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The visualisation of individual flow paths in a porous media and how they relate to the overall hydrodynamics is crucial to improving our understanding of a number of systems. Unsaturated flow through larger particles (order of millimetres and a few centimetres) in heap leaching systems where both gravity and capillarity play an important role in the structure of the flow paths is complex and still not fully understood. A variety of laboratory methods have been employed for this purpose, with UV light being used in several studies. Flow studies have typically involved millimetre and sub-millimetre scale particles and the flow is typically capillary-dominated. This paper instead concentrates on gravity-dominated flows pertaining to heap leaching and is particularly focused on developing methods for using the UV fluorescence to obtain quantitative measurements of liquid spreading, such as average lateral liquid spread for a point source liquid addition. This study uses a pseudo2-D system with larger ore particles than in previous UV flow studies. The UV fluorescence results were analysed using image analysis to determine the overall liquid spreading and the locations of the flow paths. Both narrowly sized and realistic ore systems were investigated to understand the effect of length scale on flow paths and dynamics of liquid spreading through the gravity-dominated ore beds. It was shown that both ore systems experience distinct flow channelling compared to the more uniform flow profiles observed in capillary-dominated systems. Lateral liquid spreading coefficients were calculated, with the narrowly sized ore system showing higher values, probably due to the larger effective length scale of the inter-particle spaces.

Stirred aerated tanks are a key unit operation in many industries, including froth flotation. Reliable and robust level control is of great importance in maintaining steady operation for successful implementation of higher level optimising control strategies, particularly when such tanks are arranged in series. When changes are made to the rate of aeration, there is a corresponding change in the pulp bubble size and gas holdup (the volume fraction of air in the tank), and consequently the pulp height. Stable operation of flotation tanks must, therefore, include the effect of air rate on pulp height in level control systems, especially if air rate is being actively controlled. In this paper, a model is developed from first principles to link the change in gas holdup with variation in air rate under dynamic conditions, accounting for the variability in gas holdup with height that results from differences in gas compressibility. This is validated experimentally. In order to test the model, experiments were carried out using a 70 L laboratory tank comprising water and reagent systems. For both simple and complex changes in air rate, the model showed good agreement with the experimental results when predicting the change in pulp height at steady state. Under dynamic conditions, the experimental system exhibited a slightly slower response than is predicted by the model; this is likely to be due to the well mixed assumption not being adequately met. This model provides a method to improve the operating stability of aerated tanks through better modelling of the dynamic pulp height changes that result from changes in air flowrate. In flotation tanks, this will enable greater control over froth height, which has been found to affect significantly mass pull, froth stability and flotation performance.

The growth of fractures around an undercut of a block cave is simulated. A finite element based approach is used, in which fractures are represented as non-planar 3D surfaces that grow in response to boundary stresses and interaction. A new mesh is recreated at each step to compute the displacement field. Stress intensity factors are computed around fracture tips using a technique that computes the interaction integral over a virtual disk. Fracture geometry is updated using Paris and Schöllmann propagation laws, and a geometric fracture pattern ensues from the simulation. The growth of fractures is examined in the lower 20 m of a mine at 812 m depth. The growth of 30, 60 and 90 fractures is examined. Realistic extraction schedules for over 100 draw points control the rate of mass extraction. The effect of rock bridges as overburden stress shields is investigated. Bridges are modelled by constraining the vertical displacement of the top boundary. This case is compared to a Neumann-type overburden stress boundary condition in which the overburden is felt throughout the top of the cave. In both cases, fractures grow to form a dome shape above and around the cave during extraction. For the case of a fixed top boundary, fracture growth is observed away from the cave, while in the direct overburden stress case, fractures tend to grow close to the cave. Over-arching fractures concentric to the undercut continue to grow as the cave progresses.

