Evaluating the stability and volumetric flowback rate of proppant packs in hydraulic fractures using the lattice Boltzmann-discrete element coupling method

The stability and mobility of proppant packs in hydraulic fractures during hydrocarbon production are numerically investigated by the lattice Boltzmann-discrete element coupling method(LB-DEM).This study starts with a preliminary proppant settling test,from which a solid volume fraction of 0.575 is calibrated for the proppant pack in the fracture.In the established workflow to investigate proppant flowback,a displacement is applied to the fracture surfaces to compact the generated proppant pack as well as further mimicking proppant embedment under closure stress.When a pressure gradient is applied to drive the fluid-particle flow,a critical aperture-to-diameter ratio of 4 is observed,above which the proppant pack would collapse.The results also show that the volumetric proppant flowback rate increases quadratically with the fracture aperture,while a linear variation between the particle flux and the pressure gradient is exhibited for a fixed fracture aperture.The research outcome contributes towards an improved understanding of proppant flowback in hydraulic fractures,which also supports an optimised proppant size selection for hydraulic fracturing operations.

Analysis and experimental study on resistance-increasing behavior of composite high efficiency autonomous inflow control device

Bottom water coning is the main reason to reduce the recovery of horizontal bottom water reservoir. By water coning, we mean the oil-water interface changes from a horizontal state to a mound-shaped cone and breaks through to the wellbore. Autonomous inflow control device(AICD) is an important instrument maintain normal production after bottom water coning, however, the resistance increasing ability of the swirl type AICD is insufficient at present, which seriously affects the water control effect. Aiming this problem, this paper designs a multi-stage resistance-increasing and composite type AICD. The separation mechanism of oil-water two phases in this structure, the resistance form of oil-water single phase and the resistance-increasing principle of water phase are analyzed. Establishing the dual-phase multi-stage separation and resistance-increasing model, and verified by measuring the throttling pressure drop and oil-water volume fraction of the AICD, it is found that the composite type AICD has the effect of ICD and AICD at the same time, which can balance the production rate of each well section at the initial stage of production, delay the occurrence of bottom water coning. In the middle and later stages of production, water-blocking can be effectively increased to achieve water control and stable production.After structural sensitivity analysis, the influence law of various structural parameters on the water control performance of composite AICD was obtained. The simulation calculation results show that,compared with the existing swirl type AICD, composite AICD has higher sensitivity to moisture content,the water phase throttling pressure drop is increased by 4.5 times on average. The composite AICD is suitable for the entire stage of horizontal well production.

Numerical and experimental study on the falling film flow characteristics with the effect of co-current gas flow in hydrogen liquefaction process

Liquid hydrogen storage and transportation is an effective method for large-scale transportation and utilization of hydrogen energy. Revealing the flow mechanism of cryogenic working fluid is the key to optimize heat exchanger structure and hydrogen liquefaction process(LH2). The methods of cryogenic visualization experiment, theoretical analysis and numerical simulation are conducted to study the falling film flow characteristics with the effect of co-current gas flow in LH2spiral wound heat exchanger.The results show that the flow rate of mixed refrigerant has a great influence on liquid film spreading process, falling film flow pattern and heat transfer performance. The liquid film of LH2mixed refrigerant with column flow pattern can not uniformly and completely cover the tube wall surface. As liquid flow rate increases, the falling film flow pattern evolves into sheet-column flow and sheet flow, and liquid film completely covers the surface of tube wall. With the increase of shear effect of gas-phase mixed refrigerant in the same direction, the liquid film gradually becomes unstable, and the flow pattern eventually evolves into a mist flow.

Depositional process of hyperpycnal flow deposits:A case study on Lower Cretaceous Sangyuan outcrop in the Luanping Basin,Northeast China

Sedimentary process research is of great significance for understanding the distribution and characteristics of sediments.Through the detailed observation and measurement of the Sangyuan outcrop in Luanping Basin,this paper studies the depositional process of the hyperpycnal flow deposits,and divides their depositional process into three phases,namely,acceleration,erosion and deceleration.In the acceleration phase,hyperpycnal flow begins to enter the basin nearby,and then speeds up gradually.Deposits developed in the acceleration phase are reverse.In addition,the original deposits become unstable and are taken away by hyperpycnal flows under the eroding force.As a result,there are a lot of mixture of red mud pebbles outside the basin and gray mud pebbles within the basin.In the erosion phase,the reverse deposits are eroded and become thinner or even disappear.Therefore,no reverse grading characteristic is found in the proximal major channel that is closer to the source,but it is still preserved in the middle branch channel that is far from the source.After entering the deceleration phase,normally grading deposits appear and cover previous deposits.The final deposits in the basin are special.Some are reverse,and others are normal.They are superimposed with each other under the action of hyperpycnal flow.The analysis of the Sangyuan outcrop demonstrates the sedimentary process and distribution of hyperpycnites,and reasonably explain the sedimentary characteristics of hyperpycnites.It is helpful to the prediction of oil and gas exploration targets in gravity flow deposits.

