Evaporation Problem

March 22, 2019 | Author: Jahre El Leonard Tañedo | Category: Latent Heat, Heat Transfer, Steam, Heat, Evaporation
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A problem on Evaporation Chemical Engineering...

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Example 1: A single efect evaporator is to be used to concentrate a ood solution containing 15% (by mass)dissolved solids to 50% solids. The eed stream enters the evaporator at !1 " #ith a eed rate o 1.0 $g s 1. &team is available at a pressure o .' bar and an absolute pressure o 0.0 bar is maintained in the evaporator. Assuming that the properties o the solution are ar e th the e sa sam me as th thos ose e o #a #ate ter r an and d ta ta$i $ing ng th the e ov over eral alll he heat at tr tran ans ser er coe*cient to be +00 , m " 1 calculate the rate o steam consumption and the necessary heat transer surace area. ,or$ing in units o $g s 1 the overall material balance becomes 1.0 -  /  &ubstituting into the component material balance or  2 - 0.15 and  - 0.50 gives 0.15 3 1.0 - 0.50 

-4

 - 0.+$g s1   - 0.$g s1

rom steam tables (6 the steam and condensate remain saturated at .'0 bar) h& - 15$7 $g1 and h8 - 5+0$7 $g1  The eed enthalpy is determined determined by its temperature. temperature. Assuming the eed to be pure #ater h 2 is e9ual to h   at  at !1 " and thereore h2 - 5.5$7 $g1.  The enthalpies o the vapour and li9uor streams are a unction o the pressure pressure #ithin the evaporator h  - 5 $7 $g1 (hg at 0.0 bar) and h  1:+$7 $g1 (h  at  at 0.0 bar). The enthalpy balance &(15  5+0) - (0.0 3 5) / (0.+0 3 1:+)  (1.0 3 5.5) & - 0.;1 $g s1 and

< - 0.;1(15 0.;1(15  5+0)$, - 1'$,

 The temperature o steam at .' bar is T & - 1:.1=8 and the temperature o  saturated li9uid #ater at the evaporator pressure o 0.0 bar is T > - +!.0=8.  Thus rom the rate e9uation e9uation the heat transer area area is

Example 2:  An a9ueous solution at 15.5=8 and containing '% solids is concentrated to 0% solids. A single efect evaporator #ith a heat transer surace area o +. m  and an overall heat transer coe*cient o 000 , 1

m " 1 is to be used. The calandria contains dry saturated steam at a pressure o 00 $?a and the evaporator operates under a vacuum o ;1.+ $?a. 6 the boiling point rise is 5 " calculate the evaporator capacity.

At 00 $?a the steam and condensate enthalpies are h & - 0 $7 $g 1 h 8 505 $7 $g1 Ts-10.=8.  The pressure #ithin the evaporator is 101.+  ;1.+ - 0.0 $?a at #hich the boiling point o #ater is :0.1=8. The evaporator temperature is no# :0.1=8 plus the boiling point elevation and thereore T > - :5.1=8.

-4 & - 1.;: $g s1 2rom steam tables the eed enthalpy at 15.5=8 is h2 - :5 $7 $g1. apour enthalpy h - :0! $7 $g1 (hg at 0.0 bar) / (1.!1 3 5) $7 $g 1 :1;.: $7 $g1 8p (#ater vapour at :0.1=8)- 1.!1 $7 $g1 " 1  The enthalpy o the concentrated li9uor stream at the evaporator temperature is h   -  $7 $g1 (h   at :5.1=8). The component balance becomes 0.0'F - 0.0L => F - 5L , V - 'L S(h&  h8) - 'Lh / Lh  5Lh2 1.;:(0  505) - ('L 3 :1;.55) / L  +5L L - 0.+!+ $g s1 and the evaporator capacity is F - 1.! $g s1

EXAMPLE 3. Single efect evaporator: steam usage and eat trans!er sur!ace A single efect evaporator is re9uired to concentrate a solution rom 10% solids to +0% solids at the rate o 50 $g o eed per hour. 6 the pressure in the evaporator is  $?a absolute and i steam is available at 00 $?a gauge calculate the 9uantity o steam re9uired per hour and the area o heat transer surace i the overall heat transer coe*cient is 100 7 m @ s@1 8@1. 

Assume that the temperature o the eed is 1;8 and that the boiling point o  the solution under the pressure o  $?a absolute is !18. Assume also that the speciBc heat o the solution is the same as or #ater that is '.1;:  10+ 7 $g@18@1 and the latent heat o vaporiCation o the solution is the same as that or #ater under the same conditions. 2rom steam tables the condensing temperature o steam at 00 $?a (gauge) D+00 $?a absoluteE is 1+'8 and latent heat 1:' $7 $g @1F the condensing temperature at  $?a (abs.) is !18 and latent heat is ;1 $7 $g @1.

