ΕΘΝΙΚΟ ΜΕΤΣΟΒΙΟ ΠΟΛΥΤΕΧΝΕΙΟ ΤΜΗΜΑ ΧΗΜΙΚΩΝ ΜΗΧΑΝΙΚΩΝ ΕΡΓΑΣΤΗΡΙΟ ΣΧΕΔΙΑΣΜΟΥ & ΑΝΑΛΥΣΗΣ ΔΙΕΡΓΑΣΙΩΝ Μάθημα: ΤΕΧΝΙΚΗ ΦΥΣΙΚΩΝ ΔΙΕΡΓΑΣΙΩΝ ΙΙ 6ο Εξάμηνο Χημικών Μηχανικών ΞΗΡΑΝΤΗΡΕΣ 1
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 30-50 - 1-3 days Tray Pieces 40-60 0.2-2 3-10 h Tunnel Pieces 50-80 5-15 0.5-3 h Conveyor belt Pieces 50-80 5-15 0.5-3 h Rotary Grains, granules 60-100 30-100 0.2-1 h Dru m Sheet 80-110 5-30 10-30 s Fluid bed Grains, granules 60-100 30-90 2-20 min Pneumatic flash Grains, granules 60-120 10-100* 2-20 s Spray Powder 60-130 1-30* 10-60 s Vacuum/Freeze Pieces 10-20 1-7 5-24 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) 100 50 Fluidized Rotar y Conveyor Tunne l Tray Bin Vacuum 0 0. 00 01 0.001 0.01 0.1 1 10 Residence time (h) 2
Bin Tray Vacuum Tunnel Conveyor Drum Fluidized Rotary Spray Pneumatic 0.1 1 10 100 Evaporation capacity (kg/m 2 h, kg/m 3 h) 3
BIN (SILO) DRYERS ΕΙΔΗ ΞΗΡΑΝΤΗΡΩΝ Air out Air in Recycle air Fan Heater Bin 4
ΞΗΡΑΝΤΗΡΕΣ ΜΕ ΡΑΦΙΑ Air out Air in Recycle air Fan Heater Cabinet 5
Ξηραντήρες Σήραγγας Fan Heater Air in Recycle air Air out Trucks 6
Ξηραντήρες Μεταφορικής Ταινίας Air out Air in Fan Heater Recycle air Belt Feed Product 7
Περιστροφικοί Ξηραντήρες Air out Feed Recycle air Air in Fan Heater Product 8
Ξηραντήρες Τύμπανου Feed Product Knife Heated drums 9
Ξηραντήρες Ψεκασμού Air in Feed Air out Bag filter Fan Heater Cyclone Product 10
ΠΝΕΥΜΑΤΓΙΚΟΣ ΞΗΡΑΝΤΗΡΑΣ Air out Feed Cyclone Product Air in Fan Heater 11
ΞΗΡΑΝΤΗΡΑΣ ΡΕΥΣΤΟΣΤΕΡΕΑΣ ΚΛΙΝΗΣ Air out Feed Recycle air Air in Fan Heater Product 12
Vacuum pump Feed Product 13
Refrigerated condenser Vacuum pump Drying chamber 14
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
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 = 0.622 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 = 1.19 10 1 Antoine equation constants for water a 2 = 3.99 10 3 a 3 = 2.34 10 2 Degrees of Freedom Analysis Psychrometric variables 17 Model equations 14 Degree of freedom 3 16
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
Humidity versus temperature at various water activities. Pressure = 1 bar. 0.250 Water activity = 1.00 Humidity (kg/kg db) 0.200 0.150 0.100 0.050 0.80 0.60 0.40 0.20 0.000 0 20 40 60 80 100 Temperature ( o C) Humidity at saturation versus temperature at various pressures. Water activity = 1. 0.250 0.200 Humidity (kg/kg db) 0.150 0.100 Pressure (bar) = 0.5 1 2 5 0.050 0.000 0 20 40 60 80 100 Temperature ( o C) 18
Humid air specific enthalpy versus temperature at various humidities. Pressure = 1 bar. 300 Humid enthalpy (kj/kg db 250 200 150 100 Humidity (kg/kg db) = 0.060 0.045 0.030 0.015 0.000 50 0 0 20 40 60 80 100 Temperature ( o C) Humid air specific enthalpy versus humidity at various water activities. Pressure = 1 bar. Humid enthalpy (kj/kg db 150 100 50 Water activity 0.25 0.50 0.75 1.00 0 0.000 0.050 0.100 0.150 0.200 0.250 Humidity (kg/kg db) 19
0.250 Water activity = 1.00 0.200 (T,Ys) 0.80 0.60 Humidity (kg/kg db) 0.150 0.100 0.40 0.20 (Tw,Yw) 0.050 (Td,Y) (T,Y) 0.000 0 20 40 60 80 100 Temperature ( o C) Numerical Values of the Characteristic Variables Presented in Figure 7.18 P = 1 bar Pressure T = 65 o C Temperature Y = 0.035 kg/kg db Humidity a w = 0.214 Water activity T d = 34.0 o C Dew temperature T w = 39.4 o C Wet bulb temperature Y s = 0.206 kg/kg db Saturation humidity at temperature T Y w = 0.048 kg/kg db Saturation humidity at temperature T w 20
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) 0.3 0.2 onion carrot 0.1 pepper potato 0.0 (a) 0.0 0.2 0.4 0.6 0.8 1.0 0.5 Material moisture content (kg/kg db) 0.4 0.3 0.2 0.1 Temperature ( o C) = 25 50 75 0.0 (b) 0.0 0.2 0.4 0.6 0.8 1.0 Water activity 21
