Hydraulic Fracturing Desing Variables

1. 1
Fracture Design Variables
H , E , C , KIc-App m , Q, V
or
Building A “Basis of Design”

2. Fracturing – Physics
H, E, C, KIC m, Q, TP



































Sd
Sh
Net
App
Ic
Net
Net
Closure
P
P
P
P
f
H
H
K
E
L
Q
H
E
P
E
P
H
E
P
H
w
H
w
T
H
C
T
Q
L

m



4
/
1
2
4
4
4
'
2
'
2
)
(
3

3. Fracture Height =

4. Major Factors
Closure Stress Differences
 Formation Thickness Effects
 Fracture “Pressure”
 Modulus Contrasts
 Bedding Plane Slip
(Probably Only At Shallow Depths)
 Rock Ductility
 Stress/Fluid Pressure Gradients
 Strength (Toughness) Differences

5. In Situ Stress Differences

8. Major Factors
Closure Stress Differences
 Formation Thickness Effects
 Fracture “Pressure”
 Modulus Contrasts
 Bedding Plane Slip
(Probably Only At Shallow Depths)
 Rock Ductility
 Stress/Fluid Pressure Gradients
 Strength (Toughness) Differences

9. Effect of Formation Thickness
Pay Zone
2
0
3
0 5
0 1
0
0 2
0
0
3
0
0
2
0
0
3
0
0
5
0
0
1
,
0
0
0
2
,
0
0
0
3
,
0
0
0
F
r
a
c
t
u
r
e
H
e
i
g
h
t
,
H
(
f
t
)
P
n
e
t
,
N
e
t
P
r
e
s
s
u
r
e
(
p
s
i
)
Q
=
3
0
b
p
m
m
=
1
5
0
c
p
C
=
0
.
0
0
1
f
t
/

m
i
n
X
f
=
7
0
0
f
t
E
=
2
E
=
6
x
1
0
p
s
i
6
E
=
4
x
1
0
p
s
i
6
E
=
1
x
1
0
p
s
i
6
F
Net Pressure
for Near Perfect
Height
Confinement

10. Effect of Formation Thickness
Boundary Layers

12. Major Factors
Closure Stress Differences
 Formation Thickness Effects
 Fracture “Pressure”
 Modulus Contrasts
 Bedding Plane Slip
(Probably Only At Shallow Depths)
 Rock Ductility
 Stress/Fluid Pressure Gradients
 Strength (Toughness) Differences

13. Modulus Contrasts
Very Little Effect on Height
E2
E1
E2
xf
H
5 1
0 2
0 3
0
4
0
1
2
3
E
/
E
(
2
X
f
/
H
)
21
m
a
x

14. Major Factors
Closure Stress Differences
 Formation Thickness Effects
 Fracture “Pressure”
 Modulus Contrasts
 Bedding Plane Slip (Elastic Debonding)
(Probably Only At Shallow Depths)
 Rock Ductility
 Stress/Fluid Pressure Gradients
 Strength (Toughness) Differences

15. Bedding Plane Slip
Only At Shallow Depths
5
0
0 1
0
0
01
5
0
02
0
0
02
5
0
0
5
0
0
1
,
0
0
0
1
,
5
0
0
2
,
0
0
0
N
e
t
O
v
e
r
b
u
r
d
e
n
S
t
r
e
s
s
(
p
s
i
)
(
O
v
e
r
b
u
r
d
e
n
-
P
o
r
e
P
r
e
s
s
u
r
e
)
T
e
n
s
i
l
e
S
t
r
e
n
g
t
h
f
o
r
B
o
u
n
d
i
n
g
F
o
r
m
a
t
i
o
n
(
p
s
i
)
F
r
a
c
t
u
r
e
S
t
o
p
p
e
d
A
t
I
n
t
e
r
f
a
c
e
F
r
a
c
t
u
r
e
C
r
o
s
s
e
d
I
n
t
e
r
f
a
c
e

16. Interface Slip/Elastic Debonding
Mineback experiments,
BUT essentially “0”
Net Overburden

17. Major Factors
Closure Stress Differences
 Formation Thickness Effects
 Fracture “Pressure”
 Modulus Contrasts
 Bedding Plane Slip (Elastic Debonding)
(Probably Only At Shallow Depths)
 Rock Ductility
 Stress/Fluid Pressure Gradients
 Strength (Toughness) Differences

18. Stress/Pressure Gradients
Only Important After Massive Height Growth
Depth
Closure Stress
Fluid Pressure Gradient
A Fracture
WOULD Rather
Grow Up Than
Down.

