Simulation Of Propagation Research Articles

Finite Element Simulation of Stoneley Wave Propagation in Fracture Zones in Wells

The formation and development of fractures increase reservoir heterogeneity and improve reservoir performance. Therefore, it is of great research value to accurately identify the development of fractures. In this paper, two- and three-dimensional models are constructed based on the finite element method and compared with the real axis integration method. The influence of different geometric parameters on the Stoneley wave amplitude is studied to assess the propagation of Stoneley waves in the fracture zone in the well. The results show a significant positive correlation between the width and number of fractures and the attenuation coefficient of Stoneley waves. The fracture angle has a negative correlation with the attenuation coefficient and lesser impact on Stoneley waves. In addition, Stoneley waves are less sensitive to changes in fracture location, while the sensitivity to fracture spacing is significant in the range of 50 cm to 75 cm. The main propagation depth of Stoneley waves occurs 20 cm from the wall of the well. Quantitative analyses of the fracture width, number, location, spacing, depth, and angle are conducted to determine the influence of the fracture parameters on the Stoneley wave attenuation coefficient, clarify Stoneley wave propagation in wells, and provide a theoretical basis for the accurate evaluation of fractures.

Simulation and Experimental Analysis of Surface Crack Propagation in Oscillating Bearings

: This study investigates the propagation of surface cracks in bearings under oscillating conditions. Voronoi elements are employed to simulate the microstructure of bearings, and combined with a cohesive zone model of continuum damage mechanics to simulate the propagation of cracks. A new type of oscillating contact fatigue test machine was designed to conduct experiments on contact crack propagation under oscillating conditions, and the experimental results were analyzed. By comparing the simulation results with experimental data, the validity of the theoretical analysis was confirmed.

Acoustic and soliton propagation using fully-discrete energy preserving partially implicit scheme in homogeneous and heterogeneous mediums

This study presents an energy preserving partially implicit scheme for the simulation of wave propagation in homogeneous and heterogeneous mediums. Despite its implicit nature, the developed scheme does not require any explicit numerical or analytical inversion of the coefficient matrix. Theoretical analysis and numerical experiments are performed to validate the energy preserving properties of the fully-discrete scheme. Convergence analysis is also performed to assess the rate of convergence of the developed scheme. The efficiency and accuracy of the developed scheme are validated by numerical solutions of wave propagation in layered heterogeneous mediums. Furthermore, simulations of soliton propagation following nonlinear sine-Gordon and Klein-Gordon equations in homogeneous and heterogeneous mediums are discussed. Numerical solutions are also compared with the results available in the literature. The present method accurately resolves the physical characteristics of the chosen problems, competing well with existing multi-stage time-integration methods. Moreover, it has significantly lower computational complexity than the four-stage, fourth-order Runge-Kutta-Nyström method.

Propagation of Hydraulic Fractures and Natural Fractures: The Bypassing Behavior in 3D Space

Summary The interaction between natural fractures (NFs) and hydraulic fractures (HFs) in 3D space poses significant challenges to numerical simulation. The interaction behaviors between HFs and NFs in 3D space include crossing, offset, stopping, and bypassing. Many existing numerical simulators are 2D, which inherently limits their ability to account for the vertical growth of fractures. Consequently, they are unable to model the bypassing behavior effectively. In this paper, a mathematical model for the propagation of HFs and NFs in a naturally fractured reservoir is established. The displacement discontinuity method (DDM) is used to solve the rock deformation, while the finite difference method (FDM) is utilized to solve the fluid flow within fractures. The undirected graph structure is used to represent the complex fracture network, and a dynamic adjustment of grid connectivity method is implemented to describe the process by which HFs bypass NFs. By integrating with graphics processing unit (GPU) computing, an efficient 3D simulator for HFs and NFs propagation is developed. The accuracy is verified against analytical solutions and reference solutions. Subsequently, a series of numerical studies on the bypassing behavior are conducted. The primary findings are as follows: (1) The simulator can accurately capture the interactions between HFs and NFs in 3D space, including crossing, arresting, and bypassing behaviors. (2) The bypassing behavior is characterized by three distinct processes—intersection, height growth of HF, and bypassing. (3) During the intersection stage, both the injection pressure and maximum NF width increase. During the height growth stage, the pressure is relatively stable, while the maximum NF width continues to increase. These two stages together result in the “storage” phenomenon. Once the bypassing behavior occurs, both the pressure and the maximum NF width decrease sharply, leading to a “release” phenomenon. Additionally, the “storage” and “release” phenomena may impact proppant transport. (4) Given the presence of bypassing behavior, it is essential to consider the NFs in 3D fracture simulators. The simulator and its findings can provide valuable insights for field design.

