FACTORIAL ANALYSIS OF HYDRATED LIME PRODUCTION
FROM QUICK LIME
Salisu Nuhu
a
Department of Polymer Technology School of Science And Technology
Hussaini Adamu Federal Polytechnic Kazaure, Jigawa State,Nigeria
a
Email: salis4real29@yahoo.com
Abstract The most stable form of lime produced by the interaction of calcium oxide with
water is slake lime. This reaction process is a typical occurrence in industry. Due to the
influence of certain operation parameters, including the source of the lime, the chemistry of
the slaking water, the level of agitation, the water to lime ratio, and the water temperature,
the slaking process can be quite difficult. The outcome of the factorial analysis interaction
also reveals the significant influence that stirrer speed, water temperature, and water
calcination carbonate concentration have on the reactivity of hydrated lime. The results of
the factorial study indicate that when the slaker stirrer speed is high, the increase in
hydrated lime reactivity is greater as the water temperature is changed from the high level
(70 oC) to the low level (28 oC). ) than when it is low (400 rpm for the slaker stirrer) ( 100
rpm). Additionally, when quicklime was slaked with water with a calcium carbonate content
of 200 mg/L at a temperature of 28C using a slaker stirrer speed of 400 rpm, the best
hydrated lime reactivity of 0.5351 oC/s was obtained. The hydrated lime producing
businesses can utilize the factorial empirical model created in this study to determine the
parameters of the lime slacking process that will maximize hydrated lime quality. This will
enhance sales, reduce product returns, and improve consumer satisfaction with hydrated
lime purchases.
Key: lime, factorial analysis, calcination
Introduction
Due to the abundance of limestone in Nigeria and the need for economic
diversification, commercial quicklime manufacturing from limestone development is
a necessity. Sodium carbonate, glass, cement, steel, and quicklime are just a few of
the industrial products that may be made using limestone as a raw material ( Akande
2015). Quicklime, a solid substance created by the thermal disintegration of
limestone from which carbon dioxide gas is released, is hydrated to form white
powder and releases a significant amount of heat. Due to its chemical, physical, and
mineralogical characteristics, as well as its commercial importance and ease of
manufacturing, hydrated lime is an important mineral ( Akande, 2015). Lime is one of
the most extensively used and least expensive alkalis utilized globally. It is frequently
used as slacked calcium hydro oxide slurry in chemical processes. Calcium
hydroxide is created when un-slaked lime from limestone is calcined and combined
with water to create calcium hydroxide. The desired outcome is the species of
calcium hydroxide ( moja etal.2001)
Aim and Objectives of the research
Utilizing an experiment methodology, factorial analysis is applied to the manufacture
of hydrated lime
The goals are to
*Identify the quick lime slaking process parameters ( slaker, stirrer speed,
water temperature and water calcium carbonate concentration ) that have
significant effect on hydrated lime reactivity.
*identify the optimal setting of the slaking process parameters parameters
( slaker, stirrer speed, water temperature and water calcium carbonate
concentration ) that will maximize hydrated lime reactivity.
Material and Methods
The major equipment used is briefly described in Table 3.2
Sample Collection
The quicklime used was produced from Obajana Limestone found in Kogi state.
Various samples from the deposit site were picked randomly for the purpose of
research work.
Sample Preparation
Prior to the experiment, the limestone sample collected was washed clean and dried
to remove external impurities. The limestone sample was crushed using jaw crusher
2-4 cm. the sample was grinded using Ball Mill grinding machine. The sample was
collected and sieved using mechanical agitator with different Tyler mesh arranged to
obtain a particle sizes of ( 80µ, 100µ, 210µ,300µ,400µ, and 450µ microns. The 450µ
was weighed and introduced into a Carbolite Furnace with a temperature of of 900
O
C for about 60 min the quicklime obtained from calcination was slaked in a
quicklime slaker for different types of water and also at different water
temperature(S). The hydrated lime produces was analysed using various techniques.
REULT AND DISCUSSION
Factorial analysis method Results
The FAM screen calcination process variable by determining the calcination variable
that have significant effect on output response using factorial analysis.The factorial
analysis software selected for implementing FAM is Minitab 17 software.
