Evaporator Excel

Simulation of a multiple-effect evaporator

Instructions 1. a. On the Tools menu, click Options, then click the Calculation tab and tick on the Iteration box. O

2. For a forward feed 2-effect evaporator In the spreadsheet "2-Effect" a. Insert parameter values in the yellow cells b. Turn the "SWITCH" ON (set the value in the cell B9 (red cell) equal to 1) c. Iterate (by pressing F9) until "FINISH" or "ALARM" signal is shown in the control panel d. If a signal to "REDUCE Ts or mwin" is shown in the control panel, turn the SWITCH OFF, reduce th in cells B28 or B29 respectively and start again from 2b e. If a signal to "INCREASE Ts or mwin" is shown in the control panel, turn the SWITCH OFF, increas in cells B28 or B29 respectively and start again from 2b f. When "FINISH" is shown in the control panel, read the results in the green cells (B34-B38) g. If a solution can not be reached under any combination of Ts and mwin values, change the heat tra and repeat steps 2a to 2f h. To recalculate for different parameter values turn the "SWITCH" OFF (set the value in the cell B9

3. For a forward-feed 4-effect evaporator In the spreadsheet "4-Effect Forward" a. Insert parameter values in the yellow cells b. Turn the "SWITCH" ON (set the value in the cell B9 (red cell) equal to 1) c. Iterate (by pressing F9) until "FINISH" or "ALARM" signal is shown in the control panel d. If a signal to "REDUCE Ts or mwin" is shown in the control panel, turn the SWITCH OFF, reduce th in the cells B28 or B29 respectively and start again from 2b e. If a signal to "INCREASE Ts or mwin" is shown in the control panel, turn the SWITCH OFF, increas in the cells B28 or B29 respectively and start again from 2b f. When "FINISH" is shown in the control panel, read the results in the green cells (B33-B37) g. If a solution can not be reached under any combination of Ts and mwin values, change the heat tra and/or Q19 and repeat steps 2a to 2f h. To recalculate for different parameter values turn the "SWITCH" OFF (set the value in the cell B9

4. For a backward-feed 4-effect evaporator In the spreadsheet "4-Effect Backward" a. Insert parameter values in the yellow cells b. Turn the "SWITCH" ON (set the value in the cell B9 (red cell) equal to 1) c. Iterate (by pressing F9) until "FINISH" or "ALARM" signal is shown in the control panel d. If a signal to "REDUCE Ts or mwin" is shown in the control panel, turn the SWITCH OFF, reduce th

in the cells B28 or B29 respectively and start again from 2b e. If a signal to "INCREASE Ts or mwin" is shown in the control panel, turn the SWITCH OFF, increas in the cells B28 or B29 respectively and start again from 2b f. When "FINISH" is shown in the control panel, read the results in the green cells (B33-B37) g. If a solution can not be reached under any combination of Ts and mwin values, change the heat tra and/or Q19 and repeat steps 2a to 2f h. To recalculate for different parameter values turn the "SWITCH" OFF (set the value in the cell B9

nd tick on the Iteration box. On Maximum iterations box write 1000

n the control panel n the SWITCH OFF, reduce the value of either T s or mwin

urn the SWITCH OFF, increase the value of either T s or mwin

green cells (B34-B38) mwin values, change the heat transfer area in the cells H19 and/or J19 and/or M19

F (set the value in the cell B9 equal to 0) and repeat steps 2a to 2f



green cells (B33-B37) win values, change the heat transfer area in the cells H19 and/or J19 and/or L19 and/or N19




green cells (B33-B37) win values, change the heat transfer area in the cells H19 and/or J19 and/or L19 and/or N19


The following assumptions are used

1) The pressure drop in the vapour lines is neglected 2) The effect of superheating on the vapour enthalpy due to the BPE is neglected 3) The heat losses to the environment are taken into account. If cells B23 or B24 for Ulos and Ao L are se 4) The condensate from each effect exits at the condensation temperature 5) The condenser is assumed to be a surface condenser

