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 522 2008-05-21 23:21:12Z arge $ |
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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 | == Options == |
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125 | You can choose the equation for the liquid outlet flow and the vapour |
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126 | inlet flow calculation through the VapourFlowModel and LiquidFlowModel |
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127 | switchers. |
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128 | |
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129 | == References == |
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130 | * ELGUE, S.; PRAT, L.; CABASSUD, M.; LANN, J. L.; CéZERAC, J. Dynamic models for start-up operations of batch distillation columns with experimental validation. Computers and Chemical Engineering, v. 28, p. 2735-2747, 2004. |
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131 | * FEEHERY, W. F. Dynamic Optimization with Path Constraints. Tese (Doutorado) - Massachusetts Institute of Technology, June 1998. |
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132 | * KLINGBERG, A. Modeling and Optimization of Batch Distillation. Dissertação (Mestrado) - Department of Automatic Control, Lund Institute of Technology, Lund, Sweden, fev. 2000. |
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133 | * OLSEN, I.; ENDRESTOL, G. O.; SIRA, T. A rigorous and efficient distillation column model for engineering and training simulators. Computers and Chemical Engineering,v. 21, n. Suppl, p. S193-S198, 1997. |
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134 | * REEPMEYER, F.; REPKE, J.-U.; WOZNY, G. Analysis of the start-up process for reactive distillation. Chemical Engineering Technology, v. 26, p. 81-86, 2003. |
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135 | * ROFFEL, B.; BETLEM, B.; RUIJTER, J. de. First principles dynamic modeling and multivariable control of a cryogenic distillation column process. Computers and Chemical Engineering, v. 24, p. 111-123, 2000. |
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136 | * WANG, L.; LI, P.; WOZNY, G.; WANG, S. A start-up model for simulation of batch distillation starting from a cold state. Computers and Chemical Engineering, v. 27, p.1485-1497, 2003. |
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137 | "; |
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138 | |
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139 | PARAMETERS |
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140 | Ah as area (Brief="Total holes area"); |
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141 | lw as length (Brief="Weir length"); |
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142 | g as acceleration (Default=9.81); |
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143 | hw as length (Brief="Weir height"); |
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144 | beta as fraction (Brief="Aeration fraction"); |
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145 | alfa as fraction (Brief="Dry pressure drop coefficient"); |
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146 | w as Real (Brief="Feehery's correlation coefficient", Unit='1/m^4', Default=1); |
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147 | btray as Real (Brief="Elgue's correlation coefficient", Unit='kg/m/mol^2', Default=1); |
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148 | fw as Real (Brief = "Olsen's correlation coefficient", Default=1); |
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149 | Np as Real (Brief = "Number of liquid passes in the tray", Default=1); |
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150 | Mw(NComp) as molweight (Brief = "Component Mol Weight"); |
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151 | |
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152 | VapourFlow as Switcher(Valid = ["on", "off"], Default = "on"); |
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153 | LiquidFlow as Switcher(Valid = ["on", "off"], Default = "on"); |
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154 | VapourFlowModel as Switcher(Valid = ["Reepmeyer", "Feehery_Fv", "Roffel_Fv", "Klingberg", "Wang_Fv", "Elgue"], Default = "Reepmeyer"); |
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155 | LiquidFlowModel as Switcher(Valid = ["default", "Wang_Fl", "Olsen", "Feehery_Fl", "Roffel_Fl"], Default = "default"); |
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156 | |
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157 | SET |
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158 | Mw = PP.MolecularWeight(); |
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159 | |
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160 | VARIABLES |
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161 | rhoL as dens_mass; |
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162 | rhoV as dens_mass; |
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163 | |
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164 | btemp as Real (Brief="Temporary variable of Roffel's liquid flow equation"); |
