1 | #*------------------------------------------------------------------- |
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2 | * EMSO Model Library (EML) Copyright (C) 2004 - 2007 ALSOC. |
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3 | * |
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4 | * This LIBRARY is free software; you can distribute it and/or modify |
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5 | * it under the therms of the ALSOC FREE LICENSE as available at |
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6 | * http://www.enq.ufrgs.br/alsoc. |
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7 | * |
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8 | * EMSO Copyright (C) 2004 - 2007 ALSOC, original code |
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9 | * from http://www.rps.eng.br Copyright (C) 2002-2004. |
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10 | * All rights reserved. |
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11 | * |
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12 | * EMSO is distributed under the therms of the ALSOC LICENSE as |
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13 | * available at http://www.enq.ufrgs.br/alsoc. |
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14 | * |
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15 | *---------------------------------------------------------------------- |
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16 | * Author: Paula B. Staudt |
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17 | * $Id: tray.mso 448 2008-01-22 17:14:11Z paula $ |
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18 | *--------------------------------------------------------------------*# |
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19 | |
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20 | using "streams"; |
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21 | |
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22 | Model trayBasic |
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23 | ATTRIBUTES |
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24 | Pallete = false; |
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25 | Icon = "icon/Tray"; |
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26 | Brief = "Basic equations of a tray column model."; |
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27 | Info = |
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28 | "This model contains only the main equations of a column tray equilibrium model without |
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29 | the hidraulic equations. |
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30 | |
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31 | == Assumptions == |
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32 | * both phases (liquid and vapour) exists all the time; |
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33 | * thermodymanic equilibrium with Murphree plate efficiency; |
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34 | * no entrainment of liquid or vapour phase; |
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35 | * no weeping; |
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36 | * the dymanics in the downcomer are neglected. |
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37 | "; |
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38 | |
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39 | PARAMETERS |
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40 | outer PP as Plugin(Brief = "External Physical Properties", Type="PP"); |
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41 | outer NComp as Integer; |
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42 | V as volume(Brief="Total Volume of the tray"); |
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43 | Q as heat_rate (Brief="Rate of heat supply"); |
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44 | Ap as area (Brief="Plate area = Atray - Adowncomer"); |
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45 | |
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46 | VARIABLES |
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47 | in Inlet as stream (Brief="Feed stream", PosX=0, PosY=0.4932, Symbol="_{in}"); |
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48 | in InletL as stream (Brief="Inlet liquid stream", PosX=0.5195, PosY=0, Symbol="_{inL}"); |
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49 | in InletV as stream (Brief="Inlet vapour stream", PosX=0.4994, PosY=1, Symbol="_{inV}"); |
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50 | out OutletL as liquid_stream (Brief="Outlet liquid stream", PosX=0.8277, PosY=1, Symbol="_{outL}"); |
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51 | out OutletV as vapour_stream (Brief="Outlet vapour stream", PosX=0.8043, PosY=0, Symbol="_{outV}"); |
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52 | |
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53 | M(NComp) as mol (Brief="Molar Holdup in the tray"); |
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54 | ML as mol (Brief="Molar liquid holdup"); |
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55 | MV as mol (Brief="Molar vapour holdup"); |
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56 | E as energy (Brief="Total Energy Holdup on tray"); |
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57 | vL as volume_mol (Brief="Liquid Molar Volume"); |
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58 | vV as volume_mol (Brief="Vapour Molar volume"); |
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59 | Level as length (Brief="Height of clear liquid on plate"); |
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60 | yideal(NComp) as fraction; |
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61 | Emv as Real (Brief = "Murphree efficiency"); |
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62 | |
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63 | EQUATIONS |
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64 | "Component Molar Balance" |
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65 | diff(M)=Inlet.F*Inlet.z + InletL.F*InletL.z + InletV.F*InletV.z |
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66 | - OutletL.F*OutletL.z - OutletV.F*OutletV.z; |
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67 | |
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68 | "Energy Balance" |
