Discrete Numerical Simulations Research Articles

Research on Water Invasion Law and Control Measures for Ultradeep, Fractured, and Low-Porosity Sandstone Gas Reservoirs: A Case Study of Kelasu Gas Reservoirs in Tarim Basin

The exploitation of ultradeep, fractured, and low-porosity gas reservoirs often encounters challenges from water invasion, exacerbated by the presence of faults and fractures. This is particularly evident in the Kelasu gas reservoir group, located in the Kuqa Depression of the Tarim Basin. The complexity of the water invasion patterns in these reservoirs demands a thorough investigation to devise effective water control measures. To elucidate the water invasion patterns, a combined approach of large-scale physical modeling and discrete fracture numerical simulations was adopted. These models allowed for the identification and categorization of water invasion behaviors in various gas reservoirs. Furthermore, production dynamic analysis was utilized to tailor water control strategies to specific invasion patterns. The large-scale physical simulation experiment revealed that water invasion in gas reservoirs is primarily influenced by high-permeability channels (faults + fractures), and that the gas production rate serves as the key factor governing gas reservoir development. The range of gas extraction rates spans from 3% to 5%. As the gas extraction rate increases, the extraction intensity diminishes and the stable production duration shortens. On the basis of the changes in the water breakthrough time and water production rate, a 2% gas extraction rate is determined as the optimal rate for the model. The embedded discrete fracture numerical simulation model further supports the findings of the physical simulation experiments and demonstrates that ① this type of gas reservoir exhibits typical nonuniform water invasion patterns, controlled by structural location, faults, and degree of crack development; ② the water invasion patterns of gas reservoirs can be categorized into three types, these being explosive water flooding and channeling along faults, uniform intrusion along fractures, and combined intrusion along faults and fractures; ③ drawing from the characteristics of water invasion in various gas reservoirs, combined with production well dynamics and structural location, a five-character water control strategy of “prevention, control, drainage, adjustment, and plugging” is formulated, with the implementation of differentiated, one-well, one-policy governance. The study concludes that a proactive approach, prioritizing prevention, is crucial for managing water-free gas reservoirs. For water-bearing reservoirs, a combination of three-dimensional water plugging and drainage strategies is recommended. These insights have significant implications for extending the productive lifespan of gas reservoirs, enhancing recovery rates, and contributing to the economic and efficient development of ultradeep, fractured, and low-porosity gas reservoirs.

Direct numerical simulation of fluid/solid particles flow inside a channel

The modeling of moving solid particles in fluid flow has been the focus of many studies and has succeeded to attract significant attention from researchers. However, commonly used modeling approaches such as discrete element modeling (DEM) and direct numerical simulations (DNS) lack simplicity and have been computationally intensive. The aim of this paper is to develop a new approach to simulate solid transport in an incompressible Newtonian fluid flow. This method is based on the Finite element method with penalization of the deformation tensor. The fluid behavior is governed by the Navier-Stokes equations within the investigation domain. To take into account collisions, we present an algorithm which allows us to handle contacts between rigid particles. In this paper, 2D fluid/particles flow simulations are performed; the results are validated by comparison with results from other methods. We attempt to simulate the conveying of solid particles behavior of circular particles in a fluid flow inside a pipe. The numerical tests show that the present method provides a very efficient approach to directly simulate the solid transport inside the channels.

Modeling shear-induced solid-liquid transition of granular materials using persistent homology

This paper investigates the transition between the solid and liquid phases of sheared granular materials from the perspective of the contact network. Tools from persistent homology are employed to quantify the dynamics of contact network during the solid-liquid transition from a global perspective, and two important topological invariants, i.e., components and loops, are mainly investigated from discrete numerical simulations. The highly heterogeneous composition of the contact network is revealed, and a rationale partition threshold for distinguishing between strong and weak contact subnetworks can be determined through the emergence and death of these topological invariants. During the shearing process, we recognize mechanical precursors forecasting the occurrence of solid-liquid transition when the assembly is still stable. Furthermore, we provide the panorama of the solid-liquid transition from the evolution of contact network and its homology groups. Finally, this study suggests that the persistent homology method is capable of quantitatively bridging the microscopic dynamics with macroscopic responses through the contact network, which paves an efficient way to further include the evolution of the contact network in the constitutive modeling of granular materials.

