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Miguel A. Granero Experiment 3 30/01/2013
Miguel A. Granero
Experiment 3:
Report on Flow through a
granular bedExperiment completed on the 24 th January 2013
he relation!hip between the Re"nold! number and
the #ri$tion #a$tor $an be determined b" !tud"ing the
%ow rate! and di&eren$e! in pre!!ure! through twodi&erent granular bed!. he $on$lu!ion! will pro'ide
in#ormation on the !i(e and !hape o# the bed! #or the
optimal de'elopment o# the de!ired $hemi$al rea$tion.
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able o# $ontent!:
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Introductionhttp://www.!$ien$edire$t.$om/!$ien$e/arti$le/pii/+000,2-0,0-00-,
In chemical processing, a packed bed is a hollow tube, pipe, or other vessel that is filled with apacking material. The packing can be randomly filled with small objects like Raschig rings or else it
can be a specifically designed structured packing. Packed beds may also contain catalyst particles or
adsorbents such as zeolite pellets, granular activated carbon, etc.
The purpose of a packed bed is typically to improve contact between two phases in a chemical or
similar process. Packed beds can be used in a chemical reactor , a distillation process, or ascrubber ,
but packed beds have also been used to store heat in chemical plants. In this case, hot gases are
allowed to escape through a vessel that is packed with a refractory material until the packing is hot.
ir or other cool gas is then fed back to the plant through the hot bed, thereby pre!heating the air or
gas feed.
he appli$ation o# heterogeneou! $atal"!i! gi'e! ri!e to a 'ariet" o# rea$tor t"pe!. #
tho!e the pa$ed bed rea$tor! belong to the mo!t widel" applied rea$tor! their
popularit" originating #rom their e&e$ti'ene!! in term! o# per#orman$e a! well a! low
$apital and operating $o!t!. he rea$tant! %owing through a pa$ed bed rea$tor $an be
both in the #orm o# ga! or liuid. 4n numerou! appli$ation! both pha!e! are pre!ent.
5owe'er a !tud" o# !ingle6pha!e %ow i! o# parti$ular intere!t to thi! wor !in$e it i! not
onl" e!!ential #or !ingle6pha!e appli$ation! but al!o $on!titute! the ba!i! #or !tud"ing
two6pha!e %ow through pa$ed bed! a! di!$u!!ed in part 2 o# thi! wor 7 8eme$ and
9e'e$ 200-.
he !hape and !i(e o# $atal"!t parti$le! that mae up the bed are determined b" the
$hara$teri!ti$! o# the pro$e!! in ue!tion. A! a general rule the parti$le !i(e and !hape
!hould aim at high e&e$ti'ene!! !o a! to utili(e the $atal"!t material! and rea$tor
'olume and there#ore in$rea!e the bed a$ti'it" 7;or!tell 1,,2. For pra$ti$al rea$tion
rate! a! appl" to mo!t pro$e!!e! and t"pi$al di&u!i'itie! in ga!6
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uadrolobe! are o#ten u!ed !in$e the" o&er a greater !ur#a$e to 'olume ratio than
$"lindri$al extrudate! o# the !ame maximal out!ide diameter and al!o retain their
ad'antage in liuid pha!e operation 7+ie 1,,3.
5owe'er it ha! to be ept in mind that di&erentl" !haped parti$le! al!o pa$ with
di&erent degree! o# bed poro!it" whi$h re!ult! in di&erent pre!!ure drop! a! well a!
di&erent o'erall bed a$ti'itie!. A! a rough rule it i! !aid that the bed poro!it" in$rea!e!
the more the !hape o# parti$le! de'iate! #rom the !pheri$al !hape. hi! problem $an be
met to !ome degree with the u!e o# loading te$hniue! whi$h gi'e higher bed den!itie!
7;ooten 1,,>. b'iou!l" the $ompari!on o# e@$ien$" o# di&erent parti$le! i! not
!traight#orward a! the $hoi$e o# the appropriate !hape and !i(e o# the $atal"!t parti$le!
a! well a! the loading te$hniue will be determined b" the !pe$i
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Ergun euation 7Ergun 1,-2 whi$h $an al!o be written in dimen!ionle!! #orm in term!
o# modi
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Theory
The porosity of granular bed, defined as the volume of empty space between the particles, will be
used to determine the friction coefficient of the two different granular beds that are going to be
studied. The larger the porosity of a material is, the higher the flow of li"uid that can go throug ∆
ht
it is as there is more empty space through which li"uids can flow.