Efficient layerwise multiphysics spectral element model for delaminated composite strips with PWAS transducers

Efficient structural element-based models are essential for fast simulations of wave propagation in composite structures for model-based and physics-informed data-driven structural health monitoring. This article introduces the first efficient multiphysics time-domain spectral structural element for wave propagation analysis of beam and panel-type composite structures with piezoelectric transducers (patch or full layers) containing delaminations. A general framework is presented to model multiple delaminations and transducer patches located arbitrarily. The intact host and patch transducer-bonded laminates and sub-laminates between delaminations are modelled separately using an electromechanically coupled efficient layerwise zigzag theory (ZIGT) for kinematics and a piecewise quadratic variation for the electric potential across piezoelectric layers. The high-order spectral element (SE) features a virtual electric node to model equipotential surfaces of piezoelectric transducers apart from the usual physical nodes having mechanical and internal electric degrees of freedom. A hybrid point-least squares continuity approach is employed to maintain continuity at the intersections of delaminated sub-laminates or the patch-bonded laminate with the host laminate. The model’s performance in capturing electroelastic waves’ interaction with delamination is examined with reference to the conventional finite element (FE) solution based on the ZIGT, continuum-based FE solutions, and the SE solution based on a non-layerwise version of the laminate theory. Finally, the model is used to examine the impact of interfacial location and size of delaminations on wave propagation behaviour.

D̅arkRayNet: emulation of cosmic-ray antideuteron fluxes from dark matter

Cosmic-ray antimatter, particularly low-energy antideuterons, serves as a sensitive probe of dark matter annihilating in our Galaxy. We study this smoking-gun signature and explore its complementarity with indirect dark matter searches using cosmic-ray antiprotons. To this end, we develop the neural network emulator D̅arkRayNet, enabling a fast prediction of propagated antideuteron energy spectra for a wide range of annihilation channels and their combinations. We revisit the Monte Carlo simulation of antideuteron coalescence and cosmic-ray propagation, allowing us to explore the uncertainties of both processes. In particular, we take into account uncertainties from the Λ b production rate and consider two distinctly different propagation models. Requiring consistency with cosmic-ray antiproton limits, we find that AMS-02 shows sensitivity to a few windows of dark matter masses only, most prominently below 20 GeV. This region can be probed independently by the upcoming GAPS experiment. The program package D̅arkRayNet is available on GitHub, https://github.com/kathrinnp/DarkRayNet.

Study on Acoustic Variability Affected by Upper Ocean Dynamics in South Eastern Arabian Sea