Control of Nozzle Flow Using Rectangular Ribs at Sonic and Supersonic Mach Numbers

This study deals with base pressure management in a duct for various values of the Mach number(M),namely,Mach number corresponding to sonic and four supersonic conditions.In addition to the Mach number,the nozzle pressure ratio(NPR),the area ratio,the rib dimension,and the duct length are influential parameters.The following specific values are examined at M=1,1.36,1.64,and 2,and NPRs between 1.5 and 10.The base pressure is determined by positioning ribs of varying heights at predetermined intervals throughout the length of the square duct.When the level of expansion is varied,it is seen that the base pressure initially drops for overexpanded flows and increases for under-expanded flows.When ribs are present,the flow field in the duct and pressure inside the duct fluctuate as the base pressure rises.Under-expanded flows can achieve a base pressure value that is suitably high without experiencing excessive changes in the duct flow in terms of static pressure if a rib height around 10%of the duct height close to the nozzle exit is considered.Rectangular rib passive control does not negatively affect the duct’s flow field.

Extending homogeneous fluidization flow regime of Geldart-A particles by exerting axial uniform and steady magnetic field

The homogeneous/particulate fluidization flow regime is particularly suitable for handling the various gas–solid contact processes encountered in the chemical and energy industry.This work aimed to extend such a regime of Geldart-A particles by exerting the axial uniform and steady magnetic field.Under the action of the magnetic field,the overall homogeneous fluidization regime of Geldart-A magnetizable particles became composed of two parts:inherent homogeneous fluidization and newly-created magnetic stabilization.Since the former remained almost unchanged whereas the latter became broader as the magnetic field intensity increased,the overall homogeneous fluidization regime could be extended remarkably.As for Geldart-A nonmagnetizable particles,certain amount of magnetizable particles had to be premixed to transmit the magnetic stabilization.Among others,the mere addition of magnetizable particles could broaden the homogeneous fluidization regime.The added content of magnetizable particles had an optimal value with smaller/lighter ones working better.The added magnetizable particles might raise the ratio between the interparticle force and the particle gravity.After the magnetic field was exerted,the homogeneous fluidization regime was further expanded due to the formation of magnetic stabilization flow regime.The more the added magnetizable particles,the better the magnetic performance and the broader the overall homogeneous fluidization regime.Smaller/lighter magnetizable particles were preferred to maximize the magnetic performance and extend the overall homogeneous fluidization regime.This phenomenon could be ascribed to that the added magnetizable particles themselves became more Geldart-A than-B type as their density or size decreased.

Numerical simulation on the multiphase flow and reoxidation of the molten steel in a two-strand tundish during ladle change

A 3D mathematical model was proposed to investigate the molten steel–slag–air multiphase flow in a two-strand slab continuous casting(CC)tundish during ladle change.The study focused on the exposure of the molten steel and the subsequent reoxidation occurrence.The exposure of the molten steel was calculated using the coupled realizable k–εmodel and volume of fluid(VOF)model.The diffusion of dissolved oxygen was determined by solving the user-defined scalar(UDS)equation.Moreover,the user-defined function(UDF)was used to describe the source term in the UDS equation and determine the oxidation rate and oxidation position.The effect of the refilling speed on the molten steel exposure and dissolved oxygen content was also discussed.Increasing the refilling speed during ladle change reduced the refilling time and the exposure duration of the molten steel.However,the elevated refilling speed enlarged the slag eyes and increased the average dissolved oxygen content within the tundish,thereby exacerbating the reoxidation phenomenon.In addition,the time required for the molten steel with a high dissolved oxygen content to exit the tundish varied with the refilling speed.When the inlet speed was 3.0 m·s^(-1)during ladle change,the molten steel with a high dissolved oxygen content exited the outlet in a short period,reaching a maximum dissolved oxygen content of 0.000525wt%.Conversely,when the inlet speed was 1.8 m·s^(-1),the maximum dissolved oxygen content was 0.000382wt%.The refilling speed during the ladle change process must be appropriately decreased to minimize reoxidation effects and enhance the steel product quality.

