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Dr Saad Al-ShahraniChE 334: Separation Processes
FLASH CALCULATION
A flash is a single-equilibrium stage distillation in witch a feed is partially vaporized to give a vapor richer in the most volatile components than the remaining liquid.
a) Adiabatic flashAs shown in fig. (4.10, Seader), a liquid feed is heated under pressure and flashed adiabatically across a valve to lower pressure, resulting in the creation of a vapor phase that is separated from the remaining liquid in a flash drum.
Dr Saad Al-ShahraniChE 334: Separation Processes
FLASH CALCULATION
b) Isothermal flash
If the valve is omitted, a low-pressure liquid can be partially vaporized in the heater and then separated into two phases in the flash drum (when TV is specified).
Dr Saad Al-ShahraniChE 334: Separation Processes
FLASH CALCULATION
Alternatively, a vapor can be cooled and partially condensed, with phase separation in a flash drum as in figure (4.10b, Seader), to give a liquid that is richer in the less volatile components.
In both cases, if the equipment is properly designed, the vapor and liquid leaving the drum are in equilibrium
Dr Saad Al-ShahraniChE 334: Separation Processes
Isothermal flash calculations
FLASH CALCULATION
In this process an entering stream (a liquid at high pressure) flash as it comes into a vessel that is at lower pressure. Significant quantities of both liquid and vapor phases are formed.
TV=TL
PV=PL
V= vapor flow rate (moles/ time)
L= Liquid flow rate (moles/ time)
F= Feed flow rate (moles/ time)
zi,xi,yi= mole fraction of component i in the feed, liquid, and vapor streams respectively.
Dr Saad Al-ShahraniChE 334: Separation Processes
In a typical isothermal flash calculation,
FLASH CALCULATION
Given: F , zi , T and P in the vessel.
unknown: V , L, yi , and xi.
We have (C) component balances, C more equations are required. They
are obtained from phase equilibrium.
Total mass balance (1 eqn)
(1) VLF
Dr Saad Al-ShahraniChE 334: Separation Processes
FLASH CALCULATION
(2) VyiLxFz ii
(4) )( xiVKxVFFz iii
Component mass balance (C) equation:
Phase equilibrium (C) equation:
(3) and (1) are substituted in (2):
Solving for xi:
(3) P
PKxy iL
sati
ii
i
(5) i
ii VKVF
Fzx
Dr Saad Al-ShahraniChE 334: Separation Processes
FLASH CALCULATION
Dividing numerator and denominator by F yields
(6) ]1)[/(1
i
ii KFV
zx
(7) ]1)[/(1
PPFV
zx sati
ii
If the system is ideal, iL= 1.0, Ki =Pisat/P
Equations 6,7 can be written for each of the (C) components in the system
Ci
i i
iCi
ii KFV
zx11
0.1]1)[/(1
Dr Saad Al-ShahraniChE 334: Separation Processes
FLASH CALCULATION
iii xKy ]1)[/(1
i
iii KFV
Kzyand
Ci
i i
iiCi
ii KFV
Kzy11
0.1]1)[/(1
If
Then
A flash calculation is an iterative trial and error procedure where the problem is to guess (V/F) ratio until:
0.11
Ci
iix
Dr Saad Al-ShahraniChE 334: Separation Processes
FLASH CALCULATION
Flash calculation iteration for ideal systems The first thing to do in any flash calculation is to make sure that something
will flash (there is liquid and vapor phases).
If we are in a region where nothing flashes P of the system must higher than the bubble point P of the feed at the specific T.
Ci
i
satiiBUB PzP
1
If P>PBUB, nothing will flash, V/F=0 and xi=zi x,y
Sub-cooled liquid
0 1.0
Superheated Vapor
y
z
Pressure
x
x1 y1
P1
yBPxDP
Saturated vapor line
Saturated liquid line
PBP
PDP
T= constant
ni
1iiBUB
ni
1i
i
zP
0.1z
,
sati
sati
satii
i
P
PP
PPz
y
Dr Saad Al-ShahraniChE 334: Separation Processes
FLASH CALCULATION
Dew point
Ci
i
satii
Dew
PzP
1
/(
1
If P< PDew, every thing flashes, V/F=1 and yi=zi
ni
i
satii
Dew
ni
i
ni
isat
i
ii
PzP
PPz
x
1
1 1
/(
1
0.1
Once we know that two phases will be present, equation (7) must be solved for (V/F).
Dr Saad Al-ShahraniChE 334: Separation Processes
FLASH CALCULATION
Example: A liquid feed stream containing 40 mole perercent benzene, 35 mole percent toluene and 25 mole percent o-xylene is flashed to 110°C and 760 mm Hg (14.7psia). Determine the flow rates and compositions of the vapor and liquid streams after the flash for 100 kg-mole/hr of feed. The VLE relationships can be assumed to be ideal. i.e the system obeys Raoult's Law.
Solution
The first thing to do in any flash calculation is to check whether the actual pressure P is between the bubble point and dew point pressures of the feed at the operating temperature.
The vapor pressures at 110°C (230°F) are read from the Cox chart.
Dr Saad Al-ShahraniChE 334: Separation Processes
FLASH CALCULATION
Pisat at 110 oC from Cox chart.
Benzene (1) = P1sat = 33 psia
Toluene (2)= P2sat = 14 psia .
