ΕΘΝΙΚΟ ΜΕΤΣΟΒΙΟ ΠΟΛΥΤΕΧΝΕΙΟ ΤΜΗΜΑ ΧΗΜΙΚΩΝ ΜΗΧΑΝΙΚΩΝ ΕΡΓΑΣΤΗΡΙΟ ΣΧΕΔΙΑΣΜΟΥ & ΑΝΑΛΥΣΗΣ ΔΙΕΡΓΑΣΙΩΝ

Transcript

1 ΕΘΝΙΚΟ ΜΕΤΣΟΒΙΟ ΠΟΛΥΤΕΧΝΕΙΟ ΤΜΗΜΑ ΧΗΜΙΚΩΝ ΜΗΧΑΝΙΚΩΝ ΕΡΓΑΣΤΗΡΙΟ ΣΧΕΔΙΑΣΜΟΥ & ΑΝΑΛΥΣΗΣ ΔΙΕΡΓΑΣΙΩΝ Μάθημα: ΤΕΧΝΙΚΗ ΦΥΣΙΚΩΝ ΔΙΕΡΓΑΣΙΩΝ ΙΙ 6ο Εξάμηνο Χημικών Μηχανικών ΞΗΡΑΝΤΗΡΕΣ 1

2 Characteristics of Food Dryers Product Evaporation Residence Dryer type Product form Temperature Capacity time o C kg/m 2 h Bin or Silo Pieces, Grains days Tray Pieces h Tunnel Pieces h Conveyor belt Pieces h Rotary Grains, granules h Dru m Sheet s Fluid bed Grains, granules min Pneumatic flash Grains, granules * 2-20 s Spray Powder * s Vacuum/Freeze Pieces h * kg/m 3 h. Pieces >5 mm, grains-granules 0. 5 mm, powders < 0.5 mm 150 Spray Pneumatic Drum Product tem pera ture ( o C) Fluidized Rotar y Conveyor Tunne l Tray Bin Vacuum Residence time (h) 2

3 Bin Tray Vacuum Tunnel Conveyor Drum Fluidized Rotary Spray Pneumatic Evaporation capacity (kg/m 2 h, kg/m 3 h) 3

4 BIN (SILO) DRYERS ΕΙΔΗ ΞΗΡΑΝΤΗΡΩΝ Air out Air in Recycle air Fan Heater Bin 4

5 ΞΗΡΑΝΤΗΡΕΣ ΜΕ ΡΑΦΙΑ Air out Air in Recycle air Fan Heater Cabinet 5

6 Ξηραντήρες Σήραγγας Fan Heater Air in Recycle air Air out Trucks 6

7 Ξηραντήρες Μεταφορικής Ταινίας Air out Air in Fan Heater Recycle air Belt Feed Product 7

8 Περιστροφικοί Ξηραντήρες Air out Feed Recycle air Air in Fan Heater Product 8

9 Ξηραντήρες Τύμπανου Feed Product Knife Heated drums 9

10 Ξηραντήρες Ψεκασμού Air in Feed Air out Bag filter Fan Heater Cyclone Product 10

11 ΠΝΕΥΜΑΤΓΙΚΟΣ ΞΗΡΑΝΤΗΡΑΣ Air out Feed Cyclone Product Air in Fan Heater 11

12 ΞΗΡΑΝΤΗΡΑΣ ΡΕΥΣΤΟΣΤΕΡΕΑΣ ΚΛΙΝΗΣ Air out Feed Recycle air Air in Fan Heater Product 12

13 Vacuum pump Feed Product 13

14 Refrigerated condenser Vacuum pump Drying chamber 14

15 ΨΥΧΡΟΜΕΡΤΙΚΟΣ ΧΑΡΤΗΣ Psychrometric Model P S = exp [a 1 - a 2 / (a 3 + T)] Y S = m P S / (P- P S ) Y V = min ( Y, Y S ) Y L = Y - Y V Y V = m a w P S / (P- a w P S ) H = Cp A T + Y V ( H 0 + Cp V T) + Y L Cp L T (E01) (E02) (E03) (E04) (E05) (E06) T b = -a 3 + a 2 / (a 1 - lnp) T d = a 2 / (a 1 - ln[y P/ (m+y)]) - a 3 P d =exp [a 1 - a 2 / (a 3 +T)] (E07) (E08) (E09) P w = exp [a 1 - a 2 / (a 3 + T w )] Y w = m P w / (P- P w ) Cp = Cp A + Y V Cp V H S = H 0 - (Cp L - Cp V ) T (Y V - Y W ) / (T - T W ) = - Cp / H S (E10) (E11) (E12) (E13) (E14) 15

