136 Ind. Eng. Chem. Res. 1991, 30, 136-141

Ltd.: Exeter, U.K., 1984; pp 95-105. Lakin, W. D.; Van den Driessche, P. Time scales in population bi-

ology. SIAM J. Appl. Math. 1977,32,694-705. Lasalle, J. P. Stability Theory for Ordinary Differential Equations.

J . Differ. Equations 1968, 4 , 57-65. Mc Carty, P. L. Anaerobic Waste Treatment Fundamentals. Public

Works 1964, Sept, 107-112; Oct, 123-126; Nov, 91-94; Dec, 95-99. Mosey, F. E. Mathematical Modelling of the Anaerobic Digestion

Process: Regulatory Mechanisms for the Formation of Short- chain Volatile Acids from Glucose. Water Sci. Techno!. 1983,15,

Pauss, A.; Beauchemin, C.; Samson, R.; Guiot, S. Continuous Mea- surement of Dissolved H2 in Anaerobic Digestion Using a Com- mercial Probe Hydrogen/Air Fuel Cell-based. Biotechno!. Bioeng.

Peiffer, K.; Rouche, N. Liapunovs Second Method Applied to Par-

209- 23 2.

1990, 35, 491-502.

tial Stability. J . MBc. 1969, 8 (2), 323-334.

Pomerleau, Y. Mod6lisation et contrBle dun procBdB fed-batch de cultures des levures ti pain. Ph.D. Thesis, Ecole Polytechnique de MontrBal, Canada, 1990.

Pomerleau, Y.; Perrier, M.; Dochain, D. Adaptive nonlinear control of the Bakers yeast fed-batch fermentation. Proc. 1989 Am. Control Conf. (Invited Session on Intelligent Systems and Ad- vanced Control Strategies in Biotechnology), 1989,2,2424-2429.

Renard, P.; Dochain, D.; Bastin, G.; Naveau, H. P.; Nyns, E. J. Adaptive Control of Anaerobic Digestion Processes. A Pilot-scale Application. Biotechno!. Bioeng. 1988, 31, 287-294.

Taylor, D. G.; Kokotovic, P. V.; Marino, R.; Kanellapoulos, I. Adaptive Regulation of Nonlinear Systems with Unmodelled Dy- namics. IEEE Trans. Autom. Control 1989, 405-412.

Received for review February 2, 1990 Revised manuscript received July 2, 1990

Accepted July 24, 1990

A General Equation for the Heat-Transfer Coefficient at Wall Surfaces of Gas/Solid Contactors

Daizo Kunii Fukui Institute of Technology, 3-6-1 Gakuen, Fukui City, 910 Japan

Octave Levenspiel* Chemical Engineering Department, Oregon State University, Coruallis, Oregon 97331 -2702

The general equation derived here accounts for the thermal properties of the solids, the particle size, the properties of the gas, the state of the gas/solid system (bubbling characteristics), and the contribution of radiation transfer. This equation reduces to a variety of simpler special case ex- pressions: for fine particle and for large particle fluidized beds, for low-temperature operations, a t the surfaces immersed in both fluidized and moving beds, and for the tube wall surfaces of fast fluidized beds. All these expressions are simple to use, and we point out where these expressions have been tested against the reported experimental data.

The study of heat interchange between surfaces and fluidized beds has a long history, and numerous expres- sions have been proposed to represent the heat-transfer coefficient in this situation. Reviews of these studies can be found in Gelperin and Einstein (I), Botterill (2), Xavier and Davidson (3), and Baskakov ( 4 ) .

In this paper, we propose to develop a general equation for h to encompass a broad spectrum of conditions and operations. I t reduces to a number of special cases for various contacting regimes, including the freeboard, moving bed, and fast fluidization regimes.

Development of the General Equation We start by considering heat transfer in fixed and in-

cipiently fluidized beds and then extend this analysis to bubbling fluidized beds, to the freeboard region, and to fast fluidized beds.

Within a Fixed Bed with Stagnant Gas. If heat flows in parallel paths through the gas and the solid, then the effective thermal conductivity of the fixed bed would be given by

(1) k: = tm$g + (1 - emf)ks

Here, the superscript 0 refers to stagnant gas conditions, and 4b = d,,,/d, represents the equivalent thickness of stagnant gas film around the contact points between particles, which aids in the transport of heat from particle to particle. Since 4b depends on the bed voidage and since we are interested in using eq 2 later in our fluidized bed development, Figure 1 gives the values of 4b for the loosest packing of a normal fixed bed, which is at about = 0.476.

