FLUIDIZED-BED COMBUSTION OF GRAPHITE-BASE NUCLEAR REACTOR FUELS HARTMUT 0 . WITTE'
Oak Ridge National Laboratory, Oak Ridge, Tenn. 37830 The first step in a proposed processing method for the recovery of uranium and thorium from graphite-base nuclear reactor fuels is combustion of the fuel in a fluidized bed of alumina. The reaction kinetics involved in this process was analyzed, and an empirical equation for the combustion rate was derived, from which the effects of temperature, feed-gas composition, and particle diameter on the combustion rate could be predicted. The experimehtal results from fluidizedbed combustion studies on both unirradiated and irradiated fuel specimens compared favorably with the predictions.
FUELelements consisting of pyrolytic carbon-coated ura-
nium carbide or uranium-thorium carbide microspheres dispersed in a graphite matrix have been developed for high temperature, gas-cooled reactors. The first step in a proposed processing method for recovery of uranium and thorium from these fuels is combustion of the crushed fuel in a fluidized bed of alumina (Nicholson et al., 1965; Wachtel et al., 1966), which is an efficient heat-transfer medium for conducting highly exothermic gas-solid reactions, At the Oak Ridge National Laboratory, the fluidized-bed combustion process has been studied (Flanary et al., 1969) with unirradiated and irradiated fuel specimens. The primary purpose of these experiments was to study off-gas handling and leachability of the combustion ash; however, enough data were obtained to permit comparison of the effects of some of the process variables with those predicted from a mathematical analysis of the fluidized-bed combustion system. Derivation of the Rate Equation
Carbon Oxidation. An analysis of the combustion of graphite-base fuel in a fluidized bed involves interrelated problems in heat and mass transfer, fluid dynamics, and reaction kinetics. Since graphite is the major chemical species in the fuel (>80 weight %), only its oxidation is considered in the determination of the combustion rate; oxidation of any carbides present is neglected. T u and coworkers (Tu et al., 1934) point out that neithe; carbon dioxide nor carbon monoxide can be considered as the sole primary product of the reaction between carbon and oxygen, and that both gases are evolved simultaneously through the formation and subsequent decomposition of the physicochemical activated complex CrOy. The COZ/ CO ratio of the primary combustion was shown to be a function of temperature and dependent on the characteristics of the carbon investigated (in general, it increased with the degree of graphitization). Further, carbon monoxide in the presence of oxygen is partly oxidized to carbon dioxide. This reaction is catalyzed by available surfacefor example, of metal oxide ash (Scott, 1966a,b)-therefore, the COZ/COratio in the final off-gas can differ considerably from the ratio a t the reaction site.
Below 1300"C., carbon is consumed in a first-order chemical reaction. The activation energy varies from 20,000 to 30,000 cal. per mole up to 1500°C. (Meyer, 1932; Scott, 1966a):
N oe-hlRY; - K 1 T-0.6 s
POJ
(1)
Mass Transport. When the rate of chemical reaction is sufficiently high, resistance due to the mass transport of oxygen from the bulk gas to the reaction surface will contribute to the control of the carbon-oxygen reaction. In developing a model to describe the transport of oxygen toward the reaction surface, the surface is assumed to be capable of sorbing oxygen but not nitrogen. A partial pressure gradient will be established, causing oxygen to diffuse toward, and nitrogen away from, the surface. Also, a total pressure gradient will be produced, causing movement of both oxygen and nitrogen from the bulk gas toward the surface, in addition to the transfer by diffusion. Since there is 110 net transfer of nitrogen, its rate of flow from the bulk gas must balance its transfer by diffusion. This concept of a stagnant layer, through which oxygen diffuses and is consumed a t the reaction surface, is described by Stefan's law (Coulson and Richardson, 1964):
N o= --D aPog ' A R T ~ay P - pot where
N o = rate a t which oxygen diffuses through the stagnant film, moles per second Po? = oxygen pressure at y, atm. Integration of Equation 2 for a spherical stagnant layer, with the boundary conditions
y=r
' Present addreas, Heisae Zellen, Kernforschungsanlage, Juelich, Germany. VOL. 8 N O . 2 A P R I L 1 9 6 9
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results in:
r+X
r
Or, after suitable rearrangement:
The same result can be obtained by integration of Stefan's law for a linear film,
The influence of the film curvature can be estimated by multiplying the right side of Equation 3b by the ratio of the geometric mean film area to the particle surface area:
[.rrd27r(d+ 2x)2]' rd' After the multiplication and some rearrangement, Equation 3a is obtained. In the term ( l / X + 2 / d ) in Equation 3a, l / X describes the linear case where the film thickness is small compared with the particle diameter, whereas the complete term applies to the case where the film thickness is large compared with the particle diameter and when the increased diffusional resistance due to the film curvature cannot be neglected. Specific Reaction Rate. The final expression for the specific reaction rate is obtained by combining Equations 1 and 3a and eliminating Po?,s:
X+d Let rc be the rate of combustion of carbon, moles per second. If the sole primary product is carbon dioxide, r, equals No. If the product is all carbon monoxide, rc equals 2N,. I n reality:
r, = $No
(5)
where 6, the correction factor for primary CO production, is: 1 $ 2 and 4 = $ ( T ) ;$ is also a function of the type of carbon being investigated. Combining Equations 4 and 5 gives:
