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

CO2 sequestration in deep geological formations has been suggested as an option to reduce greenhouse gas emissions. Saline aquifers are one of the most promising options for carbon dioxide storage. It has been shown that the dissolution of CO2 into brine causes the density of the mixture to increase. If the corresponding Rayleigh number of the porous medium is enough to initiate convection currents, the rate of dissolution will increase. Early time dissolution of CO2 in brine is mainly dominated by molecular diffusion, while late time dissolution is predominantly governed by a convective mixing mechanism. In this paper, linear stability analysis of density-driven miscible flow for carbon dioxide sequestration in deep inclined and homogeneous saline aquifers is presented. The effect of inclination and its influence on the pattern of convection cells has been investigated and the results are compared with the horizontal layer. The current analysis provides approximations for the initial wavelength of the convective instabilities and the onset of convection that helps in selecting suitable candidates for geological CO2 sequestration sites. Introduction Carbon dioxide sequestration is the capture and safe storage of carbon dioxide that would otherwise emit to the atmosphere. Sequestration refers to any storage scheme that can keep CO2 out of the atmosphere(1). In general, proposed storage sites of carbon dioxide can be divided into two categories: geological sites and marine sites. Carbon dioxide sequestration in deep geological formations has been suggested as a way of reducing greenhouse gas emissions. Geologic sequestration of CO2 is the capture of CO2 from major sources, transporting it usually by pipeline, and injecting it into underground formations such as oil and gas reservoirs, saline aquifers and unmineable coal seams for a significant period of time(2, 3). Unlike coalbed methane reserves and oil reservoirs, sequestration of CO2 in deep saline aquifers does not produce value-added by-products, but it has other advantages. While there are uncertainties regarding the scope, the world's total capacity to store CO2 deep underground is large(4). Underground formations are generally unused and are available in many parts of the world(5). It has been estimated that deep saline formations in the United States could potentially store up to 500 billion tonnes of CO2. Most existing large CO2 point sources are within easy access to a saline formation injection point and, therefore, sequestration in saline formations is compatible with a strategy of transforming large portions of the existing energy and industrial assets to near-zero carbon emissions via low-cost carbon sequestration retrofits(3). However, it is important to investigate the behaviour of CO2 injected into aquifers for effective and safe use of storage. Geological storage of CO2 as a greenhouse gas mitigation option was proposed in the 1970s(6), but little research was done until the early 1990s when the idea gained credibility through the work of individual research groups(7–10). When CO2 is injected into the formation above its critical temperature and pressure, the density of supercritical carbon dioxide is usually less than brine. This density difference causes CO2 to migrate upwards to the top of the formation under an impermeable caprock.

Disposal of carbon dioxide (CO2) into saline aquifers appears to be one of the best CO2 sequestration options in terms of capacity and technology. Injected CO2 migrates invariably upwards due to buoyancy forces. In most common aquifer settings, the density difference between CO2 and brine is sufficiently high that gravity force is a pre-dominant factor that controls the upward migration of a CO2 plume. Any scheme that can retard the vertical movement of the plume can enhance the entrapment of the injected CO2 and reduce the risk of potential leakage back into the atmosphere. An appealing scheme for sequestration projects in aquifers involves simultaneous injection of brine and CO2 from vertical wells, where brine is injected in the upper part of injection well(s) and CO2 is injected in the lower portion of the well(s). This scheme inhibits the rapid upward migration of CO2, since the injected CO2 is forced to move horizontally during the injection period. The horizontal displacement increases the volume of the aquifer that is contacted by the injected CO2, and hence, the residual entrapment of the CO2-rich phase can be increased significantly. The upward migration of CO2 away from the injector occurs predominantly in a counter-current flow mode. In this study, we compare residual entrapment of CO2 for the simultaneous injection of CO2 and brine in four different aquifer settings. The four aquifer settings are selected from the classification scheme proposed by Kopp et al. (2009). It is shown that for large gravity numbers, there is a significant difference between the four aquifer settings in terms of storage capacity with warm aquifers having the least storage capacity and cold aquifers providing the largest storage capacity. The distance at which segregation of brine and CO2 is complete, not only depends on the gravity number, but also on the aquifer setting. It is indicated that residual entrapment of CO2 depends on brine injection rate and higher rates of brine (lower gravity number) increase the fraction of CO2 that is trapped in a residual phase. Finally, we demonstrate that the reduction in the relative permeability of both phases, due to counter-current flow, has a major impact on the sweep efficiency of the injected CO2 and hence impact both the distance traveled before full segregation and the level of residual entrapment.

Carbon dioxide (CO2) injection into saline aquifers is one of the promising options to sequester large amounts of CO2 in geological formations. During as well as after injection of CO2 into an aquifer, CO2 migrates towards the top of the formation due to density differences between the formation brine and the injected CO2. The timescales of CO2 migration towards the top of an aquifer and the fraction of CO2 that is trapped as residual gas depends strongly on the driving forces acting on the injected CO2. When CO2 migrates to the top of an aquifer, brine may be displaced downwards in a counter-current flow setting particularly during the injection period. A majority of the published work on counter-current flow settings have reported significant reductions in the associated relative permeability functions as compared to co-current measurements. However, this phenomenon has not yet been considered in the simulation of CO2 storage into saline aquifers. In this paper we study the impact of changes in mobility for the two-phase brine/CO2 system as a result of transitions between co- and counter-current flow settings. We have included this effect in a simulator and studied the impact of the related mobility reduction on the saturation distribution and residual saturation of CO2 in aquifers over relevant time scales. We demonstrate that the reduction in relative permeability in the vertical direction changes the plume migration pattern and has an impact on the amount of gas that is trapped as a function of time. This is to our best knowledge the first attempt to integrate counter-current relative permeability into the simulation of injection and subsequent migration of CO2 in aquifers. The results and analysis presented in this paper are directly relevant to all ongoing activities related to the design of large-scale CO2 storage in saline aquifers.