REACTION KINETICS OF THE PRODUCTION OF AMMONIUM SULFATE FROM ANHYDRITE G . B. CORDELL Agricultural Dioision, Imperial Chemical Industries, Ltd., Billingham, County Durham, England
An investigation of the reaction between natural anhydrite and a solution of carbon dioxide and ammonia to produce ammonium sulfate shows that the reaction takes place predominantly by the replacement of sulfate by carbonate within the original rock particle at an interface which moves slowly inward from the surface of the particle.
The observed reaction rates have been interpreted in terms of a diffusional resis-
tance within the calcium carbonate layer and a reaction first order in carbonate ions a t the interface. A simplified mathematical model has been used to describe the operation of an existing plant. This plant consists of 1 1 stirred tanks in series; ground anhydrite is added to the first tank and the carbonated ammonia solution is divided among the first three tanks. The method has proved particularly useful for predicting the residual sulfate in the chalk under various operating conditions. This is important, as appreciable quantities of sulfate in the by-product chalk make it unsuitable for cement manufacture.
declining in relative importance as a nitrogenous fertilizer, ammonium sulfate is still required in very large tonnages, particularly by developing countries. Considerable quantities are made throughout the world by the double decomposition of calcium sulfate and ammonium carbonate. Three sources of calcium sulfate are used: natural anhydrite, natural gypsum, and by-product gypsum from phosphoric acid manufacture. Ammonium sulfate is made from natural anhydrite by Imperial Chemical Industries. Ltd., a t Billingham, County Durham. Anhydrite, mined from below the factory site, is fed to the first of 11 vessels connected in series. Each vessel is of 70-cu. meter capacity and is agitated to maintain the solids in suspension. A solution which may be considered as ammonium carbonate is prepared by dissolving carbon dioxide in aqueous ammonia, and is fed to the first three vessels. T h e resultant slurry is filtered, reslurried with water to remove residual ammonium sulfate, and refiltered. The by-product chalk is used for cement manufacture and to be acceptable a conversion of 93 to 94% of the anhydrite is required. A schematic diagram of the process with maximum present flow rates is shown in Figure 1. A more detailed description of a similar plant is given by Higson (195 1).
A
LTHOUGH
lSOCU METERS CARBONATED AMMONIA LIQUOR
BALL MILLS
100000 K,/hr ANHYDRITE
The reaction temperature is approximately 70' C. in all vessels. The molar ratio of free ammonia to carbon dioxide in the solution is approximately 2.6. Free ammonia is defined as the total ammonia present in the solution in all species except ammonium sulfate? and carbon dioxide is defined as the total carbon dioxide present in the solution in all species. The rate of conversion rises with increasing carbon dioxide (or free ammonia) content but falls to zero if the concentration falls to 0.088M. The rate of reaction falls very rapidly with increasing conversion, for although the conversion in tank 1 is SO%, the final conversion in tank 11 is only 96%. The liquor is fed to vessels 1, 2, and 3 and is split so as to achieve carbon dioxide concentrations of 0.4 to 0.5Min these vessels. Higher values give rise to excessive losses of gaseous ammonia and carbon dioxide. A concentration in the final vessel of 0.2 to 0.3h.i is normally achieved. The ammonium sulfate concentration varies little from tank to tank and is in the range 4.2 to 4.6M.
/Y
FILTERS
fl
Cas04 1
SOLID
T o assess the possible ways of improving the reaction system it is necessary to have a complete description of the process. Certain data were available from plant records and plant tests (Table I ) .
Table 1.
CHALK TO CEMENT KILNS
CaSOc
Plant Experience
I f STIRRED REACTION VESSELS IN SERIES ( 7 0 CU.METERS EACH)
I
t= 90%
The object of the investigation was to find a method of increasing the output of ammonium sulfate, while simultaneously increasing the quality of the chalk by achieving higher conversions of anhydrite. As a first step it was decided to obtain a clear understanding of the mechanisms involved, and to produce a n adequate kinetic description of the process.
t
CO;' SOLUTION
-
AMMONIUM SULFATE SOLUTION TO EVAPORATORS
CacOl SOLID
+
so4'' 50LUlION
Anhydrite feed rate, kg./hr. Fraction of Cas04 in feed, 70 Total liquor rate, cu. meters/hr. Liquor to first vessel, cu. meters/hr. Liquor to second vessel, cu. meters/hr. Liquor to third vessel, cu. meters/hr. Inlet liquor concentration, molar No. of vessels on line a
Figure 1.
