Freddy Lucay

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.

Design of desalinated water distribution networks including energy recovery devices

Abstract The objective of this work is to develop a methodology to determinate the location and size of desalination plants, the water distribution network, and the location and size of energy recovery devices to provide desalinated water in regions with complex topography. The novelty of the methodology is that energy recovery devices such as pumps as turbines are incorporated as an option to produce energy. The methodology proposed uses a superstructure that represents the set of alternatives on which the optimal solution is found. A mathematical model is generated that correspond to an MINLP problem which is then transformed into an MILP problem and solved using Cplex-GAMS. A case study is presented to demonstrate the applicability of the methodology designed. Based on a case study it is concluded that the methodology proposed can be useful for designing the whole water distribution network, including energy recovery devices, for users located in places with a complex topography.

A new group contribution method for mineral concentration processes

Abstract In this work, a group contribution model to predict the behavior of mineral concentration circuits is presented. The new model is an expansion and modification of an existing model in the literature ( Sepulveda et al., 2014 ). The modifications extend the number of process groups from 35 to 143, which makes it possible to extend the number of concentration circuits that can be represented from 1492 to over 274 million circuits and to increase the maximum number of stages from 6 to 9. The errors observed between the fitting and the prediction results of concentration circuits that were not included in the fitting verifies that the new model could be extremely useful in the design of mineral concentration circuits.

Optimization Approach to Designing Water Supply Systems in Non-Coastal Areas Suffering from Water Scarcity

This article presents a novel optimization approach to designing water supply systems in non-coastal areas with water scarcity. In such areas, high water demand caused by population increases and economic development can only be satisfied with seawater supply. Furthermore, most of the non-coastal users are located at long distances and sometimes at altitudes very diverse from the coastline, meaning long pipelines and several pumping stations will be required to effectively supply water. The proposed optimization approach based on a mixed integer nonlinear programming model offers optimal designs of water supply systems from an economic and technical perspective. It determines the location and size of desalination plants and the design of the water transport network including pipelines of specified length and diameter and pumping stations that minimize capital and operational costs of the whole system. A case study in a hyper-arid region of Chile was used to validate the applicability of the proposed model and the results show its aptitude for determining global optimal solutions to real-scale problems.

Mineral Concentration Plants Design Using Rigorous Models

Abstract The design of a mineral concentration plant plays an important role, since the operation of the plant depends on the structure of the process (Mendez et al., 2009). The concentration plant is formed by several concentration stages interconnected within a particular arrangement. Currently, the selection of the flotation circuit is based on the experience of the designer, and is complemented by laboratory tests and simulations. In the literature there are many studies that design concentration plants using mathematical programming. However, these strategies use a non-convex MINLP model that is difficult to solve. For that reason, usually simple models and systems with fewer species are used. This paper presents a methodology for the design of a mineral concentration circuit based in two steps: 1) Identify the set of optimal structures using discrete values of stage recoveries and solving several mixed integer linear programming (MILP) problems; 2) Determine the optimal design for each of the structures obtained in the previous step, using a Mixed Integer Nonlinear Programming model (MINLP) and a rigorous model for the recovery at each concentration stage. This work is based on the assumption that there are little optimal structures within a given space of species recoveries at each stage. A case study is used to validate the proposal using a system with several species.

Global Sensitivity Analysis of Reverse Osmosis Processes

Abstract The desalination of seawater is generally performed by reverse osmosis (RO), because of the product quality and the low costs involved. Models describing the RO process are generally used for the simulation or design of industrial plant. However, none of the existing models in the related literature have been used to study the effect of the distribution of the input variable uncertainties on plant responses and the sensitivity of these, which is the objective of this work. The results indicate that the type of uncertainties of the input variables does not substantially influence on the model responses and on its sensitivity. In addition, the histogram associated with the permeate salt concentration has a similar behavior to the log-normal distribution, while the histogram of water recovery has a not known tendency. Finally, the results of this study indicate that global sensitivity analysis (GSA) can supplement modelling studies of RO plants.

Retrofitting of Concentration Plants Using Global Sensitivity Analysis

Abstract This work presents the use of global sensitivity analysis to retrofit mineral concentration plants. The ore that is fed to a concentration plant is heterogeneous, and it changes over time as the mine is operated. Moreover, the costs and the selling price of the concentrate can undergo significant changes. This situation forces readjustment of mineral concentration plants to new conditions. The methodology consists of three steps: 1) process modeling, 2) global sensitivity analysis to identify key variables, and 3) economic optimization of the plant. Sobol’s method is used to identify the variables that most significantly affect the recovery of the species and the grade of the final concentrate. The methodology is applied to a copper and molybdenum concentrator plant of three concentration stages. The species present in the mineral correspond to chalcopyrite, chalcocite, covellite, molybdenite, pyrite, and quartz. The results show that the methodology could be helpful to improve the revenue of a flotation plant by making targeted changes to it.