The following empirical relationships are used in the calculations a) Heat capacity of liquid foods (equation of Dickerson), J/kgoC c p  1672  2508 x w

where xw is the mass fraction of water content b) Boiling Point Elevation, oC BPE  2.7 x s  8.8x s2  21 .2 x 3s

where xs is the mass fraction of solids content c) Heat capacity of liquid water, J/kgoC

c p  4211 1.34T  0.015T 2 where T is temperature in oC d) Enthalpy of saturated steam and vapour, kJ/kg H v  2501  1.919 T  0.0017 T 2

where T is temperature in oC e) Latent heat of vaporization of water, kJ/kg   2501  2.265T  0.0018T 2

where T is temperature in oC f) Vapour pressure of liquid water, atm (Ref. 15) log p w  10.79586(1  )  5.02808log   1.50474x10 4 1  10  273.16  where with T in Kelvin T

    3   0.42873x10

8.29692 1 1 





273.16 T

or B24 for Ulos and Ao L are set equal to 0, the heat losses are neglected

 10

    3 4.769551   1  2.2195983   0.42873x10 10

8.29692 1 1 



Forward-Feed 2-Effect Evaporator

Control panel

SWITCH=

1

FINISHED 0.000

Input data Feed flow rate, Feed solids content, Desired product solids content, Feed temperature, Temperature of the environment,

mf = xf = Xspec = Tf = Te =

10000 kg/h 10% 30% o 70 C o 20 C

Outside Area of each effect of the evaporator, AoL=

2o 0 W/m C 2 50 m

Cooling water temper. at the inlet of the cond., Twin=

o 25 C

Overall Heat transfer coeffic. for heat losses,

Ulos=

Control variables Steam temperature,

Ts =

Mass flow rate of cooling water in the conden.,mWin =

o 122 C

38300 kg/h

Results Concentrated product flow rate, Solids content at the outlet, Steam consumption, Steam economy Cooling water flow rate,

m p= x p= m s= m Win=

3332 kg/h 30.0% 3937 kg/h 1.7 kg/kg 38300 kg/h

mi2, xi2, Ti2

mf , xf , Tf

mWin Twin

ms,Ts

mv1,Tv1 mc1,Tc1 Tb1

mWout Twout mc,Tc

mv2,Tv2 mc2,Tc2 Tb2

mo1, xo1,To1 mp, xp,Tp liquid food

steam/vapour/condensate

Parameters

cooling water

1st EFFECT 2nd EFFECT 2

Heat transfer area (m ),

A

CONDENSER

80

80

1800

1000

Overal heat transf. coef.

2.778

1.878

Cooling water flow rate in

0.1

0.148

Cooling water temper. in

Ti

70

105.3

Water vapour temper. in

Tb

105.3

79.8

Cooling water temp. out

Saturation temperature ( C),

Tv

105.0

79.2

Condensation temperat.