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165 | |
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166 | EQUATIONS |
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167 | "Liquid Density" |
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168 | rhoL = PP.LiquidDensity(OutletL.T, OutletL.P, OutletL.z); |
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169 | "Vapour Density" |
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170 | rhoV = PP.VapourDensity(InletV.T, InletV.P, InletV.z); |
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171 | |
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172 | switch LiquidFlow |
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173 | case "on": |
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174 | switch LiquidFlowModel |
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175 | case "default": |
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176 | "Francis Equation" |
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177 | OutletL.F*vL = 1.84*'1/s'*lw*((Level-(beta*hw))/(beta))^2; |
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178 | |
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179 | case "Wang_Fl": |
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180 | OutletL.F*vL = 1.84*'m^0.5/s'*lw*((Level-(beta*hw))/(beta))^1.5; |
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181 | |
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182 | case "Olsen": |
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183 | OutletL.F / 'mol/s'= lw*Np*rhoL/sum(Mw*OutletV.z)/(0.665*fw)^1.5 * ((ML*sum(Mw*OutletL.z)/rhoL/Ap)-hw)^1.5 * 'm^0.5/mol'; |
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184 | |
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185 | case "Feehery_Fl": |
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186 | OutletL.F = lw*rhoL/sum(Mw*OutletL.z) * ((Level-hw)/750/'mm')^1.5 * 'm^2/s'; |
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187 | |
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188 | case "Roffel_Fl": |
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189 | OutletL.F = 2/3*sqrt(2*g)*rhoL/sum(Mw*OutletL.z)*lw*(2*btemp-1)*(ML*sum(Mw*OutletL.z)/(Ap*1.3)/rhoL/(2*btemp-1))^1.5; |
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190 | end |
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191 | when Level < (beta * hw) switchto "off"; |
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192 | |
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193 | case "off": |
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194 | "Low level" |
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195 | OutletL.F = 0 * 'mol/h'; |
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196 | when Level > (beta * hw) + 1e-6*'m' switchto "on"; |
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197 | end |
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198 | |
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199 | btemp = 1 - 0.3593/'Pa^0.0888545'*(OutletV.F*sum(Mw*OutletV.z)/(Ap*1.3)/sqrt(rhoV))^0.177709; #/'(kg/m)^0.0888545/s^0.177709'; |
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200 | |
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201 | switch VapourFlow |
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202 | case "on": |
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203 | switch VapourFlowModel |
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204 | case "Reepmeyer": |
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205 | InletV.F*vV = sqrt((InletV.P - OutletV.P)/(rhoV*alfa))*Ah; |
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206 | |
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207 | case "Feehery_Fv": |
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208 | InletV.F = rhoV/Ap/w/sum(Mw*OutletV.z) * sqrt(((InletV.P - OutletV.P)-(rhoV*g*ML*vL/Ap))/rhoV); |
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209 | |
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210 | case "Roffel_Fv": |
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211 | InletV.F^1.08 * 0.0013 * 'kg/m/mol^1.08/s^0.92*1e5' = (InletV.P - OutletV.P)*1e5 - (beta*sum(M*Mw)/(Ap*1.3)*g*1e5) * (rhoV*Ah/sum(Mw*OutletV.z))^1.08 * 'm^1.08/mol^1.08'; |
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212 | |
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213 | case "Klingberg": |
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214 | InletV.F * vV = Ap * sqrt(((InletV.P - OutletV.P)-rhoL*g*Level)/rhoV); |
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215 | |
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216 | case "Wang_Fv": |
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217 | InletV.F * vV = Ap * sqrt(((InletV.P - OutletV.P)-rhoL*g*Level)/rhoV*alfa); |
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218 | |
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219 | case "Elgue": |
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220 | InletV.F = sqrt((InletV.P - OutletV.P)/btray); |
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221 | end |
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222 | when InletV.F < 1e-6 * 'kmol/h' switchto "off"; |
