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8/13/2019 CO2 Injection Paper
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Pressure Buildup atCO2 Injection Wells
Sally M. Benson
Lawrence Berkeley National Laboratory
Berkeley, California 94720
Second Annual Conference on Carbon Sequestration
May 5-8, 2003
Main Menu Technical Sessions Plenary Sessions Poster Presentations Participants
8/13/2019 CO2 Injection Paper
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8/13/2019 CO2 Injection Paper
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Applications
Estimation of injection pressures at CO2
injection wells Pressure transient analysis at CO2 injection
wells
Evaluation of the influence of CO2/water/rock
interactions on formation permeability
Characterization and monitoring of CO2sequestration processes and progress
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Physical Processes During Injection
of CO2 into Water Immiscible displacement of water
by CO2 Relative permeability effects
Capillary pressure effects
Adverse mobility ratio
water>>CO2
Pressure and temperature
dependent CO2 viscosity and
density Partitioning of CO2 into the
water phase
Partitioning of water into theCO2 phase
Relative Permeablity
0
0.2
0.4
0.6
0.8
1
0 0.25 0.5 0.75 1
sw
0
0.2
0.4
0.6
0.8
1krCO2
krw
Relative Permeablity
0
0.2
0.4
0.6
0.8
1
0 0.25 0.5 0.75 1
sw
0
0.2
0.4
0.6
0.8
1krCO2
krw
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Implications for Pressure Buildup
During CO2 Injection
Relative permeability of CO2
and water will vary in theregion behind the CO2-front
Saturation of CO2 and
water will vary in the regionbehind the CO2- front
Saturation Distribution
0
0.2
0.4
0.6
0.8
1
0 50 100 150 200r (m)
Saturation Distribution
0
0.2
0.4
0.6
0.8
1
0 50 100 150 200r (m)
Sharp Front
Relative Pemeability
0
0.2
0.4
0.6
0.8
1
0 50 100 150 200r (m)
Relative Pemeability
0
0.2
0.4
0.6
0.8
1
0 50 100 150 200r (m)
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A New Approximate Analytical Solution
For Pressure Buildup Assumptions
Buckley-Leverett type
displacement
Vertical equilibrium
Horizontal reservoir
Homogeneous reservoir
Neglect capillary pressure
(not required)
Slightly compressible fluid
Based on technique
developed by Benson(1984, 1987)
rw rf
qCO2
hk,ct,
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New Pressure Buildup Solution
Solution consists of two components
Steady state pressure buildup behind the CO2
front (ps.s.) Pressure transient buildup outside of the front
(pt)
)4(4),(
),(
),(
),(
),(
2),(
),(),(),(
2
..
..
2
2
2
2
2
22
kt
cr
Eikh
q
trp
r
dr
trk
tr
tr
trf
kh
q
trp
trptrptrp
twf
CO
wCO
ft
r
CO
r
r CO
COCO
wss
ftwssw
CO
f
w
=
=
+=
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Evaluating p s.s.
r
dr
trk
tr
tr
trf
kh
qtrp
CO
f
w r
CO
r
r CO
COCO
wss ),(
),(
),(
),(
2),(
2
2
2
22
..
=
Density Distribution
After 30 Days of Injection
700
725750
775
800
0 50 100 150
r (m)
CO2
< 10% variation
Density Distribution
After 30 Days of Injection
700
725
750
775
800
0 50 100 150
r (m)
CO2
< 10% variation
Viscosity Distribution
After 30 Days of Injection
6.0E-05
6.5E-057.0E-05
7.5E-05
8.0E-05
0 50 100 150
r (m)
CO2
< 10% variation
Viscosity Distribution
After 30 Days of Injection
6.0E-05
6.5E-05
7.0E-05
7.5E-05
8.0E-05
0 50 100 150
r (m)
CO2
< 10% variation
Assign average values for and behind the front
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Multi-phase Flow Behind the CO2 Front
22
2
2
2
2
CO
CO
sCO
CO
CO
CO
ss
f
h
tqr
=
)(
)(1
1)(
22
22
2
22
COrw
wrCOCOw
CO
COCO
sk
skqq
qsf
CO
w
+
=+
=
Fractional Flow of CO2
0.00
0.20
0.40
0.60
0.80
1.00
0 0.2 0.4 0.6
sCO2
sf
Fractional Flow of CO2
0.00
0.20
0.40
0.60
0.80
1.00
0 0.2 0.4 0.6sCO2
sf
Buckley-Leverett Solution
Saturation Distribution
0
0.2
0.4
0.6
0.8
1
0 50 100 150 200r (m)
Saturation Distribution
0
0.2
0.4
0.6
0.8
1
0 50 100 150 200
r (m)
Buckley-Leverett Solution
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Evaluating p s.s.
