Dissolution of a South Africa n calcium based material ...
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Transcript of Dissolution of a South Africa n calcium based material ...
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†To whom correspondence should be addressed.
E-mail: [email protected]
Korean J. Chem. Eng., 29(1), 1-8 (2012)DOI: 10.1007/s11814-011-0136-z
INVITED REVIEW PAPER
Dissolution of a South African calcium based material using urea: An optimized process
Hilary Rutto*,† and Christopher Enweremadu**
*Department of Chemical Engineering, Vanderbijlpark Campus, Vaal University of Technology,**Department of Mechanical Engineering, Vanderbijlpark Campus, Vaal University of Technology,
Private Bag X021,1900 Vanderbijlpark, South Africa(Received 17 February 2011 • accepted 14 May 2011)
Abstract−The rate at which limestone dissolves is very important in wet flue gas desulfurization process (FGD).
High dissolution rates provide better alkalinity, which is important for sulfur dioxide (SO2) absorption. This study inves-
tigates the use of urea to improve the dissolution rate of limestone. The dissolution characteristics have been studied
by using a pH-Stat method. The dissolution rate constant was measured according to the shrinking core model with
surface control, i.e. (1−(1−X)1/3)=krt. The effect of experimental variables such as temperature, amount of urea, solid
to liquid ratio and stirring speed on the dissolution rate of limestone were investigated. Using a central composite design
(CCD) of experiments variables, a mathematical model was developed to correlate the experimental variables to the
dissolution rate constant. The experimental value was found to agree satisfactorily with predicted dissolution rate con-
stant. The model shows that high temperature and low solid to liquid ratio improves the dissolution rate. The dissolution
rate increased slightly with increase in the stirring speed. In the presence of urea the dissolution rate constant increased
by 122%. The dissolution reaction follows a shrinking-core model with the chemical reaction control as the rate-con-
trolling step.
Key words: Temperature, Urea, Dissolution Rate, pH-stat
INTRODUCTION
Wet flue gas desulfurization (FGD) process is the most wide-
spread method of removing sulfur dioxide in thermal power plants
[1-5]. In this process, limestone is dissolved in an absorption slurry
unit where sulfur dioxide from burning coal or oil is converted to a
solid product (CaSO4). However, limestone is insoluble in nature
and does not completely dissolve in the scrubber system. This causes
inefficiency when operating wet FGD system. The dissolution rate
is the rate-controlling step in sulfur dioxide absorption and there-
fore plays an important role in the overall kinetics.
Calcium carbonate kinetics has been studied widely for many
years [6-8]. Siagi et al. [9] investigated the dissolution rate of South
African calcium-based material using HCl solution at constant pH
using a pH-Stat apparatus. Results obtained from the study show
that the dissolution rate increased with an increase in temperature
and a decrease in particle size. The shrinking core model with sur-
face control was in excellent agreement with dissolution results.
Shih et al. [10] investigated the dissolution rate of limestone from
six diverse sources with HCl acid solution using pH-Stat apparatus
at pH 4 and 6. The results showed that the dissolution rate was con-
trolled by mass transfer of H+ accompanied by chemical reaction in
the liquid film surrounding the limestone particle. The calculated
value of the mass transfer coefficient increased with an increase in
pH value and stirrer speed but remained constant with particle size.
Hosten and Gulsum [11] showed that the particle size and dolo-
mite content are the most important parameters that determine the
reactivity. The concept of solubility equilibrium involves the study
of application of chemical principles and constants to predict solu-
bility of substances under specific conditions. The factors affecting
solubility include particle size, temperature, solubility constant the
common ion, salt, speciation, and phase [12].
