The Study On Fractal Characteristics And Net-work Model Of Pore-structure Of Porous Media

Porous reservoir rock is one kind of complex porous geological materials, in which, the microscopic pore structure and parameters not only influence the oil and gas reserves, but also directly affect the oil and gas well production and ultimate recovery. Therefore, it is very significant and meaningful to analyze the microscopic pore structure and prepare the basic data for the subsequent theoretical analysis and numerical simulation studies of the oil and gas recovery.Microscopic pore structure of porous media is very complicated and irregular. The macroscopic pore parameters given by Euclidean geometry theory and the traditional experiment methods cannot reach the reasonable results. In this paper, the Fractal Theory and Pore Net-work Model are used to analyze the pore structure of porous media. The microscopic pore structure of different rocks has been distinguished by the provided feature parameters for quantitative description of the complexity and irregularity of microscopic pore structure.During the studies of developing the algorithms for estimating the fractal dimension, Box-counting (BC) method for binary image, Differential Box-counting (DBC) method for gray-level image, and3D Fractal Dimension (3D FD) method for a series of3D images have been developed and improved. The factors which influence the accury of the estimated fractal dimension have also been discussed, which contain the box size sequence, image resolution, and threshold value for image binaryzation.For selecting appropriate box size sequence, a divisor sequence of the image size is proposed, which is different from the other two conventional methods:geometric sequence and arithmetic sequence. The proposed method can not only provide enough points for fitting a straight line, but also partition the image completely to eliminate the influence of image boundary effect.At higher resolution, more microscopic pore structure can be detected. The detected extra pore structure increased its complexity and irregularity. The corresponding estimated fractal dimension will become larger. That is to say, high image resolution is helpful to obtain more reasonable and accurate estimation of fractal dimension. Therefore, for avoiding the influence of image resolution, the high resolution should be firstly considered when allowed by the conditions of experiments. For the MR images, if a higher threshold value is chosen, the pore cannot be fully extracted. Conversely, if a low threshold is chosen, some parts of solid structure would be extracted as pore. In either case, the estimated of fractal dimension is not accurate. Through the studies in this paper, the minimum error method has been found it can be used to select the reasonable appropriate threshold value for image binaryzation.Based on the analysis on fractal characteristics of the binary and gray-level images of artificial cores and the series of3D images of sand packed beds, it has been found that all the estimated fractal dimensions using three different algorithms can be used to distinguish the different kinds of pore structure of sand cores. Moreover, the fractal dimension can build the mathematic relationships with porosity and permeability. If the porosity of one kind of sand core is known, those relationships can be used to predict the fractal dimension of the corresponding pore structure, or to predict the porosity of one kind porous median with the known fractal dimension.In addition, this paper has extracted the pore net-works of four kind sand packed beds from their digital cores, respectively, using the Maximal Ball (MB) algorithm. By the statistical analysis and comparison of the different parameters of those net-work models, it has been found that the difference of the parameters of net-work structures among the different sand packed samples is obvious. This result, on the one hand, demonstrated that the extracted pore net-works using Maximal ball algorithm is reasonable and right. On the other hand, it provided the basic data for the subsequent prediction of multiphase flow.