chapter_4 hydraulic fracturing 1

8/10/2019 Chapter_4 Hydraulic Fracturing 1

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WELL STIMULATION TECHNIQUES

CHAPTER 4 HYDRAULIC FRACTURING 1

1

LESSON OUTCOME

At the end of this section, the students will be able to :

Understand different fracturing fluids.

Design hydraulic fracturing treatment.

Identify selection criteria for fracturing.

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MECHANICS OF FRACTURING

Naturally occuring underground stresses resist wellbore

fracturing.

The general stress condition underground can be defined

in terms of the effective stresses, z, along the vertical Zaxis and xand yalong the horizontalXandYaxes.

In the absence of external forces, the stress at any point is

due to the weight of the overburden.

Using an average density rock to be 144 lbm per cu ft, thevertical stress at any point is expressed by the equation

3

WhereDis the depth in feet.

Under the influence of this vertical stress, the rock tends

to expand laterally but is prevented from doing so by the

surrounding rock.

In the elastic zones of the earths crust, since no horizontal

movement has occured.

According to Hookes law, thehorizontal strainis expressed

(4.1)

(4.2)


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Where E is Youngs modulus.

For rock in compression, xis essentially zero and since the

lateral stress xequals the lateral stress y,

(4.3)

Where his the horizontal stress in general.

SincePoissons ratio for consolidated sedimentary rocks

ranges from 0.18 to 0.27, the horizontal compressive stressis between 0.22 and 0.37 psi per ft of depth.

In the absence of external forces the horizontal stress is

always less than the vertical stress.


5

If fluid pressure is applied within rocks and increased until

parting of the rocks occurs that plane along which fracture

or parting may first occur is the one perpendicular to the

least principal stress (Fig 4.1).

When a well is drilled the preexisting stress field in the

rock is distorted.

An approximate calculation of this distortion has beenmade by assuming the rock to be elastic, the borehole

smooth and cylindrical, and the borehole axis vertical.


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Using0 to 500 psi as the range of tensile strenghts for

competent sandstones and limestones, the pressure

necessary to induce vertical fracturing should lie between

and

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Once a fracture has been started, the pressure is applied

to the walls of the fracture.

According to Hubbert and Willis, the minimum down-the-

hole injection pressure requried to hold open and extend a

fracture isslightly in excess of the original stress normal to

the plane of the fracture.

Loss of fluid slightly decreases the pressure required toproduce vertical fractures.

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In the case of horizontal fractures, the confining stress

holding the fracture planes together is equal to the

effective overburdenat the depth of the fracture.

In the case of vertical fractures, the confining stress

holding the planes together is some function of the

effective overburden.

In the lower limiting case, horizontal fracturing can take

place when

(4.5)

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The approximate maximum depth at which horizontal

fracturingshould occur, can be determined from Eqn (4.4)

and (4.5) by assuming

(4.6)

Using a vertical stress (overburden) gradient of 1.0 psi perft, a Poissons ratio of 0.25, and a tensile strength of 1000

psi, the maximum depth for horizontal fracture is found to

be 3000 ft.

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PRODUCTION INCREASE FROM FRACTURING

Reasons for production increases from fracturing are:

1. new zones exposed,

2. reduced permeability zone is bypassed, and

3. flow pattern in reservoir changed from radial to

linear.

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New Zones Exposed

In a carbonate formationwhere productivity depends on

porosity or

in a fractured zonewhere primary flow capacity is related

to the fracture system or

in a deltaic sand formationwhere permeability is related

to regional depositional geometry,

the possibility of increasing well productivity by fracturinginto a new zone may be significant.

In some situation, however, the new zone might be

water or gas.

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By-passed Damage

Production increase from bypassing reduced permeability

zone is afunction ofthedepth of the damaged zoneand

theratio of damaged to undamaged permeability.

Production increase can be estimated more effectively

from transient pressure tests.

Only a short fracture is needed to bypass most damagezones, but it is very important to prop the fracture in the

area near the well-bore to provide a highly conductive

path through the damaged zone. 15

Radial Flow pat tern changed to Linear Pat tern

Production increase from changing the flow pattern results

from creation of a high conductivity fracture (relative to

the formation), extending a long distance from the well-

bore.

