Triple Effect evaporator

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Multiple-Effect Evaporator Design The design calculations required for a multiple-effect evaporator are complex enough to provide a real challenge for implementation using a spreadsheet program. The elements of the spreadsheet integrate much of what we have introduced in the course. To create a spreadsheet of this or greater complexity, it is necessary to understand and plan out the calculation scheme. This we do first here before considering the spreadsheet solution. The example chosen is a triple-effect evaporator used to concentrate a caustic soda solution. The process is depicted in the figure below with key variables shown.

T T T

wf

ws

e1 e2 e3

T1 T2 T3

w1 w2 wp

ws e1 e2

Ts

Tf

xfx1 x2 xp

Above, variables:

w mass flow rate of liquid, kg/s e mass flow rate of vapor, kg/s T temperature, °C x mass fraction NaOH

and subscripts: s steam f feed p product 1,2,3 effects 1, 2, 3, respectively

Steam feed to the first effect on the left and the vapor boiled up in effects 1 and 2 is used to heat the subsequent effect. The final vapor stream is condensed. To compute the energy balances for the units, enthalpy information is required. Boiling point elevations are significant for aqueous solutions of NaOH; so, these data are required too. Heat transfer coefficients or correlations are required for the three effects. The pressure at which the third effect is operated, often at vacuum, must be known. Consider the following basic data: Feed

Flow rate wf 6 kg/s Temperature Tf 75 °C Composition xf 0.14 mass fraction NaOH

Triple-Effect Evaporator Design

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Steam

Temperature Ts 150 °C

Final Vapor Condensation Temperature T3 39 °C [7 kPa pressure] Required Product Concentration xp 0.47 mass fraction NaOH Heat Transfer Coefficients Effect U W/(m2

•K) 1 3000 2 2000 3 1250 Data for enthalpy of NaOH-H2O liquid mixtures at different compositions and temperatures are presented in Section 1. Data for enthalpy of water and steam at different temperatures are available readily from the steam tables. A Dühring plot for boiling point elevation of NaOH-H2O mixtures yields the following data:

Composition Boiling Pt. Elev. (mass fraction) (ºF)

0.00 0 0.10 4 0.20 14 0.30 25 0.35 35 0.40 47 0.45 65 0.50 75 0.55 88 0.60 100 0.65 120 0.70 138

The calculation scheme is now developed.


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1. Overall Material Balance Total NaOH H2O Feed wf xf •wf (1-xf)wf Product wp = xf •wf / xp xf •wf (1-xp)wp Water Evaporated etot = wf-wp or (1-xf)wf - (1-xp)wp

2. Boilup Rates Estimate values for boilup rates in effects 1 and 2 e1 e2 e3 = etot - e1 - e2 3. Material Balances in the Effects Effect 1 w1 = wf - e1 x1 = xf •wf / w1 Effect 2 w2 = w1 - e2 x2 = xf •wf / w2 Effect 3 wp = w2 - e3 x3 = xp = xf •wf / wp

[must equal basic data specification] 4. Boiling Point Elevations Get values BP1, BP2, and BP3 from table for x1, x2, and x3 ( = xp ) respectively. Convert ºF to ºC by

dividing by 1.8. 5. Overall Temperature Drops Total Available ∆T ∆Ttot = Ts - T3 Sum of Boiling Point Elevations ΣBP = BP1 + BP2 + BP3 Net Available ∆T ∆Tnet = ∆Ttot - ΣBP 6. Effect Temperature Drops Estimate ∆T1 ∆T2 Compute ∆T3 = ∆Tnet - ∆T1 - ∆T2


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7. Effect Temperatures Effect Actual Solution Temperature Steam Saturation Temperature 1 T1 = Ts - ∆T1 Ts1 = T1 - BP1 2 T2 = Ts1 - ∆T2 Ts2 = T2 - BP2 3 T3 = Ts2 - ∆T3 Ts3 = T3 - BP3 [must confirm basic data specification] 8. Effect Enthalpy Balances Note: enthalpy values from tables, except where noted. Effect 1 No Stream Temp Sat Temp Comp Superheat Enthalpy Flow Rate Steam Ts Ts Hs ws Feed Tf xf Hf wf Boilup T1 Ts1 Hs1 H1 e1 Condensate Ts hc ws Effluent T1 x1 h1 w1

w H e h w h wH hs

f f

s c=

+ −−

1 1 1 1

[from enthalpy balance on effect 1] and, to account for superheat: H1 = Hs1 + R • BP1 [R: gas law constant] Effect 2 No Stream Temp Sat Temp Comp Superheat Enthalpy Flow Rate Steam T1 Ts1 Hs1 H1 e1 [from Boilup, Effect 1] Feed T1 x1 h1 w1 [from Effluent, Effect 1] Boilup T2 Ts2 Hs2 H2 e2 Condensate Ts1 hc1 e1

[from Boilup, Effect 1, condensed] Effluent T2 x2 h2 w2 To account for superheat: H2 = Hs2 + R • BP2


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Effect 3 No Stream Temp Sat Temp Comp Superheat Enthalpy Flow Rate Steam T2 Ts2 Hs2 H2 e2 [from Boilup, Effect 2] Feed T2 x2 h2 w2 [from Effluent, Effect 2] Boilup T3 Ts3 Hs3 H3 e3 Condensate Ts2 hc2 e2

[from Boilup, Effect 2, condensed] Effluent T3 xp hp wp To account for superheat: H3 = Hs3 + R • BP3 9. Compute Effect Heat Duties and Required Heat Transfer Areas Effect 1: q1 = (Hs - hc) ws A1 = q1 / (U1 ∆T1) Effect 2: q2 = (H1 - hc1) e1 A2 = q2 / (U2 ∆T2) Effect 3: q3 = (H2 - hc2) e2 A3 = q3 / (U3 ∆T3) 10. Convergence to Equal Areas If areas are not equal, return to step 6, re-estimate ∆T1 and ∆T2 and recalculate through step 9 until

areas are equal, at least approximately. 11. Enthalpy Balances H w h w h w h w H es s f f s s+ = + +1 1 1 1 H e h w h w h e H ec1 1 1 1 2 2 1 1 2 2+ = + + H e h w h w h e H ep p c2 2 2 2 2 2 3 3+ = + +

Rearrange to form three simultaneous equations to determine ws, e1, and e2. [ ] ( )[ ] [ ] [ ]H h w H h e e h h ws s s f f− + − − + = −1 1 1 2 10

[ ] [ ] ( )[ ] [ ]0 1 1 2 1 1 2 2 2 2 1w H h h h e H h e h h ws c f+ − + − + − − = −

[ ] [ ] [ ] [ ] ( )[ ]0 3 2 1 2 2 3 2 2 3 2 3w H h e H h H h e H h w H h ws c f p p+ − + − + − = − + − −

Solve these equations for ws, e1, and e2.


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12. Convergence to Consistent Boilup Values Check to see if the boilup values (e1 and e2) resulting from step 11 are equal to the starting estimates

from step 2. If they aren’t equal, substitute the values from step 11 into step 2 and repeat the calculation through step 11. Repeat as necessary until consistent boilup values are obtained.

13. Energy, Economy, and Capacity Summary Steam Requirement: ws Vapor Generated: etot Overall Economy: etot/ws Economy per Effect: 1: e1/ws 2: e2/e1 3: e3/e2 Capacity: Feed Processed / Steam Required: wf/ws Product Produced / Steam Required: wp/ws

The spreadsheet in workbook file EVAP.XLS is created to implement this calculation scheme.

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Triple Effect evaporator