X+d This simple model involving two distinct steps, diffusion and chemical reaction, is only one possible model for the 146
l & E C PROCESS D E S I G N A N D DEVELOPMENT
mechanism of the carbon-oxygen reaction. For example, Essenhigh et al. (1965) used a model involving two chemical steps, adsorption (first-order) and desorption (zero-order), along with mass transfer that fitted the data of Tu et al. (1934) at least as well as. the original model. The simple model was used here because the purpose of this work was not to investigate ihe mechanism of the reaction in detail; furthermore, the experimental procedure permitted only a limited test of Equation 6. The following parameters could be computed from the experimental data: the rate of combustion, rc, grams per minute; the feed gas oxygen pressure, Po-, and inert gas pressure, P,, atm.; the bulk gas temperature in the fluidized bed, T , OK.; and the weight of original carbon remaining in the bed, W , grams. The parameters in Equation 6 have to be replaced by these calculated or measured parameters. The oxygen pressure in the bed, Po.,a,and the mean film inert gas pressure were assumed to vary linearly with the respective feed gas pressures. This assumption will not be valid a t high combustion rates and low oxygen pressures because most of the oxygen will be consumed near the feed gas entrance. In this case, the assumption will lead to oxygen pressures for the whole bed that are too high for the measured combustion rate. Another important variable is the reaction surface area. The crushed fuel particles had a mean diameter of about 1 mm. but were far from spherical. The particle size of the final combustion ash was a factor of 10 smaller. The relationship between the fraction of unburned carbon in the bed and the number of particles, their size, shape, and surface roughness is unknown. Assuming that the total surface area available for reaction varies regularly with the fuel weight, one may write a weight-area relationship of the form A = kW", where k is a constant and 0 5 a 5 1.67 for shapes from thin flat flakes to uniform spheres, respectively. The simplest relationship was chosen for this correction-A = kW. The data of Tu and coworkers (Tu et al., 1934) indicate that the difference between the bulk gas and surface temperatures is less than 1 7 5 of the absolute temperature. Violent fluidization should efficiently prevent local hot spots. The bulk gas temperature, T , will be used to replace the mean film temperature, Ti, and the surface temperature, T,. According to Gilliland's equation (Perry et al., 1963), the diffusivity is expected to vary with TI". The group d / X is proportional to the Sherwood number and, thus, is a power function of the Reynolds and Schmidt numbers. Since the Schmidt number is substantially independent of temperature, we find:
(7) The Reynolds number, calculated using the total gas flow rate and the average particle diameter of the initial fuel load, was about 20. Actually, an appreciable fraction of the gas did not take an active part in fluidization but passed through the fluidized bed as bubbles and through channels. This was established by visual observations in a glass model. Therefore, following a two-phase fluidization model originally proposed by Toomey and Johnstone (1952) and refined by Partridge and Rowe (1966a,b), the effective Reynolds number in the homogeneous phase of the fluidized bed is expected to be much lower. Data
on mass transfer in fluidized beds a t this low Reynolds number are extremely scarce. Chu et al. (1953), studying the evaporation of naphthalene from glass and lead particles into a stream of air, varied NRefrom 1 to 30 and found the relation
-
NSh
NR:.*'
TO OFF GAS PROCESSING
(8)
If this is adopted, the term 1 / X in Equation 6 becomes:
I n Equation 9, velocity u was held constant, p varies by T - ' and F by TO.'. Substituting these expressions into Equation 6 results in :
FEED GAS INLET
Figure 1. Schematic diagram of fluidizedbed combustion apparatus
Rearrangement yields:
(11) The denominator of Equation 11 contains two additive terms, the first corresponding to a diffusional resistance and the second to a chemical resistance. Thus, two limiting cases are obtained: When the term e'"'' is large,
Here, the rate of combustion is determined by the rate of chemical reaction. The reaction is first-order with respect to oxygen pressure. When el' '?' is small, which should be the case a t elevated temperature, diffusion is the controlling factor and two possibilities exist: d is large compared with X:
heating and cooling coils. Temperatures a t various elevations were monitored by three thermocouples. Metered, preheated dry air. nitrogen, oxygen, or mixtures of these gases were piped into the bottom of the burner through a ball-check valve at a rate of 4 liters per minute a t STP. The off-gas was passed through continuous CO, and CO analyzers and then through a wet-test meter. Both the unirradiated and irradiated fuel compacts [2.75inch-o.d , 1.75-inch-i.d., 1.5-inch-high annular rings of hotpressed graphite interspersed with 30 volume % (Th,U)C? pyrocarbon-coated particles] were crushed to -4 mesh, and a charge of 100 grams of fuel was loaded ipto the reactor, together with 200 grams of 60- to 120-mesh fused alumina. The bed was fluidized with nitrogen during startup. When the reaction temperature was stabilized, air was blended into the nitrogen feed gas. The oxygen content in the feed gas was then gradually increased, with the upper limit being determined by the maximum heat removal rate. A more detailed description of the experimental procedure is given by Flanary et al. (1969). Results and Discussion
