluid. To be applicable for non-Newtonian

fluids, Nolte and Smith generalized that for a

power law fluid (with a power law exponent n’),

the bounds would be as follows:

1/(4n’ + 4) < e < 1/(2n’ + 3) (13-2)

For n’ values typical of actual fracturing fluids

used in the industry, this exponent normally falls

between 0.18 and 0.33. From this work, it was

concluded that the constantly increasing net pressure in this range is that of a relatively contained

fracture within the zone of interest and most fracture growth is length extension in the reservoir.

To explain the other pressure modes, the continuity equation was solved as follows:

ch = ch + LpCh + + +--~- (13-3)

where:

ch = injection rate

ch = leakoff rate

L = fracture length

p = net pressure

C = average width to net pressure ratio def’med by Nolte as *h/2E

h = fracture height

E = Young’s modulus

For a constant injection rate, the right side of

the equation is a constant and places a restriction

on the permissible changes in the variables with

respect to each other. As a r,esult, any large positive change in height or fluid loss would result in a

decLine in the rate of pressure change. With this

reasoning, Nolte and Smith interpreted a constant

net pressure (Mode II) as either sLightly accelerated

height growth over Mode I or accelerated fluid

loss. In addition, they interpreted a significant

pressure decline (Mode IV) as unrestricted height

growth.

Nolte’s interpretation of an increasing net

pressure which follows a unit slope (Mode III) is

similar. Since there is no plausible basis, under the

conditions of increasing pressure, for height, compLicance, or fluid loss to decrease significantly, it

follows that the rate of length extension must have

decreased significantly relative to Mode I. The

implication of this is that the only variable changing significantly during the unit slope model is the

pressure. Also, since length extension has been

reduced significantly, relatively little fluid is reaching the fracture tip (e.g., the fracture screened out

with proppant at some point in the fracture). As a

result, the fluid being pumped into the fracture

essentially is being stored by increasing width and

increasing pressure.

Summarizing the interpretations of the four

pressure modes as referenced in Figure 13.1:

 ̄ Mode I is a gradual pressure increase that, in

general, means that the fracture is being relatively contained and most movement is length

extension into the reservoir.

 ̄ Mode II is a constant pressure in which accelerated height growth or fluid loss is causing

less efficient length extension.

 ̄ Mode III is a unit slope pressure increase in

which the fracture has screened out and no

further length extension takes place. The pressure increase rate of the screenout is inversely

proportional to the distance from the wellbore

the treatment screened out.

 ̄ Mode IV is a gradual pressure decline in

which uncontrolled height growth is occurring, resulting in narrow fracture width and

poor fracture length propagation.

Real.Time Treating Pressure Analysis in

Field Operations

Since Nolte and Smith’s introduction of bottornhole treating pressure (BHTP) analysis and

interpretation for hydraulic fracturing in 1979,

HESI303185
8 ,hydraulic fracturing,

service companies have developed a large fleet of

computerized vans for the recording and analysis

of fracturing pressure. However, most fracturing

applications do not permit the use of tubing without a packer to directly record BHTP from the

surface while fracturing. This wellbore configuration is not generally used because it may not be

operationally possible, it may add significantly to

the cost, or it may reduce the desirable injection

rate. Consequently, attempts have been made to

predict the BHTP from surface recordings of the

injection pressure. This prediction requires calculations of the change in hydrostatic head due to

proppant, the friction pressure for the fluid, and a

correction to the friction pressure due to proppant.

From densometer recordings, the concentration of

proppant in the fluid can be accurately determined, and hence the change in hydrostatic head.

The primary deficiency in predicting BHTP

from surface measurements is the calculation of

friction due to fluid flow within the wellbore tubulars.79 This calculation must include the coupling

of the complex flow behavior of the viscoelastic

fluids generally used, and the effect of large volume fractions of proppant on this flow behavior.

Current methods of calculations are either based

on empirical correlations, models for simple fluid

behavior or correlations derived from matching

acutal field data. Some of these current methods

can produce errors that are significantly greater

than the changes in BHTP required for an accurate

interpretation.

One additional flaw in the application of realtime pressure analysis is the failure to measure the

value for the fracture closure pressure. An assumed value for closure pressure may be several

hundred psi in error, which can influence the decisions of when to continue pumping or to abort a

job.

When a valid closure pressure value is used

and an accurate calculation of BHTP is achieved, it

is possible to detect the onset of the large pressure

increase which occurs when a treatment is in the

process of a "screen-out." For this condition, realtime calculation of BHTP provides a significant

advantage over surface pressure alone in predicting

tiffs condition, and consequently permits the proppant slurry to be displaced to the bottom before

pumping must be terminated. The displacement of

the proppant into the fracture, compared to reacting too late and leaving the wellbore filled with

Revised 6YH

proppant, provides significant enough cost savings

that many operators require the computerized vans

on most treatments. Because of the uncertainties of

some fluid friction calculation models, the full

potential of BHTP interpretations and analyses are

not always available to the operator, even though a

computerized van is on site during the treatment.

As better friction calculation models are developed, the accurate prediction of BHTP can be

achieved for most cases with a computerized van

on location. This can result in a significant increase in the effectiveness of hydraulic fracturing

treatments.

Minifrac Process

A "minifrac" is a series of tests on a small

fracture performed on a well to determine thefracture extension pressure, closure pressure, the fluid

loss coefficient, and fluid efficiency3~*’ 80-8~ Included in minffracturing are:

 ̄ the step rate test

 ̄ the pump-in/flow-back test

 ̄ the pump-in/shut-in test.

Step Rate Test

The step rate test is performed after a fracture

has already been created. The step rate is begun by

injecting fluid into the well at a low matrix flow

rate, usually on the order of .3 to .5 barrels per

minute with any fluid. The injection rate is increased at increments of .3 to 1.0 barrels per minute until the pressure stabilizes or for 4 - 5

minutes. The pressure is monitored throughout

the test. The maximum pressure at each flow rate

is plotted versus the corresponding flow rate. Two

straight lines are drawn through the plotted points "

which define two slopes. The intersection of the

two lines yields the fracture extension pressure

(Fig. 13.2). The slope of the data beyond the fracture extension pressure can be valuable in predicting maximum desired injection rates when fracture

height growth is a problem.

Pump-in/Flow-Back Test

The pump-in flow-back test, when performed

by itself, is begun by injecting into the well with

any non-damaging fluid at a rate that will extend

the fracture. The total volume pumped should be

approximately 50 to 100 barrels. The well is then

HESI303186
shut in (get instantaneous shut-in pressure ISIP)

and flowed back at a low, constant rate, usually .25

to 1.5 barrels per minute. The pressure is monitored as shown in Figure 13.3 and an inflection

point should be observed. The inflection point

from Figure 13.3 is the fracture closure pressure.

This test can be repeated as necessary with different flowback rates to develop confidence in the

measure value of fracture closure pressure.

The inflection point (closure pressure) is interpreted according to different preferences, but

for the most part the differences are negligible. For

purposes of comparison, the same method should

be used when interpreting closure pressures. The

dominant opinion is that the closure pressure exists

at the intersection of two straight lines defined by

the pressure vs. time curve as shown in Figure

13.3. A second method uses the straight line in the

upper fracture flow portion of the flow-back curve.

The point on the line where the curve begins to

become "concave down" is the inflection point.

Pump-In/Shut-In Test

The pump-in/shut-in test is performed by

injecting 50 to 300 barrels of the actual treatment

fluid at the expected fracturing treatment rate and

then shutting the well in. Upon shutting in the

well, the ISIP should be noted. The pressure

should be allowed to decline for a time period of at

least twice the pumping time (see Fig. 13.4) in

order to obtain enough data to calculate the effective fluid loss coefficient. Normally, a computer

program will be used, since curve fitting of the

data is necessary. It is very important to only take

data during the decline that is above the fracture

closure pressure.

 ̄ FCP - Frecture Closure Pressure as detm’mlned by mini-free and pressure decline

/

1.0 ~0 3.0 4.0 S.O 6.0 7.0 8.0 9~ 10.0

Fl~w Rate (bbl/mln)

Fig. 13.2 - Example Step Rate Test

154) 160

F~g. 13.3 - Example Pump-in/Flow-back Test

3900

~ ’ PREVK~ISLY DETERMINED CLOSURE PRI~JRE

TI min

Fig. 13.4 - Example Pump-in/Shut-in Data for Pressure Decline

Analysis

The data required for a minifrac analysis are:

 ̄ Young’s modulus

 ̄ gross height

 ̄ net height

 ̄ flow behavior index

 ̄ gel degradation factor

 ̄ pump rate and injection time

 ̄ ISIP time and pressure

 ̄ closure pressure

 ̄ pressure/time data during the decline period.