Table 3.1: Chemical Used in their Specification
S/NO
1
o
Chemical
Purity %
Distilled
Water
(DW)
Well Water ( WW)
2
Table 3.2: List of Equipment
S/No Equipment
1.
Gyratory jaw crusher
2.
Ball Mill
3.
Mechanical sieve agitator
4.
Carbolite furnace
5.
Electronic
balance
Model/Year
AAF/11/18/2012
weighing
Boiling Point C
Manufacturer
Pascal
Engineer
Corporation Limited
Pascal
Engineer
Corporation Limited
Pascal
Engineer
Corporation Limited
Pascal
Engineer
Corporation Limited
Pascal
Engineer
Corporation Limited
.
Factorial Analysis Methodology
This methodology screens the calcination process variables by determining the
calcination variables that have significant effect on output responses using factorial
analysis. The factorial analysis software selected for implementing the factorial
analysis methodology is Minitab 17 software.
3.3.1 Factorial analysis experimental matrix determination
The geometric and experimental designs of the factorial analysis are shown in Figure
3.3 and Table 3.3 respectively.
Figure 3.3. Geometric design of three factors at two level settings
Where
- represents low level setting
+ represents high level setting
Factor A = Temperature = x1
Factor B = Time = x2
Factor C = Particle size = x3
The number of experimental run required for the factorial analysis experimental
matrix was determined using Equation 3.4.
N
3
No of Experimental Run = (L )R = (2 )2 = 16
3.4
The factorial analysis experimental design matrix for the three factors and each of
the sixteen experimental runs was generated using Minitab 17 software and the
result is shown in Table 3.3.
Table 3.3. Experimental Design and response factors of Factorial Analysis of
Hydrated lime production in a slaker
Water
Water
calcium
Slaker stirrer
temperature
Reactivity (C/s)
Run
1
2
3
4
5
6
7
(speed)
(rpm)
+
+
+
+
+
-
(OC)
+
+
+
carbonate
(mg/L)
+
+
-
8
9
10
11
12
13
14
15
16
+
+
+
+
+
+
+
+
+
+
+
-
-
Limestone calcination Experiment
Factorial Analysis Results
The results and discussion of factorial design analysis, of hydrated lime production
from quick lime in a slaker, which methodology was presented in this section .the
factorial analysis was carried out using Excel 2013 and Minitab release 17.
Table 3.4. Experimental Design and response factors of Factorial Analysis of
Hydrated lime production in a slaker
Water
Slaker stirrer
temperature
Water calcium Reactivity (C/s)
Run
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
(speed)
(rpm)
400
400
400
100
100
400
100
100
400
400
100
100
400
400
100
100
O
( C)
28
28
70
70
28
70
70
70
28
70
28
28
70
28
70
28
Carbonate
(mg/L)
200
2000
200
200
200
2000
200
2000
2000
2000
2000
200
200
200
2000
2000
0.547987013
0.481509434
0.279259259
0.218834356
0.179272727
0.245477707
0.216319018
0.164910179
0.45931677
0.248301887
0.155266272
0.181333333
0.281358025
0.522222222
0.178181818
0.162071006
The next procedure carried out in the factorial analysis methodology is the
determination of the calcination process responses, which was done by carrying out
calcination, yield and reactivity experiments.
.
Factorial analysis experimental matrix quicklime yield determination methodology
The yield of calcined Eggshell composite (quicklime) produced was determined
according to ASTM C25.19 using Equation 3.2. The experimental procedure is
described below.
For each varied calcination temperature, the loss on ignition and the yield of the
quicklime produced from calcination experiment were calculated using Equations
3.1 and 3.2 respectively. The loss of mass on ignition (LOI) is the loss of carbon
dioxide released during thermal decomposition of Eggshell composite. It is the
actual material lost during the calcination of the Eggshell composite in the furnace. It
is mathematically given as described in the Standard ASTM C25.19 method and
Meieret al . (2004):
A-B
LOI =
%
3.1
C
Where
LOI is the Loss of mass on ignition
A is the mass of crucible + Eggshell composite sample before
calcination in grams
B is the mass of crucible + Eggshell composite sample after
calcination in grams
C is the mass of the Eggshell composite sample charged into the
calciner in grams.
