Dissolution of Graphite-Base Reactor Fuels by Pressurized Aqueous

Publication Date: July 1966. ACS Legacy Archive. Cite this:Ind. Eng. Chem. Process Des. Dev. 1966, 5, 3, 234-238. Note: In lieu of an abstract, this i...
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DISSOLUTION OF GRAPHITEDBASE REACTOR FUELS B Y PRESSURIZED AQUEOUS PROCESSES PAUL A. HAAS AND LESLIE M. FERRIS Chemical Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tenn.

The combustion of the graphite matrix and dissolution of the uranium and thorium carbides or oxides in graphite-base nuclear reactor fuels were studied in a single vessel containing nitric acid solutions and oxygen under pressure. Both batch autoclaves and a continuous reactor system were utilized. With excess oxygen 0 2 * C02. With fuel containing Th-U dicarbide particles present, the net combustion reaction was C coated with pyrolytic carbon, complete combustion of the carbon coatings and the graphite, and dissolution of the thorium and uranium, were achieved in 2 to 10M " 0 3 in 24 hours when the HN03/(Th U) mole ratio was greater than 50. Oxidation of unfueled graphite was studied in a system where gases were continuously added and removed. Rate constants, as grams of graphite oxidized to COZper hour per gram of graphite remaining, were 0.06 to 0.25 hr.-l, and increased with increasing agitation and/or external surface area o f the graphite. Corrosion of the stainless steel vessels was less than 80 mils per year at 300' C. in 1 to 2M " 0 3 , but was excessively high when the acid concentration was higher. Pressurized aqueous combustion of graphite-base fuels appesrs technically feasible, but applicability of the method i s seriously limited by the high pressure and high HNOI/(Th U) ratio required, the corrosion rate, and the moderate rate of reaction.

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processes for the recovery of uranium and fuel from high-temperature gas-cooled reactors (HTGR's) are being developed a t the Oak Ridge National Laboratory (ORNL). Fuel elements for these reactors consist of Th-U carbide or oxide fuel particles coated with pyrolytic carbon and dispersed in a graphite matrix. One potential processing method for H T G R fuels, the burn-leach process (5), involves combustion of the fuel a t 700' to 750' C. in a fluidized bed of inert alumina and transfer of the resultant bed to another vessel where the uranium and thorium are recovered by acid leaching. An alternative method, described in this paper, consists in combustion of the graphite and dissolution of the thorium and uranium in a single pressurized vessel containing nitric acid solution and oxygen. This pressurized aqueous combustion (PAC) process derives from results reported for the Zimmerman process for sewage or waste disposal (8, 70) and for the oxidation of coal (3, 7). Possible advantages of the PAC process over the burn-leach process include: uniform and easily controlled rates of reaction a t a relatively low temperature; dissolution of the uranium and thorium in the combustion vessel; elimination of the EAD-END

H thorium from spent graphite-base

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possibility of formation of sintered oxides a t high temperatures; elimination of the production of CO, which can form potentially explosive mixtures with oxygen ; and minimization of the volatilization and entrainment of fission products. I n this study, variables affecting the oxidation of graphite and solubilization of thorium and uranium were investigated as necessary for the evaluation of the PAC process, using nitric acid and other aqueous solutions in stainless steel batch autoclaves and in a continuous reactor system. The behavior of fission products was not studied nor were potential materials of construction fully evaluated. Equipment and Procedures

Fuel. Fuel used in most of the experiments was unirradiated, prototype, Peach Bottom (HTGR) fuel (12'% T h , 670 U, %?yo C). The uranium and thorium were present in the fuel as 500-micron.diameter Th-U dicarbide particles coated with 50 microns of pyrolytic carbon and dispersed homogeneously throughout the graphite matrix. I n this fuel, about 90% of the carbon was present as the matrix, and only about 10% was contained in the carbide particles and pyrolytic carbon coatings. I n some experiments, a nuclear-moderator grade of graphite was used to study the oxidation of carbon itself.