The computer calculation (or manual analysis)

yields the match pressure (symbolized by P’)

which in turn yields the fluid loss coefficient, the

fluid efficiency, the fracture width and length, and

the closure time. P" is determined using theory

developed by Nolte. The essence of the analysis is

to obtain the match pressure through one or more

of these methods:

 ̄ curve matching method

 ̄ graphical method

 ̄ mathematical computer simulation method.

Revised 6YH

HESI303187
Nolte and Smith use the Perkins and Kern

geometry which generally predicts a long narrow

fracture;77 it shows the width to be proportional to

fracture height (H). More recently, Lee has modeled the treating pressure analysis problem using

Kristianovich and Zheltov and ".Penny" shaped

geometries?° The Kristianovich and Zheltov geometry generally predicts a short, wide fracture,

where width is proportional to length (L). Lee also

has presented a more valid analysis of the ellipsoidal shaped geometry model for the case where a

fracture propagates in an unbounded zone or

across botmdariesY The effects of compressibility

and of temperature change on the analysis of minifrac data have been published recently by Solimarl.

POST-FRAC ANALYSIS

Part 14

The final result we seek to obtain with a hydraulic fracturing treatment is increased production. However, in most cases, a treatment is

considered successful only if the resultant production rates meet or exceed the operator’s pre-frac

expectations. When the increased production rate

is still considerably below expectations, this means

one of two things: pre-frac expectations were

falsely optimistic, or there needs to be some improvements made in the design or implementation

of the fracturing treatment. An operator should

not ignore the possibility of the former, but the

discussion in this text will only relate to possible

changes in the application of hydraulic fracturing.

Disappointing production results can be

broadly classified as one of two possible types:

inadequate initial response, or rapid production

decline.

Inadequate Initial Response

Sometimes within days of (or at least a few

weeks after) a frac job, it may become obvious that

the production capability of the well is inadequate.

A check list of possibilities that should be considered would include:

 ̄ inadequate k, +, and/or reservoir pressure

 ̄ fracturing out of zone

 ̄ insufficient propped fracture length

 ̄ inadequate fracture conductivity

 ̄ fluid-rock incompatibilities.

It is always possible that it is a poor well. The

effective reservoir permeability may be lower than

was originally believed or the porosity may be

much lower than was estimated from the logs. The

reservoir may be much smaller than anticipated

due to faults, pinch-outs, etc. If the well is in an

exploratory area, or is a large step-out in an existing field, there possibilities are much greater than

if the well is a f’fll-in or development well in an

older field.

If the fracture does not stay within the reservoir "pay zone" due to upward and/or downward

migration, the production results can be disappointing. As has been discussed earlier in this text,

the fracture will prefer to grow where the lowest in

situ stress is encountered. Post-frac surveys (e.g.,

temperature, radioactive, etc.) are usually necessary to identify where the fracture has grown out

of zone.

In a well with very low reservoir permeability,

it is very important to achieve a long propped fracture. If excessive height growth occurs, as mentioned above, the propped fracture length will be

much shorter than if the fracture height is well

contained. If post-frac surveys indicate excessive

height, then it it obvious that the resultant

propped length is shorter. Post-frac build-up tests

may also allow an operator to determine if the effective propped length is significantly less than

designed?7"~

For a hydraulic fracturing treatment to be

successful, it is necessary that the propped fracture

has adequate conductivity to allow high production

rates without a significant pressure drop .down the

fracture. Proppant crushing, plugging from gel

residue or produced formation fines and embedment of the proppant into a soft fracture face are

the traditional concerns about losing conductivity

in the fracture. One additional concern of great

importance is the possibility that the proppant may

have mostly settled into the bottom part of the

fracture and, due to downward fracture growth, is

not propping open the fracture within the productive pay interval. The propped fracture may have

excellent fracture conductivity, but if the propped

fracture is in essentially a non-productive part of

the reservoir, a post-frac pressure build-up analysis

Revised 6YH

HESI303188
hydraulic fracturing 61

will calculate very low fracture conductivity, which

is correct for the closed fracture up in the productive interval.

The last consideration listed above is incompatibility between the treating fluid and the reservoir rock or possibly incompatibilities with the

reservoir fluid(s). Water-based frac fluids reacting

with formation clay minerals is the most commonly

considered problem, but another possibility is the

dissolving or weakening of the grain to grain cementation of a sandstone causing Frees to be released into the proppant bed. Another major

problem is for the treating fluid to react with iron

compounds in either the rock or the reservoir water. This can cause severe plugging of both the

reservoir permeability and the proppant bed due to

the precipitation of iron oxides. Other potential

problems include precipitation of paraff’m or asphaltenes and scale deposits. In many instances, a

viscous emulsion may form and cause blockage.

Sometimes emulsions that are stabilized by formation fines can be very viscous and difficult to

break.

Rapid Production Decline

In some instances, the earty time post-frac

production rates may meet or exceed the anticipated levels, but follow an abnormally steep decline. It is important to accurately know the true

"normal" decline for the well. In-depth modeling

and simulation of reservoir production rates vs.

time may show that rapid decline rates are to be

expected for many wells following hydraulic fracturing stimulation treatments. If an operator is

certain that a well is experiencing an abnormal

decline, major considerations to help identify the

problem are:

 ̄ limited reservoir

 ̄ loss of fracture conductivity with time

 ̄ fracture closure at the wellbore

 ̄ insufficient propped fracture length.

A reservoir that has a small volume may give

excellent production rates immediately after a

stimulation treatment and fall off rapidly as the

reservoir pressure dissipates. Transient pressure

testing methods will identify near-wellbore boundaries assuming the test is conducted properly and

for a sufficient length of time. In an established

field where the geology has been well defined,

there is less possibility that abnormal declines are

due to a limited reservoir. During exploratory

drilling or early in a field development program, it

is important to do adequate transient pressure testing before assuming a rapid decline rate is abnormal.

During the producing life of a well, the

propped fracture may suffer a significant loss of

fracture conductivity. The conductivity loss may

result from proppant crushing as the closure stress

on the proppant increases or from gradual plugging of the proppant bed. The gradual plugging

may be from formation fines. Some formations

naturally produce fines, while in some instances

the treating fluid may cause the release of f’mes. As

the proppant grains imbed into the fracture wails,

this can cause the breaking loose of small formation grains that can migrate into the proppant

pack. Over a long time period, f’mes may migrate

through the propped fracture toward the wellbore

and a high degree of plugging may occur as the

concentration of fines becomes very high. Other

possible sources of fines would be precipitation

products such as paraffin or scale deposits. In a

retrograde condensate reservoir, the conductivity

may drop significantly as the reservoir pressure

decreases and the liquid saturation increases, often

resulting in three phases being present in the proppant pack.

Fracture closure in the near-wellbore area can

result when this area is inadequately propped.

Overdisplacement at the conclusion of the fracturing treatment can be one cause for this situation.

However, some wells have a tendency to allow part

of the proppant to be flowed back in the wellbore

during cleanup and/or production. Flow back of

proppant during cleanup may not be a problem if

there is other movement of proppant toward the

wellbore to replace the lost proppant. Also, the

proppant that is carried back into the wellbore is

not necessarily material that was adjacent to the

wellbore. If there is significant proppant settling

prior to fracture closure, there may an unpropped

void area above the top of the proppant pack. The

fluid velocity through this open crack may be sufficient to pick up and transport proppant back into

the wellbore from significant distances. This phenomenon is most plausible during post-frac

cleanup or early in the well’s producing life. With

HESI303189
time, the fracture will continue to close and hold

the proppant in place.

If the propped fracture penetration distance is

insufficient, a rapid production decline may be

evidenced even if the initial production rates were

below expectations. See the previous discussion

concerning "inadequate initial response" for possible reasons that the propped length may be less

than anticipated.

Refrac Treatments

To design a successful refracturing treatment,

it is necessary to identify the problem(s) with the

original treatment,r2~83 Some refrac treatments are

the result of a premature screen-out during the

original attempt to stimulate the well. For this type

of refrac design, refer to Part 12 of this section

where treatment design is discussed. The primary

discussion here relates to a refrac when the original

treatment was successfully completed, but production results were disappointing or at least less than

optimum.

First, determine why the initial treatment was

unsuccessful. Possible reasons for desiring to refrac

a well include:

 ̄ inadequate producible reserves

 ̄ depleted drainage area

 ̄ insufficient fracture conductivity

 ̄ insufficient propped fracture length

 ̄ insufficient propped fracture height

 ̄ formation damage.

Next, determine the possible alterations in the

refrac design from the original stimulation treatment. The potential design changes that may be

needed include:

 ̄ Change fracturing fluid.

- higher or lower viscosity

- more compatible with formation.

 ̄ Change proppant.

- different sieve size

- higher strength proppant

- curable resin-coated proppant

- significantly higher volume of proppant.

 ̄ Change design variables to alter propped

length.

 ̄ Use multistage treatment.

 ̄ Alter injection rate.