ε= Volume of empty space∈the bedTotal volume occupied by the bed
#here both volumes need to be in the same unit so thatε
. Is dimensionless.
In this e$periment, pressure differences will be recorded using a two!fluid manometer which is a
relatively dense pink!red fluid which fills a the lower part of an %!shaped tube with a less dense fluid
lying on top on both sides. In both parts of our e$periment this lighter was water.
#hen the there is no flow, the manometer levels are e"ual on both sides.
&owever, when a flow is created, the manometer levels on both sides become une"ual and the
difference of pressure can be obtained by recording the difference in the height of the coloured
heavier fluid. This is the reason why the fluid needs to be coloured, so that it is possible to record
height differences. The difference in pressure is given by the e"uation'
∆ P+ ρm gh= ρw gh
∆ P= ( ρm− ρw ) gh=∆ pgh
#here'
Pw is the density of water in (g)m*
Pm is the density of the heavier fluid in the manometer in (g)m*
g is the acceleration of gravity + .- m)s/
h is the height different between both interfaces of the %!shaped tube filled zith the heavier
fluid and is measured in m.
The results obtained are only applicable when water is flowing through a bed containing only one siwe
of particles. This causes the results of be of a limited use as they can not be used in other calculations
treating a flow of water going through a different bed used in the e$periment. Therefore, they can
neither be used for granular beds in other li"uids other than water norfor granular beds of different
height or diameter. nother case that would make the e"uation useless is when the shape or
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diameter of the particles in the bed is not the same. This caused engineers to investigate other ways
of presenting the data in order to be able to analyse a much wider range of different bed sizes. This
eventually led to the Reynolds number and the friction coefficient factor.
4t i! important to highlight the dimen!ionle!! propert" o# the Re"nold! number
and the #ri$tion $oe@e$ient #a$tor wa! 'eri
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Pw is the density of water in (g)m*
0 is the average size of the particles in m.
P is the pressure difference in Pa or (g)m)s/
3 is the height of the granular bed in m
is the crosssectional area of the column in m/
u is the viscosity of li"uid flowing through in the granular bed in (g s!m!
1 is the flowrate measured in m*)s
ε accounts for the volume of empty space in the bed and is dimensionless
Therefore,
f =
m m22 Kg
ms2
Kg
m3 . m.
m
s2
32=
m4 Kg
s2
m4 Kg
s2
=¿ Dimensionless
This will be useful to then compare and relate the friction coefficient factor to the Reynolds number.
Fir!tl" the taller and thinner bed wa! !tudied b" $hanging the water %ow rate a!
well a! anal"!ing and plotting the pre!!ure di&eren$e! 7mea!ured with the
rotameter! in a granular bed on a log6log graph in order to later the Re"nold!
number and the #ri$tion $oe@$ient #a$tor #or %ow through a granular bed.
+e$ondl" the !ame !tep! were done #or the !horter and wider bed.
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Apparatus and experimental procedure
A photograph o# the apparatu! and it! $orre!ponding !$hemati$ diagram
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The water fow
he water !tored in the tan under the table i! pumped with the aid o# an
ele$tri$al pump powered b" ele$tri$it". he %uid i! then !plit into two $ondu$t!whi$h $ontain a 'al'e ea$h 7labelled Ale#t and ? right. A#ter going through the
'al'e! both $ondu$t! merge again and go up to the highe!t point o# the !et up
where another 'al'e i! lo$ated. hi! one i! to !ele$t whi$h route or bed i! the
water going to %ow through.
4# the 'al'e i! !et with the handle on the le#t the water will %ow in that dire$tion
into the taller and thinner bed. here i! a manometer whi$h $onne$t! the top
and the bottom o# the bed 7+EE 5ERK and it mea!ure! the pre!!ure di&eren$e
between both part! . he water exit! the bed in the bottom and merge! with the
other $ondu$t #rom the unu!ed !ide. ?e#ore going ba$ to the water tan and
being re$"$led the water goe! upward! again and there i! an exhau!t !o that
water 'apour and other ga!e! $an exit the !"!tem.
4# the 'al'e i! !et to the right the water will %ow in thi! dire$tion through a
!imilar $ir$uit. he onl" thing that $hange! i! the bed whi$h in thi! $a!e i! wider
and !horter and the parti$le! in it are larger.
The Procedure
Fir!tl" the 'al'e! F G A and 5 mu!t be $lo!ed and the liuid in the manometer
need! to be in euilibrium 7when the height di&eren$e between the two
inter#a$e! i! 0. More importantl" the dire$tion o# 'al'e 5 need! to be $he$ed
to mae !ure that the water will %ow into the right bed the one that i! going to
be anal"!ed.
