Simulation of viscous fingering during miscible displacement in nonuniform porous media
Miller, Clarence A.
Doctor of Philosophy
Numerical simulation is used to study the effect of different factors on unstable miscible displacement and to clarify the mechanisms of finger growth and interaction. The two-dimensional equations of miscible displacement in a rectangular slab are dedimensionalized and the factors that affect their solution are combined into dimensionless parameters. These parameters are the viscosity ratio, the aspect ratio (ratio of longitudinal to transverse dimension), Peclet numbers for molecular, longitudinal and transverse dispersion and the gravity number. To study the effect of the structure of the porous medium, simulations are performed on different random permeability fields, generated by a statistical method, so that they have a given coefficient of permeability variation and a given correlation length. The concentration equation is solved by an implicit finite element modified method of characteristics, which performs backward characteristic tracking. A mixed finite element method is used for the solution of the pressure equation. The initial number and locations of fingers are dictated by the permeability distribution near the inflow end. The initial number of fingers is reduced by shielding and merging to a smaller number of "active fingers". Large viscosity ratio, aspect ratio, correlation length and coefficient of permeability variation facilitate merging and reduce the number of active fingers. With these parameters fixed, the latter is largely independent of the specific permeability distribution. Growth of individual fingers is approximately linear in time, provided they do not interact with other fingers. Root mean square (RMS) length also grows linearly. The RMS growth rate increases with increasing viscosity ratio and seems to approach an asymptotic value as the viscosity ratio tends to infinity. As the correlation length increases, RMS growth rate passes through a maximum. Large heterogeneity of the medium results in large RMS growth rate; the effect of heterogeneity increases with increasing correlation length. For large gravity numbers, the displacement is dominated by gravity override. In that case a gravity tongue forms and fingering is suppressed. The tongue breaks through early and recovery efficiency after breakthrough is greatly reduced. The effect of gravity weakens as the aspect ratio increases.
Environmental science; Chemical engineering