Schematic diagram of ammonium sulfate plant
b
off. Reaction temperature 'v 70' C.
278
l & E C PROCESS D E S I G N A N D D E V E L O P M E N T
Plant Test Conditions Test 1
87 93
x
103
142 121" 9 .5*
11.5a 4.38* 9
Test 2
85 X 10 89 123 107" 8a 8a 4 . 63b 10
Calculated by material balance over tanks I , 2, and 3, respectiveb. Calculated by over-all mass balance to account for losses due to gassing
Examination of Reaction System
Examination of Solution Equilibria
Examination of the ground anhydrite feed shows that it contains a wide distribution of particle sizes. Typical distributions are shown in Table 11. Chemical analysis of the rock indicates about 90% C a S 0 4 , mainly as anhydrite but with a small fraction of dihydrate (gypsum). T h e remainder is mainly siliceous material with some chalk. Samples of the anhydrite were made to react under the microscope with solutions of composition similar to that found in the plant vessels. There was little apparent reaction, only a few small crystals of chalk (calcium carbonate) forming in the solution away from the anhydrite particles. However, treatment of the resulting particles with dilute hydrochloric acid dissolved away the outer layers, indicating that the reaction was taking place predominantly by replacement of sulfate by carbonate within the original rock particle, and that a distinct sulfate-carbonate interface was formed which moved in a n irregular manner inward from the particle surface. T h e experiments were then repeated using pure gypsum and by-product gypsum from phosphoric acid manufacture. I n each case the reaction took place entirely by dissolution of the gypsum. with simultaneous precipitation and growth of calcium carbonate crystals from the solution. T h e differences in reaction mechanism may be due to the low solubility of anhydrite in water compared with gypsum, or the presence of impurities in the anhydrite which act as nuclei for the calcium carbonate. X-ray diffraction measurements show that the chalk has about 60y0 as the vaterite form and 4070 as the calcite form; from the measured densities of these crystal forms and of anhydrite a voidage of 18.5970 was calculated for the chalk layer. This will be sufficient to allow reasonable rates of diffusion of reactants and products though the chalk layer. Examination of the reaction equation shows that the cation plays no part in the over-all reaction; thus
T h e chemistry of solutions containing ammonia and carbon dioxide has been studied by Faurholt (1925) and Hatch and Pigford (1962), who show that the following carbon dioxidecontaining species may be present:
Hence if diffusion is the only rate-limiting process, the reaction rates of sodium and ammonium carbonates should be similar. However, bench scale tests showed that the reaction rates using the sodium salt were much faster, even though the modes of reaction as observed under the microscope were identical. I n a n attempt to explain these differences the chemistry of the solution of ammonium carbonate and ammonium sulfate was examined.
Table 11.
Size, Microns 5
10 15 20 30 40 60 76 104 150 210 295 420 600 ~~
Size Distribution for Tests 1 and 2
Weight 70Less than Stated Sire Test 7 Test 2 16.3 28 8 36.9 49.1 56.5 65.7 75.5 81.8 84.5 87.5 91.5 95.3 97.8 99.3 99.8
10.3 21.5 31.9 55.5 65.4 72.8 77.1 81.4 83.2 87.4 93.4 97.0 98.7 99.5 100.0
C O Zor H 2 C 0 3 . Un-ionized carbonic acid HCOa-. Bicarbonate ion co3-2. Carbonate ion NH2COOH. Un-ionized carbamic acid NHzCOO-. Carbamate ion T h e following species are also present: NH3 or NH4OH. NH4+.
