| Three-dimensional miscible displacements with gravity override are investigated in homogeneous and heterogeneous porous media using high accuracy numerical simulations. Special emphasis is placed on the interpretation of the dynamics in terms of the vorticity production related to viscosity, permeability and gravity. Comparison with experimental results show that three-dimensional neutrally buoyant displacements give a better estimate of the displacement efficiency than two-dimensional displacements. Gravity override profoundly influences the flow dynamics both by creating a gravity layer where most of the displaced fluid is bypassed as well as by enhancing the horizontal and vertical mode interactions. Heterogeneous displacements are classified into regimes of viscous fingering, harmonic resonance and channeling depending upon the relative magnitudes of the viscous and permeability length scales. A complex coupling between the viscous instability and permeability spectra leads to intricate fingering patterns that profoundly influence the displacement efficiency. |
