Comparison of breakage models in DEM in simulating impact on particle beds

Highlights

• Three breakage models in DEM have been analyzed.

• Models were fitted to single-particle breakage data and simulated impacts on beds.

• The particle replacement model described well product size.

• The fast-breakage model fitted well breakage probability.

• The bonded-particle model described well force–deformation response.

Abstract

The discrete element method (DEM) has proven to be a powerful tool to simulate processes involving particulate material. When simulating materials handling operations that lead to mechanical degradation as well as several types of crushers and mills, description of particle breakage inside the DEM environment becomes indispensable, since flow of solids, energy transfer and size reduction are deeply intertwined. However, breakage modeling in DEM is still in an earlier stage of development and comparatively limited work has been carried out demonstrating the validity and limitations of the various models pursued in the literature and already available in commercial DEM packages. The work analyzed particle breakage using three models available in commercial DEM simulation platforms: the bonded-particle model (BPM), the particle replacement model (PRM) and the fast-breakage model (FBM). These were initially calibrated on the basis of the distribution of breakage probabilities of individual 6.3–4.75 mm copper ore particles and, whenever possible, progeny size distributions. Breakage of particles in beds by impact by a falling steel ball is an interesting case for testing breakage models, besides an important microprocess in some comminution operations, since particles interact with each other and with the grinding medium. As such, the potential of the three models to describe size reduction was demonstrated through comparison of unconfined particle bed breakage experiments and simulations. The models demonstrated different abilities to describe the various aspects of breakage. The work then identified opportunities for improvement in each of the models.

Introduction

The discrete element method (DEM) is a simulation tool proposed by Cundall and Strack [1], which allows reproducing virtually the motion and the interaction of rigid independent particles from the alternate use of Newton’s second law of motion and contact models such as Hertz-Mindlin [2] and linear hysteresis [3]. The use of this tool has proven to be valuable for opening the black box of understanding of several industrial processes involving particulate material [4], [5], [6].

The performance of size reduction equipment has been described over the years on the basis of empirical, phenomenological and, most recently, mechanistic mathematical models. Mechanistic models are based on the incorporation of description of particle breakage microprocesses as well as the energy transfer of the comminution equipment described using DEM [4], [7]. In the case of some size reduction processes, in particular ball mills, DEM has been successfully used to describe the mechanical environment, leaving the prediction of breakage to a post-processing stage [7], [8], [9]. However, when simulating several types of crushers and mills, as well as processes that cause material degradation during handling, the description of particle breakage inside the DEM simulation environment becomes indispensable, since flow of solids, energy transfer and size reduction cannot be properly decoupled [4]. In this case, the only valid alternative is to describe breakage within the DEM simulation environment. However, breakage modeling in DEM is still in its infancy and very limited work has been dedicated to either validating and/or demonstrating the limitations of the various DEM breakage models being currently pursued.

Three different approaches have been identified in the literature to describe particle breakage within the DEM simulation environment: the bonded-particle model (BPM) [10], the discrete grain breakage (DGB) [11] and the particle replacement model (PRM) [12]. Examples of application of these can be found in the studies by Khanal et al. [13], Potapov and Campbell [14], Barrios et al. [15], respectively, just to name a few.

Breakage of particles in unconfined beds by impact by a falling steel ball is an interesting test case for breakage modeling. While simple to set up in a simulation, the outcome of this test depends on a proper description of the energy and momentum transfer of the falling ball to the particles, and the nature of interaction of particles with each other. This test has been the object of some experimental and numerical investigation in the past. Among the experimental studies the works by Höfler and Herbst [16], Bourgeois [17] and Barrios et al. [18] contributed significantly to our current understanding of the phenomenon, while the numerical simulation work by Potapov and Campbell [14] already demonstrated the potential of DEM to represent some aspects of the test.

In the present work three breakage models available in commercial DEM packages have been used to initially study single particle breakage. The models have then been used to describe breakage in monodispersed unconfined particle beds under a variety of bed configurations and impact energies, and results are compared to experimental data for a hard copper ore. Simulations using both the bonded-particle model (BPM) and the particle replacement model (PRM) were carried out using EDEM 2.7 [19], whereas simulations using a variant of the particle replacement model using polyhedral-shaped particles, called fast breakage model (FBM) [20], were carried out using ROCKY 3.11 [21].