Propagation Trajectory Research Articles

Numerical simulation of fracture propagation in Russia carbonate reservoirs during refracturing

Refracturing treatment is often performed on Russian carbonate reservoirs because of the quick production decline of reservoirs. The traditional refracturing model assumes that a refracture initiates in the normal direction relative to the initial hydro-fracture. This assumption is inconsistent with oilfield measurements of refracture propagation trajectories. Indeed, the existing model is not based on an in-depth understanding of initiation and propagation mechanisms of the second hydraulic fractures during refracturing. In this study, we use the extended finite element method to investigate refracture propagation paths at different initiation angles. Both the enriched function approach and phantom mode technique are incorporated into the refracturing model, thereby ensuring that the refracture can freely extend on the structured mesh without any refinement near the crack tips. Key factors including production time, stress anisotropy and initiation angle, and the propped mechanical effect are analyzed in detail. This study provides new insight into the mechanism of refracture propagation in unconventional reservoirs.

Propagation dynamics of symmetric Pearcey-Gaussian beam with optical vortices

The propagation dynamics of symmetric Pearcey-Gaussian beam embedded with on-axis and off-axis optical vortices (OVs) is investigated. Based on the extended Huygens-Fresnel diffraction integral, influences of embedded location, the off-axis distance and topological charge (TC) of OVs on the autofocusing dynamics of the symmetric Pearcey-Gaussian vortex beam (SPGVB) are explored analytically and numerically. The results show that, the embedded location, the off-axis distance and TC of OVs can significantly affect the initial intensity distribution, the propagation trajectory, the autofocusing length and the peak intensity at the focal plane. Interestingly, the fitted expression describing the relationship between the peak intensity of SPGVB and the off-axis distance of OVs with different TC is obtained, which would provide a method to determine the off-axis distance or the TC of OV based on the intensity distribution. The results indicate that SPGVB holds potential applications in biomedical treatment, optical manipulation and optical communication.

Nonlocal finite element simulation method for fluid-induced rock damage propagation

In this paper, the equivalent strain is nonlocalized. The permeability is coupled through the damage variable into the Hydro-Mechanical coupling equation. So as to establish the fluid-driven nonlocal damage expansion model. It is used to solve the localization response problem of quasi-brittle material fracture failure finite element simulation process. So that it can effectively calculate the crack propagation process of rock mass under high pressure fluid. In view of this model, this paper first simulates and compares the experimental results of ‘L’ brittle material plate, and verifies the sensitivity of finite element mesh. Then, through the simulation of the influence of perforation angle on fracture propagation trajectory, the effectiveness of this model for Hydro-Mechanical coupling damage propagation is studied. The results show that the simulation results of the model are consistent with the experiment. It can significantly reduce the grid sensitivity difference caused by localization.

Adaptive Finite Element Modeling of Linear Elastic Fatigue Crack Growth.

This paper proposed an efficient two-dimensional fatigue crack growth simulation program for linear elastic materials using an incremental crack growth procedure. The Visual Fortran programming language was used to develop the finite element code. The adaptive finite element mesh was generated using the advancing front method. Stress analysis for each increment was carried out using the adaptive mesh finite element technique. The equivalent stress intensity factor is the most essential parameter that should be accurately estimated for the mixed-mode loading condition which was used as the onset criterion for the crack growth. The node splitting and relaxation method advances the crack once the failure mechanism and crack direction have been determined. The displacement extrapolation technique (DET) was used to calculate stress intensity factors (SIFs) at each crack extension increment. Then, these SIFs were analyzed using the maximum circumferential stress theory (MCST) to predict the crack propagation trajectory and the fatigue life cycles using the Paris' law model. Finally, the performance and capability of the developed program are shown in the application examples.

