An Investigation into the Kinetics of Reaction between Fluorspar and Sulfuric Acid
D. Candido and G. P. Mathur*
Department of Chemical Engineering, University of Windsor. Windsor, Ontario, Canada
The reaction between fluorspar and sulfuric acid has been investigated in a batch as well as a continuous reactor system. Experiments were carried out in the temperature range 250-450°F. The batch reactor, operated isothermally, provided data for initial screening of postulated rate models. The continuous reactor was designed for operation under conditions that closely simulated industrial practice. Tracer methods were used to ascertain reactor flow patterns. Three rate models were found to yield equally
satisfactory correlations for both the batch and the continuous reactor data.
A. Reaction System
Hydrogen fluoride can be produced by contacting fluorspar with concentrated sulfuric acid. The reaction
CaF,
+ HISO,
-
+
2HF
CaSO,
(1)
is endothermic. Although CaF2 is the major constituent of
fluorspar, CaC03 a n d S i 0 2 are also present in small quantities (see Table I). These lead to the following side reactions, lowering the yield of hydrogen fluoride
CaCO.
+ H$O,
4HF
-
--*
+ SiOl
+ H20 +
CaSO,
SiF,
+ 2H,O
COI
("1
(3)
Traube and Reubke (1921) showed t h a t an additional
reaction can occur under certain reaction conditions according to the equation
HF
+
HISO: f FSO,H
+
H?O
(4)
Although as much as 7% of the CaFz may be converted to
fluorosulfonic acid a t 80",the extent of conversion to fluorosulfonic acid decreases rapidly with a rise in temperature and approaches zero a t 100" (Traube and Lange,
1924).
B. Previous Investigations
Puxley and Woods (1948) have reported batch d a t a for
the temperature range 125-225". They used a heated platinum crucible stirred with a platinum bar. Their data suffer due to lack of temperature control in their set up.
Puxley and Woods' d a t a may be correlated by a zero-order
reaction rate model of the form (Mathur and Candido,
1967)
-d,V/dt
=
k
(5)
where N is in g mol of CaF2. Equation 5 is found to be
valid for conversions u p to 50% with
fl
=
().J~e-'4"o
N7'
(6)
Recently, Ostrovskii and Amirova (1969) conducted
batch experiments on the fluorspar-acid reaction by suspending a platinum dish in a 1 in. diameter steel tube
furnace which was maintained within k 2 " . Dried air was
passed through the tube a t a rate of 5 l./hr. The extent of
reaction was determined by following weight us. time.
They used 99.2% sulfuric acid and fluorspar of 98% purity.
The temperature range in their investigation was 85-145".
Ostrovskii and Amirova (1969) concluded t h a t in this
temperature range, the reaction proceeds in the kinetic
region until a conversion of 56-60% is reached. They fitted
their d a t a by the following equation
( 1 - sH)-?
- 1 = kt
(71
20
Ind. Eng. Chem., ProcessDes. Develop., Vol. 13, No. 1, 1974
where X H is the fractional conversion, t is the reaction
time, and k is the rate constant ( m i n - l ) given by the following expressions
h
I:
=
=
7.75 x 1Ol0 exp[-20,800/RT] 85
- 100"
1.38 X 10, exp[-9200/RT] 105 - 145"
(81
Ostrovskii and Amirova attributed the break point a t
about 100" to the formation of fluorosulfonic acid below
100".
C. Present Work
The present investigation was undertaken to obtain further experimental d a t a on the fluorspar-sulfuric acid
reaction. It was decided to obtain data on the reaction
under flow as well as batch conditions. The continuous reactor system was designed so as to yield rate data t h a t
may be useful for scale up. However, as the number of
physical parameters that may affect the observed rate is
quite large and their mutual interaction quite complex, it
was decided to study only the effects of temperature and
composition change keeping the other physical parameters
a t certain preselected levels (shown in Table 11). In addition, batch data were obtained to supplement t h e continuous reactor data. As stated earlier, no reliable batch d a t a
currently exist in the temperature range of interest (250 to
450°F).
