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The Dehydration Kinetics of Gypsum in a Fluidized Bed Reactor
0263±8762/00/$10.00+0.00 q Institution of Chemical Engineers Trans IChemE, Vol 78, Part A, October 2000
THE DEHYDRATION KINETICS OF GYPSUM IN A FLUIDIZED BED REACTOR S. R. CAVE and R. G. HOLDICH (AFFILIATE) Department of Chemical Engineering, Loughborough University, UK
M
easurements have been made of the rate of dehydration of desulphurized gypsum with particle diameters in the range of 35±67 m m in a ¯uidized bed reactor. Experiments were carried out at bed temperatures of 100 to 1708 C. The ¯uidizing gases were air, with water vapour pressures of between 0.001 atm and 0.35 atm, and carbon dioxide. The results show that the dehydration under all these conditions can be modelled using the two dimensional Avrami-Erofe’ev expression. In the experiments extreme care was taken to ensure that the generation of reaction products did not signi®cantly in¯uence the reaction rate. At the calcination temperature of 1408 C, the value used in industrial applications, a unique correlation between the reaction rate and water vapour pressure is apparent irrespective of the desulphurized gypsum particle diameters. Under these conditions, it is also shown that a unique relation between conversion and reduced reaction time then follows. Keywords: calcination; Avrami-Erofe’ev; calcium sulphate
INTRODUCTION
possible to obtain all the dehydration products as well as unreacted gypsum.
Calcium sulphate dihydrate, or gypsum, is a commonly found mineral and is also the by-product of several industrial processes, including ¯ue gas desulphurization and the production of wet phosphoric acid from phosphate rock. Large quantities of gypsum are processed prior to use in the building trade as an interior ®nisher. The gypsum is dehydrated to calcium sulphate hemihydrate (hereafter abbreviated to hemihydrate) before use. The hemihydrate is then either rehydrated during the industrial production of plasterboard or left unaltered and sold as plaster in bags. A number of processes have been developed to produce hemihydrate industrially using a variety of calciner designs. All the processes use the same basic principle of directly, or indirectly, heating the gypsum in order to dehydrate it to hemihydrate. Processes can either be batch or continuous depending upon the scale of production. The dehydration/rehydration reaction system for calcium sulphate is shown in outline in Figure 1. Gypsum dehydrates on heating to hemihydrate, in a reaction that is reversible in the presence of water. Hemihydrate on heating dehydrates further to calcium sulphate anhydrite, which exists in three polymorphs: AIII, AII and AI depending on the temperature of reaction. The hemihydrate to anhydrite AIII reaction is reversible in the presence of both water and water vapour. The phases of industrial importance are gypsum, hemihydrate AII and AIII. The quantity of each phase in a plaster determines the properties of the plaster. The most commonly used plaster is around 100% hemihydrate, which is used for plasterboard production, repairs and dentistry. The setting time of plaster can be modi®ed by the presence of gypsum (accelerator) and AII (retarder). Commercial building plaster is typically 50±70% hemihydrate and 50± 30% anhydrite. In a partial dehydration reaction it is
Thermodynamically Stable States and Reaction Kinetics Although gypsum calcination has been performed for several millennia, the understanding of what actually occurs in the system is incomplete. This is due to the large number of processes and interactions occurring within a gypsum calciner. A number of different phenomena occur: heat transfer, mass transfer, particle and gas mixing, particle elutriation and the dehydration reaction itself. All of these processes interact with each other. Kelly1 provided a thermodynamic analysis of the various states of gypsum dehydration, under different conditions of water vapour pressure and temperature, and this is shown in Figure 2. The reaction kinetics and associated phenomena have been studied in cylindrical ¯uidized beds for different systems and it has been found that theory and experimental results can deviate signi®cantly. A further complication to the development of a generally applicable model is that a number of physical gradients exist within industrial equipment. These include temperature, water vapour pressure and super®cial gas velocity which all change with height inside an industrial calciner. The decomposition kinetics have been studied by many investigators. There is no consensus on the mechanism. Mass transfer, heat transfer, chemical kinetics, and combinations of these have all been reported as rate limiting. In general, the reaction rate has been found to increase with: · increasing temperature2±6; · decreasing particle size3,4,7; · decreasing water vapour pressure8 with suppression of 971
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CAVE and HOLDICH A number of papers have been published which attempt to mathematically describe the dehydration reaction of both gypsum and hemihydrate. In common with the majority of solid state reactions, the reaction conversion (a ) has an expression of the form: kt
Figure 1. States of calcium sulphate during dehydration.
the hemihydrate to anhydrite reaction at high water vapour pressures9; · decreasing air pressure10 to a maximum rate at 1 mm Hg. Differences in crystalline characteristics (i.e. size and amount of defects), origin and impurities can affect the dehydration rate. There is also evidence that the reaction conditions can alter the properties of the hemihydrate by affecting the structure and surface area11. Comparison between the reported studies on reaction mechanisms is made dif®cult by the lack of a complete description of the reaction conditions. In many instances there has been little control, or even recording, of the water vapour pressure which, as a reaction product, would be expected to have a signi®cant in¯uence on the reaction kinetics.
Figure 2. Thermodynamically stable states of calcium sulphate at atmospheric pressure.
f a
1
A hypothesis of the reaction mechanism must be proposed in order to interpret an experimental rate constant for a solid state reaction. The function of a depends on the mechanism controlling the reaction. Common equations are based on diffusion, phase boundary and nucleation steps being rate determining. At least ten different models and mechanisms have been proposed for the gypsum dehydration reactions, with no general consensus. In fact, it has often been found that several different models ®t the data equally well12. The most popular methods used to derive the kinetic expressions are isothermal gravimetry and thermal analysis. The earlier papers tended to use isothermal methods: for example, McAdie9 carried out the isothermal dehydration of dihydrate and suggested a zero order kinetic relation (a kt). Molony and Ridge13 studied the dehydration of gypsum and suggested that the reaction was diffusion controlled with a diminishing rate expression A B 1 a 1/2 kt . Ball and Norwood14 and Ball and Urie15 studied the dehydration of both gypsum and hemihydrate: the dehydration of gypsum was found to have three different rate controlling expressions depending upon the prevailing conditions. Nucleation was rate controlling for temperatures less than 908 C and partial pressures of water greater than 0.005 atm; the contracting disc model was valid for temperatures 90 to 1108 C and diffusion was found to be rate controlling for temperatures greater than 1108 C. The second method used to derive the kinetic data is the use of various thermal analysis techniques. Heide16 studied gypsum decomposition using between 2 and 10 mg of sample by Differential Thermal Analysis (DTA) and stated that nucleation was rate controlling and could be modelled using Avrami-Erofe’ev expressions. Negro and Stafferi 17,18 studied the dehydration of gypsum and hemihydrate. The gypsum dehydration was nucleation controlled and was modelled using 2d Avrami-Erofe’ev expression. The hemihydrate dehydration was expressed as a reaction with an order of 0.68. Strydom et al.19 studied the dehydration by DTA using up to 50% more sample mass than Heide, and found that the reaction mechanism changed with conversion: a 0±0.1 could be represented by 3-d diffusion, a 0.1±0.7 by autocatalytic ®rst order and a 0.7±1.0 by the Sestak-Bergen expression. Hudson-Lamb et al.20 carried out a similar study, and again found that the reaction mechanism changed with conversion. Arii and Fujii 21 studied the dehydration by Controlled Rate Thermal Analysis (CRTA). They modelled the gypsum to hemihydrate reaction using 4d-Avrami-Erofe’ev and the hemihydrate to anhydrite-III reaction by a phase boundary model. Similarly, a large range of activation energies has been calculated. The activation energy for the gypsum to hemihydrate reaction has been found to range between 80± 392 kJ mol ±1 and for the hemihydrate to anhydrite-III reaction from 27±205 kJ mol±1. The most signi®cant problem with the kinetic rate expressions is a lack of reported experimental conditions Trans IChemE, Vol 78, Part A, October 2000
THE DEHYDRATION KINETICS OF GYPSUM IN A FLUIDIZED BED REACTOR
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Figure 3. Schematic diagram of experimental equipment.