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223 | |
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224 | case "off": |
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225 | InletV.F = 0 * 'mol/s'; |
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226 | when InletV.P > OutletV.P + Level*g*rhoL + 1e-1 * 'atm' switchto "on"; |
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227 | end |
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228 | |
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229 | end |
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230 | |
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231 | #*------------------------------------------------------------------- |
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232 | * Model of a tray with reaction |
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233 | *-------------------------------------------------------------------*# |
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234 | Model trayReact |
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235 | ATTRIBUTES |
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236 | Pallete = false; |
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237 | Icon = "icon/Tray"; |
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238 | Brief = "Model of a tray with reaction."; |
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239 | Info = |
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240 | "== Assumptions == |
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241 | * both phases (liquid and vapour) exists all the time; |
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242 | * thermodymanic equilibrium with Murphree plate efficiency; |
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243 | * no entrainment of liquid or vapour phase; |
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244 | * no weeping; |
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245 | * the dymanics in the downcomer are neglected. |
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246 | |
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247 | == Specify == |
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248 | * the Feed stream; |
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249 | * the Liquid inlet stream; |
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250 | * the Vapour inlet stream; |
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251 | * the Vapour outlet flow (OutletV.F); |
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252 | * the reaction related variables. |
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253 | |
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254 | == Initial == |
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255 | * the plate temperature (OutletL.T) |
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256 | * the liquid height (Level) OR the liquid flow OutletL.F |
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257 | * (NoComps - 1) OutletL compositions |
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258 | "; |
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259 | |
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260 | PARAMETERS |
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261 | outer PP as Plugin(Type="PP"); |
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262 | outer NComp as Integer; |
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263 | V as volume(Brief="Total Volume of the tray"); |
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264 | Q as power (Brief="Rate of heat supply"); |
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265 | Ap as area (Brief="Plate area = Atray - Adowncomer"); |
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266 | |
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267 | Ah as area (Brief="Total holes area"); |
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268 | lw as length (Brief="Weir length"); |
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269 | g as acceleration (Default=9.81); |
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270 | hw as length (Brief="Weir height"); |
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271 | beta as fraction (Brief="Aeration fraction"); |
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272 | alfa as fraction (Brief="Dry pressure drop coefficient"); |
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273 | |
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274 | stoic(NComp) as Real(Brief="Stoichiometric matrix"); |
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275 | Hr as energy_mol; |
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276 | Pstartup as pressure; |
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277 | |
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278 | VapourFlow as Switcher(Valid = ["on", "off"], Default = "off"); |
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279 | LiquidFlow as Switcher(Valid = ["on", "off"], Default = "off"); |
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280 | |
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281 | VARIABLES |
