Question

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A forward feed triple - effect evaporator is required to concentrate a 10% pineapple juice mixture from 5 to 70% using steam at 200 kN/m2 (gauge). The feed enters at 2 000 kg/hr at 303 K and the first effect is operated at 105 kN/m2 (gauge). Additional information: 1. The BPR's can be estimated from the following equation: BPR (°C) = 1,78 X + 6,22 X2: 2. The heat capacity of the solution is given by Cp = 4,19 - 2,35 x (kJ/kg K). The heat of solution is negligible. 3. The overall heat transfer coefficients are estimated as U1 = 3,123 ; U2= 1,987 and U3 = 1,136 kW/ m2 K. 4. The heat transfer surfaces are the same in all three effects. 1.1 With the aid of a flow diagram, show all process streams including information required for the system. (6) 1.2 Calculate the BPR's and Cp's in each effect. List all assumptions. (18) 1.3 Perform the energy balances over each effects (12) 1.4 Calculate the area of the calandrias, the amount of steam used and the steam economy. (14)

Answer 1

Given! A forward feed triple effect evaporator is used. feed mass flow rate, f = 2000 kg/hr 2F = 107. B.P. R (°C) 1,782 + 622 2? Cp = 419 235 x (kJ/kg K) U = 312 3 kw/m²K U₂ = 1987 kW/m2K Uz - 21 36 kw/m²k. The heat transfer surfaces are the same in all three effects. Vi = 2000 -4 V2=4-22 V3=4₂-₂ F=2000 kg/hr T3 P3 Hug xf = 0.1 TI, HVI Tz ,Hv2 TE=303k (2) (1) (3) S=? T52 Ts3 PF 200 kN/m2 TSI Т2 T2, L2, a T1 , L , 4 L3= Xz=0.7 flow diagram for the triple effect evaporator. → Il represent enspecific enthalpy.

S2000-285.71 3 making making an overall and a solid balance. fe 2000 = 13 + CV +V2+V3) fxf 2000 (0:1) 1300-7)+(v +uz+13)(0) 13 = 285.71 kg/hr Total vaposized = (+ V2 +13) Jolal vaporized 1714.29 kg Ihr Assuming equal amount raporized in each offect, V = V2=V2 = 1724.29 - 571143 kg/hod a total material balance on effects 1, 2&3, solving F = 2000 vitu = 571143+4 (for effects 4 = 1428:57 kg/hr] 4 = V2 +L2 = 1428457 571143 the [for effect 2] L2=857.14 kg/hr V3 thz » 85714 = 571.43th Efor effect 3] L=285.71 kg/hr → making a solid balance on each offect, fxp = 42 (for effect I 5714324 24 = 0,35 44 = L₂x2 (for effect 2 571,34 X0:35 = 85 7.24 & x = 0,23 L2= 2500x0:1 =

[for effect 3 L2 22 = 3x3 857.13x023 - 285.71 * 23 x3 = 0.7 c Check) 2.2 B.P. R and Op's in each effect. B.P. R = 1.784 +62222 (°C) for effect (1), 24 = 0.35 B.P.R(1) = 1.78447622242 = 1.78 (0'35)+ 6:22(0:35)2 = 16 38 °C B.P.R (L) Gold) = 4.19 – 213524 Cp (1) 4.19 -2.35 * 0.35 SIL) = 3.37 kJ 1 kg k) 2 for effect (2), X2 = 0.23 B.P. R (2) = 2.78 x₂ + 6.22 x 2 = 1.7810:23) + 622 (0.23)2 B.P. R (2) = 0.74 °C Cp (2) = 4.19 - 2.35% Cp (2) = 3.65 KJ 1 kg K

for effect 3, E170 (0:7)+ 6:22 (0.7)2 3= 0.7 B.P.R(3) = 1.78X3 +622232 B.P.R(3) = 4.29 ec (p3) = 4:19-235 X3 4.19 - 2:35 (07) Cp (3) = 2:55 KJ/kg k

for feed stream, Сре 4.19 – 2:35 xp 4.19 22S xe | CF = 3.96 K31 kg k 1.3 since, pressure in the vapor space of the third effect is not mentioned. so, I am considering it as 13.4kpa. P₂ = 13.4kPa from steam table, at P3 = 1314 kPa get Tsat = 51.67C. 52.67 + B.PeR (3) = 51.67 + 4.29 T3=55-96 °C T3 =