For most gas/solid systems, k, >> k,; thus, the last part of the second term in eq 2 is smaller than unity. This means that the thermal conductivity of a fixed bed is lower than for the parallel path model of eq 1.

At the Wall of a Fixed Bed with Stagnant Gas. Consider the wall region to extend a half particle diameter out from the heat-exchange surface. Then, similar to eq 2, the thermal conductivity in this layer can be represented by

However, to account for the actual geometry and the small Contact region between adjacent particles, Kunii and Smith (5) developed the following modification to the parallel path model:

where e, is the mean void fraction of this wall layer. Kunii and Suzuki (6) derived the above equation and used it successfully to represent the surface heat-transfer data reported by workers at that time. They also explained why a thickness of half a particle diameter was selected to represent the wall region.

Figure 1 shows the calculated values for 4,, defined as the equivalent thickness of stagnant film at a contact point between a sphere and the wall surface. Note that the

r 1 (2)

0888-5885/91/2630-0136$02.50/0 0 1991 American Chemical Society

Ind. Eng. Chem. Res., Vol. 30, No. 1, 1991 137

k J k s

Figure 1. Ratio of effective thickness of gas film around a contact point to particle diameter. &, for contact between adjacent particles, & for contact between particle and surface; from Kunii and Smith (5).

20

e-

s + II 10

s

0

glass, 1000 pm 'ps- 1.0

0 glass, 1000 pm 'ps- 0.78 A glass, 750 pm 'ps- 0.68

I I 1 I

Lines from eq 5 0

- 0 0.5 1 1.5

UoIUmf

Figure 2. Heat transfer between flat surfaces and stationary beds of large particles, from Floris and Glicksman (7).

thickness of the equivalent stagnant gas layer is greater for particle-wall contact than for particle-particle contact; in addition, since e, > emf, these two factors indicate that the wall layer presents a greater resistance to heat transfer than an equivalent layer in the main body of the bed.

At this point, we may define a heat-transfer coefficient for this wall region of thickness d, /2 , and containing stagnant gas, as follows:

(4)

At the Wall of a Fixed Bed with Flowing Gas. Figure 2 , reported by Floris and Glicksman (7), shows that heat transfer in fixed beds is enhanced by gas flow through the bed. This can be attributed to the lateral mixing of gas in the void spaces at the surface with adjacent voids. Yagi and Kunii (8) studied this phenomenon and came up with the following two-term expression for ordinary fixed beds, say dt /d , 1 10:

N u = hwdp - - - (transfer for no gas flow) + k,

(extra transfer because of gas flow)

Rearranging the expression gives

The lines on Figure 2 are drawn for a, = 0.05, and the fit to the data shows that this is a reasonable value for a, to use in eq 5.

In an early study, Yagi and Kunii (8) analyzed the re- ported data on h, for packed beds of larger solids, up to 12 mm in size, and found that CY, = 0.041 well represented those findings.

Time (s) Time (s)

Figure 3. Instantaneous h on a vertical dti = 6.35 mm heater in a d, = 0.1 m fluidized bed; from Mickley and Fairbanks (9).

I 1000 2000 1000 10 20 40 100 200 400

Re,, =& li

Figure 4. Correlation for h in large particle beds a t low tempera- ture, d, up to 4 mm, pressure up to 10 atm; data from G l i c k " and Decker (IO).

Bubbling Beds: Heat Transfer to Emulsion Pack- ets. In a bubbling fluidized bed, rising bubbles sweep past the heat-exchange surface, thereby washing away the particles resting there and bringing fresh bed particles into direct contact with the surface. Figure 3 indicates that the contact time of these packets of emulsion particles with the surface is of the order of 0.2-0.4 s for the conditions of the experiments reported there. More generally, this contact time depends on the experimental conditions. Let us now consider heat transfer to these packets of particles.

Large Particles for Short Contact Times. Here the particles are replaced before their mean temperature can change appreciably, the temperature gradient takes place only within the row of particles that is in direct contact with the exchanger surface, and we can ignore the thermal diffusion into the rest of the emulsion packet.

