|
0
0
0
...
K nM
/
\
Mii|inhi iiiii',',.i ii/;iiishning lokal tezliklari uchun (4) tenglama
.|ii\
11
1
111
■
i I n i imslmi olaili:
..........
I iii'lkatlagi ko‘p komponentli massa uzatishni tavsiflovchi
ii ni'litmalar tizimi 3n tenglamalar ko‘rinishida ko‘rsatilishi mumkin:
I I
/;)
I j c f - L X j
+
V y f - V y f
= 0
dh
H
1
**) g r ,K),= ^ tKV ; - ^ )
j = \,...n
Oxirgi ifodani oldingisiga qo‘yib, integro - differensial teng-
lamnlnrning 2n tizimi olinadi:
11 /;)
L x f - L X/
+
V y f - V y f =
0
j = \,...n
1 //) V ^ L = E l K f v){yt - y )
dh
H
11
"
j = \,...n
dillcrcnsial tenglamaning analitik yechimi:
f dv,
F
m
K m(v) “
„
1,1
-y,
VH
l
■'!"
k m
(
v
)
i
'* /
^
H / i
______
,
I',
v,
VH
0
0
317
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s? _
* r ~ '
l n { y j - y ' j )
y f - y )
_
y {? - y ' j
exp,
M y M O )
FMKv
Tarelkalarning samaradorligini aniqlash uchun yozamiz:
,(*)
y) -yj _y)
W - y )
(0)
*
(*) , *
y j - y j _ +yj
y f - y f
y (o)_
ys
y j - y )
(
0
)
yoki:
E , = 1 - exp
t
?M lsMtV)
F
v
Tarelkaga kelib tushuvchi, massa uzatishda qatnashuvchi bug‘
fazasining tarkibini esa oxirgidan oldingi munosabatni hisobga olib
quyidagi formula bo‘yicha hisoblash mumkin:
y f ^ y f + £ , { / , - y f ) .
M j s M ( V )
F MK u
E f - 1 - exp
j =
1
,-n
bu yerda,
Nazariy tarelkalar uchun E , = 1 va y f = y*.
Natijada tarelkadagi massa uzatish jarayonining matematik
tavsifi quyidagi ko‘rinishga ega bo‘Iadi:
Suyuq fazalar uchun tenglama:
I n) L x f - Lxj + V y f - V y f = 0
Bug‘ fazalar uchun tenglama:
2 n)
V -
E M - y f ' )
j = \ .. J i
3 n) Ej = 1 -ex p
K M(V
) ^
/
318
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I
I, .//
v.i suyuq fazalaming ideallik shartlarida:
p ( ° )
i
i,
.11
i Uihu liolda individual modda to‘yingan bug‘ining bosimi
\ iiiu.ni
k-nglamasi bo‘yicha aniqlanadi:
f
B
^
<>n)
=exp| A, + -----—
7
“ ' c ,+r
i =
hu vi uln A ^ B ^ C - - m a ’lum doimiylar.
5.1.6.1.
Tarelkali kolonnada ko‘p komponentli uzluksiz
i rhiilikutsiyalash jarayonini statsionar rejimining kompyuterli
modeli
Tarelka
i
(
a
/
i
,.,),
A V,y, (
a h
,)
I..,K ,(A //m1)
1 .......1 ...............
t
1
Uh (A/0
tashqi issiqlik oqimi (kondensatorda «minus»,
qaynatgichda «plyus»);
A//, (Ah, ) bug‘ (suyuq) fazaning entalpiyasi;
/'V
suyuqlik manbaining tashqi oqimi;
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N - tarelkalar soni;
i - tarelkalar raqami (z' = 1,
j - komponent raqami ( j = 1
Tarelkalar uchun jarayonning MT ni (ln,2n,3n,4n,5n,6n)
tenglamasini tuzishda N marta takrorlash (birinchi indeks i 1 dan N
gacha almashadi) zarur va barcha tarelkalar uchun issiqlik balans
tenglamasi hamda bug‘ va suyuq fazalar tarkibi uchun stexiometrik
munosabatlarni qushish lozim.
Natijada uzluksiz rektifikatsiya jarayonini statsionar rejimining
MT si olinadi.
