# Heap Leaching: Modelling and Forecasting Using CFD Technology

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Computational Model

#### 2.1. Liquid-Gas-Thermal Transport

_{h}is a sink/source term usually representing the boundary conditions or internal preferential flow paths that are represented as sink terms [28]. Equation (1) requires that pressure-moisture-conductivity relationships be defined to complete the model. The unsaturated soil hydraulic properties θ(h) and K(h) are in general highly nonlinear functions of the pressure head, can be temperature (T) dependent, and are represented in this work by the amended van Genuchten relationship as described by [16]. The saturated hydraulic conductivity is dependent upon the intrinsic permeability of the ore and the fluid properties that are in turn dependent upon temperature. The resulting equations are non-linear and require an iterative solution procedure.

_{i}is the concentration of species i in the solution phase, q is the Darcy flux ($q=-K\left(h\right)\nabla \mathrm{H}$, where H is the total hydraulic head, H = h + z),

_{jk}are (x,y,z) directions and S

_{i}the production or consumption of species i. The dispersion coefficient, D

_{i,jk,}is dependent upon the velocity components and longitudinal and transverse dispersivities.

_{T};

_{p}is the specific heat capacity, λ

_{p}is the thermal conductivity and ρ

_{p}is the matrix density, which are defined as in Equations (4) to (6), where the fluid, solid and air are represented by the subscript f, s, a respectively. The volumetrically averaged thermal conductivity is based on the inverse of the conductivities of the phases.

_{j}is the mass of phase j, m

_{p}is the total mass and c

_{j}is the specific heat of phase j.

_{j}is the thermal conductivity of phase j.

_{j}is the volume fraction of phase j.

_{in}is the intrinsic permeability of the porous media, k

_{g}(S) is the unsaturated permeability of the gas at liquid saturation, ε

_{g}is the volume fraction of the gas phase, μ

_{g}is the gas viscosity, and S

_{g}is the gas source term accounting for natural convection due to thermal gradients, volume changes due to saturation and other sources, such as boundary conditions.

#### 2.2. Solid-Liquid-Gas Reactions

#### 2.2.1. Solid-Liquid Dissolution

_{o}is the initial particle radius, r

_{m}is the current mineral radius, A

_{m}comes from the kinetic rate equation for the current mineral, c

_{o}is the concentration of available reactant at particle surface, R is the gas constant, T is the temperature in Kelvin, D

_{eff}is the effective rock diffusion coefficient, ε

_{p}is the rock voidage, ρ

_{ore}is the ore density, M

_{i}is the molecular weight of the mineral and x

_{i}is the mass fraction of the mineral.

_{m}comes from the general expression for the kinetic rate equations, such as those produced by [62], and the general form for which is

_{i}for mineral i, is evaluated as,

_{i}, and characteristic radius, (r

_{m})

_{i}, are then scaled back accordingly. The production and consumption of species i enters the transport Equation (2) as a source term. This approach allows minerals to react at different rates in an individual particle size, and although it requires the assumption that the minerals can be treated relatively independently, this is not unreasonable given the low concentration of reactive minerals present. This approach allows each mineral in each particle size fraction to be modelled using a single characteristic radius indicating how much has reacted. It can easily be related to experimental analysis of ore which is commonly given as mineral content by size classification, making validation easier. It also easily allows for different minerals to dominate the reactions at different stages of the leach cycle. This in turn allows the model to deal with multiple particle sizes and multiple minerals over large meshes without excessive memory usage in the overall CFD model framework. The mineral rate constants, A and B are unrelated to particle size and therefore allow the model to scale from small to large particle size distributions (e.g., from experimental column to 3D heap lifts).

#### 2.2.2. Gas-Liquid Oxygen Mass Transfer

_{g}is the mass fraction of oxygen (O

_{2}) in the gas phase, O

_{f}is the molar concentration of oxygen in the fluid phase, ${M}_{{\mathrm{O}}_{2}}$ is the molar weight of oxygen, ${M}_{{\mathrm{N}}_{2}}$ is the molar weight of nitrogen and K

_{H}is the Henry’s law constant at a given temperature

_{H}, is a function of temperature based on dissolved oxygen solubility against temperature data under atmospheric conditions. The partial pressure of oxygen can also be dependent on the level of salts in solution. An equilibrium state is solved using a Newton-Raphson scheme at the end of each time step.