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282 | in Inlet as stream (Brief="Feed stream", PosX=0, PosY=0.4932, Symbol="_{in}"); |
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283 | in InletL as stream (Brief="Inlet liquid stream", PosX=0.5195, PosY=0, Symbol="_{inL}"); |
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284 | in InletV as stream (Brief="Inlet vapour stream", PosX=0.4994, PosY=1, Symbol="_{inV}"); |
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285 | out OutletL as liquid_stream (Brief="Outlet liquid stream", PosX=0.8277, PosY=1, Symbol="_{outL}"); |
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286 | out OutletV as vapour_stream (Brief="Outlet vapour stream", PosX=0.8043, PosY=0, Symbol="_{outV}"); |
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287 | |
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288 | yideal(NComp) as fraction; |
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289 | Emv as Real (Brief = "Murphree efficiency"); |
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290 | |
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291 | M(NComp) as mol (Brief="Molar Holdup in the tray"); |
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292 | ML as mol (Brief="Molar liquid holdup"); |
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293 | MV as mol (Brief="Molar vapour holdup"); |
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294 | E as energy (Brief="Total Energy Holdup on tray"); |
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295 | vL as volume_mol (Brief="Liquid Molar Volume"); |
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296 | vV as volume_mol (Brief="Vapour Molar volume"); |
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297 | Level as length (Brief="Height of clear liquid on plate"); |
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298 | Vol as volume; |
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299 | |
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300 | rhoL as dens_mass; |
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301 | rhoV as dens_mass; |
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302 | r3 as reaction_mol (Brief = "Reaction resulting ethyl acetate", DisplayUnit = 'mol/l/s'); |
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303 | C(NComp) as conc_mol (Brief = "Molar concentration", Lower = -1); #, Unit = "mol/l"); |
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304 | |
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305 | EQUATIONS |
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306 | "Molar Concentration" |
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307 | OutletL.z = vL * C; |
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308 | |
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309 | "Reaction" |
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310 | 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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311 | |
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312 | "Component Molar Balance" |
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313 | diff(M)=Inlet.F*Inlet.z + InletL.F*InletL.z + InletV.F*InletV.z |
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314 | - OutletL.F*OutletL.z - OutletV.F*OutletV.z + stoic*r3*ML*vL; |
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315 | |
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316 | "Energy Balance" |
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317 | diff(E) = ( Inlet.F*Inlet.h + InletL.F*InletL.h + InletV.F*InletV.h |
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318 | - OutletL.F*OutletL.h - OutletV.F*OutletV.h + Q ) + Hr * r3 * vL*ML; |
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319 | |
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320 | "Molar Holdup" |
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321 | M = ML*OutletL.z + MV*OutletV.z; |
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322 | |
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323 | "Energy Holdup" |
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324 | E = ML*OutletL.h + MV*OutletV.h - OutletL.P*V; |
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325 | |
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326 | "Mol fraction normalisation" |
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327 | sum(OutletL.z)= 1.0; |
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328 | |
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329 | "Liquid Volume" |
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330 | vL = PP.LiquidVolume(OutletL.T, OutletL.P, OutletL.z); |
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331 | "Vapour Volume" |
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332 | vV = PP.VapourVolume(OutletV.T, OutletV.P, OutletV.z); |
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333 | |
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334 | "Thermal Equilibrium" |
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335 | OutletV.T = OutletL.T; |
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336 | |
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337 | "Mechanical Equilibrium" |