Batch Autoclave Systems. Both a 13.3-liter and a 350-ml. autoclave were used. Graphite or fuel was charged to the large autoclave along with 3 or 4 liters of solution, air, and 150 to 500 p.s.i.g. of oxygen a t room temperature. The system was then heated to the operating temperature, 250' to 300' C. T h e autoclave was rocked throughout the heatup period and the run. Temperatures were controlled to within k 5 " C. After the heaters were turned off and the autoclave had cooled to below 80' C., the gas was sampled by venting through sample bottles. T h e solution and any remaining solids were removed and separai.ed by filtration, and their amounts measured. T h e gas, solution, and solid samples were analyzed. Operation of the 350-ml. autoclave was similar to that of the larger one. Although the autoclave could be rocked, most of the experiments were conducted with the autoclave stationary. Pressures were determined with a calibrated 2000-pound Baldwin SR-4 pressure cell and were continuously recorded on a suppressed-range Brown pressure recorder. Temperatures were measured with calibrated iron-constantan thermocouples and were continuously recorded throughout each experiment. I n a typical experimmt, the fuel sample and the aqueous reagent were charged to the autoclave. Then, oxygen was admitted from a supply cylinder to produce the desired O Z / C mole ratio, and the system was tested to ensure that it was pressure-tight. Finally, the system was heated to the desired operating temperature (this usually required 2 to 3 hours), maintained there for the predetermined reaction time, and then cooled to room temperature before disassembly and sampling. I n some experiments, the off-gas was sampled by venting carefully into glass sample bulbs and then through a wet-test meter. T h e gases were analyzed by a gas-chromatographic procedure (2). Solutions and residual solids were analyzed for thorium, uranium, carbon, and nitrogen by conventional methods. All the material balances were reasonable, generally within =k 1O%, considering the types of measurements involved. T h e temperature, pressure, and amount of each component changed throughout each experiment; therefore, the results could be interpreted only as averages over the entire experiment. Continuous Reactor System. This system (Figure 1) was designed for continuous addition and removal of gas and solution, thus allowing mcasurernent of the approximate reaction rate as a function of temperature, concentrations, and flow rates. Graphite or fuel was charged in a screen-basket batchwise a t room temperature through a flange joint. Oxygen or gas mixtures were metered in from gas cylinders to maintain the desired pressure. The nitric acid solution was added either with the solid or by a high-pressure metering pump. The gas feed provided the agitation. Gas was bled off through a flowmeter a t atmospheric pressure, the bleed-off rate being controlled manually by a needle valve a t room temperature. T h e COS content of the efFluent gas was determined continuously by a thermal conductivity analyzer and was confirmed by analyses of gas samples. Most experiments were conducted with 1/4-inch graphite cubes in 1 or 2 M " 0 3 a t 275' or 300' C. Oxidation of Graphite

The oxidation of pure graphite or fuel (matrix and particle coatings) by aqueous solutions saturated with oxygen a t elevated temperatures and pressures was investigated in three series of experimenls. Scouting experiments (primarily with graphite) were cimducted in the large autoclave, while oxidation-dissolution of H T G R fuel was investigated in the small autoclave. Details of a n investigation of the oxidation of a moderator-grade graphite in nitric acid solutions will be reported separately (7). I n the scouting expcrirnents (9), only nitric acid solutions gave promising rates of oxidation of graphite a t temperaures u p to 300' C . T h e graphite was completely oxidized in 24 hours in 2M H N O , when excess oxygen was present (150 to 500 p.s.i.). Rates of reaction a t 300' C. were low in the following systems, each with excess oxygen present: demineralized

COOLING WATER

t

SAMPLES OR OFF GAS CONnNUOUS ANALYZER ( I Y THERMAL CONDIJCIIVI~~)

2550 P.S.1. RUPTURE

DISK

: 02 CYLINDER t LIQUID METERING PUMP

% Figure 1 .

Pressurized aqueous combustion reactor system

Material. 347 stainless steel Pipe schedule. 1 '/Z-inch Schedule 160 reactor body, 2000-p.s.i. ring joint flanges, l / 4 - and '/B-inch Schedule 80 connections to reactor. Other tubing and fittings rated >ZOO0 p.s.i. at room temperature

