Sistemas de Separação II - Destilação Binária e Multicomponentes PDF
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Transcript of Sistemas de Separação II - Destilação Binária e Multicomponentes PDF
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!"#$%&' ' )*+%,-./01' 2304'&&0& 567+%40&
8%&9'+-& 1' 8':-3-./0 ;0+0
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LM'+%4-$ 2304'&& ?'&%
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230
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230
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2-3- - &':-3-./0 1' 6+ &%&9'+- M0+0
8%&9'+-& 1' 8':-3-./0 ;0+0%E 8':-3-./0 '+ b"%40 '&9#
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8%&9'+-& 1' 8':-3-./0 ;0+0
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8%&9'+-& 1' 8':-3-./0 ;0+0
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230
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8':-3-./0 '+ T"%40 U&9# &':-3-./0 :03 ]-&M
F = V + L
F z i = V yi + Lx i
yi = K i xi
P-$-".0& R-9'3%-%&>
O'$-./0 1' UD6%$7F3%0>
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Vapor V yi
Feed
Liquid L x i
F zi
y i =zi
V F
+ 1 V F
1K i
x i =zi
(K i 1) V F
+ 1
1( ! " 22 # 3$ ,%4&5$6(78( ! " 2 9:/0 06y i z i /(V/F) V yi F z i
56-"*1-1'909-$ 1'% "-4033'"9' 1'X-:03
56-"*1-1'909-$ 1'% "-4033'"9' 1'-$%+'"9-./0
23-*4-+'"9'c 9010 40+:0"'"9' % D6' '"93- :'$- -$%+'"9-./0 &-% "-4033'"9' 1' X-:03
8':-3-./0 '+ T"%40 U&9#
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230
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?'&*$-./0
1
m
j
k
n
Reboiler
CondenseProduct
Product
Feed
2
n 1
56-"10 - X0$-*$%1-1' 3'$-*X- '"93' 0&40+:0"'"9'& "/0 ` 9/0 :30"6"4%-1-c :01'e&' -%"1- 6*$%,-3 1- &':-3-./0 -93-X`& 10 6&01' 1%X'3&0& '&9#
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?'&*$-./0
;# 1%C'3'"9'& C03+-& 1' :30+0X'3 0 40"9-90 '"93' -& C-&'& $7D6%10 'X-:03 '+ 6+- 40$6"- 1' 1'&*$-./0
(a) Conventional tray. (b) High capacity tray.
ExtendedActiveArea
Downcomer
L L
L L
Active Area
V V
P-"1'f-&N 23-90&
(a) Random or dumped packing. (b) Structured packing.
L L
V V
Y'%90& U+:-409-10&
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?'&*$-./0
(a) Conventional tray. (b) High capacity tray.
ExtendedActive
Area
Downcomer
L L
L L
Active Area
V V
P-"1'f-&N 23-90&
(a) Random or dumped packing. (b) Structured packing.
L L
V V
Y'%90& U+:-409-10&
?%C'3'".- 1' 40+:0&%./0'"93' :3-90& ` Q"%9-N1%&43'9-
?%C'3'".- 1' 40+:0&%./0 -0$0"
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?'&*$-./0
*:0& 1' F6FF$'4-: *:0& 1' X#$X6$-&
+0X%+'"90 10 X-:03 -93-X`&1' 6+ F6FF$'4-:
1%3'4%0"-+'"90 10 X-:03 -93-X`& 10 &$09
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?'&*$-./0
F-"1'f- :'3C63-1-
F-"1'f- 40+ F6FF$'4-:
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:3-90 &6:039' 1''"4M%+'"90
1%&93%F6%103 1'$7D6%10
96F0 :'3C63-10 :-3-1%&93%F6%./0 1' $7D6%10
30&'9- 6&-1- '+40$6"-& :'D6'"-&
