I n d . E n g . Chem. Res. 1989, 28, 355-362
*
= time constant
Subscripts
1 = tank dsk = sintered disk e = effective g = grain in = inlet 1 = longitudinal loc = local m = medium max = maximum out = outlet ov = overall t = transverse Registry No. Cs, 7440-46-2; montmorillonite, 1318-93-0.
Literature Cited Barclay, L. M.; Ottewill, R. H. Measurement of Forces between Colloidal Particles. Spec, Discuss, Faraday Sot. 1970, 138-147. Bird, R. B.; Stewart, W. E.; Lightfoot, W. E. Transport Phenomena; Wiley: New York, 1960; p 199. Brinkman, H. C. A Calculation of the Viscous Force Exerted by a Flowing Fluid on a Dense Swarm of Particles. Appl. Sci. Res. 1947, A I , 27-34. Caceci, M. S.; Cacheris, W. P. Fitting Curves to Data. B Y T E 1984, 9, 340-362. Crank, J , ~h~ Mathematics o f Diffusion,2nd ed.; Oxford University: London, 1975. Crank, J.; Park, G. S.Diffusion in Polymers; Academic: London, 1968. Graetz, L. Uber die Warmeleitunsfahigkeit von Flussigkeiten. Ann. Phys. Chem. 1885,25, 337-357. Grim, R. Clay Mineralogy, 2nd ed.; McGraw-Hill: New York, 1968.
355
Helfferich, F. Ion Exchange; McGraw-Hill: New York, 1962. Jahnke, F. M. The Diffusion of Electrolytes in Compacted Montmorillonite Clay Gels. Ph.D. Thesis, University of California a t Berkeley, Dec 1987. Jahnke, F. M.; Radke, C. J. Electrolyte Diffusion in Compacted Montmorillonite Engineered Barriers. In Coupled Processes Associated with Nuclear Waste Repositories; Tsang, C., Ed.; Academic: New York, 1987; pp 287-297. Jensen, D. J.; Radke, C. J. Caesium and strontium diffusion through sodium montmorillonite at elevated temperature. J. Soil Sci. 1988, 39, 53-64. Nuclepore Corporation Product Catalogue. Pleasanton, CA, 1984. Perkins, T. K.; Johnston, 0. C. A Review of Diffusion and Dispersion in Porous Media. Soc. Pet. Eng. J . 1963, 70-81. Perry, E. H.; Chilton, C. H. Chemical Engineer’s Handbook, 5th ed.; McGraw-Hill: New York, 1973. Robinson, R. A.; Stokes, R. H. Electrolyte Solutions, 2nd ed.; Academic: New York, 1959. Soudek, A., Binary and Ternary Ion Exchange on Sodium Montmorillonite for Amlication to Backfill in Nuclear Waste Disposal. M.S. Thesis, Unjiersity of California at Berkeley, 1984. Stehfest, H. Algorithm 368 Numerical Inversion of Laplace Transforms [D5]. CACM 1970, 13, 47-49, 624. Stokes, R. H. An Improved Diaphragm-cell for Diffusion Studies, and Some Tests of the Method. J . Am. Chem. SOC.1950, 72, 763-767. Stokes, R. H. Integral Diffusion Coefficients of Potassium Chloride Solutions for Calibration of Diaphragm Cells. J . Am. Chem. SOC. 1951, 73, 3527-3528. Waste Isolation Systems Panel A Study of the Isolation of Geologic Disposal of Radioactive Wastes;National Academy: Washington, DC, 1983.
