Final_Reorddddddddddddddddddddered_Waterflooding_Course.pdf

ddddddddddddddddddddddddddddd

1. Copyright 2007, NExT, All rights reserved
Introduction to Improved Oil Recovery
Through Water Injection Projects

2. Copyright 2006, NExT, All rights reserved
Objectives
Definition
Objectives
Candidates
Patterns
Oil, water, and gas saturations
Fractional flow
Performance measures
Practices and problems
Reservoir monitoring

3. Copyright 2006, NExT, All rights reserved
Primary Recovery
Hydrocarbon production resulting from natural reservoir
energy
Natural reservoir energy sources
• Rock and fluid expansion
• Solution gas drive
• Gravity drainage
• Water influx

4. Copyright 2006, NExT, All rights reserved
Conventional Improved Recovery (IOR)
Injection of immiscible fluid
• Water injection
• Nitrogen injection
• Casinghead gas reinjection
Often used in ‘secondary recovery’

5. Efficiency of Oil Displacement by Water
By: Fathi H. Boukadi

6. 1/19/2011Waterflooding/Introduction3
Figure 13

shows a saturation profile before breakthrough. Water is injected for
sometime. At position , water satura tion of plane is maximum, while at
water saturation is shock front saturation.
Need to determine location

and value of saturation at front
. We also need
to estimate average water saturation behind front
.
0Lx
1
x
2
S
wc
1-S
or
S
wf
x
S
w
S
w
Saturation profile
at t < t
bt
0Lx
1
x
2
S
wc
1-S
or
S
wf
x
S
w
S
w
Saturation profile at t < t
bt
Figure 13: Saturation profile before breakthrough
indicating shock front saturation
AVERAGE WATER SATURATION BEHIND FRONT
x
1
x
2

7. 1/19/2011Waterflooding/Introduction5
Tangent to fractional flow curve from is at .
Extrapolated tangent must intercept line at point .
wwcw
SS,f
=
=0
wf
ww wfS
ff f
=
=
w
f=1
www
SS;f
=
=1
Plot
ww
f vs S
, obtain derivative (inflection poin t indicates saturation at front).
wf
f−1
wwf
SS−
−10
wwc
SS−
w
S
wc
S
wf
S
wwf
ff=
w
f=
1
w
f=
0
wf
f−
1
wwf
SS−
−10
wwc
SS−
w
S
wc
S
wf
S
wwf
ff=
w
f=
1
w
f=
0
Figure 14: Slope of fractional flow curve
AVERAGE WATER SATURATION BEHIND FRONT

8. Copyright 2006, NExT, All rights reserved
Waterflooding
Injection of water into a reservoir
• Increases reservoir energy
• Sweeps oil towards producing wells
Most widely applied secondary recovery method
Accounts for about 50% of U.S. oil production

9. Copyright 2006, NExT, All rights reserved
History of Waterflooding
1865
~ ~
1920 1930 1940 1950 1960 1970 1980 1990
Waterflood projects in Oklahoma and Texas
Widescale waterflood
implementation
Infill drilling
Tertiary
recovery
* First recorded waterflood

10. Copyright 2006, NExT, All rights reserved
Goal of Waterflooding
Increase the amount of oil recovered from the reservoir by
• Maintaining reservoir pressure
• Displacing (sweeping) oil with water

11. Copyright 2006, NExT, All rights reserved
Pressure Maintenance
Water treatment
plant
Water
injection
OWC
Sealing
fault
Gas
Oil
Production
well

12. 1/19/2011Waterflooding/Introduction7
Oil recovery Equation
Typical values of E
R
*
are;
Waterflooding 30-40% (E
V
xE
D
=0.6x0.6=.36)
Steam injection 30-50%
Polymer injection 30-55%
CO
2
injection 30-65%
Solvent injection 35-63%
*depends on E
R
from primary and reservoir and fluid properties (Carcoana, ’92)
Volumetric sweep (E
vol
) is product of areal (E
A
) and vertical sweep (E
ver
);
where,
VA vol
EEE
=
DISPLACEMENT FUNDAMENTALS
areatotal
area contacted
E
A
=
(48)

13. 1/19/2011Waterflooding/Introduction8
DISPLACEMENT FUNDAMENTALS
Figure: Sketch of areal (top) and vertical sweep
Figure 15: Sketch of areal sweep efficiency
Therefore, using all definitions, oil recovery equation becomes;
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
o
poi
vADp
B
VS
EEEN
(49)

14. 1/19/2011Waterflooding/Introduction9
DISPLACEMENT FUNDAMENTALS
To determine recovery, we need to estimate E
A
, E
D
, and E
V
from:
1. correlations
2. scaled laboratory experiments
3. numerical simulation
Areal sweep efficiency

data is obtained from Craig (1980). Correlations are
for displacements in homogeneous, confined patterns.