19. Fracture Height Estimates
 Lithology Logs
(Bed Thickness)
 In Situ Stresses
(Pore Pressure, Pore Pressure Variations,
Stress Tests, Acid Breakdown Data)
 Special Stress Logs
(Must Be Calibrated)
 Modulus Contrasts
(Sonic Log Data)
Experience & Sound Engineering Judgement

20. 20
Fracture Design Variables
Modulus
H , E , C , KIc m , Q

21. Modulus, E

22. Core Testing
 Must Use Confining Pressure
 Horizontal Core Plug
Desirable
(2 to 1 Length to Diameter)
 Must be “Moist”
 Temperature Typically Not
Critical

23. Effect of Modulus on Design
2 4 6
1
0
2
0
3
0
4
0
M
o
d
u
l
u
s
(
1
0
p
s
i
)
S
l
u
r
r
y
V
o
l
u
m
e
(
M
-
G
a
l
)
6
H
=
H
=
1
0
0
f
t
C
=
0
.
0
0
1
f
t
/

m
i
n
S
p
u
r
t
=
0
m
=
1
5
0
c
p
Q
=
3
0
b
p
m
D
e
s
i
g
n
X
f
=
7
0
0
f
t
L

24. Effect of Modulus on Fracture
2 4 6
1
0
0
2
0
0
3
0
0
4
0
0
5
0
0
6
0
0
7
0
0
8
0
0
0
.
1
0
.
2
0
.
3
0
.
4
0
.
5
0
.
6
0
.
7
0
.
8
M
o
d
u
l
u
s
(
1
0
p
s
i
)
P
n
e
t
,
N
e
t
P
r
e
s
s
u
r
e
(
p
s
i
)
6
M
a
x
W
i
d
t
h
(
i
n
)

25. Typical Values - Sandstone
2 4 6 8
2
4
6
8
N
e
t
O
v
e
r
b
u
r
d
e
n
(
1
,
0
0
0
p
s
i
)
Y
o
u
n
g
'
s
M
o
d
u
l
u
s
,
E
(
1
0
p
s
i
)
6
L
o
w
P
o
r
o
s
i
t
y
(
<
1
0
%
)
,
V
e
r
y
F
i
n
e
G
r
a
i
n
e
d
H
i
g
h
P
o
r
o
s
i
t
y
(
>
2
5
%
)
,
C
o
a
r
s
e
G
r
a
i
n
e
d

26. Typical Values - Carbonate
2 4 6 8
2
4
6
8
N
e
t
O
v
e
r
b
u
r
d
e
n
(
1
,
0
0
0
p
s
i
)
L
o
w
P
o
r
o
s
i
t
y
,
D
o
l
o
m
i
t
e
Y
o
u
n
g
'
s
M
o
d
u
l
u
s
,
E
(
1
0
p
s
i
)
6
H
i
g
h
P
o
r
o
s
i
t
y

27. Typical Values - Shale
 What is Porosity ?
 How Much Clays ?
 How Much Calcite ?
 What is Net Overburden ?

28. Special Values
 Chalks
Porosity 35 to 50%
E of 1.5 to 0.5x106 psi
 Diatomite
Porosity 40 to 50%
E of 1.0 to 0.3x106 psi
 Unconsolidated Sands, Porosity 20%+
E of 0.2 to 1.0x106 psi

29. E From Sonic Log Data ?
5
0 1
0
0 1
5
0 2
0
0
5
.
0
E
+
5
1
.
0
E
+
6
2
.
0
E
+
6
5
.
0
E
+
6
1
.
0
E
+
7
2
.
0
E
+
7
D
y
n
a
m
i
c
Y
o
u
n
g
'
s
M
o
d
u
l
u
s
(
p
s
i
)


=
0
.
1
0


=
0
.
3
0


=
0
.
2
0
G
r
a
i
n
D
e
n
s
i
t
y
=
2
.
6
5
P
o
i
s
s
o
n
'
s
R
a
t
i
o
n
A
s
s
u
m
e
d
=
0
.
2
S
o
n
i
c
T
r
a
v
e
l
T
i
m
e
(
m
-
s
e
c
/
f
t
)

