Numerical simulation of mixing in viscous-fingering displacements
Name
696009766-MIT.pdf
Description
Full printable version
Size
14.39 MB
Format
Adobe PDF
Checksum (MD5)
6c4c6a9f40b505e94dcc6fc1bad39913
Author(s)
Jha, Birendra. S.M. Massachusetts Institute of Technology
Advisor(s)
Ruben Juanes and Luis Cueto-Felgueroso.
Date Issued
2010
Publisher
Massachusetts Institute of Technology
Abstract
Mixing of two fluids in viscously unstable displacements is far from being fully understood. It is not known how mixing efficiency depends on the viscosity contrast between the fluids, especially for advection-dominated flows (Peclet number Pe > 103). It is well known that when a less viscous fluid displaces a more viscous fluid, the displacement front is unstable and leads to the formation of a pattern known as viscous fingering. However, current simulation technology is unable to cope with large viscosity contrasts (M > 30). We develop a high-resolution simulation approach that is stable for arbitrary viscosity ratios, and we study mixing under different canonical configurations with viscosity contrasts up to M = 400. We explain the observed evolution in degree of mixing through numerical simulation and dimensional analysis. We compute degree of mixing from decay in concentration variance and relate it to the stretching of material interface between the fluids due to fingering. Our analysis predicts the optimum range of viscosity contrast and Peclet number that maximize fluid-fluid interfacial area by balancing the number of fingers with their length before diffusive mixing across the sharp interface takes over. Interesting fingering patterns such as channeling and tip-splitting play an important role in this balancing act which makes degree of mixing a non-monotonic function of viscosity contrast and Peclet number.
Description
Thesis (S.M. in Transportation)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2010.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 97-100).
Subjects
Civil and Environmental Engineering.
MIT Department
Massachusetts Institute of Technology. Department of Civil and Environmental Engineering
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