Received for review December 21, 1987 Revised manuscript received October 6, 1988 Accepted October 26, 1988
Solar Thermal, Decomposition Kinetics of Zinc Sulfate at High Heating Rates Ali Tabatabaie-Raissi* Florida Solar Energy Center, 300 State Road 401, Cape Canaveral, Florida 32920
Ravi Narayan, William S.-L. Mok, and Michael J. Antal, Jr. Department of Mechanical Engineering and Hawaii Natural Energy Institute, University of Hawaii, Honolulu, Hawaii 96822
This paper describes the experimental and analytical methods required to study decomposition of zinc sulfate in a simulated solar environment. Experiments were conducted a t sample heating rates greater than 2 K/s and temperatures in excess of 1400 K in a specially designed thermogravimetric system which employed a 30-kWe/2-kWh downward-facing beam, arc-image furnace. The zinc sulfate decomposition took place almost exclusively through the high-temperature ZnS04 @ phase under experimental conditions of this study. T h e kinetic parameters were determined from the thermogravimetric data by using a nonlinear least-squares optimization algorithm. An apparent activation energy, E, between 210 and 250 kJ/mol and an apparent reaction order, n, between 0 and 0.3 were obtained for @-phaseZnS04 decomposition reaction. T h e comparison of these results with those from lower temperature and lower heating rate zinc sulfate decomposition tends to suggest a change in reaction mechanism a t the high heating rates expected in a concentrated solar environment. Hydrogen is considered by many to be one of the most attractive energy carriers of the future. This is in part due to the many advantages from an environmental point of view as well as the possibility of its manufacture using a clean primary energy source such as solar energy. Since solar furnaces are expensive to build and operate, their successful implementation for production of hydrogen depends very much on the cost and efficiency of the hydrogen plant. The development of these techniques requires a fundamental understanding of high-temperature
and high heating rate decomposition chemistry under reaction conditions similar to those prevailing within a solar furnace. The applications of the concentrated solar energy in direct solid-phase decomposition of materials for the production of fuels has been discussed for many years (Bowman, 1980,1984; Hosmer and Krikorian, 1979,1980; Krokorian and Shell, 1982; Noring and Fletcher, 1982; Shell et al., 1983). Most of these applications relate to the use of thermochemical water-splitting cycles for the production of hydrogen. One of the reaction steps in all of
0888-5885/89/2628-0355$01.50/0 0 1989 American Chemical Society
356 Ind. Eng. Chem. Res., Vol. 28, No. 3, 1989
these thermochemical cycles involves high-temperature energy transfer and storage which can be best carried out within a concentrating solar furnace. The thermal decomposition of zinc sulfate has been proposed (Hosmer and Krikorian, 1979; Bowman, 1980; Krikorian and Shell, 1982; Shell et al., 1983) as the high-temperature reaction step in many of these thermochemical cycles and in sulfuric acid based cycles to replace the reactions involving the boiling of azeotropic sulfuric acid and its decomposition a t high temperature. Various thermal analytical instruments have been used in the past to infer kinetic and mechanistic information involving solid-state reactions. While the low heating rate decomposition studies of solid materials using conventional thermogravimetric systems is routine, no such instrumentation is available to study these processes under solar thermal environments. Most commercially available thermal analysis instruments are limited in their capabilities to achieve high temperatures and to provide the reaction conditions which mimic those existing within a solar-fired thermochemical reactor. To achieve our goals, a new thermogravimetric analyzer system was fabricated to rapidly weigh and simultaneously measure the temperature of the solids exposed to concentrated radiant energy derived from a 30-kWe/2-kWth downward-facing beam, arc-image furnace. This report presents the results of reasearch concerned with fundamental studies of high-temperature (as high as 1400 K), solid phase, radiative decomposition of zinc sulfate at high heating rates (greater than 2 K/s). The primary goal of this work was to investigate/identify the posited solar beneficial/solar unique effects of radiant heating on the decomposition behavior of zinc sulfate. A set of high heating rate results derived in this system is presented and compared to those obtained from low heating rate (less than 0.1 K/s) experiments reported earlier (Narayan et al., 1988).
