Factorial Analysis of Lead Bioextracted Using Mixed Cultures of Acidithiobacillus Ferrooxidans and Acidithiobacillus Thiooxidans on Galena

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Figure 2. XRD Analysis of the galena used

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100 cm³ leaching medium (2.0 g/dm³ Fe (ii) sulphate liquid medium) supplemented with 6.0 g of 100 μm grain sized galena concentrate (loose particles) was put in 7 flasks. Bacteria: ATF and ATT were obtained from red soil shown in Figure 3 b. The volume of the bacteria (ATF + ATT) culture inoculum used was 12 cm³ for all the flasks. The 7^th flask was without bacteria and is identified as control. The initial pH of each leaching medium used was 4.0. The experiments were started under exactly the same solution conditions of pH and redox potential (0.9926 V) of leaching medium in bacteria and uninoculated control leaching and spanned through 70 hrs. The leaching temperature was maintained at room temperature; 28C. The experiments were repeated for leaching times 140, 210, 280, 350 and 420 hrs and the corresponding leached out lead chemically analyzed. Detailed experimental procedures are stated in the report [9].

3. Results and Discussion

Variation of extracted lead with leaching time

The effect of leaching time at constant leaching temperature and ore mass-input indicates that the concentrations of extracted lead increases with increase in the leaching time which ranged from 70 - 420 hrs. Table 1 shows that for each experimental set up, the final solution pH drops compared to the initial solution pH. This was attributed to dissolution of hydrogen sulphide (H₂S) in the leaching solution thereby enhancing the inherent acidity level.

Table 1. Variation of extracted lead concentration with leaching time and final solution pH

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Formation of H₂S was due to elemental sulphur oxidation by ATT as a result of oxidation by ferric ion. The action of ATT in the mixed culture of ATH + ATT was strongly believed to have significantly enhanced solubilising of PbS as a result of elemental sulphur oxidation. This is in line with previous research ^[6]. Equations of these reactions are shown:

(3)

This oxidation produces hydrogen ions which in turn attack the minerals according to the following equations:

(4)

The bioleaching process residues were very gray in colour (as shown in Figure 3a) irrespective of the process time used. The SEM analysis of the process residues at leaching times: 70 and 420 hrs shows whitish substance sparsely distributed on the lead structures (Figure 4 (a)-.(f)). This was suspected to be secretions from the bacteria used in the leaching process. The lead structures at 70 hrs process time (Figure 4 (a-c) show sleek-like and jelly-like appearance. This was attributed to the wriggling movement of the microbes in the course of their activities. In contrast, lead structures at 420 hrs process time (Figure 4 (d-f) were larger than those at 70 hrs process time. This was perceived as lead particles clogged together by large quantity of periodic sticky-secretions by the bacteria during the leaching process.

Figure 3. (a) residue from the bioleaching process (b) source of ATF and ATT

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Figure 4. SEM of bioleaching residues (a), (b) and (c) after 70 hrs process time (d), (e) and (f) after 420 hrs process time

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3.1. Model Formulation

Computational analysis of experimental results in Table 1; generated during the leaching process indicates that;

(5)

Introducing the values of S_e, S, K and N into equation (5) reduces it to;

(6)

(7)

Where

(ξ) = Conc. of extracted Pb (g/dm³)

(ɤ) = Leaching time (hr)

(ϑ) = Leaching temperature (C)

₰ = Mass-input of galena (g)

S_e = 0.258, S = 0.0162, K = 0.0002 and N = 0.001

empirical constants determined using C-NIKBRAN [10]

4. Boundary and Initial Conditions

Consider galena placed in a flask containing leaching solution (2.0 g/dm³ Fe (II) liquid medium) and supplemented with 6.0 g of 100 μm grain sized galena concentrate. The flask atmosphere is not contaminated i.e. (free of unwanted bacteria, gases and dusts). Initially, atmospheric levels of oxygen are assumed just before the commencement of the process (due to air in the flask).

Range of leaching time: 70-420 hrs was used. Treatment temperature: 28C, initial pH: 4.0, redox potential: 0.9926, volume of leaching solution: 100 cm³ and ore grain size: 100 µm were also used. The boundary conditions are: flask oxygen atmosphere for enhancement of Fe (II) oxidation. At the bottom of the particles, a zero gradient for the gas scalar are assumed and also for the gas phase at the top of the particles. The sides of the particles are taken to be symmetries.

4.1. Model Validity

The validity of the model was strongly rooted in the core model equation (equation (6)) where both sides of the equation are correspondingly approximately equal.

Table 2. Variation of ξ - 0.258 with 0.0162 ɤ+ 0.0002ϑ - 0.001₰

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Table 2 also agrees with equation (6) following the values of ξ - 0.258 and 0.0162ɤ+ 0.0002ϑ - 0.001₰ evaluated from the experimental results in Table 1.

Furthermore, the derived model was validated by comparing the extracted lead concentrations as predicted by the model and obtained directly from the experiment. This was done using various evaluative techniques such as statistical, graphical, computational and deviational analysis.

4.2. Statistical Analysis
4.2.1. Standard Error (STEYX)

The standard errors in predicting the extracted lead concentrations for each value of the leaching times and final solution pHs as obtained from experiments & derived model-predicted results were 0.3666 & 0.0003 and 1.7626 & 1.3135 respectively.

