Determination of the optimum conditions for the leaching of Co based on simulated data

Process optimization by using experimental design

Elaboration, 2019
21 Pages, Grade: 60%


Table of Contents


1. Background

2. Objective(s)

3. Factors and Levels

4. Planned risk and simple size estimate

5. Selection, allocation of material

6. Execution and analysis of experimental results





The treatment of Cu-Co ores by hydrometallurgical processes imposes a preliminary leaching step. However, the majority of Cu-Co ores encountered contain cobalt in the form of heterogenite with a fairly high proportion in the form of cobalt 3+. This form of cobalt has a weak kinetic during leaching and requires the presence of a reducing agent for its solubilization in a sulfuric medium.

In this work, we are interested in the formulation of a Pregnant Leaching Solution. There are many variables which affect the quality and production of the product, including time, percent solids, reducer concentration, tool materials, geometry of particles, etc. but for the model purpose we only consider two. The yield of this chemical process is being studied by taking in consideration two most important variables that are thought to be the pH and the reducing agent; tree levels of each factor are selected, and a factorial experiment is performed based on simulated `data, Process optimization by using experimental design. Consequently, companies are forced to operate by using the trial and error method. The optimization of controllable variables can make a considerable contribution towards solving the problem. At this point, we are more interested in Analyzing the data and draw conclusions under the following conditions:

1. Response: yield of cobalt

Factor 1: Reducing agent, with Levels 1(20 g/L), 2(30 g/L) and 3(40 g/L)

Factor 2: pH with Levels 1, 1.5 and 2

2. Issue:

- Which level has best effect on response (means effect)?
- Which level gives smallest variance.

3. Hypothesis:

- H1: μ11 = μ12 =…= μ1a
- Ha1: at least one μ1i is different
- H2: μ21 = μ22 =…= μ2a
- Ha2: at least one μ2i is different
- H3: Interaction effects the same
- Ha3: at least one μij is different

3. Significance level: α= 0.05
4 . Confidence level: 1 – α = 0,95
5. Power of the test: 1 – β = 0.5
6. P (Type II error) = β
7. δ = 1.5
8. a = 3, b = 3, for a power of the experiment equal to 0.5 and a confidence interval of 0.95, n = 3.
9. total number of repetitions N = 27.

We will Prepare appropriate residual plots and comment on the model’s adequacy and see under what conditions we would operate this process, thus considerably reducing the number of tests needed. As a result, nowadays, this and similar methods have become the focus of interest for both academics and companies, with the goal of increasing production quality and operating with greater efficiency. In this study, the effects of leaching parameters on the recovery of Cobalt are investigated based on the 2 basic principles of experimental design; the model will be replicated 2 times in order to obtain an estimate of the experimental error and also to obtain a more precise estimate of the dependent variable which in this case is the recovery, with δ = 1.5 , a= 3, b = 3 we have obtained a value of n = 3 for a power of the experiment equal to 0.5; then the total number of repetitions is obtained, which in this case is equal to 27; another basic principle which is Randomization will be applied in the purpose of averaging out the effects of extraneous factors that are present. The analysis of variance (ANOVA) technique is carried out to investigating parameters which are statistically significant. Then the optimal plan is obtained.

As mentioned above, we are interested in the formulation of a Pregnant Leaching solution by using 2F3L factorial design to determine if this impacts the cobalt recovery based on simulated values; the main idea here is to determine if there is any indication that either factor influences cobalt recovery, Analyze the residuals from this experiment, verify if two factors interact, describe the differences in the effects of the different levels of cobalt recovery, which level of temperature we would specify in this work. The experiment is represented in Table 1. This orthogonal array is chosen due to its capability to check the interactions among factors.

1. Background


Leaching is a process of extracting a soluble component of a solid by means of a solvent. In other words, it is the dissolution of one or more valuable metals for their subsequent extraction. This chemical dissolution is done selectively with a minimum solution of impurities [Mutombo, 2007].

The choice of leaching’s agent is a function of several factors which are essentially the following:

- The chemical characteristics of the materials to be leached;
- The cost of the reagent;
- The selectivity of the reagent with respect to the constituent that one wants to leach;
- The corrosive action of the reagent and its consequences on equipment and the environment;
- The possibility of regeneration of the reagent.


For a very long time we have not been concerned with measuring the speed of a reaction. It was limited to judging it very slow, slow, fast, explosive. Then following a classic approach in science, we tried to specify more. It is not unusual to find expressions like this: the reaction is completed after 10 hours or 2 days, for example.

Lastly, precise definitions have been introduced which account for precise and non-vague facts such as the "completed" nature of a reaction. The chemical kinetics were thus constituted.

The study of chemical kinetics was very fruitful because it led to the knowledge of the mechanism of the reaction; the metallurgist is no longer satisfied with the balance sheet, he makes every moment a precise state of the reaction and he often becomes capable of changing the course of the latter [Germain and Burnel, 1975].


Heterogeneous leaching reactions include the following steps:

- The diffusion of the reactant species towards the solid-liquid interface;
- Adsorption of the reactants at the solid-liquid interface;
- The chemical reaction at the interface;
- Desorption of reaction products at the interface;
- The diffusion of the products of the interface towards the solution.

