Algorithmic approach to discrete fracture network flow modeling in consideration of realistic connections in large-scale fracture networks

Analyzing rock mass seepage using the discrete fracture network(DFN)flow model poses challenges when dealing with complex fracture networks.This paper presents a novel DFN flow model that incorporates the actual connections of large-scale fractures.Notably,this model efficiently manages over 20,000 fractures without necessitating adjustments to the DFN geometry.All geometric analyses,such as identifying connected fractures,dividing the two-dimensional domain into closed loops,triangulating arbitrary loops,and refining triangular elements,are fully automated.The analysis processes are comprehensively introduced,and core algorithms,along with their pseudo-codes,are outlined and explained to assist readers in their programming endeavors.The accuracy of geometric analyses is validated through topological graphs representing the connection relationships between fractures.In practical application,the proposed model is employed to assess the water-sealing effectiveness of an underground storage cavern project.The analysis results indicate that the existing design scheme can effectively prevent the stored oil from leaking in the presence of both dense and sparse fractures.Furthermore,following extensive modification and optimization,the scale and precision of model computation suggest that the proposed model and developed codes can meet the requirements of engineering applications.

Discrete element modeling of migration and evolution rules of coarse aggregates in the static compaction process

To investigate migration and evolution rules of coarse aggregates in the static compaction process, an algorithm of generating digital coarse aggregates that can reflect real morphology（ such as shape, size and fracture surface） of aggregate particles, is represented by polyhedral particles based on the discrete element method（ DEM）. A digital specimen comprised of aggregates and air voids is developed. In addition,a static compaction model consisting of a digital specimen and three plates is constructed and a series of evaluation indices such as mean contact force σMCF, wall stress in direction of zcoordinate σWSZZ, porosity and coordination numbers are presented to investigate the motion rules of coarse aggregates at different compaction displacements of 7. 5, 15 and 30 mm. The three-dimensional static compaction model is also verified with laboratory measurements. The results indicate that the compaction displacements are positively related to σMCF and σWSZZ, which increase gradually with the increase in iterative steps. When the compaction proceeds, the digital specimen porosity decreases, but the coordination number increases. The variation ranges of these four indices are different at different compaction displacements. This study provides a method to analyze the compaction mechanism of particle materials such as asphalt mixture and graded broken stone.

Evaluating the mechanical properties of anisotropic shale containing bedding and natural fractures with discrete element modeling

Natural fracture data from one of the Carboniferous shale masses in the eastern Qaidam Basin were used to establish a stochastic model of a discrete fracture network and to perform discrete element simulation research on the size efect and mechanical parameters of shale.Analytical solutions of fctitious joints in transversely isotropic media were derived,which made it possible for the proposed numerical model to simulate the bedding and natural fractures in shale masses.The results indicate that there are two main factors infuencing the representative elementary volume(REV)size of a shale mass.The frst and most decisive factor is the presence of natural fractures in the block itself.The second is the anisotropy ratio:the greater the anisotropy is,the larger the REV.The bedding angle has little infuence on the REV size,whereas it has a certain infuence on the mechanical parameters of the rock mass.When the bedding angle approaches the average orientation of the natural fractures,the mechanical parameters of the shale blocks decrease greatly.The REV representing the mechanical properties of the Carboniferous shale masses in the eastern Qaidam Basin were comprehensively identifed by considering the infuence of bedding and natural fractures.When the numerical model size is larger than the REV,the fractured rock mass discontinuities can be transformed into equivalent continuities,which provides a method for simulating shale with natural fractures and bedding to analyze the stability of a borehole wall in shale.

A review of discrete modeling techniques for fracturing processes in discontinuous rock masses

The goal of this review paper is to provide a summary of selected discrete element and hybrid finitediscrete element modeling techniques that have emerged in the field of rock mechanics as simulation tools for fracturing processes in rocks and rock masses. The fundamental principles of each computer code are illustrated with particular emphasis on the approach specifically adopted to simulate fracture nucleation and propagation and to account for the presence of rock mass discontinuities. This description is accompanied by a brief review of application studies focusing on laboratory-scale models of rock failure processes and on the simulation of damage development around underground excavations.