#### 2.2.3. Ferrous Oxidation

_{c}. The relationship is given by,

_{c}= 5.56 × 10

^{7}[63].

#### 2.2.4. Liquid-Solid Precipitation

_{3}O

^{+}-jarosite, one mole of hydronium jarosite formed will remove 3 moles of ferric and 2 moles of sulphate and will add back 5 moles of H

^{+}(assuming that the sulfuric acid product dissociates to H

^{+}and HSO

_{4}

^{−}). The relationship controlling hydronium jarosite precipitation can be written from the solubility product for the solid species on the right-hand side of the equation above.

_{3}O

^{+}-jarosite is precipitated is < 2. The KJar equilibrium value is calculated to give the same solubility as the hydroxide model at the pH at which jarosite starts to form.

#### 2.3. Leach Kinetics

_{2}) and pyrite (FeS

_{2}). The shrinking core model is applied to each particle size distribution.

#### 2.3.1. Pyrite Rate Kinetics

_{p}is the pyrite grain radius (m), ζ is the particle shape function, T is the temperature (K) and R

_{A}is a rate constant based on known data.

#### 2.3.2. Chalcopyrite Rate Kinetics

## 3. Column Leach Tests

^{3}and thermal conductivity of 2.1 W·m

^{−1}·K

^{−1}and specific heat capacity of 1172 J·kg

^{−1}·K

^{−1}. A number of columns were leached, each column contained similar material and was held at a constant temperature, 25 °C, 35 °C, 50 °C and 75 °C. The particle size distribution, percent weight and percent copper concentration are given Table 2. A leach solution containing 0.06 gpl of Cu

^{2+}, 7.0 gpl of H

_{2}SO

_{4}, 0.77 gpl of Fe

^{3+}and 0.02 gpl of Fe

^{2+}was applied for 331 days at a rate of approximately 0.5 litres per day with rest periods of 30 days at day 91 and day 212.

#### Model Validation

## 4. Three-Dimensional ‘Virtual’ Chalcopyrite Stockpile

^{−10}m

^{2}and a minimum of 4.87 × 10

^{−13}m

^{2}giving an average hydraulic permeability of 5 × 10

^{−3}m/s at 20 °C which is typical of a well-draining material. Bouffard [69] gives a review of ore types, permeability and agglomeration practices in heap leaching.

#### 4.1. Thermal Effect on Recovery

#### 4.2. Continuous or Intermittent Leaching

_{2}SO

_{4}in the leach solution was increased to 1.54 gpl. As can be seen in Figure 10, the grams of copper recovered per litre of solution applied almost doubled in the first year and significantly higher throughout the leach period. Increasing the acid in solution increased the copper recovery to 42%. Although the overall copper recovery is reduced, the grams of copper recovered per litre of solution applied is increased which may be advantageous when solution management is critical.