and results. Important experimental variables are often not mentioned (e.g., particle diameter, sample size, water vapour pressure). Also experimental results, such as the exact mechanism equation, frequency factor (A) and activation energies (E) are sometimes not given or merely alluded to. As a result, the previous work is useful for understanding the dehydration process, but does not provide a clear basis for predicting the calcination rate of gypsum for industrial applications, which generally employs a ¯uidized bed operating at approximately 1408 C. Also, an increasingly important source of gypsum is the product from power generation ¯ue gas desulphurization, which generally has particle diameters between 35 and 70 m m. Most of the above mentioned studies used naturally occurring gypsum with particle diameters in excess of this range. EXPERIMENTAL A ¯uidized bed reactor was used to study the gypsum dehydration reaction, as shown in Figure 3. Compressed air was passed through a ®lter/regulator followed by a 230V in-line ceramic heater. The bed was held in place by two ¯anges, one of which acts as the distributor plate plenum. The ¯anges were constructed from 10 mm thick brass. The distributor plate was an 80 mm diameter stainless steel sintered disc and the bed was contained in a glass tube of diameter 80 mm and height 300 mm. The ¯uidized bed consisted of inert glass beads with a median diameter of 152 m m. The instrumentation consisted of ®ve K-type thermocouples (T1-T5), three piezoresistive bridge type pressure transducers (P1-P3), three turbine ¯ow meters (F1-F3), three rotameter type ¯ow meters (R1-R3) and one Trans IChemE, Vol 78, Part A, October 2000
humidity probe (H1). The humidity probe contained a thin®lm polymer sensor that could measure from 0 to 100% relative humidity with a reported accuracy of 6 2%. The probe also provided a temperature measurement, which is essential in order to calculate the mass of water present in the ¯uidized bed exit stream. The experimental work used a desulphurized gypsum sample supplied by BPB Gypsum. The original sample had a median diameter of 48 m m and was over 95% CaSO4.2H2O. The sample was divided into cuts with median particle diameters of 35 m m, 40 m m, 50 m m, 60 m m and 67 m m by elutriation in air. The experiments were carried out as follows. Compressed air was dried by passing through a silica desiccator. Air with a higher relative humidity was produced by replacing the silica with water and inline water injection. The air was heated using the in-line ceramic heater and used to ¯uidize the glass beads. The temperature of the bed was controlled based on the temperature reading of T2, which is located 10 mm above the distributor plate. The thermocouple T2 was calibrated prior to each experimental run. It was found that the temperature could be controlled to an accuracy of 6 28 C. The sample to be dehydrated was injected into the bed from the sample pot by temporarily bypassing some air around the bed through the sample pot. Sample injection was achieved within a couple of seconds. The extent of the decomposition reaction was monitored using the humidity probe positioned after the ¯uidized bed. The off-gas from the bed passed from the humidity probe into a glass cyclone, followed by a bag ®lter (Radio Spares, Corby, UK). The bag ®lter was contained in a clear plastic box and there was no observable deposition of solids in the
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glass cyclone or ®lter after any of the dehydration runs, prior to deliberately elutriating the solids from the bed to separate them from the inert bed material. Hence, elutriation of ®ne material from the ¯uidized bed during the experiment was not apparent. Gas Mixing and Probe Response The relative humidity probe reading did not give a true representation of the water generated from the dehydration reaction because of gas mixing in the ¯uidized bed and the response time of the probe. The effect of both parameters was studied by a pulse tracer test on the ¯uidized bed using steam injection. The ¯uidized bed was heated up to the required temperature. When steady state was reached, i.e. when the bed temperature and relative humidity probe temperature stopped ¯uctuating, 0.1 ml of distilled water was rapidly injected into the bed via a septum in the bed wall. The water injected into the bed was instantly converted to steam and removed from the bed in the gas exit stream. The rate at which steam left the bed was recorded using the relative humidity probe. Experimental runs were carried out at temperatures of 60, 80, 100, 110, 120, 130, 140, 150, 160 and 1708 C, and the mass of water used was varied to check that it did not signi®cantly in¯uence the results. A two stage tanks in series model was found to represent the gas mixing/probe response. The model is described by the following equation22 tN 1 N N Å e Nt/t 2 Åt N 1 ! where N is the number of stirred tanks, t is time and Åt is the residence time in the N tank system. Each tank in the series has a time constant Åt tt 3 N t t was calculated for each temperature. Figure 4 shows the exit age distribution against dimensionless time plot for water injection at 1208 C, 1408 C and 1608 C. The dimensionless time is the measured time divided by the residence time, and the experimental exit age distribution was determined by normalizing the area of the relative humidity against time plot to give an area of unity. The two tanks in series model appears to adequately ®t the experimental data.
Et
N
Figure 4. Exit age distribution curve for water injection into ¯uidized bed at three temperatures.
Data Analysis Using the two tanks in series model, the actual rate of water generation in the bed can be calculated from the relative humidity probe data by applying the following equation23 dRHA RHB RHA t t 4 dt where RHA is the read data, and RHB is the reading before a completely mixed tank with time constant t t . Since the model best ®tting the gas mixing/probe response is a two tanks in series model it is necessary to apply the equation again, substituting RHA with RHB, and RHB with RHC; where RHC represents the water vapour released within the bed. A problem in analysing the data in this manner is that the data from the probe is `noisy’, and this is ampli®ed when the derivative is taken. This means that the calculated RHC curve was `noisy’ which made determining rate constants dif®cult. In order to overcome this problem MathcadTM was used to provide cubic spline ®ts to the data. Over twelve different reaction models were evaluated, representing reactions controlled by diffusion, nucleation, geometry and other parameters often in combination with the foregoing. RESULTS AND DISCUSSION Differential conditions are required for the derivation of meaningful kinetic data, and in this instance they are believed to occur when the water given off in the dehydration reaction does not affect the rate of reaction. The absence of differential conditions may be one reason why there have been many different reaction models and rates reported previously. In order to elucidate when differential conditions occurred, a number of dehydrations were performed using different masses of gypsum and different gas ¯owrates. Figure 5 shows the effect of mass on the rate of reaction. Differential conditions were found to occur with a sample mass of 0.4 g and a ¯uidizing ¯ow rate of 14 nL min ±1. The next set of dehydrations used CO2 rather than air to determine whether the reaction is affected by the ¯uidizing medium; as CO2 has markedly different properties to air. There was a possibility that the differences in conversion
Figure 5. Effect of sample mass on conversion at 1408 C, 0.001 atm water vapour pressure and 40 m m.
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Figure 6. Comparison of ¯uidizing gas on reaction rate.