Un-ionized ammonia Ammonium ion sod-2. Sulfate ion Hf. Hydrogen ion OH-. Hydroxyl ion Accurate determination of the quantities of each species present is impossible, as the equilibrium and activity coefficients under the appropriate conditions are unknown. An estimate using dilute solution theory was made. Equilibrium coefficients a t 70’ C. were estimated using data given by Faurholt (1925), Harned et a l . (1940, 1941, 1943), and Everett and Landsman (1954). When dependence on temperature was given, the results had often to be extrapolated. Where values a t a single temperature were given, the value a t 70’ C. was estimated assuming that the free energy change (AG) was independent of temperature, using the general thermodynamic relationship:
AG = - R T l n K where the symbols have normal thermodynamic significance. T h e following values were arrived a t :
Kq =
[ H + ][ N H & O O -1 = 8.0 x 10-7 [NHsCOOH]
K6 = [“][OH-]
=
1.6 X
T h e equilibria were solved for a typical solution containing 4.4 moles of ammonium sulfate, 0.30 mole of carbon dioxide, and 0.78 mole of free ammonia. It was found that the fractions of carbon dioxide present as the various possible species are :
[co3-2]/c=
1.6 x 10-4 = E [HC03-]/C = 0.41 [NHsCOO-]/C = 0.35 [NHsCOOH]/C = 0.08 [HnC03]/C = 0.16
T h e use of dilute solution theory could lead to large errors in the values of the equilibrium coefficients used, so that the above ratios will be very approximate. However, the conclusion that the carbonate ion is only a very small fraction of the total carbon dioxide-containing species is almost certainly valid. VOL. 7
NO. 2
APRIL 1968
279
Although the fraction of carbon dioxide present as carbonate ion is very low for this system and is close to unity for the sodium carbonate system, this does not explain the difference in reaction rates if a diffusion resistance alone was postulated; for as carbonate ions are removed by reaction a t the interface, the other carbon dioxide-containing species will be converted to carbonate ions to maintain the solution equilibria. Thus all carbon dioxide-containing species will diffuse through the chalk layer. As the diffusivities of all the carbon dioxidecontaining species are unlikely to be very different, the total rates of diffusion of carbon dioxide will be similar for both ammonium and sodium carbonates, and thus their 'rates of reaction should be similar. If the large differences in reaction rate are to be explained by differences in carbonate ion-carbon dioxide ratio, some other rate-limiting process which is dependent on the carbonate ion concentration must be present. I t seems probable that this process is the reaction which takes place a t the interface. I t has been assumed that this reaction is first-order in carbonate ions, as seems probable from the reaction equation. T h e very low fraction of carbon dioxide present as the carbonate ion is also consistent with the observed position of equilibrium. Consider the solubility products of calcium sulfate and calcium carbonate a t equilibrium:
A = [C03-2][Ca+2] = EC*[Ca+2]
(1)
B = [S04-2][Ca+2] = S*[Caf2]
(2)
FRACTIONAL
Figure 2. particle
7
CONVERSION,
= 1
- r3/R'
Idealized picture of
reacting
Si
CONCENTRATION
S
I
Eliminating [Ca+2]
C
C* = S*A/BE
(3)
Substituting the observed equilibrium values at 70' C. AIBE = C*/S* = 0.088/4.6 = 1.9 X
Ci
(4)
This result is comparable with values of 1.12 to 0.73 X low2 obtained by Neumann (1921) a t rather lower temperatures and concentrations. If the value for E is substituted, then AIB = 3 X 10-6. This value cannot be verified independently, as values for A and B are not available under these conditions. Indeed, it is not even apparent which solid form of calcium sulfate is appropriate to the value of B. However, estimates from the solubilities of chalk and gypsum in water show that the ratio to be of the right order of magnitude.
'
C* ANHYDRITE
w L
I "
BULK SOLUTION
_I
Conditions in chalk layer of a reacting
We are now in a position to formulate a kinetic model of the reaction. There are three possible rate-limiting processes :
l&EC PROCESS DESIGN A N D DEVELOPMENT
I
DISTANCE FROM PARTICLE CENTRE
dt
280
''
I
dN
I n order to obtain a mathematical model of the reaction process the particles were assumed to be spherical and homogeneous. Thus the interface will retreat evenly, so that it also will be spherical. When considering diffusion of reactants, all carbon dioxide-containing species must be considered, as they will be converted to carbonate ions to maintain the solution equilibria a t the interface which is disturbed by the reaction. T h e state of a reacting particle is shown in Figures 2 and 3. Assuming steady-state diffusion, the rate of diffusion of reactants is given by:
I
I I I I I I I 1
Formulation of a Mathematical Model
1. Diffusion of reactants through the chalk layer to the interface 2. Diffusion of products through the chalk layer from the interface 3. Reaction a t the interface
1
R
A
Figure 3. particle
I
CHALK
-
4 ?rRr D(C R - Y
- Ci)
(5)
A similar equation will arise from the diffusion of sulfate ion from the interface :
Other species will also diffuse as a result of the conversion of carbon dioxide-containing species to carbonate ions a t the interface :
cos-*+ 2 H +
H&03 + H C O s - + C03-2 NHzCOOH20 + c03-' NHiCOOH H20 + COS-* H + NH3 NH4+
+
+ +
+ H+ + NH4+ + + H+ "4'
As a result of the position of the solution equilibria, virtually all the hydrogen ions formed will react with un-ionized am-
monia to form the ammonium ion. Thus un-ionized ammonia and water will diffuse inward and ammonium ions will diffuse outward. However, the ions will not be able to diffuse independently but must be constrained by the requirement of electrical neutrality a t all points in the chalk layer. T h e assumption that the diffusivity of all species through the chalk layer is constant has been made; otherwise the analysis of conditions within the layer becomes very difficult. I n particular D = D,. T h e actual mechanism by which the anhydrite reacts is unknown, so that a single reaction pseudo-first order in carbonate ions has been assumed. T h e rate equation is:
Table 111.