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69 | diff(E) = ( Inlet.F*Inlet.h + InletL.F*InletL.h + InletV.F*InletV.h |
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70 | - OutletL.F*OutletL.h - OutletV.F*OutletV.h + Q ); |
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71 | |
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72 | "Molar Holdup" |
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73 | M = ML*OutletL.z + MV*OutletV.z; |
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74 | |
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75 | "Energy Holdup" |
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76 | E = ML*OutletL.h + MV*OutletV.h - OutletL.P*V; |
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77 | |
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78 | "Mol fraction normalisation" |
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79 | sum(OutletL.z)= 1.0; |
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80 | sum(OutletL.z)= sum(OutletV.z); |
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81 | |
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82 | "Liquid Volume" |
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83 | vL = PP.LiquidVolume(OutletL.T, OutletL.P, OutletL.z); |
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84 | "Vapour Volume" |
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85 | vV = PP.VapourVolume(OutletV.T, OutletV.P, OutletV.z); |
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86 | |
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87 | "Chemical Equilibrium" |
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88 | PP.LiquidFugacityCoefficient(OutletL.T, OutletL.P, OutletL.z)*OutletL.z = |
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89 | PP.VapourFugacityCoefficient(OutletV.T, OutletV.P, yideal)*yideal; |
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90 | |
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91 | "Murphree Efficiency" |
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92 | OutletV.z = Emv * (yideal - InletV.z) + InletV.z; |
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93 | |
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94 | "Thermal Equilibrium" |
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95 | OutletV.T = OutletL.T; |
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96 | |
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97 | "Mechanical Equilibrium" |
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98 | OutletV.P = OutletL.P; |
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99 | |
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100 | "Geometry Constraint" |
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101 | V = ML* vL + MV*vV; |
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102 | |
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103 | "Level of clear liquid over the weir" |
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104 | Level = ML*vL/Ap; |
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105 | end |
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106 | |
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107 | Model tray as trayBasic |
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108 | ATTRIBUTES |
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109 | Pallete = false; |
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110 | Icon = "icon/Tray"; |
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111 | Brief = "Complete model of a column tray."; |
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112 | Info = |
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113 | "== Specify == |
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114 | * the Feed stream |
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115 | * the Liquid inlet stream |
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116 | * the Vapour inlet stream |
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117 | * the Vapour outlet flow (OutletV.F) |
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118 | |
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119 | == Initial == |
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120 | * the plate temperature (OutletL.T) |
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121 | * the liquid height (Level) OR the liquid flow OutletL.F |
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122 | * (NoComps - 1) OutletL compositions |
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123 | "; |
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124 | |
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125 | PARAMETERS |
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126 | Ah as area (Brief="Total holes area"); |
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127 | lw as length (Brief="Weir length"); |
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128 | g as acceleration (Default=9.81); |
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129 | hw as length (Brief="Weir height"); |
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130 | beta as fraction (Brief="Aeration fraction"); |
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131 | alfa as fraction (Brief="Dry pressure drop coefficient"); |
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132 | |
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133 | VapourFlow as Switcher(Valid = ["on", "off"], Default = "on"); |
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134 | LiquidFlow as Switcher(Valid = ["on", "off"], Default = "on"); |
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135 | |
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136 | VARIABLES |
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137 | rhoL as dens_mass; |
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138 | rhoV as dens_mass; |
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139 | |
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140 | EQUATIONS |
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141 | "Liquid Density" |
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142 | rhoL = PP.LiquidDensity(OutletL.T, OutletL.P, OutletL.z); |
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143 | "Vapour Density" |
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144 | rhoV = PP.VapourDensity(InletV.T, InletV.P, InletV.z); |
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145 | |
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146 | switch LiquidFlow |