Collaborative behavior of intruders moving amid grains

We investigate the motion of groups of intruders in a two-dimensional granular system by using discrete numerical simulations. By imposing either a constant velocity or a thrusting force on larger disks (intruders) that move within smaller ones (grains), we obtained instantaneous positions and components of forces for each intruder and grain. We found that (i) intruders cooperate even when at relatively large distances from each other; (ii) the cooperative dynamics is the result of contact chains linking the intruders as well as compaction and expansion of the granular medium in front and behind, respectively, each intruder; (iii) the collaborative behavior depends on the initial arrangement of intruders; and (iv) for some initial arrangements, the same spatial configuration is eventually reached. Finally, we show the existence of an optimal distance for minimum drag for a given set of intruders, which can prove useful for devices stirring the ground or other granular surfaces.

Self-diffusion in inhomogeneous granular shearing flows.

In this Letter, we discuss how flow inhomogeneity affects the self-diffusion behavior in granular flows. Whereas self-diffusion scalings have been well characterized in the past for homogeneous shearing, the effect of shear localization and nonlocality of the flow has not been studied. We, therefore, present measurements of self-diffusion coefficients in discrete numerical simulations of steady, inhomogeneous, and collisional shearing flows of nearly identical, frictional, and inelastic spheres. We focus on a wide range of dense solid volume fractions, that correspond to geophysical and industrial shearing flows that are dominated by collisional interactions. We compare the measured values first with a scaling based on shear rate and, then, on a scaling based on the granular temperature. We find that the latter does much better than the former in collapsing the data. The results lay the foundations of diffusion models for inhomogeneous shearing flows, which should be useful in treating problems of mixing and segregation.

Contacts, motion, and chain breaking in a two-dimensional granular system displaced by an intruder

We investigate numerically how the motion of an intruder within a two-dimensional granular system affects its structure and produces drag on the intruder. We made use of discrete numerical simulations in which a larger disk (intruder) is driven at constant speed amid smaller disks confined in a rectangular cell. By varying the intruder's velocity and the basal friction, we obtained the resultant force on the intruder and the instantaneous network of contact forces, which we analyze at both the cell and grain scales. We found that there is a bearing network that percolates forces from the intruder toward the walls, being responsible for jammed regions and high values of the drag force, and a dissipative network that percolates small forces within the grains, in agreement with previous experiments on compressed granular systems. In addition, we found the anisotropy levels of the contact network for different force magnitudes and regions, that the force network can reach regions far downstream of the intruder by the end of the intruder's motion, that the extent of the force network decreases with decreasing the basal friction, and that the void region (cavity) that appears downstream of the intruder tends to disappear for lower values of the basal friction. Interestingly, our results show that grains within the bearing chains creep while the chains break, revealing the mechanism by which bearing chains collapse.

Dense shearing flows of soft, frictional cylinders.

We perform discrete numerical simulations at a constant volume of dense, steady, homogeneous flows of true cylinders interacting via Hertzian contacts, with and without friction, in the absence of preferential alignment. We determine the critical values of the solid volume fraction and the average number of contacts per particle above which rate-independent components of the stresses develop, along with a sharp increase in the fluctuations of angular velocity. We show that kinetic theory, extended to account for a velocity correlation at solid volume fractions larger than 0.49, can quantitatively predict the measured fluctuations of translational velocity, at least for sufficiently rigid cylinders, for any value of the cylinder aspect ratio and friction investigated here. The measured pressure above and below the critical solid volume fraction is in agreement with a recent theory originally intended for spheres that conjugates extended kinetic theory, the finite duration of collisions between soft particles and the development of an elastic network of long-lasting contacts responsible for the rate-independency of the flows in the supercritical regime. Finally, we find that, for sufficiently rigid cylinders, the ratio of shear stress to pressure in the subcritical regime is a linear function of the ratio of the shear rate to a suitable measure of the fluctuations of translational velocity, in qualitative accordance with kinetic theory, with an intercept that increases with friction. A decrease in the particle stiffness gives rise to nonlinear effects that greatly diminishes the stress ratio.