30. Special Space Sonic Log Not Required
5
0 1
0
0 1
5
0 2
0
0
5
.
0
E
+
5
1
.
0
E
+
6
2
.
0
E
+
6
5
.
0
E
+
6
1
.
0
E
+
7
2
.
0
E
+
7
D
y
n
a
m
i
c
Y
o
u
n
g
'
s
M
o
d
u
l
u
s
(
p
s
i
)

=
0
.
1
5

=
0
.
2
5

=
0
.
2
0

=
0
.
2
0
G
r
a
i
n
D
e
n
s
i
t
y
=
2
.
6
5
-
-
-
-
-
-
-
P
o
i
s
s
o
n
'
s
R
a
t
i
o
n
h
a
s
l
i
t
t
l
e
e
f
f
e
c
t
o
n
r
e
l
a
t
i
o
n
b
e
t
w
e
e
n
s
o
n
i
c
m
o
d
u
l
u
s
a
n
d
s
o
n
i
c
v
e
l
o
c
i
t
y
.
S
o
n
i
c
T
r
a
v
e
l
T
i
m
e
(
m
-
s
e
c
/
f
t
)

31. Static Vs. Dynamic Modulus
Dynamic ALWAYS High
2
4
6
8
10
4 6
2 8 10 12 14
Lab Data - Dynamic Modulus
psi x 106
Lab
Data
-
Static
Modulus
psi
x
10
6

32. Sonic Log for Modulus ?
0.1 0.2 0.3 0.5 1 2 3 5 10
0.1
0.2
0.3
0.5
1
2
3
5
10
Dynamic Modulus (e6 psi)
Static
Modulus
(e6
psi) after Morales
SPE 26561
Porosity > 25%

33. Modulus From ?
 Core Data
(Most Desirable, This is the One
Value We Can Get From Core)
 Sonic Log Data
(Modulus is ALWAYS Too High)
 Guess
(Check Against Net Pressure Data)

34. 34
Fracture Design Variables
Fluid Loss
H , E , C , KIc m , Q

35. Fluid Loss Mechanisms
3 Fluid Loss Coefficients
 Linear Flow ASSUMPTION
 Viscosity Control, CI (or CV)
(Effect of Viscous “Bank”)
 Reservoir Control, CII
 Filter Cake Control, CIII (or CW)
)
(
2
A
t
dA
C
QLoss




36. C/t --> Low Loss Near Well
1
0 2
0 3
0 4
0 5
0
0
.
0
5
0
.
1
0
0
.
1
5
0
.
2
0
0
.
2
0
.
4
0
.
6
0
.
8
T
I
M
E
(
m
i
n
)
Q
-
L
o
s
s
(
b
p
m
/
1
0
0
s
q
.
f
t
) C
=
0
.
0
0
3
f
t
/

m
i
n
V
-
L
o
s
s
(
b
b
l
/
1
0
0
s
q
.
f
t
)

37. CI , CII , & CIII

38. Lab Test For CW

39. CW + “Spurt” Loss

T
i
m
e
(
m
i
n
)
V
o
l
u
m
e
L
o
s
t
/
U
n
i
t
A
r
e
a
S
p
u
r
t
L
o
s
s
S
p
u
r
t
T
i
m
e
L
a
b
T
e
s
t
D
a
t
a
F
o
r
C
w
S
l
o
p
e
-
-
>
C
w

40. Typical CW Values
0
.
0
0
1 0
.
0
0
2
0
.
0
0
3
0
.
0
0
5 0
.
0
1 0
.
0
2
0
.
0
3
0
.
0
5 0
.
1
0
.
0
0
0
1
0
.
0
0
0
2
0
.
0
0
0
3
0
.
0
0
0
5
0
.
0
0
1
0
.
0
0
2
0
.
0
0
3
0
.
0
0
5
0
.
0
1
P
e
r
m
e
a
b
i
l
i
t
y
,
k
(
m
d
)
W
a
l
l
B
u
i
l
d
i
n
g
F
l
u
i
d
L
o
s
s
C
o
e
f
f
i
c
i
e
n
t
C
o
r
C
(
f
t
/
m
i
n
)
I
I
I
W T
y
p
i
c
a
l
L
a
b
C
V
a
l
u
e
s
-
1
5
0
°
F
W
C
r
o
s
s
l
i
n
k
C
e
l
l
u
l
o
s
e
X
-
L
i
n
k
G
u
a
r
G
u
m
P
o
l
y
m
e
r
E
m
u
l
s
i
o
n
X
-
L
i
n
k
G
u
a
r
G
u
m
+
5
%
D
i
e
s
e
l

