1 | #*------------------------------------------------------------------- |
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2 | * Models of tray with Efficiency Prediction |
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3 | * Author: Josias J. Junges |
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4 | *-------------------------------------------------------------------*# |
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5 | |
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6 | using "streams"; |
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7 | using "tray"; |
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8 | |
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9 | Model trayEffEmp as tray |
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10 | |
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11 | ATTRIBUTES |
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12 | Pallete = false; |
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13 | Icon = "icon/Tray"; |
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14 | Brief = "Tray with Efficiency Prediction - Empiric Model"; |
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15 | Info = |
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16 | "==Description== |
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17 | Prediciton based on Chan e Fair(1984) model, with entrainment correction. |
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18 | Multicomponent mixture treated with pseudo-binary approach. |
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19 | |
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20 | == References == |
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21 | *Clear Liquid Height: Bennett et al. (1983). |
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22 | *Capacity Factor: Treybal(1968). |
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23 | *Flood Velocity: Fair(1961). |
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24 | *Liquid Mixing Models: Lewis(1936). |
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25 | *Eddy Diffusivity: Molnar(1974). |
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26 | *Entrainment Correction: Colburn(1936). |
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27 | *Fraction of entrained liquid: Zuiderweg(1982). |
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28 | |
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29 | General References: |
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30 | *CHAN, H.;FAIR, J. R. Prediction of Point Efficiencies on Sieve Trays. 1. Binary Systems. Ind. Eng. Chem. Process Des. Dev., v.23, n.4, p.814-9, 1984. |
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31 | *LOCKETT, M. J. Distillation Tray Fundamentals. Cambridge: Cambridge University Press, 1986. |
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32 | "; |
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33 | PARAMETERS |
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34 | |
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35 | z as length (Brief="Liquid flow path length"); |
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36 | d as length (Brief="Plate Diameter"); |
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37 | Aa as area (Brief="Active Area or Bubbling Area = Atray - 2*Adowncomer"); |
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38 | fi as fraction (Brief="Fractional perforated tray area(hole area/ bubbling area)"); |
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39 | Ts as length (Brief="Tray spacing"); |
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40 | outer iLK as Integer (Brief="Pseudo-binary ligth key index"); |
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41 | outer iHK as Integer (Brief="Pseudo-binary heavy key index"); |
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42 | |
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43 | VARIABLES |
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44 | |
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45 | Qv as flow_vol (Brief="Vapour volumetric flow"); |
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46 | Ql as flow_vol (Brief="Liquid volumetric flow"); |
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47 | Mv as flow_mass (Brief="Vapour mass flow", Lower=0); |
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48 | Ml as flow_mass (Brief="Liquid mass flow", Lower=0); |
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49 | Dv as diffusivity (Brief="Diffusivity on Vapour Phase"); |
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50 | Dl as diffusivity (Brief="Diffusivity on Liquid Phase"); |
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51 | sigma as surf_tens (Brief="Surface Tension"); |
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52 | |
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53 | ua as velocity (Brief="Superficial velocity based on Aa"); |
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54 | fs as positive(Brief="Superficial factor", Unit='kg^.5/m^.5/s'); |
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55 | c as positive (Brief="Constant in eq. of Clear Liquid Height"); |
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56 | ae as fraction (Brief="Effective liquid volume fraction"); |
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57 | hcl as length (Brief="Clear Liquid Height"); |
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58 | tv as time_sec (Brief="Mean residence time of vapour in dispersion"); |
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59 | tl as time_sec (Brief="Mean residence time of liquid on tray"); |
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60 | us as velocity (Brief="Superficial velocity based on Ap"); |
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61 | fp as positive (Brief="Flow Parameter"); |
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62 | csb as positive (Brief="Capacity Factor"); |
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63 | uf as velocity (Brief="Flood velocity"); |
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64 | ff as positive (Brief="Flood factor"); |
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65 | lambda as Real (Brief="Stripping factor or ratio of slope of equilibrium line to slope of operating line"); |
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66 | m as Real (Brief="Slope of equilibrium line"); |
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67 | |
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68 | VinLK as Real (Brief="Pseudo-binary key "); |