AbstractThe influence of upper ocean dynamics on the acoustic field in the South Eastern Arabian Sea (SEAS) is studied using in situ oceanographic/acoustic measurements from a moored buoy, along with satellite‐derived and climatological data sets. Upper‐ocean variability at the site is quantified using Mixed Layer Depth (MLD), Isothermal Layer Depth (ILD), Barrier Layer Thickness (BLT), Maximum Spice Depth (MSD), and Sonic Layer Depth (SLD), along with surface variability factors such as Sea Surface Temperature, Sea Surface Salinity, Spice, and Sea Level Anomaly. The mixed layer acoustic duct (MLAD) varies from 2 to 100 m, with BLT varying from 5 to 99 m, and a mean SLD of 43 m. A thick transition layer connects the mixed layer with the thermocline during winter. The observations reveal that maximum SLD, MSD, and BLT occurred during January–March. Unlike other seasons when SLD follows MLD, winter SLD is influenced by BLT, suggesting strong salinity stratification due to low‐salinity water intrusion from the Bay of Bengal by East India Coastal Current. During these months, the SLD varies from 80 to 100 m, with the corresponding minimum cut‐off frequency varying from 300 to 200 Hz. Results are correlated with estimated Sound Pressure Level (SPL) from Ambient Noise Measurements during November 2018 to November 2019. SPL variation follows SLD for low and mid‐frequencies, with the highest SPL noted during January‐February. Acoustic propagation simulations at 250 and 1,000 Hz revealed features like acoustic duct leakage and channeling, indicating energy transfers between the surface acoustic duct and deeper layers.

Simulations of nerve signal propagation in axons

PurposeIn the literature, soliton solutions of the Heimburg–Jackson model have been proposed by Drab et al. (2022), but for the considered models, i.e. Eq.(1) and Eq.(2), the existence of solitons, the dispersion analysis and the pseudospectral method have been studied (Engelbrecht et al., 2006, 2018, 2020; Tamm et al., 2017, 2022; Peets et al., 2013). Therefore, the gap should be filled by this work.Design/methodology/approachWhen nonlinear terms, dissipative terms and forcing terms are ignored, the system (Eq.(2)) reduces to a single, sixth-order partial differential equation (Tamm et al., 2022). In this work, our aim is to propose analytical solutions in the explicit form via ansatz-based method. Therefore, the parameter effects in wave profile will be proposed clearly in figures.FindingsWhile progress has been made in signal propagation in nerves, thanks to many experimental studies and theoretical predictions over the last two centuries, the results obtained in this study may answer new questions that arise.Originality/valueIn the literature, the existence of solitons, dispersion analysis and pseudospectral method have been investigated for the Heimburg-Jackson model (Engelbrecht et al., 2006, 2018, 2020; Tamm et al., 2017, 2022; Peets et al., 2013), and this study fills the gap in soliton solutions. Additionally, when nonlinear terms, dissipative term and forcing terms are ignored, the system (Eq.(2)) reduced to a single equation that is sixth-order partial differential equation (Tamm et al., 2022). In this work, our aim is to propose analytical solutions in the explicit form via ansatz-based method. Therefore, the parameter effects in wave profile will be proposed clearly in figures.

Simulation study on parameter optimization of transcranial direct current stimulation based on rat brain slices

Transcranial direct current stimulation (tDCS) is an important method for treating mental illnesses and neurodegenerative diseases. This paper reconstructed two ex vivo brain slice models based on rat brain slice staining images and magnetic resonance imaging (MRI) data respectively, and the current densities of hippocampus after cortical tDCS were obtained through finite element calculation. Subsequently, a neuron model was used to calculate the response of rat hippocampal pyramidal neuron under these current densities, and the neuronal responses of the two models under different stimulation parameters were compared. The results show that a minimum stimulation voltage of 17 V can excite hippocampal pyramidal neuron in the model based on brain slice staining images, while 24 V is required in the MRI-based model. The results indicate that the model based on brain slice staining images has advantages in precision and electric field propagation simulation, and its results are closer to real measurements, which can provide guidance for the selection of tDCS parameters and scientific basis for precise stimulation.