Molecular Diameter and Equivalent ConductanceCharge of Diffusing Species Equivalent Conductivity/ Molecular Molecular] 11 Charge, Volume, Volume, Mho Cm./ Species Cc./G. Mole a Diameter Unit Charge
[
sod-'
55.2 3.80 40.0 37.0 3.33 34.7 HCOa40 .? 3.44 44.5 HzC03 43 . ? 3.54 NHzCOO56.7 3.84 40" NHzCOOH 60.4 3.92 Unknown but probably similar to C H I C O O - = 40.9 and CICH2c03-'
. . I
.
a
I
.
COO- = 39.8.
dN - = 4 nr2KE(Ci - C*) dt
(7)
By consideration of the rate of retreat of the interface:
The assumption of steady state is a reasonable approximation, as the concentration change through the system is very small. The residence time in each tank is approximately 25 minutes, but because of the relatively low capacity of the chalk layer (only 18.5% voids) the steady-state profiles will be set up quickly.
From the interfacial equilibrium :
C*
=
(3)
SiA/BE
Modification of Equation for a Single Particle to Predict Plant Performance
By a mass balance over the bulk solution:
s=co-c
(9)
From the geometry of the reacting particle, the interfacial radius is related to the fractional conversion by: 7 =
1 - r3/R3
(10)
By assuming that the ratio of carbonate ions to total carbon dioxide, E, is constant it may be shown using Equations 3 to 10 that:
1' [C
[+
A(Co - C ) / B E ]dt = - 1 6pR2 0
-
;E]
[l
-
T h e equation which has been developed describes only the reaction of a single particle of given radius and history. However, the ground anhydrite feed has a broad distribution of sizes? as indicated in Table 11. There is also a distribution of residence times due to the characteristics of the reaction system. At this stage it is convenient to define a composite variable, 7. Where T is the value of the time-concentration integral from tank 1 to n, 7
1'
[C - A(C,
=
- C ) / B E ]dt
=
j-n
[Cj
-
A(C0
-
=l j
T h e form of the above equation is worth examining: T h e left-hand side is a time-concentration integral corrected for the reversibility of the reaction and describes the history of the particle since it entered the first reaction vessel. T h e first term on the right-hand side gives the resistance attributable to diffusion through the chalk layer and the second term gives the resistance attributable to the speed of reaction a t the interface. Review of Assumptions
T h e assumption that the mean diffusivities of the diffusing ions are equal has been made to simplify the final expression. However, there is reason to believe that the diffusivities are not far different. T h e major diffusing species are negatively charged and their molecular diameters as estimated using Kopp's law are not far different. A second test which allows for the hydration of the ions is given by comparison of the equivalent ionic conductivities a t infinite dilution divide by the number of unit charges carried. Values derived from data given by Sherwood and Pigford (1952) and Parsons (1959) are given in Table 111. A further assumption is that the fraction of carbon dioxide as carbonate does not change as the liquor concentrations vary. Solution of the ionic equilibria set out above for normal conditions indicates a maximum range of this ratio, E, of 1.3 to 2.2
x
lo-'.