(i) Thermodynamic Considerations. In order to determine if any of the reactions of interest are affected by a n
equilibrium, the free-energy change for each reaction was
computed from standard free-energy, enthalpy, and heat
capacity data. For the temperature range 125-275" the
free-energy changes for all three reactions of interest (eq
1, 2, and 3) exceed -10 kcal/g mol, indicating irreversible
reactions (Mathur and Candido, 1967).
The heats of reaction were also calculated. AHr for
reaction 1 varies from +11.3 kcal/g mol a t 125" to +9.9
kcal/g mol a t 275". Reactions 2 and 3 are highly exothermic.
(ii) Experimental Setup. (a) The Continuous Reactor.
A schematic view of the experimental assembly is given in
Figure 1. The reactor itself was a flanged, &in. diameter,
14-in. long steel pipe. Semicylindrical heaters were used
to heat the reactor body and flange heaters were employed
to eliminate axial temperature gradients.
All temperatures were recorded on a strip chart recorder. The central temperature was maintained constant
( k 5 " F ) by use of a proportional controller that controlled
power input to the semicylindrical heaters. Manually controlled transformers were used to control the flange heaters t h a t maintained the temperatures a t the reactor ends
a t the same level as the central temperature.
Table I. Typical Fluorspar Composition after
Flotation of the Ore.
Wt %
CaF?
CaCOr
Q
93.9
3.5
iI 1JL$
Wt %
SiO,
RzOr
1.44
0.10
UENT
Mean particle size = 27 p.
Sulfuric acid was pumped through Teflon tubing by
means of a variable speed tubing pump. The acid passed
through a rotameter for metering and then through Teflon
tubing wrapped with heating tape to bring its temperature to about 200°F prior to entry into the reactor.
To maintain accuracy in the acid feed rate, the acid
was heated to a constant temperature (39") prior to its
passage through the rotameter. The heating was accomplished by passing the acid through a glass coil immersed
in a constant-temperature bath. The accuracy of the acid
feed rate was better than 1%.
The spar feed system consisted of two hoppers in a series arrangement. Fluorspar was metered by means of a
variable-speed screw into a second hopper equipped with
a larger ronstant-speed screw to force the solids into the
reactor.
The spar flow was monitored during the running of the
reactor and slight deviations from the desired flow rate
were quickly and easily corrected. The accuracy of the
solids feed system was also better than 1%.
The reactor contents were mixed by means of four 1-in.
wide paddles. Two of the paddles were 7 in. long and the
other two were 6 in. long. The paddles were pitched to
move the solids from the feed end to the outlet. The 7-in.
paddles a t the feed end were coated with Stellite to prevent excessive corrosion. Clearance between the paddles
and the reactor wall was kept to a minimum. A +4 hp
motor was used to rotate the paddles a t speeds from 1 to
44 rpm.
The solid products were removed from the reactor by
means of a varidble-speed 1-in. diameter screw auger.
The gaseous products were drawn out of the reactor
through a 1-in. Teflon tube wrapped with heating tape.
The vacuum and the scrubbing action was provided by a
jet ejector scrubber. Sodium carbonate solution was used
in the scrubber. Complete scrubbing of hydrogen fluoride
was confirmed by testing the exhaust gases for fluorine
content.
The procedure followed in carrying out each run was as
follows.
The spar and acid feed rates were pretested for accuracy a t the desired flow rates. Recalibration of the acid
rotameter was done as an extra precaution against large
shifts in the rotameter calibration that can be caused by
slight changes in acid concentration. The reactor was preheated to the desired temperature and the spar and acid
feeding was begun. After 4 hr of operation a small amount
of nickel sulfate (tracer) was added. Samples (of the solids out) for tracer analysis were taken for the next 4 hr.
After tracer addition ( 2 hr), six solids out and scrubber liquor samples for analysis were taken simultaneously with
the tracer samples. These samples were chemically analyzed to determine the extent of conversion of calcium fluoride.