PS Eot available = TSI - Tz (sat) - [B.P.RCI) +B.P.R(2)+B.P.R (3)] LOT avai Cable = Tsi-51.67 [130 +0.74 + 4:29] = 200 kN/m2 (gange) Ps = 200+300 kN/m2 (absolute) 300 kPa from steam table, at Ps= 300 kPa Tsi = 133.670. IPs SAT available = 133.67 -51.67 - 6.41 SAT available = 75159 cc 75.59 43123 31231487 iBo . 3123' 1987 '1136 ATI 1/UL AT = SAT 2/01+ /U2+1/03 = 14.21 °C BT2 = CAT 1/02 1 + 3 1987 فيع 755 ) i UL + 3123 DT2 = 75.59 = 1/1987 I -t 3123 1982 1136 AT2 = 22.33 °C 1U3 AT3= SAT - 39.06 °C 1 + 1 2 + 1

133.67 14.21 Actual boiling point of the solution in each effect TI= TSI - DTI Ti= 119.46°C T2 - Ti - B.P.R(1)-0T2 T2 -119.46 – 1:38 - 22:33 T2 = 95.75 oC T3 = T2 - B.P. R (2) - DT3 T3 = 95.75 -0.74 39.06 T3 = 55.95 cc Tsa Tsa 0.74 Ti - B.B.R(1) 119.46 -1.38 118.08°C Tz B.P.R(2) = 95.75 95.01 °C Ts3 Ts3

hst = И of At Ps = 300kPa (for entering steam Ts d = 133.67°C to the fust effect) specific enthalpy, tsi 71 t can be obtained using steam table, Hss 2725114 kilky specific enthalpy for condensate out, 561.96 kJ/kg. Asi = Hsi-hi = 216.18 KJ 1kg Asi = 2163.18 kJ 1 kg The values of the enthalpy the various vapor as a datum are watee at ole streams relative to obtained from the steam table as follows: Effect !! Iust 2163 '18 kJ 1kg Hvi - Hí' + Gee B.P.RCL) [H reprezeut specifie enthalpy Hi can be obtained from steam table at Ti = 119.46°C. H,'- 2705.14 kJ/kg Cps = feat capacity of superheated steam= 1.884 kJ lug k Hvi 2705414 + 1.884* 138 Hv = 2707.6 kilkg

At T = 55.95°C 1 Effect As2 = Hvi hsa At Ta 95.75°C hs2=401.24 kJ 1kg is2= 2707.6 - 401.24 ds2 2306.36 kJ 1 kg Hv2 Hv2 = H2' + cps B.P.R(2) At T2 = 95.75°C, H₂'=2669.09 kJ 1kg HV2 = 2669.09+1.884~0.74 Hv2 = 26 70-48 kJ 1 kg Effect 3- is 3 = -hs3 As3 = 2 670148 Asa = 24 36,25 kJ 1 Kg At T3=55.95°C, H3' = 2601186 kJ 1kg Hv3=431+ cps B.P. R (3) Hv3 = 2601186 + 1188 4x 4129 HV3 = 2609194 kJ 1 kg 234.23 -

1 write the heat balance on each effect Effect L F GPF CTA-0) + Siksi I 4 CPL (-0) + V, HVI 2000 x 3.96 (30-0) + 5 x 2163-18 3:37 4 (119,46 -0) + 591.4 3x2707.6 200d x 3.96 (30-0) + 5 x 2163110 = 3.37x1420157 x (119,46 -0) +571. 4. 3x27076 s=871,27 kg/hr

-Effect 2, 4CPL CT, -o) + Asali o h Cpz (T₂-0) + V₂ Hva e Effects, L₂ CP2 (Taro) + Vaasa = L3 Cp3 (T3-0) + V₃ HN3 - ③ Sisi hr 1.4 for aria calculations, น =871.27 kg x2163.18 kJ Flest transfee from kg effectl) q 871.27 kg x 2163118x103 J 3600 kg sec 21= 5.23 X 205 w

Heat transfer 92 kg from effect 2, Vg As2 = 571.43 kg x 2366.36 KS 92 = 571.43 kg x 2306: 368 1033 kg 92 = 3.67 X105W 3600 see 93 Heat transfer from effect 3, V2 is 3=572.43 kg x 2 436125 kJ kg 93=571.43 kg x 2436.250 103 g hr leg 3600 sec 193 - 3.87X1050 Arts AL- q 5:23X10S 0'0118 m2 UOTI 3123X103x)4.21 required by first Heat transfer area available for effect & is 0.0118 m² 92 3167X10S z 8.27x10-3 m² 1987X103 x 22:33 Heat transfer area available for effect 2 is 8.27 x 103 m² 3.87xlos 8.72X20-3 m2 1136X105X 39.06 A2 U₂ AT2 A3 93 UBAT3 3 m² Heat transfee area available for effect is 8. 27X10

Amount of stany used, S = 871:27 kgho steam conothy - (vi + V2+13) S I 3X 571143 871.27 Steam Economy Economy=1197