Microfracture development and chemical damage analysis of limestone based on fractal theory

2020 ◽  
pp. qjegh2020-015
Author(s):  
Luwang Chen ◽  
Ruirui Li ◽  
Lanting Wang ◽  
Jie Zhang ◽  
Qinghua Ou ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Fractal Geometry ◽  
Fractal Theory ◽  
Fractal Dimensions ◽  
Damage Evolution Equation ◽  
Fracture Width ◽  
Chemical Damage ◽  
Fracture Evolution ◽  
Rock Mechanical Properties ◽  
Geometry Method

To explore the influence of microfracture development caused by chemical dissolution on the mechanical properties of limestone, this paper presents a new numerical simulation and quantitative analysis method. First, the dissolution rate was determined by the theory of chemical kinetics, and a differential equation that can be solved for results of the fracture evolution process by COMSOL Multiphysics was established to describe the microfracture's expansion. The fractal dimensions of the microfractures were found to have a linear relationship with the damage variables at different time periods through analysis of the simulation results with the fractal geometry method using fracture width as the index, which proves that the evolution of damage has a fractal nature. After that, a damage evolution equation was fitted to predict the deterioration in rock mechanical properties under hydrochemical actions and the predictive uniaxial compressive strength of limestone is seen to be in agreement with experimental test results. The application of the fractal geometry method has important engineering significance as it relates the development of microscopic fractures to changes in the macroscopic mechanical properties and predicts the mechanical properties of the rock under chemical damage.

The Estimation of Barrel-Rifle Surface Wear Based on Fractal Theory

2007 ◽  
Vol 353-358 ◽  
pp. 750-753
Author(s):  
Chang Jing ◽  
Bing Cheng Wang ◽  
Zhao Hui Ren ◽  
Tao Yu ◽  
Nai Hui Song
Keyword(s):  
Surface Topography ◽  
Wear Surface ◽  
Fractal Geometry ◽  
Correlation Dimension ◽  
Fractal Theory ◽  
Fractal Dimensions ◽  
Internal Surface ◽  
Surface Wear ◽  
Correlation Dimension Method

In this paper, the theory of fractal geometry was used to study the barrel-rifle surface topography and correlation dimension method was adopted to calculate the fractal dimensions of the projectile worn marks shot from the barrels with different worn. The study showed that the different wears of barrel-rifle surface resulted in different fractal dimensions of the projectile wear surface and there was a correlation between the fractal dimensions of the projectile wear surface and the change of the barrel rifle surface. Therefore, through the rifle marks on the projectiles, not only the wear of the barrel’s internal surface can be analyzed, but the gun life also can be further estimated. The paper provided a new tool for analyzing the barrel-rifle surface wear.

scholarly journals Dynamic characteristics and fractal representations of crack propagation of rock with different fissures under multiple impact loadings

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Bing Sun ◽  
Shun Liu ◽  
Sheng Zeng ◽  
Shanyong Wang ◽  
Shaoping Wang
Keyword(s):  
Fractal Dimension ◽  
Crack Propagation ◽  
Crack Growth ◽  
Impact Test ◽  
Fractal Theory ◽  
Dynamic Change ◽  
Fractal Dimensions ◽  
Peak Stress ◽  
Dynamic Mechanical Properties ◽  
Gravitational Potential Energy

AbstractTo investigate the influence of the fissure morphology on the dynamic mechanical properties of the rock and the crack propagation, a drop hammer impact test device was used to conduct impact failure tests on sandstones with different fissure numbers and fissure dips, simultaneously recorded the crack growth after each impact. The box fractal dimension is used to quantitatively analyze the dynamic change in the sandstone cracks and a fractal model of crack growth over time is established based on fractal theory. The results demonstrate that under impact test conditions of the same mass and different heights, the energy absorbed by sandstone accounts for about 26.7% of the gravitational potential energy. But at the same height and different mass, the energy absorbed by the sandstone accounts for about 68.6% of the total energy. As the fissure dip increases and the number of fissures increases, the dynamic peak stress and dynamic elastic modulus of the fractured sandstone gradually decrease. The fractal dimensions of crack evolution tend to increase with time as a whole and assume as a parabolic. Except for one fissure, 60° and 90° specimens, with the extension of time, the increase rate of fractal dimension is decreasing correspondingly.