Figure 7. Reaction at different temperatures using water partial pressure of 0.001 atm, 40 m m particles.
data could be due to intraparticle diffusion or heat transfer. However, the rate was the same for both gases and therefore intraparticle diffusion and external heat transfer can be deemed not to be rate limiting. An example is shown in Figure 6 for the dehydration of 40 m m gypsum at 1008 C and 0.001 atm water vapour pressure. The rate limiting step is most likely to be due to the properties of the DSG particles themselves. In some cases resistance to mass transfer between the water vapour within the emulsion phase and the ¯uidized bed bubble phase can have a signi®cant in¯uence on the derived reaction rate constant. A graphical technique has been published to investigate this, considering different masses of reactants added to a ¯uidized bed, but with limited success24. Correlations exist for estimating the bubble gas exchange rate between the bubble and emulsion phases25. Under the prevailing experimental conditions, the calculated rate is in excess of 5000 s ±1; i.e. the bubble volume is exchanged with the surrounding emulsion phase gas over 5000 times per second. Hence, it is unlikely that signi®cant resistance to the dehydration occurred in the mass transfer between these two phases. The effect of temperature, particle diameter and water vapour pressure on the dehydration rate were studied. When AIII was the ®nal product of the dehydration as a result of the conditions in the bed, the reaction proceeded according to the following equation
determined by BET analysis typically changes from 0.2 m2 g ±1 for the desulphurized gypsum to 6.2 m2 g ±1 for the calcined product. The effective diffusivity (De) can be estimated according to the random pore model26
CaSO4 .2H2 O
CaSO4
2H2 O
5
The AIII quickly rehydrated to hemihydrate after elutriation from the ¯uidized bed, when conditions were in accordance with the hemihydrate favoured region illustrated in Figure 2. The shape of the conversion (a) versus time curves were all found to be similar, an example of these is illustrated in Figure 7. The dehydration reaction rate was not in¯uenced by particle size at the lower temperatures, water vapour pressure had a signi®cant effect and temperature had the most signi®cant in¯uence on the overall rate of reaction. An estimate of the contribution towards the overall reaction rate made by diffusion of water vapour from the interior of the particle to the surrounding ¯uidized bed can be obtained from the effective diffusivity. The gypsum particles are fractured by the homogeneous reaction due to the water vapour leaving the particles. The surface area Trans IChemE, Vol 78, Part A, October 2000
DM1
De
DK 1
1 2 eo
6
where eo is the porosity of the calcined particle, DM and DK are the molecular and Knudsen diffusivities respectively. The Knudsen diffusivity can be estimated from26,27 DK
97rp
T W
0.5
7
where rp is the average pore radius, T is the reaction temperature and W is the molecular mass of water vapour. The calcined particle porosity and average pore radius were estimated from BET analysis to be 11% and 35 nm respectively. Thus, under the reaction conditions most appropriate to the industrial calcination of desulphurized gypsum (e.g. bed temperature of 1408 C) the effective diffusivity of the water vapour in the calcined particle is 0.004 cm2 s ±1. This value is almost one order of magnitude less than one reported in the literature 28. However, for the purposes of estimation of diffusional resistance to the overall rate, the calculated and lower value will be used. This should provide an overestimation of the time taken for water vapour to diffuse out of the particle. The diffusional equation for a spherical particle, rendered dimensionless for numerical solution is ¶P ¶u
1 ¶ 2 ¶P x x2 ¶x ¶x
8
where: x
r ; R
De t R2 u
P
P2 P0
where r is radial position, R is particle radius, Pw is partial pressure of water and Po is total pressure. Equation (8) was solved using the computer package PDESOL by NumericaTM, using the upper boundary condition provided by the greatest humidity employed in the ¯uidized bed: Pw of 0.25 atmospheres. The differential lower boundary condition of ¶P ¶x
0 x
0
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CAVE and HOLDICH approximately 0.25 atmospheres. Thus, these conditions are relevant to the industrial calcination of desulphurized gypsum. From the data illustrated in Figure 8, it is apparent that the diffusion of water vapour out of ¯uidized particles under these conditions is rapid and the process is predominantly chemical reaction controlled. A large number of reaction models were considered for the homogeneous non-catalytic reaction represented by equation (5). The most suitable one for all the data was the 2d Avrami-Erofe’ev expression kt
Figure 8. Water vapour concentration pro®les inside a gypsum particle undergoing diffusion.
was also used. The resulting solution for the water vapour pressure at four times in a particle 45 m m in diameter is shown in Figure 8. The mean particle diameter of desulphurized gypsum is approximately 45 m m and a full-sized ¯uidized bed calciner could have a water partial pressure of
Figure 9. Experimental data and Avrami-Erofe’ev model using water partial pressure of 0.001 atm, 50 m m particles, 1308 C.
ln 1
a
1/2
9
where k is the reaction rate constant and a is fractional conversion. The reaction models were ®tted to experimental data between 5 and 95% conversion. In many instances solid state models are ®tted over the data range 10 to 90% conversion, hence the range taken here is assumed to be an acceptable test of the model validity. All the experimental results ®tted the model well, and a typical ®t is shown in Figure 9. Arrhenius plots were constructed for the experimental data and the activation energy and the frequency factor for the calcinations at low humidity, were found to be 81 kJ mole ±1 K ±1 and 8.5 ´ 1010 minutes ±1 respectively. Figure 10 shows the effect of temperature and particle diameter on the reaction rate at 0.001atm H2O. As can be seen, the temperature has a much greater effect on the reaction rate than the particle diameter. This was found to be true at each water vapour pressure, and is consistent with the earlier discussion on diffusional control. Figure 11 shows the effect of water vapour pressure upon the rate of reaction for different diameter particles at 1408 C and 1608 C. It can be seen that the temperature has a greater effect on the rate than the water vapour pressure although, within the experimental limits of the scattered data, there is an approximately linear reduction in the rate with increasing water vapour pressure. However, it could be argued that the reaction rate becomes stabilized above a threshold value, but the dehydration rate of gypsum has previously been shown to decrease monotonically with water vapour pressure at temperatures below 1008 C29. The data illustrated
Figure 10. Effect of temperature and particle diameter on dehydration rate (water vapour pressure 0.001 atm).
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THE DEHYDRATION KINETICS OF GYPSUM IN A FLUIDIZED BED REACTOR
Figure 11. Effect of water vapour pressure on dehydration rate at two temperatures.