Study on Fracture Mechanism of Soft Rock with Different Prefabricated Fractures during Drilling

The primary fractures in rocks have an important influence on the rock breaking efficiency. In order to understand the fracture mechanism of broken soft rock strata more deeply, this paper carried out a series of discrete element particle flow numerical simulations with different prefabricated fractures (different number of fractures and fracture angles) based on laboratory rock mechanics tests. The results show that: the overall failure of rock mass is mainly tensile and compressive failure. And, when the crack reaches a certain depth, the influence of primary cracks in rock mass on rock breaking effect will be significantly weakened. Furthermore, in the process of rock breaking, the rock mass basically shows brittle fracture, and the crack initiation stress of rock mass has a good positive correlation with the degree of rock fragmentation. The crack initiation location is often accompanied by stress concentration, which is the key to rock fragmentation. And, the angle of prefabricated cracks will affect the crack initiation position. When the prefabricated crack angle approaches the top angle of the drill, the crack initiation stress will increase. Finally, the fracture mode and initiation mechanism of rock mass are revealed in the process of rock breaking. This study can provide some reference for the optimization of drilling parameters.

An analytical method for the optical analysis of Linear Fresnel Reflectors with a flat receiver

The optical analysis of Linear Fresnel Reflectors solar concentrators deals with the calculation of the absorbed flux at the receiver. Due to concentrator discrete and complex geometry ray tracing numerical simulations is the main used method, in parallel with some analytical approaches that have been developed for specific cases. This paper presents an analytical method for Linear Fresnel Reflectors with a flat receiver. It is based on Zhu’s vector-based method and Rabl’s concepts of acceptance and effective source, although new shading (including receiver shading), blocking, and cosine losses analyzes are presented, with the inclusion of end-losses effect. As shown, the problem is better described by the concept of intercept factor, the effective aperture area used to collect the incident sunlight. Comparison tests with ray tracing simulations performed in SolTrace for three different effective sources were carried out to validate the analytical model for both factorized and biaxial models of the intercept factor, including energetic evaluations for Évora, Portugal. In general, analytical results do agree very well with ray tracing, better for the factorized model than the biaxial. Errors in the analytical estimative of intercept factor can be high up to 132% for the biaxial model at high longitudinal incidence angles; on the other hand, errors in the amount of annual absorbed energy were high up to only 3%.

Viscoelastic truss metamaterials as time-dependent generalized continua

Mechanical metamaterials provide tailorable functionality based on a careful combination of base material and structural architecture. Truss-based metamaterials, e.g., exploit structural topology and beam geometry to achieve beneficial mechanical and physical properties from stiffness and wave dispersion to strength and toughness. While the focus to date has been primarily on static metamaterial properties or elastic wave motion, 3D-printed polymeric base materials naturally come with significant viscoelasticity, making the effective truss response time- and rate-dependent. Here, we report a theoretical-numerical-experimental study which (i) deploys a linear viscoelastic corotational beam description (capturing finite rotations at small strains), (ii) implements the latter in a finite element framework, (iii) calibrates a generalized Maxwell model based on viscoelastic experiments on 3D-printed polymer samples, (iv) validates the theory and implementation through experimental truss benchmark tests, and (v) introduces a generalized continuum formulation for the efficient simulation of viscoelastic truss metamaterials containing large numbers of structural members. We show that the viscoelastic beam approach, calibrated via tension tests on individual strut samples, performs well when applied to complex truss lattices undergoing time-dependent stress relaxation — as verified by the effective mechanical response and full-field deformation maps. The resulting variational generalized continuum framework uses on-the-fly periodic homogenization based on a representative unit cell and is extended to dynamics by including inertial effects. By comparison to discrete numerical simulations we demonstrate the accuracy of the continuum approach, which is promising for modeling and optimizing 3D-printed truss metamaterials for engineering applications from shock-absorbing structures to rate-dependent architected materials and soft robotics.

