Lock-hopper systems are the most common means for feeding solids to and from coal conversion reactor vessels. The rate at which crushed solids flow by gravity through the vertical pipes and valves in lock-hopper systems affects the size of pipes and valves needed to meet the solids-handling requirements of the coal conversion process. Methods used to predict flow rates are described and compared with experimental data. Preliminary indications are that solids-handling systems for coal conversion processes are over-designed by a factor of 2 or 3

Gardner, J. F.

Hobday, J. M.

Smith, J. E.

English

NASA Technical Reports Server

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 2020-03-20T12:37:01+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  

TA
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E 
I.
 -
 
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 V
al
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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, % 
TA
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 PE
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(lb
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 b
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-
 
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. 


Gravity flow rate of solids through orifices and pipes

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