water; 0.03 to 0.17M N a O H containing 0.3 gram of Na2Crz07 per liter; H 2 S O r K M n 0 4 solution; 2 M NaNOa solution; and 1M N a O H solution. By comparison, carbon black was completely and easily oxidized in K a O H solutions a t temperatures below 250' C. These experiments also indicated that nitric acid was not consumed and that neither CO nor C H I was formed in significant amounts. T h e presence of Fe(NOa)3 or Na2Cr207in the nitric acid had no effect on the rates of reaction. Agitation was more important in obtaining high rates than crushing of large chunks because the chunks generally powdered in the early stages of reaction. T h e superiority of the nitric acid solutions was fortunate because the most highly developed method for decontaminating and recovering uranium and thorium is solvent extraction, with tributyl phosphate, from nitric acid solutions. More extensive investigation, using the 350-ml. autoclave, confirmed the result that the over-all combustion reaction was C 0 2 C 0 2 when excess oxygen was present. This was shown by gas analyses and analyses of the initial and final solutions. There was no net consumption of nitric acid when the initial O*/C mole ratio was greater than unity. The off-gas was composed mainly of COZ and oxygen, with only traces of CO and nitrogen oxides. I n experiments where gas samples were taken, the CO2 concentration in the gas found by analysis agreed well with that expected from the reaction: C 0 2 COZ (Table I). Significant amounts of carbon were oxidized in 24-hour reactions with nitric acid, even when the 0 2 / C mole ratio was finite, but less than 1. T h e oxygen was consumed quantitatively in the first few hours of reaction; however, reaction continued, yielding a final off-gas of CO2 and KO. Based on analyses of the off-gases and solutions, the most probable re4HN03 + 4NO 3c02 2 H z 0 . The action was 3C fact that carbon is oxidized in the absence of oxygen leads to the speculation that, even in systems containing a n excess of oxygen, the initial attack of the carbon is by the nitric acid. A pro-

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posed mechanism based on this assumption, consistent with the low solubility of oxygen in nitric acid solutions and the fact that no nitrogen is lost from the solution during reaction, is: Initial attack of the carbon by nitric acid yields lower oxides of nitrogen (primarily NO). The lower oxides of nitrogen are rapidly

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converted to Nz05 by gas-phase reaction with the oxygen present in the system. The N205 is then absorbed by the solution, re-forming nitric acid, which is available for reaction with more carbon. T h e variables important to the oxidation of cubes of pure graphite were systematically investigated in the continuous reactor system (Figure 1). T h e procedures and detailed results are reported separately (7). The rate constants, as grams of graphite oxidized to COn per hour per gram of graphite remaining, were :

TpP.,

7M HNOa 0.06 0.08 to 0.12

C. 275 300

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Rate Constants, Hr. -I, in 2M "03 4M " 0 s 0 . 1 0 to 0.15 0.19 to 0.25 0.15 to 0.24 ...

Results from these studies showed that the rate of reaction increased with both increasing nitric acid concentration and temperature (Figure 2 ) , and as the surface area of the graphite increased, but not in proportion to the surface area. In two tests, the rate of reaction was proportional to the external surface area to the 0.4 and the 0.7 power. These results may reflect the tendency of graphite chunks to powder during reaction. I

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0.4

0.2 FRACTION OF

Solubilization of Thorium and Uranium

0.6 0.8 ORIGINAL CHARGE CONSUMED

Figure 2. Effect of temperature, acid concentration, and fraction of %-inch graphite cubes consumed on reaction rate constant

Symbol

0 0

A A 0

Table I.

Oxygen flow rate, 2 7 rtd. cc./sec. Conditions HNOi TernD.. concn.. Expt. oc. ' M 1 .o c1 300 2.0 c2 300 1 .o c3 275 275 2.0 c4 275 1 .o c5 275 2.0 C6

The most important variables affecting combustion and dissolution of HTGR fuel in experiments a t 300' c. were nitric acid concentration, Oz/C mole ratio, HNO,/(Th f U) mole ratio, and reaction time. I n general, the amounts of carbon oxidized and uranium and thorium dissolved increased with increasing nitric acid concentration when the O*/C and HiYOa/ U) mole ratios were higher than about 1 and 50, (Th respectively (Table I). Although the number of experiments conducted was insufficient to determine the optimum reaction conditions, it appears certain that the best results will be achieved with concentrated nitric acid, a n Oz/C mole ratio greater than unity, and, possibly, a high HN03/(Th U) mole ratio.