&6:039' 1' '"4M%+'"90 :-3-40$6"-& 40+ '"4M%+'"90 1'F-%^- 1'"&%1-1'
I I I I
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?'&*$-./0
P-"1'f-& 1'X'+ &'3 6&-1-& D6-"10>
- X-,/0 1' $7D6%10 ` -$9- '+ 3'$-./0 - 1' X-:03 l04033' D6-"10 -&':-3-./0 ` 1%m4%$an
D6-"10 0 1%d+'930 1- 40$6"- `
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?'&*$-./0
U+:-409-+'"90 1'X' &'3 6&-10 D6-"10>
D6-"10 0 1%d+'930 1- 40$6"- ` :'D6'"0 l0 46&90 3'$-*X0 1'F-"1'f-& :'D6'"-& ` -$90an
40"1%.Z'& 1' X#460 &/0 6&-1-& l40$6"-& '+:-409-1-& :'3+%9'++'"03 D6'1- 1' :3'&&/0 D6' F-"1'f-&an
40"1%.Z'& 1' F-%^- D6'1- 1' :3'&&/0 &/0 "'4'&%-&n
0 &%&9'+- ` :30:'"&0 i C03+-./0 1' '&:6+- D6-"10 F-%^0& X0$6+'& 1' $7D6%10 3'*10& "- 40$6"- C03 "'4'&%0
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230
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?'&*$-./0
Stage jFeed
VaporSide Stream
Heat Transfer
Liquid fromStage Above
L j 1 x i, j 1
T j 1
T j + 1
Q j(+ ) if from stage
() if to stage
LiquidSide Stream
U j
L jV j + 1
yi, j + 1
F j zi, j
x i, j
V j
yi, j
H V j H L j 1
H V j + 1T F
j
H F j H L j
T j
T j
W j
U&9#
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?'&*$-./0
Stage jFeed
VaporSide Stream
Heat Transfer
Liquid fromStage Above
L j 1 x i, j 1
T j 1
T j + 1
Q j(+ ) if from stage
() if to stage
LiquidSide Stream
U j
L jV
j + 1
yi, j + 1
F j zi, j
x i, j
V j
yi, j
H V j H L j 1
H V j + 1T F
j
H F j H L j
T j
T j
W j
L j 1x i,j 1 + V j + 1y i,j + 1 + F j z i,j (L j + U j )x i,j (V j + W j )y i,j = 0
P-$-".0 R-9'3%-$ :03 40+:0"'"9' % ' '&9#
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?'&*$-./0
Stage jFeed
VaporSide Stream
Heat Transfer
Liquid fromStage Above
L j 1 x i, j 1
T j 1
T j + 1
Q j(+ ) if from stage
() if to stage
LiquidSide Stream
U j
L jV
j + 1
yi, j + 1
F j zi, j
x i, j
V j
yi, j
H V j H L j 1
H V j + 1T F
j
H F j H L j
T j
T j
W j
P-$-".0 1' U"'3
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?'&*$-./0
40"1%.Z'& 9`3+%4-& 1- -$%+'"9-./0
"b+'30 1' :3-90& :3-90 1' -$%+'"9-./0 :3'&&/0 3-,/0 1' 3']6^0 '94
@"C03+-.Z'& -1%4%0"-%& "'4'&%0& :-3- 3'&0$X'3 0 40"f6"90 1''D6-.Z'& &%+6$9-"'-+'"9'>
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?'&*$-./0 P%"#3%-
B, x i, B
D, x i ,D
F, x i, F
Stripping Section
Enriching Section(Rectifying Section)
F = D + B
P-$-".0 R-9'3%-$ o$0F-$
F x i,F = Dx i,D + Bx i,B
P-$-".0 R-9'3%-$ 2-34%-$ 10L0+:0"'"9' %
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B, x i, B
D, x i ,D
F, x i, F
Stripping Section
Enriching Section(Rectifying Section)
F = D + B
P-$-".0 R-9'3%-$ o$0F-$
F x i,F = Dx i,D + Bx i,B
P-$-".0 R-9'3%-$ 2-34%-$ 10L0+:0"'"9' %
86:0&%./0>
[-,/0 +0$-3 1' $7D6%10 ' X-:03 40"&9-"9'& '+ 4-1- &'./0l3'*Q4-./0 ' '.!%>>%5,a 1- 40$6"- l9$5'.45. ?$&4! $3"!@$A a
?'&*$-./0 P%"#3%-
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8'./0 1' O'*Q4-./0
1
V y1
Lx i, D Dx i , D y2
n L
n + 1
2
yn + 1
ynV
V = L + D
R = L/D
F-$-".0 +-9'3%-$
