Analysis of the convective dispersive transport in porous media

The finite-control volume technique is used to solve the convection–dispersion equation in cylindrical coordinates. In the model presented, the dispersion coefficient is dependent on both velocity and diffusion coefficient.The solution allows analyzing the dispersion transport of a slug in a steady radial flow from an injection well fully penetrating a homogeneous reservoir of uniform thickness and finite drainage area. The solution is used to study the effects of a number of parameters, like dispersivity, tortuosity, porosity, and injection rate on the mixing process. For the range of parameters investigated, and for the homogeneous porous medium simulated, the optimal solvent slug size appears to slightly vary around the vicinity of 0.1 pore volume, for an arbitrary position taken at a dimensionless radius rD = 0.5. The optimal solvent slug size appears to slightly increase with increasing porosity and dispersivity, and to decrease with increasing tortuosity.The finite-volume technique is favored over the finite-difference technique because it is known to eliminate the detrimental effects of numerical dispersion. The convection–dispersion equation arises in the simulation of miscible displacement processes where front smearing resulting from numerical dispersion can distort the behavior of the displacement process. This front smearing can, for instance, lead to false predictions of breakthrough times and optimal slug sizes. This in return causes poor reservoir management and inadequate economic forecast of EOR processes.