Discrete Software Reliability Growth Modeling for Errors of Different Severity Incorporating Change-point Concept

Several software reliability growth models （SRGM） have been developed to monitor the reliability growth during the testing phase of software development. In most of the existing research available in the literatures, it is considered that a similar testing effort is required on each debugging effort. However, in practice, different types of faults may require different amounts of testing efforts for their detection and removal. Consequently, faults are classified into three categories on the basis of severity： simple, hard and complex. This categorization may be extended to r type of faults on the basis of severity. Although some existing research in the literatures has incorporated this concept that fault removal rate （FRR） is different for different types of faults, they assume that the FRR remains constant during the overall testing period. On the contrary, it has been observed that as testing progresses, FRR changes due to changing testing strategy, skill, environment and personnel resources. In this paper, a general discrete SRGM is proposed for errors of different severity in software systems using the change-point concept. Then, the models are formulated for two particular environments. The models were validated on two real-life data sets. The results show better fit and wider applicability of the proposed models as to different types of failure datasets.

Isotropic compression behavior of granular assembly with non-spherical particles by X-ray micro-computed tomography and discrete element modeling

The particle morphological properties,such as sphericity,concavity and convexity,of a granular assembly significantly affect its macroscopic and microscopic compressive behaviors under isotropic loading condition.However,limited studies on investigating the microscopic behavior of the granular assembly with real particle shapes under isotropic compression were reported.In this study,X-ray computed tomography(mCT)and discrete element modeling(DEM)were utilized to investigate isotropic compression behavior of the granular assembly with regard to the particle morphological properties,such as particle sphericity,concavity and interparticle frictions.The mCT was first used to extract the particle morphological parameters and then the DEM was utilized to numerically investigate the influences of the particle morphological properties on the isotropic compression behavior.The image reconstruction from mCT images indicated that the presented particle quantification algorithm was robust,and the presented microscopic analysis via the DEM simulation demonstrated that the particle surface concavity significantly affected the isotropic compression behavior.The observations of the particle connectivity and local void ratio distribution also provided insights into the granular assembly under isotropic compression.Results found that the particle concavity and interparticle friction influenced the most of the isotropic compression behavior of the granular assemblies.

Discrete element modeling of acoustic emission in rock fracture

The acoustic emission （AE） features in rock fracture are simulated numerically with discrete element model （DEM）. The specimen is constructed by using spherical particles bonded via the parallel bond model. As a result of the heterogeneity in rock specimen, the failure criterion of bonded particle is coupled by the shear and tensile strengths, which follow a normal probability distribution. The Kaiser effect is simulated in the fracture process, for a cubic rock specimen under uniaxial compression with a constant rate. The AE number is estimated with breakages of bonded particles using a pair of parameters, in the temporal and spatial scale, respectively. It is found that the AE numbers and the elastic energy release curves coincide. The range for the Kaiser effect from the AE number and the elastic energy release are the same. Furthermore, the frequency-magnitude relation of the AE number shows that the value of B determined with DEM is consistent with the experimental data.

Modeling the influence of forced ventilation on the dispersion of droplets ejected from roadheader-mounted external sprayer

In order to reveal the influence of forced ventilation on the dispersion of droplets ejected from roadheader-mounted external sprayer,the paper studies the air-flowing field and the droplet distribution under the condition of gentle breeze and normal forced ventilation in heading face using the particle tracking technology of computational fluid dynamics(CFD).The results show that air-flowing tendency in the same section presents great comparability in the period of gentle breeze and forced ventilation,and the difference mainly embodies in the different wind velocity.The influence of ventilation on the dispersion of droplets is faint under the gentle breeze condition.The droplet can be evenly distributed around the cutting head.However,under the normal forced ventilation,a large number of droplets will drift to the return air side.At the same time,droplet clusters are predominantly presented in the lower part of windward side and the middle of the leeward side around the cutting head.In contrast,the droplet concentration in other parts around cutting head decreases a lot and the droplets are unable to form close-grained mist curtain.So the dust escape channel is formed.In addition,the simulation results also reveal that the disturbance of air flow on the droplet distribution can be effectively relieved when using ventilation duct with Coanda effect(VDCE).Field experiment results show that the dust suppression efficiency of total dust and respirable dust increases respectively by 10.5%and 9.3%when using VDCE,which proves that it can weaken the influence of airflow on droplet dispersion.