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Pressure. p.s.i.g. 1600 1600 1600 1600 1020 1000

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Effect of Nitric Acid Concentration, Oz/C Mole Ratio, and HN03/(Th U) Mole Ratio on Pressurized Aqueous Combustion of HTGR Fuel at 300' C. Reaction time. 24 hours

httal

HNO 3

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Uissolved, yo HAros/ of System, Oxidized, (Th U) P.S.I. % Th 26 7 15 1700 92 1 48 54 67 1625 97 2 60 96 1740 99.6 38 3 31 31 67 90 1625 1. o 4 42 36 1600 ... 71 1. o 5 2 0 1630 56 53 2.0 6 18 4 1640 92 260 0 2.0 7 69 54 1850 97 505 0 2.0 8 8 6 1600 89 58 0.58 2.0 9 18 8 1640 91 0.71 58 2.0 10 19 5 92 1620 61 0.71 2.0 11 28 57 1O5Oc 97 2.0 10 2.0 12 67 62 1440 99.9 11 1.7 2.0 13 53 50 1500 99.9 2.0 12 2.0 14 99.7 99.9 1670 99.6 57 1.1 2.0 15 100 100 100 1750 62 1.6 2.0 16 100 96 1775 100 2.2 73 2.0 17 99.5 99.4 2000 99.7 302 10.0 1.9 18 99.9 99.6 100 1820 308 2.1 10.0 19 Insuflcient HNOI to satisfy stoichiometry: 3 C 4"03 + 4NO a Based on reaction C O2 Con. Phase present in this experiment. Concn.,

Expt.

M 0.5 0.5 1. o

Oz/C 2.0 1.9 1.8 2.0 2.2 0

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3.0 5.0

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+ 3COz f 2H20.

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49 55 90 62

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59 50 91 62

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Probably no liquid

Preliminary equilibrium data have been reported ( 6 ) showing that a t 300' C. a n H N 0 3 / T h mole ratio of a t least 25 is required to prevent precipitation of T h o 2 from a solution that has a total nitrate concentration of about 2 M . Actually, the HNOs/Th mole ratio required to prevent precipitation decreases from about 250 in solutions 1M in nitrate to about 6 in solutions that are 10M in nitrate. I t is evident from the foregoing that, in the dissolution of Th02-UOz (present originally in the fuel or formed by combustion of the carbides) in pressurized nitric acid, the amount of nitric acid present must be sufficient to overcome hydrolysis of the nitrates a t the operating temperature. Thus, when dilute nitric acid is used, a high Hh'Os/(Th U) mole ratio is required. However, if a suitable material of construction were available, it would be desirable to use concentrated nitric acid not only to reduce the HNOa/(Th U) mole ratio but also to provide for the maximum rate of reaction. Several experiments were conducted to determine the dissolubility of high-density Tho2 microspheres in pressurized nitric acid solutions. These experiments were made to simulate dissolution of fuel composed initially of carbon-coated Th02-UOZ particles dispersed in a graphite matrix. T h e microspheres were 250 to 300 microns in diameter. I n 24a t 300' C., the amounts dishour reactions with 2 M " 0 3 solved were 17, 20, 35, and 49% when the H N 0 3 / T h mole ratios were 12, 30, 50, and 100. These results indicate that the PAC process is seriously limited with fuels containing high density T h O r U O 2 microspheres.

With 0.5 and 1M HNO3, roughly 90% of the carbon was oxidized in 24 hours, usually with attendant dissolution of only u p to about 5oY0 of the uranium and thorium. Oxidation of 90% of the carbon corresponded to combustion of only the graphite matrix, and, in fact, residues from these experiments appeared under the inicroscope to consist solely of coated fuel particles. Complete combustion of the carbon and solubilization of the uranium and thorium were achieved in 2 M H N 0 3systems containing excess oxygen, b u t complete reaction required about 24 hours. I n 6-hour experiments with 2 M "03 a t 300' C., 87 to 97% of the carbon was oxidized, but the uranium and thorium recoveries varied from 37 to 88% (Table 11). Nearly complete combustion of the carbon and dissolution of the uranium and thorium were achieved with 10M " 0 3 in about 6 hours (Table 11), again showing that the reaction rate increased with increasing acid concentration. T h e stainless steel autoclave was severely corroded when 10M " 0 3 was used as the reactant. Complete combustion of the carbon and solubilization of the uranium and thorium were achieved in 24 hours when the Oz/C and HNO3/(Th 4U) mole ratios were greater than about 1 and 50, respectively. At lower ratios, combustion of the carbon and dissolution of the uranium and thorium generally were incomplete. T h e necessity for having a high HNOs/(Th U) mole ratio to ensure solubilization of the uranium and thorium in dilute nitric acid is not surprising when the hydrolytic behavior of uranyl and thorium nitrate solutions a t high temperatures is considered. These nitrates partially hydrolyze to their oxides and nitric acid; thus, for thorium nitrate, the equilibrium involved is Th(N03)d 2Hz0 4HN03 T h o * . Uranyl nitrate solutions are stable a t temperatures u p to about 260' C., and even higher temperatures should be attainable without oxide formation if excess nitric acid is present in the system ( 4 ) . Thorium nitrate hydrolyzes a t much lower temperatures.