Glicksman and Decker (IO) estimated the "heating" time constant of particles resting on a surface. They found that the temperature of particles larger than 1 mm did not change appreciably for a residence time as long as 7 = 1 s. Thus, this extreme can be used for these large particles. Their experimental data combined with those reported by several other groups are shown in Figure 4 for particles of 650-4000 pm at 1-10 bar. Curve fitting gives

hd,/(l - 6) = 5.0 + 0.05PrRep k ,

(6)

Note the similarity in form with the expression for fixed beds, eq 5.

Small Particles for Long Contact Times. Here the particles near the surface closely approach the surface temperature, the thermal transient is felt many layers from the surface, and, hence, thermal diffusion into the emulsion packet becomes the controlling resistance.

Botterill and Williams (I I) solved the unsteady-state heat conduction problem for the first layer of particles a t

138 Ind. Eng. Chem. Res., Vol. 30, No. 1, 1991

the surface and found that 200-pm particles approach the temperature of the surface in as little as 10 ms. In another estimate of this extreme, Glicksman and Decker (10) suggested that the temperature of the particles contacting a surface changes substantially for particles smaller than 500 pm for a contact time of about 1 s.

In a bubbling bed, the mean contact time of a packet with the surface is related to the bubble frequency at the surface and the fraction of time that packets contact the surface by the expression

1 - 6 , 7=-

n W ( 7 )

Mickley and Fairbanks (9) analyzed this unsteady-state conduction into the packets, giving an equation for the local instantaneous heat-transfer coefficient. Assuming that all packets of emulsion contact the surface for the same length of time 7, given by eq 7, the time-averaged heat-transfer coefficient between the packet and surface was determined by Kunii and Levenspiel (12) to be given by

I I. ,n

Bubbling Beds: h at a Heat-Exchanger Surface. At this point, we are ready to develop the general expression for the heat-transfer coefficient between a bubbling fluidized bed and the exchanger surface. This expression should account for the fact that part of the time the surface is bathed by gas and part of the time by emulsion packets, or

= hbubble at surface6w + hemulaion at surface(l - (9) Now when the bubble is present a t the surface, there

are two contributions to heat transfer: radiation and convection. With the emissivities of bed solids and wall given by e, and e,, the radiation coefficient becomes

5.67 X 10-8(T2 - 7'2) hr = [ 53 (lo) (t + $ - l)(Ts - Tw)

The gas convection contribution when a bubble contacts the surface is normally very small compared to the other contributions to heat transfer. However, for fast fluidized beds and in the freeboard above a dense bed where the fraction of solids in not small, the convection term can become important. Thus, we write, in general,

- hbubbleat surface - hgas convection + hradiation (I1)

When the emulsion packet is present on the surface, we have heat transfer in series-through the wall region of thickness dp/2 followed by transfer through the emulsion packet. In addition, through the wall region, we have both convection and radiation. These three terms sum to

- 1 / ( + 1 hemulaion at surface -

hat wall layer hthrough packet 1

Replacing eq 5 in eq 12 and eq 11 and 12 in eq 9 gives the general expression for heat transfer a t a surface

I I 1

(13)

emulsion at surface

where hpacket is given by eq 8, h, by eq 10, and kiw by eq 3.

Special Cases of the General Equation For the Extreme of Fine Particles and High Tem-

perature. Here radiation between the emulsion packet and the surface can be ignored because the particles at the surface very quickly approach the surface temperature. Also, gas flow through the emulsion is negligible (small Re,). Finally, since the wall temperature reaches many particle layers in the emulsion packet resting on the sur- face, the additional resistance of the first surface layer can be neglected. With these three simplifications, eq 13 re- duces to

or

h = 6,hr + 1.13[k:ps(l - tmf)Cpsnw(l - 6w)]1/2 (14) For the Extreme of Fine Particles and Low Tem-

perature. Here we ignore radiation, so eq 14 reduces to

h = 1.13[ktps(1 - tmf)Cpsnw(l - (15)

For the Extreme of Large Particles. Here transfer through the emulsion packet can be ignored because the temperature change only occurs in the first layer a t the surface. In bubbling beds, h, can also be ignored. For this situation, eq 13 reduces to

or h = hr + (1 - 6,)[2kEw/d, + 0 .05Cpgpg~o] (16)