Cj)/BE]tj (12)
T h e mean fraction of unconverted anhydrite in a given tank is given by the relation: n m
where F(R)dR is the fraction of particles in the size range R to R dR and F ( T ) ~isTthe fraction of particles which have a value of the time-concentration integral in the range 7 to T dT. T h e value of (1 - 7 ) is given by the implicit equation for a single particle:
+ +
T =
pR2/6 D[1
+ A / B E ] [ l - 3(1 - 7)2/3+ 2(1 - 7 ) ] + pR/Ek[I
- (I
-
7)"3]
(Ila)
F ( R ) is simply the negative differential of the cumulative size curves, but the estimation of F ( T ) gives rise to some difficulties. We are able to define the mean value of 7 in t a n k j which will be denoted by 8,. This is given by: 8j
= [(Cj
- A(C0 - C j ) / B E ] T j
where Tj = V / ( u j
+
(14)
(15)
uj)
Now T will be distributed about 8, in exactly the same manner as the residence time, t j , is distributed about its mean, T,. Thus it is possible to determine how 8, is distributed for a series of tanks whose mean values of T are 81, 8 2 , . ,8". An VOL. 7
NO. 2
APRIL 1 9 6 8
281
exact solution exists for this case if perfect mixing is assumed, but the mathematical expression is very cumbersome. A simpler expression is given by MacMullins and Weber (1935) for tanks of equal residence time:
If we replace our system with a system of tanks having the same value of e,, having the same total value of then:
EO,,
F(r) =
(n
-
exp (-
(r/6,)"
I)!
TI&)
where
I t can be shown that the errors introduced by the use of this simplified expression are very small, provided that the values of O3 d o not vary very widely. This is true for the system under consideration. I t is now possible to calculate the conversion on the plant using the above relationships together with the equation describing the material balances over each vessel : wq]-
1
+
u]- IC,-
+ f&
1
= wq,
+ ujc,
(1 9)
T h e solution of these equations is extremely tedious, requiring many iterative steps and graphical integrations. They are, however, ideally suited to solution by computer. A schematic diagram of the main program is shown in Figure 4. Verification of Mathematical Model
T h e first step in the determination of the reaction constants was to treat particles of anhydrite with a solution in which READ DATA GENERATE F I R ) A S HISTOGRAM
I
1 1 1 ESTIMATE 1
SET
1
n = V E S S E L No = 1
CALCULATED C,
FROM
h MASS BALANCE
J CALCULATED
FROM C & n
4 - I
CALCULATED
5
= 1 -
ff
d t dR
0 0
IS
I I CALCULATED Ti - ESTIMATED nl ) E
SET n = n + 1
Figure 4. 282
T h e results are plotted in Figure 5 as a plot of r against 7 . T h e results show considerable random scatter, but no systematic deviations are apparent which would disprove the basic theory. T h e scatter is probably due to: T h e difficulty of defining the reaction time, particularly as it was often only a few minutes, and filtration and washing of the solids take an appreciable time. T h e assumption that the small quantity of sodium detected in the solid was present in sodium sulfate. Variation of the impurities present in the anhydrite. Analytical errors. From these results the best value of parameter p/6 D was estimated by drawing the curves for the various values and judging the fit by eye. A value of 4.0 X IO7 (kilomoles) (hr.) (meter) -5 was obtained. Substituting p = 16.5 kilomoles/ cu. meter,
D = 7.0 X 10-8 sq. meter/hr.
I
SOLVE SINGLE PARTICLE EQUATION FOR RANGE OF R h t
the sodium ion replaces the ammonium ion. A complete analogy was not possible because of the relatively low solubility of sodium sulfate. Anhydrite with a narrow size range was added to a large excess of solution containing approximately 0.45 mole of sodium carbonate and 2.5 moles of sodium sulfate a t 70' C. Samples of solid and solution were extracted periodically and analyzed. For the sodium carbonate-sodium sulfate system it was calculated that the carbon dioxide is present mainly as the carbonate ion-Le., E 'V I-because of the absence of the buffering effect of the ammonia. Because of this high value it was shown that the concentration ( E ) of free carbon dioxide in equilibrium with calcium sulfate is so low that it may be neglected. I t can be shown that this high value of E also makes the reaction resistance term negligible except for the very smallest particles. T h e reaction equation thus reduces to :
'
gni 9 CALCULATED Cn =CnCALCULATED
Simplified diagram of computer program
l & E C P R O C E S S DESIGN A N D DEVELOPMENT
