ucrl- 89887 preprint incipient fluidization

UCRL- 89887 PREPRINT

INCIPIENT FLUIDIZATION CHARACTERISTICS OF CRUSHED OIL SHALE

David E. Chnstiansei

This Paper was Prepared for Submittal to Powder Technology

February 1, 1983

This is a preprint of a paper intended for publication in a journal or proceedings. Since changes may be made before publication, this preprint is made available with the understanding that it will not be cited or reproduced without the permission of the author.

DISCLAIMER

This document was prepared as an account or work sponsored by an agency of the United States Government. Neither the United States Government nor the University of California nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial products, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement recommendation, or favoring of the United States Government or the University of California. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or the University of California, and shall not be used for advertising or product endorsement purposes.

UCRL-1823K

INCIPIENT FLUIDIZATION CHARACTERISTICS OF CRUSHED OIL SHALE

David E. Christiansen

February I, 1983

Prepared for submittal to Powder Technology

INCIPIENT FLUIDIZATION CHARACTERISTICS OF CRU5HED OIL SHALE*

David E. Christiansen Lawrence Livermore National Laboratory

Livermore, CA 94550

ABSTRACT

We have measured the gas velocity for incipient fluidization of crushed

shale as a function of particle size, particle-size distribution, shale grade,

crushing method and temperature. This velocity varied as the square of

particle size for 0.0063- to 0.1-cm particles ano approximately as the square

root of particle size for particles larger than 0.5 cm. We observed no

regular dependence of this velocity upon shale grade. Slightly higher

velocities were found for cone-crushed than For hammer-milled shale

particles. For 0.0125 to 0.10-cm partic. es we found that raising the

temperature to 450°C reduced the velocity by 28 percent from 20°C measurements.

The harmonic mean of a mass-based particle-sze Distribution was found to

be the particle size which gave the best: estimate of incipient fluidization

velocity.

The Zenz-Othmer graph predicts velocities three to five times higher than

those observed. The Kunii-Levenspiel correlation predicted velocities 25 to

270 percent higher than observed at 20°C but was within experimental error for

measurements at 450°C.

INTRODUCTION

Although considerable experience has been gained in the application and

operation of fluidized beds, including extensive commercial operation since

1942 in the petroleum industry, the extension of this experience to oil shale

*Work performed under the auspices of the U.S. Department of Energy by the Lawrence Livermore National Laboratory under contract number W-7405-ENG-48 for submittal to Powder Technology.

1823K

-2-

processing presents a new challenge. Early experience in petroleum refining

with fluidized beds of catalyst emphasized the use of smaller (less than 1 mm),

uniformly sized, round or nearly round (cubic) particles. These particles

were made small to enhance reaction rates and selectivity. And, because they

could be used for processing relatively large quantities of material, it was

economically feasible to make these particles very uniform in size and regular

in shape. The economics of oil shale processing, nowever, are much different

because of the relatively large solids-to-product ratio. A kilogram of oil

shale yields about 100 grams of oil as compared to a kilogram of catalyst

which may be used to process hundreds of kilograms of petroleum. Thus the

cost of preparing the crushed oil shale may be very significant relative to

the oil produced. As a result, the application uf fluidized beds to oil-shale

processing presents a new challenge in that the shale particles will be much

larger, probably up to 5 or 6 mm, the particle-sice range may approach an

order of magnitude, and the particle shape wi'1 iie very irregular.

At this time there is very little published information regarding the

incipient fluidization of crushed oil shale. Thii, study is intended to help

fill this gap in the technology of fluidized-bec applications.

We have measured gas velocities and void fractions at incipient

fluidization over a range of particle sizes, particle-size distributions and

conditions that may be used for processing oil shale. Particle sizes ranged

from 0.063 to 6.3 mm. Temperatures ranged from 23 to 450°C. The pressure in

all cases was one atmosphere,. The fluidizing gas was air for the

room-temperature measurements and nitrogen for he high-temperature

measurements.

EXPERIMENTAL TECHNIQUE

Apparatus

The equipment used for these measurements comprised cylindrical beds,

rotameters, pressure gauges, and thermocouples with indicators. Three bed

sizes were used. The smallest was 5.1 cm in dia, by 45-cm high. This bed was

constructed with a steel plenum, a Pyrex tube in the body and equipped with

heaters for operation at up to 450°C.

