Thermal decomposition of doped calcium hydroxide for chemical energy storage

Solar Energy Vol. 36, No. 1, pp. 53-62, 1986 Printed in the U,S,A.

THERMAL

0038-092X/86 $3.00 + .00 ¢~ 1966 Pergamon Press Ltd.

DECOMPOSITION

HYDROXIDE

FOR

OF

CHEMICAL

DOPED

ENERGY

CALCIUM STORAGE

M. S. MURTHY,P. RAGHAVENDRACHARand S. V. SmRAM Department of Chemical Engineering, Indian Institute of Science, Bangalore 560 012, India (Received 25 June 1984; revision received and accepted 27 March 1985)

AbstractmThermal decomposition of Ca(OH)2with and without additives has been experimentally investigated for its application as a thermochemical energy storage system. The homogeneous reaction model gives a satisfactory fit for the kinetic data on pure and Ni(OH)2-, Zn(OH)2- and Al(OH)rdoped Ca(OH)2 and the order of reaction is 0.76 in all cases except for the Al(OH)rdoped sample for which the decomposition is zero order. These additives are shown not only to enhance the reaction rate but also to reduce the decomposition temperature significantly. Some models for solid decomposition reactions, and possible mechanisms in the decomposition of solids containing additives, are also discussed.

1. INTRODUCTION Effective utilization of solar energy depends on the development of efficient storage systems. Without storage the energy has to be used as soon as it is received. This is a disadvantage because supply and demand are not necessarily at the same time. Chemical methods of storage provide one of the many solutions to this problem. F o r storage of high temperature heat some reversible chemical reaction systems (having high heat of reaction) appear to be attractive. Advantages of thermochemical storage include high energy density (compared to sensible or phase change storage), ambient temperature storage for long periods without thermal loss and potential for heat pumping and energy transport over long distances. Wentworth and Chen[1], Mar and Bramlette[2] and Ervin[3] listed many potential chemical reaction systems for storage of solar energy and discussed their characteristics. The decomposition of alkaline-earth hydroxides, carbonates and some metal oxides appear to be promising chemical reaction systems for development of heat storage systems. Considerable amount of work has already been reported on the CaO/Ca(OH)2 system[4-7]. The effect of additives on the decomposition of Ca(OH)2 has been investigated in some detail in the present study. The results reported in this paper and the discussion on models for solid decomposition reaction may also find applications in other investigations in the field of gas-solid reactions.

The reaction occurs spontaneously if the fleeenergy change A G O for the reaction is negative or 0 at any elevated temperature, say T, A G o = A H ° - TASO.

(1)

The equilibrium constant " K " for a reaction is defined as AG o = -RTIn

K.

(2)

F r o m eqns (1) and (2)

T=

~H o ASO- RINK"

(3)

A H ° and A S ° are independent of temperature, if the change in heat capacity A Cp = 0. However, if A G O is slightly positive reaction may still be possible because of errors in calculation of A G Ovalues. Catalysts may be of help in all the cases. A temperature T* (turning temperature or equilibrium temperature) may be defined when K = 1, i.e. In K = 0 in eqn (3). T* = AH°/ASO, [ACp = 0;

K = 1;

A G o = 0]

(4)

Thus the turning temperature is the temperature at which the reaction turns in favour of forming products. Large A H ° is desirable to maximize storage capacity and small molar volume (6) of products to minimize storage volume, i.e. maximum H ° ~ desirable. I f A H ° is to be large then from eqn (4) AS° must also be large so that T* falls within the practical limit attainable with concentrated solar radiation. However, there are few reversible chemical reactions involving condensed phases for which A S o exceeds 80 J/mol K. If we wish to generate heat at

2. THERMODYNAMIC CONSIDERATIONS

Thermochemical energy storage is illustrated by a hypothetical reaction AB ~ A + B where the forward reaction takes place at a high temperature using concentrated solar energy to yield products A and B which can be combined at a later time to recover the input thermal energy. 53

M. S. MURTHYet al.

54

400°C (673 K and store energy at 800°C (1073 K the ratio AH°/AS ° = T* ~- 673-1073 K. The concept of turning temperature thus becomes a screen to choose the candidate reactions for the energy storage scheme[l]. Reversible dehydration-hydration of Ca(OH)2/ CaO satisfies many criteria and appears to be a suitable reaction. Concentrated solar energy may be used to decompose Ca(OH)2 and the product CaO can be stored under normal conditions in the absence of water and CO2. When necessary water or steam can be added to regenerate heat. 3. MODELS FOR DECOMPOSITIONREACTIONS