41. Combined Fluid Loss , CT
f
r
I
p
k
C
m
 
 0015
.
0
m

Ct
k
p
CII 
 0012
.
0
)
( data
lab
from
C
C wall
III 
III
II
I
T C
C
C
C
1
1
1
1


 BUT

42. Spurt Loss
 Strange Behavior
 “0” for low permeability (small pore
throat diameter) cases
 Increases with k
 Returns to “0” for high k formations
Behavior somewhat “statistical in nature

43. Spurt Loss Lab Data
0
.
1
0
.
2
0
.
5
1
2 5
1
0
2
0
5
0
0
.
0
0
2
0
.
0
0
5
0
.
0
1
0
.
0
2
0
.
0
5
0
.
1
0
.
2
0
.
5
P
e
r
m
e
a
b
i
l
i
t
y
(
m
d
)
S
p
u
r
t
(
g
a
l
/
s
q
.
f
o
o
t
) 2
0
p
p
t
(
l
b
/
M
-
G
a
l
)
5
0
6
0
8
0
p
p
t
(
l
b
/
M
-
G
a
l
)
g
e
l
4
0
H
P
G
X
-
L
i
n
k
G
e
l
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
5
d
e
g
F

44. Effect of Temperature on Cw
1
0
01
5
02
0
02
5
03
0
0
1
2
3
T
e
m
p
e
r
a
t
u
r
e
(
d
e
g
F
)
T
e
m
p
e
r
a
t
u
r
e
E
f
f
e
c
t
o
n
C
w W
a
t
e
r
B
a
s
e
F
l
u
i
d
s
T
e
s
t
a
t
8
0
d
e
g
F
T
e
s
t
a
t
1
2
5
d
e
g
F

45. Effect of Temperature on Cw
1
0
0
1
5
0
2
0
0
2
5
0
3
0
0
0
.
0
0
2
0
.
0
0
4
0
.
0
0
6
0
.
0
0
8
0
.
0
1
T
e
m
p
e
r
a
t
u
r
e
(
d
e
g
F
)
C
w
(
f
t
/
m
i
n
^
1
/
2
) H
P
G
T
i
t
i
n
a
t
e
X
-
L
i
n
k
G
e
l
3
0
l
b
g
e
l
d
a
t
a
4
0
l
b
g
e
l
d
a
t
a
5
0
l
b
g
e
l
d
a
t
a
S
o
l
i
d
L
i
n
e
s
=
C
w
(
a
t
8
0
d
e
g
F
)
X
(
m
)
-
1
/
2
W

46. Fluid Loss Additives
 ONLY Two Types
- Solid
- Liquid (3 to 5% hydrocarbon)
 Solids
- Used to reduce or eliminate spurt loss
and
allow a wall cake to build
- Do NOT Reduce CW or CT
- Many flavors !
 Liquids
- Used to reduce CW
- Wall cake MUST from first

47. Solid FLA --> Reduce Spurt
1
0 2
0 3
0 4
0
0
.
0
0
0
5
0
.
0
0
1
0
.
0
0
2
0
.
0
0
3
0
.
0
0
5
0
.
0
1
F
L
A
C
o
n
c
e
n
t
r
a
t
i
o
n
(
l
b
o
r
g
a
l
/
M
-
G
a
l
)
)
C P
o
l
y
m
e
r
-
R
e
s
i
n
S
i
l
i
c
a
F
l
o
u
r
P
o
l
y
m
e
r
-
S
i
l
i
c
a
-
C
l
a
y
D
i
e
s
e
l
(
0
.
1
-
1
0
m
d
)
W

48. 48
Fracture Design Variables
Tip Effects
H , E , C , KIc-App m , Q

49. Laboratory Toughness (KIc) Values
0 1000 2000 3000 4000 5000
0
1000
2000
3000
4000
Mesaverde
SS
Berea SS
Indiana LS
Mesaverde
Mudstone
Confining Pressure (psi)
K
(psi

in)
Ic

50. Basic Physics – Tip Effects
PTip
)
(
24
)
(
)
(
ft
H
inch
psi
K
psi
P App
Ic
Tip



20 40 60 80
20
40
60
80
100
120
140
160
180
Net
Pressure
(psi)
H (ft)
K-Ic = 4000
K-Ic = 2000
K-Ic = 1000

