Numerical simulation of hydraulic fracturing and associated microseismicity using finite-discrete element method

Hydraulic fracturing （HF） technique has been extensively used for the exploitation of unconventional oiland gas reservoirs. HF enhances the connectivity of less permeable oil and gas-bearing rock formationsby fluid injection, which creates an interconnected fracture network and increases the hydrocarbonproduction. Meanwhile, microseismic （MS） monitoring is one of the most effective approaches to evaluatesuch stimulation process. In this paper, the combined finite-discrete element method （FDEM） isadopted to numerically simulate HF and associated MS. Several post-processing tools, includingfrequency-magnitude distribution （b-value）, fractal dimension （D-value）, and seismic events clustering,are utilized to interpret numerical results. A non-parametric clustering algorithm designed specificallyfor FDEM is used to reduce the mesh dependency and extract more realistic seismic information.Simulation results indicated that at the local scale, the HF process tends to propagate following the rockmass discontinuities; while at the reservoir scale, it tends to develop in the direction parallel to themaximum in-situ stress. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

Simulation of a Laboratory Scale Ball Mill via Discrete Element Method Modelling

Discrete Element Method (DEM) is a powerful tool for simulating different types of mills. It also used for computing different types of particles such as rocks, grains, and molecules. DEM has been widely used in the field of rock mechanics. In the present work, DEM approach is applied to model the milling media (powder particles and balls) inside a planetary ball mill and to estimate the distribution of particles of a dry powder during milling. In fact, the efficiency of the DEM strongly depends on the input parameters. The DEM simulation results indicated that DEM is a promising tool for the simulation of the dynamic particles motion and interactions within planetary ball mill. These results could be utilized to further develop the synthesis performance, anticipate the reaction, and reduce the wear in the dry milling reactions.

Parallel Computing of Discrete Element Method on GPU

General purpose computing on GPU for scientific computing has been rapidly growing in recent years. We investigate the applicability of GPU to discrete element method (DEM) often used in particle motion simulation. NVIDIA provides a sample code for this type of simulation, which obtained superior performance than CPU in computational time. A computational model of the contact force in NVIDIA’s sample code is, however, too simple to use in practice. This paper modifies the NVIDIA’s simple model by replacing it with the practical model. The computing speed of the practical model on GPU is compared with the simple one on GPU and with the practical one on CPU in numerical experiments. The result shows that the practical model on GPU obtains the computing speed 6 times faster than the practical one on CPU while 7 times slower than that of the simple one on GPU. The effects of the GPU architectures on the computing speed are analyzed.

Geo-engineered buffer capacity of two-layered absorbing system under the impact of rock avalanches based on Discrete Element Method

Many rock avalanches were triggered by the Wenchuan earthquake on May 12,2008 in southwest China.Protection galleries covered with a single soil layer are usually used to protect against rockfall.Since one-layer protection galleries do not have sufficient buffer capacity,a two-layered absorbing system has been designed.This study aims to find whether an expanded poly-styrol(EPS) cushion,which is used in the soil-covered protection galleries for shock absorption,could be positioned under dynamic loadings.The dynamic impacts of the two-layered absorbing system under the conditions ofrock avalanches are numerically simulated through a 2D discrete element method.By selecting reasonable parameters,a series of numerical experiments were conducted to find the best combination for the twolayered absorbing system.The values of the EPS layer area as a percentage of the total area were set as 0%(S1),22%(S2),and 70%(S3).22% of the area of the EPS layer was found to be a reasonable value,and experiments were conducted to find the best position of the EPS layer in the two-layered absorbing system.The numerical results yield useful conclusions regarding the interaction between the impacting avalanches and the two-layered absorbing system.The soil layer can absorb the shock energy effectively and S2(0.4-m thick EPS cushion covered with soillayer) is the most efficient combination,which can reduce the impact force,compared with the other combinations.

Micromechanical modeling of asphalt concrete fracture using a user-defined three-dimensional discrete element method

A user-defined micromechanical model was developed to investigate the fracture mechanism of asphalt concrete(AC)using the discrete element method(DEM).A three-dimensional(3D)AC beam was built using the "Fish" language provided by PFC3D and was employed to simulate the three-point bending beam test at two temperature levels:-10°C and 15°C.The AC beam was modeled with the consideration of the microstructural features of asphalt mixtures.Uniaxial complex modulus test and indirect tensile strength test were conducted to obtain material input parameters for numerical modeling.The 3D predictions were validated using laboratory experimental measurements of AC beams prepared by the same mixture design.Effects of mastic stiffness,cohesive and adhesive strength on AC fracture behavior were investigated using the DEM model.The results show that the 3D DEM fracture model can accurately predict the fracture patterns of asphalt concrete.The ratio of stress at interfaces to the stress in mastics increases as the mastic stiffness decreases;however,the increase in the cohesive strength or adhesive strength shows no significant influence on the tensile strength.

