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SINTEF Petroleum Research
Modelling blow-out from a CO2 well
Erik LindebergSINTEF Petroleum Research
Trondheim CCS-6 14. - 16. June 2011
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SINTEF Petroleum Research 2
Objective
To model multi-phase CO2 flow in a blow-out situation taking into account Phase changes occur along the well Heat is exchanged between the rock and the flowing CO2
Accurate modelling of the strong adiabatic cooling due to expansion (while reservoir condition has been simplified)
Suggest possible experiments that could verify modelling
SINTEF Petroleum Research
Application on the Sleipner CO2injection well 15/9-A16
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0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
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25
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31
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0 100 200 300
Volu
me
fract
ion
gas
in w
ell s
tream
CO
2te
mpe
ratu
re, °
C
Depth from well head, m
Temperature in well
Volume fraction of gas in well stream
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
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25
26
27
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29
30
31
32
0 100 200 300
Volu
me
fract
ion
gas
in w
ell s
tream
CO
2te
mpe
ratu
re, °
C
Depth from well head, m
Temperature in well
Volume fraction of gas in well stream
Two phaseflow at the well head is the typical injection situation
SINTEF Petroleum Research 4
Basic equations Bernoulli equation:
Energy balance in the fluid:
Heat flow:
Combining heat flow and the adiabatic contribution
Integrating along direction of flow:
Boldizar (1958) :
2
sin4
dp dv vg v fdz dz r
ρρ α ρ= + +
sin 0dH dv Qv gdmdz dz dt
α+ + + =
, ( , , )Q KF F F D t rτ= =
( ) ( ),
ad
p p
dTdzd KF KFs s b where b and s
dmdz b dldmc cdt dt
στ τ τ
− = − = − = =
( )0bdls e sτ τ= − +
2
44 / ln , 0.5772.. (Eulers const.)DtFrγπ γ ≈ =
SINTEF Petroleum Research 5
Numerical solution by discretizing the well into length steps (typically < 1000). At each step the flow equation is solved analytically
A rate is applied at the perforation and the corresponding pressure is calculated at the well head
Phase regimes has to be located to avoid a single step to cross the phase boundary.
The rate is iteratively altered until the desired blow-out pressure is reached (typically 1 atmosphere)
Solution method
SINTEF Petroleum Research 6
Perforation depth: 1092 m (from well head)Length: 3100 m Radius: 0.1 mAdiabatic section: 160 m (platform leg)Reservoir conditions: 106 bar, 37 °C
Well features
CO2
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Perforation depth: 1092 m (from well head)Length: 1092 m Radius: 0.1 mAdiabatic section: 160 m (platform leg)Reservoir conditions: 106 bar, 37 °C
Well featuresVertical well
CO2
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Temperature and pressure profiles
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Phase diagram for CO2 in the p and T space
0
20
40
60
80
100
120
140
160
180
-90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40
Pres
sure
, bar
Temperature, °C
Triple pointCritical pointMelting curveSublimation curveDew point curve
LiquidGas
Solid
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p-T path along deviated well
0
20
40
60
80
100
120
140
-90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50
Pres
sure
, bar
Temperature, °C
p-T path along wellTriple pointCritical pointMelting curveSublimation curveDew point curveReservoir condition
LiquidGas
Solid
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Condensed phase fraction in well
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CO2 heat capacity, cp, and total density of as function of depth
0
100
200
300
400
500
600
700
800
0
2000
4000
6000
8000
10000
12000
14000
0 100 200 300 400 500 600 700 800 900 1000 1100
Den
sity
of C
O2,
kg/m
3
Hea
t cap
aciy
, cp,
J/(k
g K
)
Depth from well head, m
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CO2 densities along the well
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Solubility of H2O in CO2If CO2 is saturated at reservoir conditions - free water will be present in the well
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Phase diagram for CO2 in the p and T space
0
20
40
60
80
100
120
140
160
180
-90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40
Pres
sure
, bar
Temperature, °C
Triple pointCritical pointMelting curveSublimation curveDew point curveHydrate curve
Liquid
Gas
SolidCO2 ice
SINTEF Petroleum Research
Summary of some cases
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WellReservoirconditions Blow out
Massrate
Blow out speed
Blow out temp.
Depthsublimation
Depthgas+liquid
Depth hydrate
bars °C kg/s m/s °C m m m
Vertical 106 37 Well head 244 1165 -81.2 4.7 671 356
Deviated 106 37 Well head 181 935 -79.3 5.8 848 544
Vertical 106 37 Sea floor1) 284 183 -45.8 704 428
Deviated 106 37 Sea floor1) 195 150 -47.5 874 620
Vertical 130 37 Well head 313 1586 -97.1 3.7 465 252
Deviated 130 37 Well head 225 1374 -96.1 26.2 698 440
Johansen 220 100 Well head 268 1232 -74.8 2.2 389 205
1) Sea depth 82 m giving a blow out pressure of ~ 8.2 bars
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p-T path along deviated well “Johansen”
SINTEF Petroleum Research
Conclusions The injection well approaches adiabatic conditions relatively
fast, i.e. the transient heat effect can then be neglected Stored CO2 will be water saturated (0.01 – 0.02 mole fraction
H2O) and solubility will decrease up along the well. At clogging due to hydrates (or unlikely dry ice) heat transfer
from the rock will melt the plugs and cause the release pulse step release.
The recent fast CO2 release tests in Germany from a pipe 10 000 tonne per 10 hours = 278 kg/s are in the range of typical
blow-out rate from wells This test lack the gravity effect Are approximately adiabatic This suggest similar tests to be performed on an abounded well
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