Computation of fractal dimension of rock pores based on gray CT images

Abstract

The characterization of pore structure in rocks is relevant in determining their various mechanical behaviors. Digital image processing methods integrated with fractal theory were applied to analyze images of rock slices obtained from industry CT, elucidating the characteristics of rock pore structure and the relationship between porosity and fractal dimensions. The gray values of pixels in CT images of rocks provide comprehensive results with respect to the attenuation coefficients of various materials in corresponding rock elements, and these values also reflect the effect of rock porosity at various scales. A segmentation threshold can be determined by inverse analysis based on the pore ratios that are measured experimentally, and subsequently binary images of rock pores can be obtained to study their topological structures. The fractal dimension of rock pore structure increases with an increase in rock pore ratio, and fractal dimensions might differ even if pore ratios are the same. The more complex the structure of a rock, the larger the fractal dimension becomes. The experimental studies have validated that fractal dimension calculated directly from gray CT images of rocks can give an effective complementary parameter to use alongside pore ratios and they can suitably represent the fractal characteristics of rock pores. As complex geological materials, rocks have discontinuous, non-homogeneous, multi-phase composite structures. Many irregular pores occur at different scales that affect the physical, mechanical and chemical properties of rock materials; such as strength, elastic modulus, permeability, conductivity, wave velocity, particle surface adsorption, and the capacity of a rock reservoir. A significant problem in petroleum exploration, mining, metallurgy, civil and hydraulic engineering is how to understand and quantitatively characterize the evolution of pore structures in rock materials. Thus far, more than 30 kinds of parameters have been proposed to describe rock pore structures [1,2]; these include density or volume fraction of pores (poreratio), pore size and its distribution, and specific surface area. These parameters mainly characterize the average pore structure from a macroscopic view. Pore ratio is the most readily available basic parameter, the effect of which is far greater than all the other factors; therefore, studies related to pore ratios are the most common. Determining pore ratios involves use of microscopic image analysis, weighing method, immersion method and mercury, which have been discussed in detail elsewhere [1,3]. Because pore structures in rocks are very complex [4][5][6], advanced measurement techniques have gradually been introduced to describe pore structures at different scales [7]. Pore morphology and microstructure in rocks can be observed and analyzed over different magnifications using optical or scanning electron microscopy. X-ray fluoroscopy methods also have been adopted to observe internal rock structures. A more effective method is Computerized Tomography (CT...

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“…The fractal dimension of fracture systems can be estimated from photographs of the outcrops and samples (Barton, 1995;Verbovek, 2009;Jie et al, 2007;Baveye et al, 1998;Davy & Bour, 2006;Peng et al, 2011). As the photographs are characterized by two dimensions (length and width), the fractal dimension of fracture systems in photographs are in the range .…”

Prediction of permeability and its anisotropy of tight oil reservoir via precise pore-throat tortuosity characterization and “umbrella deconstruction” method

“…Similarly, pore-throat tortuosity measurement methods of image processing are mostly concentrated in the manual measurement based on the cast slice images under the polarizing microscope. It may cause the lack of automation program, and the measurement process has built into it a certain randomness, so the limitation is obvious: A simplified estimation model of the pore-throat is too idealistic, so the accuracy of the calculated result is worth considering (Piela et al, 2009;Peng et al, 2011;Rajkumar et al, 2012;Beckingham et al, 2013;Ren et al, 2015;Kenneth et al, 2018).…”

Effect of Acetic Acid Pretreatment on Wood Pore Structure and Fractal Dimension

“…There are many methods for the fractal characterization of porous materials, such as nitrogen adsorption (Qi et al 2002), mercury intrusion porosimetry (Smith et al 1990), small angle X-ray scattering (Malekani et al 1996), digital image analysis (Raynaud et al 1989;Peng et al 2011), and so on, of which the nitrogen adsorption method is most widely used. This is mainly owing to the success of the BET (Brunauer Emmet Teller) multi-layer adsorption theory on pore analysis.…”