Integration of Chemofacies and Rock Mechanical Properties Using Machine Learning Algorithms: Implications for Geomechanics and Hydraulic Fracture Stimulations in Paleozoic Formations, Saudi Arabia

2021 ◽  
Author(s):  
Maaruf Hussain ◽  
Abduljamiu Amao ◽  
Khalid Al-Ramadan ◽  
Sunday Olatunji ◽  
Ardiansyah Negara
Keyword(s):  
Machine Learning ◽  
Mechanical Properties ◽  
Saudi Arabia ◽  
Spatial Distribution ◽  
Chemical Composition ◽  
Rock Strength ◽  
Machine Learning Algorithms ◽  
Unconventional Reservoirs ◽  
Geochemical Properties ◽  
Rock Mechanical Properties

Abstract The knowledge of rock mechanical properties is critical to reducing drilling risk and maximizing well and reservoir productivity. Rock chemical composition, their spatial distribution, and porosity significantly influenced these properties. However, low porosity characterized unconventional reservoirs as such, geochemical properties considerably control their mechanical behavior. In this study, we used chemostratigraphy as a correlation tool to separate strata in highly homogenous formations where other traditional stratigraphic methods failed. In addition, we integrated the chemofacies output and reduced Young's modulus to outline predictable associations between facies and mechanical properties. Thus, providing better understanding of lithofacies-controlled changes in rock strength that are useful inputs for geomechanical models and completions stimulations.

scholarly journals Approximate Dynamic Programming Based Control of Proppant Concentration in Hydraulic Fracturing

Mathematics ◽  
2018 ◽  
Vol 6 (8) ◽  
pp. 132 ◽  
Author(s):  
Harwinder Singh Sidhu ◽  
Prashanth Siddhamshetty ◽  
Joseph Kwon
Keyword(s):  
Mechanical Properties ◽  
Dynamic Programming ◽  
Hydraulic Fracturing ◽  
Young’S Modulus ◽  
Large Scale ◽  
Approximate Dynamic Programming ◽  
Young's Modulus ◽  
Computational Cost ◽  
Control Technique ◽  
Rock Mechanical Properties

Hydraulic fracturing has played a crucial role in enhancing the extraction of oil and gas from deep underground sources. The two main objectives of hydraulic fracturing are to produce fractures with a desired fracture geometry and to achieve the target proppant concentration inside the fracture. Recently, some efforts have been made to accomplish these objectives by the model predictive control (MPC) theory based on the assumption that the rock mechanical properties such as the Young’s modulus are known and spatially homogenous. However, this approach may not be optimal if there is an uncertainty in the rock mechanical properties. Furthermore, the computational requirements associated with the MPC approach to calculate the control moves at each sampling time can be significantly high when the underlying process dynamics is described by a nonlinear large-scale system. To address these issues, the current work proposes an approximate dynamic programming (ADP) based approach for the closed-loop control of hydraulic fracturing to achieve the target proppant concentration at the end of pumping. ADP is a model-based control technique which combines a high-fidelity simulation and function approximator to alleviate the “curse-of-dimensionality” associated with the traditional dynamic programming (DP) approach. A series of simulations results is provided to demonstrate the performance of the ADP-based controller in achieving the target proppant concentration at the end of pumping at a fraction of the computational cost required by MPC while handling the uncertainty in the Young’s modulus of the rock formation.

scholarly journals Development of Back-calculation Model for Aggregate Gradation Determination Using Fractal Theory

2018 ◽  
Vol 159 ◽  
pp. 01006
Author(s):  
Bagus Hario Setiadji ◽  
Supriyono ◽  
Djoko Purwanto
Keyword(s):  
Fractal Dimension ◽  
Fractal Theory ◽  
Asphalt Mixture ◽  
Fractal Dimensions ◽  
Calculation Model ◽  
Careful Consideration ◽  
Upper And Lower Bounds ◽  
Aggregate Gradation ◽  
Fractal Characteristic ◽  
Fractal Characteristics

