Fractal Analysis of Viscous Fingering Instability of Two Reactive Miscible Fluids through Homogeneous Porous Media

Viscous fingering instability in porous media is one of the natural processes which is widely used in many different type of problems, such as Enhanced oil recovery process. In this paper nonlinear simulation of viscous fingering instability of miscible reactive interface through homogeneous porous medium is examined. In this case, the fluid produced at the interface can be considered similar to the coastline, so mono and multi fractal analysis can be performed. First the concentration contours are plotted in differnet models of instability, then by using image processing, the fractal dimension of image is computed for both fractal and multifractal cases in different times. It can be seen that the fractal dimension in the instability problems can be one of the important parameters that describes the complexity of the patterns. The multifractal spectrum curves are plotted for different image of instability and the results show that when the leading or trailing front is unstable the growth of disturbances over the time lead to an increase in the amount of fractal dimension. However when both leading and trailing fronts are unstable, the interaction between the fingers and different fingers pattern may lead to a decrease in fractal dimension.