Prior Research on Zinc Sulfate Decomposition A brief review of literature pertaining to thermal decomposition of zinc sulfate related to thermochemical hydrogen production cycles is given here; more can be found elsewhere (Tabatabaie-Raissi and Antal, 1985; Narayan et al., 1988). Low heating rate, thermogravimetric studies of the controlled dehydration and thermal decomposition of zinc sulfate have been reported by many investigators using both isothermal and nonisothermal techniques (Ostroff and Sanderson, 1959; Watanabe and Yoshida, 1959; Hoschek, 1962; Ingraham and Marier, 1967; Kolta and Askar, 1975; Mu and Perlmutter, 1981; Ducarroir et al., 1982; Ibanez et al., 1984; Tagawa, 1984). Zinc sulfate has been shown to exist as stable hepta-, and tetra-, or monohydrate (Mu and Perlmutter, 1981). At about 1015 K, zinc sulfate undergoes a solid-state phase transition from the low-temperature (Y phase with a closepacked orthorhombic structure to the high-temperature @ phase having a cubic high-cristobalite-type structure (Hosmer and Krikorian, 1980). A t low heating rates (less than about 0.167 K/s), the decomposition of zinc sulfate to zinc oxide proceeds through a stable intermediate, zinc oxysulfate. There appears to be a common consensus to regard the composition of this intermediate oxysulfate as Zn0.2ZnS04 (Ingraham and Kellogg, 1963; Hosmer and Krikorian, 1980; Krikorian and Shell, 1982; Ibanez et al., 1984, Narayan et al., 1988). The subsequent decomposition of this oxysulfate into the final product, zinc oxide, takes place at much higher temperatures. Recently, Narayan et al. (1988) carried out detailed experimental and numerical studies of the low heating rate, zinc sulfate de-
Table I. Summary of the Low Heating Rate Kinetic Values ReDorted i n the Literature kinetic parameter for (E in kJ/mol. A in s-*) researcher zinc sulfate zinc oxysulfate Narayan et al.,” 1988 E = 297 (13)* E = 251 (0.5) In A = 32 (2) In A = 23 (0.05) order = 0.9 (0.1) order = 0 (0.01) Ibanez et al., 1984 E = 306 (25) E = 320 (34) In A = 21 (4) In A = 20 (2) zero order zero order Ducarroir et al., 1982 E = 150 E = 197 Mu and Perlmutter, 1981 E = 353 C In A = 37.7 order = 2/3 Kolta and Askar, 1975 E = 96 a Zinc sulfate heptahydrate, ceramic boat, and air as carrier gas. *Values in the parentheses refer to the l a deviations. Not given.
composition mechanism by using a conventional TGA and determined the corresponding kinetic parameters. They found that the thermogravimetric parameters, such as sample size, material of the sample holder, type of carrier gas, and extent of sample hydration, influenced the decomposition significantly. This may explain in part the large discrepancies which exist in the literature regarding the reported kinetic values and decomposition temperatures of zinc sulfate (Kolta and Askar, 1975; Mu and Perlmutter, 1981; Ducarroir et al., 1982; Ibanez et al., 1984). According to Narayan et al. (1988), the formation of the intermediate takes place via a competitive reaction, whereas its decomposition appears to follow a simple, single-reaction step. The decomposition mechanism was found to be unaffected by the experimental conditions. The values of the kinetic parameters, on the other hand, appeared to be dependent on the thermogravimetric parameters studied. The reported parameters in the literature have been summarized in Table I. Although there have been numerous studies of low heating rate decomposition studies of zinc sulfate, very little is known regarding its high heating rate decomposition mechanism and kinetics in a radiative environment. Krikorian and Shell (1982) were first to use radiant heating to study zinc sulfate decomposition in an arc-image furnace consisting of four 1-kW tungsten lamps. The objective of their research was to alleviate the problems associated with the formation of the intermediate oxysulfate. Although they could not explain with confidence the behavior of zinc sulfate particles under high radiant flux conditions, their qualitative results appeared to indicate that the rapid heating of fine zinc sulfate particles enhanced the ZnSOl decomposition rate appreciably. Later, Shell et al. (1983) carried our similar experiments a t the focus of a 30-kW solar furnace at the White Sands Solar Facility, White Sands, NM, but unfortunately, the results from that effort provided only limited qualitative information. They found that the irradiated zinc sulfate material began to react at temperatures below those normally required for its decomposition at lower heating rates and using conventional heating techniques. This finding appears somewhat puzzling since the decomposition temperature of a reacting solid in a single-reaction pathway should shift toward higher temperatures as the heating rate is increased (Zakharov, 1982). Shell et al. (1983) concluded their effort with a recommendation that, instead of trying to obtain quantitative data on the field, it would be more useful to design a laboratory, thermogravimetric system capable of rapidly heating zinc sulfate particles. Such a system would be able to determine the relationship between decomposition rates and other themogravimetric parameters under
Ind. Eng. Chem. Res., Vol. 28, No. 3, 1989 357 shielded FUSED SILICA TUBE
ELECTRO-MICROBA LA NCE
I
\
PARABOLIC M I R R O R S
Figure 2. Flux density measurement near the focus of the high heating rate TGA furnace (at 15.9-kW input power to lamp).