Alternative Theoretical Approaches. A large num- ber of models have been proposed to explain the mecha- nism of heat transfer in fluidized beds (9,10,13-24). Some are much too complicated to use for design calculations, some only represent data in a narrow range of conditions, and none are general enough to account for all the factors considered in eq 13.

h between Moving Beds and Heat-Exchange Walls. For gently descending emulsion solids, the residence time of the emulsion in contact with the exchanger wall is very long, the temperature boundary layer extends many par- ticle layers into the bed, no bubbles are present, and ra- diation can be neglected. In this situation, eq 13 reduces to

(17) 1 h =

dp/2k;w + l/hpacket

where kZw is given by eq 3 and hpacket by eq 8. Freeboard Region, Fast Fluidization, and Circu-

lating Solid Systems. Here a thin layer of fine particles flows down along the container walls. Also, when hori-

Ind. Eng. Chem. Res., Vol. 30, No. 1, 1991 139

400

% E 200 5 N

lr:

I '-A 0 I I I I I I I 0 200 400 600 800

d , (m) Figure 5. Decay constant for freeboard agglomerates, for u, 1.25 m/s. (1) Chen et al. (26), (2) Bachovchin et al. (27), (3) Hoggen et al. (28), (4) Walsh et al. (29), (5) Zhang et al. (30), (6) Nazemi et al. (32), (7) Lewis et al. (32).

zontal tubes are present in the freeboard, clusters of particles hit these now and then. This behavior results in fairly high heat-transfer rates. Since the gas velocity is high in these systems, the gas convection heat-transfer coefficient may have to be considered; see the discussion above eq 11. Also, the exchanger surfaces are bathed by the lean phase most of the time; thus, 6 = 1. With these conditions, eq 13 becomes

h = hr + hg + (1 - 6w)hpecket (18)

and with eq 8 and 11,

h hr + h, + 1.13[k'&,(l - c)C,,,n,(l - 6,)]'/2 (19) Next, it is reasonable to assume that the rate a t which clumps of emulsion solids hit the tubes is related to the upward flux Cup of solids a t that level in the bed, or

(1 - a,),, G", (20) Above a vigorously bubbling or turbulent fluidized bed, the upward flux of solids into the freeboard falls off ex- ponentially with height into the freeboard z , or

G,, a exp(-az) (21)

On the basis of reported data in these systems, Kunii and Levenspiel (25) correlated the decay constant a with particle size and gas velocity, as shown in Figure 5. For fast fluidized beds, see ref 25 for estimates for a.

Combining the above three equations then gives the heat-transfer coefficient a t level z in terms of the coeffi- cient a t the bed surface, or

This expression, with a found from Figure 5, tells ap- proximately how h should change with height in the freeboard of a fluidized bed or in a fast fluidized bed.

Comparison of Prediction with Experiment h on a Horizontal Tube Bundle in a Fine Particle

Bed. We tested the predictions of the above equations

1 Lines from eq 15

\ ' 180"c } 82 pm sand o i i 0 4 c I h 135C - 57 Urn FCC catalyst I

0 0 0.2 0.4

uo "S)

Figure 6. h on a horizontal tube bundle. Data from Beeby and Potter (33); calculated lines from eq 15.

2000 1 I I I I 1

200 I I I I I I 0.005 0.01 0.02 0.05 0.1 0.2 0.5

k, (W/m-K) Figure 7. Effect of gas thermal conductivity on h,. Data from Mickley and Fairbanks (9); see Martin (24); calculated lines from eq 15.

with the data of Beeby and Potter (33) because their bed was not too small (0.305 X 0.305 m), fluidizing conditions were well described, and two kinds of particles are used. Values for h were calculated from eq 15 by using estimated values of n, as follows:

FCC catalyst: d = 57 pm, k, = 0.20 W / ( m K )

at 135 "C, n, (9-l) 2.0 3.1 3.4 3.5 u, (m/sf 0.05 0.1 0.2 0.35

sand: d, = 82 pm, k , = 1.2 W / ( m K ) u, (m/s) 0.05 0.2 0.4

at 110 "C, n, (s-') 0.50 1.4 2.4 at 180 "C, n, (9-l) 0.83 1.9 3.0

The results of these calculations are presented in Figure 6 and show that the derived equation does account for the observed maximum in h at some intermediate velocity. For details of these calculations, see Example 13.1 in Kunii and Levenspiel (34).