Typical liquid phase diffusivities are about 100 times greater than this value. These experiments were then repeated using the ammonium carbonate-ammonium sulfate solution of similar composition to that found in the plant vessels. The results showed even greater scatter than those using sodium carbonate. This is almost certainly because of evolution of ammonia and carbon dioxide during the experiments. T h e results were not considered reliable enough to estimate the value of the reaction rate constant, k , so it was decided to abandon this approach and to use full scale plant test results to estimate k . The results, however, confirm one qualitative prediction which can be made from Equation 11 : As particle size increases, the conversion for the ammonium carbonate system approaches that for the sodium carbonate system a t the same value of r because the diffusional resistance which is assumed to be the same for both systems is proportional to R2 and thus increases more rapidly with increasing size than the reaction resistance which is proportional to R. Two tests were carried out on the plant to measure the concentration in the solid and liquid phase in various tanks in the reaction system, for given feed conditions (Table IV). These were then predicted using the computer program for various values of the parameter p I E K , assuming that the diffusivity, D ,was identical to that determined for the sodium carbonate system. T h e best fit was judged by eye, and gave a value of:
p / E K = 4.0 X l o 4 (kilomoles) (hr.) (meter)-4
R = 4 27 - 300
R = 147-105~
R =52-38p
Na2C03
/ 0
0
0
0
0.2
0.6 0.8
0.4
0
0.2
0-4
0.6
0.8
TIME- CONCENTRATION INTEGRAL Figure
5. Laboratory experiments
Substituting p = 16.5 kilomoles/cu. meter and E = 1.6 X K = 2.6 meters/hr. I n both tests the calculated rate of conversion falls very rapidly in a similar manner to the measured results but the conversion in the first t\vo vessels is appreciably lower than measured. T h e liquor concentrations are correspondingly higher, as required by the material balance. This feature may be explained by reference to our initial assumption of spherical symmetry. T h e anhydrite feed is produced by grinding mined rock, and has a n irregular shape and in particular will have a much higher surface-volume ratio than a sphere. Thus the initial reaction rates will be much higher
Table IV.
Tank iYo., n
1 2 3 4
6 9
Measured and Predicted Results for Tests 1 and 2
scConoerted cas04 Measd.
Calcd.
81.3 88.7 90.9 94.1 94.7
72.3 84.5 89.8 92.3 94.7
81.3 89.0 91.1 92.5 93.0 96.1 96.5 97.5
74.2 86.0 90.8 93.0 94.3 95.1 95.8 97.0
Molar COSConcn. Measd. Calcd. TEST1 0.42 0.81 0.37 0.58 0.5 0.45
en from Concn. Measd. Calcd.
TEST2 1 2 3 4 5 6 7 10
0.47 0.40 0.53 0.47 0.34 0.31 0.30 0.24
0.78 0.47 0.53 0.43 0.37 0.33 0.30 0.25
0.17 0.30 0.48 0.63 0.73 0.82 0.91
..,
0.30 0.43 0.61 0.74 0.85 0.95 1.04
...
(TI
in batch reactor
than predicted; however, as the reaction proceeds the error introduced will diminish, because the receding interface will tend towards the spherical form. Deviations from the perfect mixing assumption will also have their greatest effect in the early vessels. T h e model could be adjusted by the use of a particle geometry more closely resembling that of the original particle, but this Ivould greatly complicate the mathematics. Alternatively it may be possible to simulate a n irregular particle by several equivalent spheres of similar reaction characteristics; this would require only manipulation of the size distribution function before feeding into the computer. Neither of these options was pursued, as a n adequate fit for a large part of reaction system was obtained. As a further check to the model, samples of the solid were taken from vessels 1, 3, and 7 during test 2 and three size ranges separated by sieving or sedimentation techniques. These were then analyzed to determine the conversion and plotted in Figure 6 using the median size as estimated from the complete size analysis. These were then compared with the calculated values. Because of the discrepancies in the calculated and measured values of the carbon dioxide concentrations for the first t\vo tanks, t\yo possible values of parameter 8" can be derived. T h e results show reasonable agreement for tanks 3 and 7 with the curves based on the calculated solution concentrations. T h e conversions in the first tank are generally higher than predicted, for the reasons noted above. Application of Model
T h e equations developed for the reaction of a single particle have been utilized to derive a clear picture of what is happening in the plant reactors. T h e anhydrite rock feed VOL. 7
NO. 2
APRIL
1968
283
0.5
-
o
/
cesses-diffusion through the chalk layer which forms within the particle and a reaction a t the sulfate-carbonate interface, Laboratory and plant results have been used to demonstrate the validity of the model a t all but low fractional conversions; a t low conversions discrepancies are found owing to the uncertainty of the surface-volume ratio of the particles. T h e diffusion coefficient for the chalk layer has been estimated a t 7 X 10-8 sq. meter per hour. T h e rate constant for the reaction, first order in carbonate ions, a t the interface has been estimated a t 2.6 (kilomoles) /(sq. meter) (hr.) (kilomoles/cu. meter). T h e model has been used to predict the effect of various plant modifications on the residual sulfate level of the by-product chalk. This is particularly important, as the chalk is used in the manufacture of cement and appreciable sulfate levels make it unsuitable for this purpose.