15. 1/19/2011Waterflooding/Introduction10
DISPLACEMENT FUNDAMENTALS
E
A
, is a function of mobility ratio (M) and injected volumes (V
d
);
From curve, we can conclude that E
A

:
1. increases

with increasing

throughput (V
d

), injection volumes
2. increases

with decreasing

mobility ratio (M)

16. 1/19/2011Waterflooding/Introduction12
DISPLACEMENT FUNDAMENTALS
Mobility ratio (M) is:
where,
k
rw
( ); evaluated at average water saturation behind front at BT,
k
ro
(S
wc
); evaluated in oil bank ahead of front, S
wc
Mobility ratio characterizes stability of displacement front;
1. M is constant before breakthrough.
2. M increases after breakthrough.
3. if M <

1, displacement

is stable.
4. if M >

1, displacement

is unstable.
5. if M >

1, viscous fingering and early breakthrough.
(50)
w
S
w
S
w
o
wcro
wrw
owcro
wwrw
)S(k
)S(k
/)S(k
/)S(k
M
μ
μ
=
μ
μ
=

17. 1/19/2011Waterflooding/Introduction13
DISPLACEMENT FUNDAMENTALS
Viscous fingering

also results in prolonged injection to achieve sweep out.
Need to optimize injection rate, q
w
, and number of injectors by using voidage
replacement.
water
w
o
wcro
wrw
owcro
wwrw
)S(k
)S(k
/)S(k
/)S(k
M
μ
μ
=
μ
μ
=

18. 1/19/2011Waterflooding/Introduction14
DISPLACEMENT FUNDAMENTALS
M’, end-point mobility ratio,

is:
where,
k’
rw
is end-point relative permeability at S
orw
k
ro
is end-point relative permeability at S
wc
If M <

1 and M’

<

1, piston-like displacement.
For waterflooding , typical mobility ratio range is; 0.02 <

M <

2
(52)
w
o
wcro
orw
'
owcro
w orw
'
'
)S(k
)S(k
/)S(k
/)S(k
M
rw rw
μ
μ
=
μ
μ
=

19. Copyright 2006, NExT, All rights reserved
Gas Phase Effects
Reduction in reservoir pressure can cause
• Gas-cap expansion
• Secondary gas cap creation
• Gas saturation creation in pore spaces
Water injection can prevent or reverse these effects

20. Copyright 2006, NExT, All rights reserved
Reservoir Performance
Gas/oil ratio
Pressure
Cumulative oil production
GOR
Too depleted for
WF success
p
i

p
b

R
si
Gas saturation
Pressure
Gas
saturation

21. Copyright 2006, NExT, All rights reserved
Primary Drive Mechanisms
Most applicable:
• Solution-gas drive
• Gas-cap drive
• Weak water drive
• Gravity drainage
Not applicable
• Strong water drive

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Example 1 Solution
1. Fair
2. Fair
3. Poor
4. Good
5. Poor
6. Good
7. Fair

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Water Injection To Sweep Oil
Five - spot
Production well
Injection well
Future inj. well

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Peripheral Flooding
Injectors
Producers

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Line Drive Patterns
Direct Drive Staggered Drive
Injection
Well
Production
Well
No-flow
Boundary

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5-Spot Pattern
Injection well
Production
well
No-flow
boundary

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9-Spot Pattern
Normal
Nine - Spot
Inverted
Nine - Spot
Injection
Well
Production
Well
No-flow
Boundary

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Typical Initial Oil Field Development
1 Mile
1 Mile
Producing well
Dry hole

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Typical Peripheral Waterflood Development
Producing well
Injection well
Dry hole

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Typical Center-Line Injection Waterflood
Development
Producing well
Injection well
Dry hole

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Typical 160-Acre Inverted 9-Spot Waterflood
Development
Producing well
Injection well
Dry hole

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Typical Infill Drilled
40-Acre 5-Spot Development
Existing
injection well
New conversion
to injection
New infill
producing well
Dry hole

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Typical Infill Drilled 40-Acre Direct
Line Drive Development
Existing
injection well
New conversion
to injection
New infill
producing well
Dry hole
Existing
producing well

34. Copyright 2006, NExT, All rights reserved
Factors in Pattern Selection
Current well locations
Fracture azimuths
Permeability anisotropy
Field geometry
Injectivity
Infill drilling plans
Casing integrity of conversion injection candidates
Adjacent lease considerations

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Pattern Orientation
Unfavorable
orientation
Favorable
orientation
Permeability
or
fracture
orientation

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Pattern Selection/Orientation Problem
N
NE NW
W E
SE SW
S
Existing
producer
Existing
injector
New
producer
New
injector
Convert to
injector

37. Copyright 2006, NExT, All rights reserved
Solution - Pattern Selection/Orientation Problem
N
NE NW
W E
SE SW
S
Existing
producer
Existing
injector
New
producer
New
injector
Convert to
injector

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Frontal Advance Theory
Water
Oil
S
wi