## 5. Conclusions

## Author Contributions

## Conflicts of Interest

## Nomenclature

A | dimensionless | Experimentally calibrated mineral rate constant |

B | dimensionless | Experimentally calibrated mineral rate constant |

c_{j} | J·kg^{−1}·K^{−1} | Specific heat of phase j. |

c_{p} | J·kg^{−1}·K^{−1} | Specific heat capacity of matrix |

c_{o} | mol·m^{−3} | Concentration of available reactant at particle surface |

C_{i} | mol·m^{−3} | Concentration of species i |

D | m^{2}·s^{−1} | Dispersion coefficient |

D_{eff} | m^{2}·s^{−1} | Effective rock diffusion coefficient |

$e$ | e | Electronic charge |

h | m | Liquid pressure head |

H | m | Total hydraulic head |

k_{in} | m | Intrinsic permeability |

k_{g}(S) | m·s^{−1} | The unsaturated permeability of gas at liquid saturation |

K | m·s^{−1} | Hydraulic conductivity |

K_{H} | L·mol^{−1} | Henry’s law constant |

K_{c} | dimensionless | Equilibrium constant |

M_{i} | kg·mol^{−1} | Molecular weight of the mineral |

m_{j} | kg | Mass of phase j |

m_{p} | kg | Matrix mass |

O_{j} | mol·L^{−1} | Oxygen in phase j |

${p}^{g}$ | m | Gas pressure head |

q | m·s^{−1} | Darcy flux $q=-K\left(h\right)\nabla \mathrm{H}$ |

r_{o} | m | Initial particle radius |

r_{m} | m | Unreacted mineral radius |

${r}_{p}$ | m | Mineral grain radius |

$R$ | J·mol^{−1}·K^{−1} | Universal gas constant |

${R}_{A}$, ${R}_{B}$ | dimensionless | Adjustable rate parameters |

S_{g} | s^{−1} | Gas sink-source |

S_{h} | s^{−1} | Liquid sink-source |

$t$ | s | Time |

${t}_{e}\sigma $ | S·m^{−1} | Electrical conductivity of the sulfur layer |

$T$ | K | Temperature |

VF_{j} | m^{3}·m^{−3} | Volume fraction of phase j. |

x_{i} | kg·kg^{−1} | Mass fraction of the mineral |

z | m·s^{−1} | Gravity direction |

$a$ | dimensionless | Apparent activity that is based on bulk species concentration |