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338 | OutletV.P = OutletL.P; |
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339 | |
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340 | "Level of clear liquid over the weir" |
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341 | Level = ML*vL/Ap; |
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342 | |
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343 | Vol = ML*vL; |
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344 | |
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345 | "Liquid Density" |
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346 | rhoL = PP.LiquidDensity(OutletL.T, OutletL.P, OutletL.z); |
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347 | "Vapour Density" |
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348 | rhoV = PP.VapourDensity(InletV.T, InletV.P, InletV.z); |
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349 | |
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350 | switch LiquidFlow |
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351 | case "on": |
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352 | "Francis Equation" |
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353 | OutletL.F*vL = 1.84*'1/s'*lw*((Level-(beta*hw)+1e-6*'m')/(beta))^2; |
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354 | when Level < (beta * hw) switchto "off"; |
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355 | |
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356 | case "off": |
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357 | "Low level" |
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358 | OutletL.F = 0 * 'mol/h'; |
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359 | when Level > (beta * hw) + 1e-6*'m' switchto "on"; |
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360 | end |
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361 | |
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362 | switch VapourFlow |
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363 | case "on": |
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364 | #InletV.P = OutletV.P + Level*g*rhoL + rhoV*alfa*(InletV.F*vV/Ah)^2; |
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365 | InletV.F*vV = sqrt((InletV.P - OutletV.P - Level*g*rhoL + 1e-8 * 'atm')/(rhoV*alfa))*Ah; |
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366 | when InletV.P < OutletV.P + Level*g*rhoL switchto "off"; |
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367 | |
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368 | case "off": |
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369 | InletV.F = 0 * 'mol/s'; |
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370 | when InletV.P > OutletV.P + Level*g*rhoL + 3e-2 * 'atm' switchto "on"; |
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371 | #when InletV.P > OutletV.P + Level*beta*g*rhoL + 1e-2 * 'atm' switchto "on"; |
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372 | end |
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373 | |
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374 | "Chemical Equilibrium" |
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375 | PP.LiquidFugacityCoefficient(OutletL.T, OutletL.P, OutletL.z)*OutletL.z = |
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376 | PP.VapourFugacityCoefficient(OutletV.T, OutletV.P, yideal)*yideal; |
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377 | |
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378 | OutletV.z = Emv * (yideal - InletV.z) + InletV.z; |
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379 | |
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380 | sum(OutletL.z)= sum(OutletV.z); |
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381 | |
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382 | "Geometry Constraint" |
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383 | V = ML* vL + MV*vV; |
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384 | end |
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385 | |
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386 | #*------------------------------------- |
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387 | * Model of a packed column stage |
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388 | -------------------------------------*# |
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389 | Model packedStage |
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390 | ATTRIBUTES |
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391 | Pallete = false; |
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392 | Icon = "icon/PackedStage"; |
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393 | Brief = "Complete model of a packed column stage."; |
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394 | Info = |
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395 | "== Specify == |
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396 | * the Feed stream |
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397 | * the Liquid inlet stream |
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398 | * the Vapour inlet stream |