/
-
-
c‘
0.6
0.9
1.0
0
20
Nomenclature
PARTICLE SIZE (MICRONS)
0 X 0
Figure 6. vessels
20-40p 40-60,U 76-104p
-
FROM MEASURED CONCENTRATIONS CALCULATED CONCENTRATIONS
---FROM
Conversion of samples taken from plant
A
= solubility product of calcium carbonate, (kilo-
moles/cu. meter)z solubility product of calcium sulfate, (kilomoles/cu. meter)2 = total concentration of all carbon dioxideC containing species, kilomoles/cu. meter = value of C in feed liquor, kilomoles/cu. meter CO = mean diffusivity of all carbon dioxide containing D species through chalk layer, sq. meters,/hr. = fraction of carbon dioxide in solution existing E as carbonate ion = fraction of anhydrite feed in size ranges R to F(R)dR R f dR = fraction of anhydrite having values in range F(r)dT r to 7 d7 = liquor feed rate to tankj, cu. meters/hr. f, = interfacial reaction rate constant, kilomoles/ k (sq. meter) (hr.) (kilomoles/cu. meter) K I , K z , etc. = equilibrium coefficients; concentrations measured in kilomoles/cu. meter = number of moles of sulfate reacting at interN face, kilomoles = number of tanks, measured from the first, under n consideration = initial radius of particle, meters R = instantaneous radius of reaction interface, meter r = concentration of sulfate ions, kilomoles/cu. S meter = mean residence time of all particles, hr. T = residence time of a given particle, hr. t = volume flow rate of liquor, cu. meters/hr. U = volume flow rate of solids, cu. meters/hr. U = volume of each tank, cu. meters V = mass rate of C a s 0 4 in anhydrite feed, kilomoles/ W hr . P = molar density of C a s 0 4 in anhydrite feed, kilomoles/cu. meter = time-concentration integral (see Equation 12) 7 kilomoles hr./cu. meter = mean value of r for all particles, kilomoles hr./ e cu. meter = total value of for tanks 1 to n, kilomoles hr./ 8, cu. meter = fractional conversion of a given particle 7 = mean value of 7 for all particles ti = concentration of speciesy, kilomoles/cu. meter IVI
B
=
+
IF PARTICLES
>15Op REMOVED
ae
I I
,
1m ANHYDRITE RATE IKglhr
t
75
125 a
IO-’)
Figure 7. Effect of modifications on plant performance
has a wide size range, which includes a large quantity of fine material and a small quantity of large material. T h e calculations show that only the larger material has failed to react completely. This can be demonstrated by calculating the conversions with all material greater than 150 microns (6% of the feed) removed. T h e over-all conversion rises from 96.3 to 98.8%. If this is repeated for a limit of 100 microns (1170 of the feed removed), the conversion rises to 99.4% (see Figure 7 ) . An increase in the maximum rate to 120 X IO3 kg. per hour of anhydrite was assumed to be possible a t the expense of a n increase in particle size of 20y0 over that given for test 2 in Table 11. T h e resulting calculation shows (see Figure 7 ) that the sulfate level in the chalk is unacceptable. T h e model has also been used to investigate several other possible changes, without recourse to expensive pilot plant work. I n particular, the use of certain size separation devices on the feed and also on the partially reacted magma have been examined using simple modifications to the main computer program. Conclusions
A mathematical model has been developed to describe the reaction between a solution of carbon dioxide and ammonia with natural anhydrite. There are two rate-limiting pro284
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Acknowledgment
T h e author acknowledges the contribution of J. A. Wildsmith in writing the computer programs used in the preparation of this paper and also the value of discussion held with P. P. King. Acknowledgment is also given to Imperial Chemical Industries, Ltd., for permission to publish this paper. literature Cited
Everett, D. H., Landsman, D. A., Trans. Faradav SOC.50, 1221 11954).
Fauyiol;,. C. J., Chim. Phys. 22, 1 (1925). Harned, H. S., Davis, R., J.A m . Chem. SOC. 65, 2030 (1943).