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69 | VoutLk as Real (Brief="Pseudo-binary key"); |
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70 | LinLK as Real (Brief="Pseudo-binary key"); |
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71 | LoutLk as Real (Brief="Pseudo-binary key"); |
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72 | |
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73 | NV as positive (Brief="Number of vapour phase transfer units"); |
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74 | NL as positive (Brief="Number of liquid phase transfer units"); |
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75 | NOG as positive (Brief="Number of overall vapour phase transfer units"); |
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76 | EOG as positive (Brief="Point Efficiency"); |
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77 | |
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78 | De as Real (Brief="Eddy diffusivity for liquid mixing"); |
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79 | Pe as positive (Brief="Peclet Number"); |
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80 | n as Real (Brief="Constant"); |
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81 | Emv1 as positive (Brief="Murphree tray efficiency"); |
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82 | |
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83 | hb as length (Brief="Height on spray regime"); |
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84 | l as positive (Brief="Fraction of entrained liquid"); |
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85 | uh as velocity (Brief="Gas velocity through holes"); |
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86 | Emv2 as positive (Brief="Apparent Murphree tray efficiency"); |
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87 | |
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88 | EQUATIONS |
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89 | |
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90 | "Vapour Volumetric Flow" |
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91 | Qv=OutletV.F*vV; |
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92 | |
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93 | "Liquid Volumetric Flow" |
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94 | Ql=OutletL.F*vL; |
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95 | |
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96 | "Vapour Mass Flow" |
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97 | Mv=Qv*rhoV; |
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98 | |
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99 | "Liquid Mass Flow" |
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100 | Ml=Ql*rhoL; |
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101 | |
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102 | "Superficial Velocity" |
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103 | ua=Qv/Aa; |
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104 | |
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105 | "Superficial Factor" |
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106 | fs=ua*rhoV^.5; |
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107 | |
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108 | "Constant c" |
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109 | c=.5+0.438*exp(-137.8*'1/m'*hw); |
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110 | |
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111 | "Effective liquid volume fraction" |
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112 | ae=exp(-12.55*(ua*'s/m'*(rhoV/(rhoL-rhoV))^0.5)^0.91); |
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113 | |
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114 | "Clear Liquid Height" |
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115 | hcl=ae*(hw*'1/m'+c*((Ql*'s/m^3')/(lw*'1/m'*ae))^.67)*'m'; |
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116 | |
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117 | "Mean residence time of vapour in dispersion" |
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118 | tv=(1-ae)*hcl/(ae*ua); |
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119 | |
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120 | "Mean residence time of liquid on tray" |
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121 | tl=hcl*z*lw/Ql; |
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122 | |
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123 | "Superficial velocity based on Ap" |
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124 | us*Ap=Qv; |
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125 | |
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126 | "Flow Parameter" |
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127 | (fp*Mv)^2*rhoL=Ml^2*rhoV; |
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128 | |
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129 | "Capacity Factor" |
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130 | csb=(0.0744*Ts*'1/m'+0.0117)*(log(abs(1/fp)))+0.0304*Ts*'1/m'+0.0153; |
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131 | |
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132 | "Flood velocity" |
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133 | uf = csb*(sigma*'1/(N/m)'/0.02)^.2*(abs((rhoL-rhoV)/rhoV))^.5*(fi/.1)^.44*'m/s'; |
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134 | |
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135 | "Flood Factor" |
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136 | ff*uf=us; |
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137 | |
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138 | if NComp > 2 then |
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139 | |
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140 | "Pseudo-binary Approach" |
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141 | VinLK=InletV.z(iLK)/(InletV.z(iLK)+InletV.z(iHK)); |
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142 | VoutLk=OutletV.z(iLK)/(OutletV.z(iLK)+OutletV.z(iHK)); |
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143 | LinLK=InletL.z(iLK)/(InletL.z(iLK)+InletL.z(iHK)); |
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144 | LoutLk=OutletL.z(iLK)/(OutletL.z(iLK)+OutletL.z(iHK)); |
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145 | |
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146 | else |
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147 | VinLK=1; |