Figure 12. Reduced conversion plot for all experimental conditions and model results during calcination at 1408 C.
in Figure 11 shows that particle size does not appear to have a signi®cant in¯uence on the calcination rate when operating at 1408 C. Considering the operating conditions most relevant to the calcination of industrial desulphurized gypsum, bed temperature of 1408 C, it is possible to empirically ®t a single linear equation valid for all the particle sizes illustrated in Figure 11. The equation can be used to determine the reaction rate constant for a given water partial pressure, which can then be combined with the overall material balance on the water produced during the calcination, following the stoichiometry given by equation (5), and the 2d Avrami-Erofe’ev reaction rate expression. Following this procedure it is possible to predict the time taken for the reaction to become 50% complete (t50), and the fractional conversion with respect to reaction time. The reaction time may be rendered dimensionless by the t50 value and a single curve results from the analysis regardless of the initial particle size or water vapour pressure. This is plotted in Figure 12, together with the experimental data covering all the operating conditions: humidity ranging from 0.001 to 0.3 atmospheres and particle diameters between 30 and 70 m m. It is evident that all the data in this region of reaction conditions relevant to the industrial calcination of desulphurized gypsum can be successfully correlated in such a fashion. CONCLUSIONS A laboratory ¯uidized bed reactor containing inert particles has been used to study the isothermal dehydration Trans IChemE, Vol 78, Part A, October 2000
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of gypsum, arising from ¯ue gas desulphurization, to form calcium sulphate hemihydrate. These reaction conditions are closer to those applied in the industrial production of hemihydrate than experimental studies employing thermal balances. Also, the reaction conditions, such as humidity, can be more reliably controlled because of the ef®cient mixing within the ¯uidized bed. However, this experimental system permitted back-mixing. The mass of water evolved from the gypsum was measured by an on-line humidity probe and corrected for mixing. The experimental arrangement could be modelled using two well mixed tanks in series. In order to prevent the reaction product from in¯uencing the rate of reaction differential condition tests showed that the sample mass within the bed had to be less than 0.1% of the total bed mass. Experiments with air and carbon dioxide as the ¯uidizing gases indicated that the reaction is not signi®cantly in¯uenced by heat transfer, or diffusion of the reaction products. Order of magnitude calculations based on the physical properties of the calcined gypsum particles (internal porosity of 11% and average pore radius of 35 nm) con®rm that diffusion of water vapour within the particle is unlikely to have a signi®cant in¯uence on the overall rate under the experimental conditions used. All the reactions studied could be modelled by the 2d Avrami-Erofe’ev expression, and the activation energy and frequency factor were calculated to be 81 kJ mole ±1 K ±1 and 8.5 ´ 1010 minutes ±1 respectively. At a reaction temperature of 1408 C the evolution of water vapour with respect to reduced reaction time could be correlated on a single curve, irrespective of particle size and prevailing humidity during the reaction. The curve could be adequately predicted by the 2d Avrami-Erofe’ev expression coupled with a material balance. NOMENCLATURE De DK DM k N RH rp T t Åt W
effective diffusivity, m2 s ±1 Knudsen diffusivity, m2 s ±1 molecular diffusivity, m2 s ±1 reaction rate, min ±1 number of stirred tanks relative humidity average pore radius, m reaction temperature, K time, s residence time in N tank system, s nolecular mass of water vapour, mol g ±1
Greek letters a conversion eo internal porosity of particle
REFERENCES 1. Kelly, K. K., Southard, J. C. and Anderson, C. F., 1941, US Bur Mines Tech Paper, 625. 2. Hensen, F. E. and Clausen, H., 1973, Dehydration of gypsum, Zem Kalk Gips, 26 (5): 223±226. 3. Kondrashenkov, A. A. and Bobov, E. A., 1980, Kinetics of the dehydration of gypsum in water vapour at 1208 C to 2008 C, Izv Akad SSSR Neorg Mater, 16 (4): 707±709. 4. Khalil, A. A., 1982, Kinetics of gypsum dehydration, Thermochimica Acta, 55: 201±208. 5. Holdridge D. A. and Walker, E. G., 1967, The Dehydration of Gypsum and Rehydration of Plaster, Trans Brit Ceram Soc, 66 (10): 485±509. 6. Lavrov, M. N., 1968, Gypsum dehydration kinetics, Uch Zap Gor’k Gos Pedagog Inst, 73: 101±115.
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7. Li, G. and Cao, Y., 1987, Dehydration of gypsum and its kinetics, Yankuang Ceshi, 6 (4): 279±282. 8. Bobrov, B. S., Zhigun, I. G., et al., 1978, Kinetics of the dehydration of CaSO42H2O, Izv Akad Nauk SSSR Neorg Mater, 14 (7): 1333±1337. 9. McAdie, H. G., 1964, The effect of water vapour upon the dehydration of CaSO4.2H2O, Can J Chem, 42: 792±801. 10. Taylor, J. B and, Baines, J. E., 1970, Kinetics of the calcination of calcium sulphate dihydrate, J Appl Chem, 20 (4): 121±122. 11. Beretka, J. and Brown, T., 1983, Studies into the reactivity and physical properties of calcined gypsum as a function of time and temperature, J Aust Ceram Soc, 19 (2): 38±41. 12. Deutch, Y., Nathan, T. and Sarig, 1994, Thermogravimetric evaluation of the kinetics of gypsum-hemihydrate-soluble anhydrite transitions, J Ther Anal, 42: 159±174. 13. Molony, B. and Ridge, M. J., 1968, Kinetics of the dehydration of calcium sulphate dihydrate in vacuo, Aust J Chem, 21: 1063±1065. 14. Ball, M. C. and Norwood, L. S., 1969, Studies in the system calcium sulphate-water. Part 1. The kinetics of dehydration of b -CaSO4.1/2H2O, J Chem Soc (A), 11: 1133±1137. 15. Ball, M. C. and Urie, R. G., 1970, Studies in the system calcium sulphate-water. Part 2. The kinetics of dehydration of calcium sulphate dihydrate, J Chem Soc (A): 528±530. 16. Heide, K., 1969, The thermal decomposition of gypsum, CaSO42H2O, Silkattecknik, 20 (7): 232±234. 17. Negro, A. and Stafferi, L., 1972, Kinetics of dehydration of aCaSO41/ 2H2O and b CaSO41/2H2O, Il Cemento, 69 (2): 101±108. 18. Negro, A. and Stafferi, L., 1973, Dehydration kinetics of various types of dihydrate gypsum, Zem Kalk Gips, 26 (5): 227±231. 19. Strydom, C. A., Hudson-Lamb, D. L., Potgieter, J. H. and Dagg, E., 1996, The thermal decomposition of synthetic gypsum, Thermochimica Acta, 269/270: 631±638. 20. Hudson-Lamb, D. L., Strydom, C. A. and Potgieter, J. H., 1996, The thermal analysis of natural gypsum and pure calcium sulphate dihydrate (gypsum), Thermochica Acta, 283/282: 483±492. 21. Arii, T. and Fujii, N., 1997, Controlled rate thermal analysis kinetic studies in thermal dehydration of calcium sulphate dihydrate, J Anal Appl Pyrol, 39: 129±143.
22. Levenspiel, O., 1972, Chemical Reaction Engineering, 2nd edition (John Wiley and Sons, New York, USA). 23. Cave, S., 2000, Fluidised bed dehydration of ¯ue gas desulphurisation gypsum, PhD thesis (Loughborough University, UK). 24. Marban, G. and Fuertes, A. B., 1994, A simple method for studying the kinetics of gas-solid reactions in a ¯uidized bed reactor, Chem Eng Comm, 130: 241±250. 25. Sit, S. P. and Grace, J. R., 1981, Effect of bubble interaction on interphase mass-transfer in gas-¯uidized beds, Chem Eng Sci, 36: 327±335. 26. Wakao, N. and Smith, J. M., 1962, Diffusion in catalyst pellets, Chem Eng Sci, 17: 825±834. 27. Fuertes, A. B., Marban, G. and Rubiera, F., 1993, Kinetics of thermal decomposition of limestone particles in a ¯uidized bed reactor, Trans IChemE, 71: 421±428. 28. Isida, M., Kamata, M. and Shirai, T., 1970, Kinetic studies of thermal dehydration of gypsum and application of reaction diagram, J Chem Eng Japan, 3: 201±206. 29. Gardet, J. J., Guilhot, B. and Soustelle, M., 1976, The dehydration kinetics of calcium sulphate in¯uence of the gaseous atmosphere and the temperature, Cement & Concrete Res, 6: 697±706.