The yield of quicklime which is a measure of degree to which the Eggshell composite
was calcinated to produce quicklime, defined by Meier et al . (2004) is shown in
Equation 3.2.
LOI
Yield =
3.2
0.4392
The computation of LOI and quicklime yield using Equations 3.1 and 3.2 was done
using Microsoft Excel and it is shown in Appendix B. The results of Eggshell
composite LOI and quicklime yield for Eggshell composite are shown in Appendix B
respectively
Factorial Analysis Results
The results and discussion of factorial design analysis, which methodology was
presented in section 3.3are presented in this section. The factorial analysis was
carried out using Excel 2013 and Minitab release 17. Microsoft Excel 2013was used
to validate model results with experimental results using Mean Absolute Percentage
Error (MAPE)statistical parameter.
Table 3.5 Response Factors (Quicklime Reactivity and Yield) for Factorial Analysis of
Eggshell CompositeCalcination Experimental Design
Experimental
Run
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Calcination
Temperature
(oC)
600
600
600
900
600
900
900
900
600
900
600
900
600
900
900
600
Calcination
Time (min)
30
30
150
30
150
150
150
150
150
30
150
30
30
150
30
30
EggshellParticle
Size (mm)
0.1
0.45
0.1
0.1
0.1
0.45
0.1
0.1
0.45
0.45
0.45
0.1
0.1
0.45
0.45
0.45
EggshellQuicklime
Yield [R(oC/s)]
3.4571
1.8899
13.0611
89.3264
13.29
88.9174
93.5232
94.0473
8.5664
85.8504
6.7904
88.1304
4.6252
89.5973
85.0209
3.5045
For this analysis, the t-distribution, coefficients, P-values and estimated effects for
the experimental results were obtained. The sum of squares and the F-distribution
were also determined. The 95% confidence level was used for the statistical
calculations.
The effect defined as the increase or decrease of the quicklime yield and reactivity
when process factor was changed was also determined. A negative effect indicates
a decrease in quicklime yield and reactivity as the process factorsetting is increased.
A positive effect designates an increase in quicklime yieldand reactivity as the
process factorsetting is increased. The effect magnitude used in ranking the
influence of the factors on the experimental results. The regression Equation
coefficients were also acquired from the fit of the quicklime yield results. The
statistical significance of a particular result based on the sample means were
determined using F and T distributions. Values for the t- and F-distributions were
compared to tabulated values based on the number of degrees of freedom and 95%
confidence interval. If the tabulated value is less than the calculated value, then a
particular result was pronounced statistically significant. The P-value is the smallest
level of significance that would lead to the rejection of the null hypothesis and the
conclusion that data is statistically significant (Montgomery, 1999). Also, if the Pvalue is <0.05, then the factor is significant statistically at the chosen 95%
confidence level. A replicated full factorial experimentwas conducted to evaluate the
interaction and main effects of calcination variablesin quicklime production by
thermal decomposition of Eggshell Composite. The full factorialdesign presented in
Table 3.3 and their encoded values are shown in Table 4.3.
Factorial analysis results showing effects of calcination temperature,
calcination time and Eggshell Composite particle size on quicklime yield
The factorial design quicklime yield test result is shown in Tables 4.3of section 4.3.1.
Calcination process factors used are calcination temperature, calcination time and
Eggshell Composite particle size.
The P-values, coefficients and t-distribution and effectsfor the quicklime yield are
given in Table 4.7.The P-values and the t-distribution were determined to test the
statistics significance. The statistics is considered significant whenthe P-value
isless than 0.05 for 95% confidence level. Table 4.7shows that quicklime yield
factorial designsare significant except Time*Eggshell Composite Particle Size
Interaction. The reason for this exception is that calcination temperature is the prerequisite and predominant factor required for thermal decomposition of
EggshellComposite to occur and Time*Eggshell Composite Particle Size term does
not have interaction with temperature.