Particle flow simulation of crack propagation and penetration in Brazilian disc under uniaxial compression

The presence of rock mass fractures has always been a subject of study for the prevention and control of related natural disasters. To understand the effects of different dip angles and horizontal distances on crack development, numerical simulation experiments on Brazilian disks under uniaxial compression were con-ducted using the PFC2D particle flow program. A function module was utilized to monitor the expansion and quantity of cracks. The numerical simulation results under 0° conditions were in good agreement with the experimental results, validating the rationality of the numerical simulation. The simulation results indicate that: under single fracture conditions with different dip angles, samples with angles between 30° and 60° produced typical wing-shaped cracks. At 0°, cracks propagat-ed through the center of the fracture, while at 90°, cracks initiated from the tip of the fracture and propagated through the sample. The peak stress and the number of cracks in the samples first decreased and then increased with the increase of the dip angle, reaching a maximum at 90°. For samples with double fractures and varying horizontal distances, all produced wing-shaped cracks. Their peak stress and the number of cracks increased monotonically with the increase in distance, reaching a maximum at a distance of 30mm. The experimental results confirmed that the PFC2D program can effectively simulate the process of crack initiation and development, and the research findings provide a reference for correctly understanding the fracture mechanics of fractured rock masses.

Simulations of X-ray focusing by zone plates in rotationally symmetric optical field utilizing the matrix-free Finite Difference Beam Propagation Method

We present the use of a finite difference method based on Crank-Nicholson scheme and recurrence scheme for computationally efficient simulation of the X-ray propagation through a zone plate. By introducing boundary and central conditions and by avoiding large matrix operations, the method achieves considerable speed, little memory occupation and low background noise. Accommodating refractive index profiles of arbitrary shape, it can be applied to assist optimizing X-ray zone plates and understanding focusing mechanism.

Efficient Simulation of Viral Transduction and Propagation for Biomanufacturing.

The design of biomanufacturing platforms based on viral transduction and/or propagation poses significant challenges at the intersection between synthetic biology and process engineering. This paper introduces vitraPro, a software toolkit composed of a multiscale model and an efficient numeric technique that can be leveraged for determining genetic and process designs that optimize transduction-based biomanufacturing platforms and viral amplification processes. Viral infection and propagation for up to two viruses simultaneously can be simulated through the model, considering viruses in either the lytic or lysogenic stage, during batch, perfusion, or continuous operation. The model estimates the distribution of the viral genome(s) copy number in the cell population, which is an indicator of transduction efficiency and viral genome stability. The infection age distribution of the infected cells is also calculated, indicating how many cells are in an infection stage compatible with recombinant product expression or viral amplification. The model can also consider the presence of defective interfering particles in the system, which can severely compromise the productivity of biomanufacturing processes. Model benchmarking and validation are demonstrated for case studies of the baculovirus expression vector system and influenza A propagation in suspension cultures.

Size-dependency and lattice-discreetness effect on fracture toughness in 2D crystals under antiplanar loading

AbstractFracture toughness is the material property characterizing resistance to failure. Predicting its value from the solid structure at the atomistic scale remains elusive, even in the simplest situations of brittle fracture. We report here numerical simulations of crack propagation in two-dimensional fuse networks of different periodic geometries, which are electrical analogs of bidimensional brittle crystals under antiplanar loading. Fracture energy is determined from Griffith’s analysis of energy balance during crack propagation, and fracture toughness is determined from fits of the displacement fields with Williams’ asymptotic solutions. Significant size dependencies are evidenced in small lattices, with fracture energy and fracture toughness both converging algebraically with system size toward well-defined material-constant values in the limit of infinite system size. The convergence speed depends on the loading conditions and is faster when the symmetry of the considered lattice increases. The material constants at infinity obey Irwin’s relation and properly define the material resistance to failure. Their values are approached up to $$\sim 15\%$$ ∼ 15 % using the recent analytical method proposed in Nguyen and Bonamy (Phys Rev Lett 123:205503, 2019). Nevertheless, the deviation remains finite and does not vanish when the system size goes to infinity. We finally show that this deviation is a consequence of the lattice discreetness and decreases when the super-singular terms of Williams’ solutions (absent in a continuum medium but present here due to lattice discreetness) are taken into account.