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8'./0 1' O'*Q4-./0
1
V y1
Lx i, D Dx i , D y2
n L
n + 1
2
yn + 1
ynV
R R + 1
x 1
y2
y1
x D
yn + 1
Slope =
12
n
x n
n + 1 yn
y i,n + 1 =R
R + 1x i,n +
1R + 1
x i,D
( %BH k * %BC UD6%$7F3%0
?%-
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8'./0 1' E.!%>>%5,
y i,m + 1 =LV
x i,m BV
x i,B
Y%"M- 1' ):'3-./0>O'$-4%0"- 0 X-:03 10 '&9#
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L xi,m = V yi,m + 1 + Bx i,B
V yi,n + 1 = Lx i,n,i + Dx i,D &'./0 1' 3'*Q4-./0
&'./0 1' '.!%>>%5,
V yi = Lx i + Dx i,D
V y i = L x i Bx i,B%"9'3&'4./0 1-& 16-& $%"M-& 1' 0:'3-./0
(V V )y i = (L L )x i + F x i,F
U&9#
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1 k 4-$03 "'4'&%0 :-3- X-:03%,-3 H +0$ 1- -$%+'"9-./04-$03 $-9'"9' 1' X-:03%,-./0 +0$-3 1- -$%+'"9-./0
1 k H $7D6%10 &-963-101 k q X-:03 &-963-10
F
V L
V L
(1
q) F qF
V = V + (1 q)F
L = L + qF
?'&*$-./0 P%"#3%-
1 k C3-4%0"#3%0 &' - -$%+'"9-./0'&*X'3 :-34%-$+'"9' X-:03%,-1-
lq r 1 r HalC3-./0 $7D6%1- 1- -$%+'"9-./0a
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1 k 4-$03 "'4'&%0 :-3- X-:03%,-3 H +0$ 1- -$%+'"9-./0
4-$03 $-9'"9' 1' X-:03%,-./0 +0$-3 1- -$%+'"9-./0
F
V L
V L
(1 q) F
qF
V = V + (1 q)F
L = L + qF
?'&*$-./0 P%"#3%-
>A(64#"0
1 k HcJ V = !V " 0, 2 F ! L = L + 1,2 F
! L = L + F + 0, 2 F
2-34'$- 10 X-:03-&4'"1'"9' D6' `
40"1'"&-10 -0 10-34-$03 :-3- - +%&963-$7D6%1- &6Fe3'&C3%-1-
-$%+'"9-1-
1 s Ht l&6Fe3'&C3%-10a
>BC$DE(F $&7'$ +G#&'$FH
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V = V + (1 q)F L = L + qF
(V V )y i = (L L )x i + F x i,F
?'&*$-./0 P%"#3%-
86F&*96%"10 '
"- 'D6-./0 D6' 3':3'&'"9- - %"9'3&'4./0 1-& 16-& $%"M-& 1' 0:'3-./0
4M'
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OptimumFeed Plate
1
2
3
4
5
x B x F x D
y
@I$8" J%6" '( $#&6(78$DK"0@"9'3&'4./0 1-& $%"M-& 1' 0:'3-./0 '1- $%"M-e1E L033'&:0"1' -0 :3-90 '+
D6' - -$%+'"9-./0 1'X' &'3 C'%9- -Q+ 1' +%"%+%,-3 0 "b+'30 909-$ 1':3-90& 9'S3%40&
?'&*$-./0 P%"#3%-
R`9010 1' F49=4#" D 7-%"&"
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OptimumFeed Plate
1
2
3
4
5
x B x F x D
y
! -$%+'"9-./0 C'%9- -4%+- 06 -F-%^0 10:3-90 S*+0 4-6&- 6+ -6+'"90 10"b+'30 1' :3-90& 9'S3%40& 1- 40$6"-
?'&*$-./0 P%"#3%-
Feed Plate
Feed Plate
1
2
34
5
6
1
23
4
5
6
x B x B x F x F x D x D x x
y y
L#&6(78$DK"$M$&A" '"4I$8" J%6"l'^9'"&/0 1-&'./0 1'3'*Q4-./0a
L#&6(78$DK"$5&6$ '" 4I$8"J%6"l'^9'"&/0 1-&'./0 1''.!%>>%5,a
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230
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?'&*$-./0 P%"#3%- G W%:0& 1' L0"1'"&-103'&
y A, 1
x A, D x A, D L D1
2
3
y A, 1
x A, R
y A, D
L
D
12
3
V V
x A x A
y A y A
1
2
y A, 1
y A, 1 y A, 2
x A, 2 x A, 1 x A, 1 x A, D x A, R
y A, D
Condenser
40"1'"&-./0 909-$
40"1'"&-./0 :-34%-$
y i,n + 1 =R
R + 1xi,n +
1R + 1
x i,D
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230
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?'&*$-./0 P%"#3%- G W%:0& 1'G"#$%&"!'