1823K

The mid-sized bed was 5.7-cm ID by 60-cm high (see Figure 1). This bed

was constructed using a Plexiglas tube for the body of the bed, a modified

pipe fitting for the plenum and a perforated plate for gas distribution. This

bed was used for measurements on shale particles up to 2.4 mm in screen size.

The largest bed was 14 cm ID by 165 cm high. Like the last bed described

above, this bed was constructed using a P'iexiglas tube for the body of the bed

and standard pipe fittings to form the plenum. I this case we joined the bed

body to the plenum with a modified pipe flange so that the distributor plate

could be easily changed.

For each size of oed we used a series of distributor plates which differed

only in the size of the perforations. For the smaller beds we used a

seven-hole pattern based on an equilateral triai'iqie. For the large bed we

used a similar 19-hole pattern. This se'ection o~" plates was used to ensure

uniform gas distribution for each range .)f gas ates

Each bed was instrumented to measure >ed ami listributor pressure drops,

gas velocity and temperature, Superficial gas velocities in the beds were

measured by means of calibrated rotameters whir vere equipped with pressure

gauges and thermocouples. When heated, tie bed was equipped with

thermocouples to measure temperatures of the ga leaving the heater, the gas

in the plenum and the mixture of gas and solids i the oed.

Air was used for nearly all of the >"oom-tempe-ature measurements.

Nitrogen was used for the measurements on burne ihale to avoid damage to the

gas heater.

Shale Source and Preparation

The measurements reported here are for a number of shale samples which

differed in grade, location from which they came., method of preparation and

particle size. These shales came from the 432-foot level of the Rio Blanco

mine (150 L/Mg), the 560-foot level of the Rio ranco -nine (75 L/Mg), and the

Anvil Points mine (100 L/Mg)., All of these shades were roll-crushed to

-1.3 cm as the first step in their preparation,

In order to study the variations of incipient fluidization velocity as a

function of the type of mill used for t.ht final tep in crushing the shale,

the two Rio Blanco shales were divided to two 'ots each. The first lot was

crushed in a gyratory-cone crusher. The second iot *as hammer-mi lied in a

1823K

- 4 -

Scale for bed height measurement

5.7 cm id plastic tube

Bed pressure tap

Plenum pressure tap

- 2" X 3 /4" Pipe reducer bored to receive plastic tube.

Distributor plate

"- Gas inlet

Figure 1, Schematic drawing of mid-sized bed used in these studies.

Weber Brothers mill to obtain fine particle size* (< 0.1 cm) and in a

Sturtevant mill to get coarse (0.1 to 0.6 cm) shale particles. Each of these

lots was then classified using a Fritsch shaker and screens for the smaller

particles and a SWECO classifier and screens for the larger particles.

The Anvil Points shale was crushed in a Sturtevant hammer mill and

screened using a SWECO classifier to obtain the larger particles and a Fritsch

shaker and screens for the finer particles.

An additional lot of shale was prepared for me purpose of making

measurements on shale which had been retorted and burned. For this purpose a

quantity of the Rio Blanco 560-foot-level shale was crushed in the

gyratory-cone crusher and screened using the SWECO classifier. This shale was

retorted using hot nitrogen, then burned ,n a mix'.ure 3f" air and nitrogen.

The air rate was regulated to keep the burn temperature below 600°C to

preclude carbonate decomposition. After burninc, this shale was classified

using the Fritsch shaker and screens,

Measurement Method

For each measurement a distributor piate was selected that would have

sufficient pressure drop to ensure good gas distribution yet not create such a

high pressure drop that the resulting gas jets wojld significantly penetrate

the shale bed,

With the distributor plate in place and the bed assembled, a shale sample

of known weight was poured into the bed. The gas flow was then started and

gradually increased until the bed was brought into a well-fluidized (often

slugging) condition. The gas rate was then step-vise reduced. After each

rate reduction the gas rate (rotameter eading, ")tameter pressure and

temperature), bed and plenum pressures, tied hevin: ana temperature were

recorded. For measurements on shale samples hanng a oroad particle-size

distribution, the samples were mixed between oo .e-vations using a high gas

velocity, to prevent erroneous reading; lue to M>-ti •: 'e-size segregation.