Fatigue life assessment and verification of turbine joints: current status and prospects

The research status of fatigue life assessment technology for turbine joint structures is introduced. The progress, shortcomings and development trends of existing research are discussed from the aspects of multi-field load analysis, crack initiation life assessment, crack propagation simulation and test technology. The evaluation methods of service life and damage tolerance of turbine joint structures are discussed in detail. The results show that the existing analysis and test methods can basically realize the fatigue life assessment of turbine joints, but due to various limitations, the engineering applicability needs to be improved urgently. Robust load reduction analysis methods, life assessment methods based on physical mechanisms and data-driven, load history-related crack propagation life assessment methods and test technologies under complex thermal environments are still needed to establish a fatigue life assessment and verification system for advanced aero-engine turbine joint structures.

Numerical Simulation of Hydraulic Fracture Propagation in Unconsolidated Sandstone Reservoirs

In order to comprehensively understand the complex fracture mechanisms in thick and loose sandstone formations, we have carefully developed a coupled finite element numerical model that captures the complex interactions between fluid flow and solid deformation. This model is the cornerstone of our future exploration. Based on this model, the crack propagation problem of hydraulic fracturing under different engineering and geological conditions was studied. In addition, we conducted in-depth research on the key factors that shape the geometry of hydraulic fractures, revealing their subtle differences and complexities. It is worth noting that the sharp contrast between the stress profile and mechanical properties between the production layer and the boundary layer often leads to fascinating phenomena, such as the vertical merging of hydraulic fracture propagation. The convergence of cracks originating from adjacent layers is a recurring theme in these strata. Sensitivity analysis clarified our understanding, revealing that increased elastic modulus promotes longer crack propagation paths. As the elastic modulus increases from 12 GPa to 18 GPa, overall, the maximum crack width slightly decreases, with a less than 10% reduction rate. The increased fluid leakage rate will significantly shorten the length and width of hydraulic fractures (with a maximum decrease of over 70% in fracture width). The increase in viscosity of fracturing fluid causes a change in fracture morphology, with a reduction in length of about 32% and an increase in fracture width of about 25%. It is worth noting that as the leakage rate of fracturing fluid increases, the importance of the viscosity of fracturing fluid decreases relatively. Strategies such as increasing fluid viscosity or adding anti-filtration agents can alleviate these challenges and improve the efficiency of fracturing fluids. In summary, our research findings provide valuable insights that can provide information and optimization for hydraulic fracturing filling and fracturing strategies in loose sandstone formations, promoting more efficient and influential oil and gas extraction work.

Geological and Engineering Integration Fracturing Design and Optimization Study of Liushagang Formation in Weixinan Sag

The Weixinan Sag in the Beibuwan Basin is rich in shale oil resources. However, the reservoirs exhibit rapid phase changes, strong compartmentalization, thin individual layers, and high-frequency vertical variations in the thin interbedded sandstone and mudstone. These factors can restrict the height of hydraulic fracture propagation. Additionally, the low-porosity and low-permeability shale oil reservoirs face challenges such as low production rates and rapid decline. To address these issues, the Plannar3D full 3D fracturing model was used to simulate hydraulic fracture propagation and to study the main controlling factors for fracture propagation in the second member of the Liushagang Formation. Based on the concept of geological–engineering integration, a sweet spot evaluation was conducted to identify reservoirs with relatively better brittleness, reservoir properties, and oil content as the fracturing targets for horizontal wells. The UFM model was then applied to optimize fracturing parameters. This study indicates that the matrix-type oil shale has a high clay mineral content, resulting in a low Young’s modulus and poor brittleness. This makes hydraulic fracture propagation difficult and leads to less effective reservoir stimulation. In contrast, hydraulic fractures propagate more easily in high-brittleness interlayer-type oil shale. Therefore, it is recommended to prioritize the extraction of shale oil from interlayer-type oil shale reservoirs. The difference in interlayer stress is identified as the primary controlling factor for cross-layer fracture propagation in the study area. Based on the concept of geological–engineering integration, a sweet spot evaluation standard was established for the second member of the Liushagang Formation, considering both reservoir quality and engineering quality. Four sweet spot zones of interlayer-type oil shale reservoirs were identified according to this evaluation standard. To achieve uniform fracture initiation, a differentiated segment and cluster design was implemented for certain high-angle sections of well WZ11-6-5d. Interlayer-type oil shale was selected as the fracturing target, and the UFM was used for hydraulic fracture propagation simulation. Fracturing parameters were optimized with a focus on hydraulic fracture characteristics and the estimated ultimate recovery (EUR). The optimization results were as follows: a single-stage length of 50 m, cluster spacing of 15 m, pump injection rate of 10 m3/min, fluid intensity of 25 m3/m, and proppant intensity of 3.5 t/m. The application of these optimized fracturing parameters in field operations resulted in successful fracturing and the achievement of industrial oil flow.