Jarayonning matematik tavsifi
i = 1 ,...N
j = \,...n
2 v * « )
y v =
+ E,j{yl - y MJ)
i = \,...N
j = \,...n
i = \,...N
j = \,...n
i = 1,..
j
V
j = \,...n
i = 1 ,...N
j = \,...n
3 2 0
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■•/•«) P ^ =
exp
'
Bj '
A
H-----------------
;
C +T
i - l,..N; j = 1
S te x io m e trik nisbat:
7
n
) £ y « = 1
y'=i
i = l,...iV
8/v) Z ^ = l
/ = i
/ =
9W
F tN h f +
L ^ A h ^
- L A h , + Vi+lA H M - V , A H , +
AQ?
i = 1,.. JV
F o v)
Ah, = ! > ' " %
/=I
/ = 1,..JV
H w)
A H , = ± A H f XiJ
/=1
/ = 1 , . J V
F2
a
/*„)
= a ■
+ b
1;T, + c)T} + d f f
/ = l,.../V;y = l,...M
1 2 « . « ) A //'" 1' =
+
t f T , + c rjT } + d r T }
i = l,...N;j = \,..si
n' J i ' ' , c ' , d ' , a v,b v, c v, d v
- su y u q v a b u g ‘ faz a la r u ch u n m a ’lum
d o im iy la r.
I Iis o b la s h la r d a q u la y b o 'lis h i u ch u n
T)
te n g la m a la rn i 7 ) v a 8)
■ .tcxiom etrik m u n o sa b a tla rn i h is o b g a o lib q o ‘sh ish lo zim , natijada
lini bir ta re lk a d a g i o q im la r b a la n s in in g te n g la m a sin i o lam iz , 8’)
im m o 'jib a tn i esa q u y id a g i tiz im d a n to p a m iz:
8’) F^ + L ^ - L t + V ^ - V ^ O
i = 1,,.JV
N atijtKla 8
N * n -t- 5 N m u sta q il te n g la m a la r tiz im i o lin ad i:
321
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- 8
N*n
te n g la m a : lj;2 j;3 j;4 j;5 j;6 j;1 2 j;1 3 j;
- 5
te n g la m a : 7);8);9);10);ll);
v a a n iq la n a d ig a n o ‘z g a r u v c h ila r sifa tid a h a m
8
N*n
+
5
N
o ‘z g a r u v c h ila r ta n la n ad i:
XN*t,;yN,„;EN*n; y N,„;KN *n; P ; T
n
; L
n
; V
n
;
a
J
i n
; A H
w
;A/
z
N*n; & H N*n
y a ’n i y e c h is h u c h u n q u y id a k e ltirilg a n a x b o ro t m a tr itsa sid a n
fo y d a la n ib m a te m a tik d e k o m p o z it s iy a u su li b ila n y e c h ila d ig a n
n o c h iz iq li t e n g la m a la r tiz im i ( N T T ) o lin a d i.
Axborot matritsasi
Tarelkali rektifikatsiya kolonnasining statsionar rejimini
VR (bubble point) usuli bilan hisoblash algoritmining blok -
sxemasi
3 2 2
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(
Yechimning eng tashqi sikli
)
( Yechimning tashqi sikli)
Ichki iteratsiya siklida NTT ( l ) * ga nisbatan yechiladi.:
4-,x,_i,y - L,x,j + Vi+ly i+l J{x} - V,y
0 {?} = -F,xli}
i = \,...N
j = 1 ,...n
!■)/
I ho'lganda nazariy tarelkalar uchun keltirilgan tenglama
(|iiyidM|',icha yozilishi mumkin:
3 2 3
do
js
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yoki
L i - \ X i - \ J
L j X j j + V j + i K j + Y j X j + i j
V j K j j ) i j j —
F j X j j
i = \,...N
j = 1 ,...n
L i - i x , - u
~ L i x o + V j + l K j + l j X i + l j
-
V j K j j y ^ + F j x f j
=
0
i = 1 ,...N
j = 1 ,...n
Bu tenglamani har komponentning konsentratsiyasiga nisbatan
n marta yozish mumkin (masalan,y komponentning):
A xi-\,rx
i = \,...N
j = 1 ,...n
yoki( j komponent uchun):
fi{xu r x2 j ^ j ) = Q
f n - \ { ^ N - 2 J ’ X N - \ J
’ X bl J ) ~ 0
f n { X N - \ J ’ X N , j ) = ®
Oxirgi tenglamalar tizimi uch diagonalli tenglamalar tizimini
yechish usulidan foydalanilib, har bir komponent uchun n marta
yechiladi.
f \ { x \ . j ' ’ x i . j ) = °
f l { X \ j ’ X 2 J ’ X l j ) =
0
f n - \ i X N - 2 J '■>X N - \ , j :>X N , i )
f n { X N - \ J ’ X N , j ) =
^
3 2 4
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