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The purpose of this paper is to apply the numerical methods to study the heap leaching process in a bed of porous and spherical ore particles. This study is performed in two stages: first, modeling the leaching process of a soluble mineral from a spherical and porous ore particle to obtain the distribution of mineral concentrations, leaching solvent concentration and dissolved mineral in the particles (the particle model), and second, modeling the heap leaching of the mineral from a porous bed consisting of spherical and porous ore particles to obtain the distribution of mineral concentrations, leaching solvent concentration and dissolved mineral in the bed (the bed model).

The governing equations are derived for the particle model, and then converted into non‐dimensional form using reference quantities. The non‐dimensional equations are discretised on a uniform spherical grid fitted to the particle using finite difference method. The resulting algebraic equations are solved using Tri‐Diagonal Matrix Algorithm, and the governing equations are derived for the bed model, and then converted into non‐dimensional form using reference quantities. The non‐dimensional equations are discretised explicitly on a one‐dimensional and uniform grid fitted to the bed. The unknown quantities are evaluated using the corresponding values at the previous time interval.

The results obtained from numerical modeling show that, when the particle has a low diffusion resistance or a high chemical resistance, the reaction takes place slowly and homogeneously throughout the ore particle. On the other hand, when the bed has a low convection resistance, the reaction takes place homogeneously throughout the bed. As the convection resistance increases, the non‐homogeneous (local) behavior predominates. It is also noticed that, when the chemical reaction resistance is high, the reaction takes place homogeneously throughout the bed.

The dynamic diffusion and movement of solution in the ore particles and ore bed are not modeled and volumetric ratio of solution in the particles and the bed and also vertical velocity of solution in the bed are assumed to be fixed constants.

This study shows that the reaction takes place homogeneously throughout the bed when the convection resistance is low, the diffusion resistance is high, the concentration resistance is low, and the chemical reaction resistance is high.

Homogeneous reaction conditions being suitable for heap leaching operations are identified. Thus, it is recommended to approach the above conditions when preparing ore heaps and designing the relevant operation.

The macroscopic properties of dried sand can be correctly modelled when the accurate determination of the microscopic properties is available. The microscopic properties between the particles such as the coefficients of rolling (µ _r) and sliding (µ _s), are numerically determined in two different ways: with and without considering the fluid effect. In an earlier study, the microscopic properties were determined by discrete element method (DEM) and without considering the air effect on the macroscopic properties such as the Angle of Repose. The purpose of this paper is to recalibrate the microscopic properties through a coupling between the DEM and computational fluid dynamics (CFD).

The first step is dedicated to the calibration of the CFD-DEM model through modelling a single particle sedimentation within air, water, and silicon oil. The voidage and drag models, the grid size ratio (D/dx), the domain size ratio (W/D), and the optimum coupling interval between the CFD and DEM were investigated through comparing the CFD-DEM results with the analytical solution and experimental data. The next step is about modelling an Hourglass with the calibrated CFD-DEM model to recalibrate the µ _r and µ _s of dried sand particles.

It was concluded that the air has a minor effect on the macroscopic properties of the dried sand and the µ _r and µ _s that were obtained with the DEM can be utilized in the CFD-DEM simulation.

Utilizing the granulometry of dried quartz sand in the calibration process of the CFD-DEM method has raised the possibility of using the µ _r and µ _s for other applications in future studies.

The purpose of this paper is to perform the computational fluid dynamics (CFD) simulation with experimental validation to investigate the particle segregation effect in abrupt and smooth shapes circulating fluidized bed (CFB) risers.

The experimental investigations were carried out in lab-scale CFB systems and the CFD simulations were performed by using commercial software BARRACUDA. Special attention was paid to investigate the gas-particle flow behavior at the top of the riser with three different superficial velocities, namely, 4, 6 and 7.7 m/s. Here, a CFD-based noble simulation approach called multi-phase particle in cell (MP-PIC) was used to investigate the effect of traditional drag models (Wen-Yu, Ergun, Wen-Yu-Ergun and Richardson-Davidson-Harrison) on particle flow characteristics in CFB riser.