(b) Batch Reactor. A batch reactor was constructed
and operated to supplement the data from the continuous
reactor. The batch reactor consisted of a 3-in. diameter
steel pipe, 4.25 in. high, with a YB-in. thick steel plate
welded to the bottom. The reactor wall was machined to a
Y8 in. thickness. A thermocouple was located centrally on
the flange and extended 0.5 in. into the reactor. Electrical
heaters were used on the bottom plate as well as-the walls.
Figure 1. Schematic of reactor assembly.
The temperature was recorded continuously on a strip
chart recorder and controlled by means of an on-off controller.
Batch runs were conducted by preheating the spar (40
g) and acid (48 g) to the desired temperature and mixing
them in the preheated reactor. Samples were taken a t appropriate times and analyzed for calcium fluoride content.
Although the temperature dropped about 20°F upon initial contact of the reactants, the period of this drop was
only 45 sec to 1 min after which the temperature could be
controlled to within 8°F of the setpoint.
(iii) Product Analysis. The six solids out samples for
each continuous reactor run were collected with a spoon,
and quenched in situ in 500 ml of 1 N NaOH solution to
ensure termination of all reactions. Prior to chemical
analysis, the samples were filtered, washed, and dried a t
200" to drive off all possible water of hydration of C a S 0 4 .
Analysis of the solids and the liquor of these samples was
subsequently carried out at the Aluminum Co. of Canada
Works Laboratory. The solids were analyzed for CaF2,
CaS04, and SiOZ, while the liquor was analyzed for sulfate, calcium, and fluorine content.
The six scrubber effluent samples required no elaborate
preparation prior to analysis. After a filtration to remove
any fine solids present, the samples were passed through
an automatic sample handling apparatus. This equipment
first carried out a sulfuric acid distillation to drive off all
fluorine from the original samples, and thus separate it
from possible interfering ions. The amount of fluorine collected was subsequently determined by photometric analysis using a complexing reagent. All scrubber liquor samples were analyzed a t least twice.
The overall standard error of the estimate of the fractional conversion (on the basis of six samples with two
replicate analyses for each sample) was determined to be
0.0142. This estimate accounted for errors in the scrubber
liquor flow rate, the fluorspar feed rate, as well as deviations observed from sample to sample.
Replicate analyses were not carried out on the solids out
samples from the continuous reactor due to time and expense considerations. An estimate of the overall error for
these can, however. be obtained indirectly from replicate
runs made on the batch reactor. For the batch reactor, the
solids samples were immediately quenched and subsequently analyzed following the same procedure as outlined
for the continuous reactor samples. The standard error (on
a fractional conversion basis) for the solids analysis is estimated to be 0.030.
The primary aim of the chemical analysis of the solids
out and scrubber liquor samples from the continuous reactor was to ascertain the extent of conversion of the
fluorspar to hydrogen fluoride. Although one can obtain
the conversion by measuring either the amount of CaF2
leaving in the solids out stream, or the amount of hydrogen fluoride in the scrubber liquor, one would also like to
Ind. Eng. Chem., Process Des. Develop., Vol. 13, No. 1, 1974
21
Table 11. Run Conditions and Conversionsa
Acid: spar ratio
Fluorspar
feed rate,
g/hr
Reactor
temp,
no.
Acid
feed
rate,
g: h r
11A
12A
13A
14A
15A
16A
17A
18A
19A
575
582.1
648
592
579
619
642
642
580
463
470
496
507
495
504
495
496
494
300
370
300
300
370
450
450
370
450
Run
Fluorspar composition, shown in Table I; mixing speed
O F
=
As
fed
1,009
1,008
1.063
0.950
0,952
1,000
1.056
1.053
0.955
Corrected
for boiloff
and CaC03
in spar
fluorspar
converted
t o HF
0.998
0.987
1,055
0.940
0.931
0.873
0,965
1.008
0.875
74.6
84.3
76.8
69.2
78.9
80.3
87.7
82.5
80.2
%
10 rpm.
Table 111. Partial List of Reaction R a t e Models
Model
no.
Rate constant
unitsa
Model equation
2
6
7
min -1 X - 1
8
min-1
9
min-1 X-2
10
O
X
=
X-1
x-2
11
min -1 X - 2
16
min
-1
X-2
concentration (moles per mole of calcium).
achieve accurate mass balances by doing hoth measurements in order to substantiate the conversion data.
