Immiscible Radial Newtonian and non-Newtonian Flow Displacements in Porous Media
Date
2019-09-12
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Abstract
Immiscible flows that involve radial displacements of shear-thinning or shear-thickening fluids by a Newtonian fluid in a homogeneous porous medium, are modeled numerically. The interfacial instabilities are tracked in time for different values of the rheological parameters, namely the Deborah number (De) and the power-law index (n) and are characterized through the effective number of fingers and the finger area density. The results of the study reveal that the effects of these two parameters on the instability are not monotonic, and it is found that the flow is least unstable for some critical value of either De or n. The dependence of these critical values in particular on the mobility ratio (M) and Capillary number (Ca) is analyzed. It is found that when all other parameters are fixed, the critical Deborah number (Dec) increases as the power-law index increases in shear-thinning fluids or decreases in shear-thickening ones. Similarly, the critical power-law index (nc) increases with increasing (decreasing) Deborah number in shear-thinning (shear-thickening) flows. Furthermore, both critical parameters are found to vary monotonically with the mobility ratio, with the dependence most noticeable at small values of M. Their variation with the Capillary number is however non-monotonic reaching an extremum at an intermediate value of Ca. An examination of the rate of shear strain at the interface reveals that it consistently shows the smoothest variation and smallest average value at the critical parameter. In addition to non-Newtonian flow displacements, immiscible radial displacement flows between two Newtonian fluids in a non-homogeneous porous media are also examined numerically. The non-homogeneous porous medium is modeled to vary periodically in the radial direction. Simulations are performed for different values of the Capillary number (Ca) and the mobility ratio (M) varying the frequency of the periodic permeability. The results show that the periodic permeability has negligible effects on the finger structures when the Capillary number and the mobility ratio are small. However, the instability of an interface can be noticeably enhanced in a higher frequency periodic permeability field when the Capillary number and the mobility ratio are large enough.
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Keywords
Interfacial tension, Viscous fingering, Interfacial instability, Fluid mechanics, Shear thinning, Non Newtonian fluids, Laminar flows, Shear thickening, Porous media
Citation
Lee, Y. H. (2019). Immiscible Radial Newtonian and non-Newtonian Flow Displacements in Porous Media (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.