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Dissolution and Residual Trapping:Dissolution and Residual Trapping:Length & Time Scales of Trapping Processes Length & Time Scales of Trapping Processes
Hamdi TchelepiEnergy Resources Engineering, Stanford
SIAM Lecture Series, Stanford
May 7, 2009 SIAM 2
Acknowledgement
• Marc Hesse– Ph.D at Stanford– Post-doc at Brown– Going to UT GeoSciences
• Amir Riaz
– Post-doc & RA at Stanford
– Now at College Park, U. of Maryland
May 7, 2009 SIAM 3
Outline
• CO2 storage• Leakage vs. trapping• Trapping processes
• Models for limiting cases
• Length & time scales• Site selection & numerical simulation
May 7, 2009 SIAM 4
King Coal!King Coal!
“Every week or so inthe next 5 years, anew coal-fired powerstation will be built inChina. ”(FT 22 Jan. 2007)
May 7, 2009 SIAM 5
Coal and CCS!Coal and CCS!
“Carbon capture and storage technology is the only way forward as China and India will inevitably burn their cheap coal.”
(Sir David King FRS, Chief Scientific Advisor U.K., BBC 12/6/05)
May 7, 2009 SIAM 6
COCO22 StorageStorage
porous formation
injection well1-3 km deep
May 7, 2009 SIAM 7
COCO22 StorageStorage
Geological storage options:1. Deep saline aquifers2. Oil & gas fields3. Coal beds
Saline Aquifers
IPCC, 2005
10,0001,000Saline aquifers
2003–15Coal seams
900a675aOil and gas fields
Upper Estimate of Global Storage Capacity
(billion t CO2)
Lower Estimate of Global Storage Capacity
(billion t CO2)
Reservoir Type
May 7, 2009 SIAM 9
Saline AquifersSaline Aquifers
Schl
umbe
rger
, O
il Fi
eld
Glo
ssar
y
large CO2 storage volumes + source/sink matching
May 7, 2009 SIAM 10
Outline
• CO2 storage• Leakage vs. trapping• Trapping processes
• Models for limiting cases
• Length & time scales• Site selection & numerical simulation
May 7, 2009 SIAM 11
Injected COInjected CO22 is Buoyant!is Buoyant!
from:
(Ide et al. 2007)
500 1000 1500 2000 2500 30000.3
0.4
0.5
0.6
0.7
0.8
GeothermalGradient: 25 C/kmde
nsity
CO
2 /
dens
ity b
rine
depth [m]
May 7, 2009 SIAM 12
COCO22 LeakageLeakage
Old well
Fault
Seal
May 7, 2009 SIAM 13
Outline
• CO2 storage• Leakage vs. trapping• Trapping processes
• Models for limiting cases
• Length & time scales• Site selection & numerical simulation
May 7, 2009 SIAM 14
Definition Trapping ProcessDefinition Trapping Process
Cause of Leakage:CO2 is buoyant & mobile
Trapping Process:Physical or chemical process that either makes CO2 immobile ormakes CO2 negatively buoyant
May 7, 2009 SIAM 15
3 Trapping Processes3 Trapping Processes
2.2 mm
1) Residual Trapping 3) Mineral trapping
(Benson et al. 06)
2) Dissolution Trapping
(Riaz et al. 06) Ankerite(www.mindat.org)
10 m 1 cm
May 7, 2009 SIAM 16
Evolution of COEvolution of CO22
dissolution of residual CO2
min
eral
trap
ping
mineralizedCO2
leakedCO2
dissolution
tapping
dissolvedCO2
residual trapping
residualCO2
injectedCO2
primarytrapping
secondarytrapping
May 7, 2009 SIAM 17
Primary TrappingPrimary Trapping
dissolution
tapping
dissolvedCO2
residual trapping
residualCO2
injectedCO2
primarytrapping
How long does it take to trap the injected CO2?