In many granular material simulation applications, DEM capability is focused on the dynamic solid particulate flow properties and on systems in which millions of particles are involved. The time of relevance is many seconds or even minutes of real time. Simplifying assumptions are made to achieve run completion in practical timescales. There are certain applications, typically involving manufactured particles, where a representative pack is of the order of a thousand particles. More accurate capturing of the influence of complex shape is then often possible. Higher accuracies are necessary to model the topology of the void space, for example, for further CFD simulation and optimisation of fluid flow properties. Alternatively, the accuracy may be critical for structural performance and the force or stress transmission through the contact points is to be controlled to avoid material damage and poor function. This paper briefly summarises methods for simulation of shape effects on packing structures in the granular community and narrows the scope to problems where shape effects are of overriding concern. Two applications of mono-sized, mono-shaped packing problems are highlighted: catalyst support pellets in gas reforming and concrete armour units in breakwater structures. The clear advantages of FDEM for complex-shaped particle interactions in packed systems with relatively few particles are discussed. A class of particulate problems, ‘FDEM-suited’ problems, ones that are ideal to be solved by FDEM rather than by DEM, is proposed for science and engineering use.

Particle-scale effects are critically important to the performance of heap leaching operations. In a heap-scale simulation, the transport of fluid phases and reactive species external to the ore particles might be modelled with thousands of grid elements by the finite volume or finite element method. The inter- and intra-particle diffusions and reactions are usually parametrised by a deterministic model, such as the shrinking core model (SCM), that translates the external conditions into an effective product extraction rate. However, the rate equation takes the form of an implicit or partial differential equation for all but the simplest models and kinetic regimes, becoming expensive to solve on large grids. We instead propose an economical, easily calibrated semi-empirical approach in which the dependencies on external conditions and the current state of the ore are considered to be mathematically separable. We show that the standard SCM does not suffer greatly from this approximation even when there is a mixed control regime with nonlinear kinetics. The dependency on the state of the ore is derived empirically, inherently capturing heterogeneous features and cluster-scale effects. We demonstrate that this method scales correctly when fitted to data from physical column leaching experiments.

A novel domain integral approach is introduced for the accurate computation of pointwise J-integral and stress intensity factors (SIFs) of 3D planar cracks using tetrahedral elements. This method is efficient and easy to implement, and does not require a structured mesh around the crack front. The method relies on the construction of virtual disk-shaped integral domains at points along the crack front, and the computation of domain integrals using a series of virtual triangular and line elements. The accuracy of the numerical results computed for through-the-thickness, penny-shaped, and elliptical crack configurations has been validated by using the available analytical formulations. The average error of computed SIFs remains below 1% for fine meshes, and 2–3% for coarse ones. The results of an extensive parametric study suggest that there exists an optimum mesh-dependent domain radius at which the computed SIFs are the most accurate. Furthermore, the results provide evidence that tetrahedral elements are efficient, reliable and robust instruments for accurate linear elastic fracture mechanics calculations.

This paper discusses the reproduction of the square root singularity in quarter-point tetrahedral (QPT) finite elements. Numerical results confirm that the stress singularity is modeled accurately in a fully unstructured mesh by using QPTs. A displacement correlation (DC) scheme is proposed in combination with QPTs to compute stress intensity factors (SIF) from arbitrary meshes, yielding an average error of 2–3%. This straightforward method is computationally cheap and easy to implement. The results of an extensive parametric study also suggest the existence of an optimum mesh-dependent distance from the crack front at which the DC method computes the most accurate SIFs.

Scanning Electron Microscopy (SEM) based assessments are the most widely used and trusted imaging technique for mineral ore quantification. X-ray micro tomography (XMT) is a more recent to the mineralogy toolbox, but with the potential to extend the measurement capabilities into the three dimensional (3D) assessment of properties such as mineral liberation, grain size and textural characteristics. In addition, unlike SEM based assessments which require the samples to be sectioned, XMT is non-invasive and non-destructive manner. The disadvantage of XMT, though is that the mineralogy must be inferred from the X-Ray attenuation measurements, which can make it hard to distinguish from one another, whereas SEM when coupled with Energy-Dispersive X-raySpectroscopy (EDX) provides elemental compositions and thus a more direct method for distinguishing different minerals. A new methodology that combines both methods at the mineral grain level is presented. The rock particles used to test the method were initially imaged in 3D using XMT followed by sectioning and the 2D imaging of the slices using SEM-EDX. An algorithm was developed that allowed the mineral grains in the 2D slice to be matched with their 3D equivalents in the XMT based images. As the mineralogy of the grains from the SEM images can be matched to a range of X-Ray attenuations, this allows minerals which have similar attenuations to one another to be distinguished, with the level of uncertainty in the classification quantified. In addition,the methodology allowed for the estimation of the level of uncertainty in thequantification of grain size by XMT, the assessment of stereological effects in SEM 2D images and ultimately to obtain a simplified 3D mineral map from low energy XMT images. Copper sulphide ore fragments, with chalcopyrite and pyrite as the main sulphide minerals, were used to demonstrate the effectiveness of this procedure.