 ̄ Use large pre-pad or pad to repressure formation.

Each point in both of the lists above has been

extensively discussed previously in this text.

HESI303190
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HESI303192
45.

References (Continued)

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High Closure Stresses;’ SPEJ. (April 1985). 58.

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Revised 6YH

HESI303193
66 hydr.ulic ,tra¢’~uring~

References (Continued)

66. Allam, A.M.; Crichlow, H.B.; and Soliman, 75. Nolte, K.G.: "Fracture Design Considerations "

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Revis~l 6YH

HESI303194
APPENDIX A

MECHANICS OF HYDRAULIC

FRACTURING

Mechanical Behavior of Rocks

Like other engineering materials, rocks are

deformable. Let S be a cylinder of rock with radius,

r, to which a force, F, is applied in the manner shown

in Fig. A. 1. The effect of F on S is the inducement of

a stress, or, which is equal to the force divided by the

base area of the cylinder; i.e.,

F (A-l)

The direction of this stress is parallel to the axis,

z, and therefore is called Crz. In the x or y directions

there are no stresses; i.e., o-,~ = O’y = 0. Thus,

although stresses in the solids are calculated by the

same manner as pressures in the liquids (and have the

same dimensions), there are important differences

between the two. For example, pressures have the

same magnitude in every direction but stresses do

not.

The effect off on S is a compression of S.

Therefore, o’z is called a compressive stress. If the

force F had a direction opposite what is shown in Fig.

A. 1, then the rock sample, S, would have been under

tension (material particles would have been pulled

apart from each other) and the stresses would have

been tensile.

Z

F

~-AL

Fig. A.1

Thus, by changing the magnitude or the

direction of the force, F, compressive or tensile

stresses of any magnitude can be created in the

sample (assuming that it does not fail). In solid

mechanics, the type of stress is usually identified by a

sign. If a compressive stress is designated by a plus

sign; i.e., + ~rz, then a tensile stress will be shown by

a minus sign; i.e., - o’z. This means that stresses can

theoretically have values anywhere between + ~

to- ~. This is another major difference between

pressures and stresses. The lowest value a pressure

can have is zero. It is never negative.

One important aspect of stresses is that their

magnitude and direction can change from point to

point within a body. Indeed, the solution of the rock

mechanics problems often reduces to obtaining

equations that express the variations of the stresses in

a given body.

The study of the mechanical behavior of rock is

not limited to an investigation of the stresses induced

in it by the external forces. It is necessary to know

how the rock has deformed as a result of the stresses

existing in it. This is usually done by a study of the

strain. Suppose the cylinder in Fig. A. 1 had an

original length, L. After the force, F, is applied to it,

its length will change by an amount, denoted by AL.

Its deformed length is L - AL. The strain, ~, is

defined as the ratio orAL to L:

~ = (L - AL) - L = _ AL

L L

and has no dimension. Like stresses, strains in a

body may have different values and directions at

different points. For example, the strain in the z

direction in Fig. A. 1 is:

AL

L

(A-2)

After the application of F, the radius of the

cylinder changes from r to r + Ar:

( Ar ~x = ~y = ,r + _r~ -r =

r r

(A-3)

Notice that ~x and ~y have a plus sign while ez has

a minus sign. The reason is that ~z is associated with a

decrease in length while ~,, and % represent increases

in radius.

HESI303195
The relationship between the stresses and

strains is usually obtained through the theory of

elasticity (although other theories may also be used

for this purpose). In an elastic material, the strains

induced by stresses are linearly proportional to them:

~z = 1 Crz (A-4)

E

The constant E is called the Young’s modulus of

the material. In addition to this constant, to be

completely defined, isotropic, homogeneous, elastic

materials need another constant. This constant is

called Poisson’s ratio. For the example used here,

this constant is equal to the ratio Of~x to ~z:

(A-5)

in which v is Poisson’s ratio. The Young’s modulus

(E) has dimensions of pounds per square inch while

Poisson’s ratio (v) is dimensionless.

The solution of most rock mechanics problems

begin with a mathematical treatment of the problem.

Like all other branches of engineering, these

solutions are generally based on certain assumptions.

In rock mechanics, it is usually assumed that rocks

are isotropic, homogeneous and elastic. The

definition of these terms is as follows:

Elasticity: If the deformations produced in a

body by external forces completely disappear by

the removal of the forces, the material is

considered to be perfectly elastic.

Homogeneity: A material is homogeneous if the

smallest element of it has the same physical

properties as the body itselL

I sotropy: If the elastic properties of a body do not

change with direction, the body is isotropic.

Let us examine the reasons for, and the validity

of, the above assumptions.

1. Elasticity: No rock is completely elastic.

However, some rocks have an elastic behavior up

to a certain value of stress.

Theory of elasticity has yielded many

reasonable and accurate solutions to rock

mechanics problems. In cases in which the rocks

do behave elastically up to a given stress the

elastic solutions are correct as long as the stresses

have not exeeded the elastic limit. In other cases,

elasticity, in general, is the most workable theory

and any deviations from it may make the

problem immensely difficult to solve. Among the

presently known theories, elasticity often yields

the closest fit to the actual results.

There are cases that require the use of

non-elastic theories, such as studying the creep

in rock salt. Such cases will have to be handled

individually and are not considered here.

Homogeneity: Strictly speaking, rocks are not

homogeneous materials. A block of rock contains

different crystals of various kinds, macro- andmicro-fractures, etc. However, this assumption

is quite reasonable if the dimensions of the body

under consideration are large compared to the

dimensions of the discontinuity.

Isotropy: The assumption ofisotropy is

necessary for mathematical simplification. In

most problems, the amount of deformation that

can be produced by the applied forces is of

interest. For instance, the width of hydraulic

fractures is the deformation caused by the fluid

pressure existing inside the fracture. The

assumption ofisotropy simplifies the

mathematical relationship between the forces

and the created deformations.

The force-deformation equations for an

isotropic, homogeneous, linearly elastic body

contain only two constants: Young’s Modulus

and Poisson’s ratio.

If it is not assumed that the material is

isotropic, then, in general, 21 independent

coefficients are needed to identify the material

mechanically. This explains the need for the

assumption.

Strength of Rocks

As in most other materials, rocks can bear a

certain amount of force without failure. The

magnitude of the force bearable by rocks depends on

the type of force (compressive, tensile, shear, etc. )

and the type and size of rock. The compressive and

tensile strengths of rock def’me the load per unit

surface area needed for compression and tensile

failure.

The compressive and tensile strengths of rocks

usually are measured in the laboratory (Fig. A.2). A

cylindrical sample of rock is placed in a loading

Revised 6~’1"1

HESI303196
machine. A compressive or tensile load is applied to

the specimen and increased until failure occurs. The

load at failure divided by sample surface area will

yield the sample strength. Due to natural variations

in rocks, their strength usually is measured several

times on different samples and averaged to yield a

representative value.

I~g. A.2

Laboratory experiments on most rocks will

show that their compressive strength is anywhere

from 10 to 100 times larger than their tensile

strength. This means that rocks can be broken much

easier in tension than in compression.

The result of compressive failure of most rocks

is a crushed material consisting of particles with

irregular shapes and sizes. Tensile failure, on the

other hand, yields a fracture. The specimen usually

breaks into two pieces along the fracture plane.

Fracture Initiation

Every point of an undergrotmd formation is

under the actions of stresses caused by overburden

and tectonic forces. Existence of these stresses can be

proved by the presence of structural features such as

faults, folds, overthrusts, etc. Any study of the

mechanical response of a reservoir rock will require

the knowledge of the magnitude and the direction of

all the stresses present in it.

It has been proven mathematically that any

system of stresses acting at a point (regardless of the

number or the directions) can always be replaced by

three normal stresses called "the principal stresses."

These three stresses are mutually perpendicular and

equivalent to the initial system from which they have

been derived. Furthermore, for any system of

stresses, there exists only one set of principal

stresses. Thus, the stresses present in a formation

can always be replaced by their equivalent "in situ

principal stresses." This permits investigation of the

mechanical behavior of that formation.

Obviously, if every individual component of

stress acting at a point is not known the in situ

principal stresses cannot be computed. But the

problem can be solved for a general set of principal

stresses. Then, how changes in the magnitude and

direction of the principal stresses will affect the

mechanical behavior of the material can be observed.

If the only force acting in a formation were the

weight of the overburden (which is a rare case), the

magnitude of the three principal stresses in an

isotropic, homogeneous and linearly elastic

formation could be calculated by the following

equations:

crz = pgh (A-6)

crx ---- cry

~

crz (A-7)

1 -v

in which

density of the rock

gravity acceleration

depth of the point under consideration

Poisson’s ratio of the formation

In this particular case, one principal stress, o’z,

is vertical and the other two, crx and cry, are

horizontal.