A Review on Discrete Element Method Simulation in Laser Powder Bed Fusion Additive Manufacturing

Laser powder bed fusion(LPBF)is a popular metal additive manufacturing technique.Generally,the materials employed for LPBF are discrete and particulate metal matters.Thus,the discontinuous behaviors exhibited by the powder materials cannot be simulated solely using conventional continuum-based computational approaches,such as finite-element or finite-difference methods.The discrete element method(DEM)is a proven numerical method to model discrete matter,such as powder particles,by tracking the motion and temperature of individual particles.Recently,DEM simulation has gained popularity in LPBF studies.However,it has not been widely applied.This study reviews the existing applications of DEM in LPBF processing,such as powder spreading and fusion.A review of the existing literature indicates that DEM is a promising approach in the study of the kinetic and thermal fluid behaviors of powder particles in LPBF additive manufacturing.

Visualization of the formation and features of soil arching within a piled embankment by discrete element method simulation

Piled embankments are widely used in highway and railway engineering due to their economy and efficiency inovercoming several issues encountered in constructing embankments over weak soils. Soil arching, caused by the pile-subsoilrelative displacement （△s）, plays an important role in reducing the embankment load falling on weak soil, however, the funda-mental characteristics （e.g., formation and features） of soil arching remain poorly understood. In this study, a series of discreteelement method （DEM） modellings are performed to study the formation and features of soil arching with the variation of As inpiled embankments with or without geosynthetic reinforcement. Firstly, calibration for the modelling parameters is carried out bycomparing the DEM results with the experimental data obtained from the existing literature. Secondly, the analysis of the macro-and micro-behaviours is performed in detail. Finally, a parametric study is conducted in an effort to identify the influences of threekey factors on soil arching： the friction coefficient of the embankment fill （f）, the embankment height （h）, and the pile clear spacing（s-a）. Numerical results indicate that △s is a key factor governing the formation and features of soil arching in embankments. Tobe specific, soil arching gradually evolves from two inclined shear planes at a small △s to a hemispherical arch at a relatively largeAs. Then, with a continuous increase in △s, the soil arching height gradually increases and finally approaches a constant value of0.8（s-a） （i.e., the maximum soil arching height）. For a given case, the higher the soil arching height, the greater the degree of soilarching effect. The parametric study shows that the friction coefficient of the embankment fill has a negligible influence on theformation and features of soil arching. However, embankment height is a key factor governing the formation and features of soilarching. In addition, pile clear spacing has a significant effect on the formation of soil arching, but not on its features.

Numerical simulation of particle flow behavior in a screw conveyor using the discrete element method

Particle motion in a screw conveyor was simulated w让h the discrete element method. The particle flow behavior and transport processes at different screw rotating speeds and filling levels were investigated in this study. The spatial distributions of particle velocity were predicted. The predicted mass flow rate increased w让h increasing screw rotating speed and filling level. The contact forces and granular temperatures of particles were also calculated. The simulation results showed that the translational granular particle temperatures were higher than the rotational granular particle temperatures. In add让ion, the configurational temperatures of particles were calculated from simulated instantaneous particle overlaps, and results indicated that deformation of elastic particles contributed to the rate of energy dissipation. Good agreement between the numerical simulation and experimental results was achieved in this study.

Discrete element method dynamic simulation of icosahedral particle packing under three-dimensional mechanical vibration

Packing densification of monosized regular icosahedral particles under three-dimensional mechanical vibration has been simulated by the discrete element method (DEM).The effects of the vibration conditions and container size on packing densification were systematically investigated.In addition to the macroscale properties (packing density and porosity),the microscale properties,such as the coordination number (CN),radial distribution function (RDF),particle contact type,particle orientation distribution,and stresses/forces,in random loose packing (RLP) and random close packing (RCP) were also characterized and analyzed.The results show that transformation of icosahedral particle packing from RLP to RCP can be realized by properly controlling the vibration conditions.The maximum random packing density without the wall effect reaches 0.7078.Microscale property analysis shows that the average CN increases after vibration.The RDF curves contain two clear peaks for RLP and three for RCP.From RLP to RCP,the probability of face to face contact between two particles increases,while the probabilities of edge to edge,edge to face,and face to vertex contact decrease.The orientation correlation functions indicate the randomness of the vibrated packing structure.In addition,more uniform force and stress distributions are observed within the dense packing structure.

