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# Crystallization - Questions, Transfer Processes- I, Engineering, Semester Notes | EduRev

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## : Crystallization - Questions, Transfer Processes- I, Engineering, Semester Notes | EduRev

``` Page 1

Crystallization
CH-206: Transfer Processes-l
Department ofChemical Engineering, IITRoorkee
1. Calculate the maximum diameter ofa crystal of KCL that will not grow in a solution of having 5%
supersaturation (C/Cs=1.05) at 200C.Given density ofsolid KCL= 1990kg/m
3
; molecular weight =
74.5g/gmol; solid-liquid interfacial tension =0.030J/m
2
.
2. An MSMPR crystallizer of5m
3
working volume produces crystals ofmass average particle size 1.0
mm. Iftheproduct stream iswithdrawn at arate of4m
3
/h, calculate the crystal growth rate and the
rate ofsecondary nucleation, 80.Themagma density is150kg/ m3,and thetrue density ofthecrystal is
1900kg/ m
3
.Thevolume shape factor is0.6.
3. An MSMPR crystallizer yields crystal of mediam size LM = 0.8mm when a holding time of 1.8h is
maintained. The working volume of the equipment is 5 m
3
, and the suspension density is 150kg
crystals per cubic meter. The crystal have adensity ofpc=2500kg/m
3
and thevolume shape factor is
<pv=0.65.What isthe production rate ofcrystals? Calculate the secondary nucleation rate BO,and the
zero-size population density nO.Alsocalculate themass fraction and thenumber fraction ofthecrystals
smaller than 0.2mm intheproduct.
4. Abatch crystallizer receives 2500kg ofasaturated solution ofsodium chromate at800C.The solution
isseeded with 1.2kg of the crystals (Na2Cr204,10H20) of 70 }lffi average size and cooled to 300C.
About 3%ofthewater present inthe solution evaporates out during thecooling process. What are the
quantity and average size oftheproduct crystals? Ifthecrystallization process takes 6h,calculate the
average growth rate. Given: pc=1480kg/m
3
; <pv=0.45;Cs=125gsalt (anhydrous) per 1000gwater at
80oC,and 88.7gper 1000gwater at30oC.
5. The following size distribution function of the crystal from an MSMPR has been obtained by sieve
analysis data ofasample.
n=nOexp (-L/C-r);nO=4.52 x10
7
(m-
2
)(}lffi)-1; G=2.31X10-8m/s
(a) For an average residence time of 2 h, determine the cumulative mass distribution function, the
dominant sizeLDand themedian sizeLMofthecrystals.
(b) The working volume ofthe crystallizer is2m
3
. Calculate the volumetric rate ofwithdrawal ofthe
product if the dominant size of the product crystals should be 0.6mm. What mass fraction of the
II
crystals willhave asize,below 0.2mm?
6. Crystals ofanaverage sizeof1.1mm have tobeproduced inabatch evaporative crystallizer atarate of
500kg per batch. Thefollowing data and information are given: solubility, Cs=275kgper m
3
solvent;
crystal density, pc=1750kg/m
3
; volume shape factor, <pv=0.95;maximum allowable growth rate, G=6
x 10-
8
m/ s;seed size,Ls=70}lffi; average density ofthesolution =1150kg/ m
3
;maximum allowable
suspension density =180kgper m
3
solution. Determine (a)thebatch time, (b)theevaporation profile,
and (c)theinitial and final evaporation rates.
Page 2

Crystallization
CH-206: Transfer Processes-l
Department ofChemical Engineering, IITRoorkee
1. Calculate the maximum diameter ofa crystal of KCL that will not grow in a solution of having 5%
supersaturation (C/Cs=1.05) at 200C.Given density ofsolid KCL= 1990kg/m
3
; molecular weight =
74.5g/gmol; solid-liquid interfacial tension =0.030J/m
2
.
2. An MSMPR crystallizer of5m
3
working volume produces crystals ofmass average particle size 1.0
mm. Iftheproduct stream iswithdrawn at arate of4m
3
/h, calculate the crystal growth rate and the
rate ofsecondary nucleation, 80.Themagma density is150kg/ m3,and thetrue density ofthecrystal is
1900kg/ m
3
.Thevolume shape factor is0.6.