S
or

•  Piston - like displacement
Connate water

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Frontal Advance Theory
Water
Saturation
Distance
Connate water
Initial oil
saturation Injected
water
bank
Oil
•  ‘Leaky piston’

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Frontal Advance Theory
Saturation
Distance
Water
bank
Oil
bank
Unaffected
reservoir
Water
Oil
Trapped gas
Initial
free gas
Connate water

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Fractional Flow Equation

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Fractional Flow Equation
Capillary pressure term
(usually ignored)
Gravity term

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Fractional Flow Equation
Horizontal reservoir

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Fractional Flow of Water is Affected by:

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Fractional Flow Curves

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Information From the Fractional Flow Curve
f
w
=1
f
W

S
wi
1-S
or

f
WF

Fraction of water
flowing at the
flood front
S
w

S
w
at the
flood front
Average reservoir
water saturation
at breakthrough
Tangent point
1
0
0

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Example 2: Fractional Flow Curve

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Example 2
Solution
• Fractional Flow Curve
1. S
w
= 55%
2. f
w
= 82.5%
3. = 63%
4.

49. Copyright 2006, NExT, All rights reserved
Waterflood
Performance Efficiencies
Recovery efficiency
E
R
= E
p
E
I
E
D
= E
v
E
D
= E
A
E
I
E
D

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Areal Sweep Efficiency (E
A
)
E
A

Water invaded
area
Producer
Injector
Areal Sweep Efficiency (E
A
)

51. Copyright 2006, NExT, All rights reserved
Areal Sweep Efficiency (E
A
)
Fraction of the horizontal plane of the reservoir that is
behind the flood front at a point in time
Factors affecting E
A

• Mobility ratio
• Well spacing
• Pattern geometry
• Areal heterogeneities

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Mobility

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Mobility Ratio

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Mobility Ratio Effects

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Areal Sweep Efficiency
Pattern geometry influences areal sweep efficiency
Correlations exist for common pattern geometries as a
function of mobility ratio.

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Vertical Sweep Efficiency
INJECTION PRODUCTION
E
I
=

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Factors Affecting Waterflooding
Gravity
Barriers to vertical flow
Lateral pay discontinuities
Completion interval inconsistencies

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Effects of Gravity
Water
Injector Producer
Oil

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Lateral Pay Discontinuities
Producing
well
Injection
well
Trapped oil

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Lateral Pay Discontinuities
Effect of infill drilling
Producing
well
Injection
well
Infill
well

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Completion Interval Inconsistencies
Producing
well
Injection
well
Trapped
Oil - Completions
Trapped oil -
lateral pay
discontinuities

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Prediction Methods
Analytical methods
• Typically single-layer, single-pattern, iso-properties
• Requires scale-up of answers to get full field results
(Buckley-Leverett, Stiles, Craig-Geffen-Morse, Dykstra-
Parsons)
• Largely replaced by numerical methods such as 3-
dimensional, 3-phase computer reservoir simulation

63. Copyright 2006, NExT, All rights reserved
Development Philosophy
Understand the reservoir
Start waterflooding early
Infill drill to reduce effects of lateral pay discontinuities
Develop field on pattern waterflood
Open all of the pay in all wells

64. Copyright 2006, NExT, All rights reserved
Operating Philosophy
Keep producing wells pumped off
Inject below formation parting pressure
Inject clean water
Manage waterflood by injection well tests
Conduct a surveillance program

65. Copyright 2006, NExT, All rights reserved
Producing Well Operations
Minimal production/crossflow Maximum production
P
WF
= 1000 psi
Well not
pumped off
Well
pumped off
P
R
= 1500 psi
P
R
= 500 psi
P
WF
= 100 psi

66. Copyright 2006, NExT, All rights reserved
Injection Well Operations
Inject at 50 psi below formation parting pressure
Inject clean water
Keep wellbore cleaned out
• Scale
• Fill
Maintain good injection conformance

67. Copyright 2006, NExT, All rights reserved
Injection Water Quality
Undesirable contaminants
• Dissolved, scale-forming solids
• Oil and suspended solids
• Dissolved oxygen
• Bacteria

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Injection Well Testing
Conduct periodic injection well tests to determine:
• Skin damage
• Formation parting pressure
• Injection conformance

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Waterflood Surveillance
Accurate data collection
• Monthly 3-phase production well tests
– Measure oil, water, & gas production during test
• Daily injection volumes & pressures
• Maintain & properly use instruments
Reservoir pressure history

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Waterflood Surveillance
3D finite difference full-field reservoir simulation
• Monitor and evaluate flood performance

71. Copyright 2006, NExT, All rights reserved
Summary
During the past few hours we have learned
1. What waterflooding is
2. Why we inject water into oil reservoirs
3. Which reservoirs are candidates for
waterflooding

72. Copyright 2006, NExT, All rights reserved
Summary
4. How to recognize the different
waterflood patterns.
5. Why pattern orientation is important.
6. How fluid saturations change during a
waterflood.