Effect of h on Gas Thermal Conductivity. For fine particle systems, the data of Mickley and Fairbanks (9), shown in Figure 3, is the best available for studying the effect of gas thermal conductivity because a wide variety of gases were tested in that study. Since particles were fine and the temperature was not too high, eq 15 should apply. From Figure 3, we estimate that n, = 3 s-l and 6, = 0.2 for glass beads of k, = 1.2 W/(m.K). Again in Figure 3, we see that n, for the microspherical catalyst is roughly double the value of n, for glass beads at the same flow conditions. Thus, we select n, = 6 s-* and k, = 0.2 W/ (m-K) for this case. With these values, eq 15 gives two lines in Figure 7, accounting for the effect of thermal conduc- tivity of gas. For more details, see Example 13.2 in ref 34.

140 Ind. Eng. Chem. Res., Vol. 30, No. 1, 1991

2ooJ 10 d, (Pn) 100 1 (mm) 10 (b)

Figure 8. Effect of particle size on h,,, from Martin (14). Data from Baskakov (13), Wicke and Fetting (15), and Wunder and Mersmann (35); dashed line calculated from eq 13.

For large particle systems, d, > 1 mm, eq 16 should apply. A t not too high a temperature, eq 16 with 6 = 6, and 2kzw/k, = 5 reduces to eq 6, and Figure 4 shows that this expression fits the reported data.

Effect of Particle Size on h mar in Fluidized Beds. Figure 8 summarizes the experimental data on h, versus particle size as reported by Baskakov et al. (13), Wicke and Fetting (15), and Wunder and Mersmann (35). A t not too high a temperature and for their gently bubbling beds, we use the following estimates for our simple calculations: n, = 5 S-', 6, = 0.1, u, a dk12, h,

Taking as a base point h,, = 250 W/(m2-K) at d, = 10 mm and inserting the known physical properties of the systems studied allows us to evaluate the only unknown term in eq 13, a,CPgpgu,. With this value, we can then determine how h,, changes with d,. The results of these calculations are shown in Figure 8. Note that the particle size at which h,,, becomes a minimum, d, = 2 mm, is correctly predicted by eq 13; see Example 13.3 in ref 34 for more details. Also note that for d I 20 pm eq 13 does not predict the sharp drop in h,. dowever, this is where the system enters the cohesive solids (Geldart C) regime, with its very poor fluidization and low h values. These equations do not apply in this regime.

h on Heat-Exchange Tubes in the Freeboard. Let us see how well eq 22 fits the measured h values at surfaces in the solids-lean freeboard above a dense bubbling fluidized bed, as reported by Guigon et al. (36).

Start by taking h = 350 W/(m2-K) at zf = 0 and h = 20 W/(m2.K) in the equivalent gas stream. These are rea- sonable values. Next, even though Figure 5 is prepared from data where u, I 1.25 m/s, let us assume that it can be applied to Guigon's experiments at u, = 2.4 m/s.

For d, = 260 pm, Figure 5 gives au = 1.5 s-l; thus, a = 1.5/2.4 = 0.625 m-l, Inserting into eq 22 then gives

0.

-- - 2o - e -0 .626~f /2 350 - 20

The line in Figure 9 represents this equation and is seen to approximately account for the decrease of h with height in the freeboard.

Design Comments. To apply the above equations for design, it is necessary to have good estimates of n, and 6,, obtained from data such as shown in Figure 3, and for

_ - 400 I I I I I

d, - 260 pm 300

? m- E p 200 - -r:

100

0

u o - 2.4 mls -

- 0 L, = 0.93 m from Eq. (22) -

L, = 0.53 m -

Figure 9. h on horizontal tube banks, dti = 50 mm, immersed in a 1.19 X 0.79 m fast circulating fluidized bed. Data from Guigon et al. (36); calculated line from eq 22.

fluidizing conditions close to the planned conditions. For a review of such data, see Kunii and Levenspiel (34).