In the early runs (not reported here), there were serious
discrepancies observed in the caicium, fluorine, and sulfate halances. These discrepancies were attributed largely
to poor chemical analysis of t h e solids samples, and to a
lesser degree to inaccuracies in the fluorspar feeder system
used a t that time. Once the analytical techniques were
modified, and a new screw feeder fabricated, the mass
balances became much more satisfactory (to 5% or better).
(iv) Experimental Data. The conversion-time d a t a ohtained from the hatch reactor runs are shown in Figures
2-3.
Using the continuous reactor, nine runs were conducted
varying temperature and the acid:spar ratio. In these runs
the calcite and silica content, as well as t h e mixing speed,
were maintained constant.
The run conditions, as well as the conversions obtained,
are shown in Table 11.
(v) Analysis of D a t a . (a) Batch D a t a Analysis. Reaction rate models of t h e form
dn,; dt = /.f(A. x14)
(9)
were tested for fit to the batch data. Here x~ is the degree
of conversion of CaFz and A is the acid:spar ratio.
The initial test of fit consisted of plotting the integral I
us. time.
22
Ind. Eng. Chem., Process Des. Develop., Vol. 13, No. 1, 1974
If the proposed model is a good fit of the d a t a the plot
should be linear. An initial estimate of k was obtained by
least-squares regression of Z to t as in eq 10. This estimate
of k was refined by least-squares regression of xtI onto t.
The criterion was minimization of
Because iHi cannot be expressed as a n analytical function
of k and t , the jt,il values were determined by the NewtonRaphson root-seeking technique. The program GAUSHAUS (Meeter, 1964) employing the method of steepest
descent was used to determine the best estimate of the
rate constant.
Sixteen rate equations were tested for their fit to the
batch data. Eight of these equations are shown in Table
111. Five of the rate models were purely empirical hut the
remainder were either theoretical solutions for different
control assumptions or empirical variations of those equations. For example, eq 9, 10. and 11 are all empirical variations of eq 7. Equation 7’ itself is the pseudo-steady-state
solution for the shrinking unreacted core model for a diffusion-controlled reaction when the surface concentration
of the solid is constant and the concentration of the fluid
reactant is proportional to the unconverted amount of the
fluid reactant.
(b) Continuous Reactor Data Analysis. The analysis
of d a t a from the continuous reactor is not quite as
straightforward due t o the nonideality of t h e reactor. Figure 4 shows a typical grams of Si out per minute cs time
plot (from a pulse nickel sulfate tracer input signal). The
response indicates t h a t the experimental reactor is neither
a plug flow nor a continuous stirred tank reactor. To analyze the d a t a obtained, it is first necessary to consider the
nature of t h e reacting system itself.
The following statements are made on the basis of t h e
state of the mass observations under different reaction
conditions for the batch reactor mix and t h e continuous
reactor output.
Near the feed end of the reactor the reaction mass consists chiefly of a pasty mixture of reactants and products.
In the remainder of the reactor the reaction mass is substantially in the form of hard. dry granules. Transformation from a wet to dry mixture occurs in the early sections
of the reactor. The passage of these noninteracting dry
granules may be considered equivalent to t h a t of separate
batch elements that remain in the reactor for different
lengths of time. The length of stay can be determined
from t h e tracer data.
The fraction of solids remaining within t h e reactor for a
,
that
period of time t , to t , -tA t l is ( E ( t ) A t )such
0
I
c
5
15
1
'IME
(MINUTES)
I
,
25
30
I
35
Figure 2. Batch reactor conversion d a t a and conversion curves
predicted by n o n l i n e a r least-squares fit of reaction rate model 6.
'
=I
I
20
I
I0
0
°
~
where n is the number of stream elements. In accordance
with the above ideas about the progress of the reaction.
one can write the exit concentration of B as follows
PREDICTED
201
t h e exit s t r e a m
25O.F
03
300.F
0
350.F
A
-
-__-_
in t h e reactor for
lot
01
I
0
5
I
IO
,
I
IS
20
I
25
,
30
T I M E (MINUTES)
Figure 3. Batch reactor conversion d a t a and concersion curves
predicted by least-squares fit of reaction rate model 10.