N 1 N
y A, B
x A, B
B
N 1 N
x A, B
B
Reboiler
N
y A, B
y A, N
x A, B x A, N x A, N 1 x A
y A
N 1
y A, N
y A, N 1
x A, B x A, N 1 x A, N 2 x A
y A
N
!"#$%&"! :-34%-$ !"#$%&"! 9'3+0e&%C/0
! "# %
! "# %
y i,m + 1 =LV
x i,m BV
x i,B
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230
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No Feed
No Products
1
2
3
4
00 x B x F 1
1
M o l e
F r a c t
i o n
A i n
V a p o r , y
?'&*$-./0 P%"#3%- G L-&0& Y%+%9'&
O']6^0 W09-$
y i,n + 1 =R
R + 1x i,n +
1R + 1
x i,D
y i,m + 1 =LV
x i,m BV
x i,B
L033'&:0"1' i 40"Q
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No Feed
No Products
1
2
3
4
00 x B x F 1
1
M o l e
F r a c t
i o n
A i n
V a p o r , y
?'&*$-./0 P%"#3%- G L-&0& Y%+%9'&
O']6^0 W09-$
!" $%"&'()*
! 0:'3-./0 40+ 3']6^0 909-$ "/0 9'+ -:$%4-./03'-$ +-& 03%'"9- 0 :30f'90 1- 40$6"- :-3- -&'
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?'&*$-./0 P%"#3%- G L-&0& Y%+%9'&
!
"
#
$%
$&
! $! %! '!
()* +,- /+ 0,12-3 /1 4-56(1
, 1 7
8 -
/ + , + 9 5 6 : -
!"#$%& () a,+2,;5# :, +,D5# :% +%1-'Q#
.#) # /=)%+# :% 7+,$#0 :, .#-'/,A
!
%!!!
"!!!
&!!!
#!!!
! $! %! '!
()* +,- /+ 0,12-3 /1 4-56(1
+ ( + , ; < 1
= > ?
4@ABCADEB@F
+GHIJB@F
!"#$%& *) b/1-'c/.2, :# /=)%+# :% 7+,$#0
:, .#-'/, /, %/%+*2, .#/0')2:,A
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?'&*$-./0 P%"#3%- G L-&0& Y%+%9'&
O']6^0 R7"%+0 40+ :%59- "0 :3-90 1' -$%+'"9-./0
! 3-,/0 1' 3']6^0 ` &'$'4%0"-1-1' +-"'%3- D6' -& $%"M-& 1'0:'3-./0 %"9'3&'49-+ "- 463X- 1'
'D6%$7F3%0 ) "b+'30 1' :3-90& -1%4%0"-10&
-0 &' -:30^%+-3 1- $%"M-e1 9'"1'-0 %"Q"%90 '+ -+F-& -& &'.Z'&1- 40$6"-
L033'&:0"1' i 40"1%./0 1'3']6^0 +7"%+0 "- D6-$ M# ,0"-&1' 40+:0&%./0 40"&9-"9'
Pinch at theFeed Stage
Feed
Bottoms
Distillate
x B
1
00 1
q line
PinchPoint
RectifyingOperatingLine
StrippingOperatingLine
x F x D M o l e
F r a c
t i o n
A i n V
a p o r , y
)
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230
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?'&*$-./0 G L0"1%.Z'& ):'3-4%0"-%&
! &':-3-./0 &' 903"- +-%& 1%m4%$ lX0$-*$%1-1' 3'$-*X- 1%+%"6%ac 0&'f-c +-%& '&9#
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?'&*$-./0 G L0"1%.Z'& ):'3-4%0"-%&
):'3-./0 "- 40"1%./0 1' X#460n O'C3%
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?'&*$-./0 G L0"1%.Z'& ):'3-4%0"-%&
@I(FFK"0
! "#$ %
E /10556+ (0 F)=G9+=2@0=8+ (25 G+*)=25 (0 (0589*236+ 058; 9=89@2@0=80 10*2G9+=2(2 G+@ + =HD0*(0 80@/0128)12 2*G2=32(+ =+ 50) 9=8019+1I !29+105 /1055405 10J)010@ 80@/0128)125 @295 0*0D2(25