Several studies have shown that fractal theory can be used to analyze the morphology of aggregate materials in designing the gradation. However, the question arises whether a fractal dimension can actually represent a single aggregate gradation. This study, which is a part of a grand research to determine aggregate gradation based on known asphalt mixture specifications, is performed to clarify the aforementioned question. To do so, two steps of methodology were proposed in this study, that is, step 1 is to determine the fractal characteristics using 3 aggregate gradations (i.e. gradations near upper and lower bounds, and middle gradation); and step 2 is to back-calculate aggregate gradation based on fractal characteristics obtained using 2 scenarios, one-and multi-fractal dimension scenarios. The results of this study indicate that the multi-fractal dimension scenario provides a better prediction of aggregate gradation due to the ability of this scenario to better represent the shape of the original aggregate gradation. However, careful consideration must be observed when using more than two fractal dimensions in predicting aggregate gradation as it will increase the difficulty in developing the fractal characteristic equations.

scholarly journals FRACTAL APPROACH TO MECHANICAL AND ELECTRICAL PROPERTIES OF GRAPHENE/SIC COMPOSITES

2021 ◽  
Vol 19 (2) ◽  
pp. 271
Author(s):  
Yu-Ting Zuo ◽  
Hong-Jun Liu
Keyword(s):  
Carbon Nanotubes ◽  
Electrical Properties ◽  
Fractal Theory ◽  
Bright Light ◽  
Fractal Dimensions ◽  
Mechanical Analysis ◽  
New Era ◽  
Fractal Approach ◽  
Mechanical And Electrical Properties ◽  
Sic Composites

Graphene and carbon nanotubes have a Steiner minimum tree structure, which endows them with extremely good mechanical and electronic properties. A modified Hall-Petch effect is proposed to reveal the enhanced mechanical strength of the SiC/graphene composites, and a fractal approach to its mechanical analysis is given.  Fractal laws for the electrical conductivity of graphene, carbon nanotubes and graphene/SiC composites are suggested using the two-scale fractal theory. The Steiner structure is considered as a cascade of a fractal pattern. The theoretical results show that the two-scale fractal dimensions and the graphene concentration play an important role in enhancing the mechanical and electrical properties of graphene/SiC composites. This paper sheds a bright light on a new era of the graphene-based materials.

Moisture adsorption thermodynamics of wood from fractal-geometry approach

Holzforschung ◽  
2004 ◽  
Vol 58 (3) ◽  
pp. 274-279 ◽  
Author(s):  
J. Cao ◽  
D.P. Kamdem
Keyword(s):  
Thermodynamic Properties ◽  
Moisture Content ◽  
Adsorption Isotherms ◽  
Fractal Geometry ◽  
Moisture Sorption ◽  
Fractal Dimensions ◽  
Future Research ◽  
Differential Heat ◽  
Internal Surfaces ◽  
Differential Heat Of Adsorption

Abstract The fractal-geometry approach was used to calculate the thermodynamic properties of moisture sorption by wood from the adsorption isotherms in this study. The results were compared with those from an isosteric approach and a calorimetric approach. The adsorption isotherms of Southern yellow pine (Pinus spp.) were measured at 4, 15, 30, and 40°C to provide source data for the calculation of both fractal-geometry and isosteric approaches. The results show that the fractal dimensions of the internal surfaces of wood vary between 2.4 and 2.5. The curves of the differential heat of adsorption −∆H against moisture content from the fractal-geometry approach are similar to those from calorimetric measurements in previous research. The −∆H values from the isosteric approach increased with moisture content within a moisture content range up to 3%. And, at moisture contents higher than 3%, the −∆H values from this method are much higher than those from the fractal-geometry approach and calorimetric approach. As a result, the fractal-geometry approach is applicable to calculate the differential thermodynamic properties of moisture sorption by wood in future research.

Sign in / Sign up

Export Citation Format

Share Document