I
+ JUNCTION
I
ALUMINA VIAL
u
1
Figure 1. High heating rate thermogravimetric analyzer system.
controlled radiative environment. The main thrust of the work presented here was to design and fabricate a novel, thermogravimetric system. The apparatus was utilized to determine the solar thermal reaction kinetics of zinc sulfate at high heating rates and high temperatures under a controlled radiative environment.
Thermogravimetric Apparatus Description A schematic diagram of the apparatus is shown in Figure 1. An electromicro/macrobalance (Mettler Model AE 163) with dual range and resolution (30 g/O.Ol mg or 163 g/O.1 mg), used as a thermobalance, was integrated into a 30kWe/2-kW,h downward-facing beam, arc-image furnace. A detailed description and specifications of the furnace were presented elsewhere (Tabatabaie-Raissi and Antal, 1986). There are two important features to this furnace. First, due to the optics of the parabolic concentrator used in this system, a high flux level (approaching lo6 W/m2) a t the focal plane is available. A water-cooled xenon arc lamp used in our solar simulator provided a continuous spectral output in the visible region very similar to that of the sun. An asymptotic, rapid-response-type, heating rate transducer (Medtherm calorimeter Model 64-750-18T) was used to measure the radiant fluxes at the sample location. The output of the calorimeter correlated linearly with the lamp’s operating current. This criteria was used to continuously monitor the radiant fluxes near the samle by simply recording the lamp’s operating current. Figure 2 depicts typical results of radiative flux measurements in three spatial directions about the focus a t 15.9-kW total input power to the lamp. The total power collected by the optical system of the furnace near the focus was determined from these flux density measurements. For example, a t 15.9-kW input power, the total power received at the focal plane was calculated to be about 900 W. We used a 0.035-m-0.d. and 0.64-m-long fused silica tube as the reaction vessel, which was connected at the bottom to a gas metering and supply system. It contained the sample holder assembly and an alumina hang-down tube suspended from the balance. The Mettler balance was utilized in a bottom loading configuration in our system. The experiments employed a high-purity carrier gas (air, nitrogen, or helium), flowing upward through the fused
silica tube a t the rate of approximately 1-8 mL/s. A specially fabricated type S, hair thin thermocouple (with 0.05-mm bead size) was attached to the alumina sample holder in the manner shown in Figure 1. With this arrangement, the thermocouple junction was embedded within the sample material inside the alumina sample holder (boat). The alumina boat used had a capacity of approximately 0.2 cm3and weighed 1245 mg. The sample holder assembly was then suspended from the 1.6-mm-0.d. alumina hang-down tube (attached to the balance arm) by means of the thermocouple leads. The entire fused silica reaction tube was shielded from incoming radiation except for a small window section along the suspended sample boat. A movable light shield arrangement around this window prevented the sample heatup after the lamp was ignited and while the system was stabilizing. The initial drift in the lamp’s current and output flux subsided within 5-10 min after the system start-up. A steady-state sample irradiation was then obtained for the duration of the experiment. The weight change and temperature data were acquired by using an IBM-PC/AT unit. The Mettler balance was capable of providing a t least five distinct digitized weight change signals per second. These readings were transmitted along with the amplified (50:l) and zero-point compensated temperature data to the PC unit and were stored for later analysis.
