Mario E. Mellado

On scalable analytical models for heap leaching

Abstract In this paper we present analytical models suitable for scaling up the heap leaching process of solid reactants from porous pellets. The models are based on first order ordinary differential equations together with some constitutive relations derived from models based on ordinary and partial differential equations and other relations based on insight. The models are suitable for applications in which the scale-up is neccesary. This approach allows to obtain accurate solutions for actual industry heap leaching operations. Novelty of this approach is the simple form of the models and its accuracy as compared with more complex models. Due to the models simplicity, they can be used for analysis, design, control and optimization of heap leaching processes without mathematical complexities. The models include the effect of heap height, particle sizes, flow rates, and several operation-design variables. Finally, some numerical experiments which confirm our theory are presented.

An analytical-numerical method for solving a heap leaching problem of one or more solid reactants from porous pellets

In this paper we present an alternative method based on analytical and numerical solutions for solving the differential equations which describe heap leaching of one or more solid reactants from porous pellets. We propose to use analytical solutions for the differential equations which describe rate dissolutions along the pores and the surface of the particles under suitable regularity conditions. Moreover, we propose to use continuous and discontinuous solutions for the continuity partial differential equations describing balances. We comment on the efficient numerical solving of the remaining partial differential equations within the proposed numerical scheme. All of this, allows to obtain a numerical algorithm which is fast and accurate for the heap leaching problem. Also, we include particle size distributions on the proposed numerical methodology. This method applies to the case where the rate-controlling reagent is a component of the lixiviation solution only and not of the gas phase. The model includes the effects of particle scales, kinetic factors, heap scales and several operation variables. Finally, numerical experiments are presented.

Separation Circuits Analysis and Design, Using Sensitivity Analysis

Abstract Sometimes, the recovery and/or concentration of value components can not be done in one operational stage, which is why separation circuits are used. Usually, the component to be separated is distributed with different concentrations into different particle sizes, showing different levels of recovery by size and concentration. Other times, we want to selectively remove more than one value component, taking advantage of differences in the components floatability at different values of pH and pulp potential. In literature, several methods for the design of these circuits have been presented. These methodologies can be classified among those that use heuristics and those that use mathematical optimization techniques. However, none of these options is used actually in industry. This is, the former is very simple to incorporate the complexities of the problem and the latter requires more specialized training for the designer. In this work, we use a sensitivity analysis to analyze and design separation circuits. We study the effect of each stage on the general circuit, identifying relationships between the recovery of each stage and the global recovery of the circuit. Based on these results, we propose a novel methodology to analyze and design separation circuits. This new method can be regarded as hybrid, since it uses a mathematical analysis, coupled with the experience of the designer. An example is given for flotation separation in copper mining.

A method for the design and planning operations of heap leaching circuits

Abstract Heap leaching is a widely used extraction method for low-grade minerals, including copper, gold, silver, and uranium. This method has new applications in nonmetallic minerals such as saltpeter and soil remediation. Although a number of experimental studies have been carried out as well as modeling, which allows better understanding of the phenomena and its operation, few studies have been carried out with the objective of optimizing the process. Most of the studies which consider optimization, either experimentally or through the use of models, have been done from a technical perspective. The aim of this work is to develop a methodology for the design and planning of the heap leaching circuit. A superstructure which includes a number of alternative circuits is proposed. Then a mathematical model is developed that represents the constraints of the system and maximizes the profits. An example is considered to validate the proposed methodology. The results show that the current mode of operation of these systems can be improved using this methodology.

Water and Energy Use in Mineral Processing: A Case Study in Copper Flotation

Abstract The mineral industry is seeking ways to reduce the impacts of its mining and mineral processing operations. Members of this industry face several challenges in designing sustainable mineral operations with lower environmental and social impacts while remaining profitable. These challenges must be addressed in the design, operation and postclosure phases, but the design phase affords the greatest opportunity to reduce the impact of operations and increase profits. Some of the most important challenges are the efficient use of water and energy. For example, because of the decline in ore grades in mineral concentration is being used to reduce the particle size to increase the mineral liberation. However, this increase in grinding increases energy consumption and affects the water recovery in the dewatering stages. This manuscript examines these and other effects through process simulation of a flotation plant for copper ores. Based on these simulations, the relationship between particle size, energy consumption, and water recovery is established. This makes it possible to explore the trade-off between energy, liberation, and water recovery.