GRAVITY FLOW R A T E O F SOLIDS THROUGH

O R I F I C E S A N D P I P E S

J. F. G a r d n e r

J. E. S m i t h

J. M. Hobday

U. S. E n e r g y R e s e a r c h a n d Deve lopment A d m i c i s t r a t i o n , Morgan town E n e r g y R e s e a r c h

C e n t e r Morgantown. IVest Vi rg in ia

?REZEDIN0 PAGB BLANK HOT FUm

https://ntrs.nasa.gov/search.jsp?R=19780005317 2020-03-19T03:03:03+00:00Z

ABSTRACT

Lock-hopper s y s t e m s a r e the m o s t common means fo r feeding sol ids to and f rom coal conversion reac to r vesse l s . The ra te a t which crushed sol ids flow by gravity through tho ve r t i ca l pipes and valves in lock- hopper sys tems affects the s i ze of pipes and valves needed t o m e e t the solids-handling requi rements of the coal conversion p rocess . Methods used to predict flow r a t e s a r e descr ibed and compared with exper imenta l date. P re l iminary indications a r e that solids-handling s y s t e m s for coal conversion p r o c e s s e s a r e over-designed by a fac tor of 2 o r 3.

Sravi t y Flow Rate o f Solids Thmugh Or i f ices and Pipes

by

3. F. Gardnerl, 3. E. Smith2, and 3. H. Hobday3

Lockhopper systems are the most colnnon means for feeding sol i ds

t o and from coal conversion reactor vessels. The required rates a t

which these sol ids must flow af fec ts the size o f p ip ing and valves

used i n the lockhopper systems.

The Worgantown Energy Research Center conducted a l i t e r a t u r e

review on sol ids feeding t o analyze valve size requirements for

sol ids handling service i n coal conversion plants. From t h i s

1 i terature review, i t i s apparent tha t 1 i m i ted investigations have

been performed t o determine the ra te a t which crushed sol ids f l r

by grav i ty from hoppers, pipes and valves.

Most experimental work on grav i ty f low o f sol ids occurred during

the pos t - W I I years o f 1945-1 955. ( ) ~ r e ~ o r ~ ( ') i n 1952 appraised

the problem o f grav i ty flow o f sol ids and drew the fol lowing con-

clusions:

1. The internal pipe diameter should be a t least 5 t o 7 times

as large ds t h ~ largest pa r t i c l e size encountered i n the

charge.

Y mchanical Engineer, U.S. ERDA - Morgantcmn Energy Research Center, Morgantown, W

9 Contractor, U.S. ERDA - A r g a n t m Energy Research Center, Morgantown, W

1/ Mechanical Engineer, U.S. ERDA - Argantown Energy Research Center, Morgantown, WV

2. Materials o f narrow size range tend t o f low mre readi ly.

Haterials wi th wide size spectra may exh ib i t s t ick ing tend-

encies, as do conparit ively small par t ic les (on the order

of Dp c0.003 in.).

3. M i ld steel encourages pa r t i c l e s t ick ing whereas smoother

surfaces o f stainless steel and glass are more amendable t o

unimpeded f 1 ow.

4. Flow may be severely affected by surface moisture. Thus a

sol ids surface moisture content i n excess o f 1 t o 2 percent

should be avoided.

Gregory's work was a good s t a r t on determining the variables which

a f fec t grav i ty f low o f sol ids. Other investigations have determined

that the fol lowing factors also a f fec t sol ids flow.

1. Solids Density.

2. Surface properties o f the sol id.

3. Size and shape o f storage reservoir.

4. Length and shape o f the standpipe.

5. Temperature o f the sol ids.

6. Velocity e f fec ts (transonic effects o r Reynolds Number effects. )

7. Electrostat ic influences.

Rausch i n 1948(~) investigated a wide var iety o f sol ids f a l l i n g

through tubes o f 3" t o 8" diameter. His experinental equipment con-

s isted o f a simple hopper wi th or i f ices and discharge :vbes. tie varied

the o r i f i c e diameters from 1/16" t o 2 W i l e varying Do/Dp from 2.5 t o

250. Rausch observed the fo1 lowing ef fects I

1. Solids head had l i t t l e e f fec t .

2. The diameter o f the discharge duct had l i t t l e ef fect on

sol ids flourate.

