Model for Prediction of the Concentration of Extracted Tin during Leaching of Cassiterite in Potassium Hydroxide Solution

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Journal of Minerals and Materials Characterization and Engineering, 2012, 11, 730-734

Published Online July 2012 (http://www.SciRP.org/journal/jmmce)

Model for Prediction of the Concentration of Extracted

Tin during Leaching of Cassiterite in Potassium

Hydroxide Solution

Onyedika Gerald1*, Ugwu Priscilla1, Ogwuegbu Martin1, Ejike Emmanuel1,

Nwoye Chukwuka2, Jiann-Yang Hwang3

1Mineral Processing Unit, Department of Chemistry, Federal University of Technology, Owerri, Nigeria

2Department of Metallurgical and Materials Engineering, Nnamdi Azikiwe University, Awka, Nigeria

3Materials Science and Engineering, Michigan Technological University, Houghton, USA

Email: *[email protected]

Received May 8, 2012; revised June 19, 2012; accepted July 10, 2012

ABSTRACT

Model for prediction of the concentration of tin extracted during potassium hydroxide leaching of cassiterite has been

derived. The model: A = Nt1.53, indicates that the concentration of tin extracted is dependent on the residence time. It

was found that the validity of the model is rooted in the expression LogA = Log(Nt1.53). Tin extraction per unit time as

obtained from experiment and derived model are 2.6666 and 2.6268 mg/min respectively. The maximum deviation of

the model-predicted concentration of dissolved tin from the corresponding concentration obtained from the experiment

was found to be less than 8%, which is quite within the acceptable deviation limit of experimental results and hence,

impacting about 92% confidence coefficient on the model.

Keywords: Model; Tin; Potassium Hydroxide; Cassiterite; Leaching

1. Introduction

Tin presently finds extensive use in industrial and do-

mestic applications. As a result of this, extraction of tin

from ores has continued to attract considerable attention.

Extraction of metals from their ores and recovery from

their various industrial wastes are a major step towards

judicious utilization and conservation of our mineral re-

sources. Various works have been done to extract metals

from their ores [1-4]. Cassiterite, otherwise known as tin

ore is the only tin mineral from which tin can be ex-

tracted in a commercial quantity. Matell [5] studied the

extraction of tin from its ores by reduction of cassiterite

to tin metal and then extracting the tin with aqueous in-

organic acids.

Models are of central importance in many scientific

contexts, useful for testing, analysis or training where

real-world systems or concepts can be represented by a

model [6,7]. One of such models as reported by Hwang

et al. [7] is a numerical simulation of heat transfer during

the microwave heating process of a two dimensional,

magnetic dielectric, magnetite, subjected to heat conduc-

tion, convection and radiation. The heat transfer process

was modeled using an explicit finite difference approach

and the temperature profile for different heating parame-

ters was generated through developing a code in mathe-

matica 7.0.

The derivation of models for the evaluation of the

concentration of some metal values leached in some ores,

concentrates, calcine or other solid materials containing

metal(s) in some aqueous solutions of acids, bases, com-

plexing agents, etc has gained very wide interest among

researchers in recent time. Many models have been evalu-

ated involving the use of different acids for the leaching

of some ores. One of such works as reported by Nwoye

[8] is the model for the computational analysis of the

solution temperature during leaching of iron oxide ore in

hydrochloric acid solution. The model is expressed as:



(1) 



8.9055



(2) 

where T is the solution temperature (˚C) during leaching

of iron oxide ore using hydrochloric acid; N = 8.9055 (pH

coefficient for hydrochloric acid solution during leaching

of iron oxide ore) determined by Nwoye et al. [9];



the final pH of the leaching solution at the time t when the

solution temperature is evaluated.

Nwoye [10] also derived a model for computational

analysis of the concentration of dissolved haematite and

*Corresponding author.

O. GERALD ET AL. 731

heat absorbed by oxalic acid solution used during leach-

ing of iron oxide ore. The models are:

OK%Fe











(3)



(4) 

where

%Fe2O3 = Concentration of dissolved haematite in ox-

alic acid solution;



= Final pH of the leaching solution at time t at which

%Fe2O3 was obtained;

µ = Weight of iron oxide added into the oxalic acid

leaching solution (g);

K = Constant of proportionality associated with heat

absorption;

Q = Quantity of heat (J) absorbed by oxalic acid solu-

tion during the leaching process (J).

