Chilingarian G.V. et al. Surface Operations in Petroleum Production, II
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105
100
80
z
E
60
s
40
;
20
'
1950
1954 1958 1962 1966 1970 1974
YEAR
Fig.
4-6.
Trends
in
the use
of
oil-base and aqueous-base fracturing fluids. (Courtesy of the Halliburton
Co.,
1976, fig.
2.2,
p.
5.)
operators experimented with larger, higher-injection-rate type jobs, more sustained
production increases were noted. Gradually, the job sizes and injection rates began
to increase. In the latter part of 1952, use
of
refined petroleum residuals and heavier
crude oils became popular (Halliburton, 1976, p.5).
As
a result, treatment became
more economical and the treatment trend curve has risen steadily since then. In
1974, treatments averaged about 40,000 gal with 42,000 lbs of sand, i.e., a sand/fluid
ratio of approximately
1.1
lb/gal. Figures
4-5,
4-6 and 4-7 illustrate the changes that
took
place between 1950 and 1974 for fracturing technique.
The use of acids along with a wide variety of fracture fluids and proppants have
been developed to cover a wide range of low-temperature (shallow) to high-tempera-
ture (deep) reservoirs. Hydraulic fracturing is often used as a well stimulation
technique for both
(1)
improving damaged matrix permeability surrounding the
wellbore, and (2) creating deep-penetrating fractures for fluid flow from deep within
the producing formation. The latter dramatically increases the surface drainage area
for the wellbore.
As
pointed out by Halliburton
Co.
(1976), the success of a fracturing treatment
heavily depends upon reliability of pumping and blending equipment. The blender
or proportioner transfers the fracturing fluid from the storage area to the high-pres-
sure pumping equipment (Fig. 4-8).
A
uniform mixture of chemicals and propping
agent is added to the fluid, as it passes through the blender. Uniform mixture must
be maintained regardless
of
the injection rates and volumes. Proportioning equipment
YEAR
Fig. 4-7. Evolution
of
fracturing techniques. (Courtesy
of
the Halliburton
Co.,
1976, fig.
2.3,
p.
5.)
I
=
Volume
of fluid;
2
=
injection rate;
3
=
hydraulic horsepower.
106
BASIC FLUID
PUMP
B
DRY CHEMICAL
PROPORTIONER
FRACTURING FLUID
SUPPLY PUMP
/
AGITAT
OR
SAND
OR
SACK
BASIC FLUID
CONTROL
SAND
BULK
OR
SACK
CHEMICAL METERING
PUMP A
ja
pi
A
J
CHEMICAL METERING
Rr
PUMP
B
/
I
1
,--FLOWMETER
&%
4
SAND-FLUID
MIXTURE TO
PUMP TRUCK
/
STABILIZER
PRESSURIZER PUMP
Fig. 4-8. Schematic diagram of sand proportioner which permits:
(1)
continuous operation as long as
supplied by fracturing ingredients,
(2)
maintaining constant ratio
of
materials within narrow limits
regardless of injection rates, and
(3)
instantaneous variation of the sand/fluid ratio, either higher or
lower, by manipulation of a simple control. (Courtesy
of
the Halliburton Co., 1976, fig. 1.9, p.
4.)
can alter the concentration of chemicals and propping agents during the job as
dictated by the treatment requirements.
GENERAL CRITERIA
OF
WELL SELECTION
Maly and Morton (1951), Clark,
J.B.
et al. (1952), and Clark,
R.C.
et al. (1953)
pointed out that most formations can be fractured. Not all formations, however,
respond similarly (increase in production) as a result
of
fracturing. In general,
formations that have been classified as medium to hard appear to give better results.
Possibly, this may be due to “healing” and/or proppant embedment in the case
of
softer formations. Limestones, dolomites, well-cemented sandstones, and con-
glomerates are potential candidates for fracture treatment. In general, softer forma-
tions such as unconsolidated sandstones are poor candidates.
Prior to selecting a well for a hydraulic fracturing treatment, the petroleum
engineer must establish that the reservoir contains sufficient fluids along with the
pressure to produce at rates high enough to cover the cost
of
the treatment.
Generally, better results (larger and more sustained production increases) are
obtained from fracturing if treatments are made early in the life of the field
(Howard and Fast, 1970). Comparison of gross and net fluid production rates
should be compared whenever possible with those
of
nearby wells. Potential
candidates are those wells which show a significantly lower production.