Lal'e! A and ? are gentl" opened. hi! $au!e! the rotameter to mo'e along the
tube. ;hen the metalli$ pie$e i! !table on both A and ? 'al'e! we $an open the
F and G 'al'e! i# we are u!ing the le#t bed in the !$hemati$ diagram or the F1
and G1 'al'e! i# the bed that i! going to be anal"!ed i! on the right !ide.
he height di&eren$e in the manometer i! re$orded and the 'alue on the A and ?
'al'e! i! $he$ed to mae !ure it ha! not $hanged a#ter opening the other !et o#
'al'e! 7thi! i! al!o to mae !ure that the 'al'e! ha'e not mo'ed a! the" are
extremel" !en!ible.
he !et o# A and ? 'al'e! are $lo!ed %ow rate i! (ero and then the 'al'e! F and
G or F1 and G1 depending on whi$h bed i! being u!ed are $lo!ed when the
$oloured %uid in the manometer i! in euilibrium 7height di&eren$e i! (ero.
hi! pro$edure i! repeated to obtain more
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Finall" the 'al'e! A and ? are $lo!ed then the 'al'e! F and G a! well a! the F1
and G 1 one! are $lo!ed. hen the pump $an be turned o&.
he data obtained with the experiment i! the #ollowing:
6 Reading on 'al'e! A and ? mea!ured in $entimetre!6 5eight di&eren$e between the two inter#a$e! o# the manometer al!o
mea!ured in $m.
8ext to the table are two Rotameter $alibration graph! that allow the $on'er!ion
o# the height o# the rotameter! A and ? into %owrate!. 5ere i! a photograph o#
the graph!.
Graph 1
hi! graph $orre!pond! to 'al'e A.
4t! 'erti$al axi! i! the tube reading and i!
in $entimetre! and it! hori(ontal axi! i!
the %owrate o# water at 20°C in
9itre!/minute.
he label at the top !tate! the 'al'e to
whi$h it re#er!: alibration #or water.
Metri$ !erie! tube J. +tainle!! !teel
%oat t"pe + !i(e J. d: J.B0 mm and w:
2.> gm.
Graph 2
hi! graph $orre!pond! to 'al'e ?.
4t! 'erti$al axi! i! the tube reading
and i! in $entimetre! and it!
hori(ontal axi! i! the %owrate o# water
at 20°C in 9itre!/minute.
he label at the top !tate! the 'al'e
to whi$h it re#er!: alibration #or
water. Metri$ !erie! tube 10.
+tainle!! !teel %oat t"pe + !i(e 10. d:
10.00 mm and w: -.J- gm.
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on'er!ion #rom tube reading to %owrate example!
1 nl" 'al'e A i! open.Read the 'alue in the tube. Eg. 1-.00$mN!ing graph 1 get the hori(ontal $oordinate o# the point whi$h inter!e$t!
the line o# the graph with the hori(ontal line at 1-.00 on the 'erti$al axi!.4n thi! $a!e it would be 0.- 9/min whi$h i! the total %owrate a! 'al'e ? i!
$lo!ed.2 nl" 'al'e ? i! open:
Read the 'alue in the tube. Eg. 1>.00$mN!ing graph 2m get the hori(ontal $oordinate! o# the point whi$h
inter!e$t! the line o# the graph with the hori(ontal line at 1>.00 on the
'erti$al axi!. 4n thi! $a!e it would be 0.,3 9/min whi$h i! the total %owrate
a! 'al'e A i! $lo!ed.3 ?oth 'al'e! are open:
Read the 'alue! in both tube!: Eg. 10$m #or tube $orre!ponding to 'al'e A
and 1$m #or tube $orre!ponding to 'al'e ?.N!ing graph 1 get the hori(ontal $oordinate o# the point whi$h inter!e$t!
the line o# the graph with the hori(ontal line at 10.00 on the 'erti$al axi!.
4n thi! $a!e the %owrate allowed b" 'al'e A would be 0.33 9/min. N!ing
graph 2 get the hori(ontal $oordinate! o# the point whi$h inter!e$t! the
line o# the graph with the hori(ontal line at 1.00 on the 'erti$al axi!. 4n
thi! $a!e it would be 0.JJ 9/! whi$h i! the %owrate allowed b" 'al'e ?. he
total %owrate will be the !um o# %owrate A O %owrate ? P 0.33 O 0.JJ P
1.10 9/min
hen the total %owrate re!ult! were $on'erted into +4 unit! u!ing the #ollowing
method:
1
min=1
d m3
min .
min
60 s .
m3
10000d m3 P 0.00001B m3/!