Experimental assessment of the effective friction at the base of granular chute flows on a smooth incline.

We report on direct measurements of the basal force components for granular material flowing down a smooth incline. We investigate granular flows for a large range of inclination angles from θ=13.4^{∘} to 83.6° and various gate openings of the chute. We find that the effective basal friction coefficient μ_{B}, obtained from the ratio of the longitudinal force to the normal one, exhibits a systematic increase with increasing slope angle and a significant weakening with increasing particle holdup H (the depth-integrated particle volume fraction). At low angles, the basal friction is slightly less than or equal to tanθ.The deviation from tanθcan be interpreted as a contribution from the sidewall to the overall friction. At larger angles, the basal friction μ_{B} saturates at an asymptotic value that is dependent on the gate opening of the chute. Importantly, our data confirm the outcomes of recent discrete numerical simulations. First, for steady and fully developed flows as well as for moderately accelerated ones, the variation of the basal friction can be captured through a unique dimensionless number, the Froude number Fr, defined as Fr=U[over ¯]/(gHcosθ)^{1/2}, where U[over ¯] is the mean flow velocity. Second, the mean velocity scales with the particle holdup H with a power exponent close to 1/4, contrasting with the Bagnold scaling (U[over ¯]∼H^{3/2}).

Structural Features and Evolution of the Northwestern Sichuan Basin: Insights From Discrete Numerical Simulations

The northwestern Sichuan Basin has experienced Meso-Cenozoic intracontinental compressional tectonic processes and formed multi-detachment stratigraphic distribution of foreland basins and fold-thrust belts, which have caused complicated structural deformations in the deep buried layers. Rapid uplift with accelerated erosion and two sets of detachments in the Lower Triassic and Lower Cambrian controlled the multilevel deformation structure. We conducted discrete numerical simulations with double weak detachments and erosion under extrusion conditions in order to examine the mechanics and kinematics of the frontalpiedmont zones of the NW Sichuan Basin. The following findings were made. (1) With continuous compression, the weak detachments promoted the decoupled and ladder-like deformation of the thrust belt, where the deformation above the slip layer extended further than it did below it. Rapid uplift and erosion at the thrust front contributed to the formation of a passive roof fault and a monocline in the upper layer, a series of forward and backward thin-skinned thrust-buried structures in the middle layer sandwiched between two weak detachments and stacking structures in the lower layer. (2) Erosion effectively prevents the deformation from propagating above the upper detachment, but can advance a horizontal transition in the deformation style generated within the middle brittle layer: from oblique and tight fault propagation folds to symmetrical, wide, and gentle detachment folds. (3) The model results consistent with tectonic deformation in the NW Sichuan Basin indicate a possible evolutionary mechanism under compression. There is hierarchical deformation of uncoordinated contraction controlled by the Lower Triassic and Early Cambrian weak layers, with the characteristics of the shallow monocline, the middle thin-skinned thrusts, and the deeper basement-involved folds. Continuous compression contributed a sequential pattern of steps as a whole, from the frontalpiedmont zones to the foreland basin, autochthonous stacking thrusts, and the huge buried structure in the NW Sichuan Basin. During the Himalayan period, syntectonic erosion along with the uplifted thrust front maintained the development of a passive-roof duplex and a huge forward buried structure.

Research on the Evolution Characteristics of Rock Mass Response from Open‐Pit to Underground Mining

This study is based on the engineering background of pit no. 2 in Jinning Phosphate Mine, China. In order to systematically analyze the movement, deformation, and failure laws of surrounding rocks in underground stopes. The room and pillar method is used to excavate and stop the ore bodies in the mining area. Combined with the similar physical model experiments and discrete element MatDEM numerical simulations, it reveals the deformation and failure laws and evolution characteristics of the surrounding rock of the stope in the process of converting from open‐pit to underground mining. The results show the following: (1) Along the inclination of the ore body, the farther the horizontal and vertical displacements are from the underground stope, the less the impact of mining stress. On the other hand, along the inclined vertical direction of the ore body, the farther the measuring point is from the stope, the smaller the range of mining influence will be. (2) In the process of ore body recovery, the rupture of the overlying strata of the stope has an obvious layered structure, with collapse zones, fissure penetrating zones, and microfracture loosen zones appearing from the bottom to top. In addition, the movement and destruction of the overlying strata of the entire stope is an “elliptical arch.” Therefore, the results of similar simulation experiments and numerical simulation are basically consistent.