73. Copyright 2006, NExT, All rights reserved
Summary
7. How to determine the fraction of water
flowing at a point in the reservoir, and
how to determine the water saturation
and the average water saturation in the
reservoir at breakthrough.

74. Copyright 2006, NExT, All rights reserved
Summary
8. How recovery efficiency is affected by
the fluid mobility ratio, areal sweep efficiency, vertical
sweep efficiency, displacement efficiency, and lateral
pay discontinuities.

75. Copyright 2006, NExT, All rights reserved
Summary
9. Why producing wells should be pumped off.
10. How to maximize water injection without damaging
the reservoir.

76. Copyright 2006, NExT, All rights reserved
Summary
11. Why we inject clean water.
12. How to manage a waterflood by injection well testing.
13. What data we need to collect to monitor waterflood.

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References

78. Copyright 2006, NExT, All rights reserved
References

79. Copyright 2006, NExT, All rights reserved
References

80. Copyright 2006, NExT, All rights reserved
References

81. 1/19/2011Waterflooding/Introduction16
DISPLACEMENT FUNDAMENTALS
Vertical Sweep Efficiency
1. heterogeneity
9stratified layers with different perm
9breakthrough earlier in layer 1
9sweep out when layer 4 breakthrough
Layer 1
Layer 4

82. 1/19/2011Waterflooding/Introduction17
DISPLACEMENT FUNDAMENTALS
Vertical Sweep Efficiency
2. Gravity Effect
9important with good vertical communication for large R
L
;
where,
L= distance injector/producer
H= reservoir thickness
k
v
= vertical permeability
k= areal permeability
¾practically speaking, k
v
<k
¾L >H (gravity is an issue in waterflooding )
5.0
v
L
k
k
H
L
R⎟
⎠
⎞
⎜
⎝
⎛
=

83. 1/19/2011Waterflooding/Introduction18
DISPLACEMENT FUNDAMENTALS
Vertical Sweep Efficiency
2. Gravity Effect
9gravity forces are strong compared to viscous forces; N
g
is large;
where,
λ= mobility of displacing fluid
Δρ= density difference (displacing-displaced)
ν= superficial velocity
¾injection at low rate, higher N
g
¾L >H (gravity is an issue in waterflooding)
w
owrw
g
g)(kkgk
forces viscous
forces gravity
N
νμ
ρ
−
ρ
=
ν
ρ
Δ
λ
= =

84. 1/19/2011Waterflooding/Introduction19
DISPLACEMENT FUNDAMENTALS
Vertical Sweep Efficiency
2. Gravity Effect
9gravity tonguingoccur for large R
L
and N
g
.
¾water bypasses oil in upper region.
¾CO
2
injection for EOR.
oil water

85. 1/19/2011Waterflooding/Introduction20
DISPLACEMENT FUNDAMENTALS
Displacement Sweep Efficiency
It is defined as;
¾efficiency is directly measured from a core flood (since E
v
=1).
¾can also be evaluated from Buckley-Leverett.
¾for immiscible displacement E
D
is bounded by residual oil saturation, S
or
.
¾E
D
is a function of:
¾Mobility ratio
9E
D
as M (increasing μ
water
, polymer)
¾Throughput
¾Wettability
¾Dip angle
¾Capillary number
volumeoil contacted
volum
e
oil mobilized
E
D
=

86. 1/19/2011Waterflooding/Introduction22
DISPLACEMENT FUNDAMENTALS
Trapped Oil Saturation
Capillary de-saturation curves (CDC) indicates that for waterflooding ,
10
-7
≤N
c

≤10
-5
.
For S
or
to drop from 0.3 to 0.2, N
c
has to increase to 5*10
-4
(polymer flooding).

87. 1/19/2011Waterflooding/Introduction23
Oil recovery

is estimated

depending on type of reservoir:
1. Homogeneous;
9Buckley-Leverett Method
2. Layered or Stratified;
9Stiles Method
9Dykstra-Parsons/Johnson Method APPLICATION OF FRACTIONAL FLOW THEORY IN
OIL RECOVERY CALCULATIONS

88. 1/19/2011Waterflooding/Introduction24
Buckley-Leverett

Method
Before water breakthrough, oil recovery is equal to injected water. Let us
estimate oil recovery after breakthrough as well.
After breakthrough at producing well, , let =dimensionless
number of injected pore volumes, with .
Figure 15

shows water saturation distribution s at breakthrough and at a later
time.
x=L
2
i
id
W
W
LA
=
φ
PV LA=φ 1
HOMOGENEOUS RESERVOIRS