For vertical fractures the productivity increase dependsprimarily upon the formation permeability.

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PRODUCTIVITY RATIO

Productivity ratio is the ratio of the productivity index of

the well after fracturing to that of the well before

fracturing,Jf/J.

For thecase of a horizontal fracture (fracture gradient

1.0 psi per ft), an equation for the productivity ratio can be

obtained provided it is assumed that there is zero vertical

permeabilityin the fracture zone.

It has been shown that

(4.7)

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PRODUCTIVITY RATIO

where

kavgis the average permeability of thefractured formation

kis thepermeability of the unfracturedformation

From Fig. (1.5) that the average permeability of the

fracture zone is equal to the average permeability

predicted for radial flow in parallelbeds.

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PRODUCTIVITY RATIO

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Fig.1.5

PRODUCTIVITY RATIO

Where

kfzis the average permeability of the fracture zone

kf

is the permeability of the fracture

Wis the thickness of the fracture

k is the formation permeability

(4.8)

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PRODUCTIVITY RATIO

The average permeability of the fractured formation,kavg,is equal to the average permeability predicted for series

beds in radial flow:

(4.9)

Where

re

is the drainage radius of the well

rwis the wellbore radius

rfis the radius of the fracture21

PRODUCTIVITY RATIO

(4.10)

Substituting Eq (4.8) to Eq (4.9), and into Eq (4.7), and

multiplying numerator and denominator byh,

Factoring,

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PRODUCTIVITY RATIO

To facilitate rapid calculation of the productivity ratio of

horizontal fractures, Fig (4.6) was constructed with the use

of Eqn (4.10).

The correlation between Fig. (4.6) and Eq (4.10) is shown

in Example (4.1).

Fig (4.7) shows the permeability of commonly usedfracture sands.

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Fig. 4.6

Estimated

productivity

ratio after

fracturing

(horizontal

fractures)

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Fig. Estimated

productivity

ratio after

fracturing

(vertical

fracture)

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Fig. 4.7 Effect of

pressure on

frac-sand

permeability

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Example (4.1)

Calculate the productivity ratio for a horizontal fracture,

given:

Fracture width = 0.1 in

Net pay thickness = 50 ft

Permeability of propping agent (10 20 mesh) = 32500 md

Horizontal permeability of formation = 0.54 md

re/ rw = 2000

Fracture penetration rf/ re = 0.40

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Example (4.1)

Solution

The value ofkfW/k his

The term ln (re/ rw)in Eq (4.10) can be expressed as

Then substituting in Eq (4.10),

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Example (4.1)

In Fig (4.6), the PR is 5.0

It is also desirable to estimate the productivity ratio for the

vertical fractures (fracture gradient0.7 psi per ft).

The Mobile Oil Company correlated productivity ratios for

various fracture penetrations with the factor C= kfW/ k,

as shown in Fig (4.8), whereWis the fracture width in feetand kfand k are the effective fracture and horizontalformation permeability in milli-darcies respectively.

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PROPPING THE FRACTURE

The object of propping is to maintain desired fracture

conductivity economically.

Fracture conductivity depends upon a number of

interrelated factors: type, size, and uniformity of the

proppant; degree of embedment, crushing, and/or

deformation; and amount of proppant and the manner of

placement. Commonly used proppant types and size ranges are:

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Commonly used proppant types and size ranges are:

Placement of propping agent in a fracture (either vertical or

horizontal) in any pattern other than a packed condition isdifficult to achieve with low viscosity fluids.

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PROPPANT HAS TO

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Not to crush at formation closure stress

and temperature

Keep desired conductivity over time

Be smaller than perforations

Not to flow back from the fracture


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PROPPANT SELECTION

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3. Review Proppant Database finding proppants matchingrequired mesh sizes, formation closure stress and temperature

1. Calculate optimal fracture half-lengthand conductivity

4. Select proppants with required conductivity

5. Sort selected proppants by price;Select proppant flowback control additives

2. Determine applicable proppant mesh sizes


1. First portions of sand entering fracture drop out to the

bottom of the fracture near the wellbore. Jetting action

through perforation tends to wash sand back several feet

from borehole.

