The Influence of Bimodal Heterogeneity on Viscous Fingering of a Miscible Interface in Porous Media

The flow regimes and the dynamics of the front in miscible displacements are controlled by the interactions between the mechanisms of instability involved in such processes. The instabilities may be driven by the unfavorable relative characteristics of the fluids (like unfavorable gravity or mobility ratios) or by the heterogeneity of the medium, providing favorable paths for the more mobile fluid. This work investigates the effect of porous medium heterogeneity with two scales of permeability variations on the frontal instability and fluid mixing. The base mode of permeability variations has a smaller wavelength and higher frequency, while the imposed mode has a larger wavelength. The effect of such a bimodal heterogeneity on the growth of mixing zone length (MZL) has been studied and the development of the previously recognized flow regimes in layered porous media have been examined. The combination of a short wave which induces faster growth of instabilities at initial stages of the flow, and a relatively longer wavelength heterogeneity with elongated channeling period, distorts the consecutive appearance of the flow regimes observed in single wavelength heterogeneity profiles of previous studies. Compared to the unimodal medium comprising the base wave, in the bimodal cases with large contrast between the wavelengths of the two periodic profiles the dominance of each wavelength at a different time scale predictably enhances the growth of fingers in the early and late stages. Interestingly and less intuitively, even in cases with close wave numbers between the combined modes (e.g. 15 layers combined with 11 layers) faster growth of the mixing zone length is observed. In such cases, the coherence of equal layers in a unimodal layered medium is disturbed by the second wave number, which results in fading of the lateral diffusion regime. However, bimodal heterogeneity may attenuate the instability compared to the unimodal system with the imposed wave’s frequency.