Ind. Eng. Chem. Res. 1992,31,694-700
694
u = dummy variable for velocity U = x component velocity, m/s
W d m r ( N s r dolo)
2-Propanol
(Nmw data)
wotvr (Simon h Wiu) Water (Fullto & U*da)
c
i
0
0
a I
W = z component velocity, m/s gravity y = coordinate perpendicular to heated surface z = coordinate perpendicular to x and y Greek Letters r = mass flow rate, kg/(m s) y = temperature coefficient of surface tension, N/(m K) Bo = contact angle, rad p = viscosity, kg/(m s) T = 3.14159... p = liquid density, kg/m3 u = surface tension, N/m 7 = shear stress x = coordinate aigned with
E. Glycol (NOW data)
1 o1
Experimental Breakdown Heat Flux (W/m2)
Figure 11. Parity plot of predicted versus experimental breakdown heat flux.
model. This requires the surface to be characterized before the model is used. New experimental data have been provided by this study. In addition to the usual data obtained with water, these new experiments included measurements with two organic liquids. The correlation presented here has been tested for various geometries and fluids and shows significant improvement over earlier models for predicting film breakdown. Nomenclature A = area d = tube diameter, m D,= integration constant and correlation parameter F = force per z component width, N/m g = acceleration due to gravity, 9.8 m/sz h = film thickness, m k = thermal conductivity, W/(m K) L = heated length, m Pr = Prandtl number q = heat flux, W/m2 R = radius of curvature Re = Reynolds number
Subscripts
o = initial condition c = critical i = interface s = stagnation
Literature Cited Chung, J. C.; Bankoff, S. G. Initial Breakdown of a Heated Liquid Film in Cocurrent Two-Component Annular Flow: 11. Rivulet and Drypatch Models. Chem. Eng. Commun. 1980,4,455-470. Fujita, T.; Ueda, T. Heat Transfer to Falling Liquid Films and Film Breakdown-I, Subcooled Liquid Films. Int. J. Heat Mass Transfer 1978,21,97-108. Hartley, D. E.; Murgatroyd, W. Criteria for the Break-up of Thin Liquid Layers Flowing Isothermally Over Solid Surfaces. Int. J. Heat Mass Transfer 1964, 7, 1003-1015. McPherson, G. D. Axial Stability of the Dry Patch Formed in Dryout of a Two Phase Annular Flow. Znt. J. Heat Mass Transfer 1970, 13, 1133-1152. Murgatroyd, W. The Role of Shear and Form Forces in the Stability of a Dry Patch in Two-Phase Film Flow. Int. J. Heat Mass Transfer 1965,8, 297-301. Simon, F. F.; Hsu, Y. Y. “Thermocapillary Induced Breakdown of a Falling Liquid Film”; NASA T N D-5624, Lewis Research Center, 1970. Zuber, N.; Staub, F. W. Stability of Dry Patches Forming in Liquid Films Flowing Over Heated Surfaces. Znt. J. Heat Mass Transfer 1966, 9,897-905.
Received for review January 18,1991 Revised manuscript received May 1, 1991 Accepted May 9,1991
Kinetics of Boehmite Formation by Thermal Decomposition of Gibbsite Lawrence Candela and Daniel D. P e r l m u t t e r * Department of Chemical Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104
The kinetics of the thermal decomposition of well-crystallized macrogranular gibbsite [Al(OH),] to boehmite [AlOOH] was studied under water vapor pressures from 100 to 3200 Pa,over the temperature range from 448 to 478 K, and for particle sizes between 38 and 180 km. Nitrogen adsorption was used to characterize the porous structure via surface area measurements. The empirical kinetics were found to be consistent with three-dimensional reaction interface movement, with growth behavior controlled by the interaction of chemical reaction with water vapor diffusion. The activation energy for the process was found to be 142 f 10 kJ/mol. A model was developed that describes the conversion process in terms of the growth of nucleated boehmite sites, coupled with the eventual escape of product water vapor to the particle surfaces. Introduction With proper preparation and thermal treatment, alumina and its partial hydrates assume highly porous crys-
* To whom correspondence should be addressed.
