Edelmira D. Gálvez

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.

Modeling of grinding and classification circuits as applied to the design of flotation processes

Abstract This study reports on the preparation of linear models of grinding, grinding–classification, classification–grinding, and classification–grinding–classification circuits based on material balances supported by population balances. For these procedures, particles were described by size and chemical composition, and the parameter ϕ is introduced which represents the fraction of one class of particles which delivers material to another. An index is introduced to evaluate the effect of the proposed circuits on the characteristics of the floatability of the material. The methodology can be amplified to include other types of circuits, and the models can be used to evaluate, compare, and select grinding circuits with classification. As examples of their application, some of these models are used for the synthesis of flotation circuits, following the methodology employed by [Cisternas, L., Mendez, D., Galvez, E., & Jorquera, R. (2006). A MILP model for design of flotation circuits with bank/column and regrind/no regrind selection. International Journal of Mineral Processing , 79 (4), 253–263] with some variations, showing how the selection of these circuits can affect the design and yields of a mineral processing plant.

The use of global sensitivity analysis for improving processes: Applications to mineral processing

Abstract This paper analyzes the application of global sensitivity analysis (GSA) to the improvement of processes using various case studies. First, a brief description of the methods applied is given, and several case studies are examined to show how GSA can be applied to the study to improve the processes. The case studies include the identification of processes; comparisons of the Sobol, E-FAST and Morris GSA methods; a comparison of GSA with local sensitivity analysis; an examination of the effect of uncertainty levels and the type of distribution function on the input factors; and the application of GSA to the improvement of a copper flotation circuit. We conclude that GSA can be a useful tool in the analysis, comparison, design and characterization of separation circuits. In addition, we conclude that using the stages recoveries of each species as input factors is a suitable choice for the GSA of a flotation plant.

A methodology for the conceptual design of concentration circuits: Group contribution method

Abstract This paper presents a new methodology for the conceptual design of concentration circuits based on the group contribution method. The methodology includes three decision levels: (1) definition and analysis of the problem, (2) synthesis and screening of alternatives, and (3) final design. In this manuscript, the emphasis is on the description of the methodology, justification of the assumptions, and group contribution method. The group contribution models were developed to estimate the global recovery in concentration circuits. The procedure is general and can be applied to any circuit consisting of stages that generate two product streams: concentrate and tail. The developed models can be applied to estimate the recoveries in concentration circuits with a maximum of six stages. The models were fitted using mass balance data from 46 circuits, generating 35 process groups. Case studies were used to illustrate the methodology.

Simultaneous Design of Desalination Plants and Distribution Water Network

Abstract Northern Chile is characterized by significant mineral resources, particularly copper, nitrate, lithium, molybdenum, rhenium, among others. Moreover, these resources are located in the Atacama Desert, the driest in the world. Water resources are exhausted, but Chile has an extensive coast from where to get water. Then, any new operation or expansion of a current operation must use seawater. The distance from the coast to mining operations ranging from a few kilometers to about 300 kilometers, but even more significant, these operations can be found from 600 to 4,000 meters above sea level. Then, the cost of transporting desalinated water can be greater than the cost of desalination. This paper presents a methodology to design the system of desalination plant and desalinated water transport. The objective is to determine the location and size of desalination plants and the water distribution system that minimizes capital and operational costs. The methodology uses a superstructure that represents the set of alternatives on which the optimal solution is found. A mathematical model is generated to represent the desalination plant and water distribution system. The end model corresponds to a MINLP problem which is solved in two steps using commercial software. A case study is used to demonstrate the applicability of the methodology developed.

Principles for chemical products design

Abstract In this work it is suggested to develop a theory for chemical products, that defines the bases and serves to guide and put in order the development of knowledge in the area. A nature representation of chemical products is carried out based on the simple observation that a chemical product is a system consisted of different chemical substances, and that it is manufactured for one or more purposes, in other words, it is formed by components, an organization and an environment. This representation is used to identify different kinds of chemical products design problems.

A model of grinding-classification circuit including particles size distribution and liberation of material: Application to the design and retrofit of flotation circuit

Abstract In this study models were developed based on population balances which included the effects of redistribution of material of different composition classes and particle sizes with four configuration alternatives of grinding and classification circuits (grinding, grinding-classification, classification-grinding, classification-grinding-classification). The models for all these configurations were linear in character, and applicable in design or retrofit strategies in which there is an influence of particle size and composition in the recovery of materials such as in separation of plastics from metals and the recovery of ferromagnetic materials in the recycling industry, as well as in the separation of materials in treatments of urban solid wastes, refining of pharmaceutical products, and in the mineral industry. As an example of application, one of the models is incorporated into a strategy for the design of flotation circuits.

The Effect of Stage Recovery Uncertainties on the Selection of Process Structures

Abstract In mineral processing, ores are concentrated using flotation – a technology that requires several stages (forming a flotation circuit) to separate the valuable minerals from the gangue. The flotation circuit design is a complex task, which is why several authors have proposed design procedures based on optimization. However, the modeling of the recovery of each flotation stage is complex, requires experimentation, and depends on many variables, including the selected circuit and mineral feed (which changes over time). These difficulties indicate that there are uncertainties in the actual values of the recovery of each stage and the information necessary to create the circuit design. This manuscript analyzes the effect of uncertainty on the recovery during each stage to facilitate the selection of an optimal circuit. We conclude that approximate values for stage recoveries are sufficient for the selection of flotation circuits.

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.

Applications of grey programming to process design

Abstract One of the methodologies utilized for process design consists on the application of optimization techniques, e.g. mathematical programming, to identify the best design inside a set of alternatives. In spite of the efforts and advances, this approach faces the problem that it is not broadly utilized in the industrial practice. One reason, among other, is that their implementation requires complex mathematical developments and therefore a good knowledge of the mathematical programming techniques. Therefore, it is important to develop procedures that can consider real situations, but on the other hand does not require complex mathematical methods. In this work the potential application of grey programming (GP) and grey system to process design is analyzed. GP is a simple technique to consider uncertainty. The design of flexible heat-exchange network is used as an example. Complete methodologies is developed, which include the grey composite curve, the determination of the grey minimum utility consumption, and the determination of grey number of interchangers units. The utilized techniques consider grey linear programming (GLP) and grey mixed-integer linear programming (GMILP).