A comparison of fractal methods for evaluation of hydraulic fracturing surface roughness

2020 ◽  
Vol 60 (1) ◽  
pp. 184 ◽  
Author(s):  
Abbas Movassagh ◽  
Xi Zhang ◽  
Elaheh Arjomand ◽  
Manouchehr Haghighi
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Hydraulic Fracturing ◽  
Fractal Analysis ◽  
Roughness Length ◽  
Variation Method ◽  
Fracture Surfaces ◽  
Wide Range ◽  
Surface Profiles ◽  
Fractal Methods

Surface roughness is a crucial parameter in the hydraulic fracturing process, affecting rock toughness, fluid flow and proppant transport; however, the scale-dependent nature of hydraulic fracture surfaces is not well studied. In this paper, we examined four fractal methods, compass, box-counting, variation and roughness-length, to evaluate and compare the fractal dimension of the surface roughness profiles created by laboratory hydraulic fracturing. Synthetic surface profiles were generated by the Weierstrass-Mandelbrot function, which was initially used to test the accuracy of the four methods. Each profile had a predefined fractal dimension that was revisited by these methods. Then, the fractal analysis was performed for experimental fracture surfaces, which were created by a hydraulic fracturing experiment in a true triaxial situation. By comparing fractal analysis results, we found that for both synthetic and laboratory fracture height profiles, the roughness-length method provides a relatively more reliable estimation of the fractal dimension. This method predicts the dimension for synthetic surface within an error of less than 1%, considering a wide range of surface heights from centimetres down to micrometres. By increasing the fractal dimension of surface profiles, the error of fractal estimation increased for all four methods. Among them, the variation method provided the closest results to the roughness-length method when considering both experimental and synthetic surfaces. The evaluated fractal dimension may provide a guideline for either field- or laboratory-scale hydraulic fracturing treatments to evaluate the effects of surface roughness on fracture growth.

Fractal analysis with scanning probe microscopy

1992 ◽  
Vol 50 (2) ◽  
pp. 1046-1047
Author(s):  
Paul E. West ◽  
Sid Marchesse-Rugona ◽  
Zhuoning Li
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Physical Properties ◽  
Fractal Analysis ◽  
Three Dimensional ◽  
Optical Microscope ◽  
Two Dimensional ◽  
Atomic Force ◽  
Dimensional Measurements ◽  
Surface Profiles

Surface roughness determined qualitatively by direct visualization can be correlated to several physical properties. However, finding a suitable method of quantifying surface roughness, until recently, has been difficult. The concept of Fractal Dimension, recently popularized by Mandelbrot(1982) has been extremely successful in quantifying surface roughness and relating it to such measurable physical properties such as; cleanability, catalytic activity, rate of corrosion, and even flavor.Atomic Force Microscopes permit direct three dimensional measurements of surface microstructure. AFM images are obtained by measuring the motion of a sharp stylus as it is scanned across a surface. Because the AFM directly measures three dimensional topograms, it is ideally suited for two dimensional and three dimensional fractal analysis. Other microscope techniques such as the scanning electron or optical microscope give only two dimensional magnification and fractal measurements are not easily made.The Atomic Force Microscope enables us to obtain the fractal dimension of surface profiles as well as surface areas. For surface profiles we use a box counting method (Mandelbrot 1986, Chesters et al. 1989).

Optimal Density Determination of Bouguer Anomaly Using Fractal Analysis (Case of study: Charak area,IRAN)

2005 ◽  
Vol 1 (1) ◽  
pp. 21-24
Author(s):  
Hamid Reza Samadi
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Fractal Analysis ◽  
Fractal Geometry ◽  
Host Rock ◽  
Bouguer Anomaly ◽  
Research Area ◽  
Density Difference ◽  
Optimal Density

In exploration geophysics the main and initial aim is to determine density of under-research goals which have certain density difference with the host rock. Therefore, we state a method in this paper to determine the density of bouguer plate, the so-called variogram method based on fractal geometry. This method is based on minimizing surface roughness of bouguer anomaly. The fractal dimension of surface has been used as surface roughness of bouguer anomaly. Using this method, the optimal density of Charak area insouth of Hormozgan province can be determined which is 2/7 g/cfor the under-research area. This determined density has been used to correct and investigate its results about the isostasy of the studied area and results well-coincided with the geology of the area and dug exploratory holes in the text area

A Three-Dimensional Fractal Analysis Method for Ground Monocrystal Sapphire Surface

2014 ◽  
Vol 1017 ◽  
pp. 187-192
Author(s):  
Qiu Yan Wang ◽  
Zhi Qiang Liang ◽  
Xi Bin Wang ◽  
Wen Xiang Zhao ◽  
Yong Bo Wu ◽  
...  
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Fractal Analysis ◽  
Three Dimensional ◽  
Ground Surface ◽  
Surface Characteristics ◽  
Surface Phenomenon ◽  
Analysis Method ◽  
Characterization Methods ◽  
Box Counting

