MISCIBLE POROUS-MEDIA DISPLACEMENTS IN THE QUARTER 5-SPOT CONFIGURATION - PART 2 - EFFECT OF HETEROGENEITIES

Direct numerical simulations are employed to investigate the coupling between the viscous fingering instabilty and permeability heterogeneit ies for miscible displacements in quarter five-spot flows. Even modera te inhomogeneities are seen to have a strong effect on the how, which can result in a complete bypass of the linear growth phase of the visc ous fingering instability. In contrast to their homogeneous counterpar ts (cf. Part 1, Chen & Meiburg 1998), heterogeneous quarter five-spot flows are seen to exhibit a more uniform dominant length scale through out the entire flow domain. In line with earlier findings for unidirec tional displacements, an optimal interaction of the mobility and perme ability related vorticity modes can occur when the viscous length scal e is of the same order as the correlation length of the heterogeneitie s. This resonance mechanism results in a minimal breakthrough recovery for intermediate correlation lengths, at fixed dimensionless flow rat es in the form of a Peclet number Pe. However, for a constant correlat ion length, the recovery does not show a minimum as Pe is varied. Conf irming earlier observations, the simulations show a more rapid breakth rough as the variance of the permeability variations increases. Howeve r, this tendency is far more noticeable in some parameter regimes than in others. It is furthermore observed that relatively low variances u sually cannot change the tendency for a dominant finger to evolve alon g the inherently preferred diagonal direction, especially for relative ly small correlation lengths. Only for higher variances, and for large r correlation lengths, are situations observed in which an off-diagona l finger can become dominant. Due to the nonlinear nature of the selec tion mechanisms at work, a change in the variance of the heterogeneiti es can result in the formation of dominant fingers along entirely diff erent channels.