Three-dimensional heat transfer in a particulate bed in a rotary drum studied via the discrete element method

We simulated three-dimensional heat transfer inside a horizontal rotating drum using the discrete element method and a thermal conduction model.The aim was to determine the effect of end-wall heating on thermal behavior of a granular bed.The simulation showed that the end-wall heating significantly affects the axial temperature profile of the bed,particularly when the length-to-diameter ratio is low.Particles near the wall heated faster and became more thermally uniform than those in the center of the drum.The region affected by the end heating gradually increased over time.Increasing the rotation speed enhanced the heat conduction rate,and increasing the fill level reduced the mean temperature and thermal uniformity of the granular bed.Heat transfer was also simulated for drums with different length-to-diameter ratios.

Discrete element method for high-temperature spread in compacted powder systems

The discrete element method is applied to investigate high-temperature spread in compacted metallic particle systems formed by high-velocity compaction. Assuming that heat transfer only occurs at contact zone between particles, a discrete equation based on continuum mechanics is proposed to investigate the heat flux. Heat generated internally by friction between moving particles is determined by kinetic equations. For the proposed model, numerical results are obtained by a particle-flow-code-based program. Temperature profiles are determined at different locations and times. At a fixed location, the increase in temperature shows a logarithmic relationship with time. Investigation of three different systems indicates that the geometric distribution of the particulate material is one of the main influencing factors for the heat conduction process. Higher temperature is generated for denser packing, and vice versa. For smaller uniform particles, heat transfers more rapidly.

Discrete Element Modeling of Asphalt Concrete Cracking Using a User-def ined Three-dimensional Micromechanical Approach

We established a user-defined micromechanical model using discrete element method （DEM） to investigate the cracking behavior of asphalt concrete （AC）. Using the ＂Fish＂ language provided in the particle flow code in 3-Demensions （PFC3D）, the air voids and mastics in asphalt concrete were realistically built as two distinct phases. With the irregular shape of individual aggregate particles modeled using a clump of spheres of different sizes, the three-dimensional （3D） discrete element model was able to account for aggregate gradation and fraction. Laboratory uniaxial complex modulus test and indirect tensile strength test were performed to obtain input material parameters for the numerical simulation. A set of the indirect tensile test were simulated to study the cracking behavior of AC at two levels of temperature, i e, -10 ℃ and 15 ℃. The predicted results of the numerical simulation were compared with laboratory experimental measurements. Results show that the 3D DEM model is able to predict accurately the fracture pattern of different asphalt mixtures. Based on the DEM model, the effects of air void content and aggregate volumetric fraction on the cracking behavior of asphalt concrete were evaluated.

New Method to Measure the Fill Level of the Ball Mill I——Theoretical Analysis and DEM Simulation

The accurate measurement of the fill level in the ball mill has not been resolved because of the interplay of many variable factors, which led the mill to be operated under the uneconomical condition and lost a lot of energy. At present, some methods, such as vibration method and acoustic method, have been applied for measuring the fill level by the researchers. Aiming at the problem of the traditional methods for measuring the fill level, that is, the feature variables of the fill level suffer the influences of the ball load and the water content of the coal, a novel method to measure the fill level is proposed and a possible relation between the fill level and the angular position of the maximum vibration point on the mill shell is investigated. The angular positions of the maximum vibration point on the mill shell for different fill level cases are calculated theoretically under two assumptions, respectively. Meanwhile the charge motions of the mill for different fill level cases are simulated with the discrete element method （DEM）. And the simulation results are verified by comparing the motion trajectories of steel balls and power draft of the mill. The simulated movement trajectories of the outmost layer steel balls in the mill are monitored and analyzed to obtain the angular positions of the maximum vibration point on the mill shell. Both the results of the theoretical calculation and the 3D DEM simulation show that the position of the maximum vibration point on the mill shell moves to a lower angular positions as the fill level decreasing, which provides a new idea for measuring the filllevel accurately.

Simulation Research on the Effect of Spreading Process Parameters on the Quality of Lunar Regolith Powder Bed in Additive Manufacturing

Lunar surface additive manufacturing with lunar regolith is a key step in in-situ resource utilization.The powder spreading process is the key process,which has a major impact on the quality of the powder bed and the precision of molded parts.In this study,the discrete element method(DEM)was adopted to simulate the powder spreading process with a roller.The three powder bed quality indicators,including the molding layer offset,voidage fraction,and surface roughness,were established.Besides,the influence of the three process parameters,which are roller’s translational speed,rotational speed,and powder spreading layer thickness on the powder bed quality indicators was also analyzed.The results show that with the reduction of the powder spreading layer thickness and the increase of the rotational speed,the offset increased significantly;when the translational speed increased,the offset first increased and then decreased,which resulted in an extreme value;with the increase of the layer thickness and the decrease of the translational speed,the values for voidage fraction and surface roughness significantly reduced.The powder bed quality indicators were adopted as the optimization objective,and the multi-objective parameter optimization was carried out.The predicted optimal powder spreading parameters and powder bed quality indicators were then obtained.Moreover,the optimal values were then verified.This study can provide informative guidance for in-situ manufacturing at the moon in future deep space exploration missions.