3. Part ic le size had l i t t l e islpact except when considered i n

combination with o r i f i c e diameter.

4. With Do/Dp ~ 2 5 the bulk density o f the solids passing through

the o f i f ice appeared t o be reduced.

5. The angle o f approach i n the bottom o f a delivery hopper

(as shown i n f igure 1) had an influence on f l o w rate.

FIGURE I ! ~ ) - Ang!e of Approach Correction Factor for Gravity Feed Systems

Rausch also developed a correction factor t o take i n to account

the pipe wall effect. This i s given i n Figure 2.

C o r r e l a t i o n proposed by Rausch -

FIGURE 2 ( 5 ) - Wall E f f e c t C o r r e c t i o n F a c t o r f o r G r a v i t y F low o f S o l i d s

The experimental data o f ~ausch'') was cor re la ted and used t o

develop the fol lowing equation:

( D o l D p ~ ~ . 'O gcowspb Ma = C Co D~~ ,

tan 8,O.S

When rearranged t h i s equation y ie lds :

Cs i s a constant t ha t i s cha rac te r i s t i c of the so l i ds involved.

A s i m i l a r form of t h i s equation has been proposed by a v a r i e t y

o f experimenters. These equations d i f f e r in the values of CS and i n

the exponent of the o r i f i c e diameter. These di f ferences are

l i s t e d i n Table 1.

Zenz( l o ) concluded tha t the ~ a u s c h ( ~ ) co r re la t i on i s r e l a t i v e -

l y accurate f o r a wide range o f sol ids f low conditions. Zenz f e l t

t h a t fur ther tes ts should be performed t o v e r i f y and cor rec t the

cor rzc t ion factors used i n equation 2.

A series o f so l ids f low experiments were performed a t the

Morgantown Energy Research Center. Limestone sol i ds w i t h the character-

i s t i c s given i n Table 2 flowed from a so l ids storage b i n through a pipe

o r o r i f i c e p la te f o r a speci f ied time i n t o a receiving hopper. The

so l ids were then weighed and a f lowrate calculated.

The discharge configurations used i n the experiments consisted

of 7-font lengths of 1-1/2, 2, 4, 6, and 8-inch diameter, Schedule 40

carbon s tee l pipes, and 4, 6, and 8-inch diameter f l a t p la te o r i f i c e s .

For each ind iv idua l tes t , the pipe o r p la te was attached t o the bottom

of a 25-ton capacity storage hopper kqving an inverted-frustrum bottom.

Addit ional experiments were a lso condustea using a va r ie t y o f types

of reducer sections (both canical and concentric i n shape) located be-

tween the hopper bottom and the discharge o r i f i c e .

The resc l t s of these experiments are given i n Table 3. Photo-

graphs of the tes ts and a t yp i ca l experimental conf igurat ion are

shown i n Figures 4, 5, and 6.

Observations from these experiments were:

1. A uniform f low o f the so l ids occurred i n a l l tests. The

observed f low of the so l ids (as photographed through a p l e x i -

glass tube) indicated an accelerat ion of p a r t i c l e s and a

near ly f u l l tube o f so l i ds a t the s t a r t . The flow stream then

tapered w i t h increasing distance from the beginning o f the tube.

2. The f l ow o f s o l i d s was un i form dur ing the e n t i r e per iod of

the t es t s .

3. A "choked" f l ow cond i t ion d i d n o t occur dur ing the tes ts .

A "choked" f l ow cond i t ion , however, could be induced by

r e s t r i c t i n g a small amount o f the f l ow area.

Table 4 compares p red ic ted f lowrates w i t h the ac tua l f l ow ra tes

found i n the MERC tes ts .