This can be written in t h e form
X H is t h e average conversion of
B in the exit stream, and
. x H ( ~ ~ )is the conversion of B in the exit stream element
with a mean age t, = t , + ( l t , / 2 ) .
The value of ~ ( 7 , is
) determined from the rate model
being considered. If the rate model is analytically integrable a n expression of the form
is used. For a particular run the value of A is fixed and
the 2, values are those corresponding to the residence time
distribution plot. The value of h to be determined must
be such t h a t t h e summation of eq 13 equals X H . An initial
value of k is used a n d t h e summation obtained compared
with the f H value. The I? value is then altered to correct
for the difference and the procedure continued till satisfactory convergence is achieved.
For the case where integration of the model rate equation by mathematical techniques is impractical. the ~ ( 7 , )
values are generated by numerical methods.
D. Results
( i ) Batch Data. Of the sixteen rate equations tested,
three were found to yield satisfactory fit for the batch
data. Table IV contains the results of the least-squares regression of the batch d a t a for t h e three acceptable models
(eq 9, 10, and 11 of Table 111). The results for models 6
and 7 are also included by way of comparison. Although
the correlation coefficients indicate that all five models
are of equally good fit, comparison of the mean square
about regression S2 with the estimate of the mean square
due to pure error Se2 (obtained from replicate runs) is a
better test of the goodness of fit. The results of this F
ratio test are also shown in Table IV and indicate that the
Ind. Eng. Chern., Process Des. Develop., Vol. 13, No. 1. 1974
23
Table IV. Least-Squares Analysis of Models Using Batch Data
Rate
ecl
no.
Temp,
"F
95% confidence
limits of rate
constant
Correlation
coefficient
of I us. t
0.0880 I 13%
0.130 =k 22%
0 . 2 7 3 = 24%
0.0211 i 7 . 4 %
0.0348 i 1 4 %
0.0747 i. 22%
0.0459 C 11%
0.0955 .z 12%
0 . 2 5 6 =k 14%
0.0381 i 9 . 6 %
0.0748 L 12%
0.188 I 8 . 9 7 0
0.0840 5 13%
0 . 1 7 1 & 12%
0.444 =!c 14%
0.9573
0.9276
0,9722
0.9639
0.9452
0.9772
0.9748
0.9602
0.9603
0.9748
0.9597
0.9762
0.9749
0.9602
0.9721
Mean
square
about
regression&
Fb
(S2)
v
ratio
0.00518
0.01203
0,01171
0,000699
0.002705
0.004275
0 000904
0.001030
0.00804
0.000739
18
20
5.78d
13.41*
13. O j d
~~
6
7
250
300
350
250
300
350
9
10
11
250
300
350
250
300
350
250
300
350
16
m o l e r a t e of
H2S0, reacting
with CaCO,
m o l e r a t e of
boiloff
+ H,SO,
m o l e r a t e of CaF, in
The amount of HzSO4 boiloff was determined by analysis
of the scrubber effluent samples for S 0 4 2 - content.
The rate constants obtained from the continuous reactor d a t a were then used to determine the parameters of
the Arrhenius equation of the form
The values of E and k,r=slciOlt in Table VI were determined by least-squares regression of the d a t a t o the nonlinear eq 16 using the computer program GAUSHAUS
(Meeter, 1964). The mean squares about regression are
also shown in Table VI.
24
Ind. Eng. Chem., Process Des. Develop., Vol. 13, No. 1, 1974
20
16
3 . 02d
4 . 76c
1.01
1.14
<1
<I
1.21
1.12
18
<1
20
16
<1
18
18
0.001081
0,001006
0.000824
0,001032
0,000857
'1
corrected
acid:spar =
ratio
<1
20
16
S? = z T i x HZ . f i 3 , ) 2 Y. b F = S?,'S,2. S e 2 = 0.000897 with 23 degrees of freedom.
significance. d Significant a t the 1%level of significance.
model eq 6 and 7 do not adequately fit the data. This conclusion is substantiated by Figures 2 and 3 which contrast
the poor fit of model 6 to the good fit of model 10. None of
the F ratios are significant for the rate models 9, 10, and
11 indicating no bias of fit of the three models. In addition. the S2 values for the three models are all of equal
size indicating that none of the models may be considered
better than the other two.