talline forms with good structural integrity, large specific areas, and high surface activity. These characteristics make the several dehydrated species valuable in numerous technical applications, typically as adsorbents or as catalysts. Each specific application normally calls for partic-
0888-5885/92/2631-0694$03.00/00 1992 American Chemical Society
Ind. Eng. Chem. Res., Vol. 31, No. 3, 1992 696 ular desired properties, such as the degree of crystallinity of each of these dehydration species, the distribution of pore sizea in the material, and the overall porosity (Sanchez and Herrera, 1981; Sanchez et al., 1981). Gibbsite [Al(OH),] is by far the most common industrially produced variety of the fully hydrated aluminas. Its subsequent thermal decomposition produces mixtures of boehmite and transition alumina phases, having extensive macro-, meso-, and microporom surface area (>250 m2/g). Each of the two overlapping chemical transformations is influenced differently by the operating parameters of temperature, water vapor pressure, particle size, and sodium impurity content. Moreover, these two chemical decompositionsyield distinct pore structures which in turn influence the measured kinetics. The kinetics of the decomposition that yields transition alumina have been reported previously (Candela and Perlmutter, 1986); here attention is turned to the conversion process that yields boehmite. Brown et al. (1953) and deBoer et al. (1954a,b) were among the first to recognize that large-grained Al(OH)3 particles yielded mixtures of well-crystallized boehmite (AlOOH) as well as a number of transition aluminas as their decomposition products. Their differential thermal analyses (DTA) and differential scanning calorimetry (DSC) demonstrated distinct, separate peaks for each of these decomposition processes. In addition they showed that the product boehmite phase is situated at internal sites of the macrogranular particles. Since these experimenta were performed under water vapor pressures far below those required for AlOOH production by the A1203/H20 equilibrium diagram of Ervin and Osborn (1951),deBoer et al. (1954a) suggested that intragranular sites could locally achieve the required higher pressures and thereby effect the growth of the boehmite phase. Yamaguchi and Sakamoto (1959) postulated that the boehmite formation is the result of an internal dissolution of Al(OH)3in H20 followed by a recrystallization of AlOOH, while Day and Hill (1952), Sat0 (1960), and Freund (1967) maintained that the boehmite phase is a rehydration product of an internally produced lower transition alumina hydrate. Tertian and Papee (1953,1954), Courtial and Trambouze (1957), and Rouquerol et al. (1975) demonstrated enhanced boehmite formation with increasing Al(OHI3particle sizes, attributed to the enhanced ability of large particles to withstand and maintain high internal water vapor pressures. Alevra et al. (1972) found that gibbsite crystallinity and lower initial surface area promoted boehmite production. Calvet and Thibon (1954),Eyraud and Goton (1954),and Rouquerol et al. (1975) noted that increases in the ambient water vapor pressure during thermal treatment also served the same end. Courtial et al. (1956) and Rouquerol et al. (1975) reported that low heating rates enhanced the boehmite formation by delaying the transition to the exterior decomposition of the Al(OH)3to a transition alumina; however, Wefen and Bell (1972) reported that rapid heating rates that established a gradient of water vapor pressure between the particle center and exterior were required to produce boehmite. With particular attention to sodium, deBoer et al. (1954b), Torkar and Bertsch (19611, and Sat0 (1959) showed that increases in the alkali-metal content of the gibbsite served to increase the yield of boehmite. Alkali metal is known to exist interstitially between the basal plates of the hydroxide and to lend a stabilizing effect that favors boehmite formation by enabling the crystal to withstand higher internal water vapor pressures. The
possibility of alkali metal contributing kinetically to the nucleation and growth of the boehmite phase has been addrwed by Torkar and Bertsch (19611, who noted lower decomposition temperatures for sodium-doped bayerites, and by Oomes et al. (19611, Ginsberg et al. (1957), and Puchkov and Chakhalyan (1974),who discussed the stability of intermediate aluminas and the rates of their transformations in differing alkali-metal solutions. It was found that the kinetics of nearly all aluminum hydroxide transformations in solution are enhanced by alkali metal. The importance of the evolution of the texture of the decomposing Al(OH)3particle in halting the conversion to boehmite and enhancing the decomposition to a transition alumina has been emphasized by deBoer (1954b), Tertian et al. (1954), Sing (1974), and Candela and Ferlmutter (1986). The crystal structure of gibbsite is that of a stacked layered structure common to many mineral hydroxides. deBoer established that the transition between the two decomposition processes is marked by a fwuring of the layered crystal parallel to its cleavage plane; adsorption studies revealed the generation of an internal reaction surface consisting of relatively uniform, slibshaped pores of approximately 3-nm width.
Experimental Techniques Sample Preparation. Refined grade C-31 Alcoa hydrated alumina manufactured by the Bayer process (Wefers, 1972) was used in this research. This grade is a rather large particle sized (20-200 pm) material with a pure white appearance. Ita major impurities are given to be Na20 (0.2%), Si02 (0.01%), Fez03 (0.004%), and excess moisture (0.04%). Weight loss due to ignition to 1100 "C is reported to be 34.570, compared to the theoretical loss for pure Al(OH), of 34.64%. Tyler US. Standard testing sieves were used to separate the gibbsite into a series of particle size fractions. Samples in the 75-88-pm sieve range were analyzed on a Norelco diffractometer using the Cu Kal emission of wavelength 1.5405 X lo4 pm. The peak positions and intensity ratios for both gibbsite samplea matched the standard values very closely for each diffraction peak, and there was no evidence in the X-ray pattern of the presence of any other alumina phase. Nitrogen adsorption studies were performed on undecomposed samples of several different particle size fractions. All the isotherms demonstrated a complete lack of hystereais and very low BET areas (
