Multifractal Analysis of Reservoir Rock Samples Using 3D X-Ray Micro Computed Tomography Images

Abstract

Characterizing heterogeneity in reservoir rocks at the pore scale is crucial to understand the flow patterns better, and estimate reservoir petrophysical properties such as porosity and permeability. This study introduces multifractals as descriptors for rock samples' heterogeneity at the pore scale. We analyzed twenty rock samples from sandstone and carbonate reservoirs using their 3D X-ray micro-computed tomography images. In addition, we simulated porosity and permeability properties and examined their correlation with multifractal parameters. The results show that the capacity dimension D 0 and the information dimension D 1 correlate with porosity and permeability simulated from images, respectively. Finally, we calculated several multifractal parameters such as the width of the spectrum, the asymmetry degree of the spectrum in the horizontal direction and the value of the vertical difference between the two branches of the spectrum. Results illustrate the ability of multifractal parameters to classify groups of rock samples according to their degree of heterogeneity.INDEX TERMS Heterogeneity, micro computed tomography, multifractals.

On the τ-p Transform and Seismic Data

“…we refer to 𝑅𝑓(𝑟, 𝜑) as the traditional Radon transform or simply the Radon projection of 𝑓, shown in figure 1. As said, this transform found its applications in diverse fields [5][6][7][8][9][10][11][12][13][14][15][16].…”

“…Radon transform provides the mathematical framework for a large class of reconstruction problems, and there are several types of this transform that fits different applications, nature of data, or geometry of measurements. The different forms of this transform are involved with a variety of applications in seismic data, digital rock physics, radar imaging, medical modalities such as computed tomography, magnetic resonance, and others [5][6][7][8][9][10][11][12][13][14][15][16]. Fundamentally, the Radon transform of a function f on 2-D region for example is the line integral of f along all possible lines, or some curves.…”

Advancements in 2D/3D Image Registration Methods

“…Radon showed that it is possible to recover a suitably regular real valued function from the set of all projections, [31,32]. This transform found its applications in diverse fields including medical applications, digital rock physics, image processing, and others, see for instance [33][34][35][36][37][38].…”

Computed Tomography Reconstruction Using Only One Projection Angle

“…Radon's work found applications in the field of computed tomography [2], [3], [4], [5]. In this context, f (x, y) corresponds to the density of tissue at a point (x, y) in some plane slice through a human body and the Radon transform is a measure of the logarithm of the absorption of an x-ray beam that passes through the body along the line L. In addition to its use in the medical imaging; tomography has been successfully applied in various applications such as Digital Rock Physics, for instance [6], [7]. Additionally, image registration techniques utilize the integral transforms approach including the Radon transform, and others.…”