3. An MSMPR crystallizer yields crystal of mediam size LM = 0.8mm when a holding time of 1.8h is
maintained. The working volume of the equipment is 5 m
3
, and the suspension density is 150kg
crystals per cubic meter. The crystal have adensity ofpc=2500kg/m
3
and thevolume shape factor is
<pv=0.65.What isthe production rate ofcrystals? Calculate the secondary nucleation rate BO,and the
zero-size population density nO.Alsocalculate themass fraction and thenumber fraction ofthecrystals
smaller than 0.2mm intheproduct.
4. Abatch crystallizer receives 2500kg ofasaturated solution ofsodium chromate at800C.The solution
isseeded with 1.2kg of the crystals (Na2Cr204,10H20) of 70 }lffi average size and cooled to 300C.
About 3%ofthewater present inthe solution evaporates out during thecooling process. What are the
quantity and average size oftheproduct crystals? Ifthecrystallization process takes 6h,calculate the
average growth rate. Given: pc=1480kg/m
3
; <pv=0.45;Cs=125gsalt (anhydrous) per 1000gwater at
80oC,and 88.7gper 1000gwater at30oC.
5. The following size distribution function of the crystal from an MSMPR has been obtained by sieve
analysis data ofasample.
n=nOexp (-L/C-r);nO=4.52 x10
7
(m-
2
)(}lffi)-1; G=2.31X10-8m/s
(a) For an average residence time of 2 h, determine the cumulative mass distribution function, the
dominant sizeLDand themedian sizeLMofthecrystals.
(b) The working volume ofthe crystallizer is2m
3
. Calculate the volumetric rate ofwithdrawal ofthe
product if the dominant size of the product crystals should be 0.6mm. What mass fraction of the
II
crystals willhave asize,below 0.2mm?
6. Crystals ofanaverage sizeof1.1mm have tobeproduced inabatch evaporative crystallizer atarate of
500kg per batch. Thefollowing data and information are given: solubility, Cs=275kgper m
3
solvent;
crystal density, pc=1750kg/m
3
; volume shape factor, <pv=0.95;maximum allowable growth rate, G=6
x 10-
8
m/ s;seed size,Ls=70}lffi; average density ofthesolution =1150kg/ m
3
;maximum allowable
suspension density =180kgper m
3
solution. Determine (a)thebatch time, (b)theevaporation profile,
and (c)theinitial and final evaporation rates.
(j)
r--
~ &:u'b/:'§- T~\$C5Y1 ~.'">.
~ CC/(s) ~ :2cr Mw
RT Pc Y
)/C, " /.0[; , rr ;:: o· 0 .3" ::JI'm'V , M,;)" 71,· S" Ioti/I?~
R. ~ g. 3/"{ k'J/k~''<'
T::: as:; 2>. '). K ) Pc;: /990 ~ ~/'rn3
â€¢
- ,
A ¥f~ cJ P tJ.-;y~/-ic!~
kt ~U ~ J~
5f Y~'f/<.8 Y ==- /9 ~ Oy
I Y"I ct r;; f5f"'- ?Jr c:: I.O.J G- .
Ay~
II II
II
1/
)
L
Q
~ /2(Gr(j
Lfy, = *(611;)
~ Jv!, /5 ~ .-/-o~ ~~ ~ ~ ?7~J-/cn~ p~~:J- v1~
1- ~~l\un C~~31'tn-r ~'ly) Dt-vv£ CPu IS ~ VlJe~
.9Mf '- frr-.e-~ L.}-/1T ~ b "P~ e- n°(C,'0I,.j
Page 3

Crystallization
CH-206: Transfer Processes-l
Department ofChemical Engineering, IITRoorkee
1. Calculate the maximum diameter ofa crystal of KCL that will not grow in a solution of having 5%
supersaturation (C/Cs=1.05) at 200C.Given density ofsolid KCL= 1990kg/m
3
; molecular weight =
74.5g/gmol; solid-liquid interfacial tension =0.030J/m
2
.