Mass "alance ($g h@1)  

 

&olids

i9uids

Total

2eed

5

5

50

?roduct

5

5;

;+

>vaporation

1:

#eat "alance Geat available per $g o steam - latent heat / sensible heat in cooling to !18 - .1:'  10: / '.1;:  10+(1+' @ !1) - .1:'  10: / 1.;  10 5 - .+'  10: 7 Geat re9uired by the solution - latent heat / sensible heat in heating rom 1;8 to !18 - ;1  10+  1: / 50  '.1;:  10 +  (!1 @ 1;) - +.;1  10; / .:  10  - '.5  10; "g 7 h@1 Ho# heat rom steam - heat re9uired by the solution  Thereore 9uantity o steam re9uired per hour - ('.5  10;)I(.+'  10 :) - 1!5 $g h@1 vaporation

5

#eat "alance Area o evaporator tube pDHL - p  0.0'  + - 0.+; m 8ondensing steam temperature at 10 $?a (abs) - 1158 rom &team Tables. La$ing a heat balance across the evaporator q = UA KT  - :000  0.+;  (115 @ 5) - 1.+  105 7 s@1 Geat re9uired per $g o eed or evaporation - 0.5  +::  10 + - 1.+'  10: 7

'

Mate o evaporation - (1.+  10 5)I 1.+'  10 :) - 0.1 $g s@1 Mate o evaporation - +:0 $g h @1 stimate the rate o  ra# Juice eed that is re9uired to supply the evaporator. D 5+: $gh@1 E

Pro"lem ,. >stimate (a) the evaporating temperature in each efect (b) the reirements o steam and (c) the area o heat transer surace or a t#o efect evaporator. &team is available at 100 $?a gauge pressure and the pressure in the second efect is 0 $?a absolute. Assume an overall heat@transer :

coe*cient o :00 and '50 7 m @ s@1 8@1 in the Brst and second efects respectively. The evaporator is to concentrate 15000 $g h @1 o ra# mil$ rom !.5 % solids to +5% solids.Assume the sensible heat efects can be ignored and that there is no boiling@point elevation. D (a) 1st. efect !'8 nd. efect :08 (b) 5': $gh @1 0.5+ $g steamI$g #ater (c) '50 m  E

STEAM TABLE - SATURATED STEAM

Temperature

Pressure(Absolute)

Enthalpy (sat. vap.)

Latent heat

Spe!"! volume

(#$)

(%Pa)

(%& %'-)

(%& %'-)

(m %'-)

Temperature Table *

*.+

,*

,*

,*+



*.++

,*

,//

/



,

*.0

,*

,/0

1*



*.1

,*/

,/,

0

+

*./

,,

,10

1

1

.*0

,+

,1

,

*

.,

,,*

,01

*+

,

.*

,,

,0

/./



.+*

,,0

,+1

1,.1

+

.1,

,

,+

0.

1

,.*+

,

,/

+.*

,*

,.

,1

,

0.1

,,

,.+

,,

,/

.

,

,.//

,

,

./

,+

.+

,/

,*

*.*

,1

.01

,

,

+.+

*

.,

,+

,

,./

*

0.1

,0

,*0

/.

*

,.

,/,

,1

,.*

+*

/./

,+*

,/

0.+0

0*

.,

,+,0

,

.*

1*

0.

,+

,*/

.

/*

0*.

,++*

,,1

,.+

**

*.

,+0+

,,0

.+0

*

,*.1

,+1

,,

.,

*

.

,+/,

,,*

.,



+/.

,+//

,,0

.*

,*

/1.

,0*+

,,*

*.1/,

,

,,.

,0

,1/

*.00

*

,0*.

,0,

,0

*.++/



.*

,0,0

,+*

*.1,

*

+.

,0

,

*.*/

*

0.1

,00

,

*./

+*

+0.1

,01

,*1

*.*0

1*

**,

,001

,*

*./

,**



,0/

/

*.,0

Pressure Table 0.*

.*

,

,1

,/

/.0

.,

,/

,0/

*/

,.*

.

,,

,0

/./

.*

.+

,,0

,+1

1,.1

.1

.1

,

,+

0.*

0.

,.*

,

,+*

+0.*

,.

,.

,*

,,

.

;

,.

.*

,+

,

.0

,/.*

.*

,

,

.1

,./

.*

,+,

,,

,1.,

*.

0.

,0

,*+

/.,

.1

*.*

,1

,/

.0

+*.

,*.*

,+*

,1

0.+

0./

*.*

,+0

,/

.//

/.

1*.*

,+++

,,0

,.*/

//.+

**

,+0+

,,1

.+/

*,.

/

,+1*

,,

.

*.1

,*

,+1

,,

.

*0.

*

,+10

,,1

.

*/.

*

,+/*

,,,

.,

.

*

,+/

,,,0

.+

.

+*

,+/+

,,,

.*/

.,

0*

,+//

,,+

.*

+./

1*

,0*,

,,

*./01

1.+

/*

,0*

,,*0

*./,/

,*.,

,**

,0*0

,,*,

*.11+

,0.

,*

,00

,1,

*.0/

.+

**

,0,

,+

*.+*+

1./

*

,0,

,1

*.,

.+

**

,0/

,

*.+

0./

*

,0

,,

*.

.+

**

,0/

,*/

*.0

+0.1

0*

,0++

,*0

*.,+

0/./

***

,001

,*

*./

!

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