Dynamic fluid-structure interaction of graded foam core sandwich plates to underwater blast

• Performing fluid-structure interaction analysis on fully clamped graded foam core sandwich. • Introducing cavitation evolution under the planar underwater impulsive loading. • Showing nonuniformed distribution of the cavitated bubbles during its extension and collapse. • Proposing the determining factors of cavitation evolution for the graded sandwich. • Showing superiority of the core gradient design for eliminating cavitation. The aim of this paper is to address characteristics of cavitation evolution caused by the one-dimensional fluid-structure interaction as the graded foam core sandwich panels are subjected to underwater impulsive loadings. A transparent underwater shock tube is adopted to generate controllable and planar blast impulses exerted on the fully clamped sandwich panels. The effects of the impulsive intensity, core strength, core density gradient, and boundary condition are carried out to examine the cavitation evolution during the dynamic fluid-structure interaction. The results show that the initiation, extension, and collapse of the cavitation are significantly determined by the propagations of the breaking front and the closing front, which have different correlations with the considering effects. Due to the dynamic core compression and unloading, the distinct elevating speed of the closing front is firstly found in the fluid-structure interaction under the impulsive loadings. During the cavitation evolution, the non-uniformed distribution of the cavitated bubbles indicates that the cavitation region closer to the fluid-solid interface experiences more considerable pressure drops. The dynamic response of the weakest layer of the core shows predominant influences on the propagation trajectories of wave fronts and reducing of the cavitation ratio, indicating that the core gradient design can efficiently decrease the transmitted impulse and has superiority to the uniform cores with the identical areal mass.

Changing the trajectory of Airy beam sets with spatial carriers

In this paper, we study a change in the propagation trajectory of a set of autofocusing laser beams using a fractional Fourier transform. Clusters of displaced bounded Airy-Gaussian beams supplemented by a phase function that deflects the beam similarly to a prism are considered. The shift and phase deviation (according to the carrier spatial frequencies) make it possible to change the propagation trajectory of a set of autofocusing beams. The influence of the parameters under consideration on the properties of autofocusing of a cluster of Airy-Gaussian beams is investigated by means of numerical simulation.

Chirped Lommel Gaussian vortex beams in strongly nonlocal nonlinear fractional Schrödinger equations

Chirped Lommel Gaussian vortex beams (LGVBs) propagating in strongly nonlocal nonlinear fractional Schrödinger equation (NFSE) are numerically studied for the first time. We verify that the chirped LGVBs perform autofocusing effects periodically. The propagation trajectory, the focal position and the focal intensity of the chirped LGVBs are deeply influenced by the appropriate selection of the parameters of the initial beams as well as the Lévy index of fractional diffraction effect in the strongly nonlocal NFSE. Moreover, the Poynting vector and the angular momentum of the beams are also researched. The findings demonstrate many interesting properties related to the chirped LGVBs propagating in the strongly nonlocal nonlinear fractional NFSE, which can broaden the research field of the chirped LGVBs.

Research on the propagation mechanism of hydraulic fractures in infill horizontal wells

In recent years, infill horizontal well technology has been used to develop oil and gas in the remaining oil areas of unconventional low-permeability reservoirs. However, the initial fractures in parent wells will affect the hydraulic fractures formed by fracturing infilling horizontal wells. The interaction mechanisms between initial fractures and artificial fractures in infill horizontal wells are still unclear. Combined with the boundary element method and the maximum circumferential tensile stress criterion, a numerical model of hydraulic fracturing that can simulate the evolution of fracture trajectory and stress field was established. The analytical solution of the hydraulic fracture-induced stress field was used to verify the accuracy of the model. Using this model, propagation of hydraulic fractures in infill horizontal wells under different conditions was analyzed. Simulation results show that both the fracture spacing and well spacing have a significant impact on the propagation trajectory of hydraulic fractures in infill horizontal wells. The shorter the fracture spacing and well spacing is, the stronger the inter-fracture stress interference between the initial fractures and hydraulic fractures is. Reasonable fracture spacing and well spacing can enhance the induced stress field and form a complex fracture network in the reservoir. Too small well spacing may cause artificial fractures to communicate with initial fractures, thereby reducing hydraulic fracturing efficiency and limiting the stimulation volume of the reservoir.

