Abstract
We report a modeling and numerical simulation study of density-driven natural convection during geological CO2 storage in heterogeneous formations. We consider an aquifer or depleted oilfield overlain by gaseous CO2, where the water density increases due to CO2 dissolution. The heterogeneity of the aquifer is represented by spatial variations of the permeability, generated using Sequential Gaussian Simulation method. The convective motion of the liquid with dissolved CO2 is investigated. Special attention is paid to instability characteristics of the CO2 concentration profiles, variation of mixing length, and average CO2 mass flux as a function of the heterogeneity characterized by the standard deviation and the correlation length of the log-normal permeability fields. The CO2 concentration profiles show different flow patterns of convective mixing such as gravity fingering, channeling, and dispersive based on the heterogeneity medium of the aquifer. The variation of mixing length with dimensionless time shows three separate regimes such as diffusion, convection, and second diffusion. The average CO2 mass flux at the top boundary decreases quickly at early times then it increases, reaching a constant value at later times for various heterogeneity parameters.
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Abbreviations
- A :
-
Aspect ratio of the domain H/L (–)
- A 0 :
-
Amplitude of sinusoidal perturbation
- c :
-
Dimensionless concentration (–)
- c′:
-
Concentration (mol/m3)
- D :
-
Diffusion coefficient (m2/s)
- f (x, z ):
-
Permeability variation function
- F m :
-
Average CO2 mass flux
- g :
-
Acceleration due to gravity (m/s2)
- H :
-
Height of the porous medium (m)
- i and j :
-
Index of the mesh points in x and z direction, respectively
- k :
-
Permeability (m2)
- k 0 :
-
Mean permeability (m2)
- L :
-
Length of the porous medium (m)
- P :
-
Pressure (Pa)
- R a :
-
Rayleigh number (–)
- t :
-
Time (sec)
- t d :
-
Dimensionless time (–)
- u x :
-
Dimensionless x-component velocity (–)
- u z :
-
Dimensionless z-component velocity (–)
- u X :
-
x component velocity (m/s)
- u Z :
-
z component velocity (m/s)
- w :
-
Width of domain (m)
- w(t):
-
Total dissolved CO2 concentration
- x :
-
Dimensionless distance in X coordinate
- Y :
-
Log-normal permeability distribution
- z :
-
Dimensionless distance in Z coordinate
- α :
-
Wave-number
- β c :
-
The volumetric expansion coefficient
- \({\varepsilon}\) :
-
Criteria for convergence
- φ :
-
Porosity (–)
- λ0 :
-
Wavelength of sinusoidal perturbation (–)
- λ:
-
Correlation length scale (m)
- μ :
-
Viscosity of fluid (kg/ms)
- θ :
-
Mean of log permeability
- ψ :
-
Stream function (m3 m−1 s−1)
- ρ 0 :
-
Pure liquid density (kg/m3)
- ρ :
-
Liquid density (kg/m3)
- Δρ :
-
Change in density (kg/m3)
- σ :
-
Standard deviation
- τ x :
-
Horizontal correlation length (m)
- τ z :
-
Vertical correlation length (m)
- SGSIM:
-
Sequential Gaussian Simulation
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Acknowledgments
This study was partly done as part of the CATO II programme. The authors are grateful to the Dutch Ministry of Economic Affaires and the sponsoring companies for funding. The authors are also grateful to the anonymous refereed whose comments and suggestions have help improve manuscript.
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Ranganathan, P., Farajzadeh, R., Bruining, H. et al. Numerical Simulation of Natural Convection in Heterogeneous Porous media for CO2 Geological Storage. Transp Porous Med 95, 25–54 (2012). https://doi.org/10.1007/s11242-012-0031-z
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DOI: https://doi.org/10.1007/s11242-012-0031-z