Data Reduction

From the data recorded as indicated above, M- calculated the superficial

gas velocity and the void fraction at •nctpient fluidization following the

usual methods, i.e., we plotted the bed o-ressur.j Jrop as a function of

1823K

-6-

superficial gas velocity as calculated from the gas-rate data. By simple

graphical construction, (see Figure 2a), the point at which the bed

pressure-drop reaches a plateau was determined. For cases where the

pressure-drop versus superficial velocity data did not show a well-defined

knee or break to a plateau, the linear portions of these data are extended

using straight lines until the pressure knee was determined as in Figure 2b.

The superficial gas velocity at this point was assumed to be the incipient

fluidization velocity.

The void fraction at incipient fluidization was estimated from the cross

sectional area of the bed, A, the mass of the shale, M, the shale density,

p , and the measured height, h, of the solids in the tied as follows:

e = 1 - M/(p A h).

These calculated values of void fraction were then plotted as a function

of superficial gas velocity. That value of void -fraction which corresponded

to the gas velocity for incipient fluidization wa> taken to be the void

fraction at incipient fluidization. For most cases there was a knee in the

void fraction curve at or near the incipient fluicization velocity.

RESULTS AND DISCUSS I}N

In this section it will be shown that the dominant controlling variable

for incipient fluidization is particle size. To demonstrate this point the

results from the various shale lots will be presented. These results will be

compared with published correlations and curves. The results show some

dependence upon crushing method and gas viscosity as altered by operating

temperature. Other variables such as shaie source or grade will be shown to

have relatively little effect upon incipient fli idization velocity, we will

also see that the effective particle size for a b-oad particle-size

distribution is the specific surface or harmonr mean.

Figure 3 illustrates the results of our measurements on raw cone-crushed

shales, Rio Blanco 432 and 560. Note that there is no regular difference

between the incipient fluidization velocities measured for these shales in

1823K

- 7 -

"i r

2a.

2b.

-! 1 1-

-O o

ncipient fluidization velocity

J I L L

4 6 8

Gas velocity, cm/s

10

figure Z, Plots of Dea pressure drop versu jas velocity as used in data reduction.

- 8 -

1000

100 E u

o o > c o '^ 10 N jo '5

c v

u c

' M | i—i—r

10

D Rio Blanco 560 A Rio Blanco 432

1.0

0.1 0.001

i i i I

*The data-bar ends indicate the screen sizes used to classify the sample.

I >.- i L. I - I I l _ L

0.01 0.1

Particle screen size, cm

1.0

Figure 3, Incipient fluidization velocity a for cone-crushed shales.

a function of particle size

-9-

spite of the nearly 11-percent difference in particle density. This is not to

say that there were no density effects, but rattier that the minor variations

in particle sizes probably overshadowed any density effects.

Figure 4 displays the measured results of the Rio Blanco and Anvil Points

hammer-milled shales. Like the cone-crushed shales the incipient fluidization

velocity increases with the square of particle >ize for particles up to about

0. i cm in screen size. For particles larger thar 0.1 cm the dependence upon

particle size is reduced to about the square root. This shift in

particle-size dependence is thought to be the result of a change in the fluid

flow around the particles. The Reynolds number of 0.08-cm particles at

incipient fluidization velocity in air at one atmosphere was calculated to be

13. For packed beds, other studies (1) nave shown this value of Reynolds

number to occur in the transition from laminar to turbulent flow about the

particle.

Figure 4 also indicates that for the Rio Blanco shales there was no

detectable dependence of incipient fluidization velocity on grade. The data

are slightly scattered about the curve as drawn n the figure, however the

curve would appear to represent both grades of »rale,

Figure 4 also shows that the Anvil Doints sn.ile, which has a grade

intermediate to the two Rio 81anco shales, nas i incipient fluidization

velocity which was observed to be 25 percent nigper than that for the same

size Rio Blanco shale, Lacking additional data, one cannot distinguish

whether this difference is the result of shale g> ade or the shale mineral

distribution and structure.