Effect of aspect ratio of elliptical stirred vessel on mixing time and flow field characteristics in the absence of baffles

Elliptical tanks were used as an alternative to circular tanks in order to improve mixing efficiency and reduce mixing time in unbaffled stirred tanks(USTs). Five different aspect ratios of elliptical vessels were designed to compare their mixing time and flow field. Computational fluid dynamics(CFD) simulations were performed using the k–ε model to calculate the mixing time and simulate turbulent flow field features, such as streamline shape, velocity distribution, vortex core region distribution, and turbulent kinetic energy(TKE) transfer. Visualization was also carried out to track the tinctorial evolution of the liquid phase. Results reveal that elliptical stirred tanks can significantly improve mixing performance in USTs. Specifically, the mixing time at an aspect ratio of 2.00 is only 45.3% of the one of a circular stirred tank. Furthermore, the secondary flow is strengthened and the vortex core region increases with the increase of aspect ratio. The axial velocity is more sensitive to the aspect ratio than the circumferential and radial velocity. Additionally, the TKE transfer in elliptical vessels is altered. These findings suggest that elliptical vessels offer a promising alternative to circular vessels for enhancing mixing performance in USTs.

Debris flow runout behaviors considering the influences of densely populated buildings

Debris flows pose serious risks to communities in mountainous areas,often resulting in large losses of human life and property.The impeding presence of urban buildings often affects the runout behavior and deposition of debris flows.But the impact of different building densities and sizes on debris flow dynamics has yet to be quantified to guide urban planning in debris flow risk zones.This study focused on a debris flow that occurred in Zhouqu County,Gansu Province,China on August 7th,2010,which was catastrophic and destroyed many buildings.The FLO-2D software was used to simulate this debris flow in two scenarios,i.e.the presence and the absence of buildings,to obtain debris-flow intensity parameters.The developed model was then used to further analyze the influence of large buildings and narrow channels within the urban environment.The simulation results show that considering the presence of buildings in the simulation is essential for accurate assessment of debris flow intensity and deposition distribution.The layout of buildings in the upstream urban area,such as large buildings or parallel buildings which form narrow channels,can affect the flow velocity and depth of debris flow heading towards downstream buildings.To mitigate damage to downstream buildings,the relative spacing(d/a)between upstream and downstream buildings should not exceed a value of two and should ideally be even lower.These findings provide valuable insights for improving the resistance of mountainous cities to urban debris flows.

Enhancing wood efficiency through comprehensive wood flow analysis:Methodology and strategic insights

Wood,an essential natural resource in human civilization,remains widely used despite advances in technology and material substitution.The surge in greenhouse gas emissions and environmental concerns accentuates the need for optimizing wood utilization.Material flow analysis is a powerful tool for tracking material flows and stocks,aiding resource management and environmental decision-making.However,the full extent of its methodological dimensions,particularly within the context of the wood supply chain,remains relatively unexplored.In this study,we delve into the existing literature on wood flow analysis,discussing its primary objectives,materials involved,temporal and spatial scales,data sources,units,and conversion factors.Additionally,data uncertainty,data reconciliation and crucial assumptions in material flow analysis are highlighted in this paper.Key findings reveal the significance of wood cascading and substitution effects by replacing non-wood materials,where they can reduce greenhouse gas emissions more than the natural carbon sink of forests and wood products.The immediate impact of short-term wood cascading might not be as robust as the substitution effect,with energy substitution showcasing better results than material substitution.However,it's crucial to note that these conclusions could experience significant reversal from a long-term and global perspective.Strategies for improving wood efficiency involve maximizing material use,advancing construction technologies,extending product lifespans,promoting cascade use,and optimizing energy recovery processes.The study underscores the need for standardized approaches in wood flow analysis and emphasizes the potential of wood efficiency strategies in addressing environmental challenges.

