Miscible quarter five-spot displacements in a Hele-Shaw cell and the role of flow-induced dispersion

Abstract

Miscible quarter five-spot displacements in a Hele-Shaw cell are investigated by means of experimental measurements and numerical simulations. The experiments record both the volumetric as well as the surface efficiency at breakthrough as a function of the dimensionless flow rate in the form of a Peclet number and the viscosity contrast. For small flow rates, both of these efficiency measures decrease uniformly with increasing Peclet numbers. At large flow rates, an asymptotic state is reached where the efficiencies no longer depend on the Peclet number. Up to Atwood numbers of approximately 0.5, the less viscous fluid occupies close to 23 of the gap width, which indicates a near-parabolic velocity profile across the gap. Consequently, in this parameter range a Taylor dispersion approach should be well suited to account for flow-induced dispersion effects. For larger viscosity contrasts, accompanying two-dimensional numerical simulations based on Taylor dispersion predict an increased stabilization for high flow rates, which is not confirmed by the experiments. This suggests that, in order to extend the range of applicability to larger viscosity contrasts, the components of the dispersion tensor will have to be amended in order to account for the presence of quasi-steady fingers.

Analytical study of effects of finger-growth velocity on reaction characteristics of reactive miscible viscous fingering by using a convection–diffusion–reaction model

“…This indicates that the ÿnger-ing pattern becomes largely independent of Pe v for very lager Pe v . These results correspond to those observed by Petitjeans et al (1999).…”

The effect of anisotropic dispersion on the convective mixing in long‐term CO2 storage in saline aquifers

“…Zimmerman and Homsy 10,11 conducted a full nonlinear simulation for a system with adverse viscosity ratio and anisotropic dispersion. Other works, such as miscible quarter five-spot displacements, 12 stability analysis of miscible flows in a radial Hele-Shaw cell 13 and effect of dispersion on viscous fingering, 14 can be considered as works related to anisotropic dispersion for different flow systems in porous media.…”

Viscous Fingering Instability in Porous Media: Effect of Anisotropic Velocity-Dependent Dispersion Tensor

“…In such situations, the dependence of the transverse dispersion on velocity can have profound effects on the development of the instability. Furthermore, comparisons between experimental measurements and models using Taylor dispersion in a Hele-Shaw cell show the limitations of this model particularly for high viscosity ratio flows (Petitjeans et al 1999). Finally, it should be stressed that the quadratic dependence of the longitudinal dispersion on velocity may be justified at high Péclet numbers based on the pore scale, but is not acceptable at low Péclet numbers that are commonly encountered in porous media flows .…”