16 Variables involved in the Psychrometric Model P bar Pressure P d bar Dew pressure P s bar Vapor pressure at temperature T P w bar Vapor pressure at temperature T w T C Temperature T o b C Boiling temperature C Dew temperature T d T w o C Wet bulb temperature Y kg/kg db Total humidity (liquid + vapor) Y L kg/kg db Humidity in liquid Y V kg/kg db Humidity in vapor Y s kg/kg db Saturation humidity at temperature T Y w kg/kg db Saturation humidity at temperature T w a w - Water activity H kj/kg db Enthalpy of humid air Cp kj/kgk db Specific heat of humid air H S kj/kg Latent heat of condensation of water vapor at temperature T Psychrometric Data for Air-Water Vapor Mixture R = 8.31 kj/kmol K Ideal gas constant m = Air/water molecular weight ratio Cp A = 1.00 kj/kg K Specific heat of air Cp V = 1.90 kj/kg K Specific heat of water vapor Cp W = 4.20 kj/kg K Specific heat of liquid water H 0 = 2.50 MJ/kg Latent heat of water evaporation at 0 o C a 1 = Antoine equation constants for water a 2 = a 3 = Degrees of Freedom Analysis Psychrometric variables 17 Model equations 14 Degree of freedom 3 16

17 Most Common Psychrometric Calculations Given variables: P, T, Y. (E01) -> P s (E02) -> Y s (E03) -> Y V (E04) -> Y L (E05) -> a w (E06) -> H (E07) -> T b (E08) -> T d (E09) -> P d T w trial value <- (E10) -> P w I (E11) -> Y w I (E12) -> Cp I (E13) -> H S I (E14) -> T w corrected value -> Construction Procedure of Psychrometric Charts Y V = F (T,a w,p) (E01) -> P s (E05) -> Y V Y s = F (T,P) (E01) -> P s (E02) -> Y s H = F (T,Y,P) (E01) -> P s (E02) -> Y s (E03) -> Y V (E04) -> Y L (E06) -> H H = F (Y V,a w,p) (E05) -> P s (E01) -> T (E06) -> H 17

18 Humidity versus temperature at various water activities. Pressure = 1 bar Water activity = 1.00 Humidity (kg/kg db) Temperature ( o C) Humidity at saturation versus temperature at various pressures. Water activity = Humidity (kg/kg db) Pressure (bar) = Temperature ( o C) 18

19 Humid air specific enthalpy versus temperature at various humidities. Pressure = 1 bar. 300 Humid enthalpy (kj/kg db Humidity (kg/kg db) = Temperature ( o C) Humid air specific enthalpy versus humidity at various water activities. Pressure = 1 bar. Humid enthalpy (kj/kg db Water activity Humidity (kg/kg db) 19

20 0.250 Water activity = (T,Ys) Humidity (kg/kg db) (Tw,Yw) (Td,Y) (T,Y) Temperature ( o C) Numerical Values of the Characteristic Variables Presented in Figure 7.18 P = 1 bar Pressure T = 65 o C Temperature Y = kg/kg db Humidity a w = Water activity T d = 34.0 o C Dew temperature T w = 39.4 o C Wet bulb temperature Y s = kg/kg db Saturation humidity at temperature T Y w = kg/kg db Saturation humidity at temperature T w 20

21 Drying Kinetics ΚΙΝΗΤΙΚΗ ΞΗΡΑΝΣΗΣ t = -t c ln[ (X-X e )/ (X o -X e )] X e =b 1 exp[b 2 / (273+T)] [a w / (1-a w )] b3 t c = c 0 d c1 u c2 T c3 Y c4 (E01) (E02) (E03) onion carrot 0.1 pepper potato 0.0 (a) Material moisture content (kg/kg db) Temperature ( o C) = (b) Water activity 21

22 1.00 Drying time constant (h) Humidity (kg/kg db) = Temperature ( o C) 1.00 Drying time constant (h) Velocity (m/s) = Temperature ( o C) 22

23 10 Material moisture content (kg/kg db) Temperature ( o C) Humidity (kg/kg db) Velocity (m/s) Drying time (h) 23