From Table 4 i t i s apparent t h a t f l ow ra tes ca lcu la ted from the

equations developed by previous experimenters c o r r e l a t e poor ly w i t h

the r e s u l t s obtained a t MERC. This ind ica tes t h a t good co r re l a t i ons

are no t ava i l ab le f o r d e s i g ~ ~ i n g g rav i ty-f low systems f o r haqdl i n g

crushed s o l i d s i n coal conversion processes. Fur ther i n v e s t i g a t i o n

i n t o t h i s problem area thus needs t o be done. With accurate pre-

d i c t i o n methods f o r s o l i d s f low, valves and p i p i n g f o r coal conversion

process p l an t s could be accurate ly s ized. For example, the MERC data

show t h a t 3885 tonslday o f drushed so l i ds can f l ow under g r a v i t y head

through an 8" v e r t i c a l p ipe l ine . This ind ica tes t h a t r e l a t i v e l y small

valves and p ip i ng could be s u f f i c i e n t f o r comnercial-scale coal conver-

s ion p lants . This would lower costs, and lessen design, f ab r i ca t i on , and

operat ing problems w i t h valves.

The experiments conducted a t MERC were n o t s u f f i c i e n t t o f u l l y

inves t iga te the e f f e c t s o f p ipe and valve s i ze on g r a v i t y f l ow ra tes

o f crushed so l i ds . The r e s u l t s i nd i ca te the need f o r f l r r t he r s tud ies.

MERC has proposed such s tud ie- t o Foss i l Energy, ERDA.

2 I) 6 8 10 12

O R I F I C E D I A M E T E R . Do (IN. 1

F I G U R E 3 - V A L U E S OF FLOW RATES FOR VARYING B U L K DENSITIES A N D ORIFICE D I A M E T E R S .

BASED O N RAUSCH'S E Q U A T I O N ( 5 )

OHI(;INAL PAGE 6 OF' POOR Q U A L I ~

FISIJRE 4 - V I E W OF S T O R A G F ! ~ O P P E R USED I N M E R C S O L I D S F L O W R A T E T E S T S

FIGURE 5 - T Y P I C A L CONFIGURATION USED I N S O L I D S FLCIWRATE T E S T S

TABL

E I.

- R

efer

ence

Val

ues

of

C, an

d th

e

Ori

fic

e D

iam

ete

r E

xpo

nen

t o

f V

ari

ou

s Experimenters

I R

ef e

tence

CS

Exp

on

ent

(4)

New

ton

et

al.

Ke

lly

( 3)

Fra

nk

lin

& J

ohan

son

(2)

0.0

5

2.9

3

Rau

sch

0.6

5

2.7

0

~l

-~

i

rai

(6)

3. I8

2

.50

Table 2 - Propert ies o f Limestme Sol i ds Used i n Sol i ds Gravi ty Fiow Tests d t MERC

Mater ia l - Limestone " = Bulk Density = 88.17 l$lf t3

13, = Angle o f Repose = 38"

Dp = ..verage P a r t i c l e diameter = 0.172 i n .

Size Analysis:

Screen Size

5/16" x 1/4"

1/4" x 1/8"

1/8" x 1/16"

l / i 6 " x :6 mesh

16 mesh x 30 mesh

30 wesh x 50 mesh

50 mesh x 100 mesh

100 mesh x 200 mesh

minus 200 mesh

Weigh' Percent, %

TABL

E 3

. - R

es

ult

s o

f S

oli

ds

Flo

wra

te T

ests

C

ondu

cted

at

MER

C

Tes

t Co

nf i

pu

rati

on

O

rif i

ce

Siz

e,

Pip

e L

e~lg

th A

v.

Sol

id

Flo

wra

te

Av.

Sol i

ds

lar

rate

* N

o.

Do,

in.

L,

Ft.