Table 4.7. Factorial Design Analysis for Estimated Effects and Coefficients for
Quicklime Yield
Term
Effect
Coef
P-Value
Constant
48.100
0.000
Temperature
82.404
41.202
0.000
Time
5.749
2.874
0.000
Particle Size
-3.665
-1.833
0.000
Temperature*Time
-1.309
-0.655
0.011
Temperature*Particle Size
-0.245
-0.122
0.553
Time*Particle Size
-1.347
-0.674
0.009
Temperature*Time*Particle Size
0.730
0.365
0.103
Table 4.7further reveal some important information regarding the main and
interaction effects have on the quicklime yield. The main effects, of temperature,
time and Eggshell Composite particle size have effects numbers of 82.708, 6.130
and -3.301 respectively. The magnitude of the effect of temperature is approximately
eleven times higher than time twenty times higher than Eggshell Composite particle
size because it is the predominant factor required to drive the thermal
decomposition reaction to equilibrium. Dogu (2000) reported that calcination
temperature is the driving factor for dissociation of Eggshell Composite into CaO
and CO2 and the factor required in overcoming the energy barrier (lowering of the
activation energy) required for decomposition of Eggshell Composite to occur. All of
the effect numbers are positive except Eggshell Composite particle size as increase
in calcination temperature and time results in increase in quicklime yield. Eggshell
Composite particle size is negative as increase in its value led to decrease in
quicklime yield. Hu and Scaroni (1996) reported that calcination rate of thermal
decomposition of Eggshell Composite is location-dependent and smaller Eggshell
Composite particle produced quicklime of higher yield and reactivity than smaller
Eggshell Composite particle. Also, the three main effects are significant statistically
at the 95% confidence level. Calcination temperature produced the largest change in
quicklime yield compared to all other factors because it the highest effect number.
Thus, increasing the setting of the calcination temperature increased the quicklime
yield the most. All two- and three-factor interactions have smaller effect numbers
than those of the single-process factors. The results for the factors interaction
demonstrate that there is an effect on the quicklime yield when different process
factors are combined. The order of the effects and statistical significance of the
formulation can be represented graphically in a Pareto Chart. A Pareto Chart is a bar
graph that shows information in order of magnitude to graphically show the relative
importance of the differences between groups of data. The Pareto Chart for the
quicklime yield is shown in Figure 4.33. The red line represents the 95% confidence
level. If the bar representing a formulation does not cross this line the effect of the
quicklime yield is not statistically significant. Again, this graph shows all single and
multiple process factors effects are significant for the main effects,
Temperature*Time, Temperature*Eggshell Composite Particle Size and
Temperature*Time*Eggshell Composite Particle Size at the 95% confidence are
significant. Shukla (1988) has shown that calcination temperature, calcination time
and Eggshell Composite particle size play significant role on thermal decomposition
of Eggshell Composite.
Figure 4.33. Pareto Chart of the Standardized Effect for Quicklime Yield Response
Main effect plot of the fitted means of Figure 4.34 indicate the following:




Temperature: Calcination temperature produced higher yield at temperature
of 1
900 oC than at temperature of 600 oC as the fitted mean increased from 11 to
94% respectively. This reason can be attributed to CO2 (Loss on Ignition)
being continuously released as Eggshell Composite is thermally decomposed
until only CaO is left in the quicklime product (Bogwardt, 1985).
Time: Calcination time produced higher yield at low calcination time (30 min)
than at high time (60 min) as the fitted mean decreased from temperature of
48 to 54% respectively. Zhong and Bjerle (1993) reported that calcination time
has synergistic effecton quicklime yield and high residence time in kiln will
provide enough time for continuous release of CO2 (Loss on Ignition) as
EggshellComposite is thermally decomposed until only CaO is left in the
quicklime product (Bogwardt, 1985).
Eggshell Composite Particle Size: smaller Eggshell Composite particle size
(0.1 mm) produced quicklime of higher yield than bigger Eggshell Composite
particle size (0.45 mm) as the fitted mean decreased from 52 to 48 %
respectively.Hu and Scaroni (1996) reported that the calcination rate is
location-dependent and smaller Eggshell Composite particles produced
quicklime of higher yield and reactivity than smaller Eggshell Composite
particles.
Figure 4.34.Main Effect Plot for Quicklime Reactivity Response
Table 4.8 shows the ANOVA Table for the quicklime yield. The SS, MS and Fdistribution numbers all follow the same order as the rank of effects in the factorial
design analysis and the Pareto Chart. According to the P-values reported in the
ANOVA Table, all of the process factors were in the 95% confidence level. The
ANOVA results support the previously obtained results of coefficient and main effect
results of Table 4.7.