The dissolution of limestone using additives in acidic medium
has not been fully investigated. Nevertheless Stergarsek et al. [13]
have investigated the use of ammonium salts on the limestone dis-
solution. Using a pilot plant at the Sostanj coal-fired power station,
they observed that the introduction of the ammonium ion does in-
crease the buffer capacity of the absorber slurry, and this increase
corresponds to a decrease in the required liquid/gas (L/G) ratio for
the same absorber performance. The increased buffer capacity was
thought to be caused by the increased concentration of the HCO3
−
ion. The experimental measurements in a pH-stat apparatus showed
that the ammonium ion significantly promotes the limestone disso-
lution rate. The results indicated that the linear dissolution rate con-
stant can be increased by up to 30 times. Takashina et al. [14] have
investigated the effect of the ammonium concentration on the SO2
absorption rate into limestone slurry using a stirred tank reactor at
a constant pH and high temperature (50 oC). The results showed an
improvement in the SO2 absorption rate with increase in ammo-
nium concentration in the limestone slurry. Rutto et al. [15] investi-
gated the use of various ammonium compounds to enhance the dis-
solution rate of limestone. Results showed that addition of 0.5 g of
ammonium nitrate increased the dissolution rate increased by 170%.
Urea is a cheap, biodegradable and non carcinogenic material
that can be added to limestone to produce additional transport of
H+, which can increase the dissolution rate of limestone [16]. Also,
urea may reduce the corrosion effect caused by inorganic acid; this
2 H. Rutto and C. Enweremadu
January, 2012
makes operation more flexible, which improves process reliability
in wet FGD [17]. Urea will save the energy required to pulverize
limestone into fine particles; this will reduce cost in wet FGD sys-
tems.
The main aim of this work is to study the feasibility of utilizing
urea, a source of ammonium ion to improve the dissolution rate of
limestone in wet FGD. A central composite design (CCD) was con-
ducted to study simultaneously the effects of four process variables
on the dissolution of limestone. A mathematical model was subse-
quently developed to correlate the dissolution rate to the process
variables. A kinetic analysis was performed using the shrinking core
model.
MATERIAL AND METHODS
1. Materials
Five types of limestone were obtained from different mines in
South Africa. Chemical analysis of the limestone used is shown in
Table 1.
2. Methods
The raw limestone samples were crushed and ground to average
particle size of 145µm. The particle size distribution was performed
by sedimentation method using a Sartorious balance. The particle
size distribution is presented in Table 2.
In the first step, batch dissolution of limestone from different sources
was carried out at a constant temperature, concentration of HCI so-
lution, solid-to-liquid ratio, and particle size, stirring speed and pH
of 60 oC, 1.00 mol/L, 1.50/200 g/mL, 140-145µm, 200 rpm and 5
respectively.
The cumulative dissolution was determined directly from a re-
cording of HCl added vs. time. The fraction of dissolution (X) was
obtained by the ratio of the volume of HCI acid added to that re-
quired for complete dissolution. The experimental apparatus used is
shown in Fig. 1. The pH in the reaction vessel was measured using
a pH electrode inserted in the solution; this was supplied by Eutech
instruments at resolution/accuracy of ±0.01 pH. If the pH exceeds
the set value, a peristaltic pump adds acid to the reaction vessel and
reduces the pH to the desired value.
Batch dissolution rates for B2 limestone of particle size distribu-
tion shown in Table 2 were varied with temperature, amount of urea,
solid-liquid ratio and stirring speed and measured at constant pH of
5, 1 M HCl solution was used. B2 was chosen because it had the
highest dissolution rate constant.
3. Design of Experiment
The experimental design chosen for this study was a central com-
posite design (CCD); it was used to investigate the linear, qua-
dratic, cubic and cross-product effects of the four experimental par-
ameters on the dissolution rate constant. Table 3 lists the range and
levels of the four independent variables studied. The CCD consists
of a two-level full factorial design (24=16), eight axial orstar points
and six center points. In CCD the value of α was fixed at 2 [18].
The complete design matrix of the experiments employed and re-
sults are given in Table 4.