Experimental Procedure and Calibration The samples used in the high heating rate experiments were zinc sulfate heptahydrate (Baker Analyzed Reagent grade) crystals and a specially prepared (Narayan et al., 1988) zinc oxysulfate powder. Approximately 6-20 mg of the crystalline material was loaded into the sample boat, and the entire sample holder assembly was then weighed on a Mettler H51AR analytical balance (with 0.01-mg resolution). The sample weight was then determined by subtraction. Calibration of all balances used in this study was performed by using the Rice Lake Bearings, Inc., Precision (traceable to the National Bureau of Standards), class 1 (2-g),and 1.1(1-,lo-, and 100-mg) standard weights. On the basis of these calibrations, we estimated the absolute accuracy of the weight measurements to be 0.01 mg. One of the major difficulties in the determination of the kinetics of solid-phase decompositions under conditions of rapid heating is the accurate measurement of the solid temperature. The temperature at which the decomposition occurs is influenced by the inter- as well as intra-particle heat- and mass-transfer effects. The sample temperature and intra-particle heat transfer are further affected by the endo- or exothermicity of the reactions which occur during decomposition,as well as by the phase transition of various kinds. These factors infleunce and further complicate the
358 Ind. Eng. Chem. Res., Vol. 28, No. 3, 1989 Table 11. Comparison between Demagnetization Temperatures of Four NBS Curie Point SRMs Measured in the High Heating Rate TGA System and Certified ICTA Values TIband TScfor std ref materials heating rate,O O C / s Permanorm 3 nickel Mumetal Trafoperm 0.025 253 [5]; 266 [6Id 351 [5]; 354 [5] 377 [6]; 386 [7] 750 [ l l ] ; 754 [ l l ] 1.8 e -61; -14f 2.7 -31; -11 2.9 -11; +5 6.1 -39; +14 -18; +12 6.4 9.4 -42; -6 11.7 -41; -8 26.7 -52; +26 a Averaged over duration of demagnetization weight change. TI: temperature a t the onset of demagnetization weight change. T s temperature a t the end of demagnetization weight change. ICTA values ("C) [standard deviations ("C)]. eNot given. f T,(measured) T1(ICTA); T3(measured) - T,(ICTA) ("C; "C).
calibration of the temperature measurements within the high heating rate apparatus. The calibration of the sample thermocouple a t our experimental conditions was not trivial. The temperature response of calibrants (such as melting point or transition temperature standards) is commonly used to calibrate the temperature-sensing systems of the low heating rate thermal analysis instruments. These methods, however, could not be used for calibration of the sample thermocouple in the high heating rate apparatus. We used several Curie point reference materials issued by the National Bureau of Standards (NBS), now National Institute of Standards and Technology (NITS), SRM GM-761 for calibration of temperature of the high heating rate system. These materials are ICTA certified and designed to meet the criteria for dynamic temperature standards. They include four magnetically permeable alloys (Permanorm 3, Mumetal, Permanorm 5 , and Trafoperm) and nickel. In conjucntion with a magnetic field, they provide a detectable change in apparent weight at the temperature at which thermally induced disorder or change in structure affects their magnetic properties. Consequently, each reference material shows an indication on the weight change record when the specimen reaches the demagnetization temperature. The indicated sensor temperatures are recorded and compared to the corresponding certified temperatures. In a typical calibration experiment, a piece of Trafoperm weighting 5.9 mg was embedded within the high-purity aluminum oxide powder (simulating the actual sample) and placed inside the sample holder. Similar experiments were carried out using several other Curie point reference materials and sample heating rates. It should be noted that these experiments were designed to simulate extreme cases for the differences between the actual sample temperatures and those measured at the thermocouple location. Table I1 depicts the typical temperature calibration results. In addition, the table includes ICTA values for the intial (TI)and final (T3)demagnetization temperatures and associated uncertainties given by the NBS. The values of the final demagnetization temperatures determined from these experiments agreed very favorably with those given by NBS within the reported range of temperatures. However, this was not the case for the onset of demagnetization temperature as measured by the sample thermocouple. Discrepancies as high as 50 K were observed (depending upon the magnitude of the radiant flux, sample temperature, and heating rate). These observations tend to support the role of the heat-transfer effects (even within the small volume sample holder) and the extremely difficult task of accurate temperature measurements in high heating rate experiments. In order to improve the accuracy of temperature measurements and
z!8+2
i
0.2
i
I4 0
zoo
400
TIME, (s)
Figure 3. Temperature (T), weight remaining (W), and fraction maximum flux available at the sample location (FMF) versus time for dehydration/decomposition of hydrous zinc sulfate and zinc oxide residue.