ACKNOWLEDGEMENT The authors would like to thank BPB Gypsum and the EPSRC for ®nancing this work. They would also like to thank Dr D.J. Malik for the adsorption measurements.
ADDRESS Correspondence concerning this paper should be addressed to Dr R.G. Holdich, Department of Chemical Engineering, Loughborough University, Loughborough, LE11 3TU, UK (E-mail: [email protected]). The manuscript was received 14 October 1999 and accepted for publication after revision 20 July 2000.
Trans IChemE, Vol 78, Part A, October 2000
THE DEHYDRATION KINETICS OF GYPSUM IN A FLUIDIZED BED REACTOR S. R. CAVE and R. G. HOLDICH (AFFILIATE) Department of Chemical Engineering, Loughborough University, UK
M
easurements have been made of the rate of dehydration of desulphurized gypsum with particle diameters in the range of 35±67 m m in a ¯uidized bed reactor. Experiments were carried out at bed temperatures of 100 to 1708 C. The ¯uidizing gases were air, with water vapour pressures of between 0.001 atm and 0.35 atm, and carbon dioxide. The results show that the dehydration under all these conditions can be modelled using the two dimensional Avrami-Erofe’ev expression. In the experiments extreme care was taken to ensure that the generation of reaction products did not signi®cantly in¯uence the reaction rate. At the calcination temperature of 1408 C, the value used in industrial applications, a unique correlation between the reaction rate and water vapour pressure is apparent irrespective of the desulphurized gypsum particle diameters. Under these conditions, it is also shown that a unique relation between conversion and reduced reaction time then follows. Keywords: calcination; Avrami-Erofe’ev; calcium sulphate
INTRODUCTION
possible to obtain all the dehydration products as well as unreacted gypsum.
Calcium sulphate dihydrate, or gypsum, is a commonly found mineral and is also the by-product of several industrial processes, including ¯ue gas desulphurization and the production of wet phosphoric acid from phosphate rock. Large quantities of gypsum are processed prior to use in the building trade as an interior ®nisher. The gypsum is dehydrated to calcium sulphate hemihydrate (hereafter abbreviated to hemihydrate) before use. The hemihydrate is then either rehydrated during the industrial production of plasterboard or left unaltered and sold as plaster in bags. A number of processes have been developed to produce hemihydrate industrially using a variety of calciner designs. All the processes use the same basic principle of directly, or indirectly, heating the gypsum in order to dehydrate it to hemihydrate. Processes can either be batch or continuous depending upon the scale of production. The dehydration/rehydration reaction system for calcium sulphate is shown in outline in Figure 1. Gypsum dehydrates on heating to hemihydrate, in a reaction that is reversible in the presence of water. Hemihydrate on heating dehydrates further to calcium sulphate anhydrite, which exists in three polymorphs: AIII, AII and AI depending on the temperature of reaction. The hemihydrate to anhydrite AIII reaction is reversible in the presence of both water and water vapour. The phases of industrial importance are gypsum, hemihydrate AII and AIII. The quantity of each phase in a plaster determines the properties of the plaster. The most commonly used plaster is around 100% hemihydrate, which is used for plasterboard production, repairs and dentistry. The setting time of plaster can be modi®ed by the presence of gypsum (accelerator) and AII (retarder). Commercial building plaster is typically 50±70% hemihydrate and 50± 30% anhydrite. In a partial dehydration reaction it is
Thermodynamically Stable States and Reaction Kinetics Although gypsum calcination has been performed for several millennia, the understanding of what actually occurs in the system is incomplete. This is due to the large number of processes and interactions occurring within a gypsum calciner. A number of different phenomena occur: heat transfer, mass transfer, particle and gas mixing, particle elutriation and the dehydration reaction itself. All of these processes interact with each other. Kelly1 provided a thermodynamic analysis of the various states of gypsum dehydration, under different conditions of water vapour pressure and temperature, and this is shown in Figure 2. The reaction kinetics and associated phenomena have been studied in cylindrical ¯uidized beds for different systems and it has been found that theory and experimental results can deviate signi®cantly. A further complication to the development of a generally applicable model is that a number of physical gradients exist within industrial equipment. These include temperature, water vapour pressure and super®cial gas velocity which all change with height inside an industrial calciner. The decomposition kinetics have been studied by many investigators. There is no consensus on the mechanism. Mass transfer, heat transfer, chemical kinetics, and combinations of these have all been reported as rate limiting. In general, the reaction rate has been found to increase with: · increasing temperature2±6; · decreasing particle size3,4,7; · decreasing water vapour pressure8 with suppression of 971
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CAVE and HOLDICH A number of papers have been published which attempt to mathematically describe the dehydration reaction of both gypsum and hemihydrate. In common with the majority of solid state reactions, the reaction conversion (a ) has an expression of the form: kt
Figure 1. States of calcium sulphate during dehydration.
the hemihydrate to anhydrite reaction at high water vapour pressures9; · decreasing air pressure10 to a maximum rate at 1 mm Hg. Differences in crystalline characteristics (i.e. size and amount of defects), origin and impurities can affect the dehydration rate. There is also evidence that the reaction conditions can alter the properties of the hemihydrate by affecting the structure and surface area11. Comparison between the reported studies on reaction mechanisms is made dif®cult by the lack of a complete description of the reaction conditions. In many instances there has been little control, or even recording, of the water vapour pressure which, as a reaction product, would be expected to have a signi®cant in¯uence on the reaction kinetics.
Figure 2. Thermodynamically stable states of calcium sulphate at atmospheric pressure.
f a
1
A hypothesis of the reaction mechanism must be proposed in order to interpret an experimental rate constant for a solid state reaction. The function of a depends on the mechanism controlling the reaction. Common equations are based on diffusion, phase boundary and nucleation steps being rate determining. At least ten different models and mechanisms have been proposed for the gypsum dehydration reactions, with no general consensus. In fact, it has often been found that several different models ®t the data equally well12. The most popular methods used to derive the kinetic expressions are isothermal gravimetry and thermal analysis. The earlier papers tended to use isothermal methods: for example, McAdie9 carried out the isothermal dehydration of dihydrate and suggested a zero order kinetic relation (a kt). Molony and Ridge13 studied the dehydration of gypsum and suggested that the reaction was diffusion controlled with a diminishing rate expression A B 1 a 1/2 kt . Ball and Norwood14 and Ball and Urie15 studied the dehydration of both gypsum and hemihydrate: the dehydration of gypsum was found to have three different rate controlling expressions depending upon the prevailing conditions. Nucleation was rate controlling for temperatures less than 908 C and partial pressures of water greater than 0.005 atm; the contracting disc model was valid for temperatures 90 to 1108 C and diffusion was found to be rate controlling for temperatures greater than 1108 C. The second method used to derive the kinetic data is the use of various thermal analysis techniques. Heide16 studied gypsum decomposition using between 2 and 10 mg of sample by Differential Thermal Analysis (DTA) and stated that nucleation was rate controlling and could be modelled using Avrami-Erofe’ev expressions. Negro and Stafferi 17,18 studied the dehydration of gypsum and hemihydrate. The gypsum dehydration was nucleation controlled and was modelled using 2d Avrami-Erofe’ev expression. The hemihydrate dehydration was expressed as a reaction with an order of 0.68. Strydom et al.19 studied the dehydration by DTA using up to 50% more sample mass than Heide, and found that the reaction mechanism changed with conversion: a 0±0.1 could be represented by 3-d diffusion, a 0.1±0.7 by autocatalytic ®rst order and a 0.7±1.0 by the Sestak-Bergen expression. Hudson-Lamb et al.20 carried out a similar study, and again found that the reaction mechanism changed with conversion. Arii and Fujii 21 studied the dehydration by Controlled Rate Thermal Analysis (CRTA). They modelled the gypsum to hemihydrate reaction using 4d-Avrami-Erofe’ev and the hemihydrate to anhydrite-III reaction by a phase boundary model. Similarly, a large range of activation energies has been calculated. The activation energy for the gypsum to hemihydrate reaction has been found to range between 80± 392 kJ mol ±1 and for the hemihydrate to anhydrite-III reaction from 27±205 kJ mol±1. The most signi®cant problem with the kinetic rate expressions is a lack of reported experimental conditions Trans IChemE, Vol 78, Part A, October 2000
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Figure 3. Schematic diagram of experimental equipment.
