عمليات الفصل التطبيقي

אאאא

٢٥٦٢٥٦

א ٢٥٦

אא

،،אא،אW

אא א א א אאאאאא،אאאאאאא

אאאא אאאאאאאWא

אאK

אאאאאאא א ،א אא

אאאאאא،אאא א ،א אא א א אא א א א א א א א

אא،אאאא،אK

א א ?א א ? ? ?אאאאאאאאK

אאאאאאא،א ،א א אא

אאאאאK

؛ א אא אאK

אאאא

א ٢٥٦

אא

אאאאא

אאאאאא،אאאאא

KאאאאFUnit operationsEאא،אאא Jאאאא،אאאא

אאאאאאאאאאאאאאאאאאאאK

אאאאאאאאאאאאאאא

אאאאK אאאאא

אאאאאאא،אאאאאא

אאאאאאאאאאא

،אאאאאאאאאאאאאאא

אאאאאאאא

אאאאאאאאאאאאאK


א،אאאאאאאאאאאאאא

א ٢٥٦

אא

אאאאאאאא،אאאאאא

אא، אאאאאאאאאאK

אאאא

אאאא

א

א

١

א ٢٥٦ אא אא אא

- ١ -

אאW אא

אאW

אאאW ١K אאאK ٢K אאאK ٣K אאאאאאא

אאאאK ٤K אאאאאK ٥K אאאאK

אאאW

אא٨٠K٪

אאW אאK

אאW אאאאK

אאW

אאאאאאאאאאK


- ٢ -

אאWאאSettling & Sedimentation

א؟ אאא

א،אאK אאW

אאאא ١ J אאאאאאא

אK ٢ J אאאאK ٣ J אאא

אאאאK ٤ J אאאאא

אאאאאאאאאאאאאאאאאא

אK אW

،אאFFree settlingEאאאאאאאאאא

אאK אאW

אאאאאאאאאאאאאאאא

אK אאאאאא

1:200אא0.2%אK


- ٣ -

אאא Motion of a Rigid Particle Through a Fluid

אאאאא

אאאאאאאאאאאא

אאK אmאv

אאρPאρ אא

cg g

mgF =

א

P

gmFρρ

=

א FD

AVCF DD ρ2

2

=

CDWאאא AWאאאאאאאK

אאאFg-Fb-FDאאא

Fg-Fb-FD =dtdVm

dtdV

א


- ٤ -

א

C

D

CPC gAVC

ggm

ggm

dtdVm

2

2ρ

ρρ

−−=

אאא،אאאא

אאאאא15L1אאאאאא

אVtFTerminal Falling VelocityEאאFFree Settling VelocityKE

אאW

אאאא=0dtdv

אא

( )

ρρρρ

DP

Pt CA

mgV −=

2

אאא

6

3PPDm ρπ

= DPא

א

( )ρ

ρρ

D

Ppt C

gDV

34 −

=


- ٥ -

אCDאאאW אאאאא

CDKאאאאאא

µρ Pt DV

=Re

µ א אאא،אCD

אאאאאאאאאא،אאא(wakes)

אאאאא،CDאאאאאא

אאF١Eא~1000

F1Eאא

10002×105אא105×3

אאאאאאאאא،א

אאאאאאאאאאאאאאאאאאא،


- ٦ -

אאאאCDאאF2EאאאK

אאאRigid Spheres אאRe < 1

Re24

=DC א

( )ρ

ρρ

D

Ppt C

gDV

34 −

=

( )µ

ρρ18

2−= PP

tgDV

אא

אאאאאאא،אאא1000 < Re < 2×1050.44 = CDאאא

CDאאאאאאK אאCDא

אאאאאאאאאאF١EאאאK


- ٧ -

אאאא Behaviour of very fine particles אאאאאאאאאא

אאאאאK

אאאNon rigid sphere

אאאאאאאאאאאFinternal circulationE،א

אאאאאאאאאאאאאאאאאאW

• אאאRe = 50K • אאאאאRe = 100K Re = 10Kאאאא •

אאHindered settling אאאאאאאאא

אאא،אאאאא،אאא

אאאאאאאאא

אאאאאאא،אאאW

אµאµm

pm ψ

µµ =

ψp

) 1( 8.1 2

101

εψ

−=p


- ٨ -

εאאאאאρאmρ

( )( )[ ]

( )ρρε

ρεερρρρ

ρεερρ

−=

−+−=−

−+=

p

ppmp

pm

1

1

אאאאµρρ −pmµmp ρρ −א

ε

( )µ

ψρρε18

22ppp

t

Dgv

−=

אאאpψε 2

אא

εµρ

m

mtpVD=Re

( )2

23

18µεψρρρ pmppgD −

=

אאאRe < 1K


- ٩ -

אEquipment for settling ١K אאSimple Gravity Settling Tank


אאאאאאאאK

אGravity Settling Chamber אאאאאאאאא

א،אאאאאFResidence timeEאאאאאא

אאאאאאאאאאאאאא

אאאאאK

a i r o u t

F٢Eא

אאא


- ١٠ -

F٣Eאא

אFHEאאאא

אאאאאאאאאאאאאאאאאאא

אאאK

אSedimentation אאאאא

אא،אאאFThickenerEאאאK

אThickener

אא،אאאאאאאאא،אאא

אא،אאאאא،אאאא


- ١١ -

אאאאאאאאאKאאאא

אא،אאאאאאאא


F٤Eא

א


אאאא،אאאאא

אאW ( )

ρρ

c

s

VCUYQA 00 −

=

Q0=אא Y =אאאאא U =אאאאאאא C0 =אאאא


- ١٢ -

VC =א

sρ =אא ρ =א אאאאאא

אאאW

⎟⎟⎠

⎞⎜⎜⎝

⎛+= X

Awth S

S

R

ρρ

ρ1

tRאאK XאאאאאK WאאאאK


- ١٣ -

אא F١FEאאE

20 µmאא37.8 0C 101.3 RPa،א900אkg /m3،אאאאאאא

=1.137kg/m3 1.9×10-5 Pa.sK אW

( )ρ

ρρ

D

PPt C

gDV

34 −

=

אאאאאאאאCD

אW

( )ρ

ρρ

D

PPt C

gDV

34 −

=

אCDאאאCDאאאאאK

5

3

5

3

100.2

/900.1090.1

/137.1

−

−

×=

=

×=

=

P

P

D

mkgsPa

mkg

ρ

µ

ρ

µρ PtDVN 1=


- ١٤ -

)1(137.11020

109.15

5

LLL××

××= −

− NVt

אאW

( )

2

5

137.1310208.9137.19004

tV××××−

=−

)2(207.02 LLL

tD V

C =

אאRe=100

F١EVt=83.54 m/s F٢ECD=2.965×10-5

אא1=CD אCDאאReF

CDאEאאאW

א=

CD א×CD א × 100

א CD

אCD Vt Re

CD א

99.9 12.465×10-583.542 10085.120029.616 0.083 0.1251700 1316.26 0.0125 0.015

1.283000 2961.6 8.354×10-30.01Re0.01אאF١E8.3×10-3 m/s = Vt

( )ρ

ρρ23

4

t

PPD V

gDC −=


- ١٥ -

F٢FEאאאאE אאאאאא6-4א m×1.554

2647 kg/m3א60א %Kא9980א kg/m3 1.005×10-3 Pa.sK

אW εאא

( )( ) ( )( )