The experiment sequence was randomized to minimize the effects
of the uncontrolled factors. Each response of the dissolution rate
constant was used to develop a mathematical model that correlates
the dissolution rate constant to the experimental variables through
first order, second order, third order and interaction terms, accord-
ing to the following third-order polynomial equation:
(1)
The experiments were repeated four times and the one close to aver-
age was recorded.
4. Model Fitting and Statistical Analysis
Design expert (6.0.6) software was used for regression analysis
tool to fit experimental data to the third-order polynomial regres-
sion model. The evaluation of statistical significance of the model
Y = βO + βjXj + βijXiXj + βjjXj
2
+ βkijXkXiXj + βjjjXj
3
j=1
4
∑k i j=1, ,
4
∑j=1
4
∑i j=1,
4
∑j=1
4
∑
Table 1. Chemical analysis of calcium based materials from dif-ferent sources
Component B1 B2 B3 B4 B5
AI2O3 05.85 03.58 02.84 05.95 04.48
SiO2 01.83 01.53 04.61 01.53 00.36
Fe2O3 01.93 01.33 01.61 01.83 -
CaO 87.21 91.39 51.34 88.39 53.54
MgO 03.61 01.26 37.24 01.54 36.52
Ignition loss 36.60 46.60 - 36.60 -
Table 2. Particle size distribution of the calcium based materialused
Particle size (µm) (%)
>150 02.5
145-150 03.7
140-145 81.4
135-140 02.6
130-135 02.3
125-130 03.1
120-125 02.6
<120 01.8
Fig. 1. A schematic drawing of the experimental set-up.1. Peristaltic pump 09. Reaction vessel2. pH electrode 10. RS232 Cable3. pH controller 11. Computer work station4. Acid solution Beaker 12. Wiring for pH electrode5. Electronic balance 13. Connection between6. Stirrer 13. pump and controller7, 8. Plastic tubing
Dissolution of a South African calcium based material using urea: An optimized process 3
Korean J. Chem. Eng.(Vol. 29, No. 1)
was developed.
RESULTS AND DISCUSSION
1. Dissolution Rate Constant of Limestone from Different
Sources
Fig. 2 and Fig. 3 show the conversion vs. time and (1−(1−X)1/3)
vs. time of limestone from different mines, respectively. Table 5
shows that B2 had a greater dissolution rate constant, because it
had higher percentage of CaCO3 content, as shown in Table 1. The
presence of magnesium ions reduces the dissolution rate of lime-
stone. This can be seen in the case of limestone B3 and B5: when
magnesium ions are absorbed into the limestone surface dissolu-
tion is inhibited.
2. Effect of Adding HCl Solution
Limestone is soluble in water at low degree. When hydrochloric
acid is added to a stirred limestone, dissolution reaction occurs as
follows:
CaCo3(s)↔Ca2+(aq)+CO3
−2(aq) (2)
HCl is a strong acid and it ionizes according to the following reac-
tion:
Table 3. Levels of experimental variables employed for this study
Variable Coding UnitsLevels
−2 −1 0 1 2
Temperature
Amount of urea
Solid to liquid ratio
Stirring speed
x1
x2
x3
x4
oC
g
g/200 ml
rpm
40
0
1
100
50
0.125
1.875
200
60
0.25
2.75
300
70
0.375
3.625
400
80
0.5
4.5
500
Table 4. Experimental design matrix and results
Sample
code
Experiment variable