and results. Important experimental variables are often not mentioned (e.g., particle diameter, sample size, water vapour pressure). Also experimental results, such as the exact mechanism equation, frequency factor (A) and activation energies (E) are sometimes not given or merely alluded to. As a result, the previous work is useful for understanding the dehydration process, but does not provide a clear basis for predicting the calcination rate of gypsum for industrial applications, which generally employs a ¯uidized bed operating at approximately 1408 C. Also, an increasingly important source of gypsum is the product from power generation ¯ue gas desulphurization, which generally has particle diameters between 35 and 70 m m. Most of the above mentioned studies used naturally occurring gypsum with particle diameters in excess of this range. EXPERIMENTAL A ¯uidized bed reactor was used to study the gypsum dehydration reaction, as shown in Figure 3. Compressed air was passed through a ®lter/regulator followed by a 230V in-line ceramic heater. The bed was held in place by two ¯anges, one of which acts as the distributor plate plenum. The ¯anges were constructed from 10 mm thick brass. The distributor plate was an 80 mm diameter stainless steel sintered disc and the bed was contained in a glass tube of diameter 80 mm and height 300 mm. The ¯uidized bed consisted of inert glass beads with a median diameter of 152 m m. The instrumentation consisted of ®ve K-type thermocouples (T1-T5), three piezoresistive bridge type pressure transducers (P1-P3), three turbine ¯ow meters (F1-F3), three rotameter type ¯ow meters (R1-R3) and one Trans IChemE, Vol 78, Part A, October 2000
humidity probe (H1). The humidity probe contained a thin®lm polymer sensor that could measure from 0 to 100% relative humidity with a reported accuracy of 6 2%. The probe also provided a temperature measurement, which is essential in order to calculate the mass of water present in the ¯uidized bed exit stream. The experimental work used a desulphurized gypsum sample supplied by BPB Gypsum. The original sample had a median diameter of 48 m m and was over 95% CaSO4.2H2O. The sample was divided into cuts with median particle diameters of 35 m m, 40 m m, 50 m m, 60 m m and 67 m m by elutriation in air. The experiments were carried out as follows. Compressed air was dried by passing through a silica desiccator. Air with a higher relative humidity was produced by replacing the silica with water and inline water injection. The air was heated using the in-line ceramic heater and used to ¯uidize the glass beads. The temperature of the bed was controlled based on the temperature reading of T2, which is located 10 mm above the distributor plate. The thermocouple T2 was calibrated prior to each experimental run. It was found that the temperature could be controlled to an accuracy of 6 28 C. The sample to be dehydrated was injected into the bed from the sample pot by temporarily bypassing some air around the bed through the sample pot. Sample injection was achieved within a couple of seconds. The extent of the decomposition reaction was monitored using the humidity probe positioned after the ¯uidized bed. The off-gas from the bed passed from the humidity probe into a glass cyclone, followed by a bag ®lter (Radio Spares, Corby, UK). The bag ®lter was contained in a clear plastic box and there was no observable deposition of solids in the
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glass cyclone or ®lter after any of the dehydration runs, prior to deliberately elutriating the solids from the bed to separate them from the inert bed material. Hence, elutriation of ®ne material from the ¯uidized bed during the experiment was not apparent. Gas Mixing and Probe Response The relative humidity probe reading did not give a true representation of the water generated from the dehydration reaction because of gas mixing in the ¯uidized bed and the response time of the probe. The effect of both parameters was studied by a pulse tracer test on the ¯uidized bed using steam injection. The ¯uidized bed was heated up to the required temperature. When steady state was reached, i.e. when the bed temperature and relative humidity probe temperature stopped ¯uctuating, 0.1 ml of distilled water was rapidly injected into the bed via a septum in the bed wall. The water injected into the bed was instantly converted to steam and removed from the bed in the gas exit stream. The rate at which steam left the bed was recorded using the relative humidity probe. Experimental runs were carried out at temperatures of 60, 80, 100, 110, 120, 130, 140, 150, 160 and 1708 C, and the mass of water used was varied to check that it did not signi®cantly in¯uence the results. A two stage tanks in series model was found to represent the gas mixing/probe response. The model is described by the following equation22 tN 1 N N Å e Nt/t 2 Åt N 1 ! where N is the number of stirred tanks, t is time and Åt is the residence time in the N tank system. Each tank in the series has a time constant Åt tt 3 N t t was calculated for each temperature. Figure 4 shows the exit age distribution against dimensionless time plot for water injection at 1208 C, 1408 C and 1608 C. The dimensionless time is the measured time divided by the residence time, and the experimental exit age distribution was determined by normalizing the area of the relative humidity against time plot to give an area of unity. The two tanks in series model appears to adequately ®t the experimental data.
Et
N
Figure 4. Exit age distribution curve for water injection into ¯uidized bed at three temperatures.
Data Analysis Using the two tanks in series model, the actual rate of water generation in the bed can be calculated from the relative humidity probe data by applying the following equation23 dRHA RHB RHA t t 4 dt where RHA is the read data, and RHB is the reading before a completely mixed tank with time constant t t . Since the model best ®tting the gas mixing/probe response is a two tanks in series model it is necessary to apply the equation again, substituting RHA with RHB, and RHB with RHC; where RHC represents the water vapour released within the bed. A problem in analysing the data in this manner is that the data from the probe is `noisy’, and this is ampli®ed when the derivative is taken. This means that the calculated RHC curve was `noisy’ which made determining rate constants dif®cult. In order to overcome this problem MathcadTM was used to provide cubic spline ®ts to the data. Over twelve different reaction models were evaluated, representing reactions controlled by diffusion, nucleation, geometry and other parameters often in combination with the foregoing. RESULTS AND DISCUSSION Differential conditions are required for the derivation of meaningful kinetic data, and in this instance they are believed to occur when the water given off in the dehydration reaction does not affect the rate of reaction. The absence of differential conditions may be one reason why there have been many different reaction models and rates reported previously. In order to elucidate when differential conditions occurred, a number of dehydrations were performed using different masses of gypsum and different gas ¯owrates. Figure 5 shows the effect of mass on the rate of reaction. Differential conditions were found to occur with a sample mass of 0.4 g and a ¯uidizing ¯ow rate of 14 nL min ±1. The next set of dehydrations used CO2 rather than air to determine whether the reaction is affected by the ¯uidizing medium; as CO2 has markedly different properties to air. There was a possibility that the differences in conversion
Figure 5. Effect of sample mass on conversion at 1408 C, 0.001 atm water vapour pressure and 40 m m.