2. An MSMPR crystallizer of5m
3
working volume produces crystals ofmass average particle size 1.0
mm. Iftheproduct stream iswithdrawn at arate of4m
3
/h, calculate the crystal growth rate and the
rate ofsecondary nucleation, 80.Themagma density is150kg/ m3,and thetrue density ofthecrystal is
1900kg/ m
3
.Thevolume shape factor is0.6.
3. An MSMPR crystallizer yields crystal of mediam size LM = 0.8mm when a holding time of 1.8h is
maintained. The working volume of the equipment is 5 m
3
, and the suspension density is 150kg
crystals per cubic meter. The crystal have adensity ofpc=2500kg/m
3
and thevolume shape factor is
<pv=0.65.What isthe production rate ofcrystals? Calculate the secondary nucleation rate BO,and the
zero-size population density nO.Alsocalculate themass fraction and thenumber fraction ofthecrystals
smaller than 0.2mm intheproduct.
4. Abatch crystallizer receives 2500kg ofasaturated solution ofsodium chromate at800C.The solution
isseeded with 1.2kg of the crystals (Na2Cr204,10H20) of 70 }lffi average size and cooled to 300C.
About 3%ofthewater present inthe solution evaporates out during thecooling process. What are the
quantity and average size oftheproduct crystals? Ifthecrystallization process takes 6h,calculate the
average growth rate. Given: pc=1480kg/m
3
; <pv=0.45;Cs=125gsalt (anhydrous) per 1000gwater at
80oC,and 88.7gper 1000gwater at30oC.
5. The following size distribution function of the crystal from an MSMPR has been obtained by sieve
analysis data ofasample.
n=nOexp (-L/C-r);nO=4.52 x10
7
(m-
2
)(}lffi)-1; G=2.31X10-8m/s
(a) For an average residence time of 2 h, determine the cumulative mass distribution function, the
dominant sizeLDand themedian sizeLMofthecrystals.
(b) The working volume ofthe crystallizer is2m
3
. Calculate the volumetric rate ofwithdrawal ofthe
product if the dominant size of the product crystals should be 0.6mm. What mass fraction of the
II
crystals willhave asize,below 0.2mm?
6. Crystals ofanaverage sizeof1.1mm have tobeproduced inabatch evaporative crystallizer atarate of
500kg per batch. Thefollowing data and information are given: solubility, Cs=275kgper m
3
solvent;
crystal density, pc=1750kg/m
3
; volume shape factor, <pv=0.95;maximum allowable growth rate, G=6
x 10-
8
m/ s;seed size,Ls=70}lffi; average density ofthesolution =1150kg/ m
3
;maximum allowable
suspension density =180kgper m
3
solution. Determine (a)thebatch time, (b)theevaporation profile,
and (c)theinitial and final evaporation rates.
(j)
r--
~ &:u'b/:'§- T~\$C5Y1 ~.'">.
~ CC/(s) ~ :2cr Mw
RT Pc Y
)/C, " /.0[; , rr ;:: o· 0 .3" ::JI'm'V , M,;)" 71,· S" Ioti/I?~
R. ~ g. 3/"{ k'J/k~''<'
T::: as:; 2>. '). K ) Pc;: /990 ~ ~/'rn3
â€¢
- ,
A ¥f~ cJ P tJ.-;y~/-ic!~
kt ~U ~ J~
5f Y~'f/<.8 Y ==- /9 ~ Oy
I Y"I ct r;; f5f"'- ?Jr c:: I.O.J G- .
Ay~
II II
II
1/
)
L
Q
~ /2(Gr(j
Lfy, = *(611;)
~ Jv!, /5 ~ .-/-o~ ~~ ~ ~ ?7~J-/cn~ p~~:J- v1~
1- ~~l\un C~~31'tn-r ~'ly) Dt-vv£ CPu IS ~ VlJe~
.9Mf '- frr-.e-~ L.}-/1T ~ b "P~ e- n°(C,'0I,.j
O'y I Gr = 0 .S-5 Vh VJ.-, â€¢
J.J-oe).i
rI-i~)
C ~
~
!)h-,3
::=- I· 2. S- ~
d
.â€¢......