(ii) Continuous Reactor Data. Using the residence
time distribution for each run, the apparent rate constants shown in Table V were calculated for the three rate
models which were found to acceptably fit the batch data.
The acid:spar ratio (A in the rate models) used in the calculations of the apparent rate constants were those labeled as corrected acid:spar ratio in Table V. These corrected acid:spar ratios were calculated on the basis t h a t
acid which reacts with CaC03, or is fumed away, is unavailable for reaction with CaF2. The reaction of acid with
CaC03 is assumed to occur immediately on contact and
the boiloff of acid is also assumed t o occur in the early
stages of the reaction when the acid is not yet entrained
within the solid phase or crystallized out as C a s 0 4 (OStrovskii and Amirova).
18
20
16
c
TIME
1.14
Significant at the 5% level of
IMINUTESI
Figure 4. A sample tracer curve.
Table V. Apparent R a t e Constant Values
Run
Heactor
temp,
no.
"F
11A
12A
13A
14A
15-4
16A
17A
18A
19A
Batch
Batch
Batch
300
370
300
300
370
450
450
370
450
250
300
350
Corrected
acid :
spar
ratio
0.998
0.987
1,055
0.940
0.931
0.873
0,965
1,008
0,875
Apparent
rate constant values
Es 9
Eq10
Eq11
0.123
0.0874
0.266
0.0731
0,0948
0.211
0.698
0.178
0.222
0.471
1,306
1.185
0.464
1.190
0.084
0.171
0.444
0.428
1
0.105
0.127
0.283
0.798
0.749
0.281
0.726
0.0459
I
0.0955
0.507
0.431
0,181
0.469
0,0381
0.0748
1
0.256
0.188
0.188
In order to determine if the three models were properly
accounting for t h e acid;spar ratio, plots of the residuals
about regression ( k L - k r ) us. t h e acid spar ratio (as fed
and corrected) were drawn. The plots indicated no correlation between the residuals and the acid:spar ratio, indicating t h a t there was no bias in the rate models. In addition to these plots, tests to determine whether the errors
were random were conducted and again no bias of the
models was detected.
T a b l e VI. Parameters of Least-Squares F i t of Nonlinear Arrhenius Equation
95 70 confidence
interval of
activation energy
estimate,
iBtu/lbmol) X 1 0 - 3
Rate
eq
kl=8103R,
interval of
min--' X H O - J )
= 2 16
15 21 T 2 11
15 95 z2 08
16 45
9
10
11
,
Mean
square
about
regression
957, confidence
= 10)
033
0 001421
022
0 414 =k 0 053
0 000831
0 00500
0 247
0 166
I
+0
=0
IY
Mean
square
due t o pure
error
l-, =
6)
0 00287
0 00126
0 00760
I
I
O 60
- -_
v
+008-
5006-
a
-
2a 004-
A
0011
I
CONTiNUOUS R E I C T O R
0 BbTCH R E A C T O R
1002-
06
DATb
DATA
0
8bTCH
REbCTOR
DATb
I
I
1
113
I ie
128
123
IOOO/T
I33
I38
143
(IPR)
Figure 5 . Arrhenius plot for rate constants of reaction rate model
Figure 7. Arrhenius plot for rate constants of reaction rate model
9.
11.
Figure 6. Arrhenius plot for rate constants of reaction rate model
The activation energy values found in this investigation
are higher than those obtained by analysis of the d a t a of
Puxley and Woods (1948) and agree with one of the two
values reported by Ostrovskii and Amirova (1969). The
activation energy in the 105-145" range for the model proposed by Ostrovskii and Amirova (1969) corresponds t o
16,560 Btu/lb mol and agrees well with the activation
energy values of Table VI. However, in the 85-100" range
their activation energy value is 37,440 Btu/lb mol. The
change in activation energy was attributed by Ostrovskii
and Amirova (1969) to the formation of FSOsH below
100". While this is no doubt a contributing factor, it appears t h a t the change is too large to be attributed to this
factor alone. In fact the activation energy behavior a p pears characteristic of a shift from a chemical rate controlling situation to a diffusion significant situation.