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148 | VoutLk=1; |
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149 | LinLK=1; |
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150 | LoutLk=1; |
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151 | |
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152 | end |
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153 | |
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154 | "Stripping factor or ratio of slope of equilibrium line to slope of operating line" |
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155 | lambda=m*(OutletV.F/OutletL.F); |
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156 | |
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157 | #Chan e Fair(1984) Model# |
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158 | |
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159 | "Number of vapour phase transfer units" |
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160 | NV*(abs(hcl)*'1/m')^.5=(10300-8670*ff)*ff*(Dv*'s/m^2')^0.5*tv*'1/s'; |
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161 | |
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162 | "Number of liquid phase transfer units" |
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163 | NL=19700*((Dl*'s/m^2')^.5)*(.4*fs*'1/(kg^.5/m^.5/s)'+.17)*tl*'1/s'; |
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164 | |
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165 | "Number of overall vapour phase transfer units" |
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166 | NV*NL=NOG*(NL+lambda*NV); |
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167 | |
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168 | "Point Efficiency" |
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169 | EOG=1-exp(-NOG); |
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170 | |
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171 | #Liquid Mixing Models# |
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172 | |
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173 | "Eddy diffusivity for liquid mixing" |
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174 | De=(0.0005+0.01285*ua*'s/m'+6.32*(Ql*'s/m^3'/(lw*'1/m'))+0.312*hw*'1/m')^2; |
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175 | |
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176 | "Peclet Number" |
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177 | Pe=(OutletL.F*d)/(lw*hcl*(1/vL)*De*'m^2/s'); |
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178 | |
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179 | "Constant n" |
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180 | n=Pe/2*((1+4*lambda*EOG/Pe)^.5-1); |
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181 | |
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182 | if Pe equal 0 then |
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183 | Emv1=EOG; |
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184 | else |
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185 | if Pe < 20 then |
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186 | Emv1/EOG=(1-exp(-(n+Pe)))/((n+Pe)*(1+(n+Pe)/n))+(exp(n)-1)/(n*(1+n/(n+Pe))); |
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187 | else |
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188 | lambda*Emv1=(exp(lambda*EOG)-1); |
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189 | end |
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190 | end |
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191 | |
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192 | #Entrainment Correction# |
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193 | |
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194 | "Height on spray regime" |
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195 | hb=hcl*(265*((ua/(g*hcl)^.5)*(rhoV/rhoL)^.5)^1.7+1); |
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196 | |
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197 | "Gas velocity through hole" |
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198 | uh=Qv/Ah; |
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199 | |
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200 | "Fraction of entrained liquid" |
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201 | l=1e-8*(hb/Ts)^3*(uh/(Ql/Aa))^2; |
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202 | |
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203 | "Apparent Murphree tray efficiency" |
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204 | Emv1=Emv2*(1+l*Emv1); |
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205 | |
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206 | Emv=Emv2; |
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207 | |
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208 | end |
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209 | |
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210 | Model trayEffFund as tray |
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211 | |
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212 | ATTRIBUTES |
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213 | Pallete = false; |
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214 | Icon = "icon/Tray"; |
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215 | Brief = "Tray with Efficiency Prediction - Fundamental Model"; |
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216 | Info = |
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217 | "==Description== |
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218 | Prediciton based on Prado(1986), Gracia and Fair(2000,2002) model, with entrainment and weeping correction. |
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219 | Multicomponent mixture treated with pseudo-binary approach. |
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220 | |
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221 | == Options == |
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222 | You can select the tray type: with downcomer or dualflow. |
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223 | |
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224 | == References == |
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225 | *Clear Liquid Height (Downcomer): Dhulesia (1984). |
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226 | *Clear Liquid Height (Dualflow): Garcia e Fair(2002). |
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227 | *Froth Height: Todd & Van Winkle (1972). |