The decomposition of Ca(OH)2 takes place with absorption of heat, and endothermic solid reactions of this type yield a new solid and a gas solid I ~ solid II + gas. The dissociation and recombination processes often occur simultaneously and thus experimental investigations and interpretation of results cause problems. Nevertheless, these reactions provide information about the mechanism of interface reactions, nucleation and growth processes. The most convenient and useful technique in the study of dehydration reactions is the loss of weight method because of complications in handling easily condensable water vapor. Once an interface is formed, the reaction proceeds through a layer of the solid reaction product. The specific mechanism involved will depend on the properties and condition of this product layer. The fraction of solid (Ca(OH)2) reacted is given by the expression Wo-

~t =

Wo

torily describes the experimental data. McKewan[10, 11] slightly modified eqn (7) incorporating the effect of particle diameter and obtained a straight line for particles of different sizes. For rapid chemical reactions at the interface and a low diffusion coefficient De, diffusion through the product layer may determine the rate and this aspect is discussed later in this paper. In the thermal decomposition of solids nuclei of the new phase are formed very rapidly and the surface is covered with a film of solid product almost instantaneously. Equation (7) is applicable for rapid nucleation followed hy rapid two-dimensional growth. In certain cases where particle size is large, nucleation of the reactant may not be instantaneous but may be a random process and rapid surface growth may or may not take place. Nucleous formation in many solid phase decomposition reactions occur at a limited number of sites at regions of disorder. If there are No particles (spherical shape) of uniform radius ro, the nucleation rate is given as[12] dN - - = ktNoe -k't, dt

(8)

where kl is the nucleation rate constant and N is the number of nuclei at time t. Nucleation of particles is followed by rapid two-dimensional growth leading to the formation of interface. It is assumed that nucleus formation involves a single surface chemical reaction. Once interface is formed it grows and follows shrinking or receding core model. The volume of a particle, nucleated at t = tt, which has decomposed after time t is dV = V(t, h) ( d" N ~ ) t~t, dtl,

(9)

r/3

W

1

r°3

(5)

The rate of reaction of solid (spherical particles of equal size in the powder) is proportional to the area of the interface which changes continuously. For a shrinking spherical particle, when chemical reaction controls, the rate of decomposition is given as dW/dt = k ' A = k' W 2/3,

4 3 V ( t , h) = ~ "trro -

~ [ro

-

k2(t -

tt)] 3'

(10)

where k2 is the linear growth rate constant (at time t=). The total volume of reactant decomposed at time t is (reacted material) dN V(I) = fot V(I, tl)(-'d't)tftl dtl.

(6)

where k' is a constant. In terms of fraction reacted the expression can be written as

4

(11)

From eqns (8) and (10) 4

1 -

(1 -

a ) I/3 =

k"t

(7)

where k" is constant. A plot of 1 - (I - a) t/3 against " t " gives a straight line. Equation (7) is applicable when diffusion does not influence kinetics which is generally the case when a porous solid product is formed. Dollimore and Tonge[8], Warner and Ingraham[9] and many other investigators reported that eqn (7) satisfac-

V(t) = ~ "trklNo x

e -k'''{r~-

(to-

k2t + k2tt) 3}dh.

(12)

The total volume of reactant at t = 0 (unreacted) 4

Vo = ~ xrr~No.

(13)

Thermal decomposition of doped calcium hydroxide The conversion or extent of reaction a is

partial pressure of the gaseous product at the reaction interface. J is the number of molecules of the diffusing species in time t through the product layer.

a(t) = V(t)/Vo,

~o'dpi =

therefore, ct(t) = kl

55

f/

J f~"dr 41rDe r2 ,

(20)

e -kin dh

Pi

kl ft Jo [(ro - k2t) + k2h] 3 e -kin dh.

--

Po =

4~rD~

- r,

(14) or

Evaluating the integrals

/

| (Pi - Po).

\ r o -: r i /

or(t) = 1 + e -k'' r 3k2

+ 6 \k-~r~/ J -

ro

L\

The loss of weight per unit time due to reaction of the solid is given by / dW - 41rr2p dri . dt = ~"

+ 3(r°-k2t~2(k~ro)ro /

"

(15)

dW d--7"

J =When nucleation is rapid kl = ~ and eqn (15) reduces to

~=1-

~

dW - 4 ~ r ~ p dri dt = "~"

d

(16) = 41rDe

or

(1

tk -

~)1/3

=

.-2__= = ro

k"t.