/212 50 289=
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T e m p e r a
t u r e
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0
0.2
0.4
0.6
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0 0.2 0.4 0.8
Mole Fraction of Benzene(Liquid Phase)
M o l e
F r a c
t i o n o f
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( V a p o r
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95
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P
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5gH 'D6-.Z'& P &/0 43%-1-&c 6+- :-3- 4-1- X-$03 1' | D6' 4033'&:0"1'-0& 40+:0"'"9'& '"93' 0& 40+:0"'"9'& 4M-X'&E ) 40"f6"90 1''D6-.Z'& ` 3'&0$X%10 &%+6$9-"'-+'"9' 'c 1'&9- C03+-c 1'9'3+%"-"10G+%" ' * %BC 10& 40+:0"'"9'& '"93' 0& 4M-X'&E
?'&*$ /0 R6$*40+:0"'"9'
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? &*$-./0 R6$*40+:0 9
6+- 0693- C03+- 1' &%+:$%Q4-3 - 1'9'3+%"-./0 1- 1%&93%F6%./0 10&40+:0"'"9'& "0 1'&*$-10 ` -&&6+%3 * %BC %
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? & $-./0 R6$ 40+:0 9
U^'+:$0>h+- 40$6"- 1' 1'&*$-./0 0:'3-"10 - H\ F-3 ` -$%+'"9-1- 40+ $7D6%10&-963-10 - 6+- X-,/0 1' Hqqq {+0$NM ' 40+:0&%./0 1-1- :'$- 9-F'$--F-%^0E ! X0$-*$%1-1' 3'$-*X- '"93' 0& 40+:0"'"9'& 9-+F`+ `-:3'&'"9-1-E
-1f-4'"9'&
Component f i (kmol h 1) ij
Propane 30.3 16.5i -Butane 90.7 10.5n -Butane (LK) 151.2 9.04
i -Pentane (HK) 120.9 5.74n -Pentane 211.7 5.10n -Hexane 119.3 2.92n -Heptane 156.3 1.70n -Octane 119.6 1.00
L
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? & $-./0 R6$ 40+:0 9
! +%&963- ` :-3- &'3 &':-3-1- '+ 6+ :301690 1' 90:0 D6' 3'46:'3-zz~ 1' "eF69-"0 ' zK~ 1' %e:'"9-"0 40+0 :301690 1' C6"10E2'3
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? & $-./0 R6$ 40+:0 9
N min =log
rL,D1 rL,D
rH,B
1 rH,Blog LH
L0+:0"'"9' Y'X' LM-X'> "eF69-"0L0+:0"'"9' 2'&-10 LM-X'> %e:'"9-"0
-a L-$46$' 0 "b+'30 +7"%+0 1' '&9#
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? & $-./0 R6$ 40+:0 9
Fa L-$46$' -& 40+:0&%.Z'& 1' 90:0 ' 1' C6"10 6&-"10 - 'D6-./0 1'_'"&{' E
d H
bH =
f H (1 rH,B )
f H rH,B=
1 rH,B
rH,B=
1 0.95
0.95= 0.05263
h&-"10 0 40+:0"'"9' :'&-10 4M-X' 40+0 3'C'3="4%->
d i =
N minij f i d j
b j
1 + N minij d j b j
b i =f i
1 + N minij d j b j
!& X-,Z'& +0$-3'& "0 90:0 ' "0 C6"10 &/0 1'9'3+%"-1-& -93-X`& 1'
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? & $ ./0 R6$ 40+:0 9
d i =!