.-
tr w>y~
C'YOS t-v---â‚¬
Cr~~
~
~f
ar;=
CJ.S-S- w,w> _
,. 222x/a W»
/. 2S' ~
.Nr~'7J
J>1T;=' I57J
B~~ h 0 61 == (2. It )( /; I) C ,. 2-22 XI; 7)
~/'»,3.!
B" == 2.?3'3 }Oo'l ~",3.s.l
Page 4

Crystallization
CH-206: Transfer Processes-l
Department ofChemical Engineering, IITRoorkee
1. Calculate the maximum diameter ofa crystal of KCL that will not grow in a solution of having 5%
supersaturation (C/Cs=1.05) at 200C.Given density ofsolid KCL= 1990kg/m
3
; molecular weight =
74.5g/gmol; solid-liquid interfacial tension =0.030J/m
2
.
2. An MSMPR crystallizer of5m
3
working volume produces crystals ofmass average particle size 1.0
mm. Iftheproduct stream iswithdrawn at arate of4m
3
/h, calculate the crystal growth rate and the
rate ofsecondary nucleation, 80.Themagma density is150kg/ m3,and thetrue density ofthecrystal is
1900kg/ m
3
.Thevolume shape factor is0.6.
3. An MSMPR crystallizer yields crystal of mediam size LM = 0.8mm when a holding time of 1.8h is
maintained. The working volume of the equipment is 5 m
3
, and the suspension density is 150kg
crystals per cubic meter. The crystal have adensity ofpc=2500kg/m
3
and thevolume shape factor is
<pv=0.65.What isthe production rate ofcrystals? Calculate the secondary nucleation rate BO,and the
zero-size population density nO.Alsocalculate themass fraction and thenumber fraction ofthecrystals
smaller than 0.2mm intheproduct.
4. Abatch crystallizer receives 2500kg ofasaturated solution ofsodium chromate at800C.The solution
isseeded with 1.2kg of the crystals (Na2Cr204,10H20) of 70 }lffi average size and cooled to 300C.
About 3%ofthewater present inthe solution evaporates out during thecooling process. What are the
quantity and average size oftheproduct crystals? Ifthecrystallization process takes 6h,calculate the
average growth rate. Given: pc=1480kg/m
3
; <pv=0.45;Cs=125gsalt (anhydrous) per 1000gwater at
80oC,and 88.7gper 1000gwater at30oC.
5. The following size distribution function of the crystal from an MSMPR has been obtained by sieve
analysis data ofasample.
n=nOexp (-L/C-r);nO=4.52 x10
7
(m-
2
)(}lffi)-1; G=2.31X10-8m/s
(a) For an average residence time of 2 h, determine the cumulative mass distribution function, the
dominant sizeLDand themedian sizeLMofthecrystals.
(b) The working volume ofthe crystallizer is2m
3
. Calculate the volumetric rate ofwithdrawal ofthe
product if the dominant size of the product crystals should be 0.6mm. What mass fraction of the
II
crystals willhave asize,below 0.2mm?
6. Crystals ofanaverage sizeof1.1mm have tobeproduced inabatch evaporative crystallizer atarate of
500kg per batch. Thefollowing data and information are given: solubility, Cs=275kgper m
3
solvent;
crystal density, pc=1750kg/m
3
; volume shape factor, <pv=0.95;maximum allowable growth rate, G=6
x 10-
8
m/ s;seed size,Ls=70}lffi; average density ofthesolution =1150kg/ m
3
;maximum allowable
suspension density =180kgper m
3
solution. Determine (a)thebatch time, (b)theevaporation profile,
and (c)theinitial and final evaporation rates.
(j)
r--
~ &:u'b/:'§- T~\$C5Y1 ~.'">.