Figure 5 shows the results for measurements rroro the burned Rio Blanco 560

shale at room temperature and at 450°C, Again, for particles less than .08 cm

in screen size, we found that the incipient -'lui; ization velocity was

proportional to the square of particle size for ;-oth the hot and cold

conditions. Also for particles having i screen ! ize larger than about

0.08 cm, we found that tne particle-size dependence was reduced.

Figure 6 is a compilation of all tne measure*;- results as represented by

the curves drawn on Figures 3, 4 and 5. Note tnat the results for the burned

shale and the Rio Blanco hammer-milled shales aUnost superpose on the same

curve. The burned shale shows slightly owe-" i-vipieot fluidization

1323K

-10-

100

c

10 r

9- 1.0 8 t

O Rio Blanco 560 £> Rio Blanco 432 D Anvil points

0.1 I 0.001


J l_

0.01 0 1


1.0

4, Incipient fluidization velocity as a function of particle size for hammer-milled shales.

-11-

1000 - i — i — r ~\—i—r 1—r-r

E o

o O

> c o to N jo "5

c

100

10

£ 1.0

O Data for 450°C • Data for 20°C

0.1 0.001


J L J L I 1

0.01 0 1


1.0

Figure 5, Incipient fluidization velocity as a function of particle size at two temperatures for burned, hammer-milled shale.

-12-

1000

100 E u

u o

"35 > c o * •» CO N

'5

c

o c

10

-r-q : r-^n r

Raw, hammer-milled anvil points shale at 20°C

1—r

Raw, cone-crushed Rio Blanco

shales at 20° C

1.0 -

0.1

-Burned, cone-crushed shale at 450°C

Burned, cone-crushed shale at 20° C

-Raw, hammer-milled Rio Blanco shales at 20° C

i i i I —i J i J L_L

0.001 0.01 0.1


1.0

Figure 6, Collected experimental measurements of incipient fluidization velocity versus particle size.

-13-

velocities at 450°C as discussed above. And, tne cone-crushed shales show a

slightly higher incipient fluidization velocity for the very fine particle

sizes than the Rio Blanco hammer-milled shales.

In Figure 7 we see a comparison of the experimental data with both the

Zenz-Othmer graph (3) and the Kunii-Levenspiel correlation (2). As the figure

shows, the Zenz-Othmer graph gives incipient f^dization velocity estimates

that were much higher than found by experiment. For fine (.006 cm) particles

their graph falls a factor of six above the experimental data. For larger

particles (0.3 cm) their graph was a factor of t̂ iree above the experimental

data. The reason for this difference U not known. However, it may be

related to the irregular shape of the crushed ci shale particle which was not

considered in the construction of their graph.

For the purpose of comparing our results witn the Kunii-Levenspiel

correlation we chose to modify their correlation to avoid the complications of

relating irregularly-shaped, crushed oil-shale particles to volume-equivalent

spheres. This was accomplished by carrying the lotion of specific surface

(particle surface area per unit volume of part c le) from Ergun's development

(5) directly into their expression. We assume! that:

specific surface = o/W

where W is a characteristic linear particle size and a is a specific surface

factor, a dimensionless property of crushed oi shale that can be calculated

from particle size and exterior surface-area measurements (4). The

Kunii-Levenspiel correlation then becomes

W pg(ps - p f ) 9

a_v_j5 u

where U and e are the superficial gas velocity and void fraction at

incipient fluidization respectively, p^ is the fluid density, p is

the solids density, u is the fluid viscosity ana g is the acceleration of

1823K

-14-

1000

100

o o w > c o

5 '5

c 0) 'a. '5 c

10

1.0

^ r i — r n—r-r

Zenz-Othmer graph

Anvil points hammer-milled shale

Rio Blanco hammer-milled shales

Kunii-Levenspiel correlation

0.1 ' — 0.001

_L_L± _L J L_L 0.01 0.1


1.0

Figure 7, Comparison of experimental results with two correlations.

-15-

gravity. To calculate values of incipient fluid^zation velocity, U, using

this expression, we first solved for U using the usual solution for a

quadratic equation. Then we substituted values for the variables and

constants. Values for viscosity were taken from Perry and Chilton (1). Tne

gas density was calculated from ideal gas relationships. Carley's value (4)

of 12.2 was used for o. We used experimental values of void fraction for

e. Particle densities were taken from Baughman o), and w was taken to be

the geometric mean of the nominal openings of tne pass ng and retaining

screens.