W,

1 bm

lrec

w

, lb

fhr

(xIo

3)

P 1 P

ES

-

PLAT

ES

i 6

* So

l id

s us

ed a

s D

escr

ibed

i n

TAB

LE

2

TA

BL

E

4.-

C

alc

ula

ted

Flo

w

Ra

te o

f S

oli

ds

W

a(l

bm

/se

c)

Pre

dic

ted

by

V

ari

ou

s

Re

se

arc

he

rs.

**

Act

ua

l fl

ow

ra

tes

ob

se

rie

d e

xp

eri

me

nta

lly

a

? M

ERC,

u

s sh

own

in

Ta

ble

3.

All

oth

er

valu

es

are

ca

lcu

late

d.

r

I M

.E.R

.C.

rl

2 G

RE

GO

RY

(

7)

3

NE

WT

ON

et

al

. (

4)

4

KE

LL

EY

(3)

5

FR

AN

KL

IN

&

JOH

AN

SO

N (

2)

6

RA

US

CH

(5

)

7 K

UW

AI

8

SH

IRA

I (

6)

Do, i

n

f

4

13

.99

8.9

6

8.4

8

8.2

0

2.9

0

27

.45

37

.11

5.7

6

6 4

3.1

2

24

.69

28

. 15

25

.95

9.5

3

82

.02

11

3.

17

15

.87

8 8

9.9

3

50

.69

65

.96

58

.73

22

. 13

4

17

8.3

4

24

9.6

4

32

.58

-

Non#ncl ature

Do = diameter o r i f i c e (in.)

2 = diameter par t ic le (in.) = flawrate (Ibs/hr)

C = correction factor (angle o f approach) Co = correction factor (wall effect) gc = gravity (386.5 lbm i n l l b f sec2) pb = bulk density ( lbs/ in3)

P = angle o f repose o f poured solids (degrees) = f l u i d column height ( f t . )

CS = constant characteristic o f the solids involved Wa = flowrate, 1 b/sec De = effect ive o r i f i ce diameter (in.) h = height of reservoir (f t .) d = dianeter o f reservoir ( f t . )

1. Leva, Max; Fluidization, kGraw-Hi l l Co., 1959, pp. 156-163.

2. Franklin, F. C. and L. N. Johnson: Chem. Eng. cci. 4(3): 119- 129 (1955)

3. k l l e y , A. E. Petrol. Engr., 16(13): 136-142 (1945)

4. Newton, R. H., 6. S. Dunham, and T. P. Simpson: Trans AICHE 41:215 (1945)

5. Rausch, J. M.: Ph.0. thesis. Princton University 1948.

6. Shirai, T.: Chem. Engr. (Tokyo) 16:86-89 (1952)

7. Gregory, S. A.: J. Appl. Chem. (London), 2, Suppl. Issue 1, S1-S7 (1952)

8. Kuwai, 6. : Chem. Engr. (Tokyo), 17: 453-459 (1953)

9. Zenz, F. and Othmer, D.: Flagation and f l u i d pa r t i c l e systems, Reimhold Pulb. Corp., NV (1960)

10. Zenz, Fredric: Yydrocarbon proc. and Pet. Refines, Vol . 21, No. 2 (1962)

11. Brown, R. L.: Trans Inst. Chem. Engrs. (London) 38, 243-56 (1960)

12. Kunii, D., Levenspiel, 0. : Fluid izat ion Engineering, John W i ley & Sons Inc., NY (1969) pps. 367-373.

13. Soo, S. L.: F lu id Dynamics o f Multiphase System?, Blaisdel l Pub. Co., Wattham, Mass. (1967)

14. La Forge, R. H., Hatcher, S. T., University o f 7e: paper presented t o A.S.M.E.

15. Massimilla, L., Beta, V., Della Rocca, C. paper presented a t the 40th Natl . AECHE Meeting, Kansas City, May 19, 1959.

16. Kro l l , W., Chmie Eng. Tech. 27, 33-38 (1955).

17. Tarman, Paul B. and Lee, Dr. Bernard S., Solids Feeding Devices, presented a t Pneumatic Transportation o f Sol ids Conference, U. S .B.M. Morgantm, UV, October 19-20, 1965.