59994_lecture 7

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.


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).


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


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.


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


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


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


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


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


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).


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.


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


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


FLASH CALCULATION

V =(V/F)* F =0.65 * 100= 65 kg mole/ hr

L= F - V = 100 - 65 = 35 kg mole/hr


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


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


FLASH CALCULATION

)()1(

,)()1(

21

12222

21

21111 KK

KKxKy

KKKK

xKy


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


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


FLASH CALCULATION

)/(1)/(1)/1(z i

VKLf

VKLVLVyv

i

i

iii


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


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


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.


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

59994_lecture 7

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