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Figure 6. Comparison of ¯uidizing gas on reaction rate.
Figure 7. Reaction at different temperatures using water partial pressure of 0.001 atm, 40 m m particles.
data could be due to intraparticle diffusion or heat transfer. However, the rate was the same for both gases and therefore intraparticle diffusion and external heat transfer can be deemed not to be rate limiting. An example is shown in Figure 6 for the dehydration of 40 m m gypsum at 1008 C and 0.001 atm water vapour pressure. The rate limiting step is most likely to be due to the properties of the DSG particles themselves. In some cases resistance to mass transfer between the water vapour within the emulsion phase and the ¯uidized bed bubble phase can have a signi®cant in¯uence on the derived reaction rate constant. A graphical technique has been published to investigate this, considering different masses of reactants added to a ¯uidized bed, but with limited success24. Correlations exist for estimating the bubble gas exchange rate between the bubble and emulsion phases25. Under the prevailing experimental conditions, the calculated rate is in excess of 5000 s ±1; i.e. the bubble volume is exchanged with the surrounding emulsion phase gas over 5000 times per second. Hence, it is unlikely that signi®cant resistance to the dehydration occurred in the mass transfer between these two phases. The effect of temperature, particle diameter and water vapour pressure on the dehydration rate were studied. When AIII was the ®nal product of the dehydration as a result of the conditions in the bed, the reaction proceeded according to the following equation
determined by BET analysis typically changes from 0.2 m2 g ±1 for the desulphurized gypsum to 6.2 m2 g ±1 for the calcined product. The effective diffusivity (De) can be estimated according to the random pore model26
CaSO4 .2H2 O
CaSO4
2H2 O
5
The AIII quickly rehydrated to hemihydrate after elutriation from the ¯uidized bed, when conditions were in accordance with the hemihydrate favoured region illustrated in Figure 2. The shape of the conversion (a) versus time curves were all found to be similar, an example of these is illustrated in Figure 7. The dehydration reaction rate was not in¯uenced by particle size at the lower temperatures, water vapour pressure had a signi®cant effect and temperature had the most signi®cant in¯uence on the overall rate of reaction. An estimate of the contribution towards the overall reaction rate made by diffusion of water vapour from the interior of the particle to the surrounding ¯uidized bed can be obtained from the effective diffusivity. The gypsum particles are fractured by the homogeneous reaction due to the water vapour leaving the particles. The surface area Trans IChemE, Vol 78, Part A, October 2000
DM1
De
DK 1
1 2 eo
6
where eo is the porosity of the calcined particle, DM and DK are the molecular and Knudsen diffusivities respectively. The Knudsen diffusivity can be estimated from26,27 DK
97rp
T W
0.5
7
where rp is the average pore radius, T is the reaction temperature and W is the molecular mass of water vapour. The calcined particle porosity and average pore radius were estimated from BET analysis to be 11% and 35 nm respectively. Thus, under the reaction conditions most appropriate to the industrial calcination of desulphurized gypsum (e.g. bed temperature of 1408 C) the effective diffusivity of the water vapour in the calcined particle is 0.004 cm2 s ±1. This value is almost one order of magnitude less than one reported in the literature 28. However, for the purposes of estimation of diffusional resistance to the overall rate, the calculated and lower value will be used. This should provide an overestimation of the time taken for water vapour to diffuse out of the particle. The diffusional equation for a spherical particle, rendered dimensionless for numerical solution is ¶P ¶u
1 ¶ 2 ¶P x x2 ¶x ¶x
8
where: x
r ; R
De t R2 u
P
P2 P0
where r is radial position, R is particle radius, Pw is partial pressure of water and Po is total pressure. Equation (8) was solved using the computer package PDESOL by NumericaTM, using the upper boundary condition provided by the greatest humidity employed in the ¯uidized bed: Pw of 0.25 atmospheres. The differential lower boundary condition of ¶P ¶x
0 x
0
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CAVE and HOLDICH approximately 0.25 atmospheres. Thus, these conditions are relevant to the industrial calcination of desulphurized gypsum. From the data illustrated in Figure 8, it is apparent that the diffusion of water vapour out of ¯uidized particles under these conditions is rapid and the process is predominantly chemical reaction controlled. A large number of reaction models were considered for the homogeneous non-catalytic reaction represented by equation (5). The most suitable one for all the data was the 2d Avrami-Erofe’ev expression kt
Figure 8. Water vapour concentration pro®les inside a gypsum particle undergoing diffusion.
was also used. The resulting solution for the water vapour pressure at four times in a particle 45 m m in diameter is shown in Figure 8. The mean particle diameter of desulphurized gypsum is approximately 45 m m and a full-sized ¯uidized bed calciner could have a water partial pressure of
Figure 9. Experimental data and Avrami-Erofe’ev model using water partial pressure of 0.001 atm, 50 m m particles, 1308 C.
ln 1
a
1/2
9
where k is the reaction rate constant and a is fractional conversion. The reaction models were ®tted to experimental data between 5 and 95% conversion. In many instances solid state models are ®tted over the data range 10 to 90% conversion, hence the range taken here is assumed to be an acceptable test of the model validity. All the experimental results ®tted the model well, and a typical ®t is shown in Figure 9. Arrhenius plots were constructed for the experimental data and the activation energy and the frequency factor for the calcinations at low humidity, were found to be 81 kJ mole ±1 K ±1 and 8.5 ´ 1010 minutes ±1 respectively. Figure 10 shows the effect of temperature and particle diameter on the reaction rate at 0.001atm H2O. As can be seen, the temperature has a much greater effect on the reaction rate than the particle diameter. This was found to be true at each water vapour pressure, and is consistent with the earlier discussion on diffusional control. Figure 11 shows the effect of water vapour pressure upon the rate of reaction for different diameter particles at 1408 C and 1608 C. It can be seen that the temperature has a greater effect on the rate than the water vapour pressure although, within the experimental limits of the scattered data, there is an approximately linear reduction in the rate with increasing water vapour pressure. However, it could be argued that the reaction rate becomes stabilized above a threshold value, but the dehydration rate of gypsum has previously been shown to decrease monotonically with water vapour pressure at temperatures below 1008 C29. The data illustrated
Figure 10. Effect of temperature and particle diameter on dehydration rate (water vapour pressure 0.001 atm).
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THE DEHYDRATION KINETICS OF GYPSUM IN A FLUIDIZED BED REACTOR
Figure 11. Effect of water vapour pressure on dehydration rate at two temperatures.