205.0) .6220 - 1 ( 82.110

1) - 1 ( 82.110

1/1553

2467622.01998622.0

12467

6099840

99840

3

===

=

−+=

−+=

+=

εψ

ρεερρ

p

pm

mkg

( )

( ) ( ) ( )( )

sm

gDV mpP

t

/10525.110005.118

205.0622.0 9982467 10554.1807.918

3

3

224

2

−

−

−

×=

××−×

=

−=

µρρρ

אאRe

( )( ) ( )

( )1121.0

622.0 205.0/10005.11553 10525.1 10554.1

/Re

3

34

<=×

××=

=

−

−−

εψµρ

p

mtpVD

אK


- ١٦ -

F٣FEE 5kgאkgאאא

1.5kgkgאאא،אאאאאאאW

אFkg water \ kg solidE2.5 3.1 3.7 4.2 5.0 א (mm/s) 0.050 0.070 0.094 0.12 0.20

אאא1.33kg/s؟אאא אW

( )

ρρ

C

S

vCUYQA 00 −

=

3

00

/10005.1

/33.1

mkgU

skgCQ S

=

==

ρ

ρ

אאאא

Wאא Y vC ( /s) Y-U A m2 5 0.2 3.5 23.28

4.2 0.120 2.7 29.93 3.7 0.094 2.2 31.12 3.1 0.070 1.6 30.4 2.5 0.050 1.0 26.6

אא31.12 m2אאK


- ١٧ -

١ Jאkg/m37500א0.5m/sאאאKאא ٢ Jאאא101 k , 294 kאא200 µmא900 kg \ m3

K • ؟אאא • אאאא0.457א m؟ ٣ J5 kg water/kg solidsאא

1.5 kg water/kg solidsאאאאאW

א(kg water/kg solids)2.5 3.1 3.7 4.2 5 2 1.2 0.94 0.70 0.50א (m/h)

אא0.6א kg/s؟אאא


- ١٨ -

אאWא Filtration א؟

אאאאאאאאאאאFFiltrateEא

אאא،אאאK אא

אאא،אאאאאאאא

אאאאא،אאאאאאאאא

אאאאK א

אאאאאאאאאאאאFאEאא،א

אאאאF٥EאK

F٥Eא

אאא אFVacuum Eאאאאא

אאאאאאאאאא،אאאאאאא


- ١٩ -

אאאאאאאאאK

אFiltration Theory אאאאאW

١E אאאK ٢E אK ٣E אאK ٤E אאאאK ٥E אאאאאאאאK

אאאאאאאאאא

אאאא،אאאאאאאא،אאאאא

אאאאW

( )3

1 21

εεµ OC SVk

LP −

=∆−

\ k1אאK

µ אאK vאאK

εאאאK LאאK

SOאאאאאאאK ∆PCאאאאאK


- ٢٠ -

AdtdV

V =

dtdV

=אK A=אK

= VאאK

( )3

221 1

εµε LSk

PAdtdV

O

C

−∆−

=

LvאאאאאW

( ) VCAL SP =− ρε 1

CSאאאאK

Pρאא Lאא

( )A

VCSkP

dtAdV

P

SO

c

2

21 1

ερµε−

∆−=

)1(LLL

AVC

PdtA

dVS

c

µα∆−

=

αאא


- ٢١ -

( )3

21 1

ερεα

P

OSk −=

אאאאאאאא

)2(LLLm

f

RP

dtAdV

µ∆−

=

Rmא ∆Pfאאאא

אאF١EF٢Eאאאא

)3(LLL

⎟⎟⎠

⎞⎜⎜⎝

⎛+

∆−=

mS R

AVC

pdtA

dVα

µ

Cf PPP ∆+∆=∆K

אאאאα אא

( )

3

21 1

ερεα

P

OSk −=

אאאאאεאSOαאאא εα،אאא αא∆P


- ٢٢ -

אאα∆P

( )5PB ∆−=α

S1Bא אS0.1-0.8

א

אאאאאא

)3(LLL

⎟⎟⎠

⎞⎜⎜⎝

⎛+

∆−=

mS R

AVC

pdtA

dVα

µ

אא

( ) ( ) BVKRPAPA

VCdVdt

PmS +=

∆−+

∆−=

µαµ2

( )

( )PAR

B

PAC

K

m

SP

∆−=

∆−=

µ

αµ2

אאאאא

α


- ٢٣ -

( )

VBVKt

dvBVKdt

P

V V

P

+=

+=∫ ∫2

0 0

2

BVKVt P +=

2

אאאVtV

Vt

V

tא VאאאtK אאאαאאא

אא (Rm)K

אConstant Rate Filtration אאאא

אאF3EאW

Slope = kp \ 2

Intercept = B


- ٢٤ -

⎟⎟⎠

⎞⎜⎜⎝

⎛=

⎟⎟⎠

⎞⎜⎜⎝

⎛=

+=⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛=∆−

dtdV

AR

C

dtdV

AC

K

CVKdtdV

AR

VdtdV

AC

P

m

SV

VmS

µ

αµ

µαµ

2

2

KVC1א אאאF-∆PEV

אאאאK אאContinuous Filtration


אRmאאאאא

VKdVdt

P=

2

20 0

VKt

dVVKdt

P

t V

P

=

=∫ ∫

אאאFiltration Practice אאאאW

١ J אא،אאאאאאאאא


- ٢٥ -

אאא،אאאאאאאא،אאאא

אאאאאאK ٢ J אאאאאאאאא


אאK ٣ J אאא


אאאאאאא،אאאא

אאאאא،אאאK

٤ J אאאא،אאאא

א10-210אK אFiltration Equipment


אאאאאאאא

אאKאאאאאאאאאאא

אאאאאK


- ٢٦ -

אאא F٦Eאאאאא

אאאאאאאאאא،אא

אאאאאאאאאאאא،א


אK

F٦Eאאא

אאאאPlate and Frame Filter Press

אאאאאא،אאאאאא،א

אאאאאאאאאאאאאאא،א

אאאאאאאאא،אאאאאאא

אאאאאאאאאאאאאאאאK


- ٢٧ -

F٧EאF٨Eאאאאא،אא

אאאאאאאאאאא،אאאאא

אK

f i l t r a t e

F٧Eאא


אאאאאאK


- ٢٨ -

F٨Eאא

אאאאאContinuous Rotary vacuum Filter


אאאאאאאא

אאKאאאאאאאאאאאא

אא،אאאאאאאאאאאא

،אאאאאאא،אאאאאאאאאאאאאאא

אF٩EאאאאאאK


- ٢٩ -

F٩Eאאאא


- ٣٠ -

א F١Eאא

אא298.2k338KN/mKאאאאאA = 0.0439mא

CS = 23.47kg/m3אאאαRmאאאW V ( M3 ) t ( s )

0.498×10-34.4 1.00×10-39.5

1.501×10-316.32.000×10-324.6 2.498×10-334.73.002×10-346.13.506×10-359.04.004×10-373.64.502×10-389.45.009×10-3107.3

אW

אאt/VVאאאאאK

א=2PK

6.00×106 s/m6 = 2 ×א =KP אא= B= 6400 s/m3

( )PAC

K SP ∆−

=×= 261000.6

αµ

א =10-4 pa.s×8.937 A = 0.0439 m2


- ٣١ -

( ) ( )

( ) ( )110

3

4

11

3

46

1063.10103380439.0

1093.86400

/10863.1103380439.0

47.2310937.81000.6

−

−

−

×=

××

=∆−

==

×=

×××

=×

mR

RPA

RB

kgm

m

mmµ

α

α


- ٣٢ -

F٢Eאא אאF١E20

0.873m2אאאאF١Eאאאא،אא3.37m3FאאKE

אW אאF١Eאאא:

