Study Of The Properties For Flow In Fractal Porous Media And Asymmetrical Branching Networks

Porous media and branching networks exist everywhere in nature and highly related to our daily life. Trees, rivers, biological circulatory systems, and urban water drainage systems are typical examples of branching networks. Investigation of branching networks may help us to better understand the laws existing in nature and optimize the branching networks in daily life to improve the performance of artificial branching networks. Compared to branching networks, porous media more commonly exist such as the soil, sand, and rocks, which play a very important role in human activities, especially in the petroleum extraction where the transport properties of porous media affect the productions of oilfield. As the gradual depletion of oil resources in the recent years, low permeability reservoir is becoming more and more important and the low permeability porous medium transport properties of porous media used in low permeability reservoirs are highly concerned.The main contributions of this paper include:First, based on the real branching networks, we consider the influence of branching ratio to the transport resistance of branching networks in commonly existing asymmetrical branching networks, analyze the full flow resistance in the asymmetrical branching networks that have the common size of terminal branches, such as blood circulation system which has the same size of terminal capillaries, and conclude that asymmetrical symmetrical branching networks has the better performance in the aspect of mass transfer of branch-network. Secondly, with the consideration of fractal theory, we analyze the situation where transfer property of porous media does not match the traditional Darcy's law and show a rescannable explanation that non-Darcy flow phenomenon is due to the internal structure of porous media, the fluid flow characteristics of non-Newtonian fluid and the interaction of solid-liquid. Thirdly, based on the fact that most porous media exhibit the fractal characteristics, we perform the numerical simulation and analysis to tortuosity for flow through the self-similar Sierpinski carpet fractal patterns. We obtain a new conclusion that the tortuosity has a linear relationship with the order, and compared it with other analysis results of the tortuosity. Fourthly, based on the fractal theory and the inverse transform theorem, we produce a set of data satisfying the given fractal distribution, reconstruct the simple two-dimensional porous media by using the principle of random and non-overlapping and analyze the impact of tortuosity fractal dimension and porosity in porous media on the tortuosity, and found that the tortuosity increases with the tortuosity fractal dimension under the same porosity.