89. 1/19/2011Waterflooding/Introduction25
x
S
w
S
wc
1-S
or
Saturation profile at
breakthrough, t
b
S
wbt
=S
wf
L
S
w
0
Saturation profile
at t > t
b
S
we
S
wbt
Figure 15: Water saturation distributions at breakthrough
and after, in a linear waterflood
HOMOGENEOUS RESERVOIRS
w
S
w
S

90. 1/19/2011Waterflooding/Introduction26
At breakthrough, front reaches production well and water saturation= .
Behind front, water saturation in creases suddenly from to . This confirms
existence of shock front. Let us denote,
id i
qqLA=φ
(45)
Dimensionless oil production at breakthrough is:
(
)
btbt
wbt
pd id id bt w wcbt
w
w
S
NWqtSS
df
dS
==⋅= −=
⎛⎞
⎜⎟
⎝⎠
1
(46)
Using Equation (32)
bt
id
bt
id
W
t
q
=
(47)
HOMOGENEOUS RESERVOIRS
wf
S
)SS(
wcw
−
wc
S
w
S

91. 1/19/2011Waterflooding/Introduction27
After breakthrough, both oil and water will be produced;
wc
S
we
i
id
w
w
S
W
W
LAdf
dS
==
φ⎛⎞
⎜⎟
⎝⎠
1
(48)
At this stage to evaluate oil recoveries,
()
we
wwe we
w
wS
SS f
df
dS
=+−
⎛⎞
⎜⎟
⎝⎠
1
1
(49)
Or,
(
)
wwe we id
SS fW=+−⋅1
(50)
HOMOGENEOUS RESERVOIRS
Subtract from both sides of equation, post breakthrough recovery
is estimated from:
(
)
pd w wc we wcwe id
NSSSS fW =−=−+−1
(51)

92. 1/19/2011Waterflooding/Introduction28
Stiles Method
Method applies for layered reservoirs when mobility ratio

is close to 1.0.
Stiles uses following assumptions;
1. Formation is linear and made up of a number of layers of constant
thickness.
2. No fluid crossflow takes place between layers.
3. Displacement is piston like (len gth of transition zone is zero).
4. Position of front in each layer is directly proportional to absolute
permeability of layer.
5. Volume of water injected depends on layer

capacity, k
i
h
i
.
6. Layers may have different thickness and absolute permeability.
STRATIFIED RESERVOIRS

93. 1/19/2011Waterflooding/Introduction29
Figure 16

shows stratified reservoir with 6 la yers. Natural layering is reordered
in a sequence of layers with decreasing permeability.
Natural layeringRe-ordered layers Natural layeringRe-ordered layers
Figure 16: Arranged stratified reservoir
Layers are numbered from highest permeability (top) to lowest (bottom).
For
n
layers, permeabilities are;
k
1

(highest),
k
2

,…..
k
n

(lowest) and respective
thicknesses are;
Δh
1

, Δh
2

,….. Δh
n

.
STRATIFIED RESERVOIRS

94. 1/19/2011Waterflooding/Introduction30
Total recoverable oil, in standard barrels, is:
()
(
)
worc
pt
o
WHL S S
NSTB
B
φ1
7758
−−
=
(52)
where,
W

= reservoir width, ft
φ
= porosity, fraction
H

= total reservoir thickness, ft
L

= reservoir length, ft
B
o

= oil formation volume factor, (bbl/stb)
Following example shows implementation of Stiles

method for a reservoir
with seven layers.
Absolute k-md Thickness-ft
21020
19012
705
507
3015
1030
318
Absolute k-md Thickness-ft
21020
19012
705
507
3015
1030
318
Absolute k-md Thickness-ft
21020
19012
705
507
3015
1030
318
Figure 17: Permeability and thickness lay out
STRATIFIED RESERVOIRS

95. 1/19/2011Waterflooding/Introduction32
Otherwise, recovery at time t
j

is given by:
()
jn
i
ii
iijj
jjn
i
i
K
hh
K
RRt
h
==+
=
Δ+ Δ×
==
Δ
∑∑
∑
11
1
(55)
First term

in numerator refers to flooded out layers, while second term

refers to partially flooded

portion.
j n
ij i
ii
Hh, h h
==
=Δ =Δ
∑∑
11
(56)
Using definitions of above equation, one can write;
()
n
jii
ijj
jj
hhK
k
RRt
H
=+
+
Δ×
==
∑
1
1
(57)
STRATIFIED RESERVOIRS

96. 1/19/2011Waterflooding/Introduction33
We can also write Equation (57) as:
()
tj j
j
j
CC h
R
HKH
−
=+
(58)
where,
j n
tiij ji
ii
C K h , C K h
==
=Δ =Δ
∑∑
11
(59)
Fractional flow of water at breakthrough , for layer j, at bottomhole (60)
and surface conditions (61), are defined as;
()
()
j
wj
jtj
MC
ft
MC C C
=
+−
(60)
STRATIFIED RESERVOIRS