Reaction zone structure of spontaneous reaction wave at steady subsonic and supersonic speeds

The reaction zone structure of spontaneous reaction wave at steady subsonic and supersonic speeds is discussed using numerical simulation and theoretical approaches. The main objective of this study is to develop the mathematical model of the spontaneous reaction wave propagating at a steady speed and to clarify the relationship between the reaction zone structure and non-dimensional parameters. A one-dimensional direct numerical simulation (DNS) of the spontaneous reaction wave propagation is performed, and the modeling assumptions are discussed based on the numerical results. The non-dimensional parameters, the Damköhler number and a parameter related to compressibility defined by the Mach number of the spontaneous reaction wave velocity, are introduced into the modeling. The mathematical model is developed using asymptotic techniques, and the solution of the reaction zone structure is analytically derived using Newton’s method. The relationship between reaction zone structure of spontaneous reaction wave and non-dimensional parameters is discussed based on the analytical solutions.

A method for numerical simulation of shock waves in rarefied gas mixtures based on direct solution of the Boltzmann kinetic equation

The paper proposes an approach to numerical simulation of shock waves in rarefied gas mixtures on the basis of direct solution of the Boltzmann kinetic equation. Software for simulating the gas flows was developed. The structure of a shock wave in a binary gas mixture was computed with an accuracy controlled by the computational parameters. The computations were performed for various molecular masses ratios and Mach numbers. The total accuracy of at least 1.4% for the local values of the molecular densities and temperatures of the mixture components was achieved. Numerical simulation of a shock wave propagation through a periodically perforated surface was performed. The distributions of the macroscopic characteristics of the mixture components at various points in time were obtained. Unsteady areas of strong separation of the gas mixture components were discovered.

Comparing outdoor sound propagation simulations based on geometrical and numerical methods

Conventional simulations of outdoor noise propagation often rely on geometrical acoustic methods such as ray tracing or mirror sources. Especially for low frequencies, these methods deliver physically implausible results due to their inherent approach not resolving the properties of the acoustic field. In this contribution, the results of a conventional noise propagation simulation software based on geometrical acoustics are compared to numerical results originating from solving the Helmholtz equation with the Finite Element Method (FEM). A 2.6 km long cross-section through an alpine valley with a railway line is considered as an exemple. In comparison with the FEM results, the shortcomings of geometrical acoustic methods are demonstrated, which underline the need for powerful and computationally efficient numerical approaches for outdoor noise propagation.

Enabling large-scale and high-precision fluid simulations on near-term quantum computers

Quantum computational fluid dynamics (QCFD) offers a promising alternative to classical computational fluid dynamics (CFD) by leveraging quantum algorithms for higher efficiency. This paper introduces a comprehensive QCFD method, including an iterative method “Iterative-QLS” that suppresses error in quantum linear solver, and a subspace method to scale the solution to a larger size. We implement our method on a superconducting quantum computer, demonstrating successful simulations of steady Poiseuille flow and unsteady acoustic wave propagation. The Poiseuille flow simulation achieved a relative error of less than 0.2%, and the unsteady acoustic wave simulation solved a 5043-dimensional matrix. We emphasize the utilization of the quantum–classical hybrid approach in applications of near-term quantum computers. By adapting to quantum hardware constraints and offering scalable solutions for large-scale CFD problems, our method paves the way for practical applications of near-term quantum computers in computational science.