(17)

Equation (17) is same as eqn (7) when nucleation is instantaneous, and is applicable to experimental data carried out under conditions when the chemical reaction was not influenced by gas film diffusion. Thus the variation of k2 which may also be considered as specific reaction rate constant, k,. can be expressed by means of Arrhenius equation

k, = k~ e -E/RT

(25)

_ r2i dri ro - ri = D_..~(Pi - Po). dt rori p

(26)

-~"

-

ri

Rearranging eqn (26) gives

f~' (ri - r2~r--o/dry= _ D,_p(p~ _ Po) fo t dt,

(27)

i.e.

o,

",

"

2-J~o -

(p,_

po)t.

(28)

L3roJ,o = -

E q u a t i o n (28) w h e n r e a r r a n g e d and s u b s t i t u t e d for ri in t e r m s o f ct, the f r a c t i o n a l c o n v e r s i o n [r,. = ro(1 - ¢t)1/3], s i m p l i f i e s to 1 -

3(1 -

a ) ~3 + 2(1 - a ) =

= -4"trr2De

ro

(18)

where k,o = frequency factor or rate constant at some reference temperature To. A reliable value of E has to be used in eqn (18). if the reaction rate is controlled by diffusion of gaseous product species away from the interface, then from Fick's law

J

rori

(P~ - Po),

1-

~d

1 -

(24)

Therefore,

fro - k2t] 3 L

(23)

The number of molecules of the diffusing species in time t corresponds to the weight loss at that time and hence

+6( r°-Sk2t~ / \(~iro,l

~=I-

(22)

{ k2 ] 2

Lk, r ° + 6 \ ~ r ~ }

+ 6

\

rori

J = 4~De [

6D et

pr~' (Pi - Po) =

k" t .

(29)

(19)

where De is the diffusion coefficient and pi is the

Equation (29) describes the diffusion control in the gas phase.

56

M.S. MURTHYet al.

Although eqns (7) and (29) for chemical reaction control and diffusion control processes, respectively, appear different mathematically, the difference in most experimental data on the decomposition of small particles is very small and comparable to experimental error (Fig. 10).

or C~A-m -- C~o"

(c.)'-m Cao}

H o m o g e n e o u s reaction model

For a porous solid in the form of a powder diffusion is rapid and reaction occurs throughout the solid. The concentration of the reactant solid is uniform throughout the particle and thus the rate of reaction of the solid particles may be assumed to be homogeneous type. For a reaction of order m, the rate expression is given by rA

dCA =

-

-

dt

dCA

C2

=

~..~)kt= - k ' , + 1, c2Y

(l

(1

kr =

m)k

-

C~; "

Replacing the left-hand side of the above equation with (W/Wo)", where W, Wo are weights of water in undecomposed hydroxide at any time and that in the initial sample, respectively,

kdt.

(31)

rc2-+,]

L 1 - m j c.o = kt

=

-k't

+ 1,

t

(32)

(W/Wo)" = - K t

+ a

50°C 0.8

y

4oo-c

0.6 0.5 0.4 0.3 0.2 0.t 0

7 f

I

I

2

4

6

(35)

where n, K and a are constants. The effect of tem perature on K , is given by Arrhenius equation(18).

500°C

0.7

(34)

w h e r e n = 1 - m. Britton et al.[13] in their studies on kinetics of decomposition of calcium carbonate and magnesium carbonate, found that their data could be represented as an empirical equation

0.9

Q

(33)

where

(WIWo)"

Integrating above equation between limits CA at = t and Cao at t = to, respectively, fCcadCA Ao C----~a -

1

=

(30)

-- k C ~ ,

where k is rate constant of reactant A at any instant - - -

- ( 1 - m)kt

=

or

I

I

8 t0 Time (rain)

I

I

[

12

14

t6

Fig. 1. Fraction conversion vs. time for Ca(OH)2 decomposition.