Temperature (x1)
(oC)
Urea (x2)
g
Solid to liquid ratio (x3)
(g/200 ml)
Stirring speed
(rpm)
Rate constant
(min−1)R2
C10
C20
C30
C40
C50
C60
C70
C80
C90
C10
C11
C12
C13
C14
C15
C16
C17
C18
C19
C20
C21
C22
C23
C24
C25
C26
C27
C28
C29
C30
50
70
50
70
50
70
50
70
50
70
50
70
50
70
50
70
40
80
60
60
60
60
60
60
60
60
60
60
60
60
0.125
0.125
0.375
0.375
0.125
0.125
0.375
0.375
0.125
0.125
0.375
0.375
0.125
0.125
0.375
0.375
0.250
0.250
0.000
0.500
0.250
0.250
0.250
0.250
0.250
0.250
0.250
0.250
0.250
0.250
1.875
1.875
1.875
1.875
3.625
3.625
3.625
3.625
1.875
1.875
1.875
1.875
3.625
3.625
3.625
3.625
2.750
2.750
2.750
2.750
1.000
4.500
2.750
2.750
2.750
2.750
2.750
2.750
2.750
2.750
200
200
200
200
200
200
200
200
400
400
400
400
400
400
400
400
300
300
300
300
300
300
100
500
300
300
300
300
300
300
14.7
14.9
19.7
21.3
12.7
13.7
14.3
15.1
14.8
15.2
19.9
21.4
12.6
12.9
14.4
15.2
14.9
19.5
10.7
22.7
19.3
11.4
14.3
14.5
12.2
12.3
12.4
12.6
12.5
12.9
0.989
0.997
0.981
0.983
0.988
0.975
0.989
0.991
0.989
0.993
0.996
0.987
0.983
0.984
0.978
0.987
0.988
0.986
0.991
0.987
0.994
0.967
0.978
0.985
0.987
0.998
0.997
0.989
0.987
0.993
4 H. Rutto and C. Enweremadu
January, 2012
HCl(aq)→H+(aq)+Cl−(aq) (3)
The CO3 ions react with hydrogen to form HCO−
3 (aq), the HCO−
3
(aq) further reacts with hydrogen to form CO2 (g) and H2O. This is
shown by reactions (4) and (5), respectively.
CO32−+H+
(aq)↔HCO−
3(aq) (4)
HCO−
3(aq)+H+(aq)↔CO2(g)+H2O(l) (5)
Ca2+(aq)+Cl−(aq)↔CaCl2(aq) (6)
The overall reaction during the dissolution process when lime-
stone is dissolved in HCl solution is as follows:
CaCO3(s)+2HCl(aq)+H2O(l)→CaCl2(aq)+CO2(g)+2H2O(l) (7)
More limestone dissolves because the carbonate is consumed by
reaction (4). Reaction (4) is very fast, and it has been established
by most researchers that rate also depends on the properties of lime-
stone [19-21]. More Ca2+ is consumed by reaction (6) shifting the
equilibrium to the right. Reaction (4) is very instant [22]; its equilib-
rium constant is very large, 2.27×1010 m3/kg mol at 298 K, and there-
fore all the carbonate is converted by this reaction.
3. Effects of Adding Urea
Urea reacts with water at high temperature to form ammonium
carbamate salt.
(NH2)2CO(s)+H2O(l)↔H2NCOONH4(aq) (8)
The ammonium ion in ammonium carbamate salt ionizes as fol-
lows:
NH+4(aq)+H2O(l)↔NH3(g)+H3O
+(aq) (9)
H3O+(aq)↔H+
(aq)+H2O(l) (10)
2H+(aq)+CO2−
3 (aq)↔CO2(g)+H2O(l) (11)
The additional H+ produced when ammonium ionizes causes more
limestone to dissolve as shown in Eq. (11), thereby increasing the
dissolution rate of limestone.
The overall reaction of dissolution reaction when urea is added
to limestone in HCl solution can be written as:
CaCO3(s)+2HCl(aq)+(NH2)2CO(s)+H2O(l)
→CaCl2(aq)+2NH3(g)+2CO2(g)+H2O(l) (12)
4. Kinetic Analysis
To determine the kinetic parameters and the rate controlling step
for the dissolution of limestone, the experimental data are analyzed
on the basis of the sharp interface or shrinking core model (SCM).