106 s/m6×KP= 6.00 B= 6400 s/m3

αRmא

6

26

22

211

2

22

21

1

2

2

/93.3720873.0

0439.01000.6

1,1

ms

AAKK

AA

KK

AB

AK

PP

P

P

P

=

⎟⎠⎞

⎜⎝⎛

××=

=

=

∴ αα

( )ms

AABB

/10.1620873.0

0439.064002

112

=×

==

א

( ) ( )( )

s

VBVK

t P

7.269

37.310.1637.3293.372

2

22

22

22

=

+=

+=


- ٣٣ -

F٣Eא אאF٢Eא3.37 m3

26.7 sאאאאא%10א،אאאאא20א m

אאK

( )( ) sm

BVKdtdv

fPf

/10737.110.1637.393.374

1

141

33−×=+

=

+=⎟

⎠⎞

⎜⎝⎛

s19410737.137.31.0

3 =×

×−

א =אHאHא

min73.2760

7.26960

19420 =++

א א=

א


- ٣٤ -

F٤Eאאאא א33%אאF١Eאא67 kpaאאאא0.171א kg solid/k

אאאא2אא298 kא

0.8937×10-3Pa.s996.9 kg/m3Kאא250sאאאא

( ) ( ) 3.091037.4 P∆−×=α אאאאK

אW אאאאאB = 0

2

2VKt P=

t = א = f tc = KP

V2

2

= fאאא

( )( ) ( )

3

3

3

113.039

2

/9.9961067

.108937.0

10225.110671037.4

mkgPaP

sPa

PAC

K SP

=

×=∆−

×=

×=××=

∆−=

−

ρ

µ

α

αµ

filtratem

Csolidkg S

3

אאא


- ٣٥ -

ssolidskgkg

solidkg

/1486.0s

slurry kg 0.778 slurry

191.0

=

×

א =א Jאא

0.778= א kg \ s

אא=אא×2 = 2 × 0.191×0.778

= 0.2972 kg/s א == 0.481 kg/s 0.778 - 0.2972 א=

filtratemsolidkg

C

sm

S 34

34

30810825.4

1486.09.996

481.010825.4

=×

=∴

=×

−

−

אא= 250 = 0.1206 m3 ×4.825×10-4

( )

( )( )

2

32

2

113

2

2

74.610672

1206.00.3

10255.1108937.033.02502

mAA

PAVC

ft Sc

=

×××

×××=×

∆−=∴

−

αµ


- ٣٦ -

אW

١ Jאאc25א46.2 kPaKאאא0.0439 m3אkg solid /m3filtrate

23.47אאאW t (s) V×103(M3)

17.30.541.31.072.01.5108.32152.02.5201.73

٢ JאאאF١Eא30א0.873 m2אאא46.2 kpaאא

א،אאא2.26 m3אFאאEאאא0.283א m3Kאאא

אא30 m.K ٣ Jאאא،אא

2.2 m2א28 %א300 sאאא62 kPaא =0.8937×10-3Pa.sא996.9 kg/m3א

= (4.37×109) (-∆P)0.3α؟אא


- ٣٧ -

אאWאאא Crushing Grinding and Screen Analysis

אParticle Characteristics

אאאאאאאאFSizeE،אFShapeEא(Density)،אאאאF

אאEאK אאאאאאא

،אאאאאK אParticle Size

אFאא-nominal diameter-אאא-equivalent diameter-אE אאא

א،אאאאאK


אK אאאא،אFE

אFScreen sizeE،אא א،אFUltra fine particleEא

FSquare meters/GramKE אParticle Shape

אאאאאאאאאF١٠E،אאאFsphericityE،

Kאאא،א


- ٣٨ -

١W٢W٣W

F١٠EאאK

אФs، אDp

אאאDpW

)1(//

pp

sss VS

VS= Φ

א Vp אW Sp אאW Ss Vs א

אאאW

)2(6

pp

p

SDV

Фs =

אאאFPDE 1אא،אאאא) ( DpאאאאE 1Z.

ФsאאאאאאKאאאאK


- ٣٩ -

אאאW אVp،אאאא،אא

W J אאאאאאK

J אאK אאאאאא

אאK

١W אא25א mm3K

אW ،אאDp،אאK

DpZ6L3πDp א25: Z6L3πDp

W Dp = 3.628 mm

٢W אאאאאאW

J אdL، J LK אW

J אאאW4 LVp = πL3 /4 = πd3

אDpWVs = πDp3 /6

Vp VsW Dp = 1.1447 L

אאאאK אאאWSp = 2*( πd2 /4) + π d L = 6 πL2 /4


- ٤٠ -

אW

pp

p

SDV6

Фs =

W

Фs = 1/1.1447 = 0.874

J

אאאWVp = L3 אDpWVs = πDp

3 /6 Vp VsW

Dp = 1.241 L אאאK

אאאWSp = 6 L2 אW

pp

p

SDV6

Фs =

W

Фs = 1/1.241 = 0.806

אאאא1FDp = LE


- ٤١ -

אאW ،אא

אאאאאK אFMρpEא Dp

،אV،א،A،W

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MVρ

=

)4(6

pps DM

AρΦ

=

אא:Screen analysis

אFSievingEאאא

אאK א א FStandard Screen Series E ،א א א

א،א3 in 0.0015 in ،אאאאFmesh E

א،Fmesh per inch E،אאא FThe Taylor Standard Screen SeriesE ،

א0.074 א mm 200 ،אאאFBritish Standard Screens E ،א אאא אא אאא

FאE ، א אא 41.12א =א א FאKE


- ٤٢ -

אW

אאאאDp،אאp

MρFאL

אE،אVPאFNEאאאאW

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MNρ

=

אאFAEW

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P DMSNA

ρΦ==

(6)אא،א

אא،אאאא،אא

אאאאאאאאאאאאא،

אאאאאFmass fractionEאאאאא،

אאאאאאאאKא

אאK אאאאא

אFmesh size rangeEFRangeEאאאא

14/20 אאאאא14א20אאאאK


- ٤٣ -

n،-1nאא n+1 אKאDpnאאnK

אאnX∆W אאLאאK

אאאFCumulative Analysis E،א

א א א א אK

KXאאW

)7(1

21 n

NT

nnTX ∆Χ=∆Χ++∆Χ+∆Χ= ∑

=

LL

אאFCumulative Analysis EX DpK


- ٤٤ -

:3 א א K אא

אאW ١ Jאאא، ٢ JאאאFאKE ٣ JאאאW

JאאאFHistogramE JאאFFractional-DistributionE Jאאאאא

אWא א DP Xn

٤ 4.7 ٠ ٦ 3.3 0.2

٨ 2.4 0.05

١٠ 1.7 0.11

١٤ 1.2 ١٨}٠ ٢٠ 0.8 ٢٣}٠ ٢٨ 0.6 ١٥}٠ ٣٥ 0.41 ١٠}٠ ٤٨ 0.30 ٠٦}٠ ٦٥ 0.21 ٠٥}٠

١٠٠ 0.15 ٠٤}٠ ١٥٠ 0.10 ٠٠٥}٠ ٢٠٠ 0.07 ٠٠٣}٠

א J ٠٠٢}٠


- ٤٥ -

אW אאאאא

אXאאFDpKE

אWאK

אDP Xn pD X ٤ 4.7 ٠ J ١ ٦ 3.3 0.2 ٠٥}٤ 0.98 ٨ 2.4 0.05 ٨٥}٢ 0.93 ١٠ 1.7 0.11 2.1 0.82 ١٤ 1.2 ٥}١ ١٨}٠ 0.64 ٢٠ 0.8 ٢٣}٠ ٠}١ 0.41 ٢٨ 0.6 ١٥}٠ ٧}٠ 0.26 ٣٥ 0.41 ١٠}٠ ٥٠}٠ ١٦}٠ ٤٨ 0.30 ٠٦}٠ ٣٦}٠ ١٠}٠ ٦٥ 0.21 ٠٥}٠ ٢٦}٠ ٠٥}٠ ١٠٠ 0.15 ٠٤}٠ ١٨}٠ ٠١}٠ ١٥٠ 0.10 ٠٠٥}٠ ١٣}٠ ٠٠٥}٠ ٢٠٠ 0.07 ٠٠٣}٠ ٠٩}٠ ٠٠٢}٠