24 ΙΣΟΖΥΓΙΑ ΜΑΖΑΣ ΚΑΙ ΕΝΕΡΓΕΙΑΣ Heat F a Y o Q Air T o F X T o Solid Dryer F X T F a T Material and Heat Balances Y Material balance W = F (X o - X) W = F a (Y - Y o ) (E1) (E2) Energy (heat) bal ance Q = Q we + Q sh + Q ah Q we = F (X o - X) [ H o - (Cp L - Cp V ) T] Q sh = F [Cp S + X o Cp L ] (T - T o ) Q ah = F a [Cp A +Y o Cp V ] (T - T o ) (E3) (E4) (E5) (E6) Thermal efficiency n = Q we / Q (E7) 24

25 ΣΧΕΔΙΑΣΜΟΣ ΞΗΡΑΝΤΗΡΑ ΜΕΤΑΦΟΡΙΚΗΣ ΤΑΙΝΙΑΣ F a, Y o, T o Q E f F, X o, T o u F f, Y, T V E b F, X, T Heater Fan Product Air in Air out 25

26 Belt Dryer Model Psychrometric equations P S = exp [a 1 a 2 / (a 3 + T)] Y = m a w P S / (P- a w P S ) Drying kinetics X e =b 1 exp[b 2 / (273+T)] [a w / (1-a w )] b3 t c = c 0 d c1 u c2 T c3 Y c4 t = -t c ln[ (X-X e )/ (X o -X e )] Material balance W = F (X o - X) W = F a (Y - Y o ) Thermal energy requirements Q we = F (X o - X) [ H o - (Cp L - Cp V ) T] Q sh = F [Cp S + X o Cp L ] (T - T o ) Q ah = F a [Cp A +Y o Cp V ] (T - T o ) Q = Q we + Q sh + Q ah Air heater Q = A s U s (T s -T) (E01) (E02) (E03) (E04) (E05) (E06) (E07) (E08) (E09) (E10) (E11) (E12) Belt dryer M = t F (1+X o ) M = (1-ε) ρ s H H = Z o D L A b = L D u b = L / t Fan P = f 1 Z o V 2 F f = ρ a V D L E f = P F f / ρ a (E15) (E13) (E14) (E16) (E17) (E18) (E19) (E20) Belt driver E b = e 1 L (1+X o ) F Electrical energy requirements E = E b + E f Performance indices n = Q we / Q r = W / A b (E21) (E22) (E23) (E24) 26

27 Drying air F a ton/h Fresh air flow rate F f ton/h Recycle air flow rate T C Drying air temperature Y kg/kg db Drying air humidity V m/s Drying air velocity P bar Drying pressure T o C Ambient temperature Y o kg/kg db Ambient humidity P s bar Vapor pressure at drying conditions a w - Water activity at drying conditions Material F ton/h Material flow rate X o kg/kg db Initial moisture content X kg/kg db Final moisture content X e kg/kg db Equilibrium moisture content at drying conditions d m Particle size t c h Drying time constant at drying conditions t h Drying time Dryer W ton/h Drying rate L m Dryer length D m Dryer width M ton Dryer mass holdup H m 3 Dryer volume holdup A b m 2 Belt area A s m 2 Air heater transfer area u b m/s Belt velocity Z o m Loading depth P bar Pressure loss of air flowing through belt Thermal Load Q we kw Water vaporization Q sh kw Solid heating Q ah kw Air heating Q kw Total thermal load T s o C Steam temperature Electrical Load E b kw Belt driver E f kw Fan E kw Total power requirement Performance n - Thermal efficiency r kg/h m 2 Specific rate of evaporation 27

28 Process Data ρ w ρ a ρ s C pl C pv C pa C ps H o Density (kg/m 3 ) Water Air Dry material Specific heat (kj/kgk) Water Water vapor Air Dry material Latent heat (kj/kg) Steam condensation at 0 o C Other U s Heat transfer coefficient at air heater (kw/m 2 K) ε Vo id (empty) fraction of loading a 1, a 2, a 3 b 1, b 2, b 3 c 0, c 1, c 2, c 3, c 4 e 1 f 1 Empirical constants Antoine equation for vapor pressure of water Oswin equation for material isotherms Drying kinetics equation Belt driver power equation Pressure loss equation 28