It is therefore necessary to analyze the various stages in which a reaction takes place, it being understood that it is the slowest step that imposes the overall kinetics of the heterogeneous reaction; three cases are to be considered The reaction is controlled by diffusion: when the reaction rate at the interface is greater than that of diffusion of the reactants towards the interface. In this case, the activation energy Ea is between 1 and 3 kcal / mole. This type of process is very sensitive to agitation, because it reduces the thickness of the boundary layer resulting in the increase of the reaction rate as shown in the relationship below:

Abbildung in dieser Leseprobe nicht enthalten


D: diffusion coefficient of the substance;

δ: thickness of the boundary layer;

A: interface area;

C: concentration of the reactant in the bath;

Ci: concentration of the reactant at the interface.

Temperature has a weak influence on diffusion-controlled processes as shown by the Stockes-Einstein equation:

Abbildung in dieser Leseprobe nicht enthalten


D: diffusion coefficient of the substance;

N: number of Avogadro;

R: constant of perfect gases;

T: temperature in Kelvin;

r: grain radius;

η: viscosity of the fluid.


Leaching can be influenced by the following factors:

- The particle size: The properties of the dispersed states are related to the contact surface between the phases. As a result, a fractional phase is much more reactive than a massive phase, which can even cause explosions if the reaction is exothermic:
- The concentration of reagents involved: A diffusion-controlled liquid-solid process can become a chemically controlled process when increasing the concentration of reagents in the liquid phase.
- Density: For leaching, the density of the pulp(slurry) is an important parameter of dissolution. When the density is high, very concentrated solutions are obtained after leaching.
- Acidity: when leaching cobalt hydroxide, sulfuric acid also reacts with other hydroxides in the discharge. To limit its contamination reactions, we work with very dilute acid solutions.

Despite the low acid levels in the solution, the leaching reaction of cobalt hydroxide will proceed because cobalt and copper have a high affinity for sulfuric acid.

- Temperature: In many cases, thermal energy can cross the energy barrier. (case of chemically controlled processes);
- Agitation: in a solid-liquid reaction, stirring increases the rate of dissolution when the process is controlled by diffusion [Kapya. T, 2013].

2. Objective(s)

Initially, the experimental design method is used to plan a minimum number of experiments. After identifying the working levels of the design factors and the main performance characteristics of the product under study, the method can be successfully applied to the leaching process. variations of the main leaching parameters and their interactions are investigated using orthogonal array technique. A statistical analysis of ‘signal-to-noise’ ratio follows by performing a variance analysis. After developing some special criteria, which depend on our performance objective, the optimal levels of the design factors are determined. Cobalt leach results will be discussed and commented.

3.Factors and Levels

Although several factors may influence the study during this Project, some were not considered. In the case of this work, it has been suggested to us that 2 factors, each of which has 3 levels of variation. Table 1 presents the 2 factors selected for this project and their considered levels.

Table 1. Orthogonal matrix of 2 variables studied at

3 distinct levels

Abbildung in dieser Leseprobe nicht enthalten

3.1 Description of the tests

Conducting leaching tests with 2 factors each having 3 levels is gigantic and often unrealistic when it comes to repeating the tests more than 4 times. To solve this problem, we thought it wise to use an experimental design with 2 replications.For design of experiments with two factors (pH, reducing agent) and three levels for each factor, the factorial design here is a standard L27 orthogonal array employed. Each row of the matrix represents one run. The factors and their levels are assigned in Table 2. Factors A, B are arranged in column 2, 3 respectively. The columns represented coded variables whose values ​​correspond to the levels of the factor they are associated with, and the lines represent the experimental conditions of an experiment, that is, the levels taken during this experiment by each of the factors For analysis of the results and optimization of conditions for setting the control factors, Minitab 2019 software is used. MINITAB Version 19 used for this project is the windows version software for Design and Analysis of Experiments.

Table 2. Orthogonal Matrix L27 (32)

Abbildung in dieser Leseprobe nicht enthalten

3.1.1. Interaction between factors

The notion of interaction between parameters is subjected to observations of the notion of parallelism between linear adjustment lines of various values ​​of the signal / noise functional metric (S / N) for each controlled parameter [Nkulu, G., 2012].

4. Planned risk and simple size estimate

The acid leaching process depends on many operating factors that have a direct influence on the quality of the product obtained. Whatever the field of study, the experimenter is always faced with the difficult problem of the optimal organization of his tests. It always seeks to find a compromise between, factors to consider, costs, deadlines and getting the right information on the results. ; as we explained in the introduction the model will be replicated 2 times in order to obtain an estimate of the experimental error and also to obtain a more precise estimate of the dependent variable which in this case is the recovery, with δ = 1.5 , a= 3, b = 3 we have obtained a value of n = 3 for a power of the experiment equal to 0.5; then the total number of repetitions is obtained, which in this case is equal to 27.

5. Selection, allocation of material

Having made these tests in the past based on the classical method, we are proposed to repeat the same materials because they remain the same as well even though it is a study based on simulated information

- Balloons, beakers, Buchner;
- Burette, test tube, Funnels;
- stemmed glass, magnetic stirrer (REMI MOTOR);
- electronic scale; Stopwatch;
- pH meter (METROM) with an electrode;
- potentiometer (ORION);
- vacuum pump for filtration, thermometer, thermostatic hotplate;
- stand, filter papers; a clamp; a wash bottle;


To carry out these leaching tests, an assembly was carried out during our tests with the classical method and this assembly also applies to the experimental method. This assembly would consist mainly of the following elements: Beaker, pH-meter (METROM) equipped with an electrode, potentiometer (ORION), Thermometer.


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Determination of the optimum conditions for the leaching of Co based on simulated data
Process optimization by using experimental design
University of Pretoria
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Kapya Tshinangi (Author), 2019, Determination of the optimum conditions for the leaching of Co based on simulated data, Munich, GRIN Verlag,


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