Network temporality can promote and suppress information spreading.

Temporality is an essential characteristic of many real-world networks and dramatically affects the spreading dynamics on networks. In this paper, we propose an information spreading model on temporal networks with heterogeneous populations. Individuals are divided into activists and bigots to describe the willingness to accept the information. Through a developed discrete Markov chain approach and extensive numerical simulations, we discuss the phase diagram of the model and the effects of network temporality. From the phase diagram, we find that the outbreak phase transition is continuous when bigots are relatively rare, and a hysteresis loop emerges when there are a sufficient number of bigots. The network temporality does not qualitatively alter the phase diagram. However, we find that the network temporality affects the spreading outbreak size by either promoting or suppressing, which relies on the heterogeneities of population and of degree distribution. Specifically, in networks with homogeneous and weak heterogeneous degree distribution, the network temporality suppresses (promotes) the information spreading for small (large) values of information transmission probability. In networks with strong heterogeneous degree distribution, the network temporality always promotes the information spreading when activists dominate the population, or there are relatively fewer activists. Finally, we also find the optimal network evolution scale, under which the network information spreading is maximized.

Influence of lateral confinement on granular flows: comparison between shear-driven and gravity-driven flows

The properties of confined granular flows are studied through discrete numerical simulations. Two types of flows with different boundaries are compared: (i) gravity-driven flows topped with a free surface and over a base where erosion balances accretion (ii) shear-driven flows with a constant pressure applied at their top and a bumpy bottom moving at constant velocity. In both cases we observe shear localization over or/and under a creep zone. We show that, although the different boundaries induce different flow properties (e.g. shear localization of transverse velocity profiles), the two types of flow share common properties like (i) a power law relation between the granular temperature and the shear rate (whose exponent varies from 1 for dense flows to 2 for dilute flows) and (ii) a weakening of friction at the sidewalls which gradually decreases with the depth within the flow.

Rocking Blocks Stability under Critical Pulses from Near-Fault Earthquakes Using a Novel Energy Based Approach

Following the seminal work of Housner, a novel energy based critical pulse theoretical model is derived to assess the seismic stability of rocking rigid blocks under single pulses from near-fault earthquakes. It is shown that overturning is conditional on the availability of sufficient kinetic energy in the exciting pulse and on the inception of rocking. The theoretical model is shown to be in good agreement with discrete element method numerical simulations for similar blocks of sizes 0.5, 1, and 20 m. Similitude rules are established to scale between block sizes and pulse types and tested successfully. The results agree with available experimental data. The proposed stability chart approach provides a practical and simple alternative to the presentation and study of the stability and overturning of blocks published by others in the frequency spectrum domain. For any given rigid block or inverted pendulum structure the model or normalized stability charts provide a method to determine the characteristic period and peak acceleration required for overturning and by extension to identify the critical content of the dominant pulse of a given earthquake signal. Alternatively, the approach could be used in archaeoseismology to identify the characteristics of the dominant pulse content of past earthquakes based on their impacts on various historical and heritage structures.

Discrete particle behavior in solid-liquid concave-wall jet

The aim of this paper is to reveal the solid-liquid separation mechanism in concave-wall jet. The discrete particle experiments and numerical simulations were performed to study the large particle behavior near concave-wall. The results show that the particle behavior is divided into two stages by the first collision point of particle-to-wall and the wall shear stress at the collision point quickly changes from zero to peak. The iterative formulae for particle position coordinates are used and 27.88° is obtained as the maximum of circumferential collision position when the jet width is 20 mm. Before the first collision, the particle tangential velocity is constant and the wall shear stress is 0. After the first collision, the wall shear stress and tangential velocity decrease with time. The distance of particle-to-wall is within 0.1 times of jet width. Low-frequency contact of particle-to-wall is the collision and the particle Reynolds number often exceeds 400. The large particle behavior is affected by the shape of jet inlet cross-section. Comparing to the square inlet cross-section, the particle cumulative probability of rectangle inlet cross-section is lower at the same residence time, the local maximum of turbulent kinetic energy and wall shear stress decrease 5.3 % and 5.9 %, respectively.