Modeling screening efficiency with vibrational parameters based on DEM 3D simulation

The efficiency of particle screening was studied over a range of vibrational parameters including amplitude, frequency and vibrational direction. The Discrete Element Method (DEM) was used to simulate the screening process. A functional relationship between efficiency and the parameters, both singly and combined, is established. The function is a complicated exponential. Optimal amplitude and frequency values are smaller for particles near the mesh and larger for other particles. The optimum vibration angle is 45° for nearly all kinds of particles. A transverse velocity, V⊥, was defined and V⊥=0.2 m/s was identified to be the most efficient operating point by both simulation and experimental observation. Comparison of these results with those reported by others is included.

DEM Numerical Simulation of Abrasive Wear Characteristics of a Bioinspired Ridged Surface

This paper presents numerical investigations into a ridged surface whose design is inspired by the geometry of a Farrer’sscallop.The objective of the performed research is to assess if the proposed Bioinspired Ridged Surface (BRS) can potentiallyimprove wear resistance of soil-engaging components used in agricultural machinery and to validate numerical simulationsperformed using software based on the Discrete Element Method (DEM).The wear performance of the BRS is experimentallydetermined and also compared with a conventional flat surface.Different size of soil particles and relative velocities between theabrasive sand and the testing surfaces are used.Comparative results show that the numerical simulations are in agreement withthe experimental results and support the hypothesis that abrasive wear is greatly reduced by substituting a conventional flatsurface with the BRS.

DEM simulation of particle flow on a single deck banana screen

A mathematical study of particle flow on a banana screen deck using the discrete element method (DEM) was presented in this paper. The motion characteristics and penetrating mechanisms of particles on the screen deck were studied. Effects of geometric parameters of screen deck on banana screening process were also investigated. The results show that when the values of inclination of discharge and increment of screen deck inclination are 10° and 5° respectively, the banana screening process get a good screening performance in the simulation. The relationship between screen deck length and screening efficiency was further confirmed. The conclusion that the screening efficiency will not significantly increase when the deck length L≥430 mm (L/B ≥ 3.5) was obtained, which can provide theoretical basis for the optimization of banana screen.

Simulation of random mixed packing of different density particles

This paper presents the effects of density difference on the three-dimensional （3D） distribution of random mixed packing. The random mixed packing dynamics of particles of two different densities are simulated. The initial state is homogeneous, but the final packing state is inhomogeneous. The segregation phenomenon （inhomogeneous distribution） is also observed. In the final state, the top layers are composed of mostly light particles. The several layers beneath the top contain more heavy particles than light particles. At the bottom, they also contain more heavy particles than light particles. Furthermore, at both the top and the bottom, particle clustering is observed. The current study also analyses the cause of this inhomogeneity in detail. The main cause of this phenomenon is the velocity difference after collision of these two types of particles induced by the density difference. The present study reveals that even if particles were perfectly mixed, the packing process would lead to the final inhomogeneous mixture. It suggests that special treatment may be required to get the true homogeneous packing.

Application of the DEM to screening process:a 3D simulation

The discrete element method(DEM) has been widely used to simulate microscopic interactions between particles.Screening is a deeply complicated process when considering the law of motion for the particles,themselves.In this paper,a numerical model for the study of a particle screening process using the DEM is presented.Special attention was paid to the modeling of a vibrating screen that allows particles to pass through,or to rebound,when approaching the screen surface.Inferences concerning screen length and vibrating frequency as they relate to screening efficiency were studied.The conclusions were:three-dimensional simulation of screening efficiency along the screen length follows an exponential distribution;when the sieve vibrates over a certain frequency range the screening efficiency is stable;and,higher vibration frequencies can improve the handling capacity of the screening machine.

Numerical Simulation of Interaction Between Laminar Flow and Elastic Sheet

A numerical simulation of the interaction between laminar flow with low Reynolds number and a highly flexible elastic sheet is presented. The mathematical model for the simulation includes a three-dimensional finitevolume based fluid solver for incompressible viscous flow and a combined finite-discrete element method for the three-dimensional deformation of solid. An immersed boundary method is used to couple the simulation of fluid and solid. It is implemented through a set of immersed boundary points scattered on the solid surface. These points provide a deformable solid wall boundary for the fluid by adding body force to Navier-Stokes equations. The force from the fluid is also obtained for each point and then applied on the boundary nodes of the solid. The vortex-induced vibration of the highly flexible elastic sheet is simulated with the established mathematical model. The simulated results for both swing pattern and oscillation frequency of the elastic sheet in low Reynolds number flow agree well with experimental data.