Assume that the three principal stresses in the

reservoir under consideration are O’x, Cry, crz; and that

crz is vertical. (Actually the solution of the problem is

available for any direction of cry, but here, for the

sake of simplicity, it is restricted to vertical cry).

These stresses exist at every point of the reservoir.

However, around the borehole, the state of stress

changes from the above simple form.

To study the changes occurring around the

borehole, consider a cylindrical borehole drilled in

an isotropic, homogeneous, elastic formation. A

cross-section of this borehole perpendicular to its

axis of symmetry will look like Fig. A.3. First

consider the deformation of this borehole under the

influence of crx. Intuitively, it can be seen that crx will

deform the circle into a shape similar to the dashed

curve. (This point can also be proved

mathematically).

A careful observation of the deformation of the

borehole shows that those material particles close to

HESI303197
0 hydr~uJi~

A and A’ are being stretched (tension) while around

B and B’ they are squeezed together (compression).

Mathematically, it can be proved that the tensile

stress induced at A is equal to - Crx and has the

direction shown in Fig. A.3, while the compressive

stress at points B and B’ is equal to 3o’x.

B

Fig. A.3

Rocks are considerably weaker in tension than

in compression. Therefore, if this borehole is to be

fractured, it will start at points A and A’.

Looking at the principal stresses, note that o’x

has a positive value while cry has implicitly been

assumed to be zero. The above analysis shows that

maximum tensile stress is induced at points A and

A’, which are perpendicular to the cry direction (least

principal stress).

By a similar argument, it can be shown that

when Cry has a positive value and Cr,, is zero, the

borehole will deform in a way similar to the dashed

curve in Fig. A.4, and that at point B and B’ a tensile

stress equal to - Cry and at A and A’ a compressive

stress equal to 3cry are induced.

Fig. A.4

The general situation will look similar to Fig.

A.5 in which o’x is assumed to be greater than cry. In

this case, the stresses at each point can be calculated

by adding the components induced due to o’x and cry.

Thus at A and A’ a stress equal to 3O’y - crx is present

and at B and B’ a stress equal to 3crx - cry is present.

Since Crx is assumed to be larger than cry, the stresses

at A and A’ have smaller values than at B and B’ and

therefore are more tensile. A hydraulic fracture in

this borehole will initiate at points A and A’ which, as

shown in Fig. A. 5, are perpendicular to the least

compressive in-situ principal stress.

A ~A._’

Fig. A.5

In order for a fracture to initiate, the maximum

tensile stress induced around the borehole must

exceed the tensile strength of the formation. Ifcrx and

cry are such that 3o’y -- O’x exceeds the tensile strength

of the rock, a hydraulic fracture will initiate around

the borehole. If3cry - cry, is not sufficient for the

spontaneous initiation of the fracture, a tensile stress

may be artificially induced around the borehole by

applying a fluid pressure inside it.

It is intuitively obvious (and can also be

mathematically proved) that applying a fluid

pressure inside the borehole will tend to expand it,

or, in other words, induce a tensile stress around it. It

has been theoretically proved that the effect of the

fluid pressure (ignoring leak-off) is to induce a tensile

stress that has a magnitude equal to the fluid pressure

all around the borehole. Since this tensile stress has

the same value everywhere at the wall of the

borehole, it will not change the point at which the

fracture will initiate.

In the case under consideration (crx > Cry), the

hydraulic fracture will initiate at points A and A’

whenever the tensile strength of the rock is exceeded.

Revi~ed 6YH

HESI303198
Mathematically, this condition is stated as:

-Pwh + 3Oy - crx = O’T

in which:

(A-8)

borehole fluid pressure

tensile strength of the formation

Another influence of the borehole fluid pressure

is that it induces stresses around the borehole as it

leaks into the formation. The mathematical solution

of this problem has been obtained and reported in the

literature, i This solution shows that fluid leak-off

generally decreases the breakdown pressure of a

hydraulic fracture.

As mentioned earlier, the problem of the

initiation of hydraulic fractures has been solved

mathematically, and complete solution of it is

available in the literature. For the sake of

completeness, a brief discussion of the theoretical

aspects of the problem will be presented.

Mathematical Solution of State of Stress

Around a Borehole

Suppose a borehole of radius (a) is drilled in a

formation with the axis of the borehole in the

direction (Fig. A.6). The OXY coordinate axes are

considered in the same direction as the two other

principal stresses. The stresses induced around the

borehole due to the presence oft.he regional stresses

are given by:

o’= = o’,, + o’~, (1- a2)+ (A-9)

,2 r~

o’x- % (1-3 a4)+

2 rE

(4 a2) cos20

crO0 ~"

cry- cry (1+3a4) -cos2O

2 r4

cry -- ~x (1 -- 3__ a4 ) +

2 r4

2 ( a2 ) sin2O

r2

(A-11)

inwhich

O’rr = radical stress*

o’oo = tangential stress

"r~o = shear stress

r = radial distance

0 = angles measured from the direction ofcr=

Rg. A.6

At the periphery of the borehole r = a (Fig. A.7) and

equations A-9, A-10, and A-11 become:

crrr-- 0

croo = crx + cry - 2(cr= - Cry)cos 20 (A-12)

Fig. A.7

*In polar coordinate* the stresses sge ¢all~l radial, tangentitl tnd ~etr stresses.

Rc~d6YH

HESI303199
Stresses Induced Around a Borehole Due

to Internal Fluid Pressure

Suppose a fluid is applying a pressure p on the

walls of a cylindrical cavity of radius (a). The stresses

induced around the cavity are:

a

2

crrr = P- (A-13)

cr00 = P- (A-14)

Tr0 : 0

On the internal wall of the cavity:

crr~ = P (A-15)

O’0o = -- P (A-16)

Tr0 = 0

Stresses Around A Pressurized Wellbore

The stresses induced around an impermeable

underground pressurized borehole are the sum of

two items:

1. Stresses due to in-situ forces.

2. Stresses due to fluid pressure.

Thus, on the wall of the borehole the stress

components become:

or= = p (A-17)

cr0O ~-" O’x -[- cry -- 2(cry, - cry) (A-18)

cos 20 - p

Mathematical Basis of Fracture Initiation

As mentioned earlier, the tensile strength of

rocks is much smaller than their compressive

strength. Thus, rocks will fail much easier under

tension. Let crT denote the tensile strength of the

formation. Whenever cr~ or cr00 equals err, failure

will start. If~r00 In’st reaches this value, a vertical

fracture will initiate. Suppose Cry is smaller than Crx.

It can be shown that Cr00 will have a minimum at

0 = 0 and ~" equal to:

~roo = 3Cry-Crx-p

Thus, the fracture initiates perpendicular to the

least compressive stress (in this example Cry) and:

cr00 = CrT = 3O’y - crx - P

p = 3 cry -- Crx -- CrT (A-19)

In the above analysis, no allowance was made

for any fluid leak-off. Under certain assumptions,

Haimson has shown that with leak-off the pressure

will be:

p = 3 Cry - crx - CrT + Po

1 - 2v 2

1 -v

(A-20)

in which a is a dimensionless porous rock constant

and P0 is the formation reservoir pressure.

Fracture Extension

Injection of fluid after fracture initiation results

in extension of the fracture. In the course of its

propagation, the hydraulic fracture follows the path

of least resistance, which (under the assumptions of

isotropy, homogeneity, and elasticity) is

perpendicular to the least compressive in situ

principal stress. Depending on whether the least in

situ principal stress is horizontal, vertical or inclined,

the hydraulic fracture will extend as vertical,

horizontal or inclined, respectively.

Most of the original experimental research in

the area of fracture extension was limited to the

observation of fracture orientation in the laboratory

size specimen. Fig. A.8 shows the results of one such

experiment. It shows a hydraulic fracture

propagating in one plane and perpendicular to the

least principal stress. The same results have been

observed for fractures extending from perforated

cased holes.

Figs. A.9 and A. 10 show the direction of

hydraulic fracture to be influenced more by the

principal stresses than presence of the perforations.

Similar laboratory results have been observed in

fracturing of anisotropic, naturally fractured

rocks.2’3 Fig. A. 11 shows a hydraulic fracture

extending perpendicular to the least principal stress

and unaffected by the rock anisotropy or the

presence of the large natural fracture that has been

intersected.

(

ReUsed 6YH

HESI303200
Perforations have shown a significant effect only

in the area very near the wellbore. As mentioned in

Part 4 of this section, the perforations can influence

the breakdown pressure, but the near wellbore effect

of perforation orientation will not affect the general

fracture orientation or azimuth.

Fig. A.8

Fig. A.9

Fig. A.IO

References For Appendix A

Halmson, Bezalel and Fairhurst, Charles:

"Initiation and Extension of Hydraulic

Fractures in Rocks," SPEJoumal(Sept. 1967)

310-318.

2. Personal observation ofB.W. McDaniel of

fractured coal Seam; Sesser, IL (May 30, 1974).