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228 | *Fraction of holes with vapour flow (Downcomer): Prado (1990). |
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229 | *Fraction of holes with vapour flow (Dualflow): Garcia e Fair (2002). |
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230 | *Fraction of active holes that are in jetting: Prado (1987), considering fj=60% when ua=uatp. |
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231 | *Capacity Factor (Downcomer): Treybal(1968). |
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232 | *Capacity Factor (Dualflow): Garcia e Fair(2002). |
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233 | *Flood Velocity: Fair(1961). |
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234 | *Liquid Mixing Models: Lewis(1936). |
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235 | *Eddy Diffusivity: Molnar(1974). |
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236 | *Entrainment Correction (Downcomer): Colburn(1936). |
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237 | *Fraction of entrained liquid (Downcomer): Zuiderweg(1982). |
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238 | |
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239 | General References: |
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240 | *GARCIA, J. A.; FAIR, J. R. A Fundamental Model for the Prediction of Distillation Sieve Tray Efficiency. 1. Database Development. Ind. Eng. Chem. Res., v.39, n.6, p. 1809-17,2000. |
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241 | *GARCIA, J. A.; FAIR, J. R. A Fundamental Model for the Prediction of Distillation Sieve Tray Efficiency. 2. Model Development and Validation. Ind. Eng. Chem. Res., v.39, n.6, p. 1818-25,2000. |
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242 | *GARCIA, J. A.; FAIR, J. R. Distillation Sieve Trays without Downcomers: Prediction of Performance Characteristics. Ind. Eng. Chem. Res., v.41, n.6, p. 1632-40,2002. |
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243 | *LOCKETT, M. J. Distillation Tray Fundamentals. Cambridge: Cambridge University Press, 1986. |
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244 | *PRADO, M.; FAIR, J. R. Fundamental Model for the Prediction of Sieve Tray Efficiency. Ind. Eng. Chem. Res., v.29, n.6, p. 1031-42,1990. |
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245 | "; |
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246 | |
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247 | PARAMETERS |
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248 | |
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249 | d as length (Brief="Tray Diameter"); |
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250 | dh as length (Brief="Hole Diameter"); |
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251 | Aa as area (Brief="Case Downcomer: Active Area or Bubbling Area = Atray - 2*Adowncomer. Case dualflow: total tray area"); |
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252 | Ah as area (Brief="Area of Holes"); |
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253 | fi as fraction (Brief="Fractional perforated tray area(hole area/ bubbling area)"); |
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254 | Ts as length (Brief="Tray spacing"); |
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255 | T as length (Brief="Tray thickness"); |
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256 | tray_type as Switcher (Valid = ["Dualflow", "Downcomer"], Default= "Downcomer"); |
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257 | outer iLK as Integer (Brief="Pseudo-binary ligth key index"); |
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258 | outer iHK as Integer (Brief="Pseudo-binary heavy key index"); |
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259 | |
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260 | VARIABLES |
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261 | |
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262 | Qv as flow_vol (Brief="Vapour volumetric flow"); |
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263 | Ql as flow_vol (Brief="Liquid volumetric flow"); |
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264 | Mv as flow_mass (Brief="Vapour mass flow"); |
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265 | Ml as flow_mass (Brief="Liquid mass flow"); |
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266 | Miv as viscosity (Brief="Vapour viscosity"); |
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267 | Mil as viscosity (Brief="Liquid viscosity"); |
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268 | Dl as diffusivity (Brief="Diffusivity on Liquid Phase"); |
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269 | Dv as diffusivity (Brief="Diffusivity on Vapour Phase"); |
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270 | |
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271 | lambda as Real (Brief="Stripping factor or ratio of slope of equilibrium line to slope of operating line"); |
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272 | m as Real (Brief="Slope of equilibrium line"); |
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273 | |
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274 | VinLK as Real (Brief="Pseudo-binary key "); |
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275 | VoutLk as Real (Brief="Pseudo-binary key"); |
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276 | LinLK as Real (Brief="Pseudo-binary key"); |
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277 | LoutLk as Real (Brief="Pseudo-binary key"); |
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278 | |
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279 | us as velocity (Brief="Superficial velocity based on Ap"); |
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280 | ua as velocity (Brief="Superficial velocity based on Aa"); |
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281 | fs as positive (Brief="Superficial factor", Unit='kg^.5/m^.5/s'); |
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282 | uh as velocity (Brief="Vapour velocity through holes"); |
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283 | fp as positive (Brief="Flow Parameter"); |
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284 | hcl as length (Brief="Clear Liquid Height"); |
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285 | hcld as length (Brief="Dynamic liquid head at tray floor"); |
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286 | hf as length (Brief="Froth Height"); |
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287 | e as positive (Brief="Porosity"); |