~ CC/(s) ~ :2cr Mw
RT Pc Y
)/C, " /.0[; , rr ;:: o· 0 .3" ::JI'm'V , M,;)" 71,· S" Ioti/I?~
R. ~ g. 3/"{ k'J/k~''<'
T::: as:; 2>. '). K ) Pc;: /990 ~ ~/'rn3
â€¢
- ,
A ¥f~ cJ P tJ.-;y~/-ic!~
kt ~U ~ J~
5f Y~'f/<.8 Y ==- /9 ~ Oy
I Y"I ct r;; f5f"'- ?Jr c:: I.O.J G- .
Ay~
II II
II
1/
)
L
Q
~ /2(Gr(j
Lfy, = *(611;)
~ Jv!, /5 ~ .-/-o~ ~~ ~ ~ ?7~J-/cn~ p~~:J- v1~
1- ~~l\un C~~31'tn-r ~'ly) Dt-vv£ CPu IS ~ VlJe~
.9Mf '- frr-.e-~ L.}-/1T ~ b "P~ e- n°(C,'0I,.j
O'y I Gr = 0 .S-5 Vh VJ.-, â€¢
J.J-oe).i
rI-i~)
C ~
~
!)h-,3
::=- I· 2. S- ~
d
.â€¢......
.-
tr w>y~
C'YOS t-v---â‚¬
Cr~~
~
~f
ar;=
CJ.S-S- w,w> _
,. 222x/a W»
/. 2S' ~
.Nr~'7J
J>1T;=' I57J
B~~ h 0 61 == (2. It )( /; I) C ,. 2-22 XI; 7)
~/'»,3.!
B" == 2.?3'3 }Oo'l ~",3.s.l
N~Ci:
- 34-!s pO~Srl'bl.R.. tz, ~ ~ ~/~tL";t'tTn ~- /]'
~ ~ ,?~/~ hO ~ G't.
N blL ~ ~~ h-o.1 cr-(J5~ nj ~
L
L:=D to L~L [, f]
(Ie N ~ ,.,ell
L~o
4':": nf SV'8f~;on .
130 ~ YtA-e-/~'~ ~- B
O
is ~ ~ ~ ~Jr~
z'r c~(p~ ~ 1- V~~~~ -r~ .9-t'.z£...
~
..
Page 5

Crystallization
CH-206: Transfer Processes-l
Department ofChemical Engineering, IITRoorkee
1. Calculate the maximum diameter ofa crystal of KCL that will not grow in a solution of having 5%
supersaturation (C/Cs=1.05) at 200C.Given density ofsolid KCL= 1990kg/m
3
; molecular weight =
74.5g/gmol; solid-liquid interfacial tension =0.030J/m
2
.
2. An MSMPR crystallizer of5m
3
working volume produces crystals ofmass average particle size 1.0
mm. Iftheproduct stream iswithdrawn at arate of4m
3
/h, calculate the crystal growth rate and the
rate ofsecondary nucleation, 80.Themagma density is150kg/ m3,and thetrue density ofthecrystal is
1900kg/ m
3
.Thevolume shape factor is0.6.
3. An MSMPR crystallizer yields crystal of mediam size LM = 0.8mm when a holding time of 1.8h is
maintained. The working volume of the equipment is 5 m
3
, and the suspension density is 150kg
crystals per cubic meter. The crystal have adensity ofpc=2500kg/m
3
and thevolume shape factor is
<pv=0.65.What isthe production rate ofcrystals? Calculate the secondary nucleation rate BO,and the
zero-size population density nO.Alsocalculate themass fraction and thenumber fraction ofthecrystals
smaller than 0.2mm intheproduct.
4. Abatch crystallizer receives 2500kg ofasaturated solution ofsodium chromate at800C.The solution
isseeded with 1.2kg of the crystals (Na2Cr204,10H20) of 70 }lffi average size and cooled to 300C.
About 3%ofthewater present inthe solution evaporates out during thecooling process. What are the
quantity and average size oftheproduct crystals? Ifthecrystallization process takes 6h,calculate the
average growth rate. Given: pc=1480kg/m
3
; <pv=0.45;Cs=125gsalt (anhydrous) per 1000gwater at
80oC,and 88.7gper 1000gwater at30oC.