Table 4.8. Analysis of Variance (ANOVA) for Quicklime Yield
Source
P-Value
Model
0.000
Linear
0.000
Temperature
0.000
Time
0.000
Particle Size
0.000
2-Way Interactions
0.010
Temperature*Time
0.011
Temperature*Particle Size
0.553
Time*Particle Size
0.009
3-Way Interactions
0.103
Temperature*Time*Particle Size
0.103
Normal plot of the standardized effect for quicklime yield response of Figure 4.35
also shows that there are three significant effects ( = 0.05). These significant
effects include all the three main effects  calcination temperature (A), calcination
time (B) and Eggshell Composite particle size (C). Calcination temperature (A) has
the largest effect because it is the furthest from the line. In addition, the Figure
shows the direction of the effect. Calcination temperatures (A), calcination time (B)
and the combined effects of temperature, time and particle size (ABC) reside to the
right of the line and they all have positive effects. This means quicklime yield
increases when process variables change from the low to high level. Because
Eggshell Composite particle size (C) and the combination of temperature and
particle size (AC) resides to the left of the line, it has a negative effect, meaning that
quicklime reactivity decreases when the calcination time and Eggshell Composite
particle size change from the low level to the high level.
Figure 4.35.Normal Plot of the Standardized Effect for Quicklime Reactivity
Response
For the half normal probability plot of quicklime yield of Figure 4.36, there are three
significant effects ( = 0.05). All three main effects calcination temperature (A),
calcinations time (B)and Eggshell Composite particle size (C) is significant.
Calcination temperature (A) has the largest effect because it lies furthest from the
line. Thehalf normal probability plotproduces the same rankings as previously
discussed for the order of process factors effects and their combination on
quicklime yield from Pareto plot, Normal Probability plot and Estimated Effects and
Coefficients for quicklime yield.
Figure 4.36.Half Normal Plot of the Standardized Effect for Quicklime Yield
Response
Since the lines of interaction plot of quicklime yield of Figure 4.37 are parallel to each
other, there may be no interaction present, this due to synergistic effect between
temperature and time on quicklime yield. The plot also shows that a movement of
the response mean from the low to the high level of calcination temperature is
independent of the level of calcination time. The plot indicates that the degree of
departure of the two lines of Figure 4.37 and Figure 4.38 from being parallel is
greater, this infer that the effect isstronger. The plot indicates that the increase in
quicklime yield is greater as the calcination time is moved from 30 min to 150 min
when the calcination temperature is high (red line) than when it is low (black line).
The lines of interaction plot of quicklime yield of Figure 4.37 are slightly not parallel
to each other; there may be presence of small interaction present. This occurs
because of the antagonistic effect between temperature and Eggshell Composite
particle size on quicklime yield. The plot indicates that the increase in quicklime yield
is greater as the calcination time is moved from 1.18 mm to 0.3 mm when the
calcination temperature is high (red line) than when it is low (black line).
Figure 4.37.Temperature-Time Interaction Plot for Quicklime Yield Response
Figure 4.38. Temperature-Eggshell Composite Particle Size Interaction Plot for
Quicklime Yield Response

The cube plot of Figure 4.39 illustrates that if Eggshell Composite of smaller
particle size (0.1 mm) is used, the calcination temperature is high (900oC) and
calcinations time is high (150 min), the quality of quicklime yield is 96.7837%.
This is corroborated by the work of Zhong and Bjerle (1993) and Bogwardt
(1985) that quicklime yield is increased when Eggshell Composite is calcined
at high temperature, high residence time and smaller Eggshell Composite
particles are used.
Figure 4.39.CubePlot for Quicklime Yield Response
Contour plot of quicklime yield against time and temperature of Figure 4.40 shows
how quicklime yield relates to soaking time and calcination temperature. The darkest
green area indicates the contour where the quicklime yield is highest (greater than
80%) while holding Eggshell Composite particle size at 0.1 mm. To maximize
quicklime yield, the settings for calcination temperature and calcination time should
be chosen.
