Numerical Simulation of Dispersion in Stratified Porous Media

Abstract

The transport of a solute dissolved in a fluid flowing trough porous media is, next to advection and diffusion, determined by hydrodynamic dispersion. This be- haviour is commonly characterized using the longitudinal and transverse dispersion coefficients. Laboratory and field measurements of these coefficients tend to differ, which might be attributed to heterogeneities found in field porous media. To investigate this, a stratified porous medium consisting of two layers is con- sidered. Each layer has different physical properties, resulting in a different average fluid velocity. As a consequence of the difference in velocity, transport of the solute occurs between the two layers. Under certain circumstances the layers start to be- have as one single layer, with one single effective dispersion coefficient, explaining the discrepancy between field and laboratory measurements. The two-layer stratified porous medium is characterized using a dimensionless number. It is investigated for which values of this number the porous medium acts as one single layer, and for which values the medium behaves as two separate layers. This is done by introducing an index, which effectively measures the behaviour of the medium in terms of these two limit cases. The calculation of the index is done using a numerical simulation of flow and dispersion in the stratified porous medium. It was found that the dimensionless number was in general a good predictor of the behaviour of the stratified porous medium. The system behaved as one single layer if the dimensionless number (after a correction with a certain factor) was much greater than unity. Similarly, the system behaved as two separate layers if the number was much less than unity. However, this number failed if the ratio of the two layer thicknesses was varied. A correction to the dimensionless number was suggested, taking the ratio into account.