52. Warpinski (1985) field data
Khristianovitch-Zheltov (1955)
deeper:
more p
less lag
width profiles
KIc_app ~ plag sqrt (Llag) >> KIc_rock
residual
cakes
makes fracturing robust and negates tip and multi-frac effects
Fracture Propagation: fluid lag at tip -> KIc_apparent
pc
pi
fluid lag
press
tip
negative
net_press

53. Apparent Fracture Toughness
 Very Low Modulus
Formations
 Radial Fracture, No
Height
Confinement
 Very Low Fluid
Viscosity (water)
 “Normal” Modulus
Formation
 Treatments Using
Frac Fluid
 Some (not
necessarily
perfect) Height
Confinement
May Be Important Much Less Important

54. Fracture Design Variables
 H (Height or Geometry) =
f (PNet/Sand-Shale)
 E (Young’s Modulus,
a “pure” rock property)
 C (Fluid Loss)
 KIc-App (PTip or Tip Effects)

55. Basic Physics – Net Pressure,
PNet
4
/
1
4
2
4
4
'
'














O
Ic
O
Net
H
K
E
L
Q
H
E
P
m
Viscous Tip

56. Basic Physics – Net Pressure, PNet
)
(
),
(
),
(
),
(
),
(
),
(
'
576
'
'
015
.
0
)
(
4
/
1
2
4
2
4
4
in
psi
K
ft
L
bpm
Q
cp
ft
H
psi
E
H
K
E
L
Q
H
E
psi
P
IC
O
O
Ic
O
Net
m

m
















Viscous Tip

57. PNet Behavior – Confined Height
0.2 0.5 1 2 5 10 20 50 100
20
50
100
200
500
1,000
Pump Time (min)
"Time 0" When Gel On Perfs
Net
Pressure
(psi)
Data
Confined H
m Dominated
Confined H
Tip Dominated
West Africa Frac Pack
1+ Darcy Permeability

58. PNet Behavior - Radial
0.2 0.5 1 2 5 10 20 50 100
20
50
100
200
500
1,000
Pump Time (min)
"Time 0" When Gel On Perfs
Net
Pressure
(psi)
Tip Dominated
m Dominated
Nolte-Smith Behavior
Simulations
4
/
1
4
2
4
4
'
'














O
Ic
O
Net
H
K
E
L
Q
H
E
P
m

59. Basic Physics
4
/
1
2
4
4
4
'
'














O
Ic
O
Net
H
K
E
L
Q
H
E
P
m
Viscous Tip
H
w
H
S
T
H
C
T
Q
L
P
P
P
P
P




2
3

60. 60
Fracture Design Variables
Fluid Viscosity
H , E , C , KIc m, Q

61. Fluid Viscosity
Why is it important ?
What is it ?
How do we measure it ?
How much do we need ?
How is it affected by time,
temperature, proppant, … ?

62. Viscosity
 Affects fracture net pressure & width
(but not very much, )
 May be important for fluid loss control
 Very important to proppant transport
4
/
1
)
( m
Q
w 

63. Viscosity
Strongly Changed
By Conditions
Must know viscosity
as a function of time
& temperature !
D
i
s
t
a
n
c
e
A
l
o
n
g
F
r
a
c
F
l
u
i
d
T
e
m
p
e
r
a
t
u
r
e
W
e
l
l
b
o
r
e
T
e
m
p
e
r
a
t
u
r
e
F
o
r
m
a
t
i
o
n
T
e
m
p
e
r
a
t
u
r
e
D
i
s
t
a
n
c
e
A
l
o
n
g
F
r
a
c
V
i
s
c
o
s
i
t
y
T
e
m
p
e
r
a
t
u
r
e
D
e
g
r
a
d
a
t
i
o
n
T
i
m
e
/
S
h
e
a
r
D
e
g
r
a
d
a
t
i
o
n

64. How Do We Measure It ?
d
F,
velocity
 , Shear Stress = F / A (psi)
(pressure drop or drag)
g , Shear Rate = vel / d (1/sec)
(for fracture = vel / (w/2)
A
v (x)
Ideal Test
Rotating Cup
& Bob
w (RPM)
Torque