א J ٠٠٢}٠ ٠٤}٠ ٠

Jאאא אאW

א،אאאDp א،אאאאXn


- ٤٦ -

אאאK

J אאW

אאW אאאא،pD א،אאאX

אא

J אאא אאW

א،אאא אאאאאאאK


- ٤٧ -

אאאK א

אאאאאאאאאKאאא

?א?،אאאאאא،אא،אLאK

3-5-1WאאאW אאאאאאא

אאאK א א א א א א L א

אאW

JאW

( ))8(

/

13

1

3∑=

= NT

npnn

v

DXD


- ٤٨ -

JאW

( )

( ) )9(/

/3

1

3

1

∑

∑

=

== NT

npnn

NT

npnn

s

DX

DXD

JאW

)10(/

/

1

3

1

2

⋅⎟⎠⎞⎜

⎝⎛

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⎝⎛

=

∑

∑

=

=NT

npnn

NT

npnn

L

DX

DXD

JאLאאW

( ))11(...........

/

1

1∑

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= NT

npnn

vs

DXD

אאאWSauter Mean DiameterK

:4

אאאאW J،אא

J،אא J ،אא J K


- ٤٩ -

אW Jאא8W

( )271.0

/

13

1

3==

∑=

NT

npnn

v

DXD

Jאא9W

( )

( ) 314.0/

/3

1

3

1 ==

∑

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=

=NT

npnn

NT

npnn

s

DX

DXD

Jאא10K

108.0/

/

1

3

1

2

=⎟⎠⎞⎜

⎝⎛

⎟⎠⎞⎜

⎝⎛

=

∑

∑

=

=NT

npnn

NT

npnn

L

DX

DXD

Jאא11W

( )645.0

/

1

1

==

∑=

NT

npnn

vs

DXD

אאאאא אאאאאא

،אאאאאאKאא

אאK אאאW


- ٥٠ -

J א א א K

JאאאאK Jא אא א Fאא

אKE JאאאאאK

אFאEאאאאאאאאא

אאאאK א א א א א

אאאאאאאאK


- ٥١ -

אא אא

אKאאאאאאאKאאאאK אאאאאא

אאאאאK אאW

JאWאFMohr' s ScaleEאKאאאא،אאאאאא

אאאK JאאWאאאא

אאאK JאWאאאW5٪ J50K٪ Jא Jא

אWאאאאאאאאאאאאאאK

JאWאאאK

JאאWא JאאאWאאK

אW Jא

אאאFאEK

JאWאאאאאאK


- ٥٢ -

JאWאאאKאאאאאאK

JאWאאאאאאK

JאWאאאאאK אאאאW

JאאאWDodge،אStageאאאא Gyratory Crushers K

Jאאאאא Crushing Rollsא،א Disc Crusherאא،Hammer MillsאאאSingle

Roll CrushersK JאאאאאBall MillK

2-2WאאאGaw Crushers

אאא،אKאאאאא،

אאאאKאאאאאאא

אK

F١١EFאKE


- ٥٣ -

F١٢EFKE

אאאאFאEGyratory Crushers

אאאאאאא

אאאאאאאאK

F١٣EאFאאאKE

אאאW

אאKאא،אא

אאאאאא אאאאאאאK

אאאאאאאK


- ٥٤ -

אאאאאאW אאאא

א،אאאא،אא

אאאאK אאא

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אאא،אאאאK

אאאא،אאאאאאאאאאא

אאאאKאאא،אא

אאאאK אאאW

אאאא ،אאאאא א12125א30٪ J50 ٪אאאK



אאאאאאאאאאאאK


- ٥٥ -

אאאאW אאאאאאא

אאFאאEאאאאאאאאKאאאא

K אאאאאאא

אאאאא אאאK

אאאאאW אאK

אאK אאאאאאאאא،

אא،אאאאאdXאאW

W X WאFmmE

C nWאאא אאאK אאdEאא dXא

אאXK n = 1אאאאאW

)13(2

1

2

1

XXLogK

XXCLnE K==

)12(nXC

dXdE

−=


- ٥٦ -

W KKZ אאאK

אK

אאאKאא

אK

אBONDאאאאn=105אW

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KE B=

ZKBFאאאאאKE

אאאEiFkW.h/tonEאBondא80٪א 100 K

אאאBONDW

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⎞⎜⎜⎝

⎛−Ε=

FPi DDT

P

W אאFhpE ZP

אאאFton/minE ZT

אאאאFftZEPD


- ٥٧ -

אאאאאKאאאאאאאאאאא

אאאאאאW אEi = 9.45

א Ei =11.37 אEi = 8.23

אאEi = 14.3 אא1.34K


- ٥٨ -

אאF١E א10 tons/hrא80٪אאאא

3 in F76.2 mmEא80٪ 1/8 F3.175mmE ؟אאאאFEi =12.68E

אאF٢E

אאאאא0.75 in tons / hr 129.3 hp K אא0.2 in אאא

אא10א tons / hr אאאאא0.15 in ؟

אאF٣E

١אFאEאא؟ ٢؟א אא؟א؟٣ ٤אאאאCD؟ ٥אאFאE؟ ٦אא؟אאאא

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אאא؟١٠ אאאא؟١١ אאאאא؟١٢ א؟אא؟١٣


- ٥٩ -

אאF١E אW

FD= 123

= 0.25 ft

PD = ⎟⎠⎞

⎜⎝⎛

81

/ 12 = 0.0104 ft

iE = 12.68

T= 6010

= 0.167 minton

אא15W

⎟⎟⎠

⎞⎜⎜⎝

⎛−∗∗=

25.01

0104.0168.1246.1

167.0P

∴P Z 24.1 hp = ( 17.96 kW ).