May 7, 2009 SIAM 18
Outline
• CO2 storage• Leakage vs. trapping• Trapping processes
• Models for limiting cases
• Length & time scales• Site selection & numerical simulation
May 7, 2009 SIAM 19
Dissolution of a Stationary CO2 Plume
Riaz, Hesse, Tchelepi & Orr (2006) J. Fluid Mech., 548, pp. 87-111Hesse, Riaz & Tchelepi (2007) Geochim. Cosmochim. Acta, 71, (15A), A410 Suppl.
May 7, 2009 SIAM 20
Unstable Diffusive Boundary LayerUnstable Diffusive Boundary Layer
CO2
dissolved CO2
May 7, 2009 SIAM 21
Simplified ProblemSimplified Problem
C = Ceq
0 u
gzPK
u
CDCut
C 2
C0
D
HgKRa
Experiment by Elder (1967)Experimental observation:
Critical time for the onset of convection
May 7, 2009 SIAM 22
ApproachApproach
Linear Stability Theory: (JFM 548)Onset of the instabilityCritical time & wavelength
High-Resolution Simulation:Investigate the full nonlinear evolutionLong-term dissolution rates!
May 7, 2009 SIAM 23
Linear Stability ResultsLinear Stability Results
11 , akt
dt
da
0),(),(1
),(2
ktFktFk
Ra
k
tkt
Stability problem reduces to scalar ode:
• Large Ra and t lead to instability ( > 0)
• Always stable initially critical time tc
Explicit expression for growth rate:
May 7, 2009 SIAM 24
Important ScalesImportant Scales
Time and length scales:
1) Critical time:
2) Critical wavelength:
High-K aquifer: tc < 1 yr, c < 1 m
KgK
Dc
190
2
21
146K
DgK
tc
2
1
K
K
1
May 7, 2009 SIAM 25
HighHigh--Resolution SimulationResolution Simulation
= 7.3 = 14.6 = 22.0 = 29.0
CO2 Concentration Maps0 1
4
Concentration of dissolved C
O2
May 7, 2009 SIAM 26
Steady State FluxSteady State Flux
017.0d
dC
Dis
solv
ed C
O2
dimensionless timedimensionless time
May 7, 2009 SIAM 27
Convective Dissolution TimescaleConvective Dissolution Timescale
H = 20 Sc = 0.8, c = 700 kg/m3
critical time:
time to dissolve all CO2:
permeability K: 30 mD 500 mD 2 D
2
825 150 65 yrs
0 0 yrs
porosity : 0.1 0.15 0.2
May 7, 2009 SIAM 28
Gravity Currents with Residual Trapping
Hesse, Tchelepi & Orr (2007), J. Fluid Mech. , 577, pp. 363-383
Hesse, Orr & Tchelepi (2008), J. Fluid Mech. 611, pp. 35-60
May 7, 2009 SIAM 29
Residual Trapping of COResidual Trapping of CO22
May 7, 2009 SIAM 30
Residual Trapping of COResidual Trapping of CO22
May 7, 2009 SIAM 3131
Residual Trapping of COResidual Trapping of CO22
May 7, 2009 SIAM 32
Residual Trapping of COResidual Trapping of CO22
May 7, 2009 SIAM 33
Residual Trapping of COResidual Trapping of CO22
May 7, 2009 SIAM 34
COCO22 Storage in Sloping AquifersStorage in Sloping Aquifers
May 7, 2009 SIAM 35
Sweep is ImportantSweep is Important
SH
hr
Hhr
S cr
c
S
Vx
maxVertical Sweep:
immobile residual CO2 mobile CO2 plume
brine
May 7, 2009 SIAM 36
VerticalVertical EqbmEqbm. & Sharp Interface. & Sharp Interface
ttxxQtxQSxh ccbr )),(),(()1( crSxh
May 7, 2009 SIAM 37
11M
1
f
Governing EquationGoverning Equation
ff
Pe1
ff
Pe
11
0;1
0;1
Hh 0Lx
)sin( 10
L
t
tanPe0
0
H
L
Pe
rb
b
c
rc
k
k
M
M
br
cr
S
S
1
Dimensionless height & distance:
Diffusive timescale: )cos( 1
20
HL
t
Advectivetimescale:
Discontinuouscoefficient:
flux function:
Governing parameters:
Pe
May 7, 2009 SIAM 38
Horizontal AquifersHorizontal Aquifers
May 7, 2009 SIAM 39