$\beta $ | dimensionless | Fraction of particle reacted |

$\Delta G$ | kJ·mol^{−1} | Free energy of the system |

$\Delta {\mathrm{H}}_{R}^{0}$ | kJ·mol^{−1} | Enthalpy of reaction (constant) |

$\Delta {S}_{R}^{0}$ | kJ·K^{−1}·mol^{−1} | Entropy of reaction (constant) |

ε_{g} | m^{3}·m^{−3} | Volume fraction of the gas phase |

ε_{p} | m^{3}·m^{−3} | Particle porosity |

$\zeta $ | dimensionless | Shape factor for the mineral grain |

θ | m^{3}·m^{−3} | Volume fraction of the liquid phase |

λ_{j} | W·m^{−1}·K^{−1} | Thermal conductivity of phase j. |

λ_{p} | W·m^{−1}·K^{−1} | Matrix thermal conductivity |

μ_{g} | Kg·m^{−1}·s^{−1} | Gas viscosity |

${\rho}_{b}$ | kg·m^{−3} | Molar density |

${\rho}_{p}$ | kg·m^{−3} | Matrix density |

ρ_{ore} | kg·m^{−3} | Ore density |

## References

- Nesse, W.D. Introduction to Mineralogy; Oxford University Press: Oxford, UK, 2000. [Google Scholar]
- Bartlett, R.W. Solution Mining, 2nd ed.; Gordon & Breach Science Publishers: Amsterdam, The Netherlands, 1998. [Google Scholar]
- Petersen, J. Heap leaching as a key technology for recovery of values from low-grade ores—A brief overview. Hydrometallurgy
**2016**, 165, 206–212. [Google Scholar] [CrossRef] - Ghorbani, Y.; Franzidis, J.-P.; Petersen, J. Heap Leaching Technology—Current State, Innovations, and Future Directions: A Review. Miner. Process. Extr. Metall. Rev.
**2016**, 37, 73–119. [Google Scholar] [CrossRef] [Green Version] - Beven, K.; Germann, P. Macropores and water flow in soils revisited. Water Resour. Res.
**2013**, 49, 3071–3092. [Google Scholar] [CrossRef] [Green Version] - Wu, A.X.; Yin, S.; Qin, W.; Liu, J.; Qiu, G. The effect of preferential flow on extraction and surface morphology of copper sulphides during heap leaching. Hydrometallurgy
**2009**, 95, 76–81. [Google Scholar] [CrossRef] - Zhan, G.; Haggarty, S.; Ludwick, W. Hydrological Evaluation of Gold Leach Pad Rinsing. Mine Water Environ.
**2012**, 31, 307–311. [Google Scholar] [CrossRef] - Van Staden, P.J.; Kolesnikov, A.V.; Petersen, J. Comparative assessment of heap leach production data—1. A procedure for deriving the batch leach curve. Miner. Eng.
**2017**, 101, 47–57. [Google Scholar] [CrossRef] - Marsden, J.O.; Botz, M.M. Heap leach modeling—A review of approaches to metal production forecasting. Miner. Metall. Process.
**2017**, 34, 53–64. [Google Scholar] [CrossRef] - Bouffard, S.C.; Dixon, D.G. Investigative Study into the hydrodynamics of heap leaching processes. Metall. Mater. Trans. B
**2001**, 32, 763–776. [Google Scholar] [CrossRef] - Cariaga, E.; Concha, F.; Sepulveda, M. Flow through porous media with applications to heap leaching of copper ores. Chem. Eng. J.
**2005**, 111, 151–165. [Google Scholar] [CrossRef] - De Andrade Lima, L.R.P. Liquid axial dispersion and holdup in column leaching. Miner. Eng.
**2006**, 19, 37–47. [Google Scholar] [CrossRef] - Petersen, J.; Dixon, D.G. Modelling zinc heap bioleaching. Hydrometallurgy
**2007**, 85, 127–143. [Google Scholar] [CrossRef] - Bouffard, S.C.; West-Sells, P.G. Hydrodynamic behaviour of heap leach piles: Influence of testing scale and material properties. Hydrometallurgy
**2009**, 98, 136–142. [Google Scholar] [CrossRef] - Guzman, A.; Robertson, S.; Calienes, B. Constitutive relationships for the representation of a heap leach process. In Proceedings of the Heap Leach Solutions Conference, Vancouver, BC, Canada, 22–25 September 2013; van Zyl, D., Caldwell, J., Eds.; 2013; pp. 442–458. [Google Scholar]
- McBride, D.; Gebhardt, J.E.; Croft, T.N.; Cross, M. Modeling the hydrodynamics of heap leaching in sub-zero temperatures. Miner. Eng.
**2016**, 90, 77–88. [Google Scholar] [CrossRef] - Bennett, C.R.; McBride, D.; Cross, M.; Gebhardt, J.E. A comprehensive model for copper sulphide heap leaching: Basic formulation and validation through column test simulation. Hydrometallurgy
**2012**, 127–128, 150–161. [Google Scholar] [CrossRef] - Leahy, M.J.; Schwarz, M.P. Modelling jarosite precipitation in isothermal chalcopyrite bioleaching columns. Hydrometallurgy
**2009**, 98, 181–191. [Google Scholar] [CrossRef] - Leahy, M.J.; Davidson, M.R.; Schwarz, M.P. A model for heap bioleaching of chalcocite with heat balance: Bacterial temperature dependence. Miner. Eng.
**2005**, 18, 1239–1252. [Google Scholar] [CrossRef] - Leahy, M.J.; Schwarz, M.P.; Davidson, M.R. An air sparging CFD model of heap bioleaching of chalcocite. Appl. Math. Model.
**2006**, 30, 1428–1444. [Google Scholar] [CrossRef] - Leahy, M.J.; Davidson, M.R.; Schwarz, M.P. A model for heap bioleaching of chalcocite with heat balance: Mesophiles and moderate thermophiles. Hydrometallurgy
**2007**, 85, 24–41. [Google Scholar] [CrossRef] - Wu, A.; Liu, J.; Yin, S.; Wang, H. Analysis of coupled flow-reaction with heat transfer in heap bioleaching processes. Appl. Math. Mech.