Micromechanical Exploration of the Lade–Duncan Yield Surface by the Discrete Element Method

The Lade–Duncan yield surface has long been known to outperform other yield criteria (e.g., Mohr–Coulomb, Drucker–Prager) for predicting macro-scale failure in non-cohesive granular (pressure-dependent) materials. Such yield criteria are critical for a wide variety of civil and infrastructure engineering applications, including the design and analysis of foundations and retaining walls for architectural, highway, and railway support structures. The Lade–Duncan yield surface has been repeatedly validated, not only by numerous experimental studies, but also by three-dimensional discrete element method numerical simulations performed on mono- and poly-disperse assemblies of spheres. However, a fully satisfying micromechanical explanation for the empirically-motivated Lade–Duncan yield criterion has never been offered. In particular, the increase in the macro-scale friction angle $$\phi$$ relative to the Mohr–Coulomb yield surface that occurs as the Lode angle of deviatoric stress moves from simple compression toward simple extension on the $$\varPi$$ -plane in principal stress space, which is characteristic of the Lade–Duncan yield surface, has never been given a rigorous micromechanics-based explanation. In this paper, we attempt to fill this “gap”, by presenting a simple yet rigorous analysis of micro-scale inter-particle force-equilibrium, which, when combined with detailed 3D-DEM data obtained from simulations of cubical true-triaxial tests performed on mono- and poly-disperse spheres with a variety of micro-scale or inter-particle friction coefficients $$\mu$$ , provides a meaningful micromechanics-based explanation for the shape of the Lade–Duncan yield surface. In particular, we hypothesize that the Lade–Duncan yield criterion can be motivated directly from the continuum-mechanics-based spatially mobilized plane or Matsuoka–Nakai criterion in terms of the ratio of shear stress to normal stress on the spatially mobilized plane if the magnitude of the shear stress on the SMP is increased to account for deviations in the paths of sliding particles on the SMP.

Transition from Saltation to Collisional Regime in Windblown Sand.

We report experiments on windblown sand that highlight a transition from saltation to collisional regime above a critical dimensionless mass flux or Shields number. The transition is first seen through the mass flow rate Q, which deviates from a linear trend with the Shields number and seems to follow a quadratic law. Other physical evidences confirm the change of the transport properties. In particular, the particle velocity and the height of the transport layer increases with increasing Shields number in the collisional regime while the latter are invariant with the wind strength in the saltation regime. Discrete numerical simulations support the experimental findings and ascertain that mid-air collisions are responsible for the change of transport regime.

Insights into the rheology of cohesive granular media.

Characterization and prediction of the "flowability" of powders are of paramount importance in many industries. However, our understanding of the flow of powders like cement or flour is sparse compared to the flow of coarse, granular media like sand. The main difficulty arises because of the presence of adhesive forces between the grains, preventing smooth and continuous flows. Several tests are used in industrial contexts to probe and quantify the "flowability" of powders. However, they remain empirical and would benefit from a detailed study of the physics controlling flow dynamics. Here, we attempt to fill the gap by performing intensive discrete numerical simulations of cohesive grains flowing down an inclined plane. We show that, contrary to what is commonly perceived, the cohesive nature of the flow is not entirely controlled by the interparticle adhesion, but that stiffness and inelasticity of the grains also play a significant role. For the same adhesion, stiffer and less dissipative grains yield a less cohesive flow. This observation is rationalized by introducing the concept of a dynamic, "effective" adhesive force, a single parameter, which combines the effects of adhesion, elasticity, and dissipation. Based on this concept, a rheological description of the flow is proposed for the cohesive grains. Our results elucidate the physics controlling the flow of cohesive granular materials, which may help in designing new approaches to characterize the "flowability" of powders.