107
At
.hours
,o
4600
3400
1
I
I
1oo,oO0
10.000
1000
100
(t+At)/A
t
Fig.
4-9.
Pressure buildup showing effect of wellbore damage and after-production. (After Matthews,
1961,
fig.
4,
p.
863;
courtesy
of
the Society
of
Petroleum Engineers.)
Initially, the reasons for the low productivity of a well must be established. Some
wells may only require a well wash or chemical stimulation treatment instead of the
more costly fracturing treatment. The following methods are used in examining the
formation and determining ability of a well to produce fluids:
(1)
comparison
of
its
production to those of other wells in the area, and
(2)
evaluation
of
formation
pressure buildup data. The extent of wellbore damage can be determined by
examining the pressure versus [(time
+
Ar)/Ar]
curve (Fig.
4-9).
High production
dechne rate can indicate wellbore damage and, consequently, a good candidate for
fracturing treatment. On the other hand, in the case
of
a flat production decline
curve, whch indicates good drainage, the well
is
not a good candidate for fracturing
treatment. Obviously, one can expect a greater percentage production increase from
“tighter” (low-permeability) formations, because the fracturing treatment increases
the wellbore drainage surface area, thus permitting more fluids to migrate into the
wellbore (see Fig.
4-10).
On considering a candidate for fracture treatment, previous experience with wells
in the surrounding area should always be examined carefully, i.e., the fracturing
method used and its effect on well production. New techniques, larger-sized
treatments, and/or improvements in treating materials should be considered in
order to improve the results
of
earlier jobs, which might not have been entirely
successful
.
Condition of the candidate well itself is also a very important factor. Inasmuch as
the pressures within the wellbore are likely to be high, the casing and associated
well-equipment must be in good condition and have a sufficient pressure rating to
handle the fracture treatment. Bottomhole treating pressures of
1
psi/ft of vertical
depth should be anticipated. It is also important to insure that the generated
fracture system is not extended into the water-bearing zones. Vertical fractures
should not be allowed to extend into either the gas or water zones above
or
below
the producing horizon. The treatment should not affect either the
GOR
or
WOR.
108
7
.
7
c
VI
I
c
C
0
-
a
14
12
10
a
t
L
L
C
k =formation D!rmeabilitv. md
'
L/re
=-l.O
L
=
frac length from welldore.
ft
w =propped frac width.
in.
ki
=permeability of proppant. md
wki =conductivity of fracture. md-in.
re =drainage radius of well,
ft
J
=productivity index after fracturing
I I
Curves based
on
40-acre sDacinz
h
3-in. wellbore radius.
I
Scaling factors must be used fo;other well spacings.
I
I
103
lo’
105
106
Perrnea bility contrast,
wk,
/k
Fig. 4-10. Effect
of
(1)
permeability contrast between fracture and formation, and
(2)
fracturing length on
the expected increase
of
productivity index in a hydraulically fractured well. Curves are based upon
40-acre spacing and 3-in. wellbore radius. Scaling factors must be used for other well spacings (see Table
4-1). (After McGuire and Sikora, 1960; courtesy
of
the Society of Petroleum Engineers. Also see Allen
and Roberts, 1982,
p.
125.)
Howard and Fast
(1970)
pointed out that the key to proper selection
of
a good
candidate well for hydraulic fracturing is determination
of
the cause for its low
productivity. This enables treatment
of
the cause and not the symptom.
MECHANICS
OF
HYDRAULIC FRACTURING
Hydraulic fracturing process variables
The variables that affect the stimulation process, can be grouped into three basic
categories:
(1)
controllable by engineering design,
(2)
non-controllable by engineer-
ing design, and
(3)
with limited controllability. Theoretically, the parameters of
group
(3)
may be controllable; however, limitations imposed by prior operating
procedures may limit the range of variation possible. The pumping rate during the
treatment is such an example. It may be limited due to the wellbore dimensions
whch can cause excessive pressure loss at high flow rates.