**2010**, 3, 1473–1480. [Google Scholar] [CrossRef] - Mostaghimi, P.; Tollit, B.S.; Neethling, S.J.; Gorman, G.J.; Pain, C. A control volume finite element method for adaptive mesh simulation of flow in heap leaching. J. Eng. Math.
**2014**, 87, 111–121. [Google Scholar] [CrossRef] - Mostaghimi, P.; Percival, J.R.; Pavlidis, D.; Ferrier, R.J.; Gomes, J.L.M.A.; Gorman, G.J.; Jackson, M.D.; Neethling, S.J.; Pain, C. Anisotropic Mesh Adaptivity and Control Volume Finite Element Methods for Numerical Simulation of Multiphase Flow in Porous Media. Math. Geosci.
**2015**, 47, 417–440. [Google Scholar] [CrossRef] - McBride, D.; Gebhardt, J.E.; Cross, M. A comprehensive oxide heap-leach model: Development and validation. Hydrometallurgy
**2012**, 113–114, 98–108. [Google Scholar] [CrossRef] - McBride, D.; Cross, M.; Gebhardt, J.E. Heap leach modelling employing CFD technology: A ‘process’ heap model. Miner. Eng.
**2012**, 33, 72–79. [Google Scholar] [CrossRef] - McBride, D.; Croft, T.N.; Cross, M.; Bennett, C.; Gebhard, J.E. Optimization of a CFD—Heap leach model and sensitivity analysis of process operation. Miner. Eng.
**2014**, 63, 57–64. [Google Scholar] [CrossRef] - Miao, X.; Narsilio, G.A.; Wu, A.; Yang, B. A 3D dual pore-system leaching model. Part 1: Study on fluid flow. Hydrometallurgy
**2017**, 167, 173–182. [Google Scholar] [CrossRef] - McBride, D.; llankoon, I.M.S.K.; Neethling, S.J.; Gebhardt, J.E.; Cross, M. Preferential flow behaviour in unsaturated packed beds and heaps: Incorporating into a CFD model. Hydrometallurgy
**2017**, 171, 402–411. [Google Scholar] [CrossRef] - Ghorbani, Y.; Becker, M.; Petersen, J.; Morar, S.H.; Mainza, A.; Franzidis, J.-P. Use of X-ray computed tomography to investigate crack distribution and mineral dissemination in sphalerite ore particles. Miner. Eng.
**2011**, 24, 1249–1257. [Google Scholar] [CrossRef] - Miller, G. Ore geotechnical effects on copper heap leach kinetics. In Proceedings of the 5th International Symposium Honoring Professor Ian M. Ritchie, Vancouver, BC, Canada, August 24–27 2003; TMS, 2003; pp. 329–342. [Google Scholar]
- Lin, Q.; Barker, D.J.; Dobson, K.J.; Lee, P.D.; Neethling, S.J. Modelling particle scale leach kinetics based on X-ray computed micro-tomography images. Hydrometallurgy
**2016**, 162, 25–36. [Google Scholar] [CrossRef] [Green Version] - Ferrier, R.J.; Cai, L.; Lin, Q.; Gorman, G.J.; Neethling, S.J. Models for apparent reaction kinetics in heap leaching: A new semi-empirical approach and its comparison to shrinking core and other particle-scale models. Hydrometallurgy
**2016**, 166, 22–23. [Google Scholar] [CrossRef] - Watling, H.R. The bioleaching of sulphide minerals with emphasis on copper sulphides—A review. Hydrometallurgy
**2006**, 84, 81–108. [Google Scholar] [CrossRef] - Antonijevic, M.M.; Bogdanovic, G.D. Investigation of the leaching of chalcopyrite ore in acidic solutions. Hydrometallurgy
**2004**, 73, 245–256. [Google Scholar] [CrossRef] - Córdoba, E.M.; Muñoz, J.A.; Blázquez, M.L.; González, F.; Ballester, A. Leaching of chalcopyrite with ferric ion. Part I: General aspects. Hydrometallurgy
**2008**, 93, 81–87. [Google Scholar] [CrossRef] - Córdoba, E.M.; Muñoz, J.A.; Blázquez, M.L.; González, F.; Ballester, A. Passivation of chalcopyrite during its chemical leaching with ferric ion at 68 °C. Miner. Eng.
**2009**, 22, 229–235. [Google Scholar] [CrossRef] - Pradhan, N.; Nathsarma, K.C.; Srinivasa Rao, K.; Sukla, L.B.; Mishra, B.K. Heap bioleaching of chalcopyrite: A review. Miner. Eng.
**2008**, 21, 355–365. [Google Scholar] [CrossRef] - Nazari, G.; Asselin, E. Morphology of chalcopyrite leaching in acidic ferric sulfate media. Hydrometallurgy
**2009**, 96, 183–188. [Google Scholar] [CrossRef] - Viramontes-Gamboa, G.; Peña-Gomar, M.M.; Dixon, D.G. Electrochemical hysteresis and bistability in chalcopyrite passivation. Hydrometallurgy
**2010**, 105, 140–147. [Google Scholar] [CrossRef] - Kimball, B.E.; Rimstidt, J.D.; Brantley, S.L. Chalcopyrite dissolution rate laws. Appl. Geochem.
**2010**, 25, 972–983. [Google Scholar] [CrossRef] - Li, Y.; Kawashima, N.; Li, J.; Chandra, A.P.; Gerson, A.R. A review of the structure, and fundamental mechanisums and kinetics of the leaching of chalcopyrite. Adv. Colloid Interface Sci.
**2013**, 197–198, 1–32. [Google Scholar] [PubMed] - Buckley, A.N.; Woods, R. An X-ray photoelectron spectroscopic study of the oxidation of chalcopyrite. Aust. J. Chem.
**1984**, 37, 2403–2413. [Google Scholar] [CrossRef] - Dutrizac, J.E. Elemental sulphur formation during the ferric sulphate leaching of chalcopyrite. Can. Metall. Q.