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288 | csb as positive(Brief="Capacity Factor"); |
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289 | uf as velocity (Brief="Flood velocity"); |
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290 | ff as positive (Brief="Flood factor"); |
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291 | sigma as surf_tens (Brief="Surface Tension"); |
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292 | |
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293 | ftm as Real (Brief="General Factor in equations of Units of Mass Transfer", Unit='cm/s^.5'); |
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294 | |
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295 | xf as fraction (Brief="Fraction of holes with vapour flow"); |
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296 | dj as length (Brief="Jet Diameter"); |
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297 | uj as velocity (Brief="Jet velocity"); |
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298 | Reh as positive (Brief="Reynolds number for vapour flow through hole"); |
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299 | hj as length (Brief="Jet lenght"); |
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300 | tg1 as time_sec (Brief="Residence time in Zone One"); |
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301 | NL1 as positive (Brief="Number of liquid phase transfer units in Zone One"); |
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302 | |
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303 | dbs as length (Brief="Small bubble diameter"); |
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304 | dbl as length (Brief="Large bubble diameter"); |
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305 | sigCSB as positive (Brief="Surface tension correction"); |
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306 | MilCSB as positive (Brief="Liquid viscosity correction"); |
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307 | fi3 as positive; |
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308 | dbss as length (Brief="Small bubble Sauter diameter"); |
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309 | dbls as length (Brief="Large bubble Sauterdiameter"); |
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310 | eo as positive (Brief="Etvos number"); |
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311 | mo as positive (Brief="Morton number"); |
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312 | h as positive (Brief="Constant h"); |
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313 | j as positive (Brief="Constant j"); |
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314 | usb as velocity (Brief="Terminal velocity of small bubbles"); |
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315 | ubss as velocity (Brief="Terminal velocity of small bubbles using Sauter diameter"); |
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316 | aj as fraction (Brief="Fraction of small bubbles in froth"); |
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317 | ulb as velocity (Brief="Terminal velocity of large bubbles"); |
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318 | tg2s as time_sec (Brief="Residence time of small bubbles in Zone Two"); |
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319 | tg2l as time_sec (Brief="Residence time of large bubbles in Zone Two"); |
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320 | NL2S as positive (Brief="Number of liquid phase transfer units of small bubbles in Zone Two"); |
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321 | NL2L as positive (Brief="Number of liquid phase transfer units of large bubbles in Zone Two"); |
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322 | tg3 as time_sec (Brief="Residence time in Zone Three"); |
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323 | NL3 as positive (Brief="Number of liquid phase transfer units in Zone Three"); |
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324 | ulb3 as velocity (Brief="Terminal velocity of large bubbles in Zone Three"); |
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325 | tg4s as time_sec (Brief="Residence time of small bubbles in Zone Four"); |
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326 | tg4l as time_sec (Brief="Residence time of large bubbles in Zone Four"); |
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327 | NL4S as positive (Brief="Number of liquid phase transfer units of small bubbles in Zone Four"); |
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328 | NL4L as positive (Brief="Number of liquid phase transfer units of large bubbles in Zone Four"); |
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329 | tg5 as time_sec (Brief="Residence time in Zone Five"); |
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330 | NL5 as positive (Brief="Number of liquid phase transfer units in Zone Five"); |
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331 | |
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332 | uatp as velocity (Brief="Superficial velocity based on Aa in the transition point of froth regime to spay regime"); |
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333 | fj as positive (Brief="Fraction of active holes that are in jetting"); |
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334 | flb as positive (Brief="Fraction of active holes that are producing small bubbles"); |
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335 | fsb as positive (Brief="Fraction of active holes that are producing large bubbles"); |
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336 | |
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337 | ftmg as positive (Brief="General Factor in equations of Units of Mass Transfer"); |
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338 | |
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339 | Rej as positive (Brief="Reynolds number of jet"); |
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340 | Scg as positive (Brief="Schmidt number of vapour phase"); |
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341 | kl1 as positive (Brief="Liquid phase mass transfer coefficient in Zone One"); |
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342 | kg1 as positive (Brief="Vapour phase mass transfer coefficient in Zone One"); |
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343 | NG1 as positive (Brief="Number of vapour phase transfer units in Zone One"); |
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344 | |