A
review of the past hydraulic fracture treatments indicates the following reasons
for failure of stimulation treatments (Republic Geothermal, Inc.,
1979):
(1)
the
generated fractures were not confined to the targeted interval of treatment,
(2)
109
communication
of
fracture fluid at the wellbore produced stimulation of the
non-targeted interval, (3) premature termination of the stimulation treatment, (4) an
incorrect selection of proppant,
(5)
insufficient volume of proppant, (6) the fracture
fluid was incompatible with the formation fluids, (7) an improper perforation
program, and/or
(8)
incomplete returns of treating fluids. In the case of successful
treatments, the following common procedures were noted: (1) use of water as a
fracturing fluid,
(2)
overdisplacement, at a low rate, to help minimize back produc-
tion of proppant, (3) use of spacers to help reduce proppant concentration and,
thus, reduce the possibility of a screenout, (4) reduced pumping rates near the end
of the treatment tends to enhance proppant packing and conductivity,
(5)
energizing
the last portion of the injected fluid speeds cleanup and improves productivity, and
(6) use of a surfactant for lowering the surface and interfacial tension has helped to
reduce fracturing fluid recovery from the formation. Before designing a fracture
treatment, both the successes and the failures of similar treatments must be
examined for nearby wells. Inasmuch as much equipment and materials are in-
volved, the cost of failure is high.
Rock
mechanic considerations
An excellent treatment of the mechanical behavior
of
rocks was presented by
Halliburton Co. (1976) and Craft et al. (1962). Competent rocks behave as elastic
and brittle materials over certain ranges of conditions. Dimensions of a rock change
when stressed either in tension or compression. The term “strain” refers to these
dimensional changes. The ratio
of
lateral strain to axial strain of an elastic material
is known as Poisson’s ratio,
v.
This ratio ranges from
0.05
to 0.45 for most rocks,
averaging
0.2.
The ratio of stress to strain, referred to as the modulus
of
elasticity or Young’s
modulus,
E,
is another fundamental rock property. Average values range from
0.5
x
lo6
(lightly consolidated sandstones) to 13
X
lo6
(denser limestone or
dolomite). Rocks which behave elastically up to some limiting stress, rupture or fail
in a tensile or shear failure depending upon the direction of the stress. The plane of
shear failure depends upon the direction of the stress and is located at an angle to
the axis of stress. The internal angle
of
friction, which is related to the axis of stress,
ranges from 35” to
0”.
A typical value of internal angle of friction for many
competent rocks is about
30
”.
If a rock cylinder,
S,
having a radius,
r,
is stressed by a force,
F
(Fig.
4-11), the
stress,
u,
is equal to the force divided by the cross-sectional area
of
the cylinder:
0
=
F/.rrr2
(4-1)
The direction
of
this stress is parallel to the
z-axis
and, therefore, may be referred
to as
a,.
In this case, there is no stress in the
x
or
y
direction as
no
force is applied
in that direction. The rock will shear
if
the stress along any axis exceeds the strength
of
the rock along that axis.
Compressive or tensile stresses of any magnitude can be generated by changing
110
DENSITY,
g/cm3
Fig.
4-11. Variation
of
shale bulk densities with depth in sedimentary basins.
I
=
methane-saturated
clastic sedimentary rock (probable minimum density) (after McCulloh, 1967, p. A19),
2
=
mudstone-Po
Valley Basin, Italy (after Storer, 1959),
3
=
average Gulf Coast shale densities; values derived from
geophysical data (after Dickinson, 1953, p. 427),
4
=
average Gulf Coast shale densities derived from
density
logs
and formation samples (after Eaton, 1969),
5
=
Motatan-1-Maracaibo Basin, Venezuela
(after Dallmus, 1958, p. 916), 6
=
Gorgeteg
No.
1-Hungary; calculated wet density values (after Skeels,
1943),
7
=
Pennsylvanian and Permian dry shale density values, Oklahoma and Texas; Athy's adjusted
curve (after Dallmus, 1958, p. 913),
8
=
Las Ollas-1-eastern Venezuela (after Dallmus, 1958, p. 918).
(See Rieke and Chilingarian, 1974, p. 34.)
the direction or magnitude of force on the rock cylinder. Because of lithological
variations, stresses can vary in magnitude and/or direction from point to point in
the rock.
