Abstract
The injection of supercritical CO2 in deep saline aquifers leads to the formation of a CO2 plume that tends to float above the formation brine. As pressure builds up, CO2 properties, i.e. density and viscosity, can vary significantly. Current analytical solutions do not account for CO2 compressibility. In this article, we investigate numerically and analytically the effect of this variability on the position of the interface between the CO2-rich phase and the formation brine. We introduce a correction to account for CO2 compressibility (density variations) and viscosity variations in current analytical solutions. We find that the error in the interface position caused by neglecting CO2 compressibility is relatively small when viscous forces dominate. However, it can become significant when gravity forces dominate, which is likely to occur at late times of injection.
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Abbreviations
- c r :
-
Rock compressibility
- c α :
-
Compressibility of fluid α (α = c, w)
- d :
-
Aquifer thickness
- E rel :
-
Relative error of the interface position
- g :
-
Gravity
- h w :
-
Hydraulic head of water
- k :
-
Intrinsic permeability
- \({k_{{\rm r}_\alpha}}\) :
-
α-Phase relative permeability (α = c, w)
- N :
-
Gravity number
- \({P_{{\rm t}_0}}\) :
-
Fluid pressure at the top of the aquifer prior to injection
- P DT :
-
Fluid pressure for Dentz and Tartakovsky (2009a) approach
- \({\overline{P}_{\rm DT}}\) :
-
Vertically averaged fluid pressure for Dentz and Tartakovsky (2009a) approach
- \({\overline{P}_{\rm N}}\) :
-
Vertically averaged fluid pressure for Nordbotten et al. (2005) approach
- \({\overline{P}_{0}}\) :
-
Vertically averaged fluid pressure prior to injection
- P α :
-
Fluid pressure of α-phase (α = c, w)
- Q m :
-
CO2 mass flow rate
- Q 0 :
-
CO2 volumetric flow rate
- q α :
-
Volumetric flux of α-phase (α = c, w)
- R :
-
Radius of influence
- R c :
-
CO2 plume radius at the top of the aquifer for compressible CO2
- R i :
-
CO2 plume radius at the top of the aquifer for incompressible CO2
- r :
-
Radial distance
- r 0 :
-
CO2 plume radius at the top of the aquifer
- r b :
-
CO2 plume radius at the base of the aquifer
- r c :
-
Characteristic length
- r w :
-
Injection well radius
- S s :
-
Specific storage coefficient
- \({S_{{\rm r _w}}}\) :
-
Residual saturation of the formation brine
- S α :
-
Saturation of α-phase (α = c, w)
- t :
-
Time
- z :
-
Vertical coordinate
- z 0 :
-
Depth of the top of the aquifer
- z b :
-
Depth of the base of the aquifer
- V :
-
CO2 plume volume
- α :
-
Phase index, c CO2 and w brine
- β :
-
CO2 compressibility
- \({\epsilon_{\rm v}}\) :
-
Volumetric strain
- γ cw :
-
A dimensionless parameter that measures the relative importance of viscous and gravity forces
- λ α :
-
Mobility of α-phase (α = c, w)
- μ α :
-
Viscosity of α-phase (α = c, w)
- ρ 0 :
-
CO2 density at the reference pressure \({P_{\rm t_0}}\)
- ρ 1 :
-
Constant for the CO2 density
- \({\overline{\rho}_{\rm c}}\) :
-
Mean CO2 density
- \({\overline{\rho}_{{\rm c}_{\rm DT}}}\) :
-
Mean CO2 density for Dentz and Tartakovsky (2009a) approach
- \({\overline{\rho}_{{\rm c}_{\rm N}}}\) :
-
Mean CO2 density for Nordbotten et al. (2005) approach
- ρ α :
-
Density of α-phase (α = c, w)
- σ′:
-
Effective stress
- \({\phi}\) :
-
Porosity
- ζ :
-
Interface position from the bottom of the aquifer
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Vilarrasa, V., Bolster, D., Dentz, M. et al. Effects of CO2 Compressibility on CO2 Storage in Deep Saline Aquifers. Transp Porous Med 85, 619–639 (2010). https://doi.org/10.1007/s11242-010-9582-z
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DOI: https://doi.org/10.1007/s11242-010-9582-z