2. As more sand enters the fracture, height of the pack

increases to some equilibrium point dependent on the

velocity of flow in the fracture, the viscosity of the fracfluid, the difference in density between proppant and

fluid, and the drag characteristics of the proppant.

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3. Additional sand is then carried over the pack and

deposited further out in the fracture.

4. Final height of packed fracture after closure may be a

relatively small percentage of the dynamic fracture

height created during injection.

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High viscosity fluids which suspend large proppant permit:

1. Use of much larger concentrations of proppant.

2. Placement of multilayers of large proppant throughout a

high percentage of the fracture height, particularly in the

critical area near the wellbore.

3. Placement of proppant much further away from the

wellbore.

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FRACTURE AREA

During the fracturing process, the fracture fluid is injected

at the well head at a constant rateqi.

In the fracture this injection, rate is split up into two

components as shown in Fig (4.8).

Part of the liquid,ql, enters the formation as a result ofthe differential pressure (pi- pe) between the fracture andthe external boundary, and the remainder, qf, increasesthe fracture area, i.e., it increase the volume of the

fracture. An expression for thefracture area at any timemay be

derived by using this basic concept and the following

assumptions: 37

FRACTURE AREA

An expression for the fracture area at any time may be

derived by using this basic concept and the following

assumptions:

1. The fracture is of uniform width.

2. The flow of fracture fluid into the formation is linear

and the direction of flow is perpendicular to the

fracture face Fig (4.8).3. The velocity of flow into the formation at any point on

the fracture face is a function of the time of exposure

of the point to flow.

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2


Fig. 4.8

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FRACTURE AREA

4. The velocity function v = f(t) is the same for everypoint in the formation, but the zero time for any point

is defined as the instant that the fracturing fluid first

reaches it.

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2

FRACTURE AREA

Fracture area can be expressed as follow:

(4.11)

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Thank You

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2

Thank You

43

Error Function of X

FRACTURING FLUIDS

Oil or water fluids are used to create, extend, and place

proppant in the fracture.

Two-thirds of fracture treatments use water base fluids

and one-third oil base fluids.

Recent innovations include gelled alcohol, LPG-CO2, or

aerated foam fluids.

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2

FRACTURING FLUIDS

Generally these comparative statements can be made:

1. Oil fluids are cheap and have inherent viscosity which

makes themadvantageousfor relativelylow injection

rate,shallow to medium depthfracturing. Pressure loss

down the casing and safety consideration are often

limiting factors.

2. Gelled water fluids have special advantages due to

theirhigher density and lower friction loss in deeper

wells, and where higher injection rates are needed.

Where high temperatures are involved reasonable

viscosity can be maintained above 250oF.45

FRACTURING FLUIDS

3. Ultra-highviscosity fluids arecostly and temperature

sensitive, but can provide wide, highly-conductive

fractures needed to stimulate higher permeability

zones or sand carrying capacity needed to prop long

fractures in low permeability zones.

4. Emulsion fluids provide moderate viscosity, andgood

fluid lossandcarrying capacity at a reasonable cost.5. Alcohol, LPG-CO2 and Aerated fluids have limited

application due to cost, safety and/or complexity.

Usefulness is primarily in gas or low permeability zones

where cleanup is paramount.46


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2

FRACTURING FLUIDS

The constant C in Eq (4.11) is the fracturing fluid

coefficient, and for any given type of flow system it

depends upon thecharacteristics of the fracturing fluid,

thereservoir fluids,and the rock.

The fracturing fluid coefficient is the only term which

reflects the properties of the fracturing fluid and is

therefore a measure of their relative effectiveness.

A low fracturing fluid coefficient means low fluid-loss

propertiesand thus a larger fracture area for a given fluidvolume and injection rate.

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FRACTURING FLUIDS

Fracturing fluids fall into three distinct categories:

1. Viscosity-controlled fluids

2. Reservoir-controlled fluids

3. Wall-building fluids.

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Viscosit y-cont rolled Fluids

Theviscosity of the fracture fluid controls the amount of

fluid loss to the formation.

The coefficient for this type of fracturing fluid is expressed

by

(4.12)

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Viscosit y-cont rolled Fluids

Eq (4.12) simply states that for a viscosity-controlled fluid,

therate of leak-off will depend on the permeability, the

porosity, the treating pressure differential, and the

fracture fluid viscosity.

