Modelling hydraulic fracturing with the J-integral

2021 ◽  
Author(s):  
Edoardo Pezzulli ◽  
Morteza Nejati ◽  
Saeed Salimzadeh ◽  
Stephan Matthai ◽  
Thomas Driesner
Keyword(s):  
Finite Element ◽  
Hydraulic Fracturing ◽  
Fractured Reservoirs ◽  
Fluid Pressure ◽  
Standard Technique ◽  
J Integral ◽  
The Novel ◽  
Element Analysis ◽  
Fracture Length ◽  
Propagation Regime

<p>Hydraulic fracturing plays a central role in engineering fractured reservoirs. To simulate the propagation of “dry” fractures, the J-integral has been a standard technique. Its superior accuracy at coarser resolutions make it particularly attractive, especially for reservoir-scale simulations. However, the extension of the J-integral to hydro-mechanical simulations of fluid-driven fracturing has not received the same attention or success. In particular, while several studies have highlighted the capacity of the method in simulating viscosity-dominated propagation, detailed investigations into the performance of the method are still missing. In this work, we find that the extent of hydraulic fracturing is typically overestimated by the J-integral in the viscosity-dominated propagation regime.<span>  </span>A finite element analysis is conducted which sheds light on the source of the error. The case is put forward that the inaccurate numerical solution for fluid pressure is <em>exclusively</em> responsible for the loss in accuracy of the J-integral. With this new understanding, the J-integral is reformulated to minimise its dependence on inaccurate fluid pressures, bypassing the aforementioned sources of error. The reformulation, termed the J<sub>V</sub>-integral, is both simple to implement, and general to the numerical method. Within the framework of finite elements, a propagation algorithm using the novel J<sub>V</sub>-integral is subsequently constructed with two distinct abilities compared to the original J-integral. The first is an increased ability to capture the viscosity-dominated regime of propagation at significantly coarser resolutions. Finite element simulations conducted at various levels of refinement detail the promising results relevant to hydro-mechanical simulations at reservoir scale.<span>  </span>The ability of the method in simulating the toughness regime remains as performant as the original J-integral.<span>  </span>The second, is the ability of the J<sub>V</sub>-integral in extracting the propagation velocity of the fracture; a feature particular to methods arising from hydraulic fracture mechanics. Consequently, the method demonstrates an inherent advantage when converging on the fracture length, requiring significantly fewer iterations compared to the original formulation. Fundamentally, the velocity obtained via the J<sub>V</sub>-integral has the potential to be used in combination with front-tracking schemes like the implicit level set method. As a result, the J<sub>V</sub>-integral appears to be a promising method when simulating hydraulic fracturing in geoenergy applications and beyond.<span> </span></p>

scholarly journals Sealing Performance Analysis of an End Fitting for Marine Unbonded Flexible Pipes Based on Hydraulic-Thermal Finite Element Modeling

Energies ◽  
2019 ◽  
Vol 12 (11) ◽  
pp. 2198 ◽  
Author(s):  
Liping Tang ◽  
Wei He ◽  
Xiaohua Zhu ◽  
Yunlai Zhou
Keyword(s):  
Finite Element ◽  
Fluid Pressure ◽  
Temperature Fields ◽  
Effect Of Temperature ◽  
Fe Model ◽  
Element Analysis ◽  
Sealing Capacity ◽  
Sealing Performance ◽  
Metal Seal ◽  
Essential Components

End fittings are essential components in marine flexible pipe systems, performing the two main functions of connecting and sealing. To investigate the sealing principle and the influence of the temperature on the sealing performance, a hydraulic-thermal finite element (FE) model for the end fitting sealing structure was developed. The sealing mechanism of the end fitting was revealed by simulating the sealing behavior under the pressure penetration criteria. To investigate the effect of temperature, the sealing behavior of the sealing ring under different temperature fields was analyzed and discussed. The results showed that the contact pressure of path 1 (i.e., metal-to-polymer seal) was 31.7 MPa, which was much lower than that of path 2 (metal-to-metal seal) at 195.6 MPa. It was indicated that the sealing capacities were different for the two leak paths, and that the sealing performance of the metal-to-polymer interface had more complicated characteristics. Results also showed that the finite element analysis can be used in conjunction with pressure penetration criteria to evaluate the sealing capacity. According to the model, when the fluid pressures are 20 and 30 MPa, no leakage occurs in the sealing structure, while the sealing structure fails at the fluid pressure of 40 MPa. In addition, it was shown that temperature plays a significant role in the thermal deformation of a sealing structure under a temperature field and that an appropriately high temperature can increase the sealing capacity.

