Sharif Digital Repository

Fluid flow modeling in porous media has many applications in waste treatment, hydrology and petroleum engineering. In any geological model, flow behavior is controlled by multiple properties. These properties must be known in advance of common flow simulations. When uncertainties are present, deterministic modeling often produces poor results. Percolation and Random Walk (RW) methods have recently been used in flow modeling. Their stochastic basis is useful in dealing with uncertainty problems. They are also useful in finding the relationship between porous media descriptions and flow behavior. This paper employs a simple methodology based on random walk and percolation techniques. The... 

We study loop-erased random walk (LERW) on the percolation cluster, with occupation probability p≥pc, in two and three dimensions. We find that the fractal dimensions of LERWp are close to normal LERW in a Euclidean lattice, for all p>pc. However, our results reveal that LERW on critical incipient percolation clusters is fractal with df=1.217±0.002 for d=2 and 1.43±0.02 for d=3, independent of the coordination number of the lattice. These values are consistent with the known values for optimal path exponents in strongly disordered media. We investigate how the behavior of the LERWp crosses over from Euclidean to fractal geometry by gradually decreasing the value of the parameter p from 1 to... 

It has long been understood that flow behavior in heterogeneous porous media is largely controlled by the continuity of permeability contrasts. With this in mind, we are looking in new methods for a fast estimation of the effective permeability which concentrates on the properties of the percolating cluster. From percolation concepts we use a threshold permeability value (Kth) by which the gridblocks with the highest permeability values connect two opposite side of the system in the direction of the flow. Those methods can be applied to heterogeneous media of a range of permeabilities distribution and various underlying structures. We use power law relations and weighted power averages that...