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Table II.

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Corrosion

T h e feasibility of the PAC method is very dependent on the nitric acid concentration that can be used. Increasing the concentration increases the rate of oxidation of graphite and

Effect of Reaction Time on Pressurized Aqueous Combustion of HTGR Fuel in 2 and 10M Excess Oxygen at 300' C.

Expt . 20 21 22 17 15 16 23 19 18 Table 111.

Hili0 3 Concn., M 2 .0 2.0 2 .0 2 .0 2 .0 2.0 10.0 10.0 10.0

Reaction Time, Hr. 6.0 6.0 6.3 24 24 24 6.0 24 24

Initial Mole Ratio HhT08/ Op/C (Th U) 2.0 20 2.0 137 2.1 57 2.2 73 1.1 57 1.6 62 1.6 235 2.1 308 1.9 302

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~press. ~ , of System, P.S.I. 2000 1900 1720 1775 1670 1750

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Carbon Oxidized,

Systems with

" 0 3

Amounts Dissolved, % Th U

70 97 94 87 100 99.6 100 99 100 99.7

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Rates of Corrosion of Type 347 Stainless Steel Determined in Pressurized Aqueous Combustion Experiments

System Large autoclave

Experimental Conditions "03 Temp., c. concn., M 1 275

Time, Hr. 5

2

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2 2

300 300

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Continuous react'or

Metal Fe Cr Ni Fe Cr Ni

Ni Ni Total Total Fe Total Fe Total

Calcd. Rate of Corrosion, MilslYr. 20 20 40 40 60 80 10 80 3 30 220 20 30 130

Corrosion Product w t . , g. 0.15-0.21 0.05-0.12 0 ,04-0.10 0.40 0.16 0.10 0.10 0.63 0.04 0.37 0.97 0.09-0.41 0.16 0.94 ~~

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decreases the HNOa/(Th U) mole ratio necessary to solubilize the thorium and uranium. Containment of concentrated nitric acid a t temperatures above 250’ C. will probably require special materials of construction such as tantalum or titanium. The rates of corrosion of Type 347 stainless steel determined in nitric acid systems where the oxygen overpressure was a t least 150 p.s.i. increased with both increasing nitric acid concentration and temperature. With 1 and 2 M ” 0 3 , however, the rates were not excessive, being generally less than about 80 mils per year (Table 111). I n one test with 4M ” 0 3 , the rate was about 220 mils per year; severe corSavich and rosion was encountered in a test with 10M “ 0 3 . Howard (7) reported excessive corrosion of Type 347 stainless steel pressure vessels when 4.5M “ 0 3 was used to oxidize coal in the presence of oxygen.

tures and pressures may not be a severe limitation of the PAC process. The PAC process, using dilute nitric acid, could be used first to burn the graphite matrix and particle coatings. T h e uranium and thorium oxides remaining after combustion could then be dissolved in another reagent-boiling 13M HN03-0.05M HF, for example-at atmospheric pressure to produce a solution containing uranium and thorium in concentrations of at least 0.5M. Ac knowledgment

The authors are indebted to F. L. Culler, Jr., for suggesting the use of pressurized aqueous methods in the processing of nuclear reactor fuels. They also thank J. B. Farrell, D. A. McWhirter, J. F. Land, and C. T. Thompson for aid in conducting the experiments. Analyses were provided by the ORNL Analytical Chemistry Division.