From the shrinking core model, the reaction is considered to take
place first at the outer surface of the particle. The zone of the reaction
goes into the solid and the reacting particle shrinks during the reac-
tion, finally vanishing. The following three steps are considered to
occur in series during the reaction [23].
1. Diffusion of the fluid reactant from the main body of the fluid
film to the surface of the solid.
2. Reaction on the surface between the fluid reactant and the solid
3. Diffusion of the fluid reactant through the ash layer to the sur-
face of the unreacted core.
The rate of a non-catalytic heterogeneous reaction is generally
controlled by one of the following steps: diffusion through the prod-
uct layer or the fluid film, or the chemical reaction at the surface of
the core of the unreacted particle. From these steps the rate equa-
tions can be integrated and written as follows:
Table 5. The dissolution rate constant of limestone from differentsources
Sample Rate constant (min−1) S.D
B1 09.4 0.91
B2 10.8 0.89
B3 05.7 1.01
B4 08.9 0.89
B5 06.8 0.77
Fig. 2. Conversion vs. time of limestone from different sources inSouth Africa.
Fig. 3. (1−(1−X)1/3) vs. time of limestone from different sources inSouth Africa.
Dissolution of a South African calcium based material using urea: An optimized process 5
Korean J. Chem. Eng.(Vol. 29, No. 1)
(The film diffusion control) (13)
(The product layer diffusion) (14)
(The chemical reaction control) (15)
By applying Eq. (15) to the experimental data, the apparent rates
constant were calculated. There is a linear relationship between (1−
(1−X)1/3) and the reaction time. In accordance with this result, the
equation representing the kinetic of this process was determined to
obey the chemical reaction model.
(16)
Fig. 4 shows the (1−(1−X)1/3) vs. time for the experiment C1-C6
(see Table 4). From the slope of the straight line dissolution rate
constant is determined.
5. Development of Regression Model Equation
The final equation in terms of actual values after excluding the
insignificant terms is:
Y=60.9−1.3x1+9.5x2−4.9x3−0.03x4+0.01x1
2
Y=+66.2x2
2+0.9x3
2+4.6*10−5x4
2−8.9x2x3 (17)
A positive sign in front of the terms indicates synergistic effect, while
a negative sign indicates antagonistic effect. The quality of the model
could be evaluated from the coefficient correlation. The value of R
for Eq. (17) is 0.971. The high value of R shows that there is a very
good agreement between the experimental and the predicted val-
ues from the model. The R2 for Eq. (17) is 0.943. This implies that
94.3% of the total variation in the dissolution rate response is attrib-
uted to experimental variables studied.
6. Model Adequacy Check
The analysis of variance (ANOVA) is used to check the ade-
quacy of the model as shown in Table 6.
Using a 95% confidence level, the cubic model was tested to be
significant as the theoretical F0.05 (7,12) is much lower than the com-
puted F value (58.4). This indicates that the regression model is re-
liable in predicting the dissolution rate of limestone. From Table 6,
it was observed that among the four individual variables studied,
the amount of urea (x2) has an enormous effect on the dissolution
rate. On the other hand, the solid to liquid ratio (x2) has a similar
effect. The temperature (x3) also affects the dissolution rate. The
stirring speed has very little effect on dissolution of limestone. The
quadratic terms x1 and x2 also affect the dissolution rate but less pro-
nounced than terms x3 and x4. The effect of interaction between x2
and x3 also affects the dissolution rate significantly.
Fig. 5 shows the predicted versus the experimental values using
the model developed. A line of unit slope, i.e., the line of perfect fit
with points corresponding to zero error between predicted and ex-
perimental value, is shown. This plot, therefore, visualizes the per-
formance of the model in an obvious way. The result demonstrates
X = 3bkgCA
ρBRO
-----------------t = krt
1− 3 1− X( )2/3
+ 2 1− X( ) = 6bDeCA
ρBR0
2------------------t = kdt
1− 1− X( )1/3
= 3bksCA
ρBR0
---------------- = krt
krt = 1− 1− X( )1/3
[ ]
Fig. 4. (1−(1−X)1/3) vs. time of limestone for experiment C1-C6.