18

Thermal decomposition of doped calcium hydroxide

57

1.0

6,

0.8 0.6 0.4

0.2 l

0

I

I

2

I

I

|

4

I

I

6

1

8

1

I

I

I

10 12 Time (min)

1

14

I

I

16

I

I

18

Fig. 2. Evaluation of rate constant pure (Ca(OH)2) homogeneous model. 4. EXPERIMENTALRESULTS Thermal decomposition studies on Ca(OI-I)2 samples, both pure and doped, were carried out to study the dehydration by employing thermogravimetry and differential thermal analysis. A quartz spring thermobalance was used for thermogravimetric studies and a Stanton-Redcraft thermal analyser for differential thermal analysis studies. The chemicals used were supplied by reputable firms. Thermal decomposition of Ca(OH)2 takes place between 400-500°C approximately. Fractional con-

version of Ca(OH)2 at various times is shown in Fig. 1 at 400°, 450° and 500°C. The data shown in Fig. 1 could be well fitted by eqn (34) with n = 0.24. Figure 2 shows the plots of (W/Wo)T M against time for decomposition at three different temperatures, and Fig. 3 shows a typical particle size distribution curve.

Effect of additives The decomposition temperature of Ca(OH): is about 500°C. If the decomposition temperature can

100

,,,

8O

Z LIJ t.) ¢r LU n

6O

(.9

SAMPLE M 1 Ca(OH)2 powder M e a n Grain Size in Microns = 12.45 M e a n (Moments) in Microns = 9.944

LLI > <~ _J

40 Statistical Parameters Inman (1952)

t.)

20

Mean

6.318 1.024 - 8.597 2.403

Std. Dev Kurtosis Skewness

Ok

4

5

6

7

PHI

8

9

Folk (1957)

Moments

6.321 1.028 1.034 - 5.28

6.651 1.051 - 0.8397 - 0.0401

Sample is poorly sorted Curve is near-symmetrical Sample is Mesokurtic

Fig. 3. Particle size analysis.

58

M.S. MURTHYet al. 4.0 0.8 0.6 ,,

0.4 0.2

ings '

0

4

'

I

8

42

ings I

!'

I

I

I

160

4

8

12

f I

5 % Dopings

I

I

I

I

I

160

4

8

12

16

Time (min)

Fig. 4. Effect of doping Ca(OH)2 with AI Zn Ni on decomposition at 450°C; X [] [] Ni; © © Pure Ca(OH)2. 1.0

0.6 0.4 0.2 o

. . . .

i

i

i

i

i

i

i

i

i

A Zn;

rate compared to pure Ca(OH)2. Aluminium and zinc appear to be the most effective. Figures 5-8, which are plots of ( W / W o ) °'24 vs. time indicate that eqn (34) adequately represents the decomposition rate with additives Zn(OH)2 and Ni(OHh. In the case of aluminium dopings a plot of ( W / W ) -~ vs. time (t) indicates a linear relationship and thus a zero order reaction (Fig. 9). The activation energy E found in the present investigation in the decomposition of Ca(OHh is 45.72 kJ/mol and for Zn and Ni-dopings E, has been found to be 41.45 and 90.02 KJ/mol, respectively. It appears from the curves shown in Fig. 10 that the surface reaction or diffusion through product layer might not be controlling the overall rate. Gen-

0.8

~Od <5

X AI; A

i

l

0.8 0.6

500°C

/ 0.4

0

.

.

.

2

.

4

,

I

,

,

,

6 8 10 Time (rain)

,

,

12

,

,

14

1.0

I

0.8

0.6

Fig. 5. Ca(OHh doped with Zn(OHh 3%.

0.4 (M

be lowered heat losses can be minimized and solar concentrator load is decreased. This is achieved in the present work by doping Ca(OH)z with additives such as hydroxides of aluminium, nickel, iron and zinc. The level of doping is fixed arbitrarily at 1%, 3% and 5% on weight basis for each of the above metals. A solution of the required composition of calcium chloride and the other metal chloride was prepared and sodium hydroxide solution was added to precipitate the doped Ca(OHh. Decomposition of doped Ca(OH)2 samples was carried out through thermogravimetric analyser (TGA). Figure 4 shows plots of decomposition vs. time for doped samples at various loadings, which indicates that doped samples decompose at a faster

0.2

6 0

I

I

I

I

I

I

I

I

I

I

I

I

I

1.0 0.8

0.6 0

2

4

6 o 10 Time (min)

12

Fig. 6. Ca(OHh doped with Zn(OHh 5%.

14

Thermal decomposition of doped calcium hydroxide

to

59

.

0.8 0.6

4% 0.4 O..C

04

d

3%

1.0

0.6 0.4 0

2

4

6 8 10 Time (min)

12

14

Fig. 7. Ca(OH)2 doped with Ni(OH)2.

