Bi-dimensional plume generated by the convective dissolution of an extended source of CO₂

The dynamics of a bi-dimensional solutal plume generated by the convective dissolution of an extended source of carbone dioxide (CO2) is studied from both experimental and numerical standpoints. In the experiments, the CO2 is injected into a 1 mm-thick water filled Hele-Shaw cell at pressures ranging between 1 and 5 bar. The plume is visualized using a pH-sensitive dye and the velocity field is measured by means of standard particle image velocimetry (PIV). Concentration and velocity fields are scrutinized over one order of magnitude in Rayleigh number (Ra), and for two different values of the Darcy number (Da). In order to extend the explored range of these dimensionless numbers, experiments are complemented by a comprehenvive set of numerical simulations. At low Darcy numbers (Da < 1), the morphology of the numerical plume is fairly close to that of the analytical solution previously derived by R.A. Wooding (1962) for the case of a line source in a porous medium. At larger Darcy numbers (Da > 1), the numerical solution departs on several aspects from this solution and exhibits closer similarity to the analytical solution derived by D.B. Spalding & R.G. Cruddace (1961) for the case of a line source in a viscous fluid. As the introduction of an additional length scale (the lateral size of the source) in the problem allows for the definition of a length-based Rayleigh number Ra, the respective amplitudes of the plume velocity w, plume width σ and dimensionless total injection rate (i.e., the Nusselt number Nu) can be explicitly obtained as functions of Ra and Da. The scaling laws are reasonably close to those obtained from simple mass conservation considerations: (i) w ∼ Ra, σ ∼ Ra−1/2 and Nu ∼ Ra1/2 for Ra Da < 1, and (ii) w ∼ (Ra/Da) 1/2 , σ ∼ (Ra/Da) −1/4 and Nu ∼ (Ra/Da) 1/4 for Ra Da > 1. While the concentration field measurements are marred by a large uncertainty due to the logarithmic nature of the pH-concentration relationship, the experimental data obtained from the PIV measurements show a good agreement with the numerical results.