Successful attempt has also been made [11] to derive a

model for computational analysis of heat absorbed by

hydrogen peroxide solution relative to the weight of iron

oxide ore added. It is of the form:



e O

%Fe







(5)

where µ is the weight input of iron oxide ore (g); %Fe2O3

and %Fe are the concentrations of dissolved haematite

and iron respectively in hydrogen peroxide solution dur-

ing leaching. The model is rooted on the expression

%Fe



%Fe O where both sides of the relation-

ship are correspondingly almost equal.

The aim of this work is to develop a model for pre-

dicting the concentration of extracted tin during leaching

of cassiterite in potassium hydroxide solution.

2. Materials and Methods

2.1. Materials

The sample of cassiterite ore concentrate used for this

study was obtained from Jos, Plateau State, Nigeria.

2.2. Methods

2.2.1. Leaching Experiment

The ore was crushed to particle size of −212 µm. Con-

ventional leaching experiments were carried out in glass

vessels which were put in a temperature-controlled water

bath. Stirring was carried out using an overhead mecha-

nized stirrer and a glass impeller. 250 ml of the leaching

solution was heated to the desired temperature and then

1.0 g of cassiterite ore was added. Periodic sampling of 5

ml of liquor was drawn for chemical analysis using ICP-

OES (Inductively Coupled Plasma—Optical Emission

Spectrometer).

2.2.2. Model Formulation

Experimental results shown in Table 1 were used for the

model derivation. Computational analysis on the experi-

mental data in Table 1 using C-NIKBRAN (Nwoye,

2008) as shown in Table 2 resulted to Table 3 which

indicates that







1.53

Log LogapproximatelyANt

1.53

(6)

Nt

1.53

0.1898

(7)

Introducing the value of N into Equation (7),

t (8)

where

A = Concentration (mg) of tin dissolved during leach-

ing of cassiterite ore using potassium hydroxide solution;

N = 0.1898, interaction factor between ore and leach-

ing solution);

1.53 = The leachability of the leaching solution.

Equation (8) is the derived model.

2.2.3. Model Validation

This model was validated using the correlation coeffi-

cients (CORREL), sum square techniques (SSQ) and

Table 1. Experimental result of the variation of the concen-

tration of tin obtained with time (conditions: 4 M KOH,

temperature: 80˚C, agitation speed: 500 rpm, particle size:

−212 µm).

Time (min) Aexp (mg)

10 7.2

30 30.8

45 68.9

60 112.0

90 199.3

110 257.6

120 286.8

Table 2. Analysis table showing variation of LogA with 1.53

Logt.

Time (min)Aexp (mg)LogA 1.53 Logt Log0.1898

10 7.2 0.8573 1.5300 −0.7217

30 30.8 1.4886 2.2600 −0.7217

45 68.9 1.8382 2.5294 −0.7217

60 112.0 2.0492 2.7206 −0.7217

90 199.3 2.2995 2.9900 −0.7217

110 257.6 2.4109 3.1233 −0.7217

120 286.8 2.4576 3.1812 −0.7217

O. GERALD ET AL.

732

Table 3. Variation of (LogA) with (Log0.1898 + 1.53 Logt).

Time (min) LogA Log0.1898 + 1.53 Logt

10 0.8573 0.8085

30 1.4886 1.5383

45 1.8382 1.8077

60 2.0492 1.9989

90 2.2995 2.2683

110 2.4109 2.4016

120 2.4576 2.4595

statistical cum graphical methods.

2.2.4. Correlation Coefficients

The correlation coefficient is a measure of the degree of

interaction between process parameters acting as de-

pendent and independent variables.

2.2.5. Sum Square Deviational Method

The sum square deviation is the measure of the goodness

of fit for each point. The difference between the predic-

tion by the model and the observed is value squared

given by the expression:



12 exp

kkY







SSQ Ya

 (9)

It is a direct measure of the accuracy of the average

observation when divided by the number of observations

and the square root taken. The smaller the average dis-

tance, the better the fit.

2.2.6. Statistical and Graphical Method

The validity of the model was established by comparing

the model-predicted values and the experimental values.

Comparison between these two values reveals deviations

which were due to the physiochemical interactions be-

tween the ore and the leaching solution and also due to

the surface properties of the ore, which were found to

have played vital roles during the leaching process [11].

It is then expected that a correction factor be added to

the model-predicted values to make up for those factors

neglected during the model formulation.

The deviation, Dv (%), of model-predicted A values

from the experimental values is expressed as:

Dv d exp

exp

100





Cf Dv

(10)

where

Amod is the model-predicted concentration of tin leached

out, and Aexp is the corresponding experimental value.

Correction factor (Cf), if expressed as the negative of

the deviation, then,

(11)





and

mod exp

exp

100 AA

Cf A





 





(12)

Addition of the corresponding Cf values obtained from

Equation (12) to the model-predicted values of the con-

centration of tin leached gives the exact experimental

values.