Conventional characterization methods of grinding surface using surface roughness parameters, e.g., Ra, depend on either the resolution of the measuring instrument or the length of the sample. But fractal dimension (FD) as a scale-independent fractal parameter is effective to evaluate the ground surface at any length scale and represent lots of surface phenomenon at its relevant length scales. In this paper, a three-dimensional (3D) box-counting fractal analysis method is used to investigate ground surface morphology of monocrystal sapphire by calculating 3D fractal dimension of the ground surface. The results obtained show that fractal dimension decreases with the increasing surface roughness. For the ground surface with higher fractal dimension, its microtopography is more exquisite with minor defects. Once the fractal dimension become smaller, deep cracks and pronounced defects are exhibited in ground surface. Moreover, the ground surface obtained in ductile mode has much higher fractal dimension than that in brittle mode. Therefore, the fractal analysis method has the potential to reveal the ground surface characteristics of monocrystal sapphire.

Fractal Analysis of Fracture Surfaces of Steel Charpy Specimens

2008 ◽  
Vol 399 ◽  
pp. 43-49
Author(s):  
Claudia Secrieru ◽  
Ion Dumitru
Keyword(s):  
Fractal Dimension ◽  
Fracture Surface ◽  
Fractal Analysis ◽  
Light Microscope ◽  
Vertical Section ◽  
Fracture Profile ◽  
Charpy Test ◽  
Fracture Surfaces ◽  
Box Counting ◽  
Technical Measurements

The article focuses on the technical measurements which could be applied to the fracture surfaces of the steel Charpy specimens in order to apply the Fractal Analysis. One could calculate the fractal dimension not directly for a fracture, but for a profile of the fracture. Most common methods for generation of fracture profile are cross-cut techniques and profile measurements techniques [1-2]. We apply three principal methods: Profilometer, Interferometer Light Microscope and the Vertical Section for a specimen made of XC65 after the Charpy test. We compare the advantages and the limits for each technique. We use the Box Counting algorithm applied in the Image J program for determining the fractal dimension of the fracture surface in all three experimental techniques. Then we could characterize the roughness of the fracture profile at different magnifying power by the estimated fractal dimension.

Image Reconstruction and Analysis of Three-Dimensional Fracture Surfaces Based on the Stereo Matching Method

2004 ◽  
Vol 261-263 ◽  
pp. 1593-1598
Author(s):  
M. Tanaka ◽  
Y. Kimura ◽  
A. Kayama ◽  
L. Chouanine ◽  
Reiko Kato ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Image Reconstruction ◽  
Fracture Surface ◽  
Fractal Analysis ◽  
Stereo Matching ◽  
Three Dimensional ◽  
Fractal Dimensions ◽  
Matching Method ◽  
Fracture Surfaces ◽  
Box Counting Method

A computer program of the fractal analysis by the box-counting method was developed for the estimation of the fractal dimension of the three-dimensional fracture surface reconstructed by the stereo matching method. The image reconstruction and fractal analysis were then made on the fracture surfaces of materials created by different mechanisms. There was a correlation between the fractal dimension of the three-dimensional fracture surface and the fractal dimensions evaluated by other methods on ceramics and metals. The effects of microstructures on the fractal dimension were also experimentally discussed.

Correlation between Fractal Dimension and Impact Strength for Wood Plastic Composites

2011 ◽  
Vol 411 ◽  
pp. 548-551
Author(s):  
Tao Qiang ◽  
De Mei Yu
Keyword(s):  
Fractal Dimension ◽  
Linear Regression ◽  
Impact Strength ◽  
Fractal Analysis ◽  
Impact Test ◽  
Wood Plastic Composites ◽  
Analysis Techniques ◽  
Fracture Surfaces ◽  
Plastic Composites ◽  
The Impact

Polylactide (PLA)-based wood plastic composites (WPCs) were manufactured by extrusion blending followed by injection molding. The fracture surfaces created from the impact test were recorded with SEM. Fractal analysis has been used to calculate the fractal dimension of the fracture surfaces with four different fractal analysis techniques. Then, the correlation between the fractal dimension of the fracture surfaces and its impact strength of the PLA-based WPCs was investigated by the linear regression. The results showed that there is a positive correlation between the impact strength and the fractal dimension.