Figure 7 also gives a comparison between the Kunii-Levenspiel correlation

and the experimental results. Although their correlation comes much closer

than the Zenz-Othmer graph, it stil! lies signiti:antiy above the experimental

results. This correlation comes closest to exper ment for 0.1-cm particles

where it is 10 to 40 percent high. As one goes t;> smaller particles the

difference becomes larger such that for 0,01-cm particles the correlation is

two to three times higher than experiment, For particles in tne 0.1 to 1.0

size range, the correlation appears to be 18 to 4;) percent high.

Figure 8 compares the experimental data for cone-crushed and burned Rio

Blanco 560 shale with curves calculated using t.l e Kurn i-Levenspiel

correlation. As the figure shows, we found tha :ne 3ata and curve for 450°C

correspond well over the range of experimental ;a:a. la contrast to the good

agreement at 450°C, we found that for the same hale at i?Q°C, the

Kunii-Levenspiel correlation predicts a much higher incipient fluidization

velocity than found by experiment.

At this point it is imperative to point out me oasis for particle

measurement used here because of conventions thst have been used in the past

and may come into use in the future. As indica:>d above in the section on

sample preparation, we determined our partic'e , zes by use of screens. The

average particle size was assumed to be the squi e root of the product of the

passing and retaining screen openings. This estimate of average particle size

was adopted to conform to particle-si ze-reporti *, practices used in the past

and to have our data on a basis more luj-'y jse i to formulate correlations of

particle behavior. This choice was made o ;pr:, of ,: noings (4) that the

average particle size (second-largest o'ncipa! imens^on) for narrow size

cuts is more nearly equai to the passing screer .pemng. Should the reader

1823K

-16-

1000 T — i — r

100 Kunii-Levenspiel correlation

at 20° C

10

£ 1.0

0.1 0.001

D Data at 20°C O Data at 450° C

L Kunii-Levenspiel correlation at 450° C

_L J L_l_ J _ I I I

0.01 0.1


1.0

Figure 8 , Comparison o f exper imental r e s u l t s w i t h the Kun i i -Levensp ie l c o r r e l a t i o n a t two temperatures .

-17-

choose to analyze these data with respect to the passing screen size, then the

particle size should be read as the right-hand end of the line segment drawn

through each datum.

Figure 9 gives our measured values of void traction at incipient

fluidization as a function of particle size, T M s figure shows an increase in

void fraction as the particles become smaller, "lis pattern has also been

observed for crushed particles of other materia s (2).

Figures 10 through 13 illustrate results of measurements on mixtures of

particle sizes. Figure 10 shows observations o incipient fluidization

velocity for mixtures of 0.177 mm and 0. 354 mm articles. Included with the

experimental data, are two curves calculated on the premise that the incipient

fluidization velocity is proportional to the sqiire of the mean particle size;

the upper curve using the mass fraction weighted Tiean, i.e.,

°p - £XiDpi •

the lower curve using the specific surface mean, i.e.,

B . _J

Figure 11 shows the results for mixtures of 0.354 mm and 0.707 mm particles.

Figure 11 also includes the two calculated curves as described above. Figure

12 shows the results for mixtures of .177 mm- and 0.707 mm-sized particles.

Unlike the particle mixtures for which results are shown in Figures 10 and 11,

the coarser particles are four times the size of the finer particles. In this

case it appears that there may be a discontinuity somewhere between 50 and 75%

of the coarser particles. Note that the data tend to follow the harmonic mean

curve more closely than the mass fraction mean

Figure 13 shows measured incipient fluidization velocities as a function

of particle-size distribution for shale sampler which are mixtures of these

particle sizes. In this figure the particle s i<> distribution is represented

by the weight fraction of each of three oartic!g sizes (as indicated by the

location of each datum) that were used to fornn late the sample. The observed

velocity for each sample is given by the value ; Kated by each datum. The

corners of this graph represent shale samples 'i<wing only one particle size

1823K

-18-

1.1

1.0 -c o

s °-9 CO

Z 0.8 'o £ 0.7 QJ

•5 0.6 c

0.5

0.4

| - r ^ f T r - T -O RB 560 hammer-milled 0 RB 432 hammer-milled O Anvil points hammer-milled • RB 560 cone crushed A RB 432 cone crushed O RB 560 burned, 450

