in Wiley InterScience (www.interscience.wiley.com).CO 2 storage in deep saline aquifers is considered a possible option for mitigation of greenhouse gas emissions from anthropogenic sources. Understanding of the underlying mechanisms, such as convective mixing, that affect the long-term fate of the injected CO 2 in deep saline aquifers, is of prime importance. We present scaling analysis of the convective mixing of CO 2 in saline aquifers based on direct numerical simulations. The convective mixing of CO 2 in aquifers is studied, and three mixing periods are identified. It is found that, for Rayleigh numbers less than 600, mixing can be approximated by a scaling relationship for the Sherwood number, which is proportional to Ra 1/2 . Furthermore, it is shown that the onset of natural convection follows t Dc ;Ra À2 and the wavelengths of the initial convective instabilities are proportional to Ra. Such findings give insight into understanding the mixing mechanisms and long term fate of the injected CO 2 for large scale geological sequestration in deep saline aquifers. In addition, a criterion is developed that provides the appropriate numerical mesh resolution required for accurate modeling of convective mixing of CO 2 in deep saline aquifers.
The storage of carbon dioxide and acid gases in deep geological formations is considered a promising option for mitigation of greenhouse gas emissions. An understanding of the primary mechanisms such as convective mixing and geochemistry that affect the long-term geostorage process in deep saline aquifers is of prime importance. First, a linear stability analysis of an unstable diffusive boundary layer in porous media is presented, where the instability occurs due to a density difference between the carbon dioxide saturated brine and the resident brine. The impact of geochemical reactions on the stability of the boundary layer is examined. The equations are linearised, and the obtained system of eigenvalue problems is solved numerically. The linear stability results have revealed that geochemistry stabilises the boundary layer as reaction consumes the dissolved carbon dioxide and makes the density profile, as the source of instability, more uniform. A detailed physical discussion is also presented with an examination of vorticity and concentration eigenfunctions and streamlines' contours to reveal how the geochemical reaction may affect the hydrodynamics of the process. We also investigate the effects of the Rayleigh number and the diffusion time on the stability of a boundary layer coupled with geochemical reactions. Nonlinear direct numerical simulations are also presented, in which the evolution of density-driven instabilities for different reaction rates is discussed. The development of instability is precisely studied for various scenarios. The results indicate that the boundary layer will be more stable for systems with a higher rate of reaction. However, our quantitative analyses show that more carbon dioxide may be removed from the supercritical free phase as the measured flux at the boundary is always higher for flow systems coupled with stronger geochemical reactions.
A modified pressure decay method has been designed and tested for more reliable measurements of molecular diffusion coefficients of gases into liquids. Unlike the conventional pressure decay method, the experimental setup has been designed such that the interface pressure and consequently the dissolved gas concentration at the interface are kept constant. This is accomplished by continuously injecting the required amount of gas into the gas cap from a secondary supply cell to maintain the pressure constant at the gas−liquid interface. The pressure decay is measured in the supply cell. The advantage of the new technique is that, assuming the diffusion coefficient to be constant, a simple analysis allows determination of the equilibrium concentration and diffusion coefficient.
One of the important challenges in geological storage of CO 2 is predicting, monitoring, and managing the risk of leakage from natural and artificial pathways such as fractures, faults, and abandoned wells. The risk of leakage arises from the buoyancy of free-phase mobile CO 2 (gas or supercritical fluid). When CO 2 dissolves into formation brine, or is trapped as residual phase, buoyancy forces are negligible and the CO 2 may be retained with minimal risk of leakage. Solubility trapping may therefore enable more secure storage in aquifer systems than is possible in dry systems (e.g., depleted gas fields) with comparable geological seals. A crucial question for an aquifer system is, what is the rate of dissolution? In this paper, we address that question by presenting a method for accelerating CO 2 dissolution in saline aquifers by injecting brine on top of the injected CO 2 . We investigate the effects of different aquifer properties and determine the rate of solubility trapping in an idealized aquifer geometry. The acceleration of dissolution by brine injection increases the rate of solubility trapping in saline aquifers and therefore increases the security of storage. We show that, without brine injection, only a small fraction (less than 8%) of the injected CO 2 would be trapped by dissolving in formation brine within 200 years. For the particular cases studied, however, more than 50% of the injected CO 2 dissolves in the aquifer as induced by brine injection. Since the energy cost for brine injection can be small (<20%) compared to the energy required for CO 2 compression for a 5-fold increase in dissolution, such reservoir engineering techniques might be viable and practical for accelerating dissolution of CO 2 . The environmental benefit would be to decrease the risk of CO 2 leakage at reasonably low cost.
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
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