Nomenclature

a = decay content for solid density in the freeboard [m-'1 C, = specific heat [J/(kg.K)] d,, = equivalent thickness of stagnant gas layer [m] d, = diameter of a particle [m] d, = inner diameter of bed [m] dti = outer diameter of heat-exchange tube [m] e = emissivity G , = upward flux of clumps of solids in the freeboard

h = heat-transfer coefficient [W/(m2.K)] k = thermal conductivity [W/(mK)] n = bubble frequency at a point [s-l] Nu = Nusselt number Pr = Prandtl number Re, = Reynolds number based on particle diameter and su-

u, = superficial velocity of gas passing through a fixed or

zf = distance into the freeboard or distance above the surface

Greek Symbols a, = constant in eq 5 6 = bubble fraction in a fluidized bed t = void fraction in a gas/solid system emf = void fraction at minimum fluidization M = viscosity of gas [kg/(ms)] p = density [kg/m3] T = contact time of a packet of particles at a surface [SI 4b, ?, = equivalent thickness of gas film, in terms of particle

diameter, between adjacent particles in the bed, and be- tween particle and wall, respectively = sphericity of solids

bsg/(m241

perficial gas velocity

fluidized bed [m/s]

of the bed [m]

Superscript o = refers to stationary solids

Subscripts e = effective g = gas r = radiation

Ind. Eng. Chem. Res. 1991,30, 141-145 141

s = solid w = in wall region

Literature Cited

(1) Gelperin, N. I.; Einstein, V. G. In Fluidization; Davidson, J. F., Harrison, D., Eds.; Academic Press: Orlando, FL, 1971; p 471.

(2) Botterill, J. S. M. Fluid-Bed Heat Transfer; Academic Press: Orlando, FL, 1975. Denloye, A. E.; Botterill, J. S. M. Powder Technol. 1977, 19, 197.

(3) Xavier, A. M.; Davidson, J. F. In Fluidization, 2nd ed.; Davidson, J. F., et al., Eds.; Academic Press: Orlando, FL, 1984; p 437.

(4) Baskakov, A. P. In Fluidization, 2nd ed.; Davidson, J. F., et al., Eds.; Academic Press: Orlando, FL, 1984; p 465.

(5) Kunii, D.; Smith, J. M. AIChE J. 1960,6, 71. (6) Kunii, D.; Suzuki, M. Roc. 3rd Int. Heat Transfer Conf. Chicago

1966, 4, 344. (7) Floris, F.; Glicksman, L. R. XVI ICHMT Symposium, Dubrov-

nik, Paper 2-2, 1984. (8) Yagi, S.; Kunii, D. AIChE J . 1960, 6, 97; Int. Devel. Heat

Transfer, Boulder, Part IV, Paper 90, p 742, 1961. (9) Mickley, H. S.; Fairbanks, C. A. AIChE J. 1955, 1, 374. Mickley,

H. S.; Fairbanks, D. F.; Hawthorn, R. D. Chem. Eng. Prog. Symp. Ser. 1961, 57 (32), 51.

(10) Glicksman, L. R.; Decker, N. Heat Transfer in Fluidized Beds of Large Particles. Report from Mech. Ena. Dept., MIT, Cam- - - bridge; MA, 1983.

(11) Botterill. J. S. M.: Williams. J. R. Trans. Inst. Chem. Ene. 1963. ~. 41, 217. Botterill,' J. S. M.;' et al. In Proc. Intern. S y k p . o n Fluidization; Drinkenburg, A. A. H., Ed.; Netherlands Univ. Press: Amsterdam, 1967; p 442.

(12) Kunii, D.; Levenspiel, 0. Fluidization Engineering; John Wiley: New York, 1969.

(13) Baskakov, A. P.; et al. Powder Technol. 1973,8, 273; Fluidi- zation and Its Applications; Cepadues: Toulouse, 1974; p 293.

(14) Martin, H. XVI ICHMT Symposium, Dubrovnik, Paper 2-5, 1984; Chem. Eng. Process. 1984, 18, 157, 199.

(15) Wicke, E.; Fetting, F. Chem.-Ing.-Tech. 1954, 26, 30. (16) Goosens, W. R. A.; Hellinckx, L. Fluidization and its Appli-

cations; Capedues: Toulouse, 1974; p 303.

(17) Catipovic, N. M.; et al. In Fluidization; Grace, J. R., Matsen,

(18) Xavier, A. M.; et al. In Fluidization; Grace, J. R., Matsen, J.