d is small compared with X:
Experimental
The batch-type reactor vessel (Figure 1) had a 1.5inch i.d. by 12-inch-high fluidized bed surmounted by a 3-inch i.d. by 12-inch-high particle de-entrainment section The fluidized-bed section was provided with external
Several runs were made a t 750" i 70°C. using both unirradiated fuel samples and fuel that had been irradiated to burnups as high as 41,500 megawatt days per ton (U + Th). Typical data from these experiments, plotted as specific combustion rate us. the oxygen pressure in the feed gas, are shown in Figure 2. Within the limits of experimental error, irradiation had no effect on the rates of combustion. The scatter in data is caused partly by the temperature range involved, and partly by errors in the calculation of the fuel weight, W , which was computed by difference from the COZ + CO in the off-gas. I t appears, however, that the points a t oxygen pressures less than 1 atm. are grouped along a straight line. Similar data, obtained in single experiments with irradiated fuel VOL. 8 N O . 2 APRIL 1969
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FEED GAS OXYGEN PRESSURE, a t m
Figure 2. Combustion rate
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=t70°C.
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A 550°C m 600.C
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FEED GAS OXYGEN PRESSURE, a t m
Figure 3. Log combustion rate vs. log oxygen pressure 148
I&EC PROCESS DESIGN A N D DEVELOPMENT
a t lower temperatures, are shown in Figure 3 as log-log plots of specific combustion rate us. the oxygen pressure in the feed gas. The slopes of these plots vary from about 0.8 to 1.0, in agreement with the linear relationship between combustion rate and oxygen pressure expressed in Equation 11. At 750°C., when the oxygen pressure was very low, all of the oxygen was consumed near the feed gas entrance and the actual reaction surface area and oxygen pressure in the bed were much smaller than those calculated from the assumptions. Consequently. the calculated specific combustion rates are probably too low. The steep increase of the combustion rate a t oxygen pressures greater than 1 atm., indicated by the dashed line in Figure 2, is predictable from Equation 11. Since the total pressure was about 1.3 atm., these data were obtained by decreasing the inert gas pressure or by burning with pure oxygen. Although Equation 11 is not valid for pure oxygen, the influence of the term P , / P in the denominator will cause the combustion rate to increase with diminishing inert gas pressure in a region where diffusion is controlling. Other influences on the combustion rate which are not expressed in Equation 11 are: The counterdiffusion of combustion products through the stagnant film a t high combustion rates will add to the diffusional resistance. This would tend to change the two straight lines in Figure 2 into an S-shaped curve. A comparison of the experimental data with a number of analytical functions, using the method of least squares, showed that the data were best fitted with a third-degree polynomial. The oxygen pressure was high only toward the end of a run, because of temperature control problems. Here, with the particle size very small, the surface area should decrease less rapidly than the fuel inventory, W . This would lead to higher combustion rates and could very well overshadow the increasing diffusional resistance of small particle sizes expressed in Equation 14. The data a t constant temperature have been interpolated at constant oxygen pressure to allow an Arrhenius plot of log ( r < / W )us. 10'iT (Figure 4). The slopes of these curves a t temperatures less than 600°C. yielded an apparent activation energy, E , of 18,900 cal. per mole, typical of a reaction controlled by chemical resistance as defined in Equation 12. At temperatures above 600" C., the apparent activation energy was about 2800 cal. per mole. This low value is typical of diffusioncontrolled reactions. The value of 2800 cal. per mole results in temperature exponents of about 0.24 to 0.20 between 600" and 750°C. These are not greatly different from the exponent 0.17 in Equation 13, indicating that the film thickness was probably small compared with the particle diameter. The difference between the observed exponent and the one in Equation 13 might be due in part to the influence of +(T), since T u and coworkers (Tu et al., 1934) assume from Meyer's (Meyer, 1932) data that 4 has a temperature exponent ot 0.3 between 1100" and 2000°C. The upward curvature at high temperature of the dashed line in Figure 4, representing 1.1 atm. of oxygen pressure, resembles the general tendency shown in Figures 2 and 3-that is, a t higher temperatures and feed gas oxygen pressures, the combustion rate tends to increase considerably, causing problems in temperature control. Experiments were conducted with both unirradiated fuel and fuel irradiated to a burnup of 41,500 megawatt days
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total pressure, atm. inert gas pressure in feed gas, atm. logarithmic mean of inert gas pressure in film, atm. oxygen pressure in feed gas, atm. oxygen pressure in bulk gas, atm. oxygen pressure at particle surface, atm. gas constant, cal. per mole K. mean particle radius, cm. rate of carbon combustion, moles per second bed gas temperature, OK. mean film temperature, K. reaction surface temperature, K. superficial velocity, cm. per second fuel inventory, grams film thickness, cm. N R e = Reynolds number, d p ~
a
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N,, = Schmidt number, ~ c / p D N,, = Sherwood number, N,RTd/ADAP 1 = kinematic viscosity, g. per cm. second 6 = correction factor for primary CO production p = density, g. per cc.