Horizontal Aquifer (JFM 577)Horizontal Aquifer (JFM 577)
May 7, 2009 SIAM 40
Horizontal AquiferHorizontal Aquifer
similarity solutions for (Barenblatt 1996)
footprint of the plume:
x t
plume volume:
t 3
power-law decay
May 7, 2009 SIAM 41
Sloping AquifersSloping Aquifers
May 7, 2009 SIAM 42
Hyperbolic ModelHyperbolic Model
ff
Pe
11Adv. timescalelimit Pe → :
Use MOC to solve:
Consider flux function:
11M
1
f
= 50, Pe = 2
May 7, 2009 SIAM 43
Flux FunctionFlux Function
0
1
0;1
0;1
May 7, 2009 SIAM 44
Wave InteractionWave Interaction
: distance
:
tim
e
44
May 7, 2009 SIAM 45
Effect of ResidualEffect of Residual
May 7, 2009 SIAM 46
Mobile COMobile CO22
May 7, 2009 SIAM 47
A Little Slope Goes a Long WayA Little Slope Goes a Long Way
May 7, 2009 SIAM 48
Outline
• CO2 storage• Leakage vs. trapping• Trapping processes
• Models for limiting cases
• Length & time scales• Site selection & numerical simulation
May 7, 2009 SIAM 49
CO2 Storage at Sleipner
Odin's magical eight-legged steed The first commercial
CO2 storage project
May 7, 2009 SIAM 50
CO2 Dissolution at Sleipner
(Chadwick et al. 2004)
+ Large volume
400km x 50-100km100 – 200m
High permeability
~ 0.3K ~ 3 Darcy
= Efficient dissolution
(Lindeberg & Bergmo 2003)
5,000 – 50,000 years
May 7, 2009 SIAM 51
CarrizoCarrizo--Wilcox Aquifer, TXWilcox Aquifer, TX
1/5 of the CO2 emissions from coal power stations in Texas
1 MtCO2/yr/well, 50 injection wells spaced 1 mile
displacement is approximately 2 dimensional
Nic
ot(2
007)
May 7, 2009 SIAM 52
Time for Residual TrappingTime for Residual Trapping
Assuming: H = 200 m, W = 80 km, L = 10km = 0.15, K = 500 mD, = 1.5°c = 0.08 kg/m/s, b = 0.8 kg/m/s,Src = Srb = krc = 0.2,
Parameters: M = 5, = 0.25, Pe = 1.4
Trapping time: 1550 years
Migration distance: 800 km
May 7, 2009 SIAM 53
Outline
• CO2 storage• Leakage vs. trapping• Trapping processes
• Models for limiting cases
• Length & time scales• Site selection & numerical simulation
May 7, 2009 SIAM 54
Implications: Site SelectionImplications: Site Selection
1. Trapping is driven by fluid mechanics! High permeability aquifers
2. Convective dissolution is fast in open system! Aquifers larger than dissolved CO2 volume
3. Residual trapping efficient in sloping aquifers! Structural trap may not be necessary Bad sweep leads to long migration distances
May 7, 2009 SIAM 55
Implications: SimulationImplications: Simulation
1. Plume is a travelling wave! Very large simulation domains
2. Gravity tongue is very thin 1 grid block Low resolution increases sweep Overestimate residual trapping
3. Convection has short wave length 0.1 m Low resolution delays onset & reduces diss. rate Underestimate dissolution trapping
4. Scales of 7-8 orders magnitude!
May 7, 2009 SIAM 56
Research Areas
• Investigation of post-injection miscible & immiscible CO2-Brine systems
• Consistent modeling of multiscale & multi-physics
• Uncertainty quantification of dynamic predictions
May 7, 2009 SIAM 57
DisclaimerDisclaimer
model reality
“All aquifers discussed in here are fictional. Any similarity to real aquifers, intended for storage or not, is strictly a coincidence.”
Parameter Space
