Luis A. Cisternas

An analytic correlation for the vapour pressure of aqueous and non-aqueous solutions of single and mixed electrolytes. Part II. Application and extension

Abstract A vapour pressure equation for electrolyte solutions recently proposed by the authors has been applied to the prediction of the vapour pressure of aqueous and non-aqueous, single- and mixed-electrolyte solutions. The correlation requires as input a single “ K ” value for each salt and five parameters for each solvent. K values for 111 electrolytes and solvent parameters for six solvents are reported. The K parameters can be approximated well by assigning two parameters to each ion. This correlation has been examined for 176 systems (4157 experimental points). It gives accurate results up to 44 mol kg −1 of ionic strength.

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.

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.

Binary interaction parameters in cubic equations of state for hydrogen—hydrocarbon mixtures

Abstract Three generalized cubic equations of state are applied to the calculation of vapor—liquid equilibrium of H 2 n-alkane mixtures. Binary interaction parameters are calculated from experimental PTxy data and generalized correlations are proposed. Comparison of the calculated k ij values with predictions by other correlations available in the literature are done. Solvent effects on H 2 -mixtures are also discussed. The correlations proposed here have proven to give reasonable values of the binary interaction parameter for VLE calculation in H 2 -n-alkane mixtures.

Effect of Seawater on Sulfide Ore Flotation: A Review

ABSTRACT The flotation process in seawater is highly complex and multifaceted, wherein the chemistry is very different to that of pure water. The high saline environment compresses the electrical double layers resulting in (i) enhancement of the floatability for surfaces that are already hydrophobic; (ii) mitigation of the slime coatings; (iii) increase of the entrainment; (iv) reduction of the bubbles size; and (v) better froths stability. In parallel, the secondary ions present in seawater cause a colloidal precipitation and a strong buffering effect, which difficult the operation at high alkaline condition. The objective of this review is to present a summary of the current knowledge on the subject of seawater flotation processes, highlighting the copper sulphide ores flotation. This review includes a description of the underlying flotation mechanisms affected by the presence of saline water and seawater, as well as a more practical description of industrial flotation operations.

Separation system synthesis of fractional crystallization processes with heat integration

Abstract A methodology is presented for the synthesis of fractional crystallization processes with heat integration. The methodology is based on the construction of three networks. The first network is based on the identification of feasible thermodynamic states. Using equilibrium data for a candidate set of potential operation point temperatures, a network flow model is constructed to represent the set of potential separation flowsheet structures that can result. In this network the nodes correspond to multiple saturation points, solute intermediate, process feeds and end products. The second network is used to represent the variety of tasks that can be performed at each multiple saturation point. Multiple saturation nodes can be used for different tasks depending on the characteristic of the input and output streams. These tasks include cooling crystallization, evaporative crystallization, reactive crystallization, dissolution, and leaching, This multiple task condition for each equilibrium state is modelled using disjunctive programming and then converted into a mixed integer program. Heat integration is included using a heat exchanger network which can be regarded as a transhipment problem. The method is illustrated through the design of two salt separation examples.

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.

On the synthesis of inorganic chemical and metallurgical processes. Review and extension

Abstract A review and extension of process synthesis principles to inorganic chemicals and extractive metallurgical operations is presented. It is shown that conceptualization of extractive metallurgy and inorganic chemical processes can be improved upon by the development of specific methodologies. The major issues analyzed are: 1) reaction path, 2) mineral processing circuit synthesis, 3) separation path using fractional crystallisation, 4) waste minimization and mass-exchange networks, 5) selection of mineral processing routes, and 6) synthesis of chemical induced separation. It is shown that there is a lack of methods for inorganic chemical and extractive metallurgy process synthesis, and that process synthesis has not found the place it deserves among the techniques used in inorganic chemical and extractive metallurgical operations. Research efforts conducted during the last few years, however, are a good beginning in the efforts to change this. A number of ideas are given to illustrate the potential applicability of process synthesis to this area. Several articles cited in this paper have been chosen from the chemical engineering literature which represent advances of particular interest in the organic chemical and extractive metallurgy process synthesis.

A analytic correlation of vapour pressure of aqueous and non-aqueous solutions of single and mixed electrolytes

Abstract A new analytic correlation is presented for vapour pressure of aqueous and non-aqueous solutions of single and mixed electrolyte. Many systems of single and mixed electrolytes have been treated, finding excellent results. The correlation, based on Kumar-Patwardhans method, was obtained using two reference electrolytes, viz LiBr and (NH 4 ) 2 SO 4 . The correlation requires a single “K” value to each salt and five parameters to each solvent as input parameters. Regression analysis to estimate the “K” value has been done by using Marquardts method.