Naturally fractured hydrocarbon reservoir simulation by elastic fracture modeling

Accurate fluid flow simulation in geologically complex reservoirs is of particular importance in construction of reservoir simulators.General approaches in naturally fractured reservoir simulation involve use of unstructured grids or a structured grid coupled with locally unstructured grids and discrete fracture models.These methods suffer from drawbacks such as lack of flexibility and of ease of updating.In this study,I combined fracture modeling by elastic gridding which improves flexibility,especially in complex reservoirs.The proposed model revises conventional modeling fractures by hard rigid planes that do not change through production.This is a dubious assumption,especially in reservoirs with a high production rate in the beginning.The proposed elastic fracture modeling considers changes in fracture properties,shape and aperture through the simulation.This strategy is only reliable for naturally fractured reservoirs with high fracture permeability and less permeable matrix and parallel fractures with less cross-connections.Comparison of elastic fracture modeling results with conventional modeling showed that these assumptions will cause production pressure to enlarge fracture apertures and change fracture shapes,which consequently results in lower production compared with what was previously assumed.It is concluded that an elastic gridded model could better simulate reservoir performance.

Slope stability assessment of an open pit using lattice-spring-based synthetic rock mass (LS-SRM) modeling approach

Discontinuity waviness is one of the most important properties that influence shear strength of jointed rock masses,and it should be incorporated into numerical models for slope stability assessment.However,in most existing numerical modeling tools,discontinuities are often simplified into planar surfaces.Discrete fracture network modeling tools such as MoFrac allow the simulation of non-planar discontinuities which can be incorporated into lattice-spring-based geomechanical software such as Slope Model for slope stability assessment.In this study,the slope failure of the south wall at Cadia Hill open pit mine is simulated using the lattice-spring-based synthetic rock mass(LS-SRM)modeling approach.First,the slope model is calibrated using field displacement monitoring data,and then the influence of different discontinuity configurations on the stability of the slope is investigated.The modeling results show that the slope with non-planar discontinuities is comparatively more stable than the ones with planar discontinuities.In addition,the slope becomes increasingly unstable with the increases of discontinuity intensity and size.At greater pit depth with higher in situ stress,both the slope models with planar and non-planar discontinuities experience localized failures due to very high stress concentrations,and the slope model with planar discontinuities is more deformable and less stable than that with non-planar discontinuities.

High-temperature Creep Behavior Characterization of Asphalt Mixture based on Micromechanical Modeling and Virtual Test

The high-temperature creep behavior of asphalt mixture was investigated based on micromechanical modeling and virtual test by using three-dimensional discrete element method（DEM）. A user-defined micromechanical model of asphalt mixture was established after analyzing the irregular shape and gradation of coarse aggregates, the viscoelastic property of asphalt mastic, and the random distribution of air voids within the asphalt mixture. Virtual uniaxial static creep test at 60 ℃ was conducted by using Particle Flow Code in three dimensions（PFC3D） and was validated by laboratory test. Based on virtual creep test, the micromechanical characteristics between aggregates, within asphalt mastic, and between aggregate and asphalt mastic were analyzed for the asphalt mixture. It is proved that the virtual test based on the micromechanical model can efficiently predict the creep deformation of asphalt mixture. And the high-temperature behavior of asphalt mixture was characterized from micromechanical perspective.