Warpinski, N.R.; Schmidt, R.A.; and

Northrop, D.A.: "In-Situ Stresses: The

Predominant Influence on Hydraulic Fracture

Containment," J. Pet. Tech. (Feb. 1978) 27.

HESI303201
4 laydraulic fracturing

APPENDIX B

FRACTURE GEOMETRY

CALCULATIONS

The computation of fracture geometry consists

of incorporating fracture mechanics theories with the

considerations of fluid injection, fluid flow down the

fracture, and fluid loss into the fracture faces.

The computed geometry of hydraulic fractures

is essentially an approximation. Several factors are

responsible. First of all, the formation material is

assumed to be isotropic, homogeneous and linearly

elastic; conditions seldom satisfied in reality. The

treatment fluid is assumed to behave according to a

mathematical model, which it often does not. All

design methods assume fracture height to be

constant and equal to an estimated number. This

poses the biggest restriction on the accuracy of the

computed geometries. These and other simplifying

assumptions make the computed geometries an

approximation of the true values. The accuracy of

the various design methods should be judged on the

basis of their assumptions, keeping in mind that all

the various methods yield "reasonable" results, and

none of them has an unquestionably proven

advantage over the others.

The logic behind all design procedures is

basically the same. The injected column is divided

into two parts, one lost as leak-off and the other

occupying the created fracture. The leak-off volume

is a function of the fracture face surface area,

formation properties, fluid properties and time.

Fracture volume depends on its height, length, and

the variations of width with length. The fracture

width is a function of fracture length and frictional

losses due to fluid flow in the fracture, the latter in

turn being a function of fluid and formation

properties.

These physical observations, when translated

into a mathematical language, yield a number of

relationships between fracturing parameters, the

solution of which yields the fracture geometry. The

difference between the various design methods is

mainly in the assumed equations used for the

different physical events.

Group 1 Methods-- Introduction

The various methods of designing hydraulic

fractures can be divided into two main groups,

according to the particular form of the width

equation used in arriving at the solutions. Group 1,

consisting of methods derived by Perkins and Kern~

and Nordgren2, assumes that the fracture width is

proportional to its height andhas the form

w = 4(1 - 1)2) Ape (h)

E

inwhich:

w = maximum fracture width at the wellbore

h = fracture height

An examination of this equation shows that

since E and v are formation constants, and h is

assumed to be constant, the only way the fracture

width can increase during the treatment is for Ape to

increase. Thus, since the fracture width is accepted

to increase during the treatment, recording the fluid

pressure at the bottom of the wellbore during the

treatment (so it does not include friction due to flow

in the pipes) should show an ever increasing fluid

pressure with increasing time.

Another aspect of the Group 1 design

procedures is that fracture cross-section parallel to its

height is elliptical. While this feature of these design

methods is more realistic than the Group 2 methods,

such a fracture shape cannot be used readily in

computing sand transport in the fracture. Instead,

the variable fracture width along the height has to be

replaced by an average constant width.

Group 2 Methods-- Introduction

The Group 2 Methods, consisting of the works

of Kristianovich and Zheltov3, Le Tirant and

Dupuy4, Geertsma5, and Daneshy6 use a fracture "

width equation similar to the one presented by

Kristianovich and Zheltov. In this equation

w = 4(1 -.z) Ape(L)

E

(a-2)

in which:

L = fracture length, wellbore to tip

It shows the fracture width to be proportional to

its length rather than its height as assumed by Group

1 methods.

Revised 6YH

HESI303202
Since L is a continuously increasing parameter

during the job, fracture width can increase without

any need for Ape to increase. Actual computation of

Ape based on Group 2 methods shows it to decrease

during the early stages of the treatment and then

reach a constant value. Since L usually increases at a

faster rate than Ape decreases, fracture width

consequently increases during the job.

Group 2 methods all assume that the fracture

width is constant along its height. Such a fracture

shape, although admittedly unreasonable,

considerably simplifies the problem of computing

sand transport in the fracture.

As stated earlier, it cannot be positively proved

which of the two approaches is superior. While the

comparison of the fluid pressure trends with field

observations may give an edge to Group 2 methods, it

does not prove anything about the fracture

geometry. As to the various methods within each

group, it can be stated generally that the newer ones

are more sophisticated and comprehensive.

Group 1 Methods-- Calculations

Perkins and Kern (No Leak-Of0. The design

equation derived by Perkins and Kern were the first

presented in the literature and the most widely used

for a long period of time. The equations presented by

Perkins and Kern do not consider the influence of

fluid leak-off. They cover both horizontal and

vertical fractures, turbulent or laminar flow.

For vertical fractures with fluid in laminar flow:

w(in.) = .38 [ q(bbl/min)  ̄ #(cp)  ̄ L(ft) ]v4 E(psi)

where:

injection rate of the treatment fluid

viscosity of the Newtonian fluid

Young’s modulus

length of fracture

In this equation all the parameters on the

right-hand side are known, except for L. To

calculate L use the equality of the injected volume

with the fracture volume (no leak-off).

This will yield:*

L(fl) = 51.732 x

[ q

3(bbvmin)’t4(minutes)" E(psi).]vs

~(cp)"

(B-4)

in which:

t = treatment time

For vertical fractures in turbulent flow:

w(in.) = 0.6 [ q2(bbl/min). ~  ̄ L(ff) ]1/,

E(psi)  ̄ h(fl) (B-s)

in which:

specific gravity of the fracturing fluid

and

L(ft) = 1.24 x

[ E(psi)  ̄ h(ft)" q2(bbl/min)  ̄ t4(minutes) (B-6)

The choice between using laminar or turbulent

flow equations is based on the value of the Reynolds’

number and is discussed in detail by Perkins and

Kern.

The equation for fracture width with a

non-Newtonian fracturing fluid is more lengthy and

can be found in the same reference.

Perkins and Kern (With Leak-Off). Equations

B-3, 4, 5, and 6 yield fracture widths and lengths for

the case of no fluid leak-off. In the presence of

leak-off, the computation of the fracture geometry is

more complicated but may be carried out by the

following trial and error method.

First, assume a fracture length and for this

length compute fracture width from Equation B-3.

Next, for the given length, height, and fluid and

formation properties compute the leak-offvolume.

(This may be done by several methods, e.g.,

Carter’s7 equations in appendix of Reference 7 or by Williams’s methods.) Subtracting the leak-off

volume from injected volume willyield the fracture

volume. From the fracture volume and time, a

hypothetical injection rate for fluid forming the

fracture volume can be computed. Equation B-4 may

then be used to compute a second fracture length. If

the two lengths are not equal, it is because the initial

value was not a good estimate. Thus, the

computations should be repeated with a new

assumed length untilthe two values agree. The

corresponding length, width, and leak-offvolume

will represent the geometrical status of the hydraulic

fracture.

*The equations presented here for computing L are not given i~ the paper but could be deriv~l

from it.

HESI303203
6 hydraulic fracturing

It should be noted that this method of

introducing leak-off in Perkins and Kern equations

is not desirable because the width equation and the

Ape computation ignore leak-off. Nordgren’s

equations are more handy for such computations.

As an example of designing fractures by Perkins

and Kern method, assume the following conditions

(no leak-off):

q = 10 bbl/min

E = 6 x 106psi

h = 100ft

~x = 100cp

From Equations A-7, A-8 and B-l:

t(minutes) L (~et) w (inches) Ape (psi)

10 295 .179 229

60 1,236 .256 328

100 1,859 .284 363

The presented values of Ape are the frictional

pressure losses due to fluid flow in the fracture. They

show Ape increasing with time, as stated earlier.

Nordgren. This is an extension of the work of

Perkins and Kern and includes the influence of fluid

leak-off. To obtain the fracture geometry, Nordgren

numerically solves the equations for fracture shape

and fluid leak-off. Therefore, in its pure form the use

of this design method requires access to a computer.

However, Nordgren also presents approximate

analytical expressions that can be used readily for

hand computations of the fracture geometry. These

are as follows:

No leak-off

w(in.) =

[ ~(cp)" qZ(bbl/min) ] !/5

4E(psi)" h(ft)

(minutes)

(B-7)

L(ft) = 38.5 x

1/5 t4/5 [ E(psi)" q~(bbl/min) ] (minutes)

~(cp)" h4(ft)

(B-8)

Comparison of these equations with those of

Perkins and Kern shows that Nordgren’s method

yields longer fractures with larger maximum widths

at the wellbore.

With leak-off

w(in.) = 0.238 x

[ ~(cp)  ̄ q2(bbl/min)

E(psi)  ̄ h(ft)  ̄ C_~(ft/minv2)

(B-9)

1/4

] tvs (minutes)

L(ft) = 0.447 x (B-IO)

[ q(bbl/min) ] t~ (minutes)

Cw(ft/minV2) ̄ h(ft)

inwhich:

Cw = Fluid leak-off coefficient

Equation B-10 shows that, in the presence of

leak-off, fracture length is not a function of fluid

viscosity, or the rock properties. This is a tmi.~’que

property of this equation and is not found elsewhere.

