Pressure Buildup at CO2 Injection Wells
Sally M. BensonLawrence Berkeley National Laboratory
Berkeley, California 94720
Second Annual Conference on Carbon SequestrationMay 5-8, 2003
Abstract
An approximate analytical solution for calculating pressure buildup at CO2 injection wells has been developed. It can be used to rapidly calculate the pressure buildup during injection, as well as, the rate of pressure falloff once injection stops. The solution includes the influence of the advancing CO2 front, changes in the permeability of the near-well region due to chemical reactions between the CO2 and reservoir rock, and temperature dependent viscosity. The approximate solution can be used for both open and closed systems. In addition, it can be used as the basis for designing and interpreting pressure tests as a method of monitoring the progress of CO2 injection operations.
Applications
• Estimation of injection pressures at CO2injection 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
Physical Processes During Injectionof CO2 into Water
• Immiscible displacement of water by CO2• Relative permeability effects• Capillary pressure effects• Adverse mobility ratio
µwater >>µCO2
• Pressure and temperature dependent CO2 viscosity and density
• Partitioning of CO2 into the water phase
• Partitioning of water into the CO2 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
Implications for Pressure BuildupDuring CO2 Injection
⇒ Relative permeability of CO2and water will vary in the region behind the CO2-front
Saturation of CO2 and water will vary in the region
behind the CO2- front
Saturation Distribution
00.20.40.60.8
1
0 50 100 150 200r (m)
Saturation Distribution
00.20.40.60.8
1
0 50 100 150 200r (m)
Sharp Front
Relative Pemeability
00.20.40.60.8
1
0 50 100 150 200r (m)
Relative Pemeability
00.20.40.60.8
1
0 50 100 150 200r (m)
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,φ
∞
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
ktcr
Eikhq
trp
rdr
trktr
trtrf
khq
trp
trptrptrp
twf
CO
wCOft
r
COr
r CO
COCOwss
ftwssw
CO
f
w
φµρπµ
µρπ
=∆
=∆
∆+∆=∆
∫
Evaluating ∆p s.s.
rdr
trktr
trtrf
khq
trpCO
f
w r
COr
r CO
COCOwss ),(
),(),(),(
2),(
2
2
2
22..
µρπ ∫=∆
Density DistributionAfter 30 Days of Injection
700725750775800
0 50 100 150r (m)
CO
2< 10% variation
Density DistributionAfter 30 Days of Injection
700725750775800
0 50 100 150r (m)
CO
2< 10% variation
Viscosity DistributionAfter 30 Days of Injection
6.0E-056.5E-057.0E-057.5E-058.0E-05
0 50 100 150r (m)
CO
2
< 10% variation
Viscosity DistributionAfter 30 Days of Injection
6.0E-056.5E-057.0E-057.5E-058.0E-05
0 50 100 150r (m)
CO
2
< 10% variation
Assign average values for ρ and µ behind the front
Multi-phase Flow Behind the CO2 Front
22
2
2
2
2
CO
CO
sCO
CO
CO
COs s
fhtq
r∂∂
ρπφ=
)()(
1
1)(
22
22
2
22
COrw
wrCOCOw
COCOCO
skskqq
qsf
CO
w
µµ
+=
+=
Fractional Flow of CO2
0.00
0.20
0.40
0.60
0.80
1.00
0 0.2 0.4 0.6sCO2
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
00.20.40.60.8
1
0 50 100 150 200r (m)
Saturation Distribution
00.20.40.60.8
1
0 50 100 150 200r (m)
Buckley-Leverett Solution
Evaluating ∆p s.s.
rdr
trktrf
khq
trpf
w CO
r
r r
CO
CO
COCOwss ∫=∆
),(),(
2),(
2
2
2
22.. ρπ
µ
CO2 Saturation After 30 Days
0.0
0.5
1.0
0 50 100 150r (m)
Numerical
Buckley Leverett
CO2 Saturation After 30 Days
0.0
0.5
1.0
0 50 100 150r (m)
Numerical
Buckley Leverett
fCO2/krCO2 30 Days
0.0010.0020.0030.0040.00
0 50 100 150r (m)
fCO2/krCO2 30 Days
0.0010.0020.0030.0040.00
0 50 100 150r (m)
Assign a linear variation for fCO2/krCO2 behind the front
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
khq
trp
rr
rrr
kf
rr
khq
trpf
CO
φµρπµ
ρπµ
rsCO2 =Qtπφh
∂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 0.6
sCO2
sf
Typical Pressure Buildup
195
197
199
201
203
0 30 60 90 120 150 180time (days)
Pres
sure
(bar
s)
k = 100 mDh = 20 mqCO2 = 15.86 kg/sinitial pressure = 150 barsµCO2 = 6.5 e-5 Pa-sρCO2 = 715 kg/m3
porosity = 0.12195
197
199
201
203
0 30 60 90 120 150 180time (days)
Pres
sure
(bar
s)
k = 100 mDh = 20 mqCO2 = 15.86 kg/sinitial pressure = 150 barsµCO2 = 6.5 e-5 Pa-sρCO2 = 715 kg/m3
porosity = 0.12
Semi-log Plot
195
197
199
201
203
0.10 1.00 10.00 100.00 1000.00time (days)
Pres
sure
(bar
s)
0.5
0.7
0.9
1.1
1.3
1.5
Slop
e (b
ars)
Pressure BuildupSlope
195
197
199
201
203
0.10 1.00 10.00 100.00 1000.00time (days)
Pres
sure
(bar
s)
0.5
0.7
0.9
1.1
1.3
1.5
Slop
e (b
ars)
Pressure BuildupSlope
khq
mCO
COCO
2
22
4 ρπµ
=
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)
Pres
sure
(bar
s)
Numericalsf=0.225sf=0.23
Pressure Buildup
190
195
200
205
210
0.01 0.10 1.00 10.00 100.00time (days)
Pres
sure
(bar
s)
Numericalsf=0.225sf=0.23
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 CO2sequestration 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
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