Discrete Element Modeling of a Subduction Zone with a Seafloor Irregularity and its Impact on the Seismic Cycle

Seafloor irregularities influence rupture behavior along the subducting slab and in the overriding plate,thus affecting earthquake cycles.Whether seafloor irregularities increase the likelihood of large earthquakes in a subduction zone remains contested,partially due to focus put either on fault development or on rupture pattern.Here,we simulate a subducting slab with a seafloor irregularity and the resulting deformation pattern of the overriding plate using the discrete element method.Our simulations illustrate the rupture along three major fault systems:megathrust,splay and backthrust faults.Our results show different rupture dimensions of earthquake events varying from tens to ca.140 km.Our results suggest that the recurrence interval of megathrust events with rupture length of ca.100 km is ca.140 years,which is overall comparable to the paleoseismic records at the Mentawai area of the Sumatran zone.We further propose the coseismic slip amounts decrease and interseismic slip amounts increase from the surface downwards gradually.We conclude that the presence of seafloor irregularities significantly affects rupture events along the slab as well as fault patterns in the overriding plate.

A Review of the Dynamic Modeling Approaches for Characterizing Fluid Flow in Naturally Fractured Reservoirs

Fluid flow in fractured media has been studied for decades and received considerable attention in the oil and gas industry because of the high productivity of naturally fractured reservoirs.Due to formation complexity and reservoir heterogeneity,characterizing fluid flow with an appropriate reservoir model presents a challenging task that differs relatively from homogeneous conventional reservoirs in many aspects of view,including geological,petrophysical,production,and economics.In most fractured reservoirs,fracture networks create complex pathways that affect hydrocarbon flow,well performance,hence reservoir characterization.A better and comprehensive understanding of the available reservoir modeling approaches is much needed to accurately characterize fluid flow behavior in NFRs.Therefore,in this paper,a perspective review of the available modeling approaches was presented for fluid flow characterization in naturally fractured medium.Modeling methods were evaluated in terms of their description,application,advantages,and disadvantages.This study has also included the applications of these reservoir models in fluid flow characterizing studies and governing equations for fluid flow.Dual continuum models were proved to be better than single continuum models in the presence of large scale fractures.In comparison,discrete models were more appropriate for reservoirs that contain a smaller number of fractures.However,hybrid modeling was the best method to provide accurate and scalable fluid flow modeling.It is our understanding that this paper will bridge the gap between the fundamental understanding and application of NFRs modeling approaches and serve as a useful reference for engineers and researchers for present and future applications.

Clicking through the Clickstream: A Novel Statistical Modeling Approach to Improve Information Usage of Clickstream Data by E-Commerce Entities

Success or failure of an E-commerce platform is often reduced to its ability to maximize the conversion rate of its visitors. This is commonly regarded as the capacity to induce a purchase from a visitor. Visitors possess individual characteristics, histories, and objectives which complicate the choice of what platform features that maximize the conversion rate. Modern web technology has made clickstream data accessible allowing a complete record of a visitor’s actions on a website to be analyzed. What remains poorly constrained is what parts of the clickstream data are meaningful information and what parts are accidental for the problem of platform design. In this research, clickstream data from an online retailer was examined to demonstrate how statistical modeling can improve clickstream information usage. A conceptual model was developed that conjectured relationships between visitor and platform variables, visitors’ platform exit rate, boune rate, and decision to purchase. Several hypotheses on the nature of the clickstream relationships were posited and tested with the models. A discrete choice logit model showed that the content of a website, the history of website use, and the exit rate of pages visited had marginal effects on derived utility for the visitor. Exit rate and bounce rate were modeled as beta distributed random variables. It was found that exit rate and its variability for pages visited were associated with site content, site quality, prior visitor history on the site, and technological preferences of the visitor. Bounce rate was also found to be influenced by the same factors but was in a direction opposite to the registered hypotheses. Most findings supported that clickstream data is amenable to statistical modeling with interpretable and comprehensible models.