0
IO8
113
BATCH
REbCTOR
DATA
I 28
I23
I18
I33
138
143
(I/'R)
IOOO/T
10.
E. F u r t h e r Comments
Similarily plots a n d tests for randomness revealed t h a t
no correlation could be detected between ( k l - k ) and k l .
On t h e basis t h a t there is no reason t o assume a correlation between the acid:spar ratio and the apparent rate
constant values, one may now consider t h e three runs a t
each temperature level as replicates and obtain a n estimate of the variance due to pure error.
-
,,
h, = C l i ! / n ,
)=I
where n, = number of replicates at each temperature level
= 3 and m = number of temperature levels a t which replicates were taken = 3.
The mean squares may now be compared to the estimate of t h e mean square due to pure error values to determine if they are significantly high ( F test). However,
because t h e mean squares about regression are smaller
t h a n the mean square due to pure error in every case, it
indicates t h a t all three models are providing good fits to
the d a t a .
For the experimental conditions investigated in this
work, the rate equations found to satisfactorily fit the
batch d a t a are seen to yield acceptable correlations under
flow conditions as well. This implies that any of these
three rate equations may be considered satisfactory for
design purposes for conditions not too far removed from
those indicated. The proposed equations, however, do not
clearly isolate the diffusion effects, and further experiments will be called for in order to achieve more general
results with respect to variations in mixing speed, spar
size, and calcite content. In principle, experiments may
also be designed to operate under conditions that eliniinate all diffusion resistances in order to isolate the kinetics of t h e surface reaction. For the present three-phase
system, however, such a design is not obvious. More interestingly, since the rate models found acceptable in the
present work all indicate significant diffusion interplay, it
would be logical to attempt estimation of the various diffusion coefficients. Due to system complexity, however.
meaningful estimates could not be arrived a t . In what follows, a further qualitative interpretation of the rate results is attempted under the assumption t h a t diffusion of
sulfuric acid through the product layer to the unreacted
Ind. Eng. Chem., Process Des. Develop., Vol. 13, No. 1 , 1974
25
core is a significant resistance to the progress of the reaction
All three rate models found acceptable in the present
investigation display a second-order dependence on the
acid concentration. This may be compared to a first-order
dependence that is predicted for a diffusion-controlled
reaction by the model corresponding to eq 7. To understand how a second-order acid concentration dependence
may come about, one must again consider the particular
physical aspects of the reaction system. It was mentioned
earlier t h a t the reactor contents are for the most part incompletely reacted dry granules. The acid is present within the solid phase as precipitated CaSO4.HzS04 (as suggested by Ostrovskii and Amirova, 1969), or as entrained
liquid. Diffusion of the acid toward the unreacted solid
may occur by capillary action. but as the liquid content
decreases, the capillaries would also tend to retain the
fluid rather than transport it. Yet overall conversions of
97% or better are quite common in industrial reactors. A
possible explanation for all these observations is migration
of sulfuric acid through the solid phase by way of the following scheme.
1965; Menard and Whicher, 1955) consider the effects of
calcite content on fluorspar reactivity in a batch system.
It appears that a n increase in calcite content may be expected to enhance acid penetration into t h e spar, but the
effect may be counterbalanced by a n increased tendency
of the reaction mass to become set.
F. Conclusions
Batch and continuous reactor data have been obtained
for the fluorspar-sulfuric acid reaction. Three rate models
are found to be acceptable. all of them indicating a strong
dependence on sulfuric acid concentration. The activation
energy values for the three acceptable models are all close
to 16,000 Btu/lb mol.
Acknowledgments
The financial support of t h e Aluminum Company of
Canada is gratefully acknowledged. The authors also
thank H. S. Monahan, E. Dernedde, G. Auger (Alcan),
and M. Adelman (University of Windsor) for their advice
and suggestions.
