چكيده به لاتين
Displacing fluids by another fluid is an interesting field for researchers due to its application. Viscous fingering is the well-known phenomenon that occurs in displacement interface in which displacing fluid propagate displaced fluid with a finger-shaped pattern. Viscous fingering motivated by viscosity mismatch is known as Saffman-Taylor. Generally, viscous fingering is observed as an undesirable phenomenon in a wide variety of environmental and technological processes such as liquid chromatography, geothermal reservoir recharge, enhanced oil recovery (EOR), filtration, and hydrology. In this thesis, both Newtonian and non-Newtonian miscible viscous fingering in heterogeneous and fractured porous media is studied, using direct nonlinear simulation. It is considered methanol and four different solutions of Xanthan as displacing fluid. In different scenarios, four binary solutions of glycerol-water are assumed as displacing fluid. The non-Newtonian displacing fluid has shear-thinning behavior has modeled by the Carreau-Yasuda equation. Four different geometry including fractured porous media is investigated. The specification of porous media is obtained from a rectangular flow cell, so the simulation result verified by experimental data. The miscible viscous fingering is modeled by employing Darcy’s law for the Newtonian case and modified Darcy’s law for non-Newtonian coupled with the convection-dispersion equation for concentration. An exponential equation of state for describing the dependency of viscosity on concentration is implemented. These nonlinear equation has been examined using the Comsol multi-physics CFD code,(version 5.4). The finite element method is used to discretize the model equations and mapped mesh to discretize the domain. The effect of the Peclet number, viscosity ratio, permeability, and the aperture ratio is studied in detail. The concentration contours, sweep efficiency, fractal dimension, perimeter of the interface, and breakthrough time are computed for different scenarios and are presented in the quantitative section. The qualitative result section shows that various mechanisms are observed such as shielding, tip-splitting, side-branching, etc. The Peclet numbers and the viscosity ratio have a strong effect on forming these mechanisms. In higher displacement velocity, the more tip-splitting, side-branching, and tinier fingers are observed in both cases. As the viscosity ratio increases, the coalescence mechanisms reduce, and tip-splitting increases, and fingers become tinier. The permeability and aperture ratio of fractures have a negligible effect on forming viscous fingering mechanisms. Generally, fingers in the non-Newtonian case are bigger and wider than the Newtonian case. The quantitative result shows that the sweep efficiency and the breakthrough time reduce as Peclet number and viscosity ratio increase. The finger patterns have more complexity in high Peclet numbers and viscosity ratios due to the higher fractal dimension. The effect of permeability and aperture ratio of fractures on sweep efficiency is varied in different scenarios. Overall, the shear-thinning displacing fluid case has higher sweep efficiency and breakthrough time. For more precise sweep efficiency of shear-thinning displacing fluid case is 60 percent more than another one.