Figure 5. Coefficient of determination between the extracted lead concentrations and leaching time as obtained from experiment

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Figure 6. Coefficient of determination between the extracted lead concentrations and leaching time as predicted by model

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Figure 7. Coefficient of determination between the extracted lead concentrations

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Figure 8. Coefficient of determination between the extracted lead concentrations and final solution pH as predicted by model

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Figure 9. Comparison of extracted lead concentrations (relative to leaching time) as obtained from experiment and derived model

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Figure 10. Comparison of extracted lead concentrations (relative to final solution pH) as obtained from experiment and derived model

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Figure 11. Comparison of extracted lead concentrations (relative to leaching time) as obtained from experiment, derived model and regression model

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Figure 12. Comparison of extracted lead concentrations (relative to final solution pH) as obtained from experiment, derived model and regression model

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4.2.2. Correlation (CORREL)

The correlation coefficients between extracted lead concentration and leaching time as well as final solution pH were calculated from the results of derived model and experiment. This was done by considering the coefficients of determination R² from Figure 5- Figure 8 and then evaluating them using the expression:

(8)

The evaluated correlations (using Microsoft Excel version 2003) are shown in Table 3 and Table 4. These evaluated results indicate that the derived model predictions are significantly reliable, considering the proximate agreement between actual experimental and model-predicted results.

Table 3. Comparison of the correlations evaluated from derived model predicted and ExD results based on leaching time

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Table 4. Comparison of the correlations evaluated from derived model predicted and ExD results based on final solution pH

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4.3. Graphical Analysis

Comparative graphical analysis of Figure 9 and Figure 10 shows extremely close alignment of the curves from the experimental (ExD) and model-predicted (MoD) extracted lead concentration. Furthermore, the degree of alignment of these curves is indicative of the proximate agreement between both experimental and model-predicted extracted lead concentration.

4.4. Comparison of Derived Model with Standard Model

The validity of the derived model was further verified through application of the regression model (Reg) (Least Square Method using Excel version 2003) in predicting the trend of the experimental results. Comparative analysis of Figure 11 and Figure 12 show very close alignment of curves which depicted significantly similar trend of data point’s distribution for experimental (ExD), derived model (MoD) and regression model-predicted (ReG) results of extracted lead concentration. Moreover, the evaluated correlations between extracted lead concentration and leaching time & final solution pH for regression model-predicted results gave 1.0000 & 0.8327 respectively. These values are in proximate agreement with both experimental and derived model-predicted results. The standard errors incurred in predicting the extracted lead concentration for each values of the leaching time and final solution, as evaluated from regression model-predicted results were 6.901 x 10-5 1.5437 % respectively.

4.5. Computational Analysis

Comparative analyses of the extracted lead concentrations evaluated from experimental, derived model-predicted and regression model predicted results were carried out to ascertain the degree of validity of the derived model. This was done by comparing evaluated results of extracted lead concentrations per unit leaching time and per unit final solution pH resulting from the leaching process.

4.5.1. Extracted Lead Concentration Per Unit Leaching Time

Pb/ ϑ (g/dm³ hr^-1) was calculated from the equation;

(9)

Re-written as

(10)

Equation (10) is detailed as

(11)

Where

ΔPb = Change in the extracted lead concentration Pb₂, Pb₁ at leaching times ϑ₂, ϑ₁.

Considering the points (70, 1.4101) & (350, 6.1996), (70, 1.392) & (350, 5.927) and (70, 1.1860) & (350, 6.5174) as shown in Figure 11, and designating them as (Pb₁, ϑ₁) & (Pb₂, ϑ₂) for experimental, derived model and regression model predicted results respectively, and then substituting them into equation (11), gives the slopes: 0.0171, 0.0162 and 0.0190 g/dm³ hr^-1 respectively as their corresponding extracted lead concentration per unit leaching time.

4.5.2. Extracted Lead Concentration Per Unit Final Solution pH

Similarly, substituting into equation (11) points (2.63, 1.4101) & (3.38, 6.1996), (2.63, 1.392) & (3.38, 5.927) and (2.63, 1.1860) & (3.38, 6.5174) culled from Table 1 and Figure 12, as (Pb₁, ξ₁) & (Pb₂, ξ₂) for experimental, derived model and regression model predicted results respectively also gives the slopes: 6.386, 6.0467and 7.1083 respectively as their corresponding extracted lead concentration per unit final solution pH. The proximity between values in each result set indicates significantly high validity level for the derived model.

4.6. Deviational Analysis

Critical Comparative analysis of extracted lead concentrations obtained from experiment and derived model show deviations on the part of the model-predicted values relative to values obtained from the experiment. This is attributed to the fact that the surface properties of the ore and the physiochemical interactions between the ore and bioleaching solution, which played vital roles during the extraction process,were not considered during the model formulation.

This invariably necessitated the introduction of correction factor, to bring the model-predicted extracted lead concentration to those of the corresponding experimental values.

(12)

The deviation Dv, of model-predicted extracted lead concentration from the corresponding experimental result was given by

Figure 13. Variation of derived model predicted concentration of extracted lead with leaching time relative to its associated deviation from experimental results

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Figure 14. Variation of deviation (of derived model predicted concentration of extracted lead from experimental result) with leaching time and final solution pH

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Figure 13 and Figure 14 show that the maximum deviation of the model-predicted concentrations of extracted lead from the corresponding experimental values was less than 15% and quite within the acceptable deviation limit of experimental results. The model operates with a confidence and reliability level range: 91-99.86 %, at recorded deviation range: 0.14 - 8.51 (of the model-predicted extracted lead concentration from experimental results).

Consideration of equation (12) and critical analysis of Figure 5- Figure 8 as well as Figure 13 and Figure 14 show that the least and highest magnitudes of deviation of the model-predicted extracted lead concentration (from the corresponding experimental values) were - 0.14 and -14.93%. This invariably corresponds to extracted lead concentrations: 4.793 and 7.061 g/dm³ hr^-1; leaching times: 280 and 420 hrs as well as final solution pHs: 3.22 and 3.9 respectively.

Table 5. Variation of correction factor (to model-predicted extracted lead concentration) with leaching time and final solution pH

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