3. Results and Discussion

3.1. Results

The results of the experiment on the variation of concen-

tration of tin obtained with time is shown in Table 1,

while that of the analysis of the variation of the model

variables are presented in Tables 2, 3 and 4 respectively.

The effects of residence time on the concentration of tin

dissolved from experiment and as predcted by the derived

model are presented in Figures 1 and 2 respectively. The

graph of the comparison of the results obtained from the

experiment and the derived model is as in Figure 3.

3.2. Discussion of Results

The correlation coefficients R between concentration of

tin extracted and residence time as obtained from the

experiment and derived model (Table 4) were calculated

using Microsoft EXCEL as 0.9942 and 0.9916 respec-

tively. Comparison of these proximate correlation coeffi-

cients indicates validity of the derived model.

The obtained value of the sum squared technique (SSQ)

from Equation (9) and Table 4 is compared with average

sum of the experimental results. The value is 5.92% de-

viation. This confers a high degree validity of 92% con-

fidence coefficient.

The derived model is Equation (8). The comparison of

Table 4. Comparison between concentrations of tin re-

moved as predicted by model and as obtained from experi-

ment.

Time (min)Aexp Amod Dv (%) Cf (%)

10 7.2 6.4313 −10.68 +10.68

30 30.8 34.5376 +12.14 −12.14

45 68.9 64.2261 −6.78 +6.78

60 112.0 99.7396 −10.95 +10.95

90 199.3 185.4758 −6.94 +6.94

110 257.6 252.1314 −2.12 +2.12

120 286.8 288.0338 +0.43 −0.43

O. GERALD ET AL. 733

020 40 60 80

100

150

200

250

300

100 120

Aexp ( mg )

Time ( mi n )

Figure 1. Effect of residence time on the concentration of

dissolved tin as obtained from the experiment.

0 20406080

100

150

200

250

300

100120

Amod ( mg )

Time ( mi n )

Figure 2. Effect of residence time on the concentration of tin

dissolved as predicted by the derived model.

the concentrations of dissolved tin as predicted by the

model (Amod) with those obtained from the experiments

show insignificant positive and negative deviations, hence,

depicting the reliability and validity of the model.

The data on deviations are shown in Table 4. The av-

erage deviation is calculated to be 7.15%, which is quite

within the acceptable deviation limits from experimental

results. The validity of the model is found to be rooted in

Equation (8) where both sides are correspondingly ap-

proximately equal. Table 3 is also in agreement with

Equation (6) where the values of logA is approximately

equal to the value of log (Nt1.53).

The rate of dissolution (concentration of tin dissolved

per unit time) (mg/min) was determined using the ex-

perimental values and the model-predicted values as per

the following equation:

t (12)





Equation (12) therefore, implies that a plot of concen-

tration of tin dissolved against residence time should give

a straight line (Figure 1) with a slope equal to S, where S

is:



 (13)

and ∆A = change in the concentration of tin dissolved (A1,

A2) at times t2, t1.

Figure 1 gives a slope of 2.6666 mg/min, which is the

concentration of tin removed per unit time during the

actual experimental leaching process. Also, a similar plot

(Figure 2) using the model-predicted values gave a slope

equal to 2.6268 mg/min. This is the model-predicted

concentration of dissolved tin per unit time of the leach-

ing process. A comparison of these two rates shows a

proximate agreement, indicating a high degree of validity

for the model. Figure 3 showed that both the values of

the dissolved tin from experiment (line Aexp) and the de-

rived model (line Amod) in relation to residence time are

generally quite close, indicating proximate agreement

and validity of the proposed model.

4. Conclusion

The model predicts the concentration of tin dissolved

during leaching of cassiterite in potassium hydroxide

solution. The validity of the models is rooted on the ex-

pression LogA = Log0.1898 t1.53 where both sides of the

relationship are correspondingly approximately equal. Tin

extraction per unit time as obtained from experiment and

0 20406080100120

100

150

200

250

300 Aexp

A mod

Concentration of tin removed (mg)

time

(

min u tes

)

Figure 3. Comparison of the concentration of dissolved tin

in relation to the residence time as obtained from experi-

ment and derived model.

O. GERALD ET AL.

734

derived model are 2.6666 and 2.6268 mg/min respec-

tively. The average deviation of the amount of the model-

predicted concentration of tin from the corresponding

experimental values was found to be less than 8%, which

is quite within the acceptable range of deviation limit of

experimental results. Also, the rate of dissolution as ob-

tained from experiment and derived model show proxi-

mate agreement, and hence, indicates a very high degree

of validity for the model.

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