Two-dimensional (2D) and three-dimensional (3D) computations by a particle-tracking technique are compared for unstable displacements in homogeneous and heterogeneous porous media, with and without gravity. In homogeneous porous media without gravity, 2D fingering patterns and the length of the transition zone are nearly the same as those obtained in 3D displacements. When gravity is added, however, calculated gravity tongues and fingering patterns can be very different when viscous and gravity forces are of comparable magnitude. The presence of correlated heterogeneities can alter significantly the range of viscous to gravity ratio over which the transition from gravity-dominated flow to fingering dominated flow occurs. For displacements in that transition region, 2D simulations do not reproduce accurately the behavior of 3D flows.

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