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147 | case "on": |
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148 | "Francis Equation" |
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149 | # OutletL.F*vL = 1.84*'m^0.5/s'*lw*((Level-(beta*hw))/(beta))^1.5; |
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150 | OutletL.F*vL = 1.84*'1/s'*lw*((Level-(beta*hw))/(beta))^2; |
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151 | when Level < (beta * hw) switchto "off"; |
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152 | |
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153 | case "off": |
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154 | "Low level" |
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155 | OutletL.F = 0 * 'mol/h'; |
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156 | when Level > (beta * hw) + 1e-6*'m' switchto "on"; |
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157 | end |
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158 | |
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159 | switch VapourFlow |
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160 | case "on": |
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161 | InletV.F*vV = sqrt((InletV.P - OutletV.P)/(rhoV*alfa))*Ah; |
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162 | when InletV.F < 1e-6 * 'kmol/h' switchto "off"; |
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163 | |
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164 | case "off": |
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165 | InletV.F = 0 * 'mol/s'; |
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166 | when InletV.P > OutletV.P + Level*g*rhoL + 1e-1 * 'atm' switchto "on"; |
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167 | end |
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168 | |
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169 | end |
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170 | |
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171 | Model packedStage as trayBasic |
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172 | PARAMETERS |
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173 | PPwater as Plugin(Brief="Physical Properties", |
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174 | Type="PP", |
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175 | Components = [ "water" ], |
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176 | LiquidModel = "PR", |
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177 | VapourModel = "PR" |
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178 | ); |
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179 | |
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180 | # PackingType as Switcher(Valid = ["random", "structured"], Default = "randon"); |
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181 | # PressureDropModel as Switcher(Valid = ["Leva", "Prahl"], Default = "Prahl"); |
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182 | |
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183 | a as Real (Brief="Constant used in Leva equation", Default=873.55); |
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184 | b as Real (Brief="Constant used in Leva equation", Default=0.058); |
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185 | # Fp as Real (Brief="Packing factor", Default = 300); |
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186 | e as fraction (Brief="Packing Porosity", Default=0.84); |
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187 | dp as length (Brief="Packing Dimension", Default=0.013); |
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188 | # C as Real (Brief="Prahl method constant", Unit = 'kg^0.2*m^1.8/s^2.2', Default = 2.994); |
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189 | |
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190 | # S as length (Brief="Structured packing parameter", Default=0.009); |
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191 | # teta as Real (Brief="Structured packing parameter", Unit= 'deg', Default=45); |
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192 | # C3 as Real (Brief="Structured packing parameter", Default=3.38); |
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193 | |
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194 | Across as area (Brief="Tower cross section area"); |
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195 | Mw(NComp) as molweight (Brief = "Component Mol Weight"); |
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196 | g as acceleration (Default=9.81); |
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197 | |
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198 | SET |
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199 | Mw = PP.MolecularWeight(); |
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200 | Ap = Across; |
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201 | |
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202 | VARIABLES |
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203 | rhoL as dens_mass (Brief="Liquid density"); |
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204 | rhoV as dens_mass (Brief="Vapor density"); |
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205 | viscL as viscosity (Brief="Liquid Viscosity"); |
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206 | # viscV as viscosity (Brief="Vapor Viscosity"); |
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207 | rhow as dens_mass (Brief="Water density"); |
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208 | visclw as viscosity (Brief="Water viscosity"); |
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209 | |
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210 | L as flux_mass (Brief="Liquid mass flux"); |
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211 | G as flux_mass (Brief="Liquid mass flux"); |
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212 | Llin as flux_mass (Brief="Water contribution on liquid mass flux"); |
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213 | # X as Real (Brief="Term in Prahl correlation"); |
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214 | # Y as Real (Brief="Term in Prahl correlation"); |
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215 | # Reg as Real (Brief="Packing Reynolds"); |
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216 | # Ge as velocity (Brief="Temporay variable"); |
