چكيده به لاتين
The studies related to viscous fingering instability in porous media due to it’s usage is very significant such as enhanced oil recovery, aquifers and filtration. Displacing more viscous fluid with less viscous fluid led to instability at the interface between two fluids. Consequently, patterns similar to the finger was formed which is called viscous fingering instability. In this research against most previous studies, that had been used two-phase Darcy for approximate examination of instabilities, a two-dimensional model was used based on the coupling of flow equations in a porous media and transport of dilated species with capability of simulating medias with fractures. In this model, flow movement in the cell was simulated by Darcy law. The obtained velocity derived from Darcy in each point was placed as an input in transport equation. So, in specific conditions such as non-Darcy media, the Brinkman equation can be used instead of the Darcy law. In this research for the first time different characteristics of instability was expressed both qualitative and quantitative based on non-dimensional number related to Peclet rate and viscous ratio. On the other hand, extensive study has been done on the fracture characteristics and it’s effect on the formation and growth of the fingers. In each case, the various mechanisms observed in, was described and the sweep efficiency parameters, the average velocity of the finger tips, the fractal dimension and etc. was measured and compared by the image processing. By analyzing the observed results, with increasing injection rates, shape of the fingers became more complicated and the split of the finger tips increased. These factors ultimately led to reduction in sweep efficiency. Also, increasing the viscosity difference between two fluids led to increase in perimeter of the interface and fractal dimension. In spite of the fracture in the input, the fingers were attracted to the fracture media that the absorption rate has a direct relationship with increase permeability and aperture of the fracture. By increasing the fracture angle to 90 degrees, this amount was decreased which increased sweep efficiency. Also increasing the angle, dimensions and the permeability of the fracture, reduced the complexity of the fingers and increase the sweeping efficiency.
Keywords: porous media, fracture, viscous fingering instability, darcy law, brinkman equation