(19) Levenspiel, 0.; Walton, J. S. Chem. Eng. h o g . Symp. Ser. 1954,

(20) Martin, H. Chem. Eng. Commun. 1981, 13, 1. (21) Bock, H. J.; Molerus, 0. German Chem. Eng. 1983,6,57. Bock,

H. J.; et al. German Chem. Eng. 1981, 4, 23; 1983, 6, 301. (22) Chandran, R.; Chcn, J. C. AIChE J. 1985, 31, 244. (23) Yoshida, K.; et al. Chem. Eng. Sci. 1974, 29, 77. (24) Filtris, Y.; et al. Chem. Eng. Commun. 1988, 72, 189. (25) Kunii, D.; Levenspiel, 0. Powder Technol. 1990,61, 193. (26) Chen, G.; Sun, G.; Chen, G. T. In Fluidization V; 0stergaard,

K., Ssrensen, A., Eds.; Engineering Foundation: New York, 1986; p 305.

(27) Bachovchin, D. V.; Beer, J. M.; Sarofim, A. F. Paper presented at the AIChE Annual Meeting, Nov 1979; AIChE Symp. Ser. 1981, 77 (205), 76.

(28) Hoggen, B.; Lendstad, T.; Engh, T. A. In Fluidization V; (astergaard, K., Ssrensen, A., Eds.; Engineering Foundation: New York, 1986; p 297.

(29) Walsh, P. M.; Mayo, J. E.; Beer, J. M. AIChE Symp. Ser. 1984, 80 (234), 119.

(30) Zhang Qi; et al. Proc. CIESCIAIChE Joint Meeting; Chem. Ind. Press: Beijing, 1982; p 374. In Fluidization '85, Science and Technology; Kwauk, M., et al., eds.; Science Press: Beijing, 1985; p 95.

(31) Nazemi, A.; Bergougnou, M. A.; Baker, C. G. J. AIChE Symp. Ser. 1974, 70 (141), 98.

(32) Lewis, W. K.; Gilliland, E. R.; Lang, P. M. Chem. Eng. Prog. Symp. Ser. 1962,58 (38), 65.

(33) Beeby, C.; Potter, 0. E. AIChE J . 1984, 30, 977. (34) Kunii, D.; Levenspiel, 0. Fluidization Engineering, 2nd ed.;

(35) Wunder, R.; Mersmann, A. Chem.-Ing.-Tech. 1979,51,241. (36) Guigon, P.; et al. Proc. Second Intern. Conf. Circulating

Received for review January 31, 1990 Accepted July 27, 1990

J. M., Eds.; Plenum: New York, 1980; p 225.

M., Eds.; Plenum: New York, 1980; p 209.

50 (9), 1.

Butterworth: Stoneham, MA, 1991.

Fluidized Beds; Compiegne: 1988; p 65.

Chemical Basis for Pyrochemical Reprocessing of Nuclear Fuel

John P. Ackerman Chemical Technology Division, Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, Illinois 60439-4837

The integral fast reactor (IFR) is an advanced breeder reactor concept that includes on-site re- processing of spent fuel and wastes. Spent metallic fuel from the IFR is separated from fission products and cladding, and wastes are put into acceptable forms by use of a compact pyrochemical process based on partition of fuel and wastes between molten salt and liquid metal. To minimize reagent usage and, consequently, waste volume, electrotransport between metal phases is used extensively for feed dissolution and product recovery, but chemical oxidation and reduction are required for some operations. This paper describes the processes that are used and presents the chemical theory that was developed for quantitatively predicting the results of both chemical and electrotransport operations.

Introduction On-site processing of spent metal fuel is a basic part of

the integral factor reactor (IFR) concept (Till and Chang, 1988, 1989; Burris et al., 1987). A pyrochemical process to reclaim fuel is being developed and is expected to be economically attractive for on-site use, to return essentially all actinides to the reactor, and to result in a waste form that can be stored on site but is expected to be well suited to eventual permanent disposal. The fundamentally thermodynamic theory used to predict the results of chemical and electrotransport operations on which the

0888-5885/91/2630-0141$02.50/0

pyrochemical process is based was verified at the scale of roughly 1 mol of plutonium (Tomczuk et al., 1991). This paper presents that theory and then briefly describes its application to pyrochemical reprocessing of IFR fuel.

Theory of Distribution of Elements Pyrochemical processing is based on the partition of

elements between one or more metal phases (where they exist as pure metals, as solutes in metal solution, or as intermetallic compounds) and a molten salt phase (where they are present as metal chlorides). A t the processing

1991 American Chemical Society