In order to calculate the total stress on a reservoir rock, the pore pressure must be
taken into consideration. The total stress is the sum of the intergranular stress in the
rock and the stress or pressure exerted by the formation fluid (pore pressure). The
total vertical stress (overburden load) in a formation at any depth is equal to the
pressure exerted by the weight of the fluid-saturated rock overlying the formation.
Jakosky (1950) reviewed the work of many investigators and noted that rock
densities vary from
2.0
g/cc at shallow depths to approximately
2.6
g/cc at depths
of 10,000 ft (also see
Fig.
4-11). Using an average density of 144 lb/cu ft, the
vertical stresses may be estimated by using a pressure gradient
of
1
psi/ft.
As
a
result of this overburden, the vertical force tends to deform the rock laterally.
Inasmuch as the rock is contained by the surrounding rock, however, the vertical
force results in a horizontal stress
'
Compressive stress is usually designated by a plus sign, whereas tensile stress has a negative sign. Thus,
theoretically
stress
can have values ranging from
+
w
to
-
w,
whereas the lowest possible pressure
is
zero.
111
6,”
HORIZONTAL FRACTURE
I
(CASE
I)
FRACTURE
PLANE
VERTICAL FRACTURE
(CASE
Ill)
HI
R
VERTICAL FRACTURE
(CASE
It)
&HI
>6V>6
H,
Fig. 4-12. Effect
of
relative magnitude of principal stresses on fracture orientation. (After Fertl and
Chilingarian,
1978,
fig. A-4,
p.
301; courtesy
of
Elsevier Science Publishers.)
Fractures initiate and extend in a plane perpendicular to the least principle stress
(Fig. 4-12) when the pressure exceeds the strength of the rock. Once the fracture has
been initiated, fluid enters the fracture and the fluid pressure is applied directly to
the fracture faces. This reduces the stress concentration about the wellbore. The
pressure required to hold the fracture open is equal to the opposing stress per-
pendicular to the fracture plane. The fracture will continue to extend away from the
wellbore as long as the pressure at the tip or leading edge of the fracture is above
the strength
of
the rock. Inasmuch as there is fluid friction loss in the fracture, there
is a resultant pressure drop in the fluid between the wellbore and tip of the fracture.
The rock cylinder shown in Fig. 4-13 is deformed by the applied force. Inasmuch
as the original length,
L,
of the cylinder is compressed by an amount,
AL,
the
deformed length is
(L
-
A
L).
Dimensionless strain,
c,
is equal
to:
(L-AL)-L
-
AL
E=
- -
-~
L L
(4-2)
Strains in different directions in the same body may have different values at
different points. The strain in the
z
direction is equal to:
AL
L
E
=--
z
(4-3)
The radius of the rock cylinder changes from
r
to
(Y
+
Ar)
upon application of
force
F
(r+Ar)-r
-
Ar
_-
Ex
=
Ey
=
r
r
(4-4)
112
Fig.
4-13.
Schematic
of
a rock cylinder showing deformation as a result of applied force
F.
(Courtesy
of
the Halliburton
Co.,
fig.
4.1,
p. 9.)
In an elastic material, the strain is linearly proportional to the induced stress:
(4-5)
1
E
€=
=
-a,
where the constant,
E,
is the Young’s modulus of the material. If the weight of the
overburden
(a,
=
p,
=
y,h,
where
p,
is the overburden pressure in lb/ft2,
y,
=
specific
weight of rock in lb/ft3, and
h
=
depth of burial in ft) is the only force acting in an
isotropic, homogeneous and linearly elastic formation, then the stresses in the
x
and
y
directions
(a,
and
up)
are equal to:
where
v
is Poisson’s ratio. Young’s modulus has dimensions of force per unit area
(e.g., lb/in?
),
whereas Poisson’s ratio is dimensionless. Poisson’s ratio for consoli-
dated sedimentary rocks ranges from 0.18 to 0.27 (Birch et al., 1942), whereas the
horizontal compressive stress ranges from 0.22 to
0.37
psi/ft of depth. According to
Harrison et al. (1954), the soft shales and unconsolidated sands found in the Gulf
Coast area of the
U.S.A.
appear to be in a plastic state of stress and possess
horizontal stresses in excess of
0.37.
In the absence of external forces, the horizontal
stress is always less than the vertical stress.