r
dr
trk
trf
kh
qtrp
f
w CO
r
r r
CO
CO
COCO
wss =),(
),(
2
),(
2
2
2
22
..
CO2 Saturation
After 30 Days
0.0
0.5
1.0
0 50 100 150
r (m)
Numerical
Buckley Leverett
CO 2 Saturation
After 30 Days
0.0
0.5
1.0
0 50 100 150
r (m)
Numerical
Buckley Leverett
fCO2/krCO2 30 Days
0.00
10.00
20.00
30.00
40.00
0 50 100 150
r (m)
fCO2/krCO230 Days
0.00
10.0020.00
30.00
40.00
0 50 100 150
r (m)
Assign a linear variation for fCO2/krCO2 behind the front
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Approximate Analytical Solution),(),(),( .. trptrptrp ftwssw +=
+=
+=
80907.ln4
),(
ln11ln2
),(
2
..
2
2
2
2
2
22
ftwCO
wCOft
w
f
wf
w
rr
CO
w
f
CO
COCOwss
rckt
khqtrp
rr
rrr
k
f
rr
kh
qtrp
fCO
rsCO2=
Qt
h
fCO2
sCO2 sCO2
Fractional Flow of CO2
0.00
0.25
0.50
0.75
1.00
0 0.2 0.4 0.6
sCO2
sf
Fractional Flow of CO2
0.00
0.25
0.50
0.75
1.00
0 0.2 0.4 0.6s
CO2
sf
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Typical Pressure Buildup
195
197
199
201
203
0 30 60 90 120 150 180
time (days)
Pressure
(bars)
k = 100 mD
h = 20 mqCO2= 15.86 kg/s
initial pressure = 150 bars
CO2= 6.5 e-5 Pa-s
CO2= 715 kg/m3porosity = 0.12195
197
199
201
203
0 30 60 90 120 150 180
time (days)
Pressure
(bars)
k = 100 mD
h = 20 m
qCO2= 15.86 kg/s
initial pressure = 150 bars
CO2= 6.5 e-5 Pa-s
CO2= 715 kg/m3
porosity = 0.12
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Semi-log Plot
195
197
199
201
203
0.10 1.00 10.00 100.00 1000.00
time (days)
Pressure(bars)
0.5
0.7
0.9
1.1
1.3
1.5
S
lope(ba
rs)
Pressure Buildup
Slope
195
197
199
201
203
0.10 1.00 10.00 100.00 1000.00
time (days)
P
ressure
(bars)
0.5
0.7
0.9
1.1
1.3
1.5
Slope(b
ars)
Pressure Buildup
Slope
kh
qm
CO
COCO
2
22
4
=
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How Good Is the Approximate Solution?
Comparison to numerical simulation generated using
TOUGH2 (Pruess et al., 2001)
Pressure Buildup
190
195
200
205
210
0.01 0.10 1.00 10.00 100.00time (days)
Pressure(bars)
Numerical
sf=0.225
sf=0.23
Pressure Buildup
190
195
200
205
210
0.01 0.10 1.00 10.00 100.00time (days)
Press
ure(bars)
Numerical
sf=0.225
sf=0.23
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Summary A new approximate analytical solution for
predicting pressure buildup during CO2 injection
into brine formations has been developed
Comparison to numerical simulations verifies the
applicability of this solution to typical CO2
sequestration scenarios Pressure transient analysis may provide a useful
tool for monitoring CO2 sequestration operations,
including: Validation of multiphase flow processes
Front tracking
Detection of permeability changes from CO2 injection
Recommended