1.00 Drying time constant (h). 0.75 0.50 0.25 0.001 Humidity (kg/kg db) = 0.010 0.100 0.00 20 40 60 80 100 Temperature ( o C) 1.00 Drying time constant (h). 0.75 0.50 0.25 5 1 Velocity (m/s) = 0.5 0.00 20 40 60 80 100 Temperature ( o C) 22
10 Material moisture content (kg/kg db) 1 0.1 Temperature ( o C) 55 65 75 0 1 2 3 10 Humidity (kg/kg db) 1 0.015 0.035 0.075 0.1 0 1 2 3 10 Velocity (m/s) 1 2 1 0.5 0.1 0 1 2 3 Drying time (h) 23
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
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
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
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
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
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
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
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 = 1.19 10 1 Antoine equation for vapor pressure of water a 2 = 3.99 10 3 a 3 = 2.34 10 2 b 1 = 7.35 10-4 Oswin equation for material isotherms b 2 = 1.75 10 3 b 3 = 4.00 10-1 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
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 = 0.035 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
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 = 0.035 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 = 0.010 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
600 TAC 600 TAC 500 500 400 400 Cost (k$/yr) 300 200 Cop crf Ceq Cost (k$/yr) 300 200 Cop crf Ceq 100 100 0 50 70 90 110 Temperature ( o C) 0 0.020 0.030 0.040 0.050 0.060 Air humidity (kg/kg db) 600 TAC 500 Cost (k$/yr) 400 300 200 100 Cop crf Ceq 0 0 1 2 3 4 Air velocity (m/s) 34
100 100 75 75 Belt area (m 2 ) 50 Belt area (m 2 ) 50 25 25 0 0 50 70 90 110 0.020 0.030 0.040 0.050 0.060 Air temperature ( o C) Air humidity (kg/kg db) 100 75 Belt area (m 2 ) 50 25 0 0 1 2 3 4 Air velocity (m/s) 35
2.0 2.0 Thermal load (MW 1.5 1.0 0.5 Thermal load (MW 1.5 1.0 0.5 0.0 50 70 90 110 Air temperature ( o C) 0.0 0.020 0.030 0.040 0.050 0.060 Air humidity (kg/kg db) 2.0 Thermal load (MW 1.5 1.0 0.5 0.0 0 1 2 3 4 Air velocity (m/s) 36
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
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
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
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
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
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
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 = 1.19 10 1 Antoine equation for vapor pressure of water a 2 = 3.99 10 3 a 3 = 2.34 10 2 b 1 = 7.35 10-4 Oswin equation for material isotherms b 2 = 1.75 10 3 b 3 = 4.00 10-1 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
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 = 0.045 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 = 0.045 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
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 = 0.045 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 = 0.010 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 = 0.057 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
600 600 500 500 400 TAC 400 TAC Cost (k$/yr) 300 200 Cop crf Ceq Cost (k$/yr) 300 200 Cop 100 100 crf Ceq 0 50 70 90 110 Temperature ( o C) 0 0.020 0.030 0.040 0.050 0.060 Air humidity (kg/kg db) 600 Cost (k$/yr) 500 400 300 200 TAC Cop crf Ceq 100 0 0 1 2 3 4 Air velocity (m/s) 46
150 150 Dryer volume (m 3 ) 100 50 Dryer volume (m 3 ) 100 50 0 50 70 90 110 Temperature ( o C) 0 0.020 0.030 0.040 0.050 0.060 Air humidity (kg/kg db) 150 Dryer volume (m 3 ) 100 50 0 0 1 2 3 4 Air velocity (m/s) 47
2.0 2.0 Thermal load (MW 1.5 1.0 0.5 Thermal load (MW 1.5 1.0 0.5 0.0 50 70 90 110 Temperature ( o C) 0.0 0.020 0.030 0.040 0.050 0.060 Air humidity (kg/kg db) 2.0 Thermal load (MW 1.5 1.0 0.5 0.0 0 1 2 3 4 Air velocity (m/s) 48