Conclusions

literature Cited

The pressurized aqueous combustion process for graphitebase nuclear reactor fuels containing carbon-coated carbide fuel particles appears technically feasible. When excess oxygen was present, the net combustion reaction was C 0 2 C o n ,without consumption of nitric acid. Reaction rates were about 0.2 gram of graphite oxidized to C O S per hour per gram of graphite. Although most of the tests were made with 1 and 2M HIio3 a t 275’ and 300’ C., higher nitric acid concentrations would be preferred, provided that acceptable structural materials are available. The higher nitric acid concentrations would increase the rates of graphite oxidation U) mole ratio necessary and would decrease the H N 0 3 / ( T h for complete dissolution of the thorium and uranium. The high H N 0 3 / ( T h U) mole ratio required for their complete dissolution in dilute nitric acid was probably due to the hydrolysis of their nitrate salts a t high temperature. Much more work \vi11 be required to determine whether the PAC process is applicable to fuels containing carbon-coated oxide particles. The limited experiments conducted to date showed that highdensity T h o 2 and T h O r U 0 2 microspheres are not readily dissolved in pressured nitric acid even when the H N 0 3 / T h mole ratio is 50 or greater. The fact that uranium and thorium oxides (and carbides) cannot be dissolved easily in dilute nitric acid a t high tempera-

(1) Farrell, J. B., Haas, P. A., “Pressurized Aqueous Combustion of Moderator Grade Graphite,” Division of Industrial and Engineering Chemistry, 150th Meeting, ACS, Atlantic City, N. J., September 1965. ( 2 ) Ferris, L. M., Bradley, M. J., “Off-Gases from the Reactions of Uranium Carbides with Nitric Acid at 90’ C.,” Oak Ridge Natl. Lab., ORNL-3719 (1964). 1 3 ) Howard. H. C.. in “Chemistrv of Coal Utilization.” H. H. Lowry, ed:, p. 346; LViley. New Ybrk, 1945. (4) Lane? J. A., MacPherson, H. G., Maslan, F., eds., “Fluid Fuel Reactors,” p. 99, Addison-St‘esley, Reading, Mass., 1958. (51 Nicholson, E. L., Ferris. L. M.. Roberts, J. T., “Burn-Leach Process for Graphite-Base Reactor Fuels Containing CarbonCoated Carbide or Oxide Particles,” Oak Ridge Natl. Lab., ORNL-TM-1096 (April 2, 1965). ( 6 ) Oak Ridge National Laboratory, “Homogeneous Reactor Program Quarterly Progress Report for Period Ending July 31, 1960,” ORNL-3004 (Oct. 28, 1960). ( 7 ) Savich, S. R., Howard, H. C., Znd. Eng. Chem. 44, 1409 (1952). ( 8 ) Teletzke, G. H., “Wet Air Oxidation,” 56th Annual Meeting, A.I.Ch.E., Houston, Tex., Dec. 1-5, 1963. ( 9 ) \Vhatley, M. E., et al., “Unit Operations Section Monthly Progress Report, March 1964,” Oak Ridge Natl. Lab., ORNLTM-887 (September 1964). (10) Zimmerman, F. J., Chem. Eng. 65, 117 (1958).

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RECEIVED for review August 18, 1965 ACCEPTEDFebruary 15, 1966 Division of Nuclear Chemistry and Technology, 150th Meeting, ACS, Atlantic City, N. J., September 1965. Research sponsored by the U. S.Atomic Energy Commission under contract with the Union Carbide Corp.

ELECTROCHEMICAL OXIDATION OF CHOLESTERYL ACETATE DIBROMIDE ABRAHAM COOPER’ AND CHARLES L. MANTELL Department of Chemical Engineering, Kewark College of Engineering, Newark, N . J .

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a starting material for many functional derivatives. A number of researchers in steroid chemistry sought to convert this inexpensive product by oxidation of the groups attached to the nucleus, as well as 76,77,ZO-24). by degradation cf the side chain (3,4,6,8-77, Various reagents and systems have been used to oxidize cholesterol and its derivatives. A system of interest, use of a n HOLESTEROL has been prominent as

Present address, UOP Chemical Co., East Rutherford, N. J. 238

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electrochemical cell, was reported by Kramli (75). The conditions specified by Kramli were duplicated and varied in an attempt to improve the results, with no success (5). The present paper reports achievements after modification of technique (5). Experimental

Raw Material Preparation. One hundred grams of cholesterol were refluxed with 200 ml. of acetic anhydride for