Findings from the experimentations revealed that the increase in gas velocity leads to decrease the mixing index inside the riser. Moreover, the solid holdup found more in abrupt riser than smooth riser at the constant gas velocity. Despite the more experimental investigations, the findings with CFD simulations revealed that the MP-PIC approach, which was combined with different drag models could be more effective for the practical (industrial) design of CFB riser. Well agreement was found between the simulation and experimental outputs. The simulation work was compared with experimental data, which shows the good agreement (<4%).

The experimental and simulation study performed in this research study constitutes an easy-to-use with different drag coefficient. The proposed MP-PIC model is more effective for large particles fluidized bed, which can be helpful for further research on industrial gas-particle fluidized bed reactors. This study is expected to give throughout the analysis of CFB hydrodynamics with further exploration of overall fluidization.

The main purpose of this paper is to derive a set of similarity principles for discrete element modelling so that a numerical model can exactly reproduce the physical phenomenon concerned.

The objective is achieved by introducing the concepts of particle “strain” and “stress” so that some equivalence between the physical system and the numerical model can be established.

Three similarity principles, namely geometric, mechanical and dynamic, under which the numerical model can exactly reproduce the mechanical behaviour of a physical model are proposed. In particular, the concept of the scale invariant interaction law is further introduced. The scalability of a number of most commonly used interaction laws in the discrete element modelling is examined.

This is a preliminary research for a very important and challenging topic. More research, particularly in the understanding of the convergent properties of discrete element models, is needed.

The paper provides some important theoretical guidances to computational modelling of particle systems using discrete element techniques.

The purpose of this paper is to show how particle scale simulation of industrial particle flows using DEM (discrete element method) offers the opportunity for better understanding of the flow dynamics leading to improvements in equipment design and operation.

The paper explores the breadth of industrial applications that are now possible with a series of case studies.

The paper finds that the inclusion of cohesion, coupling to other physics such fluids, and its use in bubbly and reacting flows are becoming increasingly viable. Challenges remain in developing models that balance the depth of the physics with the computational expense that is affordable and in the development of measurement and characterization processes to provide this expanding array of input data required. Steadily increasing computer power has seen model sizes grow from thousands of particles to many millions over the last decade, which steadily increases the range of applications that can be modelled and the complexity of the physics that can be well represented.

The paper shows how better understanding of the flow dynamics leading to improvements in equipment design and operation can potentially lead to large increases in equipment and process efficiency, throughput and/or product quality. Industrial applications can be characterised as large, involving complex particulate behaviour in typically complex geometries. The critical importance of particle shape on the behaviour of granular systems is demonstrated. Shape needs to be adequately represented in order to obtain quantitative predictive accuracy for these systems.

The purpose of this paper is to examine several calibration techniques that have been developed to determine the discrete element method (DEM) parameters for slow and rapid unconfined flow of granular conical pile formation. This paper also aims to discuss some of the methods currently employed to scale particle properties to reduce computational resources and time to solve large DEM models.

DEM models have been calibrated against simple bench‐scale experimental results to examine the validity of selected parameters for the contact, material and mechanical models to simulate the dynamic and static behaviour of cohesionless polyethylene pellets. Methods to determine quantifiable single particle parameters such as static friction and the coefficient of restitution have been highlighted. Numerical and experimental granular pile formation has been investigated using different slumping and pouring techniques to examine the dependency of the type of flow mechanism on the DEM parameters.

The proposed methods can provide cost effective and simple techniques to determine suitable input parameters for DEM models. Rolling friction and particle shape representation has shown to have a significant influence on the bulk flow characteristics via a sensitivity analysis and needs to be accessed based on the environmental conditions.

This paper describes several effective known and novel methodologies to characterise granular materials that are needed to accurately model granular flow using the DEM to provide valuable quantitative data. For the DEM to be a viable predictive tool in industrial applications which often contain huge quantities of particles with random particle shapes and irregular properties, quick and validated techniques to “tune” DEM models are necessary.

