Multiple-Effect Evaporator Design The design calculations required for a multiple-effect evaporator are complex enoughto 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. e1 e2 e3 T1 Ts ws wf Tf xf w1 x1 T T2 T3 T T ws e1 w2 x2 wp e2 xp Above, variables: w e T x and subscripts: s f p 1,2,3 mass flow rate of liquid, kg/s mass flow rate of vapor, kg/s temperature, °C mass fraction NaOH steam feed product 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 Temperature Composition wf Tf xf 6 75 0.14 kg/s °C mass fraction NaOH -1- Triple-Effect Evaporator Design Steam Temperature Ts 150 °C T3 xp 39 0.47 °C [7 kPa pressure] Final Vapor Condensation Temperature Required Product Concentration Heat Transfer Coefficients Effect 1 2 3 U mass fraction NaOH W/(m2 •K) 3000 2000 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 (mass fraction) 0.00 0.10 0.20 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 The calculation scheme is now developed. Boiling Pt. Elev. (ºF) 0 4 14 25 35 47 65 75 88 100 120 138 2 Triple-Effect Evaporator Design 1. Overall Material Balance Total Feed Product Water Evaporated wf wp = xf •wf / xp etot = wf-wp NaOH xf •wf xf •wf or H2O (1-xf)wf (1-xp)wp (1-xf)wf - (1-xp)wp 2. Boilup Rates Estimate values for boilup rates in effects 1 and 2 e1 3. Material Balances in the Effects Effect 1 Effect 2 Effect 3 w1 = w f - e1 w2 = w 1 - e 2 w p = w 2 - e3 x1 = xf •wf / w1 x2 = xf •wf / w2 x3 = xp = xf •wf / wp [must equal basic data specification] e2 e3 = etot - e1 - e2 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 ΣBP = BP1 + BP2 + BP3 Sum of Boiling Point Elevations Net Available ∆T ∆Tnet = ∆Ttot - ΣBP 6. Effect Temperature Drops Estimate Compute ∆T1 ∆T2 ∆T3 = ∆Tnet - ∆T1 - ∆T2 3 Triple-Effect Evaporator Design 7. Effect Temperatures Effect 1 2 3 Actual Solution Temperature T1 = Ts - ∆T1 T2 = Ts1 - ∆T2 T3 = Ts2 - ∆T3 Steam Saturation Temperature Ts1 = T1 - BP1 Ts2 = T2 - BP2 Ts3 = T3 - BP3 [must confirm basic data specification] 8. Effect Enthalpy Balances Note: enthalpy values from tables, except where noted. Effect 1 Stream Steam Feed Boilup Condensate Effluent Temp Ts Tf T1 Ts T1 ws = Sat Temp Ts Comp No Superheat Enthalpy Hs Flow Rate ws wf e1 ws w1 xf Ts1 Hs1 Hf H1 hc x1 h1 H 1 e1 + h 1 w1 − h f w f Hs − h c [from enthalpy balance on effect 1] and, to account for superheat: Effect 2 Stream Temp H1 = Hs1 + R • BP1 [R: gas law constant] Sat Temp Ts1 Comp No Superheat Hs1 Enthalpy H1 h1 Flow Rate e1 w1 e2 e1 w2 Steam T1 [from Boilup, Effect 1] Feed T1 [from Effluent, Effect 1] Boilup T2 x1 Ts2 Hs2 H2 hc1 Condensate Ts1 [from Boilup, Effect 1, condensed] Effluent T2 x2 H2 = Hs2 + R • BP2 h2 To account for superheat: 4 Triple-Effect Evaporator Design Effect 3 Stream Temp Sat Temp Ts2 x2 Ts3 Hs3 Comp No Superheat Hs2 Enthalpy H2 h2 H3 hc2 xp H3 = Hs3 + R • BP3 hp Flow Rate e2 w2 e3 e2 wp Steam T2 [from Boilup, Effect 2] Feed T2 [from Effluent, Effect 2] Boilup T3 Condensate Ts2 [from Boilup, Effect 2, condensed] Effluent T3 To account for superheat: 9. Compute Effect Heat Duties and Required Heat Transfer Areas Effect 1: Effect 2: Effect 3: q1 = (Hs - hc) ws q2 = (H1 - hc1) e1 q3 = (H2 - hc2) e2 A1 = q1 / (U1 ∆T1) A2 = q2 / (U2 ∆T2) 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 s w s + h f w f = h 1w1 + h s w s + H 1e1 H 1e1 + h 1w1 = h 2 w 2 + h c1e1 + H 2 e 2 H 2 e 2 + h 2 w 2 = h p w p + h c2 e 2 + H 3 e 3 Rearrange to form three simultaneous equations to determine ws, e1, and e2. [H s − h s ]w s + [ −( H 1 − h 1 )]e1 + [ 0]e 2 = [ h 1 − h f ]w f [ 0]w s + [H 1 − h 1 + h 2 − h c1 ]e1 + [ −( H 2 − h 2 )]e 2 = [ h 2 − h 1 ]w f [0]ws +[H3 −h2]e1 +[H2 −h2 +H3 −hc2]e2 =[H3 −h2]wf +[−(H3 −hp)]wp Solve these equations for ws, e1, and e2. 5 Triple-Effect Evaporator Design 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: Vapor Generated: Overall Economy: Economy per Effect: ws etot etot/ws 1: 2: 3: Capacity: e1/ws e2/e1 e3/e2 wf/ws wp/ws Feed Processed / Steam Required: Product Produced / Steam Required: The spreadsheet in workbook file EVAP.XLS is created to implement this calculation scheme. 6