65. What Do We Measure ?
S
h
e
a
r
R
a
t
e
(
1
/
s
e
c
)
S
h
e
a
r
S
t
r
e
s
s
(
p
s
i
)
N
e
w
t
o
n
i
a
n

=
m
g
m

i
s
v
i
s
c
o
s
i
t
y
S
l
o
p
e
=
m
S
h
e
a
r
R
a
t
e
(
1
/
s
e
c
)
S
h
e
a
r
S
t
r
e
s
s
(
p
s
i
)
B
i
n
g
h
a
m
P
l
a
s
t
i
c
S
l
o
p
e
=
P
l
a
s
t
i
c
V
i
s
c
o
s
i
t
y

=
Y
+
m
g
P
P
l
o
g
g
l
o
g

P
o
w
e
r
L
a
w
S
l
o
p
e
=
n
'

=
K
'
g
n
'
Most Common
Rheological Model
for Fracturing
Fluids

66. “Apparent” Viscosity

g
Slope = m app
)
(sec
),
/
sec
(
'
),
(
/
'
48000
)
(
1
2
'
'
1




g
m
g
m
g
g

m




ft
lb
K
cp
K
on
depends
n
f
n
app
app

67. Example
 Power Law Fluid
n’=0.6, ma=100 cp (at 170 sec-1)
 Find: K’ and ma at 50 sec -1
cp
ft
lb
K
a
n
163
100
50
170
)
/
sec
(
0163
.
0
48000
/
170
100
'
)
6
.
0
1
(
)
50
(
2
'
)
6
.
0
1
(















m

68. Slurry Viscosity
2 4 6 81
0
1
2
1
4
1
2
3
5
7
1
0
l
b
S
a
n
d
/
L
i
q
u
i
d
G
a
l
l
o
n
V
i
s
c
o
s
i
t
y
M
u
l
t
i
p
l
i
e
r

69. Fracturing - Fluid Viscosity
 Net Pressure/
Geometry
 Proppant Transport
(Prop Settling  to m)
 Fluid Loss Control
Why we WANT Viscosity
2 5 1
0 2
0 5
01
0
0
5
0
1
0
0
2
0
0
5
0
0
1
,
0
0
0
P
u
m
p
T
i
m
e
(
m
i
n
)
"
T
i
m
e
0
"
W
h
e
n
G
e
l
O
n
P
e
r
f
s
N
e
t
P
r
e
s
s
u
r
e
(
p
s
i
)
5
0
0
c
p
1
0
0
c
p
3
0
c
p
1
c
p
H
=
1
5
0
'
E
=
6
e
6
p
s
i
Q
=
3
0
b
p
m
4
/
1
' 








E
x
Q
P
f
Net
m

70. Fracturing - Fluid Viscosity
 COSTS
 Net Pressure/Geometry
 Proppant Pack Damage
(10 to 70% KFW Loss)
Why we DO NOT WANT Viscosity
Photo Courtesy of StimLab
Everything that increases viscosity
costs money & does damage!

71. How Much Viscosity Is Needed
 If n’=0.6 and g=50 sec-1, the final ref-
erence apparent viscosity is 81 cp
 1 PPG --> 10 PPG gives an average
concentration of 5 PPG, viscosity
multiplier of 2 --> 162 cp
Assume a fluid with 50 cp viscosity (at
170 sec-1) at the end of the job, just as
prop laden fluid is reaching the frac tip,
after being in the fracture for 4 hours.

72. How Much Viscosity Is Needed
 Fluid enters fracture with 500 cp and
degrades to 50, average of about 225
cp or a multiple of 4.5 --> 729 cp
 For many fluids (cross link gels,
foams) settling is much slower than
predicted by Stoke’s Law, assume a
factor of 2
--> 1,458 cp

73. How Much Viscosity Is Needed
Use 1,450 cp in Stoke’s Law
gives a predicted proppant
settling of only 15 feet during the
four hour period
Near perfect transport using
a fluid with a final lab viscosity
of only 50 cp !