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399 | * the stage pressure drop (deltaP) |
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400 | |
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401 | == Initial == |
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402 | * the plate temperature (OutletL.T) |
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403 | * the liquid molar holdup ML |
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404 | * (NoComps - 1) OutletL compositions |
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405 | "; |
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406 | |
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407 | PARAMETERS |
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408 | outer PP as Plugin(Brief = "External Physical Properties", Type="PP"); |
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409 | outer NComp as Integer; |
---|
410 | PPwater as Plugin(Brief="Physical Properties", |
---|
411 | Type="PP", |
---|
412 | Components = [ "water" ], |
---|
413 | LiquidModel = "PR", |
---|
414 | VapourModel = "PR" |
---|
415 | ); |
---|
416 | |
---|
417 | V as volume(Brief="Total Volume of the tray"); |
---|
418 | Q as heat_rate (Brief="Rate of heat supply"); |
---|
419 | d as length (Brief="Column diameter"); |
---|
420 | |
---|
421 | a as Real (Brief="surface area per packing volume", Unit='m^2/m^3'); |
---|
422 | g as acceleration; |
---|
423 | e as Real (Brief="Void fraction of packing, m^3/m^3"); |
---|
424 | Cpo as Real (Brief="Constant for resitance equation"); # Billet and Schultes, 1999. |
---|
425 | Mw(NComp) as molweight (Brief = "Component Mol Weight"); |
---|
426 | hs as length (Brief="Height of the packing stage"); |
---|
427 | Qsil as positive (Brief="Resistance coefficient on the liquid load", Default=1); |
---|
428 | |
---|
429 | VARIABLES |
---|
430 | in Inlet as stream (Brief="Feed stream", PosX=0, PosY=0.4932, Symbol="_{in}"); |
---|
431 | in InletL as stream (Brief="Inlet liquid stream", PosX=0.5195, PosY=0, Symbol="_{inL}"); |
---|
432 | in InletV as stream (Brief="Inlet vapour stream", PosX=0.4994, PosY=1, Symbol="_{inV}"); |
---|
433 | out OutletL as liquid_stream (Brief="Outlet liquid stream", PosX=0.8277, PosY=1, Symbol="_{outL}"); |
---|
434 | out OutletV as vapour_stream (Brief="Outlet vapour stream", PosX=0.8043, PosY=0, Symbol="_{outV}"); |
---|
435 | |
---|
436 | M(NComp) as mol (Brief="Molar Holdup in the tray", Default=0.01, Lower=0, Upper=100); |
---|
437 | ML as mol (Brief="Molar liquid holdup", Default=0.01, Lower=0, Upper=100); |
---|
438 | MV as mol (Brief="Molar vapour holdup", Default=0.01, Lower=0, Upper=100); |
---|
439 | E as energy (Brief="Total Energy Holdup on tray", Default=-500); |
---|
440 | vL as volume_mol (Brief="Liquid Molar Volume"); |
---|
441 | vV as volume_mol (Brief="Vapour Molar volume"); |
---|
442 | |
---|
443 | miL as viscosity (Brief="Liquid dynamic viscosity", DisplayUnit='kg/m/s'); |
---|
444 | miV as viscosity (Brief="Vapor dynamic viscosity", DisplayUnit='kg/m/s'); |
---|
445 | rhoL as dens_mass; |
---|
446 | rhoV as dens_mass; |
---|
447 | |
---|
448 | deltaP as pressure; |
---|
449 | |
---|
450 | uL as velocity (Brief="volume flow rate of liquid, m^3/m^2/s", Lower=-10, Upper=100); |
---|
451 | uV as velocity (Brief="volume flow rate of vapor, m^3/m^2/s", Lower=-10, Upper=100); |
---|
452 | dp as length (Brief="Particle diameter", Default=1e-3, Lower=0, Upper=10); |
---|
453 | invK as positive (Brief="Wall factor", Default=1, Upper=10); |
---|
454 | Rev as Real (Brief="Reynolds number of the vapor stream", Default=4000); |
---|
455 | Al as area (Brief="Area occupied by the liquid", Default=0.001, Upper=1); |
---|
456 | hl as positive (Brief="Column holdup", Unit='m^3/m^3', Default=0.01,Upper=10); |
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457 | |
---|
458 | SET |
---|
459 | Mw = PP.MolecularWeight(); |
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460 | |
---|
461 | EQUATIONS |
---|
462 | "Component Molar Balance" |
---|
463 | diff(M)=Inlet.F*Inlet.z + InletL.F*InletL.z + InletV.F*InletV.z |
---|
464 | - OutletL.F*OutletL.z - OutletV.F*OutletV.z; |
---|
465 | |
---|
466 | "Energy Balance" |
---|
467 | diff(E) = ( Inlet.F*Inlet.h + InletL.F*InletL.h + InletV.F*InletV.h |
---|
468 | - OutletL.F*OutletL.h - OutletV.F*OutletV.h + Q ); |
---|
469 | |
---|
470 | "Molar Holdup" |
---|
471 | M = ML*OutletL.z + MV*OutletV.z; |
---|
472 | |
---|
473 | "Energy Holdup" |
---|
474 | E = ML*OutletL.h + MV*OutletV.h - OutletL.P*V; |
---|
475 | |
---|
476 | "Mol fraction normalisation" |
---|
477 | sum(OutletL.z)= 1.0; |
---|
478 | |
---|
479 | "Liquid Volume" |
---|
480 | vL = PP.LiquidVolume(OutletL.T, OutletL.P, OutletL.z); |
---|
481 | "Vapour Volume" |
---|
482 | vV = PP.VapourVolume(OutletV.T, OutletV.P, OutletV.z); |
---|
483 | |
---|
484 | "Chemical Equilibrium" |
---|
485 | PP.LiquidFugacityCoefficient(OutletL.T, OutletL.P, OutletL.z)*OutletL.z = |
---|
486 | PP.VapourFugacityCoefficient(OutletV.T, OutletV.P, OutletV.z)*OutletV.z; |
---|
487 | |
---|
488 | "Thermal Equilibrium" |
---|
489 | OutletV.T = OutletL.T; |
---|
490 | |
---|
491 | "Mechanical Equilibrium" |
---|
