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

Philippe Petitjeans, Ching-Yao Chen, Eckart Meiburg*, Tony Maxworthy

*Corresponding author for this work

Research output: Contribution to journalArticle

63 Scopus citations

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 2/3 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.

Original languageEnglish
Pages (from-to)1705-1716
Number of pages12
JournalPhysics of Fluids
Volume11
Issue number7
DOIs
StatePublished - 1 Jan 1999

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