5. The following size distribution function of the crystal from an MSMPR has been obtained by sieve
analysis data ofasample.
n=nOexp (-L/C-r);nO=4.52 x10
7
(m-
2
)(}lffi)-1; G=2.31X10-8m/s
(a) For an average residence time of 2 h, determine the cumulative mass distribution function, the
dominant sizeLDand themedian sizeLMofthecrystals.
(b) The working volume ofthe crystallizer is2m
3
. Calculate the volumetric rate ofwithdrawal ofthe
product if the dominant size of the product crystals should be 0.6mm. What mass fraction of the
II
crystals willhave asize,below 0.2mm?
6. Crystals ofanaverage sizeof1.1mm have tobeproduced inabatch evaporative crystallizer atarate of
500kg per batch. Thefollowing data and information are given: solubility, Cs=275kgper m
3
solvent;
crystal density, pc=1750kg/m
3
; volume shape factor, <pv=0.95;maximum allowable growth rate, G=6
x 10-
8
m/ s;seed size,Ls=70}lffi; average density ofthesolution =1150kg/ m
3
;maximum allowable
suspension density =180kgper m
3
solution. Determine (a)thebatch time, (b)theevaporation profile,
and (c)theinitial and final evaporation rates.
(j)
r--
~ &:u'b/:'§- T~\$C5Y1 ~.'">.
~ CC/(s) ~ :2cr Mw
RT Pc Y
)/C, " /.0[; , rr ;:: o· 0 .3" ::JI'm'V , M,;)" 71,· S" Ioti/I?~
R. ~ g. 3/"{ k'J/k~''<'
T::: as:; 2>. '). K ) Pc;: /990 ~ ~/'rn3
â€¢
- ,
A ¥f~ cJ P tJ.-;y~/-ic!~
kt ~U ~ J~
5f Y~'f/<.8 Y ==- /9 ~ Oy
I Y"I ct r;; f5f"'- ?Jr c:: I.O.J G- .
Ay~
II II
II
1/
)
L
Q
~ /2(Gr(j
Lfy, = *(611;)
~ Jv!, /5 ~ .-/-o~ ~~ ~ ~ ?7~J-/cn~ p~~:J- v1~
1- ~~l\un C~~31'tn-r ~'ly) Dt-vv£ CPu IS ~ VlJe~
.9Mf '- frr-.e-~ L.}-/1T ~ b "P~ e- n°(C,'0I,.j
O'y I Gr = 0 .S-5 Vh VJ.-, â€¢
J.J-oe).i
rI-i~)
C ~
~
!)h-,3
::=- I· 2. S- ~
d
.â€¢......
.-
tr w>y~
C'YOS t-v---â‚¬
Cr~~
~
~f
ar;=
CJ.S-S- w,w> _
,. 222x/a W»
/. 2S' ~
.Nr~'7J
J>1T;=' I57J
B~~ h 0 61 == (2. It )( /; I) C ,. 2-22 XI; 7)
~/'»,3.!
B" == 2.?3'3 }Oo'l ~",3.s.l
N~Ci:
- 34-!s pO~Srl'bl.R.. tz, ~ ~ ~/~tL";t'tTn ~- /]'
~ ~ ,?~/~ hO ~ G't.
N blL ~ ~~ h-o.1 cr-(J5~ nj ~
L
L:=D to L~L [, f]
(Ie N ~ ,.,ell
L~o
4':": nf SV'8f~;on .
130 ~ YtA-e-/~'~ ~- B
O
is ~ ~ ~ ~Jr~
z'r c~(p~ ~ 1- V~~~~ -r~ .9-t'.z£...
~
..
ryo~ir-cn ~ =' ~ - -NT ~0 -:171E ~3) (tS7J ~)
:: '-t!'I Po/h '
-M~\OlN1
vr:t..e )
Lf-1
C).g
rv.n-.
=
3. (, 1- Gry
â€¢
(::/.£'-l .
- J
~'t
t).~ IN! /NJ
~~ X'ID w,
?-) G,
- -
C2 ·6 :r)(I, fi-)
3 .{,'1
(
.,-9
Mis. ~)
Gr~
3·3£1,
X /0
?-)
o
h -
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