492 | OutletL.P = OutletV.P; |
---|
493 | |
---|
494 | "Geometry Constraint" |
---|
495 | V*e = ML*vL + MV*vV; |
---|
496 | |
---|
497 | "Liquid Density" |
---|
498 | rhoL = PP.LiquidDensity(OutletL.T, OutletL.P, OutletL.z); |
---|
499 | "Vapour Density" |
---|
500 | rhoV = PP.VapourDensity(InletV.T, InletV.P, InletV.z); |
---|
501 | "Liquid viscosity" |
---|
502 | miL = PP.LiquidViscosity(OutletL.T, OutletL.P, OutletL.z); |
---|
503 | "Vapour viscosity" |
---|
504 | miV = PP.VapourViscosity(InletV.T, InletV.P, InletV.z); |
---|
505 | |
---|
506 | "Area occupied by the liquid" |
---|
507 | Al = ML*vL/hs; |
---|
508 | |
---|
509 | "Volume flow rate of liquid, m^3/m^2/s" |
---|
510 | uL * Al = OutletL.F * vL; |
---|
511 | "Volume flow rate of vapor, m^3/m^2/s" |
---|
512 | uV * ((d^2*3.14159/4)*e - Al) = OutletV.F * vV; |
---|
513 | |
---|
514 | "Liquid holdup" |
---|
515 | hl = ML*vL/V/e; |
---|
516 | |
---|
517 | "Particle diameter" |
---|
518 | dp = 6 * (1-e)/a; |
---|
519 | |
---|
520 | "Wall Factor" |
---|
521 | invK = (1 + (2*dp/(3*d*(1-e)))); |
---|
522 | |
---|
523 | "Reynolds number of the vapor stream" |
---|
524 | Rev*invK = dp*uV*rhoV / (miV*(1-e)); |
---|
525 | |
---|
526 | deltaP = InletV.P - OutletV.P; |
---|
527 | |
---|
528 | "Pressure drop and Vapor flow" |
---|
529 | deltaP/hs = Qsil*a*uV^2*rhoV*invK / (2*(e-hl)^3); |
---|
530 | |
---|
531 | "Liquid holdup" |
---|
532 | hl = (12*miL*a^2*uL/rhoL/g)^1/3; |
---|
533 | end |
---|
534 | |
---|
535 | #*------------------------------------- |
---|
536 | * Nonequilibrium Model |
---|
537 | -------------------------------------*# |
---|
538 | Model interface |
---|
539 | |
---|
540 | ATTRIBUTES |
---|
541 | Pallete = false; |
---|
542 | Icon = "icon/Tray"; |
---|
543 | Brief = "Descrition of variables of the equilibrium interface."; |
---|
544 | Info = |
---|
545 | "This model contains only the variables of the equilibrium interface."; |
---|
546 | |
---|
547 | PARAMETERS |
---|
548 | outer PP as Plugin(Brief = "External Physical Properties", Type="PP"); |
---|
549 | outer NComp as Integer; |
---|
550 | outer NC1 as Integer; |
---|
551 | |
---|
552 | VARIABLES |
---|
553 | NL(NComp) as flow_mol_delta (Brief = "Stream Molar Rate on Liquid Phase"); |
---|
554 | NV(NComp) as flow_mol_delta (Brief = "Stream Molar Rate on Vapour Phase"); |
---|
555 | T as temperature (Brief = "Stream Temperature"); |
---|
556 | P as pressure (Brief = "Stream Pressure"); |
---|
557 | x(NComp) as fraction (Brief = "Stream Molar Fraction on Liquid Phase"); |
---|
558 | y(NComp) as fraction (Brief = "Stream Molar Fraction on Vapour Phase"); |
---|
559 | a as area (Brief = "Interface Area"); |
---|
560 | htL as heat_trans_coeff (Brief = "Heat Transference Coefficient on Liquid Phase"); |
---|
561 | htV as heat_trans_coeff (Brief = "Heat Transference Coefficient on Vapour Phase"); |
---|
562 | E_liq as heat_rate (Brief = "Liquid Energy Rate at interface"); |
---|
563 | E_vap as heat_rate (Brief = "Vapour Energy Rate at interface"); |
---|
564 | hL as enth_mol (Brief = "Liquid Molar Enthalpy"); |
---|
565 | hV as enth_mol (Brief = "Vapour Molar Enthalpy"); |
---|
566 | kL(NC1,NC1) as velocity (Brief = "Mass Transfer Coefficients"); |
---|
567 | kV(NC1,NC1) as velocity (Brief = "Mass Transfer Coefficients"); |
---|
568 | |
---|
569 | EQUATIONS |
---|
570 | "Liquid Enthalpy" |
---|
571 | hL = PP.LiquidEnthalpy(T, P, x); |
---|
572 | |
---|
573 | "Vapour Enthalpy" |
---|
574 | hV = PP.VapourEnthalpy(T, P, y); |
---|
575 | |
---|
576 | end |
---|
577 | |
---|
578 | Model trayRateBasic |
---|
579 | ATTRIBUTES |
---|
580 | Pallete = false; |
---|
581 | Icon = "icon/Tray"; |
---|
582 | Brief = "Basic equations of a tray rate column model."; |
---|
583 | Info = |
---|
584 | "This model contains only the main equations of a column tray nonequilibrium model without |
---|
585 | the hidraulic equations. |
---|
586 | |
---|
587 | == Assumptions == |
---|
588 | * both phases (liquid and vapour) exists all the time; |
---|
589 | * no entrainment of liquid or vapour phase; |
---|
590 | * no weeping; |
---|
591 | * the dymanics in the downcomer are neglected. |
---|
592 | "; |
---|
593 | |
---|
594 | PARAMETERS |
---|
595 | outer PP as Plugin(Brief = "External Physical Properties", Type="PP"); |
---|
596 | outer NComp as Integer; |
---|
597 | NC1 as Integer; |
---|
598 | V as volume(Brief="Total Volume of the tray"); |
---|
599 | Q as heat_rate (Brief="Rate of heat supply"); |
---|
600 | Ap as area (Brief="Plate area = Atray - Adowncomer"); |
---|
601 | |
---|
602 | VARIABLES |
---|
603 | in Inlet as stream (Brief="Feed stream", PosX=0, PosY=0.4932, Symbol="_{in}"); |
---|
604 | in InletFV as stream (Brief="Feed stream", PosX=0, PosY=0.4932, Symbol="_{in}"); |
---|
605 | in InletL as stream (Brief="Inlet liquid stream", PosX=0.5195, PosY=0, Symbol="_{inL}"); |
---|
606 | in InletV as stream (Brief="Inlet vapour stream", PosX=0.4994, PosY=1, Symbol="_{inV}"); |
---|
607 | out OutletL as liquid_stream (Brief="Outlet liquid stream", PosX=0.8277, PosY=1, Symbol="_{outL}"); |
---|
608 | out OutletV as vapour_stream (Brief="Outlet vapour stream", PosX=0.8043, PosY=0, Symbol="_{outV}"); |
---|
609 | |
---|
610 | M_liq(NComp) as mol (Brief="Liquid Molar Holdup in the tray"); |