ij 16,6 f i 0,05263
1 + ! ij 16,616,6 0,05263
X0$-*X%1-1' 3'$-*X-'+ 3'$-./0 -040+:0"'"9' 4M-X':'&-10
fi alfa alfa(i,i-C5) numerador enominador di biC3 30.3 16.5 2.8745645 65308853 2155408.7 30.30 0.00i-C4 90.7 10.5 1.8292683 107806.7 1189.6071 90.62 0.08n-C4 151.2 9.04 1.5749129 14970.75 100.01293 149.69 1.51
i-C5 120.9 5.74 1 6.362967 1.05263 6.04 114.86n-C5 211.7 5.1 0.8885017 1.565603 1.0073954 1.55 210.15n-C6 119.3 2.92 0.5087108 8.42E-05 1.0000007 0.00 119.30n-C7 156.3 1.7 0.2961672 1.39E-08 1 0.00 156.30n-C8 119.6 1 0.174216 1.59E-12 1 0.00 119.60
1000 278.21 721.79
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? & $ ./0 R6$ 40+:0 9
Component d i bi xi,D xi,B
Propane 30.30 0.0 0.1089 0.0i -Butane 90.62 0.08 0.3257 0.0001n -Butane 149.69 1.51 0.5380 0.0021i -Pentane 6.05 114.86 0.0217 0.1591n -Pentane 1.55 210.15 0.0056 0.2911n -Hexane 0.0 119.30 0.0 0.1653n -Heptane 0.0 156.30 0.0 0.2165n -Octane 0.0 119.60 0.0 0.1657
Total 278.21 721.80 0.9999 0.9999
d i =!
ij 16,6 f i 0,5263
1 + ! ij 16,616,6 0,5263
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! # $%&%' ( $)&*+
($,
($-
(.
(%
()
/
)
%
.
/ /&- /&0 /&% /&* $ $&- $&0
! " #
$ %
& ' ( & )
!"#$+!,+-&.)
? & $ ./0 R6$ 40 :0 9
#"X,%"& / #"X,( " 3) " /
LV HEJHy\xVz\\ wEVVVKJz\V%eL\ HEqJHHxzJzz VEqyKqVxVJH
"eL\ qEzKwHwx\V HEzzKwzHzqJ
%eLK qEyKxzHHxzJ eHEJyxywwwV
"eLK qEyqyKyqHyw eJEHVHqVzHJH
"eLw qE\wKVxJxKH ewEHKHV\xyH
"eLy qEJVq\\xzJH eHqEqKHJKHzK
"eLx q eHVExywyq\q\
log d ibi
= N min log ij + log d j bj
L63X- -f6&9-1-:'$0 U^4'$
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? & $ ./0 R6$ 40 :0 9
4a L-$46$' - 3-,/0 1' 3']6^0 +7"%+0 6&-"10 -& 'D6-.Z'& 1'h"1'3}001 E
L0+0 0& 40+:0"'"9'& 4M-X'& &/0 -1f-4'"9'&c "/0 M#40+:0"'"9'& "/0 4M-X'& '"93' '$'& ' 0 4#$46$0 :01' &'3&%+:$%Q4-10 4-$46$-"10 -:'"-& 6+- 3-%, :'$- 'D6-./0 ! 1'h"1'3}001E
! 3-%, '&9-3# '"93' 0& X-$03'& 1-& X0$-*$%1-1'& 3'$-*X-& 10&40+:0"'"9'& 4M-X'&c 06 &'f-c '"93' Kcy\ ' zcq\
NC
i = 1
ij x i,F ij
= 1 q
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? & $ ./0 R6$ 40 :0 9
Table 9.3 Solution for the root of the Underwood Equation.
xF,i ij ij xi,F ij xi,F ij
= 7.0 = 7.3 = 7.2 = 7.2487
0.0303 16.5 0.5000 0.0526 0.0543 0.0538 0.05400.0907 10.5 0.9524 0.2721 0.2796 0.2886 0.29290.1512 9.04 1.3668 0.6700 0.7855 0.7429 0.76300.1209 5.74 0.6940 0.5508 0.4449 0.4753 0.46000.2117 5.10 1.0797 0.5682 0.4908 0.5141 0.5025
0.1193 2.92 0.3484
0.0854
0.0795
0.0814
0.08050.1563 1.70 0.2657 0.0501 0.0474 0.0483 0.04790.1196 1.00 0.1196 0.0199 0.0190 0.0193 0.0191
0.2797 0.0559 0.0532 0.0000
NC
i = 1
ij x i,F ij = 1 q
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? & $ ./0 R6$ 40 :0 9
Table 9.4 Solution of the second UnderwoodEquation.