COMPARISON OF SEVERAL METHODS FOR CALCULATING FRACTAL-BASED TOPOGRAPHIC CHARACTERIZATION PARAMETERS

Fractals ◽  
1994 ◽  
Vol 02 (03) ◽  
pp. 437-440 ◽  
Author(s):  
WILLIAM A. JOHNSEN ◽  
CHRISTOPHER A. BROWN
Keyword(s):  
Fractal Dimension ◽  
Fractal Analysis ◽  
Data Sets ◽  
Characterization Methods ◽  
Topographic Data ◽  
Box Counting ◽  
Correlation Methods ◽  
Analysis Methods ◽  
Wide Range ◽  
Point Correlation

The objective of this work is to compare fractal-based, topographic characterization parameters calculated by several different fractal analysis methods. Four fractal characterization methods (compass, patchwork, box counting, and 2-point correlation) are systematically applied to five topographic data sets, which encompass a wide range of scale, and the results are compared. The compass and patchwork methods calculate similar values for the fractal dimension and smooth/rough crossover. The box and 2-point correlation methods calculate similar values for the fractal dimension. The compass and patchwork methods are capable of calculating the smooth/rough crossover.

scholarly journals Fractal analysis for biosurface comparison and behaviour prediction

2009 ◽  
Vol 63 (3) ◽  
pp. 239-245 ◽  
Author(s):  
Bozica Bojovic ◽  
Zoran Miljkovic ◽  
Bojan Babic ◽  
Djuro Koruga
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Fractal Analysis ◽  
Surface Profile ◽  
Scanning Probe ◽  
Real Surface ◽  
Behavior Prediction ◽  
Functional Behavior ◽  
Probe Microscope ◽  
The Given

Fractal analysis was used in previous authors' researches for characterizations of grinded ceramics surface textures by surface profile fractal dimension. In this paper the 'skyscrapers' method was chosen for calculating fractal dimension of surface, using the image processing toolbox, as well as a custom-developed algorithm of Matlab environment. This method entails recording the surface as an image, by using a scanning probe microscope. In the given contact lens case, fractal dimension values confirm changes of the surface roughness during the cleaning and wearing processes. Examination of real surface roughness could provide comparison and functional behavior prediction.

scholarly journals Relation between geometry of fracture surfaces and impact work of wood composite materials

2006 ◽  
Vol 54 (2) ◽  
pp. 91-96
Author(s):  
Eva Přemyslovská ◽  
Petr Koňas
Keyword(s):  
Fractal Dimension ◽  
Composite Materials ◽  
Fractal Analysis ◽  
Wood Composite ◽  
Fracture Surfaces ◽  
Box Counting ◽  
Counting Methods ◽  
Richardson Method ◽  
Proportional Relationship

The aim of this work is description of geometry of fracture surfaces of wood composite materials (cement-bonded particleboard, gypsum-bonded fibreboard and wood particleboard) using fractal analysis and exploration relation between fractal dimension and impact work. Fractal dimension determinated by filtration, volumetric and robust Box-Counting methods and Richardson method is different considering type of material and method. Proportional relationship between fractal dimension (computed by robust BC method) and impact work of mentioned materials was found in other cases non-proportional relationships were founded.

scholarly journals Flow Simulation of Artificially Induced Microfractures Using Digital Rock and Lattice Boltzmann Methods

Energies ◽  
2018 ◽  
Vol 11 (8) ◽  
pp. 2145 ◽  
Author(s):  
Yongfei Yang ◽  
Zhihui Liu ◽  
Jun Yao ◽  
Lei Zhang ◽  
Jingsheng Ma ◽  
...  
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Lattice Boltzmann ◽  
Fractal Theory ◽  
Fractal Dimensions ◽  
Geometrical Parameters ◽  
Fracture Aperture ◽  
Berea Sandstone ◽  
Wide Range ◽  
Induced Fractures

Microfractures have great significance in the study of reservoir development because they are an effective reserving space and main contributor to permeability in a large amount of reservoirs. Usually, microfractures are divided into natural microfractures and induced microfractures. Artificially induced rough microfractures are our research objects, the existence of which will affect the fluid-flow system (expand the production radius of production wells), and act as a flow path for the leakage of fluids injected to the wells, and even facilitate depletion in tight reservoirs. Therefore, the characteristic of the flow in artificially induced fractures is of great significance. The Lattice Boltzmann Method (LBM) was used to calculate the equivalent permeability of artificially induced three-dimensional (3D) fractures. The 3D box fractal dimensions and porosity of artificially induced fractures in Berea sandstone were calculated based on the fractal theory and image-segmentation method, respectively. The geometrical parameters (surface roughness, minimum fracture aperture, and mean fracture aperture), were also calculated on the base of digital cores of fractures. According to the results, the permeability lies between 0.071–3.759 (dimensionless LB units) in artificially induced fractures. The wide range of permeability indicates that artificially induced fractures have complex structures and connectivity. It was also found that 3D fractal dimensions of artificially induced fractures in Berea sandstone are between 2.247 and 2.367, which shows that the artificially induced fractures have the characteristics of self-similarity. Finally, the following relations were studied: (a) exponentially increasing permeability with increasing 3D box fractal dimension, (b) linearly increasing permeability with increasing square of mean fracture aperture, (c) indistinct relationship between permeability and surface roughness, and (d) linearly increasing 3D box fractal dimension with increasing porosity.

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