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345 | Peg2s as positive (Brief="Peclet number of small bubbles in Zone Two"); |
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346 | Peg2l as positive (Brief="Peclet number of large bubbles in Zone Two"); |
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347 | Peg3 as positive (Brief="Peclet number in Zone Three"); |
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348 | Peg4s as positive (Brief="Peclet number of small bubbles in Zone Four"); |
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349 | Peg4l as positive (Brief="Peclet number of large bubbles in Zone Four"); |
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350 | Peg5 as positive (Brief="Peclet number in Zone Five"); |
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351 | |
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352 | Sh2s as positive (Brief="Sherwood number of small bubbles in Zone Two"); |
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353 | Sh2l as positive (Brief="Sherwood number of large bubbles in Zone Two"); |
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354 | Sh3 as positive (Brief="Sherwood number in Zone Three"); |
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355 | Sh4s as positive (Brief="Sherwood number of small bubbles in Zone Four"); |
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356 | Sh4l as positive (Brief="Sherwood number of large bubbles in Zone Four"); |
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357 | Sh5 as positive (Brief="Sherwood number in Zone Five"); |
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358 | |
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359 | kg2s as positive (Brief="Vapour phase mass transfer coefficient of small bubbles in Zone Two"); |
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360 | kg2l as positive (Brief="Vapour phase mass transfer coefficient of large bubbles in Zone Two"); |
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361 | kg3 as positive (Brief="Vapour phase mass transfer coefficient in Zone Three"); |
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362 | kg4s as positive (Brief="Vapour phase mass transfer coefficient of small bubbles in Zone Four"); |
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363 | kg4l as positive (Brief="Vapour phase mass transfer coefficient of large bubbles in Zone Four"); |
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364 | kg5 as positive (Brief="Vapour phase mass transfer coefficient in Zone Five"); |
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365 | |
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366 | kl2s as positive (Brief="Liquid phase mass transfer coefficient of small bubbles in Zone Two"); |
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367 | kl2l as positive (Brief="Liquid phase mass transfer coefficient of large bubbles in Zone Two"); |
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368 | kl3 as positive (Brief="Liquid phase mass transfer coefficient in Zone Three"); |
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369 | kl4s as positive (Brief="Liquid phase mass transfer coefficient of small bubbles in Zone Four"); |
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370 | kl4l as positive (Brief="Liquid phase mass transfer coefficient of large bubbles in Zone Four"); |
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371 | kl5 as positive (Brief="Liquid phase mass transfer coefficient in Zone Five"); |
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372 | |
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373 | NG2S as positive (Brief="Number of Vapour phase transfer units of small bubbles in Zone Two"); |
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374 | NG2L as positive (Brief="Number of Vapour phase transfer units of large bubbles in Zone Two"); |
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375 | NG3 as positive (Brief="Number of Vapour phase transfer units in Zone Three"); |
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376 | NG4S as positive (Brief="Number of Vapour phase transfer units of small bubbles in Zone Four"); |
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377 | NG4L as positive (Brief="Number of Vapour phase transfer units of large bubbles in Zone Four"); |
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378 | NG5 as positive (Brief="Number of Vapour phase transfer units in Zone Five"); |
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379 | |
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380 | NGFJ as positive (Brief="Number of Vapour phase transfer units of jetting"); |
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381 | NGFLB as positive (Brief="Number of Vapour phase transfer units of large bubbles"); |
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382 | EOG as positive (Brief="Point Efficiency"); |
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383 | |
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384 | De as Real (Brief="Eddy diffusivity for liquid mixing"); |
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385 | Pe as positive (Brief="Peclet Number"); |
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386 | n as Real (Brief="Constant"); |
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387 | Emv1 as positive (Brief="Murphree tray efficiency"); |
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388 | |
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389 | psi as Real (Brief="Correction factor of liquid entrainment in dualflow trays"); |
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390 | psi1 as Real (Brief="Correction factor of weeping in dualflow trays"); |
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391 | |
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392 | hb as length (Brief="Height on spray regime"); |
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393 | l as positive (Brief="Fraction of entrained liquid"); |
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394 | Emv2 as positive (Brief="Apparent Murphree tray efficiency"); |
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395 | Emv3 as positive (Brief="Apparent Murphree tray efficiency"); |
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396 | |
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397 | |
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398 | EQUATIONS |
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399 | |
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400 | "Vapour volumetric flow" |
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401 | Qv=OutletV.F*vV; |
