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Non-deformable support system in swelling and squeezing rocks
Published in Xia-Ting Feng, Rock Mechanics and Engineering, 2017
Support design is one of the most important issues in tunneling. It is an analysis of process that includes complex 3D components. Correct solutions can only be produced by applying these 3D components with knowledge and understanding (Feng & Hudson, 2010). Bending moment, shear forces and axial forces acting on the supports affect the performance of support systems. The movement of the tunnel face, stresses occurring in front of the face, and the success of precautions for these effects can only be determined by 3D analysis (Aksoy & Onargan, 2010; Aksoy et al., 2012; 2014). Design of this complex structure in 2D brings many problems. Empirical or semi-empirical 3D solutions, however, take too much time. Numerical methods are the easiest way to perform 3D analysis. There are many methods in numerical modeling, the most popular being finite element (FEM), finite difference (FDM) and boundary element methods (BEM). The principles of numerical modeling are described in Figure 1 (Feng & Hudson, 2010). As can be seen from Figure 1, numerical modeling methods are relatively simple, but at the same time incorporate long-running observations.
Non-deformable support system in swelling and squeezing rocks
Published in Xia-Ting Feng, Rock Mechanics and Engineering, 2017
Support design is one of the most important issues in tunneling. It is an analysis of process that includes complex 3D components. Correct solutions can only be produced by applying these 3D components with knowledge and understanding (Feng & Hudson, 2010). Bending moment, shear forces and axial forces acting on the supports affect the performance of support systems. The movement of the tunnel face, stresses occurring in front of the face, and the success of precautions for these effects can only be determined by 3D analysis (Aksoy & Onargan, 2010; Aksoy et al., 2012; 2014). Design of this complex structure in 2D brings many problems. Empirical or semi-empirical 3D solutions, however, take too much time. Numerical methods are the easiest way to perform 3D analysis. There are many methods in numerical modeling, the most popular being finite element (FEM), finite difference (FDM) and boundary element methods (BEM). The principles of numerical modeling are described in Figure 1 (Feng & Hudson, 2010). As can be seen from Figure 1, numerical modeling methods are relatively simple, but at the same time incorporate long-running observations.
Modeling of Thermal Systems
Published in Yogesh Jaluria, Design and Optimization of Thermal Systems, 2019
Numerical models are based on mathematical models and allow one to obtain, using a computer, quantitative results on the system behavior for different operating conditions and design parameters. Only very simple cases can usually be solved by analytical procedures; numerical techniques are needed for most practical systems. Numerical modeling refers to the restructuring and discretization of the governing equations in order to solve them on a computer. The relevant equations may be algebraic equations, ordinary or partial differential equations, integral equations, or combinations of these, depending upon the nature of the process or system under consideration.
A semi-analytical workflow to study dimethyl ether improved water flooding; a fractional flow study
Published in Petroleum Science and Technology, 2022
Pooria Soleimani, Mohammad Chahardowli, Mohammad Simjoo
To the best of our knowledge, hardly any published work can be found to investigate DEW fractional flow analysis. In this article, we introduce a semi-analytical approach for DME improved water flooding. We apply the results of Taylor linearization method to develop our numerical model. Then, a finite difference scheme was used to solve equations. Afterwards, for any given partition coefficient, the obtained results are used to plot fw-curves and perform analysis. Fractional flow curves vary with the variation of the partition coefficient, therefore, numerous fw-curves may exist and present the state of the system. We showed that there is an accurate relation between the starting point to draw the tangential line on the fractional flow, and the value of the partition coefficient. Moreover, we showed that the tangential line intersects the horizontal axis and forms a pseudo adsorption point that its value varies with the variation of the partition coefficient. This approach can be considered useful for the analysis of water/DME/oil displacement process, however, this approach could be further completed. The article is organized as follows: the mathematical model and the numerical modeling procedure is described in “Mathematical model” section. Afterwards, “Results and discussions” section discusses the main results in detail. The article ends with the “Summary and conclusions” section, which summarizes the main conclusions.
Probabilistic model for structural mechanics of fiber bundle and its application to PBO fiber
Published in The Journal of The Textile Institute, 2021
Kang Zhang, Xiaodong Liu, Fisseha Wubneh Asmare, Puxin Zhu, Ruixia Li, Dacheng Wu
PBO is a kind of high-performance fiber, and the stress-strain behavior of its single fiber conforms to Hooke’s law. The ideal stress-strain curve of PBO fiber bundle is completely coincident with that of its single fiber. Studies have shown that the strength of a single fiber has a certain degree of dispersion which directly affects the strength of the fiber bundle (Huang et al., 2015). Tensile strength of the single fiber provided by manufacturers was usually at quasi-static form. As a consequence, for a fiber bundle composed of many fibers, its tensile strength cannot be obtained simply by scaling up the tensile strength of a single fiber provided by the manufacturer (Zhu et al., 2012). Instead, it is necessary to measure the mechanical properties of the single fiber and find a distribution function consistent with the actual situation to describe and predict the strength of the fiber bundle (Zhu et al., 2012). According to the prediction of the mechanical properties of the single fiber, the micro-scale mechanical model can also be established and verified to provide the necessary supporting data for optimizing the product properties. The numerical modeling of mechanical properties of a single fiber by computer simulation is of great significance in quality analysis and fracture strength prediction of composite materials. At present, there are some distribution functions to be used to describe the strength distribution of materials, including Weibull distribution, exponential distribution, Gauss distribution, etc. (Eldeeb & Neckář, 2017; Huang et al., 2015; Sayeed & Paharia, 2019; Shi et al., 2015; Wang & Shao, 2014; Zhu et al., 2012; Zok, 2017).
The study on modeling and simulation of shale multi-scale matrix-fracture system
Published in Petroleum Science and Technology, 2023
Qichao Gao, Lingling Yu, Lulu Liao, Gao Xiaodong
The numerical modeling and simulation process in this manuscript is shown in Figure 4. The method can be divided into several basic steps. First, we create a geometric model based on the real physical model, and then assign attribute parameters and boundary conditions to the numerical model according to the research problem. Next, discretize the geometric model and discretize the system of partial differential equations. After that the model is iteratively solved. If the model converges, the numerical solution of the problem is obtained. If the model does not converge, the geometric model and parameters need to be adjusted. Finally, the simulation results are evaluated through data visualization and sensitivity analysis.