J
literature Cited
-4
1.5
I. 3
111
0.9
RECIPROCAL BED TEMPERATURE x 103, I I ~ K
Figure 4. Arrhenius plot of combustion data
per ton (U + Th). One might expect intensive irradiation to produce a disordered graphite structure and, consequently, expect irradiated fuel to behave in a manner similar to that of carbon with a low degree of graphitization. According to T u et a2. (1934), this would result in more CO in the primary products than expected from a highly graphitized carbon. The author observed in the experiments with the highly irradiated fuel that the CO concentration in the off-gas was slightly higher than in the other runs, but, since the final off-gas composition is more highly dependent on other parameters not defined in this study, this observation is inconclusive. Acknowledgment
The experimental work was done in cooperation with
J. R. Flanary, J. H. Goode, V. C. A. Vaughen, and G. E . Woodall, all of the Oak Ridge National Laboratory staff. The author thanks them, L. M. Ferris of ORNL, and W. Gans from the KFA, Juelich, Germany, for many helpful discussions on the subject of this study. Nomenclature
A d D E K1 No
= surface area, sq. cm.
= mean particle diameter, cm. = diffusivity, sq. cm. per second
= activation energy, cal. per mole = constants
= oxygen consumed per unit time, moles per sec-
ond
Chu, J. C., Kalil, J., Wetterot, W. A., Chem. Eng. Progr. 49, 141 (1953). Coulson, J. M., Richardson, J. F., “Chemical Engineering,” 2nd ed., Vol. 1, p. 296, Pergamon Press, Oxford, 1964. Essenhigh, R. M., Froberg, R., Howard, J. B., Ind. Eng. Chem. 57, 33 (1965). Flanary, J. R., Goode, J. H., Witte, H. O., Vaughen, V. C. A., “Hot Cell Evaluation of the Burn-Leach Process Using Irradiated Graphite-Base HTGR Fuels,” Oak Ridge National Laboratory ORNL-4120 (1969). Meyer, Z., Phys. Chem. B17, 385 (1932). Nicholson, E . L., Ferris, L. M., Roberts, J. T., “BurnLeach Processes for Graphite-Base Reactor Fuels Containing Carbon-Coated Carbide or Oxide Particles,” Oak Ridge National Laboratory ORNL-TM-1096 (1965). Partridge, B. A., Rowe, P. X., Trans. Inst. Chem. Engrs. (London) 44, T335 (1966a). Partridge, B. A., Rowe, P. N., Trans. Inst. Chem. Engrs. (London) 44, T349 (196610). Perry, R. H., Chilton, C. H., Kirkpatrick, S. P., “Chemical Engineers’ Handbook,” 4th ed., pp. 14-21, McGrawHill, S e w York, 1963. Scott, C. D., IND.ENG.CHEM.PROCESS DESIGNDEVELOP. 5 , 223 (1966a). Scott, C. D., “Oxidation of Hydrogen and Carbon Monoxide in a Helium Stream by Copper Oxide,” Oak Ridge National Laboratory ORXL-TM-1540 (1966b). Toomey, R. D., Johnstone, H. F., Chem. Eng. Progr. 48, 220 (1952). Tu, C. M., Davis, H., Hottel, H . C., Ind. Eng. Chem. 26, 749 (1934). Wachtel, S. J., Reilly, J. J., Bartlett, C. B., Johnson, R., Wirsing, E., “Reprocessing of Nuclear Fuels by Volatility Separations in Fluidized Beds,” Brookhaven National Laboratory BNL-973 (1966). RECEIVED for review August 3,1967 RESUBMITTED December 30,1968 ACCEPTED January 7,1969 Research sponsored by the U. S. Atomic Energy Commission under contract with the Union Carbide Corp.
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