Table 6. Analysis of variance ANOVA for the regression modelequation and coefficients after removing the insignificantterms
SourceSum of
squares
Degrees of
freedom
Mean of
squaresF-test
Model 301.2 09 33.5 58.4
x1 10.3 01 10.3 17.9
x2 121.1 01 121.1 211.3
x3 90.9 01 90.9 158.6
x4 0.004 01 0.004 0.007
x2
1 36.9 01 36.9 64.4
X2
2 29.3 01 29.3 51.2
X2
3 13.3 01 13.3 23.3
X2
4 5.8 01 5.8 10.1
X2x3 15.4 01 15.4 26.9
Residual 11.5 20 0.6 -
Fig. 5. Experimental versus predicted dissolution rate constant ob-tained from the model.
6 H. Rutto and C. Enweremadu
January, 2012
that the regression model equation provided a very accurate descrip-
tion of the experimental data, indicating that it accurately captured
the correlation between the variables to the dissolution rate.
7. Effect of Urea and Process Variable
The result in Table 4 shows that the process parameters and the
addition of urea have a great effect on the dissolution rate constant.
Varying the process parameter generated different dissolution rate
constant, and also the addition of urea produced sorbent with high
dissolution rate as compared to the sorbent without urea. These re-
sults illustrate that there is a great possibility for improving the dis-
solution rate constant of the sorbent with proper selection of pro-
cess variables. As already established, the sorbent dissolution rate
constant is the key factor to obtain sorbent with high desulfuriza-
tion activity.
There was no maximum within the experimental domain exam-
ined; therefore, the optimum conditions to obtain sorbent with the
highest dissolution rate constant cannot be derived. Hence, a three-
dimensional response surface will be used to facilitate a straight-
forward examination of the effects of the various process variables
on the dissolution rate constant.
Fig. 6 shows the response surface of dissolution rate constant with
varying temperature (x1) and amount of urea (x2). The solid to liquid
ratio (x3) and stirring speed (x4) were held at 2.75 g/200 ml and 300
rpm, respectively. From Fig. 6, when the amount of urea was held
at 0.125 g and 0.375 g, the dissolution rate increased as the reac-
tion temperature increased. When a larger amount of urea was used
(0.375 g) the dissolution rate also increased. This could be attrib-
uted to the fact that the solubility of urea in water increases with an
increase in temperature. This is explained by the additional H+ pro-
duced when ammonium carbamate ionizes; this causes more lime-
stone to dissolve (see Eq. (10)), thereby increasing the dissolution
rate of limestone.
Similarly, Rutto et al. [15] reported that the additional H+ pro-
duced from ammonium compounds improves the dissolution rate.
Furthermore, it has been reported that the dissolution rate of lime-
stone without any additives increases with temperature. Using the
Arrhenius equation, Ahlbeck et al. [21] calculated the activation
Fig. 8. Effect of amount of urea and stirring speed on the dissolu-tion reaction.
Fig. 6. Effect of amount of urea and reaction temperature on thedissolution reaction.
Fig. 7. Effect of amount of urea and solid-to-liquid ratio on the dis-solution reaction.
energy of limestone in dissolution reaction at different reaction tem-
perature. It was found out that the activation energy of limestone
increases with temperature, because the dissolution process is a dif-
fusion-controlled process which is slightly dependent on temperature
and is more of a chemical reaction controlled process which is strongly
dependent on temperature [24]. In other words, surface reaction plays
an important role in the dissolution process in this experiment.
Changes in the dissolution rate constant with varying amount of
urea (x2) and solid-to-liquid ratio (x3) are presented in Fig. 7. The
other two variables were held fixed at zero level. There is an interac-
tion effect between the amount urea (x2) and solid-to-liquid ratio
(x3). This is also confirmed by the analysis of variance shown in
Table 6 (a reasonable high value F).