74. Where Do We Get Data ?
 Routine data acceptable for
preliminary designs, scoping
studies, etc.
 SPECIFIC data required for final
design, mini-frac analysis, etc.
Lab Tests

75. 75
Fracture Design Variables
Pump Rate
H , E , C , KIc m , Q

76. Pump Rate Affects EVERYTHING
 Fluid Loss
(VL = 3 C HL tp)
 Fracture Net Pressure and Width
(but not very much , )
 Very important to proppant
transport
 Dominant parameter for surface
pressure and treatment costs
4
/
1
)
( m
Q
w 

77. Pump Rate and Fluid Efficiency
4
/
1
'
3 









E
L
Q
L
H
Q
Vol
H
C
t
Q
or
Vol
Vol
Vol
L
p
FRAC
LOST
IN
m
Pump rate involved in ALL terms of
fracture material balance. Thus Q is a
dominant parameter affecting fluid
efficiency !

78. Pump Rate and Pressure
PSurface = C - Head + Pipe Friction + PNET
for turbulent flow, Friction  Q1.75 ,
HHP = PS * Q ,  Q2.75
Horsepower almost Pump Rate CUBED
---------------------------------------
PNet  (Q m L/E’) 1/4 , (relatively insensitive)

79. Example
 Q2 = 1.5 * Q1 (50% Increase)
Friction = 2 x , +100%
HHP = 3 x , +200%
PNet = 1.1 x , +10%
 Q2 = 0.7 Q1 (30% Reduction)
Friction = 0.54 x , - 460%
HHP = 0.37 x , - 63%
PNet = 0.91 x , - 9%

80. Pump Rate & Proppant Transport
V1
V2
H
D
D/H = V1 / V2
V1 = Fluid Velocity = Q/Hw  Q/H(m Q) 1/4  Q3/4/Hm1/4
V2 = Fall Rate (Stoke’s Law)  1/m
D/H  (Q m ) 3/4 / H
(INDEPENDENT of H , Q & mEqually Important ! )

81. Fracturing - Pump Rate
 Net Pressure/
Geometry
 Proppant
Transport
 Fluid Loss
Control
Why we WANT Pump Rate
2 5 1
0 2
0 5
01
0
0
5
0
1
0
0
2
0
0
5
0
0
1
,
0
0
0
P
u
m
p
T
i
m
e
(
m
i
n
)
"
T
i
m
e
0
"
W
h
e
n
G
e
l
O
n
P
e
r
f
s
N
e
t
P
r
e
s
s
u
r
e
(
p
s
i
)
6
0
b
p
m
3
0
b
p
m
1
0
b
p
m
H
=
1
5
0
'
E
=
6
e
6
p
s
i
m
=
1
0
0
c
p
4
/
1
' 








E
x
Q
P
f
Net
m

82. Fracturing - Pump Rate
 COSTS
 Net Pressure/
Geometry
 Equipment
Failure Possibility
Why we DO NOT WANT Pump Rate
2 5 1
0 2
0 5
01
0
0
5
0
1
0
0
2
0
0
5
0
0
1
,
0
0
0
P
u
m
p
T
i
m
e
(
m
i
n
)
"
T
i
m
e
0
"
W
h
e
n
G
e
l
O
n
P
e
r
f
s
N
e
t
P
r
e
s
s
u
r
e
(
p
s
i
)
6
0
b
p
m
3
0
b
p
m
1
0
b
p
m
H
=
1
5
0
'
E
=
6
e
6
p
s
i
m
=
1
0
0
c
p
3
Q
Q
P
HHP Surface 



83. Keys For Selecting Q
 Fluid Loss -- Efficiency
( < 20 to 30% , Increase Q
or > 70 to 80%, Consider Q
Reduction)
 Surface Treating Pressure
(Pressure limits & HHP costs)
 Proppant Transport
(Particularly in hot wells)
 Bottomhole Net Pressure

84. Fracturing – Physics
H, E, C, KIC m, Q, TP



































Sd
Sh
Net
App
Ic
Net
Net
Closure
P
P
P
P
f
H
H
K
E
L
Q
H
E
P
E
P
H
E
P
H
w
H
w
T
H
C
T
Q
L

m



4
/
1
2
4
4
4
'
2
'
2
)
(
3

85. The End

86. Typical CW Values
Crosslink Cellulose Derivative
Crosslink Guar Derivative
Polymer Emulsion
Crosslink Guar Derivative + Hydrocarbon
0.001 0.01 0.1
0.0001
0.001
0.01
Permeability, k (md)
Wall
Building
Loss
Coefficient
C
(ft
/

min)
III