Harned, H. S., Robinson, R. A., Trans. Faraday Sod. 36, 977 (1940). Harned, H. S., Scholes, S. R., J . A m . Chem. SOC. 63, 1706 (1941). Hatch, T. F., Pigford, R. L., Ind. Eng. Chem. Fundamentals 1, 209 11962). Higson, G. I., Chem. Znd. (London) 1951, p. 750. MacMullins, R. B., Webber, M.. Trans. A m . Inst. Chem. Eners. . 31 409 (1935). Neumann, B. Z., 2. Angew. Chem. 34, 445 (August 1921). Parsons, R., "Handbook of Electrochemical Constants," Butterworths, London, 1959. Sherwood, T. K., Pigford, R. L., "Absorption and Extraction," 2nd ed., p. 11, McGraw-Hill, New York, 1952. RECEIVED for review March 10, 1967 ACCEPTED November 20, 1967 Division of Fertilizer and Soil Chemistry, 152nd Meeting, ACS, New York, N. Y . , September 1967.
KINETICS OF HYDROGEN REDUCTION OF MANGANESE DIOXIDE H. E. B A R N E R ' A N D C. L.
M A N T E L L
Newark College of Engineering, Newark, .?I. J .
Single porous pellets and small beds of particles of synthetic pyrolusite were reduced in hydrogen at various partial pressures in the temperature range of 200" to 500" C. The reaction kinetics were followed by recovering the water product, and the intermediate reduction products were identified b y x-ray diffraction analysis. Reductionproceeded topochemically through the sequence MnOz -+ Mn2Oa -3 Mn304+ MnO. Below 250" C. reduction subsided with the formation of MnaO4, and the process was controlled by a gas-solid chemical reaction step. Above 250" C.severe diffusional resistances were encountered, and further reduction to MnO became appreciable. Above 325" C. the over-all reduction process was again controlled by a gas-solid chemical reaction step. Variation of the reduction rate with temperature and with HZ and H 2 0 partial pressures i s consistent with the concept that the gas-solid reactions in the low (below 250" C.) and high (above 325" C.) temperature regimes involve adsorption of Hz, surface reaction, and desorption of H20, the surface rearrangement being rate-controlling.
only commercial source of pure manganese is based on electrolysis of manganese sulfate solutions. One important step is the reduction of oxidized ores to make them soluble in the recycled anolyte, usually accomplished by roasting the ore in a reducing atmosphere at approximately 1650" to 1700" F. T h e manganese content can be readily reduced in this manner to the divalent form. Very little, however, is known about the kinetics of the reduction reactions or the nature of the intermediate reduction products. T h e purpose of the present work was to study the reduction of manganese dioxide, with respect to both the kinetics and the identification and stability of the reduction products. Very few data on the reduction of MnO2 have been published. T h e only serious kinetic study heretofore made is the Russian work of Chufarov and coworkers (Chufarov et al., 1952; Tatievskaya et al., 1948, 1949). T h e first (Tatievskaya et a / . , 1948) publication of this series discusses the reduction of MnOz to M n O with hydrogen in the range of 300" to 500' C. T h e reduction rate was found to be approximately first order with respect to hydrogen partial pressure, and the apparent HE
T the
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Present address, The M. W. Kellogg Co., New Market, N. J.
activation energy was determined to be 24 kcal. per mole. T h e two later publications dealt with carbon monoxide as the reducing agent. I n a much more restricted study (Cismaru and Vass, 1962) samples of MnO2 were reduced at a hydrogen pressure of 1 atm. in the range of 350" to 490" C. Contrary to the Russian workers, Cismaru and Vass claim that the reduction terminates with the formation of MnaOa in this temperature range. Mn-H-0 Reduction Equilibria
A thermodynamic analysis of the oxide phases which are in equilibrium with gas mixtures of H f and HzO (Barner, 1967) indicates that M n O is the equilibrium reduction product throughout the realm of practical temperatures. More specifically, reduction of MnOn to M n O is thermodynamically feasible (room temperature to 1000" C.) as long as the ratio P H Z ~ / PisHless 1 than approximately 1 X 105. Conversion of the monoxide to manganese metal cannot proceed to any appreciable extent except at very high temperatures. Even at 1600" K . (above the melting point of Mn) in the ratio PBzo/PHzmust be maintained below 3 X VOL. 7
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