This paper presents a novel approach to predict the propagation of hydraulic fractures in tight shale reservoirs. Many hydraulic fracture modelling schemes assume that the fracture direction is pre-seeded in the problem domain discretisation. This is a severe limitation as the reservoir often contains large numbers of pre-existing fractures that strongly influence the direction of the propagating fracture. To circumvent these shortcomings, a new fracture modelling treatment is proposed where the introduction of discrete fracture surfaces is based on new and dynamically updated geometrical entities rather than the topology of the underlying spatial discretisation. Hydraulic fracturing is an inherently coupled engineering problem with interactions between fluid flow and fracturing when the stress state of the reservoir rock attains a failure criterion. This work follows a staggered hydro-mechanical coupled finite/discrete element approach to capture the key interplay between fluid pressure and fracture growth. In field practice, the fracture growth is hidden from the design engineer and microseismicity is often used to infer hydraulic fracture lengths and directions. Microseismic output can also be computed from changes of the effective stress in the geomechanical model and compared against field microseismicity. A number of hydraulic fracture numerical examples are presented to illustrate the new technology.

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Complementary hydro-mechanical coupled finite/discrete element and microseismic modelling to predict hydraulic fracture propagation in tight shale reservoirs

This article presents a new approach in which the explicit finite element method (EFEM) and the discrete element method (DEM) are coupled to investigate dynamics of flexible rotor systems supported by deep-groove ball bearings. In this investigation, DEM is used to develop the bearing (dynamic motion) model in which all of the components of the bearing (i.e., inner and outer race, balls, and cage) have 6 degrees of freedom. The flexible shaft is modeled with a full 3D elastic formulation using the EFEM rather than the reduced form, which implements component mode synthesis. The EFEM and DEM were combined to investigate the dynamics of flexible shaft rotor systems supported by ball bearings. Rotor and inner races of the bearings are fully coupled such that both translation and rotation of the flexible rotor are transmitted to the bearings. At each time step, the translational motion and rotation/tilt angle of the rotor cross section at the location of an inner race are applied to the inner race of the bear...

Combined Explicit Finite and Discrete Element Methods for Rotor Bearing Dynamic Modeling

This paper presents the results of an investigation on internal stress progression and the explicit dynamics simulation of the bruising behavior of potato tubers under dynamic mechanical collision. Physical measurements, mechanical tests, advanced solid modeling, and engineering simulation techniques were utilized in the study. The tuber samples used in the simulation were reverse engineered and finite element analysis (FEA) was set up to simulate the collision-based bruising behavior of the potato tubers. The total number of identical tuber models used in the simulation was 17. The numerical data of the FEA results revealed useful stress distribution and mechanical behavior visuals. These results are presented in a frame that can be used to describe bruise susceptibility value on potato-like agricultural crops. The modulus of elasticity was calculated from compression test data as 3.12 MPa. Structural stresses of 1.40 and 3.13 MPa on the impacting (hitting) and impacted (hit) tubers (respectively) were obtained. These stress values indicate that bruising is likely to occur on the tubers. This research paper provides a useful how-to-do strategy to further research on complicated bruising investigations of solid-like agricultural products through advanced engineering simulation techniques. Practical applications: This research aims to simulate realistic dynamic deformation of potato tubers during mechanical collision, which is very hard to achieve through physical or analytical expressions. This is attractive because related food processing industries have shown their interest in determining the physical properties and bruising behavior of food/agricultural products using experimental, numerical, and engineering simulation methods so that it can be used in their food processing technology. Very limited data have been found available in the literature about the subject of FEM-based explicit dynamics simulation of solid-like agricultural crops such as the self-collision case of potato tubers (which is very important for indoor or outdoor potato processing). Comparative investigations on determination of modulus of elasticity are very limited as well. Most of the research focused on single calculation theory and linear static loading assumption-based FEM simulation solutions. Here, we report a “how-to-do” case study for dynamic self-collision simulation of potato tubers.

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Mechanical collision simulation of potato tubers

Realistic representation of time-dependent internal stress progression and deformation behaviour of a potato tuber during a sample drop case has been studied in this paper A reverse engineering approach, compressive tests, slow motion camera records and finite element analysis (FEA) were employed to analyse the drop case deformation behaviour of a sample potato tuber Simulation results provided useful numerical data and stress distribution visuals The numerical results are presented in a format that can be used for the determination of bruise susceptibility magnitude on solid-like agricultural products during drop case The visual observations revealed that slow motion camera images and simulation printouts were in good correlation The modulus of elasticity of the potato specimens was calculated from experimental data to be 312 [MPa] and simulation results showed that the maximum equivalent stress was 0526 [MPa] on the tuber This value for stress indicates that bruising is not likely on the tuber under a pre-defined drop height In order to test the simulation accuracy, empirical and simulation-based estimates for total energy in this drop case were compared The relative difference between empirical and simulation results was 127 % This study provide a good “how to do” guide to further research on the utilisation of (FEM)-based time-dependent simulation approach in complex mechanical impact based damaging analyses and industry focused applications related to solid-like agricultural products such as potato

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Determination of time dependent stress distribution on a potato tuber during drop case

Due to the high cost of the experimental progressive collapse tests, numerical simulation has been widely used by researchers.
 Finite element method is applied in the majority of numerical progressive collapse studies. In this paper, the influences of finite element modeling and analysis techniques including solution procedure, mesh size, element type, column removal time (CRT), damping, strain rate and output-related issues on nonlinear dynamic column removal response of a steel framed structure are evaluated in detail. According to the results, mesh size and column removal time have major influence on the structural response in column removal scenarios, while influences of solution procedure and damping ratio on the maximum response are negligible. Considering the strain-rate effects results in lower response and the rate of decline mainly depends on column removal time. Results also show that special emphasis should be laid on the accuracy of saving outputs, because a long interval causes significant change in the estimated response and may lead to misleading conclusions.

Shen R. Wu

Papers

Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics: Wu/Finite Element Method