Finite Element Fracture Mechanics Study of Pre-Northridge Connections

2006 ◽  
Vol 324-325 ◽  
pp. 1007-1010 ◽  
Author(s):  
Hong Bo Liu ◽  
Chang Hai Zhai ◽  
Yong Song Shao ◽  
Li Li Xie
Keyword(s):  
Stress Intensity Factor ◽  
Finite Element ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Fracture Behavior ◽  
Integral Approach ◽  
J Integral ◽  
Finite Element Analyses ◽  
Element Analysis ◽  
Weld Root

The objective was to quantify the variation of stress intensity factor to weld root flaw sizes in steel frame connections. Finite-element analyses were used to study fracture toughness in welded beam-column connections. Investigations of fracture behavior mainly focused on the standard pre-Northridge connection geometry. Finite element analysis was performed using the ANSYS computer program. Stress intensity factor was calculated through a J-integral approach. Results show that stress intensity factor is not uniform and is largest in the middle of beam flange. Stress intensity factor increases nearly linear with the increase of flaw size. Backing bars have little effect on weld fractures.

Effects of Negative Biaxial Loadings and Notch on Failure Assessment Diagrams

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
K. Ragupathy ◽  
K. Ramesh ◽  
D. Hall
Keyword(s):  
Finite Element ◽  
Fracture Mechanics ◽  
Biaxial Loading ◽  
Failure Criteria ◽  
Small Scale ◽  
J Integral ◽  
Element Analysis ◽  
Worst Case ◽  
Failure Assessment ◽  
The Impact

The failure assessment diagram (FAD) is a simplified and robust flaw assessment methodology, which simultaneously connects two dominant failure criteria: linear elastic fracture mechanics on one end and plastic collapse on the other end. This interaction is in the realm of elastic-plastic fracture mechanics. It is popularly known as the R6 approach, which graphically characterizes the impact of plasticity on crack driving force. In recent years, there has been continuous interest in using FADs to assess the failure of cracked structures subjected to biaxial loadings. Biaxiality is defined as the ratio of stress applied parallel and normal to the crack. Some pressure loaded aircraft components operate under negative biaxial ratios up to −0.5. In this paper, a detailed study on FAD was conducted using finite element analysis computed J-integral methods to investigate the effect of biaxial loading using different FAD approaches for geometries with notches. Geometries with a crack that emanates at a fillet region were simulated with various biaxial loading ratios from −0.5 to +0.5 using 2014-T6 material. FAD curves were numerically generated for cracks at notched regions subjected to various biaxial loadings using J-integral values from finite element analyses. These results were compared with standard FAD approaches. All comparison studies were made between uniaxial and biaxial loading cases with FAD curves created using four different crack sizes. Under small scale yielding, this study clearly shows that FAD curves are not influenced by negative biaxial loading at low load (up to 40% of yield strength). It was clearly confirmed that the majority of previously developed analytical FAD curves do not effectively account for notch and plasticity effects due to negative biaxiality. Based on this study, tension normal to the crack and compression parallel to the crack is the worst combination, and it has a very pronounced effect on FAD curve shapes. The standard analytical FAD curves are nonconservative compared with the approach recommended here, particularly under the worst case condition. FAD curves developed are shown to predict lower failure loads as compared with the currently accepted analytical FAD approaches defined in existing standards, e.g., R6 and API 579. The impact of negative biaxial loading can be investigated directly using a J-integral FAD approach but can be compared with ease by plotting both approaches in a FAD format.