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217 | # Fr as Real (Brief="Froud number"); |
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218 | phiL as Real (Brief="Liquid holdup in packed towers"); |
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219 | |
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220 | # deltaP_z as Real (Unit = 'inH2O/ft'); |
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221 | |
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222 | EQUATIONS |
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223 | # deltaP_z = (InletV.P - OutletV.P) / (V/Across); |
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224 | |
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225 | "If the liquid is not water - mass flux correction" |
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226 | Llin = L * rhow/rhoL; |
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227 | |
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228 | "Base unit conversion (mol -> mass)" |
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229 | L = OutletL.F*sum(Mw*OutletL.z)/Across; |
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230 | G = OutletV.F*sum(Mw*OutletV.z)/Across; |
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231 | |
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232 | # "X in Prahl correlation" |
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233 | # X * G = L * (rhoV/rhoL)^0.5; |
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234 | |
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235 | # "Y in Prahl correlation" |
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236 | # Y = G^2 * Fp * (rhow/rhoL) * viscL^0.2 / (rhoV*rhoL*C) ; |
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237 | |
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238 | "Water Liquid Viscosity" |
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239 | visclw = PPwater.LiquidViscosity(OutletL.T, OutletL.P, 1); |
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240 | "Water Liquid Density" |
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241 | rhow = PPwater.LiquidDensity(OutletL.T, OutletL.P, 1); |
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242 | "Liquid Viscosity" |
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243 | viscL = PP.LiquidViscosity(OutletL.T, OutletL.P, OutletL.z); |
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244 | # "Vapor Viscosity" |
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245 | # viscV = PP.VapourViscosity(OutletV.T, OutletV.P, OutletV.z); |
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246 | "Liquid Density" |
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247 | rhoL = PP.LiquidDensity(OutletL.T, OutletL.P, OutletL.z); |
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248 | "Vapour Density" |
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249 | rhoV = PP.VapourDensity(InletV.T, InletV.P, InletV.z); |
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250 | |
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251 | # "Froud number" |
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252 | # Fr = (L/rhoL)^2 / S/g; |
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253 | # "Reynolds number" |
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254 | # Reg = S*(G/rhoV/(e*sin(teta)))*rhoV/viscV; |
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255 | # "Temporary variable" |
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256 | # Ge = G/rhoV /(e*sin(teta)); |
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257 | "Conversion from ML to phiL" |
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258 | phiL = ML*vL / V; |
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259 | |
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260 | # switch PackingType |
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261 | # case "random": |
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262 | # switch PressureDropModel |
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263 | # case "Leva": |
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264 | (InletV.P - OutletV.P)/'Pa' / (V/'m^3'/(Across/'m^2') ) = a * 10^(b*Llin/'kg/m^2/s') * (G/('kg/m^2/s'))^2/(rhoV/('kg/m^3')); |
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265 | #(InletV.P - OutletV.P) / (V/(Across) ) = a * 10^(b*Llin) * (G)^2/(rhoV); |
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266 | # case "Prahl": |
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267 | # (InletV.P - OutletV.P)/'0.03937*inH2O' = (V/Across)/'m' * Y*(1116*X+500)/(1-Y*(35*X+3)); |
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268 | # end |
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269 | phiL = (1.53e-4 + (2.9e-5*e*(dp*L/(viscL*e))^0.66 * (viscL/visclw)^0.75)) * (dp/'m')^(-1.2); |
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270 | #* case "structured": |
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271 | (InletV.P - OutletV.P)/'Pa'= (V/Across)/'m' * ( (0.171 + 92.7/Reg) * (rhoV/('kg/m^3')*(Ge/('m/s'))^2/(S/'m')) ) |
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272 | * (1/(1-C3 * sqrt(Fr) ))^5; |
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273 | |
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274 | phiL = C3 * sqrt(Fr); |
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275 | end |
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276 | *# |
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277 | end |
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278 | |
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279 | #*------------------------------------------------------------------- |
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280 | * Model of a tray with reaction |
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281 | *-------------------------------------------------------------------*# |
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282 | Model trayReact |
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283 | ATTRIBUTES |
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284 | Pallete = false; |
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285 | Icon = "icon/Tray"; |
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286 | Brief = "Model of a tray with reaction."; |
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287 | Info = |
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288 | "== Assumptions == |