אאF٢E

Bond١٥אW

⎟⎠

⎞⎜⎝

⎛ −=⎟⎠⎞

⎜⎝⎛

75.01

2.0146.1

123.9

iE

אאאW

⎟⎠

⎞⎜⎝

⎛ −=⎟⎠⎞

⎜⎝⎛

75.01

15.0146.1

10 iEP

אאאW

( )kWhpP 63.723.10=


- ٦٠ -

אאF٣E

١אCg

mg،אC

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g

gm×× ρ

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gAVC ρm

אאCDאאאVאPρאאρא،Aאא،gאאאא،

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אאאאאאאאK

٤א CDאאאאאאאאאאאאאאFאא

אאEאאאאאאאאאאא

אK ٥אאאאא

אאFאEאאאK ٦אאאאאאא

אאאאאאאאאאאFאא

אאEאאK ٧אאאאאאאא

אK ٨אאאאאאא

אאאאאK


- ٦١ -

٩אאאאאאאאאאאאאאאאא


אאK ١٠אאK ١١אאאאאאאא

אאאאאאאאאאאKאאאא

אאאאאאאאאאאאKא


אאאאאאK

١٢אאאאאאאאאאאאאאאא

אאאאאאK ١٣אאא

אאאאאK

אאאא

אאאא

א

א

٢


- ٦٢ -

Wאא אאK

אאW

אאאW ١K אאאK ٢K אאאK ٣K אאאאאאא

אאK ٤K אאאאאK ٥K אאאאK

אאאW

אא٨٠K٪

אאW אאK

אאW

אאאאאK

אאW ١ Jאא ٢ Jאאאא


- ٦٣ -

אאWDistillation א

אאאאאא


K אאאאאFMiscible

LiquidsEאאאא–אאFMore volatileE–א،אאאאאאFLess volatileE

Kאא אאא،

אאFRelative volatileKE

אא Types of Distillation אאW

١K אאאא

אאK ٢K אExtractive Distillation אאאאא،

אאאאK ٣K אאאAzeotropic Distillation אאאאאK

אאW


- ٦٤ -

١K Binary Distillation אאK

٢K Multi-component Distillation אאK

אאW ١K Continuous Distillation

אאאאFאEאאאאK ٢K Batch Distillation

אאא،אאאK

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אאאאאאאKאאאא

FEquilibrium DistillationEאאאאאאאK

٢K אאDifferential Distillation אא،אאאK

٣K אאFractionation אאאא

אאאאאאאFRefluxEאאאאFRectificationKE

٤K אאSteam Distillation אאאא

אאאK


- ٦٥ -

אא Differential Distillation

אאאאאFBatch DistillationE אאאאאאא

אאאאK

(14) אאאאFaEFxmEאFbEאא

FybEאא אאאאאאאאא،Kאאאאא

א،אאאאאK

F١٤Eאא JK


- ٦٦ -

אאאDifferential Binary Distillation א(15)אאFwoEFxoE

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אאאF∆yEאאאאF∆xKE אאאאאFWE

FxE Jאא FVE FyE J א FDE FyE.

F١٥Eאא

אאFlash Vaporization

אאFziE

אF١٦EאאאאאאאאאFyiEא

FxiEאאאFyi = kixiEאאK


- ٦٧ -

F١٦Eאא

F١٧Eאאא

אאאא א،אאאאא

אאFEquilibrium DistillationEאאאFSingle Stage DistillationEאאאFflashKE

אאאאאאאאאאאאאאאאאאFMulti Stage

DistillationEאאאאK


- ٦٨ -

א F١٧EאאFzEאFtEאFtfEאאFyE

FxEאאK אF١٧EאאאFtfEאאא

אאFtfEאFtbEאFtdEאאאK

td > tf > tb

אאאWאאאK

א א א אFPb Eא FPdEאאFPfEW

Pd < Pf < Pb

אאאאאא

אאאK אאאאאא

אθFV/FEאאאK

אאאContinuous Fractionation

אאאאאאא،אאאא

א،אאאאאK

אאאאא،אאאא


- ٦٩ -

KאאאאאאFFractionationKEאאאאKאF١٨Eאאאא

אא،אאאK

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אאאאאאאא،אאאאא

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FאאWRefluxEאFOverhead productKE


- ٧٠ -

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sectionKE אאאאאFStripping sectionE

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אאאאאK אאאאאא

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אא،אאK אאאא(Number of Transfer

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- ٧١ -

אאאFDiscreteEFStagewiseE،אאאאאאאאאאK

אאאאאFractionation in Tray Towers אאאאאאא F١٩E

FT-X-YEאאK FzEאאאאא

א JFyEFxEאאאאאא

אאאאאאK


אאK

F١٩Eאאאאא


- ٧٢ -

אאאאאFTubular heat exchangersEאאא

אKאאאאFTotal condenserEאFPartial condenserE

אאאאK אאאאאאאא

אאKאאאאאאאאאK

אאאאאאאאאאאאאא

אאאאאאאאאאאאא

אאאK אאאK


אאאFאאKE אאאא

אFpartial reboilersE،אאאאKאאאFאאאE

אאאאאאאKאאאאאאא

אK

אאExtractive Distillation אאאאאא

אאאאאא،


- ٧٣ -

אאאאאאאאאK

אאאאאאKKאאאא

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אאאאא Jאאא JאK

Kאאאאאאאאאאאא

אK אThe process

א F٢٠Eאאאאא،אאא

F1.01EK

F٢٠Eאאא


- ٧٤ -

אאאאא

אKאאאאאאKאאא

אאאאאאK ،אאא

אאKאאאאאאאK

،،אאאאאאאאאK

אSeparation Equipment

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אאאאאאאאאאאאאאK

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אאא،אאאאאK אאאאאא،אא

אאאאFStage-wise operationsKE


- ٧٥ -

אאאאאW

אאFSieve platesE

אא JFValve platesE

אאאFBubbles cap platesE

אאאא Jא Jאאאאאא

אאFDown comerEאאאאK



אאאK

F٢١Eאא


- ٧٦ -

F٢٢Eאא

אF٢١EאאאאKאF٢٢EאאK

אאאאאא

אK אא

אFHold down boltEאF٢٣EאאאאאאאאאK


- ٧٧ -

F٢٣Eאא

אאא אאאK

א F٢٤Eאאא(Slots)אאא

אא(Vapor riser)אאאאא (Slots)אאאK

F٢٤E


- ٧٨ -

F٢٥Eאא

אF٢٥EאאאאאאאאאאאאKא

אאאאאKKKאאאא אא

FWeirEאאFVapor riserEאאאאאK

אF٢٦EאאאאאאאאאאאאK

אאא،אאאאא א

FMulti pass flowEאאאK


- ٧٩ -

F٢٦Eא אאאאאא

אאאאאאאKKKאFEntrainmentKE

אאאאאKKKאאאKKK


- ٨٠ -

אאFFloodingEאאאאאאאאאאK

אאאW

١E אאאאאאאK ٢E א(Tower diameter) ٣E א(Tray diameter) ٤E א(Weir dimensions) ٥E א (Down comer dimensions) ٦E אא (Nmber of holes in the tray) ٧E א FHole diameterE ٨E אא(Distance between holes) ٩E א(Tray thickness)

אאאאא

אאאאאאאא،אאאאאא،אאאאאאאא

אא،אאאאא،אאאאאK

אאאאאאאאאאאאא،אאא

אא،א،אאאאאא

אאאאK


- ٨١ -

אאאאאאאאא،א

אאאאאאאK

אאאאאאאFPlate EfficiencyKE


- ٨٢ -

אאWאא Centrifugal Separation Processes

אאאאFEא?Force Gravitational?אאאא

אF Fluid Eאאאא،אאאאא

אאאאאאאאK

אW ١ J אאאאאK ٢ Jאאאאאאאא

אאK אאאאא

אאאאאK

אאאאאאאא

אK אאאאאW

אאא،אאא

אאאאאאא(Centrifugal Force)אאאאא אאאאאאא،א

F٢٧EאK


- ٨٣ -

F٢٧EאאFWE،אFEאאא،אFE

אאאK אFEאאאא

אאאאאאאאאאאFEאאא،FE



- ٨٤ -

אא Equations for Centrifugal force אאאא?Acceleration?אאאW

)1(2rwa c = W אאאאW(m/s2) ac אאאW(m) r אאאFWangular velocity E(rad/s) w:

