Numerical simulation of miscible fluid flows in
\nporous media

The study of miscible 
\now in porous media is an important topic in many disciplines
\nof science and engineering, especially in the field of petroleum engineering.
\nFor example, Carbon dioxide (CO₂) may be injected into an oil reservoir in order
\nto improve the oil recovery rates, which is called enhanced oil recovery (EOR). This
\nthesis focuses on the study of a miscible displacement of two 
\nfluids, such as CO₂ and
\noil, in a porous medium. An upscaling methodology for modeling multiscale features
\nof the 
\now and the porous medium has been studied, where the overall pressure drag
\nand skin friction exerted on the porous medium has been modelled by combining the
\nDarcy's law with a statistical mechanical theory of viscosity, which is an important
\ncontribution of this thesis.
\nA numerical methodology for capturing the multiphysics and multiscale nature
\nof the governing motion has been studied. The temporal discretization employs the
\nsecond order Crank-Nicolson scheme for viscous and diffusive phenomena, and an
\nexplicit method for all other terms. The nonlinear advection terms in the momentum
\nequation has been treated with an Euler explicit 
\nflux form central finite difference
\nmethod; however, the advection of the CO2 mass 
\nflux has been treated with a streamline
\nbased Lagrangian method. In order to implement the Marker-and-Cell (MAC)
\nscheme for resolving the incompressibility, a staggered arrangement of the velocity
\nand pressure has been presented on a collocated grid. This approach enhances the
\nimplementation of a multigrid solver, and is a novel computational model for simulating
\nmiscible displacement processes. The performance of the Lagrangian method
\nhas been assessed with respect to an equivalent 
\nflux form upwind method.
\nThe results indicate that the viscous forces play a signicant role compared to the
\neffect of permeability on miscible displacement of CO₂ and oil, where the injected CO₂ displaces the residual oil without being distorted, thereby enhancing the recovery
\nof hydrocarbon. Although the present results with an idealized model lacks from
\nverifications with field measurements, findings of this thesis provide useful feedback
\nto further investigations on CO₂ based EOR techniques.

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