1.0 0,8 450o~E-.--. 0.6 0,4 02 tM

d 0

1.0~ 0.8

430°C

"

0.6 0.4 0

2

4

6

8

10

12

Time (rain) Fig. 8. Ca(OH)2 doped with Ni(OH)2 5%.

14

16

M.S. MURTHYet al.

60

1%

3%

16

[]

T

-450°C

12

°C

8 4

0

'

4

'

8

'

12

'

1 6'

'

Time

4'

0

'

8'

'

12

' 16

(min)

Fig. 9. Ca(OH)2 doped with AI(OH)3.

Table 1. Initial rates of dehydration at 450°C Sample

(da/dt),. o (min- ' )

Ca(OH)2 Ca(OH)2 - 1% AI(OH)3 Ca(OH)2 - 3% AI(OH)3 Ca(OH)2 - 5% AI(OH)3

0.1167 0.70 0.724 0.78

erally, in the case of fine particles the reaction occurs homogeneously throughout the particle as the diffusion path is extremely small. Thus in the present work, the effect of dopings on the dehydration rate can be easily measured. The rate enhancement can also be seen from Table 1 where initial rate of dehydration for pure and Ca(OH)2AI(OH)3 samples are given.

It can be seen that pure Ca(OH)2 decomposes around 480°C in air medium, but the decomposition temperature is reduced when the samples are doped. Aluminium hydroxide doped samples decompose at temperatures much lower than the decomposition temperature of pure Ca(OH)2. It can also be seen that there is a pattern in the case of Zn(OH)2 doped samples. Initially the decomposition temperature is lowered, but above about 3% doping, the decomposition temperature starts increasing. Synthetic mixtures containing Ca(OH)2 and the required amount of Zn(OH)2 were also subjected to DTA. It is interesting to note that the samples containing same amount of Zn(OH)2 decom-

Table 3. Decomposition temperatures of doped samples and synthetic mixtures

Differential thermal analysis of samples D T A studies were carried out on pure and doped samples of calcium hydroxide using 5.5 mg of samples at a heating rate of 10°C/min. The air flow rate was maintained at 10 ml/min. The results are presented in Table 2.

Decomposition Temperature °C co-precipitated Mixed powders

Composition Ca(OHh - 1% Zn(OHh Ca(OH)2 - 3% Zn(OH)2 Ca(OH)2 - 5% Zn(OH)2

475 465 475

Table 2. DTA studies on samples S1. No. 1.

Sample

3.

Pure Ca(OH)2 Ca(OH)2 - 1% Zn(OH)2 Ca(OH)2 - 3% Zn(OH)2

4.

Ca(OH)2 - 5% Zn(OH)2

5.

Ca(OH)2 - 1% AI(OH)3 Ca(OH)2 - 5% AI(OH)3

2.

6.

Peak Temp. °C

Remarks

490 480 170 460 180 475 470 315

Sharp endotherm Sharp endotherm Small endotherm Broad endotherm Small endotherrn Sharp endotherm Sharp endotherm Small endotherm

480 460 475

Thermal decomposition of doped calcium hydroxide

20

Temp. 4 5 0 * C

10 E E k-

I

0 -3(1

-

0.3 a) 2/3 + 2(1 - a ) 1/3 o r 1 -

0.6 (1 - a)1/3

Diffusion model (3 - - Pure Ca(OH)2 X - - 3% Ni Chemical reaction model • - - Pure Ca(OH)2 A --

3 % Ni

Fig. 10. Diffusion and chemical reaction models for decomposition.

pose almost at the same temperature, irrespective of the method of preparation (Table 3). It appears that in order to reduce decomposition temperature, the method of mixing Ca(OHh powders may be employed instead of the costlier coprecipitation method.

CaO or Ca(OH)2 has a strong influence on the reactivity. Surface composition cannot be easily determined and leads to wrong interpretation/characterisation. Therefore it is desirable to pay attention to the methods which produce changes in composition. It is not clear whether dopings influence induction period or decomposition rate. Additives may inhibit or enhance diffusion, heat conduction and recrystallization of products. It appears logical to suppose that additives induce defects and form potential nucleation sites. The mechanism which could explain enhanced rate of decomposition with minute amounts of Ni, AI, Zn, etc. could be heterogeneous nucleation. The increase in the decomposition rate may be explained by the increase in number of nuclei from which the interface propagates. Another mechanism which can be conceived similar to catalysis is that of lowering of activation energy may be caused by dopings like catalysts by creating energetic centres and causing activation of some step during chemical transformation. In view of the large number of possible mechanisms of doping action on the reaction rate, effect of additives on hydration as well as on decomposition of CaO/ Ca(OH)2 must be established through systematic investigations. Acknowledgement--This investigation was carried out

with the financial support of the Department of Non-Conventional Energy Sources, Government of India, New Delhi. NOMENCLATURE