reduce heat- and mass-transfer intrusions, small zinc sulfate masses (about 7-10 mg of anhydrous weight) were used.
Characterization of the High Heating Rate TGA Thermogravimetric measurements are often influenced by temperature effects in the surrounding gas. These temperature-dependent effects can cause disturbances in weighing and base-line instability, including, among others, thermal gas flow and convection. A t high pressures (exceeding 100 Torr), convection effects occur as a result of differences in gas density and the interplay of the gravitational field. This in turn gives rise to the apparent weight changes and detectable noise level. The situation is further complicated due to superposition of forced flow of carrier gas on thermally induced convective flow. Various techniques exist and were used to correct and compensate for the effects of these disturbances and others on the performance of the high heating rate TGA. For example, the effects due to buoyancy on TGA measurements were accounted for by means of a blank run repeated after each decomposition experiment. In the blank experiment, the remaining residue from the previous decomposition run was left intact in place. Identical experimental conditions were used for both the blank run and its corresponding decomposition experiment. The data from blank (base-line) experiments established the extent of the spurious weight changes which occurred in the high heating rate TGA. Figure 3 presents typical results depicting dehydration and decomposition of zinc sulfate. The data for the apparent weight change and
Ind. Eng. Chem. Res., Vol. 28, No. 3, 1989 359 initial anhydrous sample weight, Wi(t) and Wo(t)refer to the actual and measured sample dry weights at time t, and D = d/dt denotes the differential operator. The response of the weighing system to an impulse is obtained by solving eq 1:
overdamped ( { > 1) (2) Static sensitivity, K , is found from static calibration, and a refers to the amplitude of the impulse. The values of the measurement-system parameters { and w, must be 0.2
1 0
200
400
TIME, (s)
Figure 4. Dehydration and decomposition of hydrous zinc sulfaw. Stoichiometric lines are with respect to zinc sulfate heptahydrate.
temperature of the remaining zinc oxide residue is also included in this figure. The sample irradiation was relatively constant during these experiments and is given in Figure 3 as well. The thermogravimetric data from the decomposition experiments and the blank (zinc oxide residue) runs were fitted with smoothing curves by using an International Mathematical and Statistical Library (IMSL) subroutine IFLSQ (which uses a set of 15 Legendre polynominals orthogonal over the time interval of the experiment). Finally, if the temporal variations of the weight change for the remaining residue (zinc oxide) are subtracted from that derived for the decomposing solid, the net weight changes due to solids' decomposition were determined. Figure 4 presents base-line-corrected results for sample weight loss versus time (for data of Figure 3) during radiative decomposition of hydrated zinc sulfate. When an experiment is carried out a t a sufficiently low sample heating rate, no further treatment of the thermogravimetric data is necessary. However, when the sample heating rates are high, the data must be examined for the possible effects of the lag times, in the sensing instruments. This is discussed briefly in the following paragraphs. Static or quasi-static (slowly changing with time) measurements are simpler to make in comparison with dynamic measurements. Dynamic measurements are more complicated due to the frequency response effects of each element in the instrumentation system on the amplitude and phase of the quantity being measured. The response characteristics of the transducers are important since large errors can occur if the frequency response of the system is improperly matched to the frequency content of the quantities being measured. The ability of an instrument to accurately and rapidly measure a given transient quantity (signal) depends upon several factors. These include the type (first order, second order, etc.) and the dynamic response parameters of the instrument and the nature of excitation (time-varying input function or quantity to be measured). Instruments which measure weight are generally considered to be second-order systems (Doebelin, 1975). Therefore, their dynamic behavior can be described by a second-order differential equation: where K is the static sensitivity, w, is the undamped natural frequency (s-l), { refers to the dimensionless damping ratio, Fi(t)= W i ( t ) / W *and Fo(t)= W o ( t ) / W * are the input and output weight functions (here they are assumed to be the normdized weight readings), W +is the
