The Ultimate Fate of CO 2 Trapping Timescales Marc Hesse
Collaborators Hamdi Tchelepi Lynn Orr Brian Cantwell Amir Riaz All errors are undoubtedly the result of my failure to follow their advice. 2
Menu Trapping Processes in CO 2 storage Dissolution Trapping - onset of convection - dissolution rate Residual Trapping - Horizontal Aquifer - Sloping Aquifer Summary 3
Injected CO 2 is buoyant! density CO 2 / density brine 0.8 0.7 0.6 0.5 0.4 20 C /km 25 C /km 30 C /km 0.3 500 1000 1500 2000 2500 3000 from: depth [m] (Ide et al. 2007) 4
CO 2 Trapping Processes Residual 2.2 mm (Benson et al. 06) rock grain water CO 2 Dissolved (Riaz, Hesse et al. 06) Mineralized unstable diffusive boundary layer brine fingers of dissolved CO 2 NaAlCO 3 (OH) 2 5
States of CO 2 in Subsurface leaked CO 2 dissolved CO 2 mineral trapping mineralized CO 2 dissolution tapping injected CO 2 residual trapping dissolution of residual CO 2 residual CO 2 6
Dissolution Trapping
Dissolved CO 2 Increases Brine Density linear relationship (Yang & Gu 2006) 8
Important Scales Time and length scales: 1) Critical time: 2) Critical wavelength: t c 2 146φμ D = 1 2 2 ( KΔρg) K 2πμD 1 λc = 0.07KΔρg K permeability K is the important factor high-k aquifers: t c ~ 1 yr, and λ c ~ 1 m (Riaz, Hesse et al. 2006) 9
Numerical Resolution? 10m x 13m 7km x 10km x 30m supercritical CO 2 dissolved CO 2 brine Mesh size: 3cm x 4cm grid blocks: 80.000 Onset time: 2yrs 100m x 100m x 2m 350.000 100yrs (Lindeberg & Bergmo 2003) 10
Open Aquifers CO 2 Concentration Maps: Evolution of Dissolution Rate: τ = 7.3 τ = 14.6 τ = 22.0 τ = 29.0 11
Closed Aquifer 12
CO 2 Dissolution at Sleipner high permeability + large volume = efficient dissolution φ ~ 0.3 K ~ 3 Darcy 400km x 50-100km 100 200m (Chadwick et al. 2004) 5,000 50,000 years (Lindeberg & Bergmo 2003) 13
Residual Trapping
Microscopic & Marcoscopic (Benson et al. 2006) (Doughty et al. 2006) How much is left behind? residual saturation How much of the aquifer is contacted? sweep 15
Derivation ΔhΔxφ(1 S wr ) = ( Q g ( x, t) Q g ( x + Δx, t)) Δt ΔhΔxφS gr 16
Non-Dimensional Form η = h η + τ Pe H Pe σ ξ η = L H 0 0 ξ = x L 0 η(1 η) η(1 η) η = ( ) + σ M 1 1 ξ η( M 1) + 1 ξ 1; ητ σ = 1 ε ; ητ > Sgr tanθ ε = 1 S wr τ = 0 0 t 2 L0 ( κ 1 H cosθ ) M = krg μ g μ k w rw 17
Horizontal Aquifer S gr = S wr = 0.2 L 0 = 2000 m H 0 = 200 m θ = 0 (M = 0) 18
Volume Decay Horizontal Aquifer volume: V t 3β-1 tip pos.: x tip t β height: h t 2β-1 (Bear & Ryzhik 1998) 19
Sloping Aquifer 20
Analytic model for large Pe τ = 50, ε = 0, Pe = 2 M = 20 M = 12 M=20 M=1 M=0 M = 4 M = 1 M = 0 numerical solution full equation analytical solution hyperbolic limit η + σ τ ξ η η(1 η) σ η(1 η) η = ( ) + 0 M 1 1 Pe ξ η( M 1) + 1 ξ 21
Evolution of Footprint τ: time back front ξ: distance 22
Volume Decay Sloping Aquifer 23
Numerical Solutions 24
Residual Trapping in Alberta Basin (Bachu et al. 2002) (Bachu & Bennion 2007) 25
Summary: Dissolution Trapping vigorous convection in high permeability aquifers linear dissolution rate in large open aquifers dissolution likely to be important at Sleipner convective dissolution is numerical challenge 26
Summary: Residual Trapping power-law plume decay in horizontal aquifers rapid plume decay in sloping aquifers residual trapping likely to be important in Alberta thin gravity tongues are numerical challenge 27
Disclaimer model reality All aquifers discussed in this presentation are fictional. Any similarity to real aquifers, intended for storage or not, is strictly a coincidence. 28
References Dissolution Trapping: Hesse, Riaz & Tchelepi (2006) Resolving density fingering during CO 2 sequestration: A challenge for reservoir simulation, Proceedings, CO2SC 2006 Riaz, Hesse, Tchelepi & Orr (2006) Onset of convection in a gravitationally unstable diffusive boundary layer in porous media, JFM., 548, pp. 87-111 Residual Trapping: Hesse, Tchelepi & Orr (in prep) Gravity Currents with residual trapping in sloping aquifers Hesse, Tchelepi, Cantwell & Orr (2006) Gravity currents in horizontal porous media: transition from early to late self-similarity, JFM 577, pp. 363-383 Hesse, Tchelepi & Orr (2006) Scaling Analysis of the migration of CO 2 in saline aquifers, SPE 102796 29