An Experimental-Numerical Hybrid Method to Determine Dynamic Elastic-Plastic Fracture Toughness

2013 ◽  
Vol 577-578 ◽  
pp. 517-520 ◽  
Author(s):  
Shi Fan Zhu ◽  
Yang Cao ◽  
Chun Huan Guo ◽  
Feng Chun Jiang
Keyword(s):  
Fracture Toughness ◽  
Finite Element ◽  
Dynamic Fracture ◽  
Dynamic Fracture Toughness ◽  
J Integral ◽  
Hopkinson Pressure Bar ◽  
Element Analysis ◽  
Three Point Bending ◽  
Elastic Plastic ◽  
Load Displacement

The dynamic fracture behavior of 7075-T6 aluminum alloy was studied by finite element method to simulate a cracked three-point bending specimen loaded by stress wave loading. In order to determine the elastic-plastic dynamic fracture toughness using quasi-static fracture mechanics theory, the nominal load measured by Hopkinson pressure bar loaded fracture testing system was input into a finite element program to calculate the loading point displacement, and then this displacement was employed to obtain the load-displacement field in the vicinity of the crack tip without the inertia effect, the variation of J-integral as a function of time was established using the load-displacement parameters determined by finite element analysis. The critical J-integral corresponding to crack initiation time detected by a small strain gauge mounted on the three-point bending fracture specimen is determined as an elastic-plastic dynamic fracture toughness (JId). The comparison between the equivalent dynamic fracture toughness(KId) given by the aforementioned procedures and the value measured in previous studies was made to verify the validation of the proposed procedure.

A review of fatigue and fracture mechanics with a focus on rubber-based materials

2017 ◽  
Vol 233 (5) ◽  
pp. 1005-1019 ◽  
Author(s):  
Pooya Behroozinia ◽  
Reza Mirzaeifar ◽  
Saied Taheri
Keyword(s):  
Finite Element ◽  
Fracture Mechanics ◽  
Strain Energy ◽  
Strain Energy Release ◽  
Fatigue Loading ◽  
J Integral ◽  
Element Analysis ◽  
Integral Estimation ◽  
Primary Focus ◽  
Energy Dissipated

Prediction of how cracks nucleate and develop is a major concern in fracture mechanics. The purpose of this study is to provide an overview of the state of the art on fracture mechanics with primary focus on different methodologies available for crack initiation and growth prediction in rubber-based materials under the static and fatigue loading conditions. The concept of fracture mechanics applied to rubber-based materials and concern of finite element analysis for J-integral estimation in elastomers are discussed in this paper. The strain energy release rate is commonly used to describe the energy dissipated during fracture per unit of fracture surface area and can be calculated by J-integral method, which represents a path-independent integral around the crack tip. As fatigue crack growth most commonly occurs in structures, the high-cycle fatigue life of components needs to be predicted by using extended finite element, strain energy density, finite fracture mechanics, and other techniques which will be covered in this review paper. In addition, some recent testing and numerical results reported in the literature and their applications will be discussed.

Characterization of Shape-Changing Panels With Embedded Rubber Muscle Actuators

2012 ◽  
Author(s):  
Larry D. Peel ◽  
Enrique Molina ◽  
Jeff Baur ◽  
Ryan Justice
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Water Pressure ◽  
Mechanical Energy ◽  
Fluid Pressure ◽  
Laminated Plate ◽  
Element Analysis ◽  
Plate Models ◽  
Optimal Spacing ◽  
Muscle Actuators