From Fig. 7 the dissolution rate constant decreases as the solid-
to-liquid ratio increases: when lesser amount of urea is used, there
Dissolution of a South African calcium based material using urea: An optimized process 7
Korean J. Chem. Eng.(Vol. 29, No. 1)
is insufficient H+ produced for limestone dissolution.
Fig. 8 shows the response surface of dissolution rate constant with
varying amount of urea (x2) and stirring speed (x4). The reaction
temperature (x1) and solid liquid ratio (x3) were held at 60 oC and
2.75 g/200 ml, respectively. The effect of stirring speed on the dis-
solution process showed that the dissolution rate constant increases
slightly as stirring speed increases. When 0.125 g and 0.375 g of
urea were used, the dissolution rate constant slightly increased at
stirring speed greater than 300 rpm increased. However the disso-
lution rate constant was higher when 0.375 g of urea was used com-
pared to when 0.125 g of urea is used. This confirms that urea is a
source of H+ (Eq. (10)) and this causes the dissolution rate constant
to increase. The effects of stirring speed on the dissolution rate of
limestone have been studied [25]. The results showed that the dis-
solution rate increases with increasing stirring speed. This was due
to the increase in mass transfer caused by stirring. Several research-
ers have studied the effect of stirring speed on liquid mass transfer
between liquid and suspended particles. Calderbank and Moo-Young
[26] found that convective liquid mass transfer resulting from the
turbulence in the surrounding fluid is independent of particle and is
affected by specific agitation power. Harriott [27] showed that mass
transfer coefficient increases with decreasing particle size for small
particles, but when the particle size is larger than 100µm, mass trans-
fer coefficient is proportional to 0.5 power of the stirring speed.
CONCLUSIONS
This study has demonstrated the feasibility of using urea as a source
of ammonium salt to improve the dissolution rate of limestone, and
hence provide better alkalinity that is important for sulfur dioxide
(SO2) absorption. A central composite design was conducted to study
simultaneously the effects of temperature, amount of urea, solid to
liquid ratio and stirring speed on the dissolution rate of limestone.
It was found that the dissolution rate obeys the shrinking core model
with surface control. A mathematical model was obtained to corre-
late the experimental variables to the dissolution rate constant of
limestone using multiple regression analysis. Analysis of the response
surface derived from the model developed showed that the experimen-
tal variables have significant effect on the dissolution of limestone.
High temperature and low solid to liquid ratio improves the dis-
solution rate. The dissolution rate slightly increased with an increase
in stirring speed. The prospect of being able to synthesize absor-
bent with high dissolution rate can be achieved using urea. Urea
may reduce the corrosion effect caused by inorganic acid, and this
makes operation more flexible, which improves process reliability
in wet FGD.
ACKNOWLEDGEMENTS
The authors wish to thank the unknown referee for the construc-
tive comments and improvements to the manuscript. Authors would
like to thank the department of Mech Eng, Tswane University of
Technology for the facilities.
NOTATIONS
CA : bulk concentration of the fluid [mol/cm3]
De : effective diffusion coefficient [cm2/s]
Kd : apparent rate constant for diffusion through the product layer
[s−1]
Kg : mass-transfer coefficient for the fluid film [cm/s]
Kr : apparent rate constant for the surface chemical reaction [s−1]
Ks : rate constant of surface reaction [cm/s]
S/L : solid-to-liquid ratio [g/mL]
R0 : average radius of solid particle [cm]
t : reaction time [min]
T : temperature [K]
X : converted fraction
ρB : molar density of solid reactant [mol/cm3]
Y : predicated dissolution reactivity [min−1]
βO : offset term
βj : linear effect
βij : first order interaction effect
βjj : squared effect
βkjj : second order interaction
βjjj : cubic effect
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