Figure 4.40.Contour Plot of Quicklime Yield against Time and Temperature
Figure 4.41 shows the plot of residual against fitted values for quicklime yield. The
residuals follow a straight line. Also, evidence of skewness, outliers and non-
normality does not exist. This Figure shows the residuals follow the normal
probabilitydistribution as all points scatter around a straight line.
Figure 4.41.The Normal Probability Plot for Quicklime Yield
Figure 4.42 shows the plot of residual against fitted value for quicklime yield. The
residuals of Figure 4.31 are randomly scattered about zero. The plot does not show
presence of outliers, missing terms and non-constant variance. In otherwords, the
predicted values variation is constant, irrespective of whether their values are small
or large.
V e r su s F it s
( r e sp o n se i s Q u i c k l i m e Y i e l d )
1 .0
R e si d u a l
0 .5
0 .0
- 0 .5
- 1 .0
0
10
20
30
40
50
60
70
80
90
Fitted V alu e
Figure 4.42.The Plot of Residual against Fitted Value for Quicklime Yield
Figure 4.43 shows the plot of residual against observation order for quicklime yield.
The residuals is randomly scattered about zero. Also, there is no suggestion that the
error terms are interrelated to one another. This shows that the residuals scatter
randomly.
Figure 4.43.The Plot of Residual against Observation Order for Quicklime Yield
Based on normal probability plot, residual against fit plot and the residual against run
order, the estimated regression model is adequate. The model Equation can be built
from estimated coefficients for quicklime yield of Table 4.7.
Ypy = 49.061 + 40.287x1 + 3.763x2 - 1.975x3 - 0.534x1x2 - 1.031x1x3 + 0.531x1x2x3 +
2
2
2
3.245x1 - 3.245x2 + 3.245x3
4.2
x1:The calcination temperature which has two levels coded 1 and - 1
x2:The calcination time which has two levels coded 1 and - 1
x3:The Eggshell - Snail shell Composite particle size which has two levels coded 1 and - 1
Ypy = Predicted Quicklime yield (℃/s)
Calcination temperature X1 =
Calcination timeX2 =
level
{-1,1, high
low level
level
{-1,1, high
low level
Eggshell Composite particle sizeX1 =
level
{-1,1, high
low level
Based on Main Effect plot, the combinations of factors that will produce the highest
quicklime reactivity are:



High level of calcination temperature of 900 oC.
High level of calcination time of 150 min
Low level of Eggshell Composite particle size of 0.1 mm.
Based on Interaction plot, the combinations of factors that will produce the highest
quicklime Yield are:



High level of calcination temperature of 900 oC and high level of calcination
time of 150 min.
High level of calcination temperature 900 oC and low level of Eggshell
Composite particle size of 0.1 mm.
High level of calcination temperature of 900 oC, high level of calcination time
of 150 min and low level of Eggshell Composite particle size of 0.1 mm.
The model Equation via the combination above of main effects and the Interaction
plot is:
Y
= 49.061 + 40.287(1) + 3.763(1) - 1.975(-1) - 0.534(1)(1)
-1.031(1)(-1) + 0.531(1)(1)(-1) = 95.052
CONCLUSION AND RECOMMENDATIONS
This study has demonstrated the application of factorial analysis in determining
calcination parameters that are having significant effect on quicklime yield. The
magnitude of the effect of the calcination parameters and their interaction were also
investigated using factorial analysis. The factorial empirical model developed were
presented as contour and surface plots in order to explore the model region of
operability and have a better understanding of the calcination process.
The following conclusions were obtained.
 From the factorial analyses, the, temperature time and particle size have
significant effect on the quicklime yield.
 The factorial analysis also suggested that there is a significant interaction
between calcination time and particle size to produce quicklime of high yield.
 Also, optimal quicklime yield of 93.7853 was obtained when quicklime was
calcined with particle size of 0.1mm and temperature of 150 min.
5.2
Recommendations
This study has demonstrated the application of factorial analysis in determining
calcination parameters that are having significant effect on quicklime yield. Through
this study, it has been found that, there are some areas that would benefit from
additional study. These areas include:
 Optimization of quicklime production from Eggshell composite in calciner
should be investigated.
 Determine the significance of other calcination parameters such as rotating
speed and inclination angle of calciner on quicklime yield using factorial
analysis should also be investigated.
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