Nomenclature
A = acid:spar ratio corrected for SO3 boiloff and con-
The ion exchange (H- and CaZ- ion migration) would
occur from an area of high concentration to one of low
concentration. and using the analogy to diffusion of electrolyte in concentrated solutions, the diffusivity would be
proportional to the acid concentration a t t h a t point
(Moore, 1963). If one further assumes t h a t the acid is
largely trapped within the ash perimeter and t h a t its concentration (on a mole per mole of calcium basis) at the
ash perimeter is linearily proportional to the amount of
acid unconverted, the pseudo-steady-state solution for diffusion-controlled mechanism becomes
where k o = cmZ/(min) (mol of HzS04/mol of calcium)
and R = reacting particle diameter. When R is constant
eq 18 reduces to
The above equation is in fact model eq 10, which has been
shown to fit the experimental data very satisfactorily.
Finally some comments may be directed toward the
utility of the rate equations presented in this work for
scale up, particularly since certain parameters of importance were set at preselected levels in obtaining these
equations. The reactivity of calcium fluoride is a strong
function of temperature and composition, the variables
investigated here in, and it is felt that the suggested rate
models will be useful in scaling u p with respect to these
variables even for conditions that differ somewhat in
terms of spar size, mixing speed, and the calcite content.
The spar size, in particular, should be relegated to secondary importance as lump formation in the reactor makes
the size of lumps, rather than the initial particle size, the
controlling parameter. Mixing speed and calcite content
may be expected to have consequences t h a t are interactive, in that variations in either should affect lump formation and breakdown. Some previous investigations (Gnyra,
26
Ind. Eng. Chem., Process Des. Develop., Vol. 13, No. 1, 1974
sumption by CaC03 in fluorspar feed, mol of H2S04/
mol bf CaF2E = activation energy, Btu/lb mol or cal/g mol
E ( t J = age distribution of exit stream in ea 12
k = app&ent rate constant, min-l/(mol of CaFz in feed/
mol of calcium in feed)n; where n = 0, 1, or 2 as in
Table I11
N = gmolofCaFz
R = gas constant, Btu/lb mol "Ror cal/g mol "K
S2 = variance of residuals
S,z = variance due to pure error
T = temperature, "Kor "K
t = time, min
t , = mean time of a n age distribution element, min
X H =~ mol of CaFz per mol of calcium in the fluorspar
feed
z8 = fractional conversion of fluorspar
zB = average fractional conversion of fluorspar in exit
stream
x H ( t , ) = fractional conversion of fluorspar in a n exit
stream element which has the mean age t ,
ikjL
= fractional conversion predicted by the rate model
Greek Letters
1 = increment
X = summation
u = degrees of freedom
Literature Cited
Gnyra, B , Report No AW-108-5. Aluminum Laboratories Limited, Arvida,
Quebec, Aua 1961
Mathur. G. P..-Candido. D.. Report No. AW-108-54-1, Aluminum Laboratories Limited, Arvida, Quebec, Aug 11. 1967.
Meeter. D. A . . "Program GAUSHAUS," Numerical Analysis Laboratory,
University of Wisconsin. Madison. Wisc.. 1964 (Revised, 1966).
Menard. W., Whicher, C H . , Report No. AW-248-TM-3, Aluminum Laboratories Limited, Arvida, Quebec, Dec 1955.
Moore, W . J . , 'Physical Chemistry," 3rd ed. Prentice Hall, Englewood
Cliffs, N. J., 1963, p 340.
Ostrovskii, S. V..Amirova, S. M., Zh. Priki. Khim. (Leningrad), 42, 2405
(1969).
Puxley. P. A,. Woods. E. A.. Report No. A-BR-74-48-20, Aluminum Laboratories Limited, Arvida, Quebec, Mar 1Y48.
Traube, W., Lange. W., Berichte. 57. 1038 (1924).
Traube, W . , Reubke, E,, Berichte, 54, 1618 (1921).
R e c e w e d for reLieu Nobember 8,1972
Accepted July 9. 1973