Steady-State Modeling of Heat Transfer on the Recovery System of Condensing Boiler

The increase of energy production is very important nowadays. It is necessary to improve the performance and efficiency of heat production facilities. The objective is to reduce pollutant emissions and regulate investment costs. One of the solutions is to control fuel and electricity consumption. This article develops a new model of simulation heat diffusion on the recovery system of condensing boiler. The method is based on the first and second thermodynamic systems. The Numerical discrete Model (NDM) was applied using MATLAB to simulate different characteristics of heat transfer in the recovery system. The result shows that the recovery unit can absorb the following temperatures;the range from 88°C to 90.7°C when the length of the tube is between respectively 110 and 111 m. the energy efficiency was between 0.55 and 0.57 which allowed confirming the model. This new model has some advantages such as;the use of an instantaneous calculation time. The heat recovered by the water tank can also serve as preheating different systems. One part of the heat recovered will be accumulated to be used as domestic hot water.

Nonlinear wave dispersion in monoatomic chains with lumped and distributed masses:discrete and continuum models

The main objective of this paper is to investigate the influence of inertia of nonlinear springs on the dispersion behavior of discrete monoatomic chains with lumped and distributed masses.The developed model can represent the wave propagation problem in a non-homogeneous material consisting of heavy inclusions embedded in a matrix.The inclusions are idealized by lumped masses,and the matrix between adjacent inclusions is modeled by a nonlinear spring with distributed masses.Additionally,the model is capable of depicting the wave propagation in bi-material bars,wherein the first material is represented by a rigid particle and the second one is represented by a nonlinear spring with distributed masses.The discrete model of the nonlinear monoatomic chain with lumped and distributed masses is first considered,and a closed-form expression of the dispersion relation is obtained by the second-order Lindstedt-Poincare method(LPM).Next,a continuum model for the nonlinear monoatomic chain is derived directly from its discrete lattice model by a suitable continualization technique.The subsequent use of the second-order method of multiple scales(MMS)facilitates the derivation of the corresponding nonlinear dispersion relation in a closed form.The novelties of the present study consist of(i)considering the inertia of nonlinear springs on the dispersion behavior of the discrete mass-spring chains;(ii)developing the second-order LPM for the wave propagation in the discrete chains;and(iii)deriving a continuum model for the nonlinear monoatomic chains with lumped and distributed masses.Finally,a parametric study is conducted to examine the effects of the design parameters and the distributed spring mass on the nonlinear dispersion relations and phase velocities obtained from both the discrete and continuum models.These parameters include the ratio of the spring mass to the lumped mass,the nonlinear stiffness coefficient of the spring,and the wave amplitude.

CO_(2)flooding in shale oil reservoir with radial borehole fracturing for CO_(2)storage and enhanced oil recovery

This study introduces a novel method integrating CO_(2)flooding with radial borehole fracturing for enhanced oil recovery and CO_(2)underground storage,a solution to the limited vertical stimulation reservoir volume in horizontal well fracturing.A numerical model is established to investigate the production rate,reservoir pressure field,and CO_(2)saturation distribution corresponding to changing time of CO_(2)flooding with radial borehole fracturing.A sensitivity analysis on the influence of CO_(2)injection location,layer spacing,pressure difference,borehole number,and hydraulic fractures on oil production and CO_(2)storage is conducted.The CO_(2)flooding process is divided into four stages.Reductions in layer spacing will significantly improve oil production rate and gas storage capacity.However,serious gas channeling can occur when the spacing is lower than 20 m.Increasing the pressure difference between the producer and injector,the borehole number,the hydraulic fracture height,and the fracture width can also increase the oil production rate and gas storage rate.Sensitivity analysis shows that layer spacing and fracture height greatly influence gas storage and oil production.Research outcomes are expected to provide a theoretical basis for the efficient development of shale oil reservoirs in the vertical direction.

Discrete Choice Models and Artificial Intelligence Techniques for Predicting the Determinants of Transport Mode Choice--A Systematic Review