29 Process Specifications F ton/h db Feed flow rate X o kg/kg db Initial material moisture content X kg/kg db Final material moisture content d m Material characteristic size T o o C Ambient temperature Y o kg/kg db Ambient humidity Z o m Loading depth P bar Ambient pressure o C Heating steam temperature T s Degrees of Freedom Analysis Process variables 37 Degree of freedom 13 Process equations 24 Specifications 9 Degree of freedom 13 Design variables 4 Design Variables Y kg/kg db Drying air humidity T o C Drying air temperature V m/s Drying air velocity D m Belt width Model Solution Algorithm (E01) -> P s (E02) -> a w (E03) -> X e (E04) -> t c (E05) -> t (E06) -> W (E07) -> F a (E08) -> Q we, (E09) -> Q sh, (E10) -> Q ah (E11) -> Q (E12) -> A s (E13) -> M (E14) -> H (E15) -> L (E16) -> A b (E17) -> u b (E18) -> P (E19) -> F f (E20) -> E f, (E21) -> E b (E22) -> Ε (E23) -> n (E24) -> r 29

30 Cost Analysis Equipment cost nbel n n exc fan C = C A + C A + C E (F01) eq bel exc s fan f Annual operating cost C = C Q C E (F02) op s + e Total annual cost (objective function) TAC = crf C eq + C op where the Capital Recovery Factor is calculated from the equation (F03) l f i ( 1+ i ) r r crf = (F04) lf ( 1+ i ) 1 r Cost Data Utility cost C e $/kwh Cost of electricity $/kwh Cost of heating steam C s Equipment unit cost C bel $/m 2 Belt dryer C exc $/m 2 Heat exchanger C fan $/kw Fan Equipment size scaling factor n bel - Belt dryer n exc - Heat exchanger n fan - Fan Other t y h/yr Annual operating time i r - Interest rate l f yr Life time (years) 30

31 ΠΑΡΑΔΕΙΓΜΑ ΞΗΡΑΝΤΗΡΑ ΜΕΤΑΦΟΡΙΚΗΣ ΤΑΙΝΙΑΣ Process Data Density (kg/m 3 ) ρ w = 1000 Water ρ a = 1 Air ρ s = 1750 Dry material Specific heat (kj/kgk) C pl = 4.20 Water C pv = 1.90 Water vapor C pa = 1.00 Air C ps = 2.00 Dry material Latent heat (MJ/kg) H o = 2.50 Steam condensation at 0 o C Other U s = 0.10 Air heater (kw/m 2 K) ε = 0.40 Vo id (e mpty) fraction (-) Empirical constants a 1 = Antoine equation for vapor pressure of water a 2 = a 3 = b 1 = Oswin equation for material isotherms b 2 = b 3 = c 0 = 0.50 Drying kinetics equation c 1 = 1.40 c 2 =-1.65 c 3 =-0.25 c 4 = 0.12 e 1 = 2.00 Belt driver power equation f 1 = 2.00 Pressure loss equation Table 7.22 Cost Data Utility cost C e = 0.10 $/kwh Cost of electricity C s = 0.05 $/kwh Cost of heating steam Equipment unit cost C bel = 25.0 k$/m 2 Belt dryer C exc = 2.00 k$/m 2 Heat exchanger C fan = 1.00 k$/kw Fan Equipment size scaling factor n bel = 0.95 Belt dryer n exc = 0.65 Heat exchanger n fan = 0.75 Fan Other t y = 4000 h/yr Annual operating time i r = 0.08 Interest rate l f = 5 yr Life time 31

32 Process Specifications F = 0.10 ton/h db Feed flow rate X o = 10.0 kg/kg db Initial material moisture content X = 0.10 kg/kg db Final material moisture content d = 0.01 m Material characteristic size T o = 25.0 o C Ambient temperature Y o = 0.01 kg/kg db Ambient humidity Z o = 0.20 m Loading depth P = 1.00 bar Ambient pressure T s = 160. o C Heating steam temperature Table 7.24 Design Variables Y = kg/kg db Drying air humidity T = 65.0 o C Drying air temperature V = 1.50 m/s Drying air velocity D = 2.00 m Belt width Table 7.25 Cost analysis results Equipment cost C bel = 900 k$ Belt dryer C exc = 45 k$ Heat exchanger C fan = 21 k$ Fan C eq = 966 k$ Equipment cost Operating cost C e = 43 k$/yr Cost of electricity C s = 229 k$/yr Cost of heating steam C op = 271 k$/yr Operating cost Objective function crfc eq = 242 k$/yr Annualized equipment cost C op = 271 k$/yr Operating cost TAC = 513 k$/yr Total annual cost 32