For the example case:

With leak-off

q = 10 bbl/min E = 6 × 106 psi

h = lOOft V. = 100cp

C~ = .001 ft/min~

FromEquafionsB-7,B-10andBl:

t (minutes) L (feet) w(inches) ~p¢(psi)

10 141 0.114 142

60 346 0.143 179

100 446 0.151 189

Without leak.off(assuming Cw = O)

FromEquationsB-7,B-8 andB-l:

t(minutes) L (feet) w(inches) ~p¢ (psi)

10 219 0.133 166

60 920 0.190 238

100 1,385 0.211 263

Note: The constant terms in these equations are

different than those given by Nordgren because of

the units.

Revised 6YH

HESI303204
Group 2 Methods-- Calculations

Kristianovich and Zheltov. All of the Group 2

design procedures are based on the width equation

derived by Kristianovich and Zheltov, or variations

of it. According to these authors, the maximum

width of the fracture at the wellbore is given by

w = 4(1 -~2) Ape(L)

E

(B-11)

which has the same form as that used in Group 1

procedures except that here the fracture length has

replaced fracture height. The basis for the derivation

of the fracture width equation is the concept that the

fracturing fluid does not wet the entire length of the

fracture, i.e., a very small part of the fracture close to

its tip is always empty of the treatment fluid.

Kristianovich and Zheltov’s method, as well as

all the other design methods in Group 2, assume that

the fracture width is constant along its height. This

assumption, although incorrect in a strict sense,

makes the computations of fracture geometry simple

enough to be mathematically tractable.

Furthermore, this shape fracture also makes the

computations of proppant transport in the fracture

feasible.

The equations derived by Kristianovich and

Zheltov can be divided in two parts. Part one consists

of the derivation of the width equation which, aside

from some typographical errors, are mathematically

sound and tractable. In part two, they derive the

equation for the computation of Ape. This part of the

paper, unfortunately, is not tractable and contains

typographical errors. In addition, from the contents

of the paper it is not easily possible to follow the

authors’ train of throught and replace their equations

by any other. The equations presented below are in

the form they appear in original paper except for

correcting the obvious typographical errors. In order

to simplify the writing of the equations, let:

R = pf/ ~y

in which:

(B-12)

pf = fracturing fluid pressure at the wellbore

o-y = least in situ principal stress

since pf = cry + Ape, pfis a measure of Ape. The

value of R is computed from:

R(R- 1)3=84x

2

(1 + ~2)2 .(~). q~

O’y O’y qqt + Pro

(B-13)

in which:

Vto = the inidal fracture volume at t = o

Assumingv = . 15 and Vto = 0 (no fluid in the

fracture before fracturing) and substituting

engineering units in Equation B-13 we obtain:

R(R- 1)3 = .21243 x 10-6 ×

2

1 [ E(psi) ]

)x(cp)

(ry(psi) (ry(psi) t(minutes)

(B-14)

Use of this equation has shown that the

magnitude of Cry does not signiflcandy change the

fracture geometry. Thus, assuming a value for cry of,

say, 2,000 psi and knowing E, I~, and t, this equation

can be solved for R. From R one calculates Ape from:

Ap¢ = (~y(R- 1)

The fracture length, L, is obtained from:

L(ft) = .956 x

1/2 [ q(bbl/min), t(minutes). E(psi) ]

Ape(psi). h(ft)

Substituting Ape in the width equation will then

yield w.

Le Tirant and Dupuy. These authors consider

the influence of fluid leak-offon the equation of

Kristianovich and Zheltov. The computations are

carried out by a computer. Although the details of

the computations are not discussed by the authors,

they seem to follow the same logic as presented

earlier for introducing leak-offinto the Perkins and

Kern equations.

Geertsma and de Klerk. Geertsma and de

Klerk introduced fluid leak-offin the design method

of Kristianovich and Zheltov. Complicated

equations of fluid leak-off and fracture growth were

first simplified by assuming simple (but not

restrictive) fracture growth behavior and then solved

analytically. The resulting equations are too

complicated to be solved by hand, but can easily be

used by a computer. However, the authors have

developed charts that can be utilized for quick hand

computations.

HESI303205
These graphical methods (for both horizontal

and vertical fractures) require the computations of

two non-dimensional terms, after which fracture

width and length (or radius) can be estimated

through simple computations.

The graphical solutions of Geertsma and de

Klerk are relatively easy to use requiring only a small

hand calculator and the design graphs. The results

are generally in good agreement with those of the

other Group 2 methods.

For our example problem,

Without leak-off

q = 100 bbl/min

E = 6x 106psi

h = lOOft

O, = 100 cp

t(minutes) L (feet) w (inches) Ape(psi)

10 227 .189 104

60 751 .343 57

100 1,056 .406 48

With leak-off

q = 10bbFmin

E = 6x 106psi

h = 100ff

~ = 100cp

Cw = .001fVmin~a

t (minutes) L (feet) w(inches) Ape (psi)

10 166 .155 117

60 456 .257 70

100 607 .296 61

Comparing the first results (no leak-off) with

those of Kristianovich and Zheltov shows this

method to yield longer but narrower fractures.

Comparing the results with leak-offwith those of

Nordgren indicate that Geertsma and de Klerk’s

method yields narrower and shorter fractures.

Daneshy. Daneshy’s method of computing the

fracture geometry is the newest of these methods. It

is an extension of the other Group 2 methods and

includes such features as use of non-Newtonian

fluids and static or dynamic fluid leak-offequations.

The fracture geometry is obtained on the basis of the

least number of assumptions compared to the other

methods. The steps followed for the numerical

solution are the closest of all methods to the actual

physical events occuring during a fracturing

treatment.

Daneshy’s numerical solution is obtained

through a computer. Thus, the method cannot be

used for hand computations.

For the example problem of:

No leak-off

q = 10bbFmin

E = 6x 106psi

h = 100ff

~ = 100cp

t(minutes) L (feet) w (inches) Ape(psi)

10 188 .230 153

60 640 .408 78

100 890 .483 68

With leak-off

q = lObbl/min

E = 6x 106psi

h = lOOft

p. = lOOcp

Cw = .001 ft/minv2

t(minutes) L (feet) w(inches) Ape(psi)

10 146 .180 154

60 400 .286 89

100 545 .328 75

A comparison of these results with those

obtained through Geertsma and de Klerk’s equations

shows that for both cases, Daneshy’s method shows a

wider but shorter fracture.

References for Appendix B

1. Perkins, T.K. and Kern, L.R.: "Width of

Hydraulic Fractures," J. Pet. Tech. (Sept.

1961) 937-949.

2. Nordgren, R.P.: "Propagation of a Vertical

Hydraulic Fracture," SPE]. (Aug. 1972)

306-314.

Kristianovich, S.A~ and Zheltov, Yu P.:

"Formation of Vertical Fractures by means of a

Highly Viscous Liquid," Proc. Fourth World

Per. Cong. 2(1955) 579-586.

R©vi~ed 6YH

HESI303206
79

o

°

o

o

LeTirant, P. and Dupuy, M.: "Dimensions des

Fractures Obtenues Par Fracturations

Hydraulic des Couches Petroliferes," Revue de

L ’Insfiurur Francais du Petrole(Jan. 1967) Vol

XXII, No. 1,44-98.

Geertsma, J. and deKlerk, F.: "A Rapid

Method of Predicting Width and Extent of

Hydraulically Induced Fractures," ]. Pet.

Tech. (Dec. 1969) 1571-1581.

Daneshy, A. A.: "On the Design of Vertical

Hydraulic Fractures," f Pet. Tech. (Jan. 1973)

83-98.

Howard, G.C. and Fast, C.R.: "Optimum

Fluid Characteristics for Fracture Extension,"

Drill an d Prod. Prac., API (1957) 261-270.

Williams, B.B.: "Fluid Loss From

Hydraulically Induced Fractures," f Pet.

Tech. (July 1970) 882-888.

HESI303207
APPENDIX C

CLAYS

Types of Clays

bon

 ̄

The clays most frequently found in hydrocarproducing formations are:

smectite: formerly called montmorillonite, gel

or bentonite

 ̄ illite: which can include glauconite and some

micas

 ̄ mixed-layer: primarily illite-smectite

 ̄ kaolinite

 ̄ chlorite.

Their presence in formation samples and approximate concentrations are usually determined

by X-ray diffraction analysis. However, the position of clays in the rock matrix and their localized

concentration in any area are also very important.

This is very difficult to resolve by X-ray techniques but can be quickly determined by the use

of dyes. Certain dyes1~2 and other chemicals exhibit characteristic colors when they are adsorbed

by the different clays. Examination of the treated

rock surface with low power magnification can be

quite revealing.