אאFc אאW )2(2mrwmaF cc ==

אא v Fm/sEwW

)3(rvw =

אאW

)4(22

rmv

rvmrF c =⎟

⎠⎞

⎜⎝⎛=

אאא FN: rev/min E

W

)5(60

2 NW π=

)6(260

rvN

π=

אF٢EאF٥EW

)7(01097.060

2 22

mrNNmrF c =⎟⎠⎞

⎜⎝⎛=

π

אאFgW


- ٨٥ -

)8(mgF g =

)9(22

gmw

mgmrw

FF

g

c ==

2WאF٥EW

)10(001118.0 2rNFF

g

c =

FcFgאאא F KKKKKKKKKאFE g forces KE


- ٨٦ -

אאW Equations for Rates of Settling in Centrifuges אאW

אאאאאאאאאאאKאF٢٨Eאא

אאאאאאא Vt (Terminal Velocity )

אאאא،אאbאאrBאא

אr2،אrB < r2אאאאא،אrB = r2אאאאK

אF٢٨EאאאK

אאFLaminar FlowEאVtאr W

)11(18

)( 22

µρρ rwD

v pPt

−=


- ٨٧ -

אW

)12(18

22)(

1

2

r

rLn

wpDPTt µ

ρρ −=

אW

)13()(18

22)( 21

22

1

2⎥⎦⎤

⎢⎣⎡ −

−= rrb

r

rLn

wpDPq πµ

ρρ

אאאאאאF13Eאאא،אאאאא

אK אאאאאאr1r2،

אאאאאאKאאאqc W

)14(2

1

22

)(

21

2218

)(⎥⎦⎤

⎢⎣⎡

⎥⎦

⎤⎢⎣

⎡−

+

−= rrb

rr

rLn

wpcDPcq 2

2π

µ

ρρ

אאאאאאאאאאאK

אאאW

)15(18

)( 222

PpP

t

rwDv Ψ

−= ε

µρρ


- ٨٨ -

אאאאא Centrifuge Equipment for Sedimentation אאא

אF٢٩Eא100 mm150 mmאאאF١٣٠٠

אE15000 rev/min،אאאאא75אmm)EאF60.000 rev/ minEאאא

Fultra-centrifugesE،אאאאאאאאאאאאאאא

אאK

אF٢٩Eאא


- ٨٩ -

אאאא אאאF٣٠Eאאאאא


אאאאאאאאאאKאאאא

אאאאאK

אF٣٠Eאא


- ٩٠ -

W אאאאאW 1 JאW

אאאאאאאF٣١Eאאאאאאאא

אאאאאאאאאK

אF٣١Eאאאא

אאאאאאW

אאאאאאאאF٣٢Eאאא


K


- ٩١ -

אF٣٢Eאאאא

אאאאאאW אאאא

אאאאאאא אאF٣٣Eאא


אF٣٣Eאא


- ٩٢ -

אאW אK

אאK אאאאK

אאאFאאאאKE אאW

F١EאK F٢EאאאאK F٣EאאאK

אאאאW אאאאK

אאאא

אאאאאאאאאא،

אאאאאאF٣٤Eאאאא

אאK

אF٣٤EאאW


- ٩٣ -

W ١ JאאאאK

٢ JאאאאאאאK

J אאאאK J אאאאאאK

٣ Jאאא53.34 m/sאא،r1 = 76.2mm

אאr2 = 305 mmKאאאאאאK אK

٤ J0.05 mmא،אא

א1050 kg/m3א1000 kg/m3א،0.0012 Pa.sKאWr1 = 5 mm،r2 = 30 mm،b = 100.1mmK

אאאK

٥ JאאאW r1 = 5 mm،r2 = 30 mm،b = 100.1mm،N = 2600 rev./minK


- ٩٤ -

אאWאExtraction אW

אאאאא،א

אאFאSolventEאאאאאאאאFExtractFEאEא

אאFSolventEאFraffinateKE אאאאאאא،א

א( Solvent Extraction)אאK אאW

١ J אFacetic acidEאאאאאFאאIsopropyl Ether Eא

א؟א،אאאאK

٢ J אאאאאאאאאאאאאK

אאאאאW J אאאא

J ،אאא J אאא

J–K J אאאאא J אא

אאאאאאא

אאF٣٥אKE


- ٩٥ -

FE

FE

F٣٥EאאFEאא،FKE

אא J Equipment of Liquid- Liquid Extraction

אא Jאאאאאא

אאאKאאאאאאאאאאאאאK

אאאW ١ JאאאאאK ٢ Jאאאא

אKאK


- ٩٦ -

אאאW JאMixer - Setter for Extraction


אאאF٣٦KE אאאאאאאK

FE FE אF٣٦EאאFWE،אFEK

Jאאאאאאאאאאאא Plate and Agitated Tower Contactors for Extraction

אאאאאאאאאאאאאאאאאאF٣٧KE

FE FE אF٣٧EאאFWEאאא،FEאאאK


- ٩٧ -

Jאאאאא Packed and Spray Extraction Tower

אא אא אא א א א אF٣٨אKE

אF٣٨Eאא


- ٩٨ -

3 JאאW אאאkg/hr 100 1 %

FEא200 kg/hr0.05 %אאK

אאא0.1 א %Kאאאאאא30%א؟

אאאאFXEאFYEW

X0.00101 0.00246 0.00500 0.007460.00988 0.02020

Y0.000806 0.0019590.0045400.009820.00904 0.01850

אW

אאאאK L * (X1-X2) = G *(Y1-Y2)

100(0.001-0.001) =200(Y1-0.0005) Y1= 0.0005

JאאאאFXEאFYEאFoperating LineEFEX2, Y2EFX1, Y1EאאאאK


- ٩٩ -

אW אאא=4א

אאא=3.04

=13


- ١٠٠ -

אאאWאאא Absorption of Gaze

א


אאאאאאאאKאאאאאK

אאא אאאאאאאאא

אאKאאאאאאאאא


אאאאאK

אא אאאאא،

אאאאKאאאאאא

אאאאאאאאKאאאאא

אאאאאאאאאאא،אאאאאאאאK


אאאאK


- ١٠١ -

אאEquilibrium Between Liquid and Gas


אאאאאאאKאאאאאאאאאאאאא

אאאאא F = C - P + 2

FWאאאאאK PWאאאK

CWאאK אאCO2אאאא،אא

FCO2،אא،אEאאאW F = 3 - 2 + 2 = 3


אאאאאאCO2אאFxAEאאCO2אאFyAEאאאא

KאאאאאאאאW

PA = H XA PAאאAאאK xAאאAאאK

אאHKאאאאxAאא

אאKאxAPAאאאאאאאאאאאKאאא


- ١٠٢ -

אאאאK

אMechanism of absorption

אאאאאאFtow Film theoryEאאאאאאאא



אאאאאKאאאאאאאאאאאא،


אאאאאאאF٣٩E

F٣٩Eאאאאא

CAi

CAL

PAf

PAi


- ١٠٣ -

אRate of Absorption אאאאאא

אאאאאאאW

NA = kG (PAG - PAi) = kL (CAi- CAL)

NAאAFKmol \ unit Area unit timeE kGאאאאאK Fmol \ unit pressure unit Area unit timeE kLאאאאאK PAGאאאאאK