33 Process design results Drying air F a = 40 ton/h Fresh air flow rate F f = 235 ton/h Recycle air flow rate T = 65 o C Drying air temperature Y = kg/kg db Drying air humidity V =1.50 m/s Drying air velocity P = 1 bar Drying pressure T o = 25 o C Ambient temperature Y o = kg/kg db Ambient humidity P s = 0.25 bar Vapor pressure at drying conditions a w = 0.21 Water activity at drying conditions Material F = 0.10 ton/h db Material flow rate X o = 10. kg/kg db Initial moisture content X = 0.1 kg/kg db Final moisture content X e = 0.08 kg/kg db Equilibrium moisture content d = 0.01 m Particle size t c = 0.81 h Drying time constant t = 4.94 h Drying time Dryer W = 1 ton/h Drying rate L = 21.7 m Dryer length D = 2.00 m Dryer width M = 5.43 ton Dryer mass holdup H = 8.70 m 3 Dryer volume holdup A = 43 m 2 Belt area A s = 120 m 2 Air heater transfer area u b = 4.4 m/h Belt velocity Z o = 0.20 m Loading depth Thermal Load Q we = 0.65 MW Water vaporization Q sh = 0.05 MW Solid heating Q ah = 0.45 MW Air heating Q = 1.14 MW Total thermal load T s = 160 o C Steam temperature Electrical Load E b = 48 kw Belt drive E f = 59 kw Fan E = 107 kw Total power requirement Performance n = 0.57 Thermal efficiency r = 22.8 kg/h m 2 Specific rate of evaporation 33

34 600 TAC 600 TAC Cost (k$/yr) Cop crf Ceq Cost (k$/yr) Cop crf Ceq Temperature ( o C) Air humidity (kg/kg db) 600 TAC 500 Cost (k$/yr) Cop crf Ceq Air velocity (m/s) 34

35 Belt area (m 2 ) 50 Belt area (m 2 ) Air temperature ( o C) Air humidity (kg/kg db) Belt area (m 2 ) Air velocity (m/s) 35

36 Thermal load (MW Thermal load (MW Air temperature ( o C) Air humidity (kg/kg db) 2.0 Thermal load (MW Air velocity (m/s) 36

37 ΣΧΕΔΙΑΣΜΟΣ ΠΕΡΙΣΤΡΟΦΙΚΟΥ ΞΗΡΑΝΤΗΡΑ F, X o, T o E r F a, Y o, T o E f Q F, X, T F f, Y, T 37

38 Rotary Dryer Model Psychrometric equations P S = exp [a 1 a 2 / (a 3 + T)] Y = m a w P S / (P- a w P S ) Drying kinetics X e =b 1 exp[b 2 / (273+T)] [a w / (1-a w )] b3 t c = c 0 d c1 u c2 T c3 Y c4 t = -t c ln[ (X-X e )/ (X o -X e )] Material balance W = F (X o - X) W = F a (Y - Y o ) Thermal energy requirements Q we = F (X o - X) [ H o - (Cp L - Cp V ) T] Q sh = F [Cp S + X o Cp L ] (T - T o ) Q ah = F a [Cp A +Y o Cp V ] (T - T o ) Q = Q we + Q sh + Q ah Air heater Q = A s U s (T s -T) Rotary dryer M =t F (1+X o ) M = (1 - ε) ρ p H H r = ½ (n f + 1) h o L V r = π D 2 /4 L t = g 1 L / N D s Fan P = f 1 L V 2 F f = ρ a V π D 2 /4 E f = P F f / ρ a Rotation M d = (2π D 2 /4 + π D L) dx ρ m E r = e 1 N D (M + M d ) Electrical energy requirements E = E r + E f Performance indices n = Q we / Q r = W / V r (E01) (E02) (E03) (E04) (E05) (E06) (E07) (E08) (E09) (E10) (E11) (E12) (E13) (E14) (E15) (E16) (E17) (E18) (E19) (E20) (E21) (E22) (E23) (E24) (E25) 38