CA c~

De E aG ° aH o

5. CONCLUSION

It is interesting to note that small quantities of additives lower the dehydration temperature of Ca(OH)2 and also increase the reaction rates significantly. In the case of powders of pure and doped Ca(OH)2, the homogeneous reaction model fits the data adequately. Fujii and Tshchiya[4] have used a homogeneous reaction model, but with a first order rate, to describe the kinetics of decomposition of calcium hydroxide powders. The activation energy reported by these workers, 13.4 x liP kJ/mol, is, however, large compared to the value obtained in the present work, and to 62.4 kJ/mol reported by Mikhall e t a/.[14]. It is generally accepted that the reactivity of Ca(OH)2 depends on a large number of factors and the activation energies reported are not usually in agreement. Lime produced by the thermal decompositions of Ca(OH)2 exhibit considerable variations in the activity due to physical and chemical changes during decomposition. The composition of the solid

61

J K kl, k2 k',k",k" k~o m

N No Po, Pi R ri ro

rA

AS o T To t

V W Wo p

concentration of reactant specific heat diffusion coefficient activation energy of the reaction standard free energy change for the reaction standard enthalpy change for the reaction rate of diffusion of the gaseous product molecules equifibrium constant for the reaction nucleation and growth rate constants respectively constants frequency factor or rate constant at some reference temperature order of reaction number of nuclei at time t number of spherical particles partial pressures gas constant radius of the unreacted core initial radius of the particle rate of reaction standard entropy change for the reaction absolute temperature equilibrium temperature reaction time molar volume volume of the reactant mass of water in Ca(OHh at any time t mass of water in Ca(OHh at t = 0 fractional conversion solid density

M. S. MURTHYet al.

62 REFERENCES

1. W. E. Wentworth and E. Chert, Simple thermal decomposition reactions for storage of solar thermal energy. Solar Energy 18, 205 (1976). 2. R. W. Mar and T. T. Bramlette, Thermochemical Storage systems. Solar Energy Handbook, pp. 811. 3. G. Ervin, Solar heat storage using chemical reactions. J. Solid State Chem. 22, 51 (1977). 4. I. Fujii and K. Tsuchiya, in T. N. Veziloglu (Ed.) Alternate Energy Sources. (Edited by T. N. Veziloglu), Vol. 9, pp. 4021. Publisher, City (1978). 5. A. Kanzawa and Y. Arai, Thermal energy storage by the chemical reaction, augmentation of heat transfer and thermal decomposition in the CaO/Ca(OH)2 powder. Solar Energy 27, 289 (1981). 6. P. O'D. Offenhartz, Chemical methods of storing thermal energy, Proc. Joint Conf. Am. Section Int. Solar Energy Soc. and the Solar Energy Soc. Can. Inc. 8, 48 (1976). 7. J.A.C. Samms and B. E. Evans, Thermal dissociation

8.

9.

10. 11. 12. 13. 14.

of Ca(OH)e at elevated pressures. J. Appl. Chem. 18, 5 (1968). D. Dollimore and K. H. Tonge, Thermal decomposition of manganese oxy-salts and the characterisation of the solid products, 5th Proc. Intern. Syrup. Reactivity of Solids, Hurich, pp. 497-508 (1965). N. A. Warner and T. R. Ingraham, Kinetic studies of the thermal decomposition of ferric sulphate and aluminium sulphate. Can. J. Chem. Engng 40, 263 (1962). W. M. McKewan, Kinetics of iron ore reduction. Trans. Met. Soc. AIME212, 791 (1958); 218, 2 (1960); 218, 2 (1960). Ibid. 218, 2 (1960). Comprehensive Chemical Kinetics. (Edited by C. H. Bamford and C. F. H. Tipper), Vol. 2. Elsevier, Amsterdam (1969). H. T. S. Britton et al., Trans. Faraday Soc. 48, 63 (1952). R. Sh. Mikhail et al., J. Colloid Interface Sci. 21,394

(1966).