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289 | * both phases (liquid and vapour) exists all the time; |
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290 | * thermodymanic equilibrium with Murphree plate efficiency; |
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291 | * no entrainment of liquid or vapour phase; |
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292 | * no weeping; |
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293 | * the dymanics in the downcomer are neglected. |
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294 | |
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295 | == Specify == |
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296 | * the Feed stream; |
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297 | * the Liquid inlet stream; |
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298 | * the Vapour inlet stream; |
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299 | * the Vapour outlet flow (OutletV.F); |
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300 | * the reaction related variables. |
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301 | |
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302 | == Initial == |
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303 | * the plate temperature (OutletL.T) |
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304 | * the liquid height (Level) OR the liquid flow OutletL.F |
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305 | * (NoComps - 1) OutletL compositions |
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306 | "; |
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307 | |
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308 | PARAMETERS |
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309 | outer PP as Plugin(Type="PP"); |
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310 | outer NComp as Integer; |
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311 | V as volume(Brief="Total Volume of the tray"); |
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312 | Q as power (Brief="Rate of heat supply"); |
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313 | Ap as area (Brief="Plate area = Atray - Adowncomer"); |
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314 | |
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315 | Ah as area (Brief="Total holes area"); |
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316 | lw as length (Brief="Weir length"); |
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317 | g as acceleration (Default=9.81); |
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318 | hw as length (Brief="Weir height"); |
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319 | beta as fraction (Brief="Aeration fraction"); |
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320 | alfa as fraction (Brief="Dry pressure drop coefficient"); |
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321 | |
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322 | stoic(NComp) as Real(Brief="Stoichiometric matrix"); |
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323 | Hr as energy_mol; |
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324 | Pstartup as pressure; |
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325 | |
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326 | VapourFlow as Switcher(Valid = ["on", "off"], Default = "off"); |
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327 | LiquidFlow as Switcher(Valid = ["on", "off"], Default = "off"); |
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328 | |
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329 | VARIABLES |
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330 | in Inlet as stream (Brief="Feed stream", PosX=0, PosY=0.4932, Symbol="_{in}"); |
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331 | in InletL as stream (Brief="Inlet liquid stream", PosX=0.5195, PosY=0, Symbol="_{inL}"); |
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332 | in InletV as stream (Brief="Inlet vapour stream", PosX=0.4994, PosY=1, Symbol="_{inV}"); |
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333 | out OutletL as liquid_stream (Brief="Outlet liquid stream", PosX=0.8277, PosY=1, Symbol="_{outL}"); |
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334 | out OutletV as vapour_stream (Brief="Outlet vapour stream", PosX=0.8043, PosY=0, Symbol="_{outV}"); |
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335 | |
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336 | yideal(NComp) as fraction; |
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337 | Emv as Real (Brief = "Murphree efficiency"); |
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338 | |
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339 | M(NComp) as mol (Brief="Molar Holdup in the tray"); |
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340 | ML as mol (Brief="Molar liquid holdup"); |
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341 | MV as mol (Brief="Molar vapour holdup"); |
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342 | E as energy (Brief="Total Energy Holdup on tray"); |
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343 | vL as volume_mol (Brief="Liquid Molar Volume"); |
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344 | vV as volume_mol (Brief="Vapour Molar volume"); |
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345 | Level as length (Brief="Height of clear liquid on plate"); |
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346 | Vol as volume; |
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347 | |
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348 | rhoL as dens_mass; |
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349 | rhoV as dens_mass; |
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350 | r3 as reaction_mol (Brief = "Reaction resulting ethyl acetate", DisplayUnit = 'mol/l/s'); |
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351 | C(NComp) as conc_mol (Brief = "Molar concentration", Lower = -1); #, Unit = "mol/l"); |
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352 | |
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353 | EQUATIONS |
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354 | "Molar Concentration" |
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355 | OutletL.z = vL * C; |
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356 | |
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357 | "Reaction" |