39 Process Variables Drying air F a ton/h Fresh air flow rate F f ton/h Recycle air flow rate T o C Drying air temperature Y kg/kg db Drying air humidity V m/s Drying air velocity P bar Drying pressure T o C Ambient temperature Y o kg/kg db Ambient humidity P s bar Vapor pressure at drying conditions a w - Water activity at drying conditions Material F ton/h db Material flow rate X o kg/kg db Initial moisture content X kg/kg db Final moisture content X e kg/kg db Equilibrium moisture content d m Particle size t h Drying time t c h Drying time constant Dryer W ton/h Evaporating capacity L m Dryer length D m Dryer weight M ton Dryer mass holdup H m 3 Dryer volume holdup V r m 3 Dryer volume A s m 2 Air heater transfer area N RPM Rotating velocity s - Dryer tilt x m Dryer wall thickness P bar Pressure loss of air flowing through belt M d ton Dryer weight n f - Number of flights h o m 3 /m Solids holdup in a flight Thermal Load Q we kw Water vaporization Q sh kw Solid heating Q ah kw Air heating Q kw Total thermal load T s o C Steam temperature Electrical Load E r kw Rotating driver E f kw Fan E kw Total power requirement Performance n - Thermal efficiency r kg/h m 2 Specific rate of evaporation 39

40 Process Data Density (kg/m 3 ) Water Air Dry material Construction material Specific heat (kj/kgc) C pl Water C pv Water vapor C pa Air C ps Dry material Latent heat (kj/kg) H o Steam condensation at 0 o C Heat transfer coefficients (kw/m 2 K) U s Air heater Empirical constants a 1, a 2, a 3 Antoine equation for vapor pressure of water b 1, b 2, b 3 Oswin equation for material isotherms c 0, c 1, c 2, c 3, c 4 Drying kinetics equation e 1 Belt driver power equation f 1 Pressure loss equation Residence time equation ρ w ρ a ρ s ρ m g 1 Table 7.31 Process Specifications F ton/h db Feed flow rate X o kg/kg db Initial material moisture content X kg/kg db Final material moisture content d m Material characteristic size T o o C Ambient temperature Y o kg/kg db Ambient humidity x m Dryer wall thickness P bar Ambient pressure o C Heating steam temperature T s Table 7.32 Degrees of Freedom Analysis Process variables 41 Degree of freedom 16 Process equations 25 Specifications 9 Degree of freedom 16 Design variables 7 Table 7.33 Design Variables Y kg/kg db Drying air humidity T C Drying air temperature V m/s Drying air velocity D m Dryer diameter n f - Number of flights h o m 3 /m Solids holdup in a flight s - Dryer slope 40

41 Model Solution Algorithm (E01) -> P s (E02) -> a w (E03) -> X e (E04) -> t c (E05) -> t (E06) -> W (E07) -> F a (E08) -> Q we (E09) -> Q sh (E10) -> Q ah (E11) -> Q (E12) -> A s (E13) -> M (E14) -> H (E15) -> L (E16) -> V r (E17) -> N (E18) -> P (E19) -> F f (E20) -> E f (E21) -> M d (E22) -> E r (E23) -> Ε (E24) -> n (E25) -> r Table 7.35 Cost Analysis Equipment cost nrot n n exc fan C = C A + C A + C E (F01) eq rot exc s fan f Annual operating cost = (F02) Cop CsQ + C e E Total annual cost (objective function) TAC = crf C eq + C op (F03) where the Capital Recovery Factor is calculated from the equation l f i ( 1+ i ) r r crf = (F04) lf ( 1+ i ) 1 r 41

42 Cost Data Utility cost C e $/kwh Cost of electricity C s $/kwh Cost of heating steam Equipment unit cost C rot $/m 3 Rotary dryer C exc $/m 2 Heat exchanger C fan $/kw Fan Equipment size scaling factor N rot - Rotary dryer n exc - Heat exchanger n fan - Fan Other t y h/yr Annual operating time i r - Interest rate l f yr Life time 42