Eg. 2.- 9/min P .1BQ106- m3/!
Furthermore the height di&eren$e re$orded #rom the manometer i! u!ed to get
the pre!!ure di&eren$e:
∆ P= ( ρm− ρw ) g h
7
Eg. *re!!ure di&eren$e #or the 1 . 0.0 . 1062 P 21.,J *a
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ResultsFir!t part o# the experiment: the thin and tall bed.
;hen onl" 'al'e A i! open:
5eight
di&eren$e
7$m
*re!!ur
e
di&eren
$e 7*a
Lal'e A
reading
7$m
Lal'e ?
reading
7$m
Flow
rate A
79/min
Flow
rate ?
79/min
otal
Flow
79/min
otal
Flow in
m3/!
106-
0.0 21.,J 2.J 0.13 0.13 0.20>0.>0 3.,- -.J 0.21 0.21 0.3-1.00 -., , 0.2> 0.2> 0.>
0.,0 ,. 11.B 0.3- 0.3- 0.-B01.0 JB.,1 13.2 0. 0. 0.B
1.J0 ,3.3, 1-.- 0.B 0.B 0.J3B
1.>0 ,>.>> 1J.2 0.-1 0.-1 0.>1B2.00 10,.>J 1J.> 0.-2- 0.-3 0.>>
2.B0 12.>3 21.0 0.B2 0.B2 0.,,23.20 1J-.>0 2.B 0.J2 0.J2 1.1-
3.0 1>B.J> 2-.> 0.JJ 0.JJ 1.232
Gi'en that onl" 'al'e A i! open the total %owrate 7 !um o# the !eparatel"$on'erted reading! o# 'al'e! A and ? i! eul to the %owrate through 'al'e A.
5eight
di&eren$e
7$m
*re!!ure
di&eren
$e 7*a
Lal'e A
reading
7$m
Lal'e ?
reading
7$m
Flow
rate A
79/min
Flow
rate ?
79/min
otal
Flow
79/min
otal
Flow in
m3/!
106--. 2,B.B- 1>.B 1.00 1.00 1.B-.B 30J.B 1,., 1.0> 1.0> 1.J3
J.3 01.03 23.J 1.32 1.32 2.11B.J 3B>.0J 23. 1.2- 1.2- 2.0010 -,.3B 2, 1.-- 1.-- 2.>Gi'en that onl" 'al'e ? i! open the total %owrate 7 !um o# the !eparatel"
$on'erted reading! o# 'al'e! A and ? i! eul to the %owrate through 'al'e ?.
5eight
di&eren$e
7$m
*re!!ure
di&eren
$e 7*a
Lal'e A
reading
7$m
Lal'e ?
reading
7$m
Flow
rate A
79/min
Flow
rate ?
79/min
otal
Flow
79/min
otal
Flow
in
m3/! 106
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-.0 21,.J 2B.2 10.3 0.J- 0.-J 1.32 2.11J.B 1J.-1 1,.- 12.> 0.-> 0.J0 1.2> 2.0-1-.B >-J.00 2J., 2.3 0.2 0.>2 1.2 1.,>1B.J ,1J.3 2.0 2J.> 0.J0 1.- 2.1- 3.
1B.> ,22.,2 22. 2>.3 0.B- 1.-- 2.20 3.-2Gi'en that both 'al'e! !tr open the total %owrate will be the !um o# the
!eparatel" $on'erted reading! o# 'al'e! A and ?.
Eg. al$ultating total %owrate.
Reading o# 'al'e A: 1,.-$m on'erted reading o# 'al'e A 7%owrate
in 9/min: 0.-> 9/min
Reading o# 'al'e ?: 12.>$m on'erted reading o# 'al'e ? 7%owrate
in 9/min: 0.J0 9/min
otal %owrate: 0.-> O 0.J0 P 1.2> 9/min P 1.2>/B0/1000 m3/! P 2.0- 106- m3/!
Eg. *re!!ure di&eren$e #or the 1 . 0.0 . 1062 P 21.,J *a
*lotted graph o# $hange in pre!!ure again!t %ow rate.