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402 | |
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403 | "Liquid volumetric flow" |
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404 | Ql=OutletL.F*vL; |
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405 | |
---|
406 | "Vapour mass flow" |
---|
407 | Mv=Qv*rhoV; |
---|
408 | |
---|
409 | "Liquid mass flow" |
---|
410 | Ml=Ql*rhoL; |
---|
411 | |
---|
412 | "Vapour viscosity" |
---|
413 | Miv=PP.VapourViscosity(OutletL.T, OutletL.P, OutletL.z); |
---|
414 | |
---|
415 | "Liquid viscosity" |
---|
416 | Mil=PP.LiquidViscosity(OutletL.T, OutletL.P, OutletL.z); |
---|
417 | |
---|
418 | if NComp > 2 then |
---|
419 | |
---|
420 | "Pseudo-binary Approach" |
---|
421 | VinLK=InletV.z(iLK)/(InletV.z(iLK)+InletV.z(iHK)); |
---|
422 | VoutLk=OutletV.z(iLK)/(OutletV.z(iLK)+OutletV.z(iHK)); |
---|
423 | LinLK=InletL.z(iLK)/(InletL.z(iLK)+InletL.z(iHK)); |
---|
424 | LoutLk=OutletL.z(iLK)/(OutletL.z(iLK)+OutletL.z(iHK)); |
---|
425 | |
---|
426 | else |
---|
427 | VinLK=1; |
---|
428 | VoutLk=1; |
---|
429 | LinLK=1; |
---|
430 | LoutLk=1; |
---|
431 | |
---|
432 | end |
---|
433 | |
---|
434 | "Stripping factor or ratio of slope of equilibrium line to slope of operating line" |
---|
435 | lambda=m*(OutletV.F/OutletL.F); |
---|
436 | |
---|
437 | "Superficial velocity based on Ap" |
---|
438 | us=Qv/Ap; |
---|
439 | |
---|
440 | "Superficial velocity based on Aa" |
---|
441 | ua=Qv/Aa; |
---|
442 | |
---|
443 | "Superficial factor" |
---|
444 | fs=ua*rhoV^.5; |
---|
445 | |
---|
446 | "Vapour velocity through holes" |
---|
447 | uh=Qv/Ah; |
---|
448 | |
---|
449 | "Flow parameter" |
---|
450 | (fp*Mv)^2*rhoL=Ml^2*rhoV; |
---|
451 | |
---|
452 | switch tray_type |
---|
453 | case "Downcomer": |
---|
454 | "Clear Liquid Height" |
---|
455 | hcl=0.42*(Ql*'1/m'/(lw*ua)*(rhoL/rhoV)^.5)^.33*(hw*'1/m')^.67*'m'; |
---|
456 | case "Dualflow": |
---|
457 | "Clear Liquid Height" |
---|
458 | hcl=(0.01728*((Ml*'1/(kg/s)')^(4.3*(fi^1.5))*(ua*'1/(m/s)'*(rhoV/rhoL)^.5)^1))/(rhoL*'1/(kg/m^3)'*fi^1.5*(T/(dh*1000*1000))^.42)*'m'; |
---|
459 | |
---|
460 | end |
---|
461 | |
---|
462 | "Dynamic liquid head at tray floor" |
---|
463 | hcld=hcl-ua*rhoV*(uh-ua)/(rhoL*g); |
---|
464 | |
---|
465 | "Froth Height" |
---|
466 | hf=0.076*'m'+32.6*'m'*(fs*'1/(kg^.5/m^.5/s)')^2/((rhoL-rhoV)*'m^3/kg')+0.82*hcld; |
---|
467 | |
---|
468 | "Porosity" |
---|
469 | e=1-hcl/hf; |
---|
470 | |
---|
471 | switch tray_type |
---|
472 | case "Downcomer": |
---|
473 | "Capacity factor" |
---|
474 | csb=(0.0744*Ts*'1/m'+0.0117)*(log(abs(1/fp)))+0.0304*Ts*'1/m'+0.0153; |
---|
475 | case "Dualflow": |
---|
476 | "Capacity factor" |
---|
477 | csb=(0.1317*fp^2-0.1747*fp+0.1124)*(0.6649*Ts*'1/m'+0.5667); |
---|
478 | end |
---|
479 | |
---|
480 | "Flood velocity" |
---|
481 | uf = csb*(sigma*'1/(N/m)'/0.02)^.2*(abs((rhoL-rhoV)/rhoV))^.5*(fi/.1)^.44*'m/s'; |
---|
482 | |
---|
483 | switch tray_type |
---|
484 | case "Downcomer": |
---|
485 | "Flood Factor" |
---|
486 | ff=us/uf; |
---|
487 | case "Dualflow": |
---|
488 | "Flood Factor" |
---|
489 | ff=ua/uf; |
---|
490 | end |
---|
491 | |
---|
492 | |
---|
493 | #Prado, Garcia and Fair Model# |
---|
494 | |
---|
495 | #Liquid Phase# |
---|
496 | |
---|
497 | "General Factor in equations of Units of Mass Transfer" |
---|
498 | ftm=(rhoL*Mv*Dl^.5)/(3.1416^.5*rhoV*Ml); |
---|
499 | |
---|
500 | #Zone One# |
---|
501 | |
---|
502 | switch tray_type |
---|
503 | case "Downcomer": |
---|
504 | "Fraction of holes with vapour flow" |
---|
505 | xf=0.9; |
---|
506 | case "Dualflow": |
---|
507 | "Fraction of holes with vapour flow" |
---|
508 | xf=0.4668*(fi/0.2)^.8*(Ts*'1/m'/0.61)^.2*exp(-0.35*(abs(ff*100-90)/45)); |
---|
509 | end |
---|
510 | |
---|
511 | |
---|
512 | "Jet diameter" |
---|
513 | dj=1.1*dh+0.25*hcl; |
---|
514 | |
---|
515 | "Jet velocity" |
---|
516 | uj=(uh*dh^2)/(xf*dj^2); |
---|
517 | |
---|
518 | "Reynolds number for vapour flow through hole" |
---|
519 | Reh=dh*uh*rhoV/Miv; |
---|
520 | |
---|
521 | "Jet Height" |
---|
522 | hj=1.1e-3*(dh*'1/m')^.2*Reh^.46*'m'; |
---|
523 | |
---|
524 | "Residence time in Zone One" |
---|
525 | tg1=hj/uj; |
---|
526 | |
---|
527 | "Number of vapour phase transfer units in Zone One" |
---|
528 | NL1=(8*ftm*tg1^.5)/dj; |
---|
529 | |
---|
530 | #Zone Two# |
---|
531 | |
---|
532 | "Small Bubble Diameter" |
---|
533 | dbs=3.34/(ua*'s/m'*9.8)^.4*(sigma*'m/N'/(rhoL*'m^3/kg'))^.6*(Mil/Miv)^.1*'m'; |
---|
534 | |
---|
535 | "Large Bubble Diameter" |
---|
536 | dbl=dbs*(0.83+41.5*((sigma*'m/N')^.6*(Mil*'1/cP'/(rhoV*'m^3/kg'))^.1)); |
---|
537 | |
---|
538 | if sigma > 5e-3 then |
---|
539 | sigCSB=1; |
---|
540 | else |
---|
541 | sigCSB=3*(sigma*'m/N')^.6; |
---|
542 | end |
---|
543 | if Mil > .6e-3 then |
---|
544 | MilCSB=4.13*(Mil*'1/cP')^1.5; |
---|
545 | else |
---|
546 | MilCSB=1; |
---|
547 | end |
---|
548 | |
---|
549 | fi3=1*MilCSB*sigCSB; |
---|
550 | |
---|
551 | "Sauter diameters" |
---|
552 | dbls=fi3*.605*(dh*'1/m')^.84*(uh*'s/m')^.18/((Ql*'s/m^3')/(lw*'1/m')^.07)*'m'; |
---|
553 | dbss=fi3*.660*(dh*'1/m')^.84*(uh*'s/m')^.085/((Ql*'s/m^3')/(lw*'1/m')^.08)*'m'; |
---|
554 | |
---|
555 | "Eotvos Number" |
---|
556 | eo=g*(rhoL-rhoV)*dbs^2/sigma; |
---|
557 | |
---|
558 | "Morton Number" |
---|
559 | mo=g*Mil^4*(rhoL-rhoV)/(rhoL^2*sigma^3); |
---|
560 | |
---|
561 | "Constant h" |
---|
562 | h=4/3*eo*mo^-0.149*((Mil*'1/cP')/9.12e-4)^-.14; |
---|
563 | |
---|
564 | if h > 59.3 then |
---|
565 | j=3.42*h^.441; |
---|
566 | else |
---|
567 | j=0.94*h^.757; |
---|
568 | end |
---|
569 | |
---|
570 | "Terminal velocity of small bubbles" |
---|
571 | usb=Mil/(rhoL*dbs)*mo^-.149*(j-0.857); |
---|
572 | |
---|
573 | "Terminal velocity of small bubbles using Sauter diameter" |
---|
574 | ubss=Mil/(rhoL*dbs)*mo^-.149*(j-0.857); |
---|
575 | |
---|
576 | "Fraction of small bubbles in froth" |
---|
577 | aj=1-0.463*((sigma*'m/N')/0.07282)^0.6*((Mil/9.12e-4)*(1.845e-5/Miv))^0.1*(994.7/(rhoL*'m^3/kg'))^0.6*(1.183/(rhoV*'m^3/kg'))^0.1; |
---|
578 | |
---|
579 | "Terminal velocity of large bubbles" |
---|
580 | ulb = us/((1 - aj)*e) - usb*aj/(1-aj); |
---|
581 | |
---|
582 | if hf > hj then |
---|
583 | tg2s = (hf-hj)/usb; |
---|
584 | tg2l = (hf-hj)/ulb; |
---|
585 | else |
---|
586 | tg2s = hf/usb; |
---|
587 | tg2l = hf/ulb; |
---|
588 | end |
---|
589 | |
---|
590 | "Number of liquid phase transfer units in Zone Two" |
---|
591 | NL2S = 12*ftm*tg2s^0.5/dbs; |
---|
592 | NL2L = 12*ftm*tg2l^0.5/dbl; |
---|
593 | |
---|
594 | #Zone Three# |
---|
595 | |
---|
596 | "Terminal velocity of large bubbles in Zone Three" |
---|
597 | ulb3 = us/e; |
---|
598 | |
---|
599 | "Residence time in Zone Three" |