Structure of Clays

Clay minerals consist of two relatively simple

building units: the silica tetrahedral sheet, and the

alumina or magnesia octahedral sheet

(Figs. C. 1 and C.2). The composition of these

building units is:

 ̄ silica tetrahedral sheet - repeating units of

silicon atoms that are surrounded by four oxygen atoms to form tetrahedrons

 ̄ alumina octahedral sheet - repeating units of

aluminum atoms surrounded by six hydroxyl

groups to form an octahedron.

A three layer, or 2:1, clay would have one

alumina octahedral sheet with tetrahedral sheets

bonded to it at each side. A crystal of this type is

known as the mineral pyrophyllite. If the octahedral sheet contains all magnesium, the three layer

mineral would be talc.

O and ~[) = Oxygens

O and O = Silicons

F]g. C.1 - Tetrahedral Sheet

O and (]’ = Hydroxyls (OH)

OAluminums, magnesiums, iron

Fig. C.2 - Octahedral Sheet

Smectite. Where some of the aluminum in

the octahedral sheet is substituted with magnesium, and a small amount of silicon in the tetrahedral sheet is substituted with aluminum, the clay

mineral smectite is formed. These substitutions

develop a charge deficiency in the crystal lattice

which is represented by a net negative charge

shown at the faces of the clay crystal. This clay has

been known by several different names; however,

the name "smectite" is preferred now.

Illite. This is similar to smectite in structure,

but has a greater degree of substitution, particularly in the silica tetrahedral layer. This develops

more negative charges in the illite crystal than in

smectite. Where an excess of potassium was

present during clay development, the potassium

was attracted to the clay at the cation exchange

sites. With the help of pressure, all water was

squeezed from the stacks of crystals and the potassium became "fLxed" between the illite platelets. It

is very difficult for water to separate illite crystal

stacks. With most of the potassium ions being obscured in the stacks, illite exhibits a lower cation

exchange capacity than smectite although its

charge density is greater. Its main cause of permeability damage is due to clumps of clay breaking

Revised 6YH

HES1303208
loose, migrating, and then bridging at flow restrictions in the rock matrix.

Kaolinite. This is a two-layer clay consisting

of one silica tetrahedral sheet and one alumina octahedral sheet. There is essentially no substitution

in the crystal lattice. Kaolinite’s cation exchange

capacity comes from broken bonds on the edge of

the crystals.

Chlorite. This is a family of clay minerals

which consist of stacked mica-like (similar to illite)

and brucite Mg3(OH)~ layers. Two layers of each

type form a unit cell. Chlorites are not found in

hydrocarbon formations as often as the other clays,

and usually exhibit no swelling properties in water.

However, they have been known to cause permeability damage by migrating and bridging at flow

restrictions, or by creating fluid retention problems in the pore spaces.

Mixed-layer clay. Any combination of clays

where the individual clay crystals are stacked on

each other to form an irregular arrangement may

make up mixed-layer clays. A stacking where two

clays are regularly alternated is seldom encountered. The most frequent mixed-layer clay found

in hydrocarbon producing formations is the illitesmectite combination. Less frequently detected is

the chlorite-smectite stack. Thus, the degree of

swelling primarily depends on the amount of smectire that is present in the mixed-layer stacks. These

days can cause considerable permeability damage

through migration and bridging actions in addition

to possible swelling.

Clay Distribution

Examples of these clay types are shown in

Figure C.3. Some correlation has been developed

as to the type of clay that may be present at various depths along the Gulf Coast. Weaver3 reported

smectite predominated to 7,000 feet with some

mixed-Layer day and discrete smectite was detected

in the 7,000 to 12,000 feet depth range. With

deeper burial (to 17,000 feet), discrete smectite

decreased to essentially zero while the mixed-Layer

clay concentration increased. Perry and Hower*

extensively studied the composition of shales obtained from wells drilled in the Galveston area of

Texas and offshore Louisiana. Shale samples were

investigated from 3,364 to 17,000 feet in the

Galveston area. Generally, the predominant clay

found was smectite-illite mixed-layer with the

smectite component being the predominant fraction (up to 85%) at the shallower depths. The percentage of the smecfite component decreased

regularly in the mixed-layer clay with depth until

only 20% smectite was present in the 10,300 to

17,000 feet shales. Small amounts of kaolinite and

chlorite were usually present at all depths. However, content of both of these clays and discrete

illite increased at depths below 9,200 feet.

The clay content of the offshore Louisiana

shales (410 to 18,400 feet) was very similar to the

above except that smectite content of the mixed.

layer clay was greater at equivalent sub-sea depths.

For example, mixed-layer clay contained 35%

smectite at 15,500 feet and did not reach the 20%

level until 18,000 feet. This difference can be explained by a greater temperature gradient for the

Texas wells since higher temperatures favors the

development of illite.

If the clay content in sand bodies is similar to

the adjacent shales, predictions regarding the clays

to expect at various depths in the sands can be

made.

Formation samples from other areas of the

United States (east of the Rocky Mountains) have

also been examined and the same general clay distribution found as described above. However, concentrations of discrete i11ite and smectite were

generally lower than in the Gulf Coast area. Kaolinite was almost always the predominant clay

detected, regardless of the depth of burial.

The relatively small number of carbonate sampies evaluated in the Gulf Coast studies showed

zero to moderate amounts of these chys to be

present. Kaolinite, illite, and mixed-layer clay were

the predominant days found.

West of the Rocky Mountains, most productive sandstone formations are much younger in

geologic age. A higher percentage of both feldspar

and day minerals is common.

Description of Clays

All of the clays noted here are flat crystals.

They exist as thin platelets that are normally

stacked like a deck of cards to form packets.

Stacking is not necessarily even, since platelets can

overlap in the packets.

HESI303209
Miocene Formation, South Louisiana showing

smectite and mixed layer clay in pore.

Mag.- 10,500X.

Douglas Formation showing illite and kaolinite

around pore.

Mag.-2,000X.

Norphlet 7ormation, Mississippi showing fibrous

illite in pore.

Mag.-1,000X.

Tuscaloosa Formation showing iron rich chlorite

coating sand grains.

Mag.-1,00OX.

Fig. C.3 - Scanning Electron Microscope Photographs

Through the use of the dye staining procedure

mentioned previously, it has been found that these

packets are distributed throughout a sand in many

ways. Quite frequently they are concentrated at

iuncfions of sand grains and are more concentrated

in the sand near shale lenses. Although variations

will occur depending on the concentration of clay

in the sand, generally the extensive studies of the

Gulf Coast sands indicated:

 ̄ kaolinite is concentrated in isolated spots

 ̄ smectite is smeared throughout the area

 ̄ illite appears in streaks close to shale lenses

 ̄ mixed-layer clay is present in irregular streaks

throughout the sand.

Cation Exchange

All Clays are negatively charged. With smecrite, these charges are predominant on the faces of

the clay crystal while the edges of the crystal are

positively charged. The density of the negative

charges can be measured by determining the number of positive charges required to neutralize the

crystal. This is known as the cation exchange capacity (CEC) of the clay and is expressed in milliequivalents (ME) for 100 grams of clay. Figure C.4

lists the CEC of several clays.

Reviled 6YH

HESI303210
Clay Range of Cation Exchange Capacity

Smectite

Illite

Kaolinite

Chlorite

Sand (2 to 62 microns)

80 to 150

10 to 40

3to 15

10 to 40

0.6

Rg. C.4 - Cation Exchange Capacity of Selected Clays and Sand

The replacement of one cation by another on

any clay is governed mainly by the law of mass

action and the valence of the cation. Generally,

where mono- and divalent cations are present in

the same concentration, the divalent cation will be

preferentially attracted to the clay. If a water solution containing only one cation is brought in contact with a clay, it will tend to replace another

cation, regardless of its valence. Among monovalent cations, potassium and ammonium are more

effective than sodium in replacing divalent calcium

on smectite.

Water Adsorption by Clays

Clays may be loosely classified as swelling and

non-swelling. Smectite is the only clay that swells

by adsorbing ordered water layers between clay

crystals. Mixed-layer clay, which contains smectite,

will also swell with water but the illite portion of

this clay is relatively nonwater swelling. In addition to illite, kaolinite and chlorite may be classed

as nonwater swelling clays. They do not build viscosity in water as effectively as smectite since their

crystals tend to remain as packets instead of being

dispersed as do the smectite crystals. However,

these so-called nonwater swelling clays do adsorb

some water. Routson~, et. al., reported that some

water is adsorbed in illite crystal packets.

Aylmore’, et. al., examined kaolinite under a variety of conditions and found that water is associated

with this clay and that the cation attracted to the

clay and its concentration have little effect on the

water content. Thus, all clays do adsorb water with

smectite adsorbing the most.