**1989**, 28, 337–344. [Google Scholar] [CrossRef] - Hackl, R.P.; Dreisinger, D.B.; Peters, E.; King, J.A. Passivation of chalcopyrite during oxidative leaching in sulfate media. Hydrometallurgy
**1995**, 39, 25–48. [Google Scholar] [CrossRef] - Harmer, S.L.; Thomas, J.E.; Fornasiero, D.; Gerson, A.R. The evolution of surface layers formed during chalcopyrite leaching. Geochim. Cosmochim. Acta
**2006**, 70, 4392–4402. [Google Scholar] [CrossRef] - Stott, M.B.; Watling, H.R.; Franzmann, P.D.; Sutton, D. The role of iron-hydroxy precipitates in the passivation of chalcopyrite during bioleaching. Miner. Eng.
**2000**, 13, 1117–1127. [Google Scholar] [CrossRef] - Tshilombo, A.F. Mechanism and Kinetics of Chalcopyrite Passivation and Depassivation during Ferric and Microbial Leaching. Ph.D. Thesis, University of British Columbia, Vancouver, BC, Canada, 2004. [Google Scholar]
- Dreisinger, D.; Abed, N. A fundamental study of the reductive leaching of chalcopyrite using metallic iron part I: Kinetic analysis. Hydrometallurgy
**2002**, 66, 37–57. [Google Scholar] [CrossRef] - Brierley, J.A.; Brierley, C.L. Present and future commercial applications of biohydrometallurgy. Hydrometallurgy
**2001**, 59, 233–239. [Google Scholar] [CrossRef] - Olsen, G.J.; Brierley, J.A.; Brierley, C.L. Bioleaching review part B: Progress in bioleaching: Applications of microbial processes by the minerals industries. Appl. Microbiol. Biotechnol.
**2003**, 63, 249–257. [Google Scholar] [CrossRef] [PubMed] - Robertson, S.; Sayedbagheri, A.; Van Staden, P.; Guzman, A. Advances in heap leach research and development. In Proceedings of the ALTA 2010 Nickel-Cobalt-Copper Conference, Perth, Australia, 24–26 May 2010. [Google Scholar]
- Panda, S.; Sanjay, K.; Sukla, L.P.; Pradhan, N.; Subbaiah, T.; Mishra, B.K.; Prasad, M.S.R.; Ray, S.K. Insights into heap bioleaching of low grade chalcopyrite ores—A pilot scale study. Hydrometallurgy
**2012**, 125–126, 157–165. [Google Scholar] [CrossRef] - Ekenes, J.M.; Caro, C.A. Improving leaching recovery of copper from low-grade chalcopyrite ores. Miner. Metall. Process.
**2013**, 30, 180–185. [Google Scholar] - Rucker, D.F.; Zaebst, R.J.; Gillis, J.; Cain, J.C.; Teague, B. Drawing down the remaining copper inventory in a leach pad by way of subsurface leaching. Hydrometallurgy
**2017**, 169, 382–392. [Google Scholar] [CrossRef] - Chen, B.-W.; Wen, J.-K. Feasibility study on heap bioleaching of chalcopyrite. Rare Met.
**2013**, 32, 524–531. [Google Scholar] [CrossRef] - Panda, S.; Akcil, A.; Pradhan, N.; Deveci, H. Current scenario of chalcopyrite bioleaching: A review on the recent advances to its heap-leach technology. Bioresour. Technol.
**2015**, 196, 694–706. [Google Scholar] [CrossRef] [PubMed] - Petersen, J. Modelling of bioleach processes: Connection between science and engineering. Hydrometallurgy
**2010**, 104, 404–409. [Google Scholar] [CrossRef] - Gebhardt, J.E.; Gilbert, S.R.; McBride, D.; Cross, M.; Bennett, C. Chalcopyrite leach kinetics described within a comprehensive CFD heap leach model. In Proceedings of the International Minerals Processing Congress (IMPC 2014), Santiago, Chile, 20–24 October 2014. [Google Scholar]
- Croft, N.; Pericleous, K.A.; Cross, M. PHYSICA: A multiphysics environment for complex flow processes. In Numerical Methods in Laminar and Turbulent Flow; Taylor, C., Durbetaki, P., Eds.; Pineridge Press: Swansea, UK, 1995; Volume 95, pp. 1269–1280. [Google Scholar]
- McBride, D.; Cross, M.; Croft, T.N.; Bennett, C.R.; Gebhardt, J.E. Computational modelling of variably saturated flow in porous media with complex three-dimensional geometries. Int. J. Numer. Methods Fluids
**2006**, 50, 1085–1117. [Google Scholar] [CrossRef] - Paul, B.C.; Sohn, H.Y.; McCarter, M.K. Model for Ferric Sulfate Leaching of Copper Ores Containing a Variety of Sulfide Minerals: Part I: Modeling Uniform Size Ore Fragments. Metall. Trans. B
**1992**, 23B, 537–548. [Google Scholar] [CrossRef] - Garrels, R.M.; Christ, C.L. Solutions, Minerals, and Equilibria; Freeman, Cooper & Company: San Francisco, CA, USA, 1965. [Google Scholar]
- Stumm, W.; Morgan, J.J. Aquatic Chemistry: An Introduction Emphasizing Chemical Equilibria in Natural Waters; Wiley-Interscience: New York, NY, USA, 1970. [Google Scholar]
- Munoz-Castillo, P.B. Reaction Mechanisms in the Acid Ferric Sulfate Leaching of Chalcopyrite. Ph.D. Thesis, University of Utah, Salt Lake City, UT, USA, 1977. [Google Scholar]
- Munoz, P.B.; Miller, J.D.; Wadsworth, M.E. Reaction Mechanism for the Acid Ferric Sulfate Leaching of Chalcopyrite. Metall. Trans. B
**1979**, 10B, 149–158. [Google Scholar] [CrossRef] - Kaplun, K.; Li, J.; Kawashima, N.; Gerson, A.R. Cu and Fe chalcopyrite leach activation energies and the effect of added Fe
^{3+}. Geochim. Cosmochim. Acta**2011**, 75, 5865–5878. [Google Scholar] [CrossRef] - Tuller, W.N. The Sulfur Data Book; McGraw-Hill Book Company, Inc.: New York, NY, USA, 1954; p. 59. [Google Scholar]
- Bouffard, S.C. Agglomeration for heap leaching: Equipment design, agglomerate quality control, and impact on the heap leach process. Miner. Eng.
**2008**, 21, 1115–1125. [Google Scholar] [CrossRef]

