The stability of density-driven flows in saturated heterogeneous porous media

This work concludes the investigations into the stability of haline flows in saturated porous media. In the first part [33] a stability criterion for density-driven flow in a saturated homogeneous medium was derived excluding dispersion. In the second part [34], the effects of dispersion were included. The latter criterion made reasonable predictions of the stability regimes (indicated by the number of fingers present) as a function of density and dispersivity variations. We found out that destabilising variables caused an increase in the number of fingers and vice versa. The investigation is extended here for the effects of the medium heterogeneity. The cell problem derived via homogenization theory [20] is solved and its solution used to evaluate the elements of the macrodispersion tensor as functions of time for flow aligned parallel to gravity. The longitudinal coefficient exhibits asymptotic behaviour for favourable and moderately unfavourable density contrasts while it grows indefinitely for higher density contrasts. The range of densities stabilised by medium heterogeneities can thus be estimated from the behaviour of the coefficient. The d3f software program is used for the numerical simulations. The code uses the cell-centred finite volume and the implicit Euler techniques for the spatial and temporal discretisations respectively.

► Investigated effect of medium heterogeneity on number and symmetry of fingers for unfavourable density contrasts.
► Large heterogeneity variances and small correlation lengths reduced the number of fingers and increased finger symmetry.
► Applied homogenization theory to derive macrodispersion tensor, which was symmetric with zero off-diagonal elements.
► Presented the temporal evolution of the leading-diagonal elements for a range of physical variables.
► Range of unfavourable densities stabilised by heterogeneities could be estimated from the longitudinal coefficient.