Numerical simulation on spatial steering rule of directional perforation hydraulic fractures in low-permeability reservoir

For purpose of clearing the spatial pattern of hydraulic fracture during directional perforation in low-permeability unconventional reservoirs, RFPA2D-Flow software is used to numerically calculate their spatial steering trajectory and deflection distance. The accuracy of numerical calculation results is verified by theoretical and experimental results. Then the influences of horizontal principal stress difference, perforation length, and azimuth on the hydraulic fractures’ spatial steering trajectory are studied. It is shown by the results that 1) the software can accurately predict the space steering trajectory and deflection distance of directional perforation hydraulic fractures, 2) both deflection distance and spatial steering trajectory of hydraulic fractures are quantitatively evaluation indexes, which are used to evaluate the hydraulic fractures’ spatial steering effects, and 3) under different horizontal principal stress differences, perforation azimuths, and lengths, the same hydraulic fracture’s propagation trajectories are presented. They initiate from the perforation end and gradually deflect along the maximum horizontal principal stress direction and finally represent curved fractures like both wings. With the increase in horizontal principal stress difference, the fractures’ deflection distance decreases. However, it increases with the increase in perforation azimuth and length. Their deflection amplitude increases first and then decreases. Initiation pressure of hydraulic fracture rises with the decrease in perforation length and increase in perforation azimuth and horizontal principal stress difference.

Controllable focusing behavior of chirped Pearcey-Gaussian pulses under time-dependent potentials.

We investigate the propagation dynamics of the Pearcey-Gaussian (PG) pulses in the presence of time-dependent potentials in a linear medium both theoretically and numerically. We demonstrate that the combination of the linear potential and the initial chirp of PG pulses can flexibly control the propagation trajectory and inherent focusing properties of the PG pulses. When the parabolic potential is taken into account, the chirped PG pulses are periodically focused and reversed. By adjusting the parabolic potential and the pulse chirp, the characteristics of the focal points, such as position, intensity, and spacing between focal points, can be manipulated effectively. The interaction of two temporally separated PG pulses still shows a periodic evolution with controllable focusing characteristics. These results can broaden the application range of PG pulses and provide some inspiration for the control of PG pulses under nonlinear conditions.

Investigation on beamforming solution for multi-receiver synthetic aperture sonar using CW pulse with sound velocity profiles in Vietnam’s sea

This paper proposes a novel beamforming solution for multi-receiver synthetic aperture sonar (SAS), which uses gated continuous-wave (CW) pulses, based on the average value of equivalent sound velocity (ESV) when considering the change of the sound velocity with depth. The main beam can be steered to desirable positions with the proposed solution. Besides, the computation time for the phase distribution from the proposed solution reduces compared with the conventional solution by dividing the propagation trajectory into straight lines, where the sound velocity is unchanged. The effectiveness of the proposed solution is validated and evaluated by the results of the beam pattern and the time for determining the phase distribution with the sound velocity profiles (SVPs) in Vietnam’s sea.

Nature-based solutions on floodplain restoration with coupled propagule dispersal simulation and stepping-stone approach to predict mangrove encroachment in an estuary

The mangrove ecosystem is significantly affected by human activities, climate change, and rising sea level. The propagules of mangroves dispersal with tide and river currents that extend upstream habitats are why mangroves are the dominant species in the tidal area. Bridging critical knowledge gaps can help to create restoration plans for mangrove extension. However, studies on the hydrodynamic and propagation trajectory model (PTM) simulation of propagule long-distance dispersal (LDD) and mangrove growth potential are scarce. By combining various numerical methods and empirical formulas and verifying them with the data obtained through field surveys, this study established a comprehensive model to assess the dispersal and growth of the propagules of Kandelia ovobata. The stepping-stone approach (SSA) and habitat suitability index (HSI) model were also employed to determine the location of the appropriate new habitats through iterative simulation in propagule dispersal. Dike removal was proposed as a nature-based solution and modeled to evaluate the benefits of ecological conservation and flood prevention. The PTM simulations indicated that the deterministic process of horizontal advection accounted for >80 %, and that the remaining variability in the model could be explained by stochastic processes in predicting mangrove propagules pathways. The integrated model of the PTM and SSA proved that propagules have LDD in an estuary. There were few matches in the regions for mangrove growth when comparing the suitability of habitat distribution and the probability of propagule movement. We suggested that the mangrove spread model incorporating the SSA and HSI models predict the potential for mangrove dispersal into new habitats. In addition, the removal of levees aids floodplain regeneration and allows propagules to disperse across the floodplain at high tide and establishment at low tide. The Guandu floodplain restoration with dike removal supplied a cobenefits on ecological demands and flood risk reduction. Future research could thus utilize the adaptation and mitigation strategies presented in this study by incorporating socioeconomic considerations to enhance practical feasibility.