Saturation pressure (atm), Temperature drop (oC),

P ΔΤ

1.194 16.7

0.453 25.2

Water vapour pressure

Boiling Point Elevation (oC),

BPE

0.3

0.6

Heat capacity of liquid at inlet (J/kg C), cpi

3929

3809

3809

3427

0

0

0.899

0.953

1.878

0.925

0.148

0.300

1.094

0.899

122

105.0

2o

Overall heat transfer coef. (W/m C),

U

Liquid flow rate at the inlet (kg/s),

mi

Solids content at the inlet,

xi o

Liquid temperature at the inlet ( C), o

Boiling temperature ( C), o

o

o

Heat capacity of liquid at outlet(J/kg C), cpo Heat losses (W),

qL

Evaporation rate (kg/s),

mv

Liquid flow rate at the outlet (kg/s),

mo

Solids content at the outlet,

xo

Heating steam/vapour flow rate (kg /s), m s o

Heating steam/vapour temperature ( C), Ts

Heat transf. area

mWout Twout

cooling water CONDENSER 2 50 m 2o 2500 W/m C

10.639 kg/s o 25 C o 79.2 C o 74.5 C o 79.1 C

0.452 atm

Forward-Feed 4-Effect Evaporator

Control panel

SWITCH=

1

FINISHED 0.0000



20000 kg/h 9% 48% o 60 C o 20 C


2o 0 W/m C 2 50 m


o 25 C


Ulos=


Ts =


o 75 C

530000 kg/h



3756 kg/h 47.9% 4244 kg/h 3.8 kg/kg 530000 kg/h

mf , xf , Tf

mi2, xi2, Ti2

mi4, xi4, Ti4

mi3, xi3, Ti3

mWin Twin

ms,Ts mv1,Tv1

mv3,Tv3

mv2,Tv2

mv4,Tv4 mc1,Tc1 Tb1

mc2,Tc2

mo1, xo1,To1

mc3,Tc3

Tb2

mo2, xo2,To2

mc4,Tc4

Tb3

Tb4

mo3, xo3,To3 mp, xp,Tp

liquid food

steam/vapour/condensate 1st EFFECT

2

Heat transfer area (m ),

A

2nd EFFECT

co

3rd EFFECT

4th EFFECT

270

270

270

270

2200

1800

1300

506

5.556

4.481

3.372

2.230

0.09

0.112

0.148

0.224

Ti

60

70.4

65.0

57.3

Tb

70.4

65.0

57.3

37.1


Tv

70.2

64.7

56.9

35.7


P ΔΤ

0.310 4.6

0.244 5.2

0.170 7.4

0.058 19.8


BPE

0.2

0.3

0.4

1.6


3954

3900

3808

3618

3900

3808

3618

2979

0

0

0

0

1.075

1.109

1.142

1.188

4.481

3.372

2.230

1.042

0.112

0.148

0.224

0.479

1.179

1.075

1.109

1.142

75

70.2

64.7

56.9

2o


U


mi


xi o



o

o


qL


mv


mo


xo



mi4, xi4, Ti4 mWin Twin

mWout Twout mc,Tc

mv4,Tv4

4,Tc4

Tb4

mp, xp,Tp

ate

cooling water CONDENSER Heat transf. area Overal heat transf. coef. Cooling water flow rate in

2 150 m 2o 2500 W/m C

147.2 kg/s


o 25 C


o 35.7 C


o 29.7 C


o 35.7 C


0.058 atm

Backward-Feed 4-Effect Evaporator

Control panel

SWITCH=

1

FINISHED 0.000



20000 kg/h 9% 48% o 60 C o 20 C


2o 0 W/m C 2 50 m


o 25 C


Ulos=


Ts =


o 75 C

220000 kg/h



3745 kg/h 48.1% 4327 kg/h 3.8 kg/kg 220000 kg/h

mi2, xi2, Ti2

mi1, xi1,Ti1

mf , xf , Tf

mi3, xi3, Ti3

mWin Twin

ms,Ts mv1,Tv1

mv2,Tv2

mc1,Tc1 Tb1

mc2,Tc2 Tb2

mo3, xo3,To3

1st EFFECT Heat transfer area (m ),

A 2o


U

mo4, xo4, To4

steam/vapour/condensate

liquid food

2

mv4,Tv4 mc4,Tc4 Tb4

mc3,Tc3 Tb3

mo2, xo2,To2

mp, xp,Tp

m

mv3,Tv3

2nd EFFECT

coo

3rd EFFECT

4th EFFECT

270

270

270

270

1214

1400

1270

1044


mi

2.202

3.312

4.350

5.556


xi

0.227

0.151

0.115

0.090

Ti

57.7

49.6

40.5

60.0

Tb

66.5

57.7

49.6

40.5


Tv

64.9

57.2

49.3

40.3


P ΔΤ

0.246 8.5

0.173 7.2

0.118 7.7

0.074 8.8


BPE

1.6

0.4

0.3

0.2


3611

3801

3892

3954

2974

3611

3801

3892

0

0

0

0

1.162

1.110

1.037

1.206

1.040

2.202

3.312

4.350

0.481

0.227

0.151

0.115

1.202

1.162

1.110

1.037

75

64.9

57.2

49.3

o



o

o


qL


mv


mo


xo



mf , xf , Tf mWin Twin mv4,Tv4

mWout Twout mc,Tc

Tc4 Tb4

mo4, xo4, To4

te

cooling water CONDENSER Heat transf. area Overal heat transf. coef.

2 150 m 2o 2500 W/m C

Cooling water flow rate in

61.1 kg/s


o 25 C


o 40.3 C


o 36.4 C


o 40.2 C


0.074 atm

Evaporator Excel

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