97. 1/19/2011Waterflooding/Introduction34
()
()
j
ws j
jtj
AC
ft
AC C C
=
+−
Fractional flow of water at surface is evaluated considering formation volume
factors of oil and water.
(61)
where,
rw o
ro w
K
M
K
μ
=
μ
(62)
and
rw o o
ro w w
KB
A
KB
μ
=
μ
(63)
Recall that;
STRATIFIED RESERVOIRS

98. 1/19/2011Waterflooding/Introduction35
()
w
ws j
wosurface
q
ft
qq
⎛⎞
=⎜⎟
+
⎝⎠
(64)
Table 4

summarizes Stiles example results. Oil and fluid properties are
included in table.
Revise calculations.
Exercise using Stiles Method Bw =1.02 krw = 0.35
Bo =1.37 kro = 0.93
μw =0.6 cp
μo =0.83 cp
Recoverable oil
=
100,000 STB
A=0.699249772
Layerabsolute k-md hΣhkhΣkh R at bt Np-STB fw
1210 20 20 4200 4200 0.3553 35532 0.4370
2190 12 32 2280 6480 0.3730 37304 0.7508
370 5 37 350 6830 0.4999 49987 0.8054
450 7 44 350 7180 0.5615 56150 0.8620
530 15 59 450 7630 0.6617 66168 0.9378
610 30 89 300 7930 0.8822 88224 0.9904
73 18 107 54 7984 1.0000 100000 1.0000
Table 4: Stiles results for provided exampleSTRATIFIED RESERVOIRS

99. 1/19/2011Waterflooding/Introduction36
Figure 18

depicts fractional flow of water versus cumulative oil recovered
using Stiles method.
Stiles Method
0.40
0.50
0.60
0.70
0.80
0.90
1.00
0 20000 40000 60000 80000 100000
Np
fw
Figure 18: Recovery at breakthrough for all the layers
Note that 80,000 STB recovered at water cuts >90% may be uneconomical?
STRATIFIED RESERVOIRS

100. 1/19/2011Waterflooding/Introduction
37
Dykstra-Parsons-Johnson Method
9Relates waterflood recovery (R), initial water saturation (S
w
)
,
mobility (M), permeability distribution (V), and producing water-oil ratio
(WOR).
9Correlation based on layered linear model with no crossflow.
9More than 200 flood tests made on more than 40 California sand
cores.
9Figure 19 to Figure 22( next slides) show Johnson correlations.
STRATIFIED RESERVOIRS

101. 1/19/2011Waterflooding/Introduction
38
Dykstra-Parsons-Johnson Method
Vertical variation V is calculated from statistical analysis of permeability
distribution;
1. by plotting permeability values on a log probability paper and
2. choosing best straight line through points.
with
K
50
= mean permeability; value with 50% probability
K
84.1
= permeability @ 84.1% of cumulative sample
.
KK
V
K
−
=
50 84 1
50
(65)
STRATIFIED RESERVOIRS

102. 1/19/2011Waterflooding/Introduction
39
()
w
RS .
.
R.
.
−=
==
−
1015
015
027
1045
w
V.
M.
S.
=
=
=
054
18
045
()
w
RS .
.
R.
.
−=
==
−
1015
015
027
1045
w
V.
M.
S.
=
=
=
054
18
045
()
w
RS .
.
R.
.
−=
==
−
1015
015
027
1045
w
V.
M.
S.
=
=
=
054
18
045
Figure 19: Johnson's correlation for a producing
water oil ratio (WOR) of 1
STRATIFIED RESERVOIRS
Fractional oil recovery

by both primary methods and waterflooding
as portion
of oil initially in place.

103. 1/19/2011Waterflooding/Introduction
40
Figure 20: Johnson's correlation for a producing
water oil ratio (WOR) of 5
STRATIFIED RESERVOIRS
For WOR<100, mobility ratio is better estimated as:
w
o
wcro
wrw
owcro
wwrw
)S(k
)S(k
/)S(k
/)S(k
M
μ
μ
=
μ
μ
=

104. 1/19/2011Waterflooding/Introduction
42
Figure 22: Johnson's correlation for a producing
water oil ratio (WOR) of 100
STRATIFIED RESERVOIRS

105. 1/19/2011Waterflooding/Introduction
43
Other Prediction Methods
Guthrie-Greenberger Method
9Based 73 sandstone reservoirs with water driveor combined water
and gas drives.
9Model implies that water drive recovery efficiency is lower in reservoirs
with higher porosity!
114403.0h0003488.05380.1
log1355.0S25569.0klog2719.0E
o w R
+ −φ−
μ
−
+
=