---|
600 | tg3 = dbls/ulb3; |
---|
601 | |
---|
602 | "Number of liquid phase transfer units in Zone Three" |
---|
603 | NL3 = 12*ftm*tg3^0.5/dbls; |
---|
604 | |
---|
605 | #Zone Four# |
---|
606 | |
---|
607 | if hf > dbls then |
---|
608 | tg4s = (hf-dbls)/usb; |
---|
609 | tg4l = (hf-dbls)/ulb; |
---|
610 | else |
---|
611 | tg4s = hf/usb; |
---|
612 | tg4l = hf/ulb; |
---|
613 | end |
---|
614 | |
---|
615 | "Number of liquid phase transfer units in Zone Four" |
---|
616 | NL4S=12*ftm*tg4s^0.5/dbs; |
---|
617 | NL4L=12*ftm*tg4l^0.5/dbl; |
---|
618 | |
---|
619 | #Zone Five# |
---|
620 | |
---|
621 | "Residence time in Zone Five" |
---|
622 | tg5=hf/ulb3; |
---|
623 | |
---|
624 | "Number of liquid phase transfer units in Zone Five" |
---|
625 | NL5=12*ftm*tg5^0.5/dbss; |
---|
626 | |
---|
627 | #Fraction of holes in jet regime estimation |
---|
628 | |
---|
629 | "Superficial velocity based on Aa in the transition point of froth regime to spay regime" |
---|
630 | uatp=((0.04302*(rhoV*'m^3/kg')^(-0.5)*(rhoL*'m^3/kg')^0.692*(sigma*'m/N')^0.06*fi^0.25*((Ql*'s/m^3')/(lw*'1/m'))^.05*(dh*'1/m')^(-0.1))*(2.58717*(hw*'1/m')+0.86))*'m/s'; |
---|
631 | |
---|
632 | "Fraction of active holes that are in jetting" |
---|
633 | fj=ua*0.6/uatp; |
---|
634 | |
---|
635 | "Fraction of active holes that are producing small bubbles" |
---|
636 | fsb=165.65*(dh*'1/m')^1.32*fi^1.33; |
---|
637 | |
---|
638 | "Fraction of active holes that are producing large bubbles" |
---|
639 | flb=1-fj-fsb; |
---|
640 | |
---|
641 | #Vapour Phase# |
---|
642 | |
---|
643 | "General Factor in equations of Units of Mass Transfer" |
---|
644 | ftmg=(Ml*rhoV)/(Mv*rhoL); |
---|
645 | |
---|
646 | #Zone One# |
---|
647 | "Reynolds number of jet" |
---|
648 | Rej=uj*dj*rhoV/Miv; |
---|
649 | |
---|
650 | "Schimdt number on vapour phase" |
---|
651 | Scg=Miv/(rhoV*Dv); |
---|
652 | |
---|
653 | "Vapour phase mass transfer coefficient in Zone One" |
---|
654 | kg1=0.046*((Dv*'s/m^2')/(dj*'1/m'))*Rej^0.96*Scg^0.44; |
---|
655 | |
---|
656 | "Liquid phase mass transfer coefficient in Zone One" |
---|
657 | kl1=1.13*((Dl*'s/m^2')/(tg1*'1/s'))^0.5; |
---|
658 | |
---|
659 | "Number of vapour phase transfer units in Zone One" |
---|
660 | NG1=ftmg*kg1*NL1/kl1; |
---|
661 | |
---|
662 | #Zones Two,Three, Four and Five# |
---|
663 | |
---|
664 | "Peclet number" |
---|
665 | Peg2s=dbs*usb/Dv; |
---|
666 | Peg2l=dbl*ulb/Dv; |
---|
667 | Peg3=dbls*ulb3/Dv; |
---|
668 | Peg4s=dbs*usb/Dv; |
---|
669 | Peg4l=dbl*ulb/Dv; |
---|
670 | Peg5=dbss*ubss/Dv; |
---|
671 | |
---|
672 | if Peg2s > 200 then |
---|
673 | Sh2s=17.9; |
---|
674 | else |
---|
675 | Sh2s=-11.878+25.879*log(Peg2s)-5.640*(log(Peg2s))^2; |
---|
676 | end |
---|
677 | |
---|
678 | if Peg2l > 200 then |
---|
679 | Sh2l=17.9; |
---|
680 | else |
---|
681 | Sh2l=-11.878+25.879*log(Peg2l)-5.640*(log(Peg2l))^2; |
---|
682 | end |
---|
683 | |
---|
684 | if Peg3 > 200 then |
---|
685 | Sh3=17.9; |
---|
686 | else |
---|
687 | Sh3=-11.878+25.879*log(Peg3)-5.640*(log(Peg3))^2; |
---|
688 | end |
---|
689 | |
---|
690 | if Peg4s > 200 then |
---|
691 | Sh4s=17.9; |
---|
692 | else |
---|
693 | Sh4s=-11.878+25.879*log(Peg4s)-5.640*(log(Peg4s))^2; |
---|
694 | end |
---|
695 | |
---|
696 | if Peg4l > 200 then |
---|
697 | Sh4l=17.9; |
---|
698 | else |
---|
699 | Sh4l=-11.878+25.879*log(Peg4l)-5.640*(log(Peg4l))^2; |
---|
700 | end |
---|
701 | |
---|
702 | if Peg5 > 200 then |
---|
703 | Sh5=17.9; |
---|
704 | else |
---|
705 | Sh5=-11.878+25.879*log(Peg5)-5.640*(log(Peg5))^2; |
---|
706 | end |
---|
707 | |
---|
708 | "Vapour phase mass transfer coefficient" |
---|
709 | kg2s=Sh2s*(Dv*'s/m^2')/(dbs*'1/m'); |
---|
710 | kg2l=Sh2l*(Dv*'s/m^2')/(dbl*'1/m'); |
---|
711 | kg3=Sh3*(Dv*'s/m^2')/(dbls*'1/m'); |
---|
712 | kg4s=Sh4s*(Dv*'s/m^2')/(dbs*'1/m'); |
---|
713 | kg4l=Sh4l*(Dv*'s/m^2')/(dbl*'1/m'); |
---|
714 | kg5=Sh5*(Dv*'s/m^2')/(dbss*'1/m'); |
---|
715 | |
---|
716 | "Liquid phase mass transfer coefficient" |
---|
717 | kl2s=1.13*((Dl*'s/m^2')/(tg2s*'1/s'))^0.5; |
---|
718 | kl2l=1.13*((Dl*'s/m^2')/(tg2l*'1/s'))^0.5; |
---|
719 | kl3=1.13*((Dl*'s/m^2')/(tg3*'1/s'))^0.5; |
---|
720 | kl4s=1.13*((Dl*'s/m^2')/(tg4s*'1/s'))^0.5; |
---|
721 | kl4l=1.13*((Dl*'s/m^2')/(tg4l*'1/s'))^0.5; |
---|
722 | kl5=1.13*((Dl*'s/m^2')/(tg5*'1/s'))^0.5; |
---|
723 | |
---|
724 | "Number of vapour phase transfer units" |
---|
725 | NG2S=ftmg*kg2s*NL2S/kl2s; |
---|
726 | NG2L=ftmg*kg2l*NL2L/kl2l; |
---|
727 | NG3=ftmg*kg3*NL3/kl3; |
---|
728 | NG4S=ftmg*kg4s*NL4S/kl4s; |
---|
729 | NG4L=ftmg*kg4l*NL4L/kl4l; |
---|
730 | NG5=ftmg*kg5*NL5/kl5; |
---|
731 | |
---|
732 | "Number of Vapour phase transfer units of jetting" |
---|
733 | NGFJ=NG1-ln(1e-8+abs(1-(aj*(1-exp(-NG2S))+(1-aj)*(1-exp(-NG2L))))); |
---|
734 | |
---|
735 | "Number of Vapour phase transfer units of large bubbles" |
---|
736 | NGFLB= NG3-ln(1e-8+abs(1-(aj*(1-exp(-NG4S))+(1-aj)*(1-exp(-NG4L))))); |
---|
737 | |
---|
738 | "Point Efficiency" |
---|
739 | EOG=fj*(1-exp(-NGFJ))+flb*(1-exp(-NGFLB))+fsb*(1-exp(-NG5)); |
---|
740 | |
---|
741 | #Liquid Mixing Models# |
---|
742 | |
---|
743 | "Eddy diffusivity for liquid mixing" |
---|
744 | De=(0.0005+0.01285*ua*'s/m'+6.32*(Ql*'s/m^3'/(lw*'1/m'))+0.312*hw*'1/m')^2; |
---|
745 | |
---|
746 | "Peclet Number" |
---|
747 | Pe=(OutletL.F*d)/(lw*hcl*(1/vL)*De*'m^2/s'); |
---|
748 | |
---|
749 | "Constant n" |
---|
750 | n=Pe/2*((1+4*lambda*EOG/Pe)^.5-1); |
---|
751 | |
---|
752 | if Pe equal 0 then |
---|
753 | Emv1=EOG; |
---|
754 | else |
---|
755 | if Pe < 20 then |
---|
756 | Emv1/EOG=(1-exp(-(n+Pe)))/((n+Pe)*(1+(n+Pe)/n))+(exp(n)-1)/(n*(1+n/(n+Pe))); |
---|
757 | else |
---|
758 | lambda*Emv1=(exp(lambda*EOG)-1); |
---|
759 | end |
---|
760 | end |
---|
761 | |
---|
762 | #Entrainment and Weeping Correction# |
---|
763 | |
---|
764 | "Height on spray regime" |
---|
765 | hb=hcl*(265*((ua/(g*hcl)^.5)*(rhoV/rhoL)^.5)^1.7+1); |
---|
766 | |
---|
767 | "Fraction of entrained liquid" |
---|
768 | l=1e-8*(hb/Ts)^3*(uh/(Ql/Aa))^2; |
---|
769 | |
---|
770 | switch tray_type |
---|
771 | case "Downcomer": |
---|
772 | "Apparent Murphree tray efficiency" |
---|
773 | Emv1=Emv2*(1+l*Emv1); |
---|
774 | case "Dualflow": |
---|
775 | "Apparent Murphree tray efficiency" |
---|
776 | Emv1=Emv2*(1+Emv1*psi/(1-psi)); |
---|
777 | |
---|
778 | end |
---|
779 | |
---|
780 | switch tray_type |
---|
781 | case "Downcomer": |
---|
782 | "Apparent Murphree tray efficiency" |
---|
783 | Emv2=Emv3; |
---|
784 | case "Dualflow": |
---|
785 | "Apparent Murphree tray efficiency" |
---|
786 | Emv2=Emv3*(1+Emv2*psi1/(1-psi1)); |
---|
787 | |
---|
788 | end |
---|
789 | |
---|
790 | Emv=Emv3; |
---|
791 | end |
---|