ABSTRACT Global warming has increased interest in quantification of the dissolution of CO2 in (sub)-surface water. CO2 is present above the surface water. Dissolution of CO2 into water (or oil) causes a density increase, with respect to pure water (or oil). This density effect causes natural convection, which enhances the mass transfer rate across the interface. This article describes a series of experiments performed in a cylindrical PVT-cell, where a fixed volume of CO2 gas was brought into contact with a column of distilled water. The results show that the mass transfer rate across the interface is much faster than predicted by Fick's law. This mass transfer rate increases with increasing initial gas pressure. However, in the long term the mass transfer rate is controlled by diffusion alone. The long term behavior, therefore, allows the determination of the diffusion coefficient. Its value agrees with values presented in the literature. A similar mass transfer behavior was observed for the experiments with an oil phase (n-C10 and n-C16). Therefore analogous experiments using oil instead of water are valuable for enhanced oil recovery projects.
A theoretical interpretation of the observed effects has been proposed, based on diffusion and natural convection phenomena. The Rayleigh number is of the order of one million whereas the Schmidt number is of the order of five hundred. The ensuing equations have been solved numerically, using the finite volume approach. There is qualitative agreement between the experiment and the numerical results and similar to the experiments the mass transfer becomes diffusion like in the long term.
1. INTRODUCTION Concerns about global warming have increased interest in quantification of CO2 dissolution in surface water. The density of the water-CO2 solution increases with increasing CO2 concentration [1]. This can lead to natural convection effects. An analogous mechanism is important for the storage of CO2 in aquifers.
Unfortunately there are only few experimental data in the literature, involving mass transfer between water and CO2 under conditions of natural convection. Lindenberg and Wessel-Berg [2] were the first to point out the importance of natural convection for sequestration of CO2 in aquifers. Yang and Gu [3] performed experiments in bulk where a column of CO2 at high pressure was in contact with water. However, their study was limited to the early time behavior and the long term behavior was not measured. Farajzadeh et al. [4] reported experimental results of the same system, showing initially enhanced mass transfer and subsequently a classical diffusion behavior in the long term. However, no fundamental explanation of the phenomena was given. Ngiem et al. [5] gave a field example to show that natural convection is an important mechanism in CO2 sequestration.
The theoretical description of temperature driven natural convection flow uses Navier-Stokes equation and can be found in classical books on fluid mechanics [6, 7]. Guçeri and Farouk [8] derived a numerical model, using finite volume, for steady state natural (turbulent) convection in various geometries. By the symmetry of the geometries considered they can use the stream function-vorticity approach. From the mathematical point of view these geometries allow a 2D description. Patankar [9] proposed a semi-implicit numerical method, which can also be used to (non-steady) 3D problems. Bairi [10] used Patankar's method to study the transient natural convection in a 2D vertical cylinder.