Figure 12. Reduced conversion plot for all experimental conditions and model results during calcination at 1408 C.
in Figure 11 shows that particle size does not appear to have a signi®cant in¯uence on the calcination rate when operating at 1408 C. Considering the operating conditions most relevant to the calcination of industrial desulphurized gypsum, bed temperature of 1408 C, it is possible to empirically ®t a single linear equation valid for all the particle sizes illustrated in Figure 11. The equation can be used to determine the reaction rate constant for a given water partial pressure, which can then be combined with the overall material balance on the water produced during the calcination, following the stoichiometry given by equation (5), and the 2d Avrami-Erofe’ev reaction rate expression. Following this procedure it is possible to predict the time taken for the reaction to become 50% complete (t50), and the fractional conversion with respect to reaction time. The reaction time may be rendered dimensionless by the t50 value and a single curve results from the analysis regardless of the initial particle size or water vapour pressure. This is plotted in Figure 12, together with the experimental data covering all the operating conditions: humidity ranging from 0.001 to 0.3 atmospheres and particle diameters between 30 and 70 m m. It is evident that all the data in this region of reaction conditions relevant to the industrial calcination of desulphurized gypsum can be successfully correlated in such a fashion. CONCLUSIONS A laboratory ¯uidized bed reactor containing inert particles has been used to study the isothermal dehydration Trans IChemE, Vol 78, Part A, October 2000
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of gypsum, arising from ¯ue gas desulphurization, to form calcium sulphate hemihydrate. These reaction conditions are closer to those applied in the industrial production of hemihydrate than experimental studies employing thermal balances. Also, the reaction conditions, such as humidity, can be more reliably controlled because of the ef®cient mixing within the ¯uidized bed. However, this experimental system permitted back-mixing. The mass of water evolved from the gypsum was measured by an on-line humidity probe and corrected for mixing. The experimental arrangement could be modelled using two well mixed tanks in series. In order to prevent the reaction product from in¯uencing the rate of reaction differential condition tests showed that the sample mass within the bed had to be less than 0.1% of the total bed mass. Experiments with air and carbon dioxide as the ¯uidizing gases indicated that the reaction is not signi®cantly in¯uenced by heat transfer, or diffusion of the reaction products. Order of magnitude calculations based on the physical properties of the calcined gypsum particles (internal porosity of 11% and average pore radius of 35 nm) con®rm that diffusion of water vapour within the particle is unlikely to have a signi®cant in¯uence on the overall rate under the experimental conditions used. All the reactions studied could be modelled by the 2d Avrami-Erofe’ev expression, and the activation energy and frequency factor were calculated to be 81 kJ mole ±1 K ±1 and 8.5 ´ 1010 minutes ±1 respectively. At a reaction temperature of 1408 C the evolution of water vapour with respect to reduced reaction time could be correlated on a single curve, irrespective of particle size and prevailing humidity during the reaction. The curve could be adequately predicted by the 2d Avrami-Erofe’ev expression coupled with a material balance. NOMENCLATURE De DK DM k N RH rp T t Åt W
effective diffusivity, m2 s ±1 Knudsen diffusivity, m2 s ±1 molecular diffusivity, m2 s ±1 reaction rate, min ±1 number of stirred tanks relative humidity average pore radius, m reaction temperature, K time, s residence time in N tank system, s nolecular mass of water vapour, mol g ±1
Greek letters a conversion eo internal porosity of particle
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7. Li, G. and Cao, Y., 1987, Dehydration of gypsum and its kinetics, Yankuang Ceshi, 6 (4): 279±282. 8. Bobrov, B. S., Zhigun, I. G., et al., 1978, Kinetics of the dehydration of CaSO42H2O, Izv Akad Nauk SSSR Neorg Mater, 14 (7): 1333±1337. 9. McAdie, H. G., 1964, The effect of water vapour upon the dehydration of CaSO4.2H2O, Can J Chem, 42: 792±801. 10. Taylor, J. B and, Baines, J. E., 1970, Kinetics of the calcination of calcium sulphate dihydrate, J Appl Chem, 20 (4): 121±122. 11. Beretka, J. and Brown, T., 1983, Studies into the reactivity and physical properties of calcined gypsum as a function of time and temperature, J Aust Ceram Soc, 19 (2): 38±41. 12. Deutch, Y., Nathan, T. and Sarig, 1994, Thermogravimetric evaluation of the kinetics of gypsum-hemihydrate-soluble anhydrite transitions, J Ther Anal, 42: 159±174. 13. Molony, B. and Ridge, M. J., 1968, Kinetics of the dehydration of calcium sulphate dihydrate in vacuo, Aust J Chem, 21: 1063±1065. 14. Ball, M. C. and Norwood, L. S., 1969, Studies in the system calcium sulphate-water. Part 1. The kinetics of dehydration of b -CaSO4.1/2H2O, J Chem Soc (A), 11: 1133±1137. 15. Ball, M. C. and Urie, R. G., 1970, Studies in the system calcium sulphate-water. Part 2. The kinetics of dehydration of calcium sulphate dihydrate, J Chem Soc (A): 528±530. 16. Heide, K., 1969, The thermal decomposition of gypsum, CaSO42H2O, Silkattecknik, 20 (7): 232±234. 17. Negro, A. and Stafferi, L., 1972, Kinetics of dehydration of aCaSO41/ 2H2O and b CaSO41/2H2O, Il Cemento, 69 (2): 101±108. 18. Negro, A. and Stafferi, L., 1973, Dehydration kinetics of various types of dihydrate gypsum, Zem Kalk Gips, 26 (5): 227±231. 19. Strydom, C. A., Hudson-Lamb, D. L., Potgieter, J. H. and Dagg, E., 1996, The thermal decomposition of synthetic gypsum, Thermochimica Acta, 269/270: 631±638. 20. Hudson-Lamb, D. L., Strydom, C. A. and Potgieter, J. H., 1996, The thermal analysis of natural gypsum and pure calcium sulphate dihydrate (gypsum), Thermochica Acta, 283/282: 483±492. 21. Arii, T. and Fujii, N., 1997, Controlled rate thermal analysis kinetic studies in thermal dehydration of calcium sulphate dihydrate, J Anal Appl Pyrol, 39: 129±143.
22. Levenspiel, O., 1972, Chemical Reaction Engineering, 2nd edition (John Wiley and Sons, New York, USA). 23. Cave, S., 2000, Fluidised bed dehydration of ¯ue gas desulphurisation gypsum, PhD thesis (Loughborough University, UK). 24. Marban, G. and Fuertes, A. B., 1994, A simple method for studying the kinetics of gas-solid reactions in a ¯uidized bed reactor, Chem Eng Comm, 130: 241±250. 25. Sit, S. P. and Grace, J. R., 1981, Effect of bubble interaction on interphase mass-transfer in gas-¯uidized beds, Chem Eng Sci, 36: 327±335. 26. Wakao, N. and Smith, J. M., 1962, Diffusion in catalyst pellets, Chem Eng Sci, 17: 825±834. 27. Fuertes, A. B., Marban, G. and Rubiera, F., 1993, Kinetics of thermal decomposition of limestone particles in a ¯uidized bed reactor, Trans IChemE, 71: 421±428. 28. Isida, M., Kamata, M. and Shirai, T., 1970, Kinetic studies of thermal dehydration of gypsum and application of reaction diagram, J Chem Eng Japan, 3: 201±206. 29. Gardet, J. J., Guilhot, B. and Soustelle, M., 1976, The dehydration kinetics of calcium sulphate in¯uence of the gaseous atmosphere and the temperature, Cement & Concrete Res, 6: 697±706.
ACKNOWLEDGEMENT The authors would like to thank BPB Gypsum and the EPSRC for ®nancing this work. They would also like to thank Dr D.J. Malik for the adsorption measurements.
ADDRESS Correspondence concerning this paper should be addressed to Dr R.G. Holdich, Department of Chemical Engineering, Loughborough University, Loughborough, LE11 3TU, UK (E-mail: [email protected]). The manuscript was received 14 October 1999 and accepted for publication after revision 20 July 2000.
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