Evaluation of frictional pressure drop correlations for air-water and air-oil two-phase flow in pipeline-riser system

Accurate prediction of the frictional pressure drop is important for the design and operation of subsea oil and gas transporting system considering the length of the pipeline. The applicability of the correlations to pipeline-riser flow needs evaluation since the flow condition in pipeline-riser is quite different from the original data where they were derived from. In the present study, a comprehensive evaluation of 24prevailing correlation in predicting frictional pressure drop is carried out based on experimentally measured data of air-water and air-oil two-phase flows in pipeline-riser. Experiments are performed in a system having different configuration of pipeline-riser with the inclination of the downcomer varied from-2°to-5°to investigated the effect of the elbow on the frictional pressure drop in the riser. The inlet gas velocity ranges from 0.03 to 6.2 m/s, and liquid velocity varies from 0.02 to 1.3 m/s. A total of885 experimental data points including 782 on air-water flows and 103 on air-oil flows are obtained and used to access the prediction ability of the correlations. Comparison of the predicted results with the measured data indicate that a majority of the investigated correlations under-predict the pressure drop on severe slugging. The result of this study highlights the requirement of new method considering the effect of pipe layout on the frictional pressure drop.

Numerical simulation of melt flow and temperature field during DC casting 2024 aluminium alloy under different casting conditions

Casting speed,casting temperature and secondary cooling water flow rate are the main process parameters affecting the DC casting process.These parameters significantly influence the flow and temperature fields during casting,which are crucial for the quality of the ingot and can determine the success or failure of the casting operation.Numerical simulation,with the advantages of low cost,rapid execution,and visualized results,is an important method to study and optimize the DC casting process.In the present work,a simulation model of DC casting 2024 aluminum alloy was established,and the reliability of the model was verified.Then,the influence of casting parameters on flow field and temperature field was studied in detail by numerical simulation method.Results show that with the increase of casting speed,the melt flow becomes faster,the depths of slurry zone and mushy zone increase,and the variation of slurry zone depth is greater than that of mushy zone.With an increase in casting temperature,the melt flow rate increases,the depth of the slurry zone becomes shallower,and the depth of the mushy zone experiences only minor changes.The simulation results further indicate that the increase of the flow rate of the secondary cooling water slightly reduces the depths of both slurry and mushy zone.

Research on the flow stability and noise reduction characteristics of quasi-periodic elastic support skin

To enhance flow stability and reduce hydrodynamic noise caused by fluctuating pressure,a quasiperiodic elastic support skin composed of flexible walls and elastic support elements is proposed for fluid noise reduction.The arrangement of the elastic support element is determined by the equivalent periodic distance and quasi-periodic coefficient.In this paper,a dynamic model of skin in a fluid environment is established.The influence of equivalent periodic distance and quasi-periodic coefficient on flow stability is investigated.The results suggest that arranging the elastic support elements in accordance with the quasi-periodic law can effectively enhance flow stability.Meanwhile,the hydrodynamic noise calculation results demonstrate that the skin exhibits excellent noise reduction performance,with reductions of 10 dB in the streamwise direction,11 dB in the spanwise direction,and 10 dB in the normal direction.The results also demonstrate that the stability analysis method can serve as a diagnostic tool for flow fields and guide the design of noise reduction structures.

Verification and Validation of High-Resolution Inviscid and Viscous Conical Nozzle Flows

Capturing elaborated flow structures and phenomena is required for well-solved numerical flows.The finite difference methods allow simple discretization of mesh and model equations.However,they need simpler meshes,e.g.,rectangular.The inverse Lax-Wendroff(ILW)procedure can handle complex geometries for rectangular meshes.High-resolution and high-order methods can capture elaborated flow structures and phenomena.They also have strong mathematical and physical backgrounds,such as positivity-preserving,jump conditions,and wave propagation concepts.We perceive an effort toward direct numerical simulation,for instance,regarding weighted essentially non-oscillatory(WENO)schemes.Thus,we propose to solve a challenging engineering application without turbulence models.We aim to verify and validate recent high-resolution and high-order methods.To check the solver accuracy,we solved vortex and Couette flows.Then,we solved inviscid and viscous nozzle flows for a conical profile.We employed the finite difference method,positivity-preserving Lax-Friedrichs splitting,high-resolution viscous terms discretization,fifth-order multi-resolution WENO,ILW,and third-order strong stability preserving Runge-Kutta.We showed the solver is high-order and captured elaborated flow structures and phenomena.One can see oblique shocks in both nozzle flows.In the viscous flow,we also captured a free-shock separation,recirculation,entrainment region,Mach disk,and the diamond-shaped pattern of nozzle flows.

