Dynamics of Viscous Fingering in Porous Media in the Presence of Injected or In Situ Generated Particles
Date
2021-01-12
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Abstract
Interfacial instabilities in the form of viscous fingers evolve when a less viscous fluid displaces a more viscous one. Such instabilities occur in a wide range of engineering applications, including subsurface contaminant transport, soil and groundwater remediation, micromixers, enhanced oil recovery, and geological storage of carbon dioxide, to name a few. This thesis focuses on the theoretical study of viscous fingering between two miscible fluids (termed as displacing and displaced fluids) in porous media. In particular, we are interested in investigating the effect of the presence of solid particles on the mixing of fluids for two main scenarios: (i) when the displacing fluid contains solid particles such as nanoparticles and (ii) when the interaction of the displacing and displaced fluids results in the formation of particles (also called precipitates) as is in the case of asphaltene precipitation in mixing of a paraffinic solvent with oil. In this study, we use a combination of theoretical techniques, including the development of analytical solutions, linear stability analysis, and nonlinear numerical simulations to quantify and characterize the effect of particles on fluids mixing. For injected particles, the numerical simulations are based on the stream function vorticity formulation in a moving frame of reference, while for in situ formed particles, a velocity vorticity formulation in a fixed frame is developed to capture the variations of porosity and permeability due to particle deposition. Our results show that non-depositing nanoparticles can be used to fully stabilize an unstable front, whereas depositing nanoparticles might only act as temporary stabilizers. We also quantify the role of each nanoparticle physical property, including their log-viscoity ratio and diffusion coefficient, on the growth of viscous fingers. For miscible viscous fingering in the presence of a nanocatalytic reaction, we show that a higher reaction rate leads to more frontal instability. Also, we define two mechanisms that control the effect of deposition of nanocatalysts on viscous fingering. In the case of in situ formed particles, we investigate the dynamics of viscous fingering in the presence of an infinitely fast and reversible precipitation reaction. Our results reveal that the formed precipitates mostly exist at the interface where the two fluids are mixing actively. Also, we show that the ultimate permeability of porous media can be scaled linearly with the log-viscosity ratio of fluids. Finally, we study the specific case of asphaltene precipitation and deposition in the context of solvent-based recovery of bitumen. In our analysis, we quantify the degree of in situ upgrading of bitumen and shed light on the difference between two commonly used viscosity relations in the literature.
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Keywords
Viscous Fingering, Porous Media, Nanoparticle, Nanocatalyst, Precipitation, Deposition, Asphaltene, Rayleigh Taylor, Flow Instability, Numerical Simulation, Linear Stability Analysis, Hartley Transform, Compact Finite Difference, Chemical Reaction
Citation
Sabet, N. (2020). Dynamics of Viscous Fingering in Porous Media in the Presence of Injected or In Situ Generated Particles (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.