Water adsorption or layering between smectite

crystals is due to hydration of the cation attracted

to the clay and hydrogen bonding. Degree of swelling depends on the cation associated with the clay

and the amount of dissolved salts in the water in

contact with the clay. Hydration numbers indicate

the number of water molecules that may be carried

to the clay surface by the cation. These water molecules act as a nucleus for the development of water layers on the clay surface. Figure C.5 lists the

ionic diameters and range of hydration numbers

for several cations.

X-ray diffraction can be used to determine the

number of layers of water between smectite crystals. The thickness of an absolutely dry smectite

crystal is generally accepted to be 9.5 A and a layer

of water is approkimately 3 A thick. (J~ is the abbreviation for Angstrom units. One Angstrom

equals 10.7 millimeters or 4 x 10" in.). Thus, if xray indicates the clay-water system is 15.5 A thick,

then two layers of water are present. The fhst

three to four layers of adsorbed water are very

ordered and have an average density of 1.2. Some

authors have called this crystalline water since its

general configuration is different from bulk water.

Where only one layer of water exists between

smectite crystals, its density is close to 1.4 and it is

very difficult to remove. As a result, the dry bentonite normally used for drilling mud has one layer

of water between the clay crystals which is equivalent to about 9% of the total weight of the clay.

The surface of the smectite crystal is a series

of oxygen atoms formed in repeating hexagonal

rings. There is a cavity inside each ring that is

approximately 2.8 A in diameter and 2.4/~, deep.

When the cation attracted to the clay has a small

hydration number and ionic diameter, it is entirely

possible for the cation to fit into the cavity and be

relatively difficult to remove.

HESI303211
4 hvdrtul:¢ trteturm[

Potassium has an ionic diameter of 2.66 A and

a small hydration number which fits these requirements quite well. However, a cation that has a

large hydration number would not be able to fit

into the cavity even if it had a relatively small ionic

diameter. Figure C.6 lists the effects of different

salts on the amount of water held between smectite

crystals under atmospheric pressure conditions.

I

Permeability Damage by Clays

As stated previously, the major permeability

damage that can occur in a clay-containing rock is

due to the migration of the clays and subsequent

bridging of these particles in pore channel restrictions. With smectite, the adsorption of additional

water between crystals forces them farther apart

and enhances their possibility of breaking loose

and migrating. This clay can migrate as single

crystals or small packets. Smectite can then be

seen as the weak points in mixed-layer clay structures. Here, packets of iRite can break loose and

migrate and these larger particles, combined with

the individual smectite crystals, cottld be more

damaging than smectite by itself. KaoLinite, illite,

and chlorite will also migrate as packets when their

natural equilibrium is disturbed by a foreign water

invading their environment.

Cation Ionic Diameter Hydration Number

Sodium 1.90A 5 to 11

Potassium 2,66A 1 to 4

Ammonium 2.86A 2 to 4

Calcium 1.98A 10 to 22

Magnesium 1.30A 12 to 33

A range in hydration numbers is given which represents data from several sources. The

variation in values is due to the method of obtaining the data and the concentration of the

various salts in solution.

Fig. C.5 - Ionic Diameter and Hydration Numbers of Several Cations

Salt Sodium Potassium Calcium

Concentration* Clay Clay Clay

Distilled Water 32 27 4

0.4 percent 14 2 4

2 percent 3 2 4

8,5 percent 2 2 3 to 4

10 percent 2 1 to 2 3

13 percent N.D. 1 3

16 percent N,D. 1 2

N.D.- Not Determined

*The salt concentration shown is used to express the percentage of sodium chloride with

sodium smectite, potassium chloride with potassium smectite and calcium chloride with

calcium .smectite.

Fig. C.6 - Effect of Salt Concentration on the Number of Water Layers (Swelling) Between Smectite Crystals

Rcvi~¢d 6YH

HESI303212
Pressure and Salt Effects

Conf’ming pressure has an effect on the

amount of water that will be held between smectite

crystals. Handy9, et. al., have used a consolidometer and x-ray to determine the degree of water expulsion from between smectite crystals at pressures

to 44,500 psi. No salts were present in the water

for this study. Their results are summarized in

Figure C.7. It may be seen that sodium smectite

retains more water than calcium smectite under

similar pressures.

SODIUM SMECTITE

Pressure, X-Ray

PSI Spacing

Approximate

Numbers

Of Water Layers

392 20.6A

1,020 20.1]k

2,825 18.7A

9,020 17.0]~

17,980 15.9A

44,500 13.6A

1,365 17.8A

2,730 16.5A

~9,110 ’ 15.5A

27,50O 14.0A

27,500 14.0A

4

4

3

2to3

2

1 to2

3

2to3

2

2

1 to2

CALCIUM SMECTITE

Approximate

Pressure, X-Ray Numbers

PSI Spacing of Water Layers

1,365 17.8A 3

2,730 16.5,~ 2 to

9,110 15.5A 2

18,220 14.7~, 2

27,500 14.0A 1 to

Fig. C.7 - Effect of Pressure on Water Retention on Two Types of

Srnectite

Unfortunately, there is no published data on

the effect of both pressure and salt concentration

on the amount of water that is retained between

smectite crystals. However, a study of Figure C.7

indicates that, for most well conditions, two layers

of water will be retained between smectite crystals

under naturally occurring conditions. Tlfis conclusion is based on the normal salts and their concentration found in most brines combined with the

effect of overburden pressure. Therefore, to minimize the possibility of clay crystals or packets of

crystals breaking loose and migrating, any water

that may penetrate a clay containing rock should

contain a chemical that will not alter the natural

water retention of the clay. This can be accomplished with the potassium cation.

The use of potassium chloride in water for

fracturing procedures constituted the first successful application of this chemical.’° Potassium chloride also has been used in drilling fluids to stabilize

water sensitive shales."12 In addition, potassium

chloride is being used in cement slurries to minimize damage that could be caused by the high pH

cement filtrate.

The ammonium ion has also shown a great

deal of promise for this use. Its use in the oil industry has been limited since salts of this ion are

more expensive than potassium salts. Ammonium

chloride has been used successfully in a few areas

in conjunction with hydrofluoric acid treatments

and water base fracturing fluids.

Potassium and ammonium cations are used to

maintain the "status quo" of clays to minimize

permeability reduction due to clay migration during a particular phase in the life of a well. They are

very effective for this use but are not recommended for conditions where a relatively dilute

brine will be flowing continuously through the

sand or where severe water conning develops.

References for Appendix C

1. Dodd, C.G.: "Dye Adsorption as a Method of

Identifying Clays; Clays and Clay Technology,

Bull. 169, Division of Mines, California (1955)

105-111.

Mielenz, R.C. and. King, M.E.: "Identification

of Clay Minerals by Staining Tests," Am. Soc.

for Testing Matedals Prec. (1951) Vol 51,

1213-1233.

3. Weaver, C.E.: "The Clay Petrology of Sediments," Clays and Clay Minerals (1957), Vol.

6, 154-187.

HESI303213
4. Perry, E. and Hower, John: "Burial Diagenesis

in Gulf Coast Sediments; Clays and Clay Minerals (1970)Vol 18, 165-177.

5. Routson, R.C.; Kittrick, J.A.; and Hope,

E.H.: "Interlayer Hydration and the Broadening of the 10A X-ray Peak in Illite;’ Soil Science (1972)Vol 113, No. 3, 167-174.

6. Aylmore, L.A.G. and Quirk, J.E: "Adsorption

of Water and Electrolyte Solutions by Kaolin

Clay Systems;’ Soil Science (1966), Vol 102,

No. 5,339-345.

7. Hewett, C.H.: "Analytical Technique for Recognizing Water-Sensitive Reservoir Rocks," J.

Pet. Tech. (Aug. 1963), 813-818.

8. Thomas, R.D. and Ward, D.C.: "Effect of

Overburden Pressure and Water Saturation on

Gas Permeability of Tight Sandstone Cores," ].

Pet. Tech. (Feb. 1972), 120-124.

9. Handy, R.L.; Demirel, T.; Ruenkrairergsa, T.;

and Olson, T.: "Adsorption Energies and

Swelling Pressures of Montmorillonite," ERI

Project 987-S (1973), Engineering Research

Institute, Iowa State University, Ames, Iowa.

10. Black, H.N. and Hower, W.E: "Advantageous

Use of Potassium Chloride Water for Fracturing Water Sensitive Formations;’ API 851-39-

F, presented at Wichita, Kansas, April 3, 1965.

11. O’Brien, D.E. and Chencrvert, M.E.: "Stabilizing Sensitive Shales with Inhibited,

Potassium-Based Drilling Fluids;’ J. Pet. Tech.

(Sept. 1973) 1089-1100.

12. Scheuerman, R.E: "Drilling Process Using a

Shale Protecting Polymer Drilling Fluid System;’ U.S.E 3,738,437.

ReUsed 6YH

HESI303214