We studied leaching of Cu and Fe from naturally occurring chalcopyrite ore using aqueous solutions of ionic liquids (ILs) based on imidazolium and ethylammonium cations and hydrogensulfate, nitrate, acetate or dicyanamide anions. Liquid, solid and gas phases of the leaching systems were characterised. We have shown that nonoxidative leaching is greatly dependant not only on temperature and pH, but on the anion species of the IL. Solutions of 1-butylimidazolium hydrogen sulfate exhibited the best leaching performance among hydrogen sulphate ILs. We have suggested that the formation of an oxide layer in some ILs may be responsible for a reduced leaching ability. The analysis of the gas phase showed the production of CO2 and CS2 in all leached samples. Our results suggested that the CS2 produced upon leaching could be responsible for decreasing the sulfur, but not oxide, layer on the surface of chalcopyrite samples and therefore more efficient leaching. This is the first study, to our knowledge, to provide a systematic comparison of the leaching performance of ILs composed of different anions and cations and without added oxidants.

Heap leaching is one of the most important hydrometallurgical techniques for the extraction of valuable metals from low grade ores due to the relatively low capital costs and limited comminution requirements. However, it is typically affected by low recoveries, compared to conventional mineral extraction techniques such as froth flotation followed by smelting. These low recoveries indicate that there is still significant scope for the improvement of the process performance. This overall process performance is governed by chemical kinetics, mass transport and hydrodynamic effects, with hydrodynamics being particularly not completely understood at the heap scale. The authors have previously presented a model for the hydrodynamics which accounts for both liquid holdup hysteresis and the influence of particle porosity on the fluid flow. In this previous work the model form was only validated for narrowly sized particles. This shortcoming is addressed in this paper, with the validation of the models being extended to cover a range of more complex size distributions representative of those encountered in industrial heap leaching. In this work load cell based gravimetric measurements of liquid holdup values were complimented with electrical capacitance tomography (ECT) measurements, which gave not only the average holdup, but also the liquid distribution within the columns. This study demonstrates that these new hydrodynamic models remain applicable for more realistic particle size distributions, with the need to distinguish between the behaviour of the liquid held within the particle porosity compared to that flowing around the particles being critical to accurate prediction of the hydrodynamics.

The distribution of the metal-bearing mineral grains within a particulate ore prepared for leaching, and the impact of this spatial heterogeneity on overall extraction efficiency is of key importance to a mining industry that must continuously target ever-reducing grades and more complex ore bodies. If accessibility and recovery of the target minerals is to be improved, a more detailed understanding of the behaviour of the system must be developed. We present an in situ analysis using X-ray computed tomography to quantify the rates of volume reduction of sulfide mineral grains in low grade agglomerated copper bearing ores during a miniature laboratory scale column leaching experiment. The data shows the scale of the heterogeneity in the leaching behaviour, with an overall reduction of sulphide mineral grains of 50%, but that this value masks significant mm3 to cm3 scale variability in reduction. On the scale of individual ore fragments, leaching efficiency ranged from 22% to 99%. We use novel quantitative methods to determine the volume fraction of the sulfide that is accessible to the leachate solution.

