Study Of The Water Movement In Two-Dimensional Porous Media

Ahadzade Namin, Kobra (2017) Study Of The Water Movement In Two-Dimensional Porous Media. Masters thesis, University of Mohaghegh Ardabili.

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Abstract

The simulation of the reservoirs is the most important method to optimize the production in petroleum engineering. Many attentions have paid to the understanding of the physics of these medium. The production optimization, the quality of the fluid injection and the estimation of the reservoir size and shape depend to this realization. The other important quantity in this study is the percolation probability which demonstrates the rate of percolation of the injected fluid at the other end of the media. In production processes, the fluid is commonly injected to a point of the reservoirs and the resulting changes in the pressure of the oil would cause it to be extracted. The statistical analysis of the percolation probability is directly related to the optimization problem. The other important quantity is the spatial range of the percolated fluid which needs a complicated analysis. The models describing the physics of the reservoirs are unable to calculate the statistical quantities and are commonly very time-consuming. Therefore sometimes the number of constructed realizations are reduced which may not be reliable. In this study we analyze statistically the observable quantities. To describe the physics of these media, we use the concept of self-organized criticality (SOC). In the local dynamics of fluids, there is a critical saturation threshold, above which the fluid overflows to the neighboring pores. The mechanism of this overflowing is reminiscent of the sand topplings in the SOC models. We use this similarity in our analysis. We expect that the movement pattern of the fluid in porous media be similar to the sand dynamics in the SOC models and the rate of percolation raise as the occupation probability of the porous media increases. There are however some competing effects which is the main concern of this project. The finding of the universality class of the Darcy's model is the other aim of this project. This enables us to find a deep relation between the SOC and Darcy's model. In this thesis it has been shown that the movement pattern of the fluid in porous media is compatible with the universality class of two-dimensional Ising model. Some other statistical observables have been also investigated in this analysis, such as the percolation probability, gyration radius of avalanches and cluster masses which confirm this hypothesis.

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