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358 | r3 = exp(-7150*'K'/OutletL.T)*(4.85e4*C(1)*C(2) - 1.23e4*C(3)*C(4))*'l/mol/s'; |
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359 | |
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360 | "Component Molar Balance" |
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361 | diff(M)=Inlet.F*Inlet.z + InletL.F*InletL.z + InletV.F*InletV.z |
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362 | - OutletL.F*OutletL.z - OutletV.F*OutletV.z + stoic*r3*ML*vL; |
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363 | |
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364 | "Energy Balance" |
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365 | diff(E) = ( Inlet.F*Inlet.h + InletL.F*InletL.h + InletV.F*InletV.h |
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366 | - OutletL.F*OutletL.h - OutletV.F*OutletV.h + Q ) + Hr * r3 * vL*ML; |
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367 | |
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368 | "Molar Holdup" |
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369 | M = ML*OutletL.z + MV*OutletV.z; |
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370 | |
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371 | "Energy Holdup" |
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372 | E = ML*OutletL.h + MV*OutletV.h - OutletL.P*V; |
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373 | |
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374 | "Mol fraction normalisation" |
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375 | sum(OutletL.z)= 1.0; |
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376 | |
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377 | "Liquid Volume" |
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378 | vL = PP.LiquidVolume(OutletL.T, OutletL.P, OutletL.z); |
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379 | "Vapour Volume" |
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380 | vV = PP.VapourVolume(OutletV.T, OutletV.P, OutletV.z); |
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381 | |
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382 | "Thermal Equilibrium" |
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383 | OutletV.T = OutletL.T; |
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384 | |
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385 | "Mechanical Equilibrium" |
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386 | OutletV.P = OutletL.P; |
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387 | |
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388 | "Level of clear liquid over the weir" |
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389 | Level = ML*vL/Ap; |
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390 | |
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391 | Vol = ML*vL; |
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392 | |
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393 | "Liquid Density" |
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394 | rhoL = PP.LiquidDensity(OutletL.T, OutletL.P, OutletL.z); |
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395 | "Vapour Density" |
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396 | rhoV = PP.VapourDensity(InletV.T, InletV.P, InletV.z); |
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397 | |
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398 | switch LiquidFlow |
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399 | case "on": |
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400 | "Francis Equation" |
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401 | OutletL.F*vL = 1.84*'1/s'*lw*((Level-(beta*hw)+1e-6*'m')/(beta))^2; |
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402 | when Level < (beta * hw) switchto "off"; |
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403 | |
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404 | case "off": |
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405 | "Low level" |
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406 | OutletL.F = 0 * 'mol/h'; |
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407 | when Level > (beta * hw) + 1e-6*'m' switchto "on"; |
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408 | end |
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409 | |
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410 | switch VapourFlow |
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411 | case "on": |
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412 | #InletV.P = OutletV.P + Level*g*rhoL + rhoV*alfa*(InletV.F*vV/Ah)^2; |
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413 | InletV.F*vV = sqrt((InletV.P - OutletV.P - Level*g*rhoL + 1e-8 * 'atm')/(rhoV*alfa))*Ah; |
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414 | when InletV.P < OutletV.P + Level*g*rhoL switchto "off"; |
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415 | |
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416 | case "off": |
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417 | InletV.F = 0 * 'mol/s'; |
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418 | when InletV.P > OutletV.P + Level*g*rhoL + 3e-2 * 'atm' switchto "on"; |
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419 | #when InletV.P > OutletV.P + Level*beta*g*rhoL + 1e-2 * 'atm' switchto "on"; |
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420 | end |
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421 | |
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422 | "Chemical Equilibrium" |
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423 | PP.LiquidFugacityCoefficient(OutletL.T, OutletL.P, OutletL.z)*OutletL.z = |
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424 | PP.VapourFugacityCoefficient(OutletV.T, OutletV.P, yideal)*yideal; |
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425 | |
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426 | OutletV.z = Emv * (yideal - InletV.z) + InletV.z; |
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427 | |
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428 | sum(OutletL.z)= sum(OutletV.z); |
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429 | |
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430 | "Geometry Constraint" |
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431 | V = ML* vL + MV*vV; |
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432 | end |
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