Particle scale simulation of industrial particle flows using discrete element method (DEM) offers the opportunity for better understanding the flow dynamics leading to improvements in equipment design and operation that can potentially lead to large increases in equipment and process efficiency, throughput and/or product quality. Industrial applications can be characterized as large, involving complex particulate behaviour in typically complex geometries. In this paper, with a series of examples, we will explore the breadth of large scale modelling of industrial processes that is currently possible. Few of these applications will be examined in more detail to show how insights into the fundamentals of these processes can be gained through DEM modelling. Some examples of our collaborative validation efforts will also be described.

The aim of this paper is to present a Eulerian–Lagrangian model of aircraft ground deicing that avoids the scale’s dispersion problem caused by the great distance between the spray nozzle and the surface to be deiced. Verification is done using the case of a hot particle liquid spray impinging on a horizontal flat plate. The impinged particles flow outwards radially from the impingement zone and form a hot film wall. The computed wall heat distribution is verified. In the end, an inclination spray’s angle study is presented.

The problem is divided into two regions. First, a 3D region is created for the evolution of the Lagrangian particles spray. A second 2D region is provided for the formation of a liquid film. The two regions exchange mass, momentum and energy through an interface. Heat losses are modelled through particles and liquid-film cooling and evaporation, particles splash and heat transfer to a fixed temperature plate.

For a chamber pressure of 1 bar, the predicted spray penetration is within 10 per cent of the experimental results. For this study case, the heat transfer is maximized with an inclination angle of approximately 30° of the spray.

The model presented makes it possible to simulate the impingement and heat transfer of a large-scale liquid spray with a reasonable computational cost. To the best of the authors’ knowledge, this model is a first attempt of the computational fluid dynamics simulation of ground deicing.

The tensile test is one of the fundamental experiments used to evaluate material properties. Simulating a tensile test can be a replacement of experiments to determine mechanical parameters of a continuous material. The paper aims to discuss these issues.

This research uses a new approach to model a tensile test of a high-carbon steel on the basis of discrete element method (DEM). In this research, the tensile test specimen was created by using a DEM packing theory. The particle-particle bond model was used to establish the internal forces of the tensile test specimen. The particle-particle bond model was first tested by performing two-particle tensile test, then was adopted to simulate tensile tests of the high-carbon steel by using 3,678 particles.

This research has successfully revealed the relationships between the DEM parameters and mechanical parameters by modelling a tensile test. The parametric study demonstrates that the particle physical radius, particle contact radius and bond disc radius can significantly influence ultimate stress and Young’s modulus of the specimen, whereas they slightly impact elongation at fracture. Increasing the normal and shear stiffness, the critical normal and shear stiffness can enable the increase of ultimate stress, however, up to maximum values.

To improve the particle-particle bond model to simulate a tensile test for high-carbon steel, the damping factors for compensating energy loss from transition of particle motions and failure of bonds are required.

This work reinforces the knowledge of applying DEM to model continuous materials.

This research illustrates a new approach to model a tensile test of a high-carbon steel on the basis of DEM.

This paper aims to present a novel approach for computing particle temperatures in simulations coupling computational fluid dynamics (CFD) and discrete element method (DEM) to predict flow and heat transfer in fluidized beds of thermally thick spherical particles.

An improved lumped formulation based on Hermite-type approximations for integrals to relate surface temperature to average temperature and surface heat flux is used to overcome the limitations of classical lumped models. The model is validated through comparisons with analytical solutions for a convectively cooled sphere and experimental data for a fixed particle bed. The coupled CFD-DEM model is then applied to simulate a Geldart D bubbling fluidized bed, comparing the results to those obtained using the classical lumped model.

The validation cases demonstrate that ignoring internal thermal resistance can significantly impact the temperature in cases where the Biot number is greater than 0.1. The results for the fixed bed case clearly demonstrate that the proposed method yields significantly improved outcomes compared to the classical model. The fluidized bed results show that surface temperature can deviate considerably from the average temperature, underscoring the importance of accurately accounting for surface temperature in convective heat transfer predictions and surface processes.

The proposed approach offers a physically more consistent simulation without imposing a significant increase in computational cost. The improved lumped formulation can be easily and inexpensively integrated into a typical DEM solver workflow to predict heat transfer for spherical particles, with important implications for various industrial applications.