0 0.- 1 1.- 2 2.- 3 3.-
0
100
200
300
00-00
B00
J00
>00
,00
1000
Bed 1 Pressure dierence against fowrate
Flowrate in m3s ! 1"#$
Pressure dierence %Pa&
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Re"nold! number! #or ?ed 1
*re!!ure
di&eren$e
Flowrate Re"nold!
number
Fri$tion #a$tor
21.,J 0.20> J.>3.,- 0.3- 12.-,-., 0.> 1B.11,. 0.-B0 20.1JB.,1 0.B 23.02,3.3, 0.J3B 2B.J,>.>> 0.>1B 2,.3-10,.>J 0.>> 30.,12.>3 0.,,2 3-.B>1J-.>0 1.1- 1.3B1>B.J> 1.232 .312,B.B- 1.B -J.-30J.B 1.J3 B2.2201.03 2.11 J-.>>3B>.0J 2.00 J1.,3-,.3B 2.> >,.1,21,.J 2.11 J-.>>1J.-1 2.0- J3.J2>-J.00 1.,> J1.21,1J.3 3. 123.J1,22.,2 3.-2 12B.-,
Eg. al$ulation o# Re"nold! number:
+ub!tituting in the euation the 'alue! to adapt the euation to bed 1
u!ing the label! on the top o# the bed 7!i(e o# the parti$le! P 0.,-2, . 1062
and diameter o# the bed P B.3- 1062
ℜ= pw Qd d
u A(1−ε )
4/5
ℜ=
1000 Kg
m3 Qd 0.9829.10
−2
10−3
! (6.35.10−2)2
4(1−0.137)
=3596343.842 Qd
For a %owrate Sd o# 1.1 Q 106- in bed 1 #or example the Re"nold! number
would be
Re P 3-,B33.>2 . 1.1 106- P 3,.-B
1B ) * a g e
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hin long bed
5eight
di&eren$e
7$m
*re!!ur
edi&eren
$e 7*a
Lal'e A
reading7$m
Lal'e ?
reading7$m
Flow
rate A79/min
Flow
rate ?79/min
otal
Flow79/min
otal
Flow inm3/!
106-1., 1,.J- .- 0.1> 0.1> 0.30
3.J 3>.J 10.- 0.33 0.33 0.--
B.- BJ.-, 1-.> 0.> 0.> 0.>0
J.B J,.03 20.1 0.-> 0.-> 0.,B11.1 11-.2 2>.J 0.>3 0.>3 1.3>Gi'en that onl" 'al'e A i! open the total %owrate 7 !um o# the !eparatel"
$on'erted reading! o# 'al'e! A and ? i! eual to the %owrate through 'al'e A.
he otal %owrate i! $al$ulated in the exa$tl" !ame wa" a! with the other taller
and thinner bed.
5owe'er the den!it" o# the bed i! not the !ame. hi! time it i! 1103=g/m3.
here#ore #or the 1 1., 1062 P 1,.JB *a
5eight
di&eren$
e
7$m
*re!!ur
e
di&eren
$e 7*a
Lal'e A
reading
7$m
Lal'e ?
reading
7$m
Flow
rate A
79/min
Flow
rate ?
79/min
otal
Flow
79/min
otal
Flow in
m3/!
106-11. 11>.- 1-.- 0.>- 0.>- 1.21-.3 1-,.10 20., 1.0- 1.0- 1.J-1>.- 1,2.3J 2.3 1.3- 1.3- 2.2-20.J 21-.2- 2J.2 1.- 1.- 2.223.> 2J., 2, 1.-- 1.-- 2.->Gi'en that onl" 'al'e ? i! open the total %owrate 7 !um o# the !eparatel"$on'erted reading! o# 'al'e! A and ? i! eual to the %owrate through 'al'e ?.
5eight
di&eren$e
7$m
*re!!ur
e
di&eren
$e 7*a
Lal'e A
reading
7$m
Lal'e ?
reading
7$m
Flow
rate A
79/min
Flow
rate ?
79/min
otal
Flow
79/min
otal
Flow
in
m3/!
106-2,.1 302.B0 21.> 2.2 0.B 1.3 1., 3.2331.1 323.0 22.3 2B., 0.B- 1.- 2.10 3.-03.2 3--.B3 2B.0 2,.0 0.J- 1.-- 2.30 3.>3
1J ) * a g e
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Gi'en that onl" 'al'e ? i! open the total %owrate 7!um o# the !eparatel"
$on'erted reading! o# 'al'e! A and ? i! eual to the %owrate through 'al'e ?.
0 0.- 1 1.- 2 2.- 3 3.- .-
0
-0
100
1-0
200
2-0
300
3-0
00
Bed ' Pressure dierence agains fowrate
Flowrate in m3s ! 1"#$
Pressure dierence %Pa&
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