There is great interest in making shape-changing aircraft structures that are more biomimetic. Cylindrical McKibben-like flexible actuators efficiently convert fluid pressure into mechanical energy and thus offer excellent force-to-weight ratios while behaving similar to biological muscle. McKibben-like Rubber Muscle Actuators (RMAs) were embedded into elastomer panels. The effect of actuator spacing on the performance of these shape-changing panels was investigated. The work included nonlinear finite element analysis, fabrication, and testing of panels where four RMAs were spaced side-by-side, 1/2, 1, and 1.3 RMA diameters apart. Nonlinear “Laminated Plate” and “Rod & Plate” finite element models of individual RMAs were created from existing RMA dimensions. After adjusting for an initial “activation pressure,” the models produced realistic RMA forces. The laminated plate models used less computer resources, but only produced small amounts of actuator contraction (actuator strain). The more resource-intensive Rod & Plate models better replicated fiber/braid re-orientation and produced axial strains up to 60% of test values. Three types of embedded RMA panel FEA models; a “2D Cross-Section,” a “Full 3D Panel” (with either Laminated Plate or Rod & Plate RMAs) and a “3D Unit Cell” (also with either Laminated Plate or Rod & Plate RMAs). The Full 3D Rod & Plate model gave the most accurate strains and forces, but required unsustainable levels of computing resources. The 2D cross-section model predicted optimal RMA spacing to be at 1 diameter. All other FEA models show optimal panel performance between 1/2 and 1 diameter spacing. Panels with embedded RMAs were fabricated and tested with air or water pressure. Panel force as a function of pressure and as a function of contraction (strain) was obtained. Overall, FEA and test results for panels indicate that optimal performance occurs when the RMAs are spaced between 1/2 to 1 diameter apart. Actuator force as a function of spacing is fairly flat in this region, indicating that minor design or manufacturing differences may not significantly affect performance. However, the total amount of axial contraction decreases significantly at greater than optimal spacing. Useful design, simulation, and test methodologies for embedded RMA panels have been demonstrated.

Numerical – Experimental Correlation of Sheet Hydroformed Component

2015 ◽  
Vol 651-653 ◽  
pp. 1140-1145
Author(s):  
Alessandro Spagnolo ◽  
Teresa Primo ◽  
Gabriele Papadia ◽  
Antonio del Prete
Keyword(s):  
Finite Element ◽  
Process Parameters ◽  
Complex Geometry ◽  
Thickness Distribution ◽  
Fluid Pressure ◽  
Experimental Tests ◽  
Element Analysis ◽  
Influence Of Process Parameters ◽  
Experimental Correlation ◽  
Hydroforming Process

Sheet hydroforming has gained increasing interest in the automotive and aerospace industries because of its many advantages such as higher forming potentiality, good quality of the formed parts which may have complex geometry. The main advantage is that the uniform pressure can be transferred to any part of the formed blank at the same time. This paper reports numerical and experimental correlation for symmetrical hydroformed component. Experimental tests have been carried out through the hydroforming cell tooling, designed by the authors thanks to a research project, characterized by a variable upper blankholder load of eight different hydraulic actuators. The experimental tests have been carried out following a factorial plane of two factors, with two different levels for each factor and three replicates for each test with a total of 12 tests. In particular two process parameters have been considered: blank holder force, die fluid pressure. Each factor has been varied between an High (H) and Low level (L). The order in which have been conducted the tests has been established through the use of the Minitab software, in order to ensure the data normality and the absence of auto-correlation between the tests. An ANOVA analysis has been performed, in addition, with the aim of evaluating the influence of process parameters on the thickness distribution of the component, its formability and feasibility. Finally, finite element analysis (FEA) was used to understand the formability of a material during the hydroforming process. In this paper, the commercial finite element code LS-Dyna was used to run the simulations. A good numerical – experimental correlation has been obtained.

Measuring Model and Design of the Novel Loaded Over-Constrained Parallel Six-Component Force/Torque Sensor

2012 ◽  
Author(s):  
Yanzhi Zhao ◽  
Chao Lu ◽  
Tieshi Zhao
Keyword(s):  
Finite Element ◽  
Theoretical Calculations ◽  
Force Sensor ◽  
The Novel ◽  
Torque Sensor ◽  
Element Analysis ◽  
Sensor Structure ◽  
Structure Scheme ◽  
Flexible Deformation ◽  
Component Force

Based on constrained screw type synthesis theory, a novel spacial over-constrained parallel six-component force/torque sensor mechanism which contains 12 SS branches was proposed. Then considering the branches flexible deformation, with the supplementary deformation coordination and physical constitutive constraint equations, structural balance equations were established respectively in six one-way measurement states. The stress and mode of the whole over-constrained parallel six-component force sensor structure scheme were analyzed with the Finite Element Method (FEM), and the analysis results were contrasted and conclused that theoretical calculations and Finite Element Analysis of conclusion were coincide.

Sign in / Sign up

Export Citation Format

Share Document