**Table 1.**Summary of model functionality [8].

Model Level | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|

Model Type | Spreadsheet No scale-up | Spreadsheet with scale-up | Spreadsheet scale-up and inventory adjustment | Mass-balance software | Fluid flow + chemical reactions | Comprehensive CFD ‘virtual 3D heap’ |

Tonnes & grade of ore over time | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |

Column leach data utilised | ✓ Extraction curve | ✓ With delay factor | ✓ + scale-up factor | ✓ + scale-up factor | ✓ calibrate leach kinetics | ✓ to calibrate leach kinetics |

Solution inventory tracked | ✓ | ✓ | ✓ | ✓ | ✓ | |

Heap permeability | Scale-up factor | Scale-up factor | ✓ dynamic by ore type | ✓ dynamically, local, depth & time | ||

Gas-liquid flow | ✓ | ✓ | ✓ | |||

Solution channelling | Discount factor | Discount factor | ✓ | ✓ | ||

Oxidation | ✓ | ✓ | ||||

Particle kinetics | ✓ | ✓ | ||||

Thermodynamics | ✓ reactions | ✓ + liquid-solid-gas | ||||

Bacteria | ✓ | ✓ | ||||

Gangue reactions | ✓ | |||||

Precipitation | ✓ | |||||

Meteorological rain, evaporation, temperature | ✓ | ✓ + internal liquid freezing |

Mesh Size (Microns) | % Weight | % Cu |
---|---|---|

6250 | 36.4 | 0.22 |

4750 | 7.5 | 0.22 |

2000 | 21.3 | 0.2 |

150 | 23.9 | 0.2 |

75 | 10.9 | 0.68 |

Average | 0.26 |

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**MDPI and ACS Style**

McBride, D.; Gebhardt, J.; Croft, N.; Cross, M.
Heap Leaching: Modelling and Forecasting Using CFD Technology. *Minerals* **2018**, *8*, 9.
https://doi.org/10.3390/min8010009

**AMA Style**

McBride D, Gebhardt J, Croft N, Cross M.
Heap Leaching: Modelling and Forecasting Using CFD Technology. *Minerals*. 2018; 8(1):9.
https://doi.org/10.3390/min8010009

**Chicago/Turabian Style**

McBride, Diane, James Gebhardt, Nick Croft, and Mark Cross.
2018. "Heap Leaching: Modelling and Forecasting Using CFD Technology" *Minerals* 8, no. 1: 9.
https://doi.org/10.3390/min8010009