43 Process Data Density (kg/m 3 ) ρ w = 1000 Water ρ a = 1 Air ρ s = 1750 Dry material ρ m = 8000 Construction material Specific heat (kj/kgk) C pl = 4.20 Water C pv = 1.90 Water vapor C pa = 1.00 Air C ps = 2.00 Dry material Latent heat (MJ/kg) H o = 2.50 Steam condensation at 0 o C Heat transfer coefficients (kw/m 2 K) U s = 0.10 Air heater Empirical constants a 1 = Antoine equation for vapor pressure of water a 2 = a 3 = b 1 = Oswin equation for material isotherms b 2 = b 3 = c 0 = 0.50 Drying kinetics equation c 1 = 1.40 c 2 =-1.65 c 3 =-0.25 c 4 = 0.12 e 1 = 1.00 Belt driver power equation f 1 = 2.50 Pressure loss equation g 1 = 0.25 Residence time equation Table 7.38 Cost Data Utility cost C e = 0.10 $/kwh Cost of electricity C s = 0.05 $/kwh Cost of heating steam Equipment unit cost C rot = 15.0 k$/m 3 Rotary dryer C exc = 2.00 k$/m 2 Heat exchanger C fan = 1.00 k$/kw Fan Equipment size scaling factor N rot = 0.85 Rotary dryer n exc = 0.65 Heat exchanger n fan = 0.75 Fan Other t y = 4000 h/yr Annual operating time i r = 0.08 Interest rate l f = 10yr Life time 43

44 Process Specifications F = 0.10 ton/h db Feed flow rate X o = 10.0 kg/kg db Initial material moisture content X = 0.10 kg/kg db Final material moisture content d = 0.01 m Material characteristic size (tubes) T o = 25.0 o C Ambient temperature Y o = 0.01 kg/kg db Ambient humidity x = 0.01 m Dryer wall thickness P = 1.00 bar Ambient pressure T s = 160 o C Heating steam temperature Table 7.40 Design Variables Y = kg/kg db Drying air humidity T = 65.0 o C Drying air temperature V = 1.50 m/s Drying air velocity D = 2.00 m Dryer diameter n f = 20 Number of flights h o = m 3 /m Solids holdup in a flight s = 4 % Dryer slope Table 7.41 Cost analysis results Equipment cost C rot = 519 k$ Belt dryer C exc = 42 k$ Heat exchanger C fan = 12 k$ Fan C eq = 572 k$ Equipment cost Operating cost C e = 38 k$/yr Cost of electricity C s = 203 k$/yr Cost of heating steam C op = 241 k$/yr Operating cost Objective function crfc eq = 143 k$/yr Annualized equipment cost C op = 241 k$/yr Operating cost TAC = 384 k$/yr Total annual cost 44

45 Process design results Drying air F a = 28.3 ton/h Fresh air flow rate F f = 28.3 ton/h Drying air flow rate T = 65 o C Drying air temperature Y = kg/kg db Drying air humidity V =1.60 m/s Drying air velocity P = 1 bar Drying pressure T o = 25 o C Ambient temperature Y o = kg/kg db Ambient humidity P s = 0.25 bar Vapor pressure at drying conditions a w = 0.27 Water activity at drying conditions Material F = 0.10 ton/h db Material flow rate X o = 10. kg/kg db Initial moisture content X = 0.1 kg/kg db Final moisture content X e = 0.08 kg/kg db Equilibrium moisture content d = 0.01 m Particle size t = 5.50 h Drying time t c = 0.82 h Drying time constant Dryer W = 1 ton/h Evaporating capacity L =13.2 m Dryer length D = 2.50 m Dryer diameter M = 6.05 ton Dryer mass holdup H = 9.70 m 3 Dryer volume holdup V r = 64.7 m 3 Dryer volume A s = 107 m 2 Air heater transfer area N = 3.59 RPM Rotating velocity s = 4% Dryer tilt x = 0.01 m Dryer wall thickness M d = 9.06 ton Dryer weight n f = 25 Number of flights h o = m 3 /m Solids holdup in a flight Thermal Load Q we = 0.65 MW Water vaporization Q sh = 0.05 MW Solid heating Q ah = 0.32 MW Air heating Q = 1.02 MW Total thermal load Electrical Load E r = 68 kw Belt driver E f = 26 kw Fan E = 94 kw Total power requirement Performance n = 0.64 Thermal efficiency r = 15.3 kg/h m 3 Specific rate of evaporation 45

46 TAC 400 TAC Cost (k$/yr) Cop crf Ceq Cost (k$/yr) Cop crf Ceq Temperature ( o C) Air humidity (kg/kg db) 600 Cost (k$/yr) TAC Cop crf Ceq Air velocity (m/s) 46

47 Dryer volume (m 3 ) Dryer volume (m 3 ) Temperature ( o C) Air humidity (kg/kg db) 150 Dryer volume (m 3 ) Air velocity (m/s) 47

48 Thermal load (MW Thermal load (MW Temperature ( o C) Air humidity (kg/kg db) 2.0 Thermal load (MW Air velocity (m/s) 48