xD,i ij ij x i,D ij x i,D ij
0.1089 16.5 1.7970 0.19420.3257 10.5 3.4202 1.05200.5380 9.04 4.8639 2.71530.0217 5.74 0.1247 0.08270.0056 5.10 0.0285 0.01330.0 2.92 0.0 0.00.0 1.70 0.0 0.00.0 1.00 0.0 0.0
3.8655
L0+ 0 X-$03 '"40"93-101' | k ycJ\xy
R min + 1 = NC
i = 1
ij xi,D ij
!&&6+%"10 D6' * %BC ` -+'&+- 4-$46$-1- :'$-&
'D6-.Z'& 1' _'"&{'
G?%5 g H k VcxwKK
G?%5 k JcxwKK
80$6./0 1- &'
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$ $
! 'D6-./0 1' h"1'3}001 '&9# F-&'-1- "- &6:0&%./0 1' D6' -&X0$-*$%1-1'& 3'$-*X-& ' -& X-,Z'& +0$-3'& &/0 40"&9-"9'& '"93' -&,0"-& 1' 40+:0&%.Z'& 40"&9-"9'&c -:'&-3 1' "/0 3':3'&'"9-3 -3'-$%1-1'E
! X0$-*$%1-1' 3'$-*X- :01' &'3 1'9'3+%"-1- F-&'-1- "- +`1%- 1-&
%"C03+-.Z'& 10 90:0 ' C6"10 40+0 C0% %"1%4-10 :-3- 0 6&0 40+ -'D6-./0 1' _'"&{'E
A0 '"9-"90c 40+0 -& ,0"-& 1' 40+:0&%.Z'& 40"&9-"9'& "03+-$+'"9''&9/0 :3S^%+-& 10 :0"90 1' -$%+'"9-./0c 40&96+-e&' 6&-3 -&
%"C03+-.Z'& 1- -$%+'"9-./0 :-3- 0 4#$46$0 1- X0$-*$%1-1' 3'$-*X- 10&40+:0"'"9'&E
!& 'D6-.Z'& 1' h"1'3}001 9'"1'+ - &6F'&*+-3 0 X-$03 1- 3-,/0+7"%+- 1' 3']6^0
230
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$
HE 8%&9'+-& 1' 8':-3-./0 ;0+0
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$ $
P"7'&DE(F T&7&8$F '( *$NK" '( *(OCA" 4$I$ Y&F8CI$F YC#%5"64"7(78(F
Y = 0.2788 1.3154 X + 0.4114 X 0.2910
+ 0.8268 ln X + 0.9020 ln X +1X
Y =N N min
N + 1X =
R R minR + 1
0"1'>OB P &/0 :-3d+'930& 1' 4033'$-./0< ` 0 "b+'30 3'-$ 1' :3-90& 9'S3%40&< +%" ` 0 "b+'30 +7"%+0 1' :3-90& 9'S3%40&G ` - 3-,/0 1' 3']6^0 3'-$ G+%" ` - 3-,/0 1' 3']6^0 +7"%+-
L033'$-./0-$
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U^'+:$0>!&&6+%"10 D6' - 40$6"- 10 '^'+:$0 -"9'3%03 0:'3' 40+ 6+40"1'"&-103 909-$c 1'9'3+%"' 0 "b+'30 1' :3-90& 9'S3%40& 3'D6'3%10&&' GNG+%" k HcH 'G+%" 40+0 1'9'3+%"-10 "0 '^'+:$0 -"9'3%03E
X =R R min
R + 1
=3.153 2.866
3.153 + 1
= 0.0691
R = 3.153R min = 2.866 10 '^'+:$0
-"9'3%03
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Y = 0.2788 1.3154 0.0691 + 0.4114 0.0691 0.2910
+ 0.8268ln0 .0691 + 0.9020 ln 0.0691 +1
0.0691
= 0.5822
Y =N N min
N + 10.5822 =
N 16 .6N + 1
N = 41 .1
2039-"90c &/0 "'4'&%0&Z[ :3-90& 9'S3%40&
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) "b+'30 1' :3-90& 3'-%& ` &'+:3' +-%03 D6' 0 "b+'30 1' :3-90&
9'S3%40& 1'X%10 -0 C-90 1' $%+%9-.Z'& 1' 93-"&C'3="4%- 1' +-&&-%+:'1%3 D6' 0 'D6%$7F3%0 &'f- -*"