According to Hubbert and Willis (1957), in areas
of
normal faulting the least
stress is horizontal and ranges from
1/2
to
1/3
of
the effective pressure
of
the
overburden. The greatest stress is approximately vertical and is equal to the effective
pressure
of
the overburden. In areas with thrust faulting and folding, on the other
hand, the greatest stress is horizontal
(2-3
times the overburden pressure) and the
least stress is vertical (equal to the effective overburden pressure).
In rock mechanics, it is assumed that rocks are isotropic, homogeneous and
113
elastic. Although this is not true, for many rocks the above equations give a
reasonable approximation of the actual values (see Halliburton, 1976).
The magnitude of the force that rocks can bear without failure depends upon the
type of force, i.e., compressive or tensile. Inasmuch as the compression strength is
10-100 times that of the tensile strength, rocks break perpendicular to the axis of
tensile force. When a rock fails as a result of compressive force, it does not exhibit a
clean break or fracture. Instead the rock crumbles yielding a crushed material of
irregular shapes and sizes. Due to lithological heterogeneities
of
rocks, the strength
is measured many times on different samples and averaged to yield a representative
value.
Fracture geometry
The results of hydraulic fracturing treatment depends upon the geometry
of
the
created fracture. In the case of horizontal fractures this means width (separation
distance of the two fracture faces) and radius. For vertical fractures this refers to
width, length (lateral dimension) and height (vertical dimension). The volume of
fluid injected into the fracture, rate of fluid flow along the fracture length, and rate
of
fluid leak-off into the formation along the fracture face affect the geometry
of
the
generated fracture.
The volume of fluid that stays in the fracture and extends it,
V,,
is equal to the
total volume of the fluid injected,
V,,
minus the volume of the fluid that leaks off,
V,,
i.e.,
V,
=
(V,
-
V,).
The
V,
volume is equal to the product of the injection rate,
q,,
of the surface pumps, and time,
t,
less the volume of fluid that leaks off during
the fracture treatment,
V,:
v,=qit-
V,
(4-7)
The term "volume efficiency",
E,,
for a fracture fluid is the ratio of the fluid
injected into the fracture,
V,,
divided by the total volume
of
fluid injected,
V,:
E,=(V,/V,:)
(4-8)
The fluid pumped inside the wellbore and out into the fracture must overcome
the frictional forces of movement over the fracture faces. The frictional losses due to
the fluid flow create a pressure drop between the wellbore and the fracture tip,
Ap,.
Christianovich and Zheltov (1955) pointed out that this drop in pressure plays an
important role in the computation of geometry
of
the fracture. The fluid does not
occupy the entire length of the hydraulic fracture. The tip of the fracture has a
cusp-like shape and does not contain fluid. Thus, if
xo
is the wetted length of a
vertical fracture, then
Ap,
can be calculated using Daneshy's (1973)
formula:
'
A.A.
Daneshy
is
one of the foremost and greatly respected experts
on
fracturing
in
the world.
114
Fig. 4-14. Schematic diagram showing cross-section
of
a fracture with "leak-off". (Courtesy
of
the
Halliburton Co., 1976, fig. 5.1, p. 16.)
where
n'
=
flow behavior index (power-law model),
K'
=
absolute consistency
(power-law model), and
q(x)
and
w(x)
denote the flow rate and fracture width,
respectively, at a point along the fracture length. The power-law constants
n'
and
K'
can be used to determine the apparent viscosity
pa
(cP):
pa=47.917K'(P)"'-' (4-10)
where shear rate,
P,
is typically equal to:
-)
=
40.464
q/w2h,
where
q
=
volumetric
rate
of
flow (bbl/min),
w
=
fracture width (in.), and
h
=
fracture height (ft). (See
Halliburton Co.,
1976;
and Chilingarian and Vorabutr,
1983.)
Assuming that
uy
is
the least in-situ principal stress (Fig.
4-14),
then the treatment pressure
of
a
hydraulic fracture,
pf,
can be calculated from the following formula (Halliburton,
1976):
Pf
=
uy
+
APC
(4-11)
The fluid pressure at the surface is computed by adding to
pf
the frictional losses
due to flow in the wellbore, tubing, and through the perforations, and subtracting
Fig. 4-15. Typical relationship between fluid
loss
from fracturing fluid and time. (Courtesy of the
Halliburton Co.,
1976,
fig.
5.2,
p.
16.)