An extended social force model on unidirectional flow considering psychological and behavioral impacts of hazard source

An accurate assessment of the evacuation efficiency in case of disasters is of vital importance to the safety design of buildings and street blocks.Hazard sources not only physically but psychologically affect the pedestrians,which may further alter their behavioral patterns.This effect is especially significant in narrow spaces,such as corridors and alleys.This study aims to integrate a non-spreading hazard source into the social force model following the results from a previous experiment and simulation,and to simulate unidirectional pedestrian flows over various crowd densities and clarity–intensity properties of the hazard source.The integration include a virtual repulsion force from the hazard source and a decay on the social force term.The simulations reveal(i)that the hazard source creates virtual bottlenecks that suppress the flow,(ii)that the inter-pedestrian push forms a stabilisation phase on the flow-density curve within medium-to-high densities,and(iii)that the pedestrians are prone to a less orderly and stable pattern of movement in low clarity–intensity scenarios,possibly with lateral collisions passing the hazard source.

Mobility and dynamic erosion process of granular flow:insights from numerical investigation using material point method

In order to understand the dynamics of granular flow on an erodible base soil,in this paper,a series of material point method-based granular column collapse tests were conducted to investigate numerically the mobility and dynamic erosion process of granular flow subjected to the complex settings,i.e.,the aspect ratio,granular mass,friction and dilatancy resistance,gravity and presence of water.A set of power scaling laws were proposed to describe the final deposit characteristics of granular flow by the relations of the normalized run-out distance and the normalized final height of granular flow against the aspect ratio,being greatly affected by the complex geological settings,e.g.,granular mass,the friction and dilatancy resistance of granular soil,and presence of water in granular flow.An index of the coefficient of friction of granular soil was defined as a ratio of the target coefficient of friction over the initial coefficient of friction to quantify the scaling extent of friction change(i.e.,friction strengthening or weakening).There is a characteristic aspect ratio of granular column corresponding to the maximum mobility of granular flow with the minimum index of the apparent coefficient of friction.The index of the repose coefficient of friction of granular flow decreased gradually with the increase in aspect ratio because higher potential energy of granular column at a larger aspect ratio causes a larger kinetic energy of granular soil to weaken the friction of granular soil as a kind of velocity-related friction weakening.An increase in granular mass reduces gradually the indexes of the apparent and repose coefficients of friction of granular soil to enhance the mobility of granular flow.The mobility of granular flow increases gradually with the decrease in friction angle or increase in dilatancy angle of granular soil.However,the increase of gravity accelerates granular flow but showing the same final deposit profile without any dependence on gravity.The mobility of granular flow increases gradually by lowering the indexes of the apparent and repose coefficients of friction of granular flow while changing the surroundings,in turn,the dry soil,submerged soil and saturated soil,implying a gradually increased excessive mobility of granular flow with the friction weakening of granular soil.Presence of water in granular flow may be a potential catalyzer to yield a long run-out granular flow,as revealed in comparison of water-absent and water-present granular flows.In addition,the dynamic erosion and entrainment of based soil induced by granular flow subjected to the complex geological settings,i.e.,the aspect ratio,granular mass,gravity,friction and dilatancy resistance,and presence of water,were comprehensively investigated as well.

Impacts of hydropower-induced flow alterations on composition and diversity of riparian vegetation in the Western Himalayas: A case study in Uttarakhand, India

The increasing demand for water and energy resources has led to widespread dam construction,particularly in ecologically sensitive regions like the Himalayan Range.This study focuses on the Uttarakhand state in the Western Himalayas,where hydroelectric projects(HEPs)have significantly altered river flow regimes.The research investigates the impact of flow alterations on the composition and structure of riparian vegetation in the Garhwal Himalayas,specifically analysing four rivers regulated by hydroelectric projects.Utilizing the paired-reach comparison method,control(undisturbed),diverted(downstream of barrage/dam),and altered flow conditions(downstream of water outlet)were examined.The research reveals diverse and unique riparian ecosystems,with 89 genera and 113 taxa identified,showcasing the dominance of families like Asteraceae and Lamiaceae.The study unveils the structural importance of key species such as Berberis asiatica and Artemisia nilagirica.The density,diversity,and richness of shrub and herb species vary significantly across flow conditions.Notably,altered flow conditions demonstrate resilience in vegetation structure,while diverted conditions exhibit decreased species richness and density.The study emphasizes the importance of nuanced environmental flow management for mitigating adverse effects on riparian biodiversity in the fragile Himalayan region.These findings contribute to the global discourse on dam impacts and riparian ecology,shedding light on the complexities of this dynamic relationship in a vulnerable ecosystem.