Effects of a circular hole on the propagation behavior of double running cracks under impact loading

In order to study effects of a circular hole on the propagation behavior of double running cracks under impact loading, the three-point-bending impact experiments of polymethyl methacrylate (PMMA) specimens with a circular hole were carried out by using the optical caustics method, and the numerical simulation was carried out by using the extended finite element method (XFEM) in ABAQUS software. The results show that under the influence of the stress field around the circular hole, the propagation trajectory of double running cracks can be divided into three stages: "exclusion" stage; first "attraction" and then "exclusion" stage; neither "attraction" nor "exclusion" stage. The circular hole defect affects the propagation velocity of double running cracks and the dynamic stress intensity factors at the crack tip. The maximum principal stress between the running cracks and the circular hole decreases with crack spacing a. When the double running cracks’ tips are on both sides of the circular hole, the maximum principal stress between the running cracks and the circular hole reaches the minimum.

Effect of the ignition location on lean light-off limits for a gas turbine combustor

The ignition performance of the spray flame is an important safety parameter in a gas turbine combustor. Previous studies have shown that the spark axial location has a significant influence on the ignition performance and flame propagation process, and further research is required. The ignition performance and flame kernel propagation at different spark radial locations in a gas turbine model combustor are studied experimentally in this paper to summarize the influence of spark location on ignition performance from the perspective of kernel propagations, and to find the optimal ignition location. The flame propagation trajectory of each ignition location is obtained through high-speed imaging tests. Four conclusions are obtained as follows: 1) In a successful ignition event, flame kernels from different ignition positions will eventually propagate to the same position, which is defined as the flame holding position (FHP). After the flame residence stage, the kernel will begin to grow until the entire combustor is ignited. The FHP is with low axial velocity, small turbulent fluctuation and appropriate fuel concentration to effectively maintain the flame. 2) The ignition performance is the worst when the ignitor is near the wall, and is the best when the ignitor is near the FHP, that is, the inner boundary of the recirculation zone. 3) The ignition performance deteriorates if the flame has to cover greater distances before reaching the FHP where it can ignite the flame stabilization zone. A spark at the FHP can greatly reduce the propagation distance of the flame kernel, thereby avoiding the obstruction of the propagation process. 4) The propagation trajectory of the flame kernel is related to the ignition location and is mainly controlled by the non-reacting flow field and fuel concentration.

Propagation properties and radiation forces of partially coherent self-shifting cosine-Gaussian beams

In the ABCD optical system, the propagation properties and the radiation forces are obtained by studying the cross spectral density of partially coherent self-shifting cosine-Gaussian beams. A self-shifting phenomenon occurs when the beams propagate in the strongly nonlocal nonlinear medium. The shifting parameters could influence the bend characteristics of the propagation trajectory and the beam center, while the power ratio affects the periods of the parabolic trajectory. Furthermore, the radiation forces on a Rayleigh particle in the focusing optical system are studied, and the obtained force distributions depend on the refractive index, the shifting parameters, and the coherence widths. What we report here has potential applications in optical communication and optical tweezing.

Controllable oscillated spin Hall effect of Bessel beam realized by liquid crystal Pancharatnam-Berry phase elements

Pancharatnam–Berry (PB) phase has become an effective tool to realize the photonic spin Hall effect (PSHE) in recent years, due to its capacity of enhancing the spin-orbit interaction. Various forms of PSHEs have been proposed by tailoring the PB phase of light, however, the propagation trajectory control of the separated spin states has not been reported. In this paper, we realize the oscillated spin-dependent separation by using the well-designed PB phase optical elements based on the transverse-to-longitudinal mapping of Bessel beams. Two typical oscillated PSHEs, i.e., the spin states are circulated and reversed periodically, are experimentally demonstrated with two PB phase elements fabricated with liquid crystal. The displacements and periods of these oscillations can be controlled by changing the transverse vector of the input Bessel beam. The proposed method offers a new degree of freedom to manipulate the spin-dependent separation, and provides technical supports for the application in spin photonics.