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2

Example (4.2)

Calculate the fracturing fluid coefficient of an oil, given:

Fracture gradient = 0.7 psi per foot

Depth = 4000 ft

Bottom-hole pressure = 1800 psi

Bottom-hole temperature = 100oF

Porosity = 20 per cent

Permeability perpendicular to fracture face = 10 md

Fracturing fluid viscosity at 100oF = 500 cp

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Example (4.2)

Solution

The differential pressure is

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2

Reservoir-cont rolled Fluids

This group includes those fracturing fluids that have low

viscosity and high fluid-loss characteristics, i.e., physical

properties identical or nearly identical with those of the

reservoir fluid.

Fracturing fluids which fall into this classification are lease

crude and water, which do not contain additives to reduce

fluid loss.

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Reservoir-cont rolled Fluids

The equation for the fluid-loss coefficient is

(4.13)

Noted that quantities and cf

in the above equation are

properties of the reservoir fluidand not ofthe fracturing

fluid. 54


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2

Wall-building Fluids

The use of modern additives to limit fluid loss (asphaltic-

type materials, synthetic gums, and insoluble solids added

to oil or water) creates a third class of fracturing fluids.

These fluids build a temporary filter cake or wall on the

face of the fracture as it is exposed.

While a small amount of fluid leaks through to form the

wall, once formed, the wall presents quite an effective

barrier to further leak-off due to its low permeability.

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The volume of fluid which has leaked off through the filter

cake at any times is proportional to the volume of the

filter cake at that time, or

(4.14)

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where

V = volume of fluid

Af= cross sectional area of filter cake

L = thickness of filter cakeC = proportional constant

If a standard fluid loss test is run on a fracturing fluid, and

If V is ploed against t, the slope of the curve is m, and it is

expressed as cu cm/min.


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2


If a spurt loss is included in the equation above, Vbecomes

57

(4.15)


Consider a fracture of areaAfwith a spurt loss ofVsp.

The volume of the fracture is AfWwhere W is the true

fracture width.

If we define a quantityW'such that the product AfW'isequal to the volume of the fracture without a spurt loss,

then

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3

Example (4.3)

Solution

Thespurt loss is used in correcting the fracture widthby Eq

(4.17). If the fracture width is 0.2 in. Thecorrected fracturewidth(W)is

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Example (4.3)

Any fracturing fluid is somewhat viscous, and so Cv

mechanism helps retard leak-off.

Also, the reservoircontains a compressible fluid, and thus

theCc

mechanismwill be operative.

Finally,many oils without additives will have a wall-building

effect, and so the Cw

mechanismusually comes into play.

Combined coefficient could be calculated similarly to thecombined conductance of a series of conductors,

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FRACTURE EFFICIENCY

Once fracturing fluid coefficient is calculated, fracture area

can be determined from the basic equation

Solution of this equation is tedious. So, in another form

will be mentioned to facilitate the calculation.

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(4.11)

FRACTURE EFFICIENCY

If we define the efficiency of a fracture job as the volume

of the fracture divided by the volume of fluid pumped,

then

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(4.18)

By substituting Eqn. 4.18 into 4.11,

(4.19)

Now, Efficiency becomes a function of x alone. Then

efficiency vs x can be plotted as shown in Fig. (4.11)


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3

FRACTURE EFFICIENCY

Fig. 4.11. Plot of

fracturing

efficiency

against its

function

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Example (4.4)

Calculate the fracture efficiency, given:

Solution

The fracture time is

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3

Example (4.4)

From Table (4.1), erfc (2.67) = 0.00016, so that the

efficiency is

and

Eff = 0.140 (1248 x 0.00016 + 3,01 1) = 31 per cent

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Example (4.4)

The use of Fig. 4.11 and Eq. (4.19) provide a simplified

method of calculating the area of the fracture at any time,

A (t).

For example, if the injection volume is 20,000 gal of fluid

with a coefficient of 2.22 x 10-3 ft/ min, the fracture width

is 0.2 in., and the pumping time is 20 min, then

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3

Example (4.4)

From Table (4.1), the efficiency is 37%. Then from Eqn.

(4.18), the fracture area is

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Q & A

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Thank You

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chapter_4 hydraulic fracturing 1

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