106. 1/19/2011Waterflooding/Introduction
44
Other Prediction Methods
API Statistical Study
9Based 312 reservoirs with water drivefromsandstone reservoirs
and for solution gas drive recoveries from sandstones and
carbonates.
where,
k [=] darcies
μ
wi
[=] water viscosity@ P
i
μ
oi
[=] oil viscosity @ P
i
9Correlation based on water drive performance has limited usefulness
for waterflooding projects.
()
2159.0
a
i
1903.0
w
0770.0
oi
wi
0422.0
oi
w
R
P
P
S
k
B
)S1(
898.54E
−
−
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
⎥
⎦
⎤
⎢
⎣
⎡
μ
μ
⎥
⎦
⎤
⎢
⎣
⎡−φ
=

107. 1/19/2011Waterflooding/Introduction
45
Other Prediction Methods
Example waterflood performance with time for 5-spot pattern Given;
Well spacing, acres 20
Thickness, ft 50
Average permeability, md 10
Porosity, % 20
Connate water saturation, %PV 10
Current average gas saturation, %PV 15
μ
o
@ P
o
1.0
μ
w
0.5
P
o
1,000 psi
Current oil recovery, % OIIP 10.4
B
oi
@ P
oi
1.29
B
o
@ P
o
1.20
Flooding pattern 5-spot using existing wells
Pattern area*, acres 40
r
w
, ft 1.0
*5-spot contains 1 injector, 1 producer

108. 1/19/2011Waterflooding/Introduction
46
Other Prediction Methods
Example waterflood performance with time for 5-spot pattern Given;
S
w

, fractionk
ro

, fractionk
rw

, fractionf
w

, fraction
0.101.0000.0000.0000
0.300.3730.0700.2729
0.400.2100.1690.6168
0.450.1480.2260.7533
0.500.1000.3000.8571
0.550.0610.3760.9250
0.600.0330.4760.9665
0.650.0120.6000.9901
0.700.0000.7401.0000

109. 1/19/2011Waterflooding/Introduction
47
Other Prediction Methods
Example waterflood performance with time for 5-spot pattern Waterflood displacement performance;
S
wf

, fractionf
wf

, fractiondf
w

/dS
w
Q
i
, PV, fraction
0.4690.7982.160.4630.563
0.4950.8481.750.5720.582
0.5200.8881.410.7110.600
0.5460.9201.130.8870.617
0.5720.9460.8511.1760.636
0.5970.9650.6491.5400.652
0.6220.9800.4772.1000.666
0.6490.9900.3173.1570.681
0.6740.9960.1955.130.694
0.7001.0000.1029.800.700
w
S
cum. pore volumes needed
to reach S
wf
We can also write that
oiwfw
fQSS +=

110. 1/19/2011Waterflooding/Introduction
48
Other Prediction Methods
Example waterflood performance with time for 5-spot pattern relative permeability, fractional and differential fractional flow curves ;
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
00.20.40.60.8
Sw, fraction
kr, fraction
kro
krw
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.2 0.4 0.6 0.8
Sw , fraction
fw, fraction
0
0.5
1
1.5
2
2.5
0.40.50.60.7
Sw , fraction
dfw/dSw
563.0S
w
=
469.0S
wf
=

111. 1/19/2011Waterflooding/Introduction
49
Other Prediction Methods
Example waterflood performance with time for 5-spot pattern
Calculation of mobility ratio ;
Calculation of ultimate waterflood recovery ;
¾initial stock tank oil in place in a pore volume of 1 barrel;
¾at producing water cut = 98%, remaining oil in 1 bbl is;
8.0)
5.0
0.1
(
0.1
4.0
)S(k
)S(k
/)S(k
/)S(k
M
w
o
wcro
wrw
owcro
wwrw
==
μ
μ
=
μ
μ
=
stb698.0
29.1
90.0
B
S1
B
S
oi
wc
oi
oi
==
−
=
stb278.0
2.1
334.0
B
S1
B
S
o
w
o
o
==
−
=

112. 1/19/2011Waterflooding/Introduction
50
Other Prediction Methods
Example waterflood performance with time for 5-spot pattern
Calculation of ultimate waterflood recovery ;
¾remaining oil in un-swept portion or reservoir in 1bbl;
¾estimate volumetric sweep efficiency using;
¾total oil remaining in 1 bbl is;
¾total oil recovery is:
stb75.0
2.1
90.0
B
S1
B
S
o
wc
o
oi
==
−
=
9375.0
8.0
)5.0(1
M
V1
2 2
=
−
=
−
stb75.075.0*)9375.01(278.0*9375.0
=
−
+
OIIPof%9.55or559.0
698.0
)3075.0698.0(
=
−

113. 1/19/2011Waterflooding/Introduction
52
Other Prediction Methods
Example waterflood performance with time for 5-spot pattern
Composite WOR-recovery performance;
¾Calculate fractional oil recovery at producing WORs of 25, 100;
@ M=0.8

and V=0.5, for WOR=25,
E
R
(1-0.52*S
w
) =.38
E
R
=0.20/(1-0.52*S
w
)=0.38/0.948= 0.400
@ M=0.8

and V=0.5, for WOR=5,
E
R
(1-0.40*S
w
) =.43
E
R
=0.20/(1-0.40*S
w
)=0.43/0.96= 0.459