O-Xylene (3)= P3sat = 5.6 psia
F100 kgmole/hr
z1= 0.4
z2=0.35
z3=0.25
V=?y1= ?y2=?y3=?
L=?x1= ?x2=?x3=?
TV=TL=110 oC
PV=PL= 1 atm
Ci
i
satiiBUB PzP
1
Ci
i
satii
Dew
PzP
1
/(
1
PDew < P=14.7 psia < PBUB So there are two phases in the drum (vap. and liq. phases
Dr Saad Al-ShahraniChE 334: Separation Processes
FLASH CALCULATION
Guess: V/F = 0.5, 0.7 and 0.65
V/F=0.5 V/F=0.7 V/F=0.65 yi
(at V/F=0.65)Component zi Pjsat xi xi xi
Benzene 0.4 33 0.247 0.214 0.22 0.496Toluene 0.35 14 0.359 0.362 0.36 0.344O-xylene 0.25 5.6 0.362 0.441 0.42 0.159
Total 1.000 0.968 1.017 1.00 0.999
]1)[/(1
PPFV
zx sati
ii law sRaoult'
PPx
ysat
iii
Dr Saad Al-ShahraniChE 334: Separation Processes
FLASH CALCULATION
V =(V/F)* F =0.65 * 100= 65 kg mole/ hr
L= F - V = 100 - 65 = 35 kg mole/hr
Dr Saad Al-ShahraniChE 334: Separation Processes
FLASH CALCULATION
Flash calculations in VLE relationship = f(T,P) only and not f(composition), the isothermal flash calculation is essentially the same as if the system were ideal.
a) Binary system (T,P are specified)
0.1 ,0.1 2121 xxyy
2
22
1
11 ,
xy
Kxy
K 1
12
1
11 1
1 ,xyK
xyK
111 xKy 2
111
1
112
1 -1 ,
11
K
xKx
xxK
K
Dr Saad Al-ShahraniChE 334: Separation Processes
FLASH CALCULATION
0.1 ,1)1( 11212 1121 KxKxKxKKx
2211 1)( KKKx
21
12
21
21
1 ,1 KK
KxKK
Kx
y1 and y2 can be obtained from yi=Kixi
The fraction vaporization (V/F) can be obtained from
, VyiLxFz ii , VLF iii xKy
Dr Saad Al-ShahraniChE 334: Separation Processes
FLASH CALCULATION
)()1(
,)()1(
21
12222
21
21111 KK
KKxKy
KKKK
xKy
Dr Saad Al-ShahraniChE 334: Separation Processes
FLASH CALCULATION
b) Multi-components systems:
, VyiLxFz ii and VLF into iii xKy
, )( VLzVxKLx iiii )( VLzVyLKy
iii
i
divide by L divide by L
)/(1)/1(
VKLVLz
yi
ii
)/(1)/1(
LVKLVz
xi
ii
iLVK i for factor stripping i
VKL
i
for factor Absorption
Dr Saad Al-ShahraniChE 334: Separation Processes
FLASH CALCULATION
product.in vapor component of moles prpduct. liquidin component of moles
feed.in component of moles
iVyviLxliFzf
ii
ii
ii
)/(1)/(1z
i
LVKf
LVKF
Lxli
i
iii
)/1( , )/(1
)(*
)/(1)/1(z
i LVLVLFLVK
VLzL
LVKLV
Lxli
i
iii
)1/( , )/(1)/1(z i
VLVVLFVVKLVLVyvi
ii
Dr Saad Al-ShahraniChE 334: Separation Processes
FLASH CALCULATION
)/(1)/(1)/1(z i
VKLf
VKLVLVyv
i
i
iii
Dr Saad Al-ShahraniChE 334: Separation Processes
FLASH CALCULATION
Case #1
If T and ( )of one component i is specified
(1) for factor Absorption1 ivf
VKL
i
i
i
(2) for factor Absorption1 jvf
VKL
j
j
j
give torearrange becan )/(1
equation TheVKL
fVyvi
iii
ii fv /
If equation (2) is divided equation. (1)
)1/()1/(
*
ii
jjij
i
j vfvf
LVK
VKL
Guess P and find
Dr Saad Al-ShahraniChE 334: Separation Processes
FLASH CALCULATION
1/)1/( jjiiij vfvf
1)1( i
iij
j
j
vf
vf
or if equation (1) is divided by equation (2)
)1/()1/(*
jj
iiji
j
j vfvf
LVK
VKL
jiij
iijij
j vfvf
1
1)1/(1
Dr Saad Al-ShahraniChE 334: Separation Processes
FLASH CALCULATION
Case # 2
P and T are specified
)1( 1)1()/(1
)/1(LVLVLF
FVKz
LVKLVz
xi
i
i
ii
)1( 1)1()/(1
)/1(
VLVVLF
FVKKz
VKLVLz
yi
ii
i
ii
1)/)(1(
)1()/()(
FVKKz
xyFVffi
iiii
It is called Rachford-Rice function
fraction vapor called is
If f(V/F) is positive at V/F =0 and negative at V/F =1.0, then two phases are present . If f(V/F) is negative at V/F =0, the system is sub-cooled. If f(V/F) is positive at V/F =1, the system is superheated vapor.
Dr Saad Al-ShahraniChE 334: Separation Processes
FLASH CALCULATION
Case # 3
P and V/F specified Guess T
Like case # 2
Case # 4
P and ( )of one component are specified
ii fv / Guess T
Like case # 1