---|
611 | M_vap(NComp) as mol (Brief="Vapour Molar Holdup in the tray"); |
---|
612 | ML as mol (Brief="Molar liquid holdup"); |
---|
613 | MV as mol (Brief="Molar vapour holdup"); |
---|
614 | E_liq as energy (Brief="Total Liquid Energy Holdup on tray"); |
---|
615 | E_vap as energy (Brief="Total Vapour Energy Holdup on tray"); |
---|
616 | vL as volume_mol (Brief="Liquid Molar Volume"); |
---|
617 | vV as volume_mol (Brief="Vapour Molar volume"); |
---|
618 | Level as length (Brief="Height of clear liquid on plate"); |
---|
619 | interf as interface; |
---|
620 | |
---|
621 | SET |
---|
622 | NC1=NComp-1; |
---|
623 | |
---|
624 | EQUATIONS |
---|
625 | "Component Molar Balance" |
---|
626 | diff(M_liq)=Inlet.F*Inlet.z + InletL.F*InletL.z |
---|
627 | - OutletL.F*OutletL.z + interf.NL; |
---|
628 | |
---|
629 | diff(M_vap)=InletFV.F*InletFV.z + InletV.F*InletV.z |
---|
630 | - OutletV.F*OutletV.z - interf.NV; |
---|
631 | |
---|
632 | "Energy Balance" |
---|
633 | diff(E_liq) = Inlet.F*Inlet.h + InletL.F*InletL.h |
---|
634 | - OutletL.F*OutletL.h + Q + interf.E_liq; |
---|
635 | |
---|
636 | diff(E_vap) = InletFV.F*InletFV.h + InletV.F*InletV.h |
---|
637 | - OutletV.F*OutletV.h - interf.E_vap; |
---|
638 | |
---|
639 | "Molar Holdup" |
---|
640 | M_liq = ML*OutletL.z; |
---|
641 | |
---|
642 | M_vap = MV*OutletV.z; |
---|
643 | |
---|
644 | "Energy Holdup" |
---|
645 | E_liq = ML*(OutletL.h - OutletL.P*vL); |
---|
646 | |
---|
647 | E_vap = MV*(OutletV.h - OutletV.P*vV); |
---|
648 | |
---|
649 | "Energy Rate through the interface" |
---|
650 | interf.E_liq = interf.htL*interf.a*(interf.T-OutletL.T)+sum(interf.NL)*interf.hL; |
---|
651 | |
---|
652 | interf.E_vap = interf.htV*interf.a*(OutletV.T-interf.T)+sum(interf.NV)*interf.hV; |
---|
653 | |
---|
654 | "Mass Conservation" |
---|
655 | interf.NL = interf.NV; |
---|
656 | |
---|
657 | "Energy Conservation" |
---|
658 | interf.E_liq = interf.E_vap; |
---|
659 | |
---|
660 | "Mol fraction normalisation" |
---|
661 | sum(OutletL.z)= 1.0; |
---|
662 | sum(OutletL.z)= sum(OutletV.z); |
---|
663 | sum(interf.x)=1.0; |
---|
664 | sum(interf.x)=sum(interf.y); |
---|
665 | |
---|
666 | "Liquid Volume" |
---|
667 | vL = PP.LiquidVolume(OutletL.T, OutletL.P, OutletL.z); |
---|
668 | "Vapour Volume" |
---|
669 | vV = PP.VapourVolume(OutletV.T, OutletV.P, OutletV.z); |
---|
670 | |
---|
671 | "Chemical Equilibrium" |
---|
672 | PP.LiquidFugacityCoefficient(interf.T, interf.P, interf.x)*interf.x = |
---|
673 | PP.VapourFugacityCoefficient(interf.T, interf.P, interf.y)*interf.y; |
---|
674 | |
---|
675 | "Geometry Constraint" |
---|
676 | V = ML*vL + MV*vV; |
---|
677 | |
---|
678 | "Level of clear liquid over the weir" |
---|
679 | Level = ML*vL/Ap; |
---|
680 | |
---|
681 | "Total Mass Transfer Rates" |
---|
682 | interf.NL(1:NC1)=interf.a*sumt(interf.kL*(interf.x(1:NC1)-OutletL.z(1:NC1)))/vL+ |
---|
683 | OutletL.z(1:NC1)*sum(interf.NL); |
---|
684 | |
---|
685 | # interf.NL(1:NC1)=0.01*'kmol/s'; |
---|
686 | |
---|
687 | interf.NV(1:NC1)=interf.a*sumt(interf.kV*(OutletV.z(1:NC1)-interf.y(1:NC1)))/vV+ |
---|
688 | OutletV.z(1:NC1)*sum(interf.NV); |
---|
689 | |
---|
690 | "Mechanical Equilibrium" |
---|
691 | OutletV.P = OutletL.P; |
---|
692 | interf.P=OutletL.P; |
---|
693 | end |
---|
694 | |
---|
695 | Model trayRate as trayRateBasic |
---|
696 | ATTRIBUTES |
---|
697 | Pallete = false; |
---|
698 | Icon = "icon/Tray"; |
---|
699 | Brief = "Complete rate model of a column tray."; |
---|
700 | Info = |
---|
701 | "== Specify == |
---|
702 | * the Feed stream |
---|
703 | * the Liquid inlet stream |
---|
704 | * the Vapour inlet stream |
---|
705 | * the Vapour outlet flow (OutletV.F) |
---|
706 | |
---|
707 | == Initial == |
---|
708 | * the plate temperature of both phases (OutletL.T and OutletV.T) |
---|
709 | * the liquid height (Level) OR the liquid flow holdup (ML) |
---|
710 | * the vapor holdup (MV) |
---|
711 | * (NoComps - 1) OutletL compositions |
---|
712 | "; |
---|
713 | |
---|
714 | PARAMETERS |
---|
715 | Ah as area (Brief="Total holes area"); |
---|
716 | lw as length (Brief="Weir length"); |
---|
717 | g as acceleration (Default=9.81); |
---|
718 | hw as length (Brief="Weir height"); |
---|
719 | beta as fraction (Brief="Aeration fraction"); |
---|
720 | alfa as fraction (Brief="Dry pressure drop coefficient"); |
---|
721 | |
---|
722 | VapourFlow as Switcher(Valid = ["on", "off"], Default = "on"); |
---|
723 | LiquidFlow as Switcher(Valid = ["on", "off"], Default = "on"); |
---|
724 | |
---|
725 | VARIABLES |
---|
726 | rhoL as dens_mass; |
---|
727 | rhoV as dens_mass; |
---|
728 | |
---|
729 | EQUATIONS |
---|
730 | "Liquid Density" |
---|
731 | rhoL = PP.LiquidDensity(OutletL.T, OutletL.P, OutletL.z); |
---|
732 | "Vapour Density" |
---|
733 | rhoV = PP.VapourDensity(InletV.T, InletV.P, InletV.z); |
---|
734 | |
---|
735 | switch LiquidFlow |
---|
736 | case "on": |
---|
737 | "Francis Equation" |
---|
738 | # OutletL.F*vL = 1.84*'m^0.5/s'*lw*((Level-(beta*hw))/(beta))^1.5; |
---|
739 | OutletL.F*vL = 1.84*'1/s'*lw*((Level-(beta*hw))/(beta))^2; |
---|
740 | when Level < (beta * hw) switchto "off"; |
---|
741 | |
---|
742 | case "off": |
---|
743 | "Low level" |
---|
744 | OutletL.F = 0 * 'mol/h'; |
---|