Forecasting travel demand requires a grasp of individual decision-making behavior.However,transport mode choice(TMC)is determined by personal and contextual factors that vary from person to person.Numerous characteristics have a substantial impact on travel behavior(TB),which makes it important to take into account while studying transport options.Traditional statistical techniques frequently presume linear correlations,but real-world data rarely follows these presumptions,which may make it harder to grasp the complex interactions.Thorough systematic review was conducted to examine how machine learning(ML)approaches might successfully capture nonlinear correlations that conventional methods may ignore to overcome such challenges.An in-depth analysis of discrete choice models(DCM)and several ML algorithms,datasets,model validation strategies,and tuning techniques employed in previous research is carried out in the present study.Besides,the current review also summarizes DCM and ML models to predict TMC and recognize the determinants of TB in an urban area for different transport modes.The two primary goals of our study are to establish the present conceptual frameworks for the factors influencing the TMC for daily activities and to pinpoint methodological issues and limitations in previous research.With a total of 39 studies,our findings shed important light on the significance of considering factors that influence the TMC.The adjusted kernel algorithms and hyperparameter-optimized ML algorithms outperform the typical ML algorithms.RF(random forest),SVM(support vector machine),ANN(artificial neural network),and interpretable ML algorithms are the most widely used ML algorithms for the prediction of TMC where RF achieved an R2 of 0.95 and SVM achieved an accuracy of 93.18%;however,the adjusted kernel enhanced the accuracy of SVM 99.81%which shows that the interpretable algorithms outperformed the typical algorithms.The sensitivity analysis indicates that the most significant parameters influencing TMC are the age,total trip time,and the number of drivers.

Extensive numerical simulations on competitive growth between the Edwards–Wilkinson and Kardar–Parisi–Zhang universality classes

Extensive numerical simulations and scaling analysis are performed to investigate competitive growth between the linear and nonlinear stochastic dynamic growth systems, which belong to the Edwards–Wilkinson(EW) and Kardar–Parisi–Zhang(KPZ) universality classes, respectively. The linear growth systems include the EW equation and the model of random deposition with surface relaxation(RDSR), the nonlinear growth systems involve the KPZ equation and typical discrete models including ballistic deposition(BD), etching, and restricted solid on solid(RSOS). The scaling exponents are obtained in both the(1 + 1)-and(2 + 1)-dimensional competitive growth with the nonlinear growth probability p and the linear proportion 1-p. Our results show that, when p changes from 0 to 1, there exist non-trivial crossover effects from EW to KPZ universality classes based on different competitive growth rules. Furthermore, the growth rate and the porosity are also estimated within various linear and nonlinear growths of cooperation and competition.

Prediction of constrained modulus for granular soil using 3D discrete element method and convolutional neural networks

To efficiently predict the mechanical parameters of granular soil based on its random micro-structure,this study proposed a novel approach combining numerical simulation and machine learning algorithms.Initially,3500 simulations of one-dimensional compression tests on coarse-grained sand using the three-dimensional(3D)discrete element method(DEM)were conducted to construct a database.In this process,the positions of the particles were randomly altered,and the particle assemblages changed.Interestingly,besides confirming the influence of particle size distribution parameters,the stress-strain curves differed despite an identical gradation size statistic when the particle position varied.Subsequently,the obtained data were partitioned into training,validation,and testing datasets at a 7:2:1 ratio.To convert the DEM model into a multi-dimensional matrix that computers can recognize,the 3D DEM models were first sliced to extract multi-layer two-dimensional(2D)cross-sectional data.Redundant information was then eliminated via gray processing,and the data were stacked to form a new 3D matrix representing the granular soil’s fabric.Subsequently,utilizing the Python language and Pytorch framework,a 3D convolutional neural networks(CNNs)model was developed to establish the relationship between the constrained modulus obtained from DEM simulations and the soil’s fabric.The mean squared error(MSE)function was utilized to assess the loss value during the training process.When the learning rate(LR)fell within the range of 10-5e10-1,and the batch sizes(BSs)were 4,8,16,32,and 64,the loss value stabilized after 100 training epochs in the training and validation dataset.For BS?32 and LR?10-3,the loss reached a minimum.In the testing set,a comparative evaluation of the predicted constrained modulus from the 3D CNNs versus the simulated modulus obtained via DEM reveals a minimum mean absolute percentage error(MAPE)of 4.43%under the optimized condition,demonstrating the accuracy of this approach.Thus,by combining DEM and CNNs,the variation of soil’s mechanical characteristics related to its random fabric would be efficiently evaluated by directly tracking the particle assemblages.