Pseudo-two-dimensional (2D) foams are commonly used in foam studies as it is experimentally easier to measure the bubble size distribution and other geometric and topological properties of these foams than it is for a 3D foam. Despite the widespread use of 2D foams in both simulation and experimental studies, many important geometric and topological relationships are still not well understood. Film size, for example, is a key parameter in the stability of bubbles and the overall structure of foams. The relationship between the size distribution of the films in a foam and that of the bubbles themselves is thus a key relationship in the modeling and simulation of unstable foams. This work uses structural simulation from Surface Evolver to statistically analyze this relationship and to ultimately formulate a relationship for the film size in 2D foams that is shown to be valid across a wide range of different bubble polydispersities. These results and other topological features are then validated using digital image analysis of experimental pseudo-2D foams produced in a vertical Hele–Shaw cell, which contains a monolayer of bubbles between two plates. From both the experimental and computational results, it is shown that there is a distribution of sizes that a film can adopt and that this distribution is very strongly dependent on the sizes of the two bubbles to which the film is attached, especially the smaller one, but that it is virtually independent of the underlying polydispersity of the foam.

Deep eutectic solvents (DESs) are exemplars of systems with the ability to form neutral, ionic and doubly ionic H-bonds. Herein, the pairwise interactions of the constituent components of the choline chloride-urea DES are examined. Evidence is found for a tripodal CHCl doubly ionic H-bond motif. Moreover it is found that the covalency of doubly ionic H-bonds can be greater than, or comparable with, neutral and ionic examples. In contrast to many traditional solvents, an "alphabet soup" of many different types of H-bond (OHO[double bond, length as m-dash]C, NHO[double bond, length as m-dash]C, OHCl, NHCl, OHNH, CHCl, CHO[double bond, length as m-dash]C, NHOH and NHNH) can form. These H-bonds exhibit substantial flexibility in terms of number and strength. It is anticipated that H-bonding will have a significant impact on the entropy of the system and thus could play an important role in the formation of the eutectic. The 2 : 1 urea : choline-chloride eutectic point of this DES is often associated with the formation of a [Cl(urea)2](-) complexed anion. However, urea is found to form a H-bonded urea[choline](+) complexed cation that is energetically competitive with [Cl(urea)2](-). The negative charge on [Cl(urea)2](-) is found to remain localised on the chloride, moreover, the urea[choline](+) complexed cation forms the strongest H-bond studied here. Thus, there is potential to consider a urea[choline](+)·urea[Cl](-) interaction.

Journal of Geophysical Research: Solid Earth, 120 (7), ISSN:2169-9313, ISSN:0148-0227, ISSN:2169-9356

A process for recovering copper from chalcopyrite is disclosed. The process includes oxidising sulphur in chalcopyrite with a solution under predetermined contact conditions and thereby releasing at least part of the copper in the chalcopyrite into the solution as copper ions. The process includes a subsequent step of reducing sulphur in a solid product from step (a) to a minus two, ie. Sulphide, valence state with a solution under predetermined contact conditions. The process further includes a subsequent step of oxidising sulphur in a solid product from step (b) with a solution under predetermined contact conditions and thereby releasing at least part of the remaining copper in the solid product into the solution as copper ions. The process further includes recovering copper from one or more of the solutions from steps (a) and (c).

This paper introduces a three-dimensional finite element (FE) formulation to accurately model the linear elastic deformation of fractured media under compressive loading. The presented method applies the classic Augmented Lagrangian(AL)-Uzawa method, to evaluate the growth of multiple interacting and intersecting discrete fractures. The volume and surfaces are discretized by unstructured quadratic triangle-tetrahedral meshes; quarter-point triangles and tetrahedra are placed around fracture tips. Frictional contact between crack faces for high contact precisions is modeled using isoparametric integration point-to-integration point contact discretization, and a gap-based augmentation procedure. Contact forces are updated by interpolating tractions over elements that are adjacent to fracture tips, and have boundaries that are excluded from the contact region. Stress intensity factors are computed numerically using the methods of displacement correlation and disk-shaped domain integral. A novel square-root singular variation of the penalty parameter near the crack front is proposed to accurately model the contact tractions near the crack front. Tractions and compressive stress intensity factors are validated against analytical solutions. Numerical examples of cubes containing one, two, twenty four and seventy interacting and intersecting fractures are presented.