PAi אאאאאK CAiאאאאK CALאאאאK

אFPAG - PAiEאאאאאאאFCAi -CALEאאאאאאאאא

אאאאאF٤٠E

אF٤٠Eאאא

D

BPAG - PAi

APAG

PAi

PA א

א PAe

CAi - CAL

CAL CAi CAe

אאאא

א


- ١٠٤ -

אא

G

L

ALAi

AiAG

kk

CCPP

=−−

אאאאאאאאא

אאG

L

kk−אאאBאא

kLkGאאאKאאאאאאW

NA = kG (PAG - PAe) = kL (CAe- CAL)

PAeאאאאאCALאאK

CAeאאאאאאא PAGK אאאאאFkC , kLEאא FkG , kLEא

( ) ( )( ) ( )

⎥⎦

⎤⎢⎣

⎡−−

=∴

−=−=−=−=

AiAG

AeAG

GG

ALAeLAeAGG

ALAiLAIAGGA

PPPP

kk

CCkPPkcCkPPkN

11

⎥⎦

⎤⎢⎣

⎡−−

+⎥⎦

⎤⎢⎣

⎡−−

=AeAG

AeAi

GAAG

AiAG

G PPPP

KPPPP

k11


- ١٠٥ -

⎥⎦

⎤⎢⎣

⎡−−

+=

⎥⎦

⎤⎢⎣

⎡−−

⎥⎦

⎤⎢⎣

⎡−−

+=∴

⎥⎦

⎤⎢⎣

⎡−−

=

ALAi

AeAi

LG

AiAG

AeAi

ALAi

AiAG

LGG

ALAi

AiAG

LG

CCPP

KK

PPPP

CCPP

kkk

CCPP

kk

11

111

11

אאא

LGG

ALAi

eAAi

kH

kk

CCPP

H

+=

−−

=

11

אא

GLL kHkk111

+=

א

LG kH

k=

1

אאkGkLאאא kGkLאKא

אאאאאK


- ١٠٦ -

אAbsorption Equipment אאאאאאאא

אאאאאאאאאאאאאאאאאא

אאאאאאאאאאK אאאPacked Columns

אאאאאאאאאK

אאאאאאאאאKא

אאאאאאאKאא

אאאאאאאא75 %אאא

אאF٤١EאאK

F٤١Eאא


- ١٠٧ -

א אאאאאאאא

אאFRingsEאFBerl saddlesEאאאאאאאא


אאאאאאאK

F٤٢Eאא א

אאאאאאKאא

אאאKאאאאאאאKא

אאאאאאאאאאאאאאאאא

אאאאאאאאאאאK


- ١٠٨ -

אאאא Calculation of Height of Packed Columns

אאאאאאאאאd2F٤٣Eא

אאאאאאאאאאאאאאאאאאא

א

AVm dY = A Lm dX

AאK VmאאאאK LmאאFאאאEא

אK YאאאאאאאK

XאאאאאFאאאEאאK

אא

Vm A d Y = NA (a dV) = kG a (PAG - PAi) A d z =kLa (CAi - CAL) A d z

aאאאאאאאK dVא= Adz

אאאאאאאאאאאאאאאאK


- ١٠٩ -

١ Jאאאאאא Height of Columns Based on Condition in Gas Film

( )

YPYP

AdzPPaKAdYV

AAG

AiAGGm

+=

−=

1

PאאאאK

( ) ( )( ) ( )

dZYY

YYaPK

VdZZ

dzYY

YYaPK

dzY

YY

YaPkdYG

Y

Y i

iZ

G

m

i

iG

i

iGm

∫∫ −++

==∴

⎥⎦

⎤⎢⎣

⎡

++−

=

⎥⎦

⎤⎢⎣

⎡+

−+

=∴

2

1

11

11

11

0

אא

)1(2

1

LL∫ −=

Y

Y iG

m

YYdY

aPKVZ

אY<1

٢ Jאאאאאא Height of Columns Based on Conditions in Liquid Film

( )

XCC

CdZCCakdXAL

AT

A

ALAiLm

=−

−=

CAאאאאאFאHאאאECTאאFאHאאאEאא

FאHאאאKE א


- ١١٠ -

( ) ( ) dZX

XX

XaCKdXLi

iTLm ⎥

⎦

⎤⎢⎣

⎡+

−+

=11

( ) ( )

)2(

112

10

LL∫∫ −==

⎥⎦

⎤⎢⎣

⎡

++−

=

X

X iTL

mZ

i

iTL

XXdX

aCkLdZZ

dZXX

XXaCk

٣ Jאאאאא

Height of Column Based on Overd אאאY-YiY-YeKGaKGaאאF١Eא

∫ −=

2

1

)3(Y

Y eG

m

YYdY

aPKVZ LL

אאאXi-XX-XeKLaKLaאאאF٢Eא

)4(2

1

∫ −=

X

X eTL

m

XXdX

aCKLZ LL

ZאאאאאאאKא

אאאK

אאאאאא Absorption of Dilute Gases אy=Y

אא ( )dZyyaAPKGMAdy eG −=∴


- ١١١ -

521

21

22

11

LLxxyy

m

cxmy

cxmy

cxmy

ee

e

e

e

−−

=

+=

+=

+=

אאאאא

( ) ( )

( )

∫ ∫ −=

−−=

−=−∴

z y

y em

G

m

m

mm

yydydz

VaPK

yyLVxx

yyVxxL

0

11

11

2

2

)6(LL

y L

m

m L

V

V y1

x

x

1, m

m


- ١١٢ -

(6)

( ) ( )[ ]( )

( ) cyyLVxmy

cxmy

LmV

ycyyLVxmdy

yydy

m

m

m

m

y

y

y

y mme

−⎥⎦

⎤⎢⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛+−

+−

⎟⎟⎠

⎞⎜⎜⎝

⎛−

=

−+−+=

−∫ ∫

1212

11

11

1

ln1

/

2

1

2

1

(5)(6)

( )

( ) ( )( )( )

( )

( )ln

ln

ln

ln

1

1

21

21

22

11

2211

21

2121

21

21

2112

11

21

21

21

21

eTG

m

e

e

e

ee

eee

e

ee

yyyy

aPKVZ

yyyy

yyyy

yyyy

yy

yyyyxx

xxyyyy

yy

yyxx

xxyy

−−

=∴

−−

=

−−

−−−

−=

−⎟⎟⎠

⎞⎜⎜⎝

⎛−−

−−

−−

−

−−

−−

−=

( )ln21

eTL

m

xxxx

aCKLZ

−−

=

אאא(KGa)(KLa)KG kLaאאאאאאy2 y1x2 x1

10K٪


- ١١٣ -

F١FEE

אאאCO2אא1.333×104 paאא1.133×105 pa،אאא CO2303 kאxACO2؟א

P =H xA

1atm1.333×104 paPA =

105×1.325 = 0.1316 atm

5

4

4

1007.710186.0

1316.0

10186.0

−×=×

=∴

×=

Ax

fractionmolatmH


- ١١٤ -

F٢FEאאE אא0.03 kil H2Skilo molא

א،אH2S1%אאאאא300א kאא،אאYe = 2X،א

אאH2S0.013 k H2Skilo molא،אאא אW

١ JאאK

٢ JאאNOGא

אאy =Y

X 2 = 0

mLmV

1100

* 0.03

2Y

mLX10.013

mVY1

0.03

2 015.0smmolk

aPKsmmolk

G 04.0 2 =

( )eG

m

YYYY

aPKV

Z−−

= 21

( )eG

m

yyyy

aPKVZ

−−

=∴ 21


- ١١٥ -

Ye1 = 2 X1

= 2 x 0.013 Ye2 = 2 X2

= 2 x zero = zero

Vm = 0.015 k mol / sm 2

( ) ( ) ( )