Effects of fracture evolution and non-Darcy flow on the thermal performance of enhanced geothermal system in 3D complex fractured rock

In fractured geothermal reservoirs,the fracture networks and internal fluid flow behaviors can significantly impact the thermal performance.In this study,we proposed a non-Darcy rough discrete fracture network(NR-DFN)model that can simultaneously consider the fracture evolution and non-Darcy flow dynamics in studying the thermo-hydro-mechanical(THM)coupling processes for heat extraction in geothermal reservoir.We further employed the model on the Habanero enhanced geothermal systems(EGS)project located in Australia.First,our findings illustrate a clear spatial-temporal variation in the thermal stress and pressure perturbations,as well as uneven spatial distribution of shear failure in 3D fracture networks.Activated shear failure is mainly concentrated in the first fracture cluster.Secondly,channeling flow have also been observed in DFNs during heat extraction and are further intensified by the expansion of fractures driven by thermal stresses.Moreover,the combined effect of non-Darcy flow and fracture evolution triggers a rapid decline in the resulting heat rate and temperature.The NR-DFN model framework and the Habanero EGS's results illustrate the importance of both fracture evolution and non-Darcy flow on the efficiency of EGS production and have the potential to promote the development of more sustainable and efficient EGS operations for stakeholders.

Properties of collective flow and pion production in intermediate-energy heavy-ion collisions with a relativistic quantum molecular dynamics model

The relativistic mean-field approach was implemented in the Lanzhou quantum molecular dynamics transport model(LQMD.RMF). Using the LQMD.RMF, the properties of collective flow and pion production were investigated systematically for nuclear reactions with various isospin asymmetries. The directed and elliptic flows of the LQMD.RMF are able to describe the experimental data of STAR Collaboration. The directed flow difference between free neutrons and protons was associated with the stiffness of the symmetry energy, that is, a softer symmetry energy led to a larger flow difference. For various collision energies, the ratio between the π^(-) and π^(+) yields increased with a decrease in the slope parameter of the symmetry energy. When the collision energy was 270 MeV/nucleon, the single ratio of the pion transverse momentum spectra also increased with decreasing slope parameter of the symmetry energy in both nearly symmetric and neutron-rich systems.However, it is difficult to constrain the stiffness of the symmetry energy with the double ratio because of the lack of threshold energy correction on the pion production.

Wind-sand flow simulation and radius optimization of highway embankment under different vertical curve radius

It is of great practical value to explore the correlation between the vertical curve radius of desert highway and the increase of sand accumulation in local lines,and to select the appropriate vertical curve radius for reducing the risk of sand accumulation.In this study,three-dimensional models of desert highway embankments with different vertical curve radii were constructed,and Fluent software was used to simulate the wind-sand flow field and sand accumulation distribution of vertical curve embankments.The results show that:(1)Along the direction of the road,the concave and the convex vertical curve embankments have the effect of collecting and diverging the wind-sand flow,respectively.When the radius of the concave vertical curve is 3000 m,5000 m,8000 m,10000 m and 20000 m,the wind velocity in the middle of the vertical curve is 31.76%,22.58%,10.78%,10.53%and 10.44%,higher than that at both ends.When the radius of the convex vertical curve is 6500 m,8000 m,10000 m,20000 m and 30000 m,the wind velocity at both ends of the vertical curve is 14.06%,9.99%,6.14%,3.22%and 2.41%,higher than that in the middle.The diversion effect also decreases with the increase of the radius.(2)The conductivity of the concave and convex vertical curve embankments with different radii is greater than 1,which is the sediment transport roadbed.The conductivity increases with the increase of radius and gradually tends to be stable.When the radius of the concave and convex vertical curves reaches 8000 m and 20000 m respectively,the phenomenon of sand accumulation is no longer serious.Under the same radius condition,the concave vertical curve embankment is more prone to sand accumulation than the convex one.(3)Considering the strength of the collection and diversion of the vertical curve embankment with different radii,and the sand accumulation of the vertical curve embankment in the desert section of Wuma Expressway,the radius of the concave vertical curve is not less than 8000 m,and the radius of the convex vertical curve is not less than 20000 m,which can effectively reduce the sand accumulation of the vertical curve embankment.In the desert highway area,the research results of this paper can provide reference for the design of vertical curve to ensure the safe operation of desert highway.