Tightly autofocusing beams along the spherical surface.

We theoretically demonstrate different propagation trajectories of tightly autofocusing beams (TABs) along the spherical surface. The generalized expression of the TAB with spherical trajectory is given based on the nonparaxial accelerating Bessel beam. The effect of the spherical trajectory on the focusing performance of the TAB is analyzed. It reveals that the focal field with strong longitudinally polarized component and sub-diffraction-limit focal spot can be further enhanced by shortening the focal length of TAB. Theoretically, the minimum size of the focal spot can be close to 0.096λ2, and the proportion of longitudinal field can go up to 98.36%.

Higher-order interaction learning of line failure cascading in power networks

Line failure cascading in power networks is a complex process that involves direct and indirect interactions between lines’ states. We consider the inverse problem of learning statistical models to find the sparse interaction graph from the pairwise statistics collected from line failures data in the steady states and over time. We show that the weighted l1-regularized pairwise maximum entropy models successfully capture pairwise and indirect higher-order interactions undistinguished by observing the pairwise statistics. The learned models reveal asymmetric, strongly positive, and negative interactions between the network’s different lines’ states. We evaluate the predictive performance of models over independent trajectories of failure unfolding in the network. The static model captures the failures’ interactions by maximizing the log-likelihood of observing each link state conditioned to other links’ states near the steady states. We use the learned interactions to reconstruct the network’s steady states using the Glauber dynamics, predicting the cascade size distribution, inferring the co-susceptible line groups, and comparing the results against the data. The dynamic interaction model is learned by maximizing the log-likelihood of the network’s state in state trajectories and can successfully predict the network state for failure propagation trajectories after an initial failure.

Flexible trajectory control of Bessel beams with pure phase modulation.

Spatial phase modulation has become an important method for the design of new self-accelerating light beams. Based on the transverse-longitudinal mapping of Bessel beam, we propose a method of pure phase modulation to directly convert a zero-order Bessel beam into a self-accelerating beam, of which the propagation trajectories can be flexibly predesigned. We experimentally demonstrate three typical types of curves that the modulated Bessel beam propagates along, and the parabolic, spiral, and teleporting self-accelarating beams are realized. The experimental results match the expected trajectory well. This method is simple to operate, and imposes fewer restrictions on the beam trajectory.

Experimental investigation on spark ignition of multi-swirl spray flames under sub-atmospheric pressures and low temperatures

Altitude relight is an increasingly important issue limiting the development of low-emission combustors due to the current trend towards lean combustion. This paper experimentally investigates the flow field features and spark ignition processes inside a multi-swirl staged combustor to further reveal the internal mechanism leading to the deterioration of ignition performances under altitude conditions including sub-atmospheric pressures and low temperatures. Laser diagnostic technologies and high-speed imaging are applied to acquire the flow structures, droplet distributions, and detailed kernel motions under various inlet conditions. A flame-tracking algorithm is developed to capture the flame features (flame intensity-centroids and flame object edges) and provide the flame propagation trajectories during 10 ms following the spark. A typical “dipper-type propagation” pattern is summarized from numerous spark events and its formation mechanism can be clarified by statistical characteristics of flow and spray inside such staged combustors. The variation of ignition limits quantitatively characterizes the degree of ignition deterioration under sub-atmospheric pressures (10 ∼ 70 kPa) and low temperatures (253 ∼ 301 K). From the analysis of air to liquid ratio and Weber number, it is demonstrated that the increased droplet size and shrunken spray cone under altitude conditions are induced by three aspects, including the insufficient aerodynamic force, increased liquid viscosity force, and increased surface tension. The poor atomization quality is detrimental to the kernel generation and flame propagation and finally leads to the deterioration of ignition performances.