Linear Stability Analysis of Double-Diffusive Convection in Porous Media, with Application to Geological Storage of CO2

Abstract

Onset of double-diffusive buoyancy-driven flow resulted from vertical temperature and concentration gradients in a horizontal layer of a saturated and homogenous porous medium is investigated using amplification factor theory. After injection of CO 2 into a deep saline aquifer, the density of the brine saturated with CO 2 increases slightly. This increase in density induces natural convection. The effect of geothermal gradient is also considered in this work as a second incentive for convection and the double-diffusion convection was studied. Linear stability analysis is used to predict the inception of instabilities and initial wavelength of the convective instabilities. The analysis presented is applied to acid gas injection (as an analogue for CO 2 storage) into saline aquifers in the Alberta basin. It is found that the geothermal gradient does not have significant effect on the onset of convection for these aquifers. It is shown that the geothermal effects on the onset of natural convection are negligible as compared to the solutal effects induced by dissolution and diffusion of CO 2 in deep saline aquifers. Therefore, the linear stability analysis and the long-term numerical simulation of CO 2 sequestration into such saline aquifers may be assumed to be isothermal in terms of natural convection occurrence. List of SymbolsA Time components of the perturbed velocity amplitude function a Dimensionless wave number B Time components of the perturbed concentration amplitude function C Concentration (kg/m 3 ) 123 442 M. Javaheri et al.D Molecular diffusion (m 2 /s) D Derivative operator E Time components of the perturbed temperature amplitude function d Derivative g Gravitational acceleration (m/s 2 ) H Porous layer thickness (m) i Imaginary number K Thermal conductivity (W/m K) k Permeability (m 2 ) Le Lewis number (dimensionless) p Pressure (kg/m s 2 ) Ra Rayleigh number (dimensionless) T Temperature (K) T 1 Temperature of the bottom layer (K) t Time (s) u Velocity in x-direction (m/s) V Volume (m 3 ) v Velocity in y-direction (m/s) v Vector of Darcy velocity (m/s) w Velocity in z-direction (m/s) w Amplification factor (dimensionless) x Coordinate direction (m) y Coordinate direction (m) z Vertical coordinate direction (m) α Thermal diffusivity (m 2 /s) β C Coefficient of density increase by concentration (m 3 /kg) β T Coefficient of thermal expansion (K −1 ) φ Porosity (dimensionless) ρ Density (kg/m 3 ) μ Viscosity (kg/m s) ρ Density difference (kg/m 3 ) σ Matrix to fluid specific heat capacity (dimensionless) ∇ 2 Laplacian operator ∇ 2 H ∂ 2 /∂ x 2 D + ∂ 2 /∂ y 2 D

Chemical control of dissolution-driven convection in partially miscible systems: theoretical classification

“…We assume that the volume of the host phase does not change significantly upon dissolution of A and do not consider any thermal 29,41 or dispersion effects 42 .…”

“…In particular, the early-stage development of this instability has been characterized both theoretically and experimentally for porous media or Hele-Shaw cells with a focus on the critical time and wavenumber for the onset of convection 5,[10][11][12]16,[18][19][20][21][22][23][24][25][26][27][28][29] . Studies have reported the impact on these properties of boundary conditions 21,22,28 , anisotropy of the permeability 16,[23][24][25]28 , geometry of the system 26 , compressibility and interface movement 27 , a geothermal gradient 28,29 , and control parameters in laboratory experiments 5,[10][11][12]19 .…”

“…Studies have reported the impact on these properties of boundary conditions 21,22,28 , anisotropy of the permeability 16,[23][24][25]28 , geometry of the system 26 , compressibility and interface movement 27 , a geothermal gradient 28,29 , and control parameters in laboratory experiments 5,[10][11][12]19 . However, an important aspect that has been less investigated is the impact of chemical reactions on such instabilities.…”

Nonmonotonic Rayleigh-Taylor Instabilities Driven by Gas–Liquid CO2 Chemisorption

“…reason, RTI are also increasingly studied nowadays in the framework of carbon dioxide (CO 2 ) sequestration in deep saline aquifers, [8][9][10] a process for which mixing is expected to add up to the effect of chemical reactions in boosting the overall efficiency. , obtained for the absorption of CO 2 in an aqueous solution of sodium bicarbonate (NaHCO 3 , 790 mol/m 3 ) and sodium carbonate (Na 2 CO 3 , 625 mol/m 3 ) shows a quite unusual behavior.…”

Evaluation of electro-osmotic pumping effect on microporous media flow

“…Fluid flow in micro porous media also has significant scientific and practical importance in many areas. In petroleum mining industrial, carbon dioxide is captured and made us of repelling the raw oil under earth (Ghesmat et al, 2011;Javaheri et al, 2010). In hydrogen storage, the particle diameters in the porous hydrogen storage alloys are 1-20 μm.…”