( )

( )

OGOG

e

e

e

e

e

eee

NHZm

Z

YY

YYYY

YYYY

YYYYYY

×==

−=∴

==

⎟⎠⎞

⎜⎝⎛

−=−∴

=−=−=−

⎟⎟⎠

⎞⎜⎜⎝

⎛−−

−−−=−

8.700143.0

0003.003.004.0015.0

00143.059.2

0037.0003.0004.0ln

0003.0004.0003.0

004.0026.003.0

22

11

22

11

2211

= NOGאאK = HOGאאאאאאK


- ١١٦ -

21375.0

8.7

375.08.7

375.004.0

015.0

==∴

×=∴

==

=

OG

OG

G

mOG

N

N

m

aKV

H


- ١١٧ -

F٣FEאE 25 mol %אאאKא

אFאHאאE181.4 mol/h303 kא 1.013×105 paאאKאא

0.005א mol fract אא2 mol %K אW١ JאאאאK

٢ Jאא1.5אK אW

אאאאאאYא

אX

XXX

XXX

yyY

YYy

−=⇒

+=

−=⇒

+=

11

11

2XLm ,X2 = 0.005

X

mV Y1,

0.2511y =

XmL 1,

mV Y1,

y =2 0.02

Y


- ١١٨ -

( )11 ,YX

( X1- Y1 ) אFline operatingEאאאא

אאאאFX2 , Y2EאאLmאאאpאאאא

אF٤٣E

F٤٣E

אpאY-YeY-YiXe-XXi-XK

( ) ( )

( )m

m

m

m

mm

VLYXX

VLY

XXLYYV

11

11

+−=

−=−

y1

y2

x1 x1 max

x2


- ١١٩ -

אאא

אאאxA

אאאyA1 atm

0.01260.0151 0.01670.0201 0.02080.0254 0.02580.0321 0.0309 0.0390 0.04050.0527 0.05030.0671 0.07370.105 0.09600.145 0.1370.235 0.1750.342 0.2100.463 0.2410.597 0.2970.945

אאאאאאאאאא( X2, Y2 )אp

( X2, Y2 )אאאא

005.0 005.01

005.0 1

02.0 02.01

02.0 1

333.0 25.01

25.0 1

2

22

2

22

1

11

=−

=−

=

=−

=−

=

=−

=−

=

XXX

yyY

yyY


- ١٢٠ -

L m \ V m )min( Vm = 0.98×181.4 = 177.8 k mol/h

א= 177.8 Lm=×الميل

∴


- ١٢١ -

א ١ JCO2FאEא303 k0.90×10-4kg CO2 /kg

waterא0.186 atm،אא CO2אאאא؟

٢ Jא0.254 mאאא293k101.3kpa،אאא4.88mאאFE3.30kg

mol/hy1 = 0.01053y2 = 0.0072x1 = 0.0072אFE =9.03kg mol/hאKGa؟

٣ Jאאאא0.015 mol fraction،א

א1%אאאאKאאאFE1kg/m2sאFE1.6kg/m2sKא

אye = 1.75xyeאאאאאxאא؟،אאא


- ١٢٢ -

אאF١E

0.2032 mא1000 rev/minאW J؟אאאאאא

J ؟אאאאאא אאF٢E

אא؟אא١ ٢אא؟אאאאא

א؟ ٣אא؟אאא ٤אאא؟ ٥א؟אא؟אאאא ٦אא؟אאאאא ٧אאאאא؟א ٨אאאאא؟אא ٩אאאאא؟א

١٠؟אאאאא


- ١٢٣ -

אאאF١E FWE אW

N = 1000 rev / min r = 0.2032/2=0.1016 m

אF10EאאאW

אFEW r = 0.2032 m

( )

.2.227

10002032.0001118.0 2

gravities

FF

g

c

=

∗∗=∴

אאF٢E

١אאאאאאאאאאאK

٢אאאאאאאאאאאאא

אאאאאאאK אאאאא


٣אאאאאאאאאאאאאא

אאKאאאאאא

אאאאאאא

( )210001016.0001118.0 ∗∗=g

c

FF


- ١٢٤ -

אאאאאאאאאאא؟אא

٤אאאאאאאאאא

אאאאאאK ٥אאאאאא

PA = H XA PAאאאA XAאאA Hאאאאאאא

אאאאאאאK ٦א

F = C – P + 2 CWא،א3 =אאאאא

אאא PWאאא،א2 =

F = 3 – 2 + 2 = 3 אFאאאאאאאE

3=אאאאאאאאאאאאאK

٧אאאאאאאאאK


אאאאאאאאאאאאאאK


- ١٢٥ -

٨אאאאאאאאא

אאאאאKאאאK ٩אאאא

אאאאKאאאאאאאאא

אאאK ١٠אאאאא


אאאאאKאאאאאאאK

א ٢٥٦ אא אא

- ١٢٦ -

אא

1. GeanKoplise C., J, "Transport Processes and Unit Operations", Mc Graw-Hill Inc., USA, 1993

2. Mc Cabe W., Smith J., Harriot P., "Unit Operation of Chemical

Engineering" 4th Edt. , Mc Graw-Hill Inc., USA, 1985

3. Coulson J. M., Richardson J. E.," Coulson's Chemical Engineering

Series", 4th Edt, Vol.2, Pergamon Press, 1991

4. אא،אאא،٥٩٣٣א J١٩٩١

5. ،،،אא،א،א،אאא،אאא٢٠٠١א

א ٢٥٦ א אא

א

אאWאאSettling & Sedimentation ........................................... - ٢ -

אאא .................................................................................. - ٣ -

אEquipment for settling .................................................................... - ٩ -

אא .............................................................................- ١٣ -

......................................................................................................- ١٧ -

אאWא Filtration ............................................................................- ١٨ -

אConstant Rate Filtration ........................................................- ٢٣ -

א .......................................................................................- ٣٠ -

אW ......................................................................................- ٣٦ -

אאWאאא ..................................................................- ٣٧ -

- ٥٨ -.................................................................................................. F١Eאא

אאF٢E ..................................................................................................- ٥٨ -

אאF٣E ..................................................................................................- ٥٨ -

אאF١E ...........................................................................................- ٥٩ -

אאF٢E ...........................................................................................- ٥٩ -

אאF٣E ...........................................................................................- ٦٠ -

אאWDistillation ٦٣ -.......................................................................... א -

אא Differential Distillation .............................................................- ٦٥ -

אאFlash Vaporization ..................................................................- ٦٦ -

אאWאא ...................................................................- ٨٢ -

אא Equations for Centrifugal force .....................................- ٨٤ -

אאW Equations for Rates of Settling in Centrifuges.- ٨٦ -

אאאאא Centrifuge Equipment for Sedimentation ..- ٨٨ -

W ............................................................................................................- ٩٣ -

א ٢٥٦ א אא

אאWאExtraction .......................................................................- ٩٤ -

אאאW ...........................................................................- ٩٦ -

אאאWאא١٠٠ - ................................................................................ א -

.................................................................................................. - ١١٣ -

א .................................................................................. - ١٢١ -

אאF١E ............................................................................................... - ١٢٢ -

אאF٢E ............................................................................................... - ١٢٢ -

אאאF١E ........................................................................................ - ١٢٣ -

אאF٢E ........................................................................................ - ١٢٣ -

א١٢٦ - ........................................................................................................... א -

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