114. 1/19/2011Waterflooding/Introduction
53
Other Prediction Methods
Example waterflood performance with time for 5-spot pattern
Composite WOR-recovery performance;
¾Tabulate fractional oil recovery at producing WORs of 1, 5, 25, 100;
*-

Primary recovery=10.4
WOR% OIIPWaterflooding RF*
122.211.8
531.220.8
2540.029.6
10045.935.5

115. 1/19/2011Waterflooding/Introduction
54
Other Prediction Methods
Waterflood performance with time for 5-spot pattern
Composite injection and production rates, WOR, and recovery vs time
√

Calculation approach of Craig, Geffen, and Morse

(1955) to relate
oil recovery and producing WOR to cumulative injected water.
√

Correlation of Caudle and Witte

(1959) for calculating five-spot water
injection rates.
√

For layered system with identical properties except permeability,
determine performance of one base layer, for others adjust performance
using permeability contrast.
√

For stratified reservoir with layers differing in k
rw
/k
ro
, performance
of each layer is calculated individually.
√

Composite performance is sum of individual layer performance.

116. 1/19/2011Waterflooding/Introduction
55
Other Prediction Methods
Waterflood performance with time for 5-spot pattern
√

Performance of 5-spot flood approximates that of many other
patterns.
√

Minimum number of layers* of equal thickness required to obtain
performance of 100-layer 5-spot waterflood @ WOR above 2.5.
Mobility
Ratio
Permeability Variation, V
0.10.20.30.40.50.60.70.8
0.05112410202020
0.111241020100100
0.211241020100100
0.512241020100100
1.013341020100100
2.0244102050100100
5.025102050100100100
*Craig, 1970

117. 1/19/2011Waterflooding/Introduction
56
Other Prediction Methods
Waterflood performance with time for 5-spot pattern Minimum number of layers* of equal thickness required to obtain
performance of 100-layer 5-spot waterflood @ WOR above 5.
Mobility
Ratio
Permeability Variation, V
0.10.20.30.40.50.60.70.8
0.0511245101020
0.11124101010100
0.21124101020100
0.51224101020100
1.01234101020100
2.02345101050100
5.02451020100100100
*Craig, 1970

118. 1/19/2011Waterflooding/Introduction
57
Other Prediction Methods
Waterflood performance with time for 5-spot pattern Minimum number of layers* of equal thickness required to obtain
performance of 100-layer 5-spot waterflood @ WOR above 10.
Mobility
Ratio
Permeability Variation, V
0.10.20.30.40.50.60.70.8
0.051112451020
0.11112551020
0.21123551020
0.51123551020
1.011235101050
2.01234101020100
5.0134510100100100
*Craig, 1970

119. 1/19/2011Waterflooding/Introduction
58
Other Prediction Methods
Waterflood performance with time for 5-spot pattern
Composite injection and production rates, WOR, and recovery vs time
√

Water injection with no free gas initially present;
¾determine
¾estimate 1 -ΔN
pu
¾calculate
¾determine ΔN
pu
+ΔN
ps
¾calculate
)SS(E
SS
N
wcwAbt
wc wsz
pu
−
−
λ=Δ
)N1(fN
pu 2ops
Δ
−
=
Δ
)NN(
)NN(1
WOR
pu ps
pu ps
p
Δ+Δ
Δ
+
Δ
−
=

120. 1/19/2011Waterflooding/Introduction
59
Other Prediction Methods
Waterflood performance with time for 5-spot pattern
Composite injection and production rates, WOR, and recovery vs time
√

Water injection with no free gas initially present;
¾determine
¾estimate in swept area
¾calculate
¾determine
¾calculate
op
B*WOR WOR
= wc w
SS
−
gi wcwA
S)SS(E −−
oi
gi wcwA
S
S)SS(E −−
STOIIP*
S
S)SS(E
oi
gi wcwA
−−

121. 1/19/2011Waterflooding/Introduction
60
Other Prediction Methods
Waterflood performance with time for 5-spot pattern
Composite injection and production rates, WOR, and recovery vs time
√

Water injection with no free gas initially present;
¾use k
rw
vs S
w
curve
¾determine M from
¾get from Figure 1
¾calculate i
w
= i
base
¾determine i
w,average
γ
γ

122. 1/19/2011Waterflooding/Introduction
61
Other Prediction Methods
Waterflood performance with time for 5-spot pattern
Composite injection and production rates, WOR, and recovery vs time
√

Water injection with no free gas initially present;
¾determine ΔW
i
¾estimate Δt =
ΔW
i/i
w,average
¾determine t = Σ(Δt)
¾calculate q = i
w
(ΔN
pu
+ ΔN
ps
)/B
o
¾determine i
w,average

123. 1/19/2011Waterflooding/Introduction
62
Other Prediction Methods