determined in order to characterize the time-dependent behavior of the weighing system. These parameters are found experimentally by measuring Fo(t),in a number of ways from step, impulse, or frequency response tests. We used a sufficiently short duration pulse whose Fourier transform magnitude curve was flat out to frequencies just beyond the point where the system's response practically cuts off. Once the time-dependent output of the short duration input pulse was known, the operational transfer function, 4(iw) with i = (-1)1/2 was determined by taking the Fourier transform of the output. The measured output was then fitted with eq 2 using the IMSL subroutine ZXSSQ to determine the unknown parameters w , and {. This subroutine provides solutions to nonlinear least-squares problems by using the Levenberg-Marquardt algorithm. The values of the damping ratio and natural frequency which best described the dynamic response of the Mettler system under our experimental conditions were found to be { = 1.022 and w, = 9.6 s-l. The dynamic response of a bare thermocouple, on the other hand, is often expressed by using a first order model (Doebelin, 1975) (70 l)To= Ti (3)
+
This assumption does not account for the heat-transfer limitations within the sample itself. A reasonable estimate of the errors introduced using thermocouples in our system has already been discussed (see Table 11). Once the weighing system parameters are determined, they can be used to reconstruct the undisturbed record of Fi(t).We used the following method to reconstruct Fi(t) according to a scheme described by Doebelin (1975). For a weighing system which follows reasonably closely a second-order instrument behavior, Fo(t)was transformed into frequency domain to obtain fo(iw) and fi(iw) = f o (iw)/~$(iw).4(iw) refers to the operational transfer function and was determined in a manner described before. Then, Fi(t)was obtained by the inverse transform of fi(iw). A computer program was developed to reconstruct the undisturbed record of the weight loss data using the methodology above. The Cooley-Tuckey algorithm (Ferziger, 1981) was used to obtain the fast Fourier transform of the data. Figure 5 presents typical results showing the effects of the dynamic response characteristics of the Mettler balance. This figure depicts the instantaneous heating rates versus fractional weight of unreacted material, F ( t ) ,for two zinc sulfate samples irradiated a t different flux levels.
Results and Discussion Several experiments were carried out using samples of zinc sulfate hydrate exposed to various levels of radiant flux at the focus of the arc-image furnace. Table I11 summarizes the important experimental parameters used during the runs discussed here. Figure 6 displays typical results for the temperature and heating rate versus time
360 Ind. Eng. Chem. Res., Vol. 28, No. 3, 1989 Table 111. ExDerimental Conditions Used for High Heating Rate DecomDosition of Zinc Sulfate a n d Zinc O x m u l f a t e run 1 2 3 4 5 1 2 material zinc sulfate (p) zinc oxysulfate (a) anhydrous sample wt,O mg 8.35 7.14 6.92 10.20 6.92 8.96 4.27 carrier gas nitrogen air air air air air helium carrier gas flow rate, mL/s 4.15 4.15 8.33 8.33 8.33 4.15 0.85 stagnationb temp, OC 1114 1120 1158 1112 1205 1245 1050 a
Back-calculated from experimental residue (ZnO) weight.
Of the remaining zinc oxide residue. 6
1
1
0.3
0.7
0.9
I
I
f' 0.5
FRACTION WEIGHT REMAINING, (.)
I
1
I
0.8
0.7
FRACTION WEIGHT REMAINING, (.)
Figure 5. Effects of the balance response characteristics on the two zinc sulfate decomposition data (uc, uncorrected weight change results; c, corrected for instrument effects): w, = 9.6 s-] and = 1.022. Stoichiometric lines are with respect to ZnSO,.