=d-d-

~r 0 0.001 0.01 0.1

Particle screen size (cm)

i3" 1.0

Figure 9, Void fractions at incipient fluidization as a function of particle size

-19-

E

u _o > c g

N

c 0)

S 2©-'

20 40 60 80

Weight percent coarser particles 100

Figure 10, Incipient fluidization velocity as a function of particle size distribution for mixtures of 0.018 cm and 0.035 cm particles of Anvil Points oil shale.

-20 -

20 40 60 80



-21 -

20 40 60 80



-22-

(2)

Dp = 0.018 cm (i,2.2 H

2.5 cm/s

Figure 13, Incipient fluidization velocity as c function of particle size distribution for binary and ternary particle size mixtures of crushed Anvil Points oil shale.

-23-

and thus are data given earlier in this report. The edges of this figure

represent samples containing two particle size fractions and as such are an

alternate representation of the data given in Figure 10, 11 and 12. The data

found within the figure boundaries contain all three particle sizes in the

fractions indicated.

The heavy lines in Figure 13 represent isokinetic contours based on the

notion that the incipient fluidization velocity is proportional to the square

of particle size and that the representative particle size is the harmonic

mean particle size. Like Figures 11, 12, and 13 these contours do not fit the

data as well as might be desired; however, the :ontours do follow the trends

shown by the data.

CONCLUSIONS

The results of our study have led us to the following conclusions:

1. For crushed oil shale particles less than 0.08-cm screen size,

incipient fluidization velocity increases with the square of particle

size indicating that the flow is generally laminar.

2. For particles greater than 0.? cm in screen size we found that

incipient fluidization velocities fol owed the square root of

particle size.

3. For particles between 0.08 and 0.2 cm the incipient fluidization

velocity was in a range where the dependence upon particle size is

rapidly changing.

4. Results of our measurements follow the trends of the Kunii-Levenspiel

expression for incipient fluidization velocity provided that a

specific surface factor of 12.2 is used along with the geometric mean

screen size as representative of the ;>article size. Exact agreement

was found only for 0.01 to 0,2-cm particles at 450°C.

5. Measured bed void fractions follow trends exhibited by other crushed

materials.

6. For a broad particle-size distribut o i, tne harmonic mean particle

size correlates best for incipient-*1jidization velocity estimates.

1823K

-24-

REFERENCES

1. Chemical Engineers Handbook, R. H. Perry and Ch i l ton , C. H.; 5th Ed i t ion ,

McGraw H i l l , (1973).

2. F lu id iza t ion Engineering, D. Kunii and Levenspiel, 0 . , R. E. Krieger

Publishing Co., (1977).

3. F lu id iza t ion and Flu id Par t i c le Systems, F. A, Zenz and Othmer, D. F.

Reinhold Publ ishing, (1960).

4. Dimensions, Exter ior Surfaces, Volume, Densities and Shape Factors fo r

Par t ic les of Crushed Colorado Oil Shale in two Narrow Sieve Fract ions,

James F. Carley, UCRL-84583 Rev. 1, Apr i l 1981, Lawrence Livermore

National Laboratory.

5. Sabri Ergun, Flu id Flow Through Packed Columns, Chem. Eng. Prog. Vol 48 p.

89 (1952).

6. Synthetic Fuels Data Handbook, Gary i„ Baughman, Cameron Engineers, Inc.

Denver (1978).

1823K

DISCLAIMER

Ihis document was prepared as an account of work sponsored by an agency of Ihe I nited Stales Government. Neither the I nited Stales Government nor the I niversitv of California nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy. completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial products, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the I nited States Government or the I niversity of California. The views and opinions of authors expressed herein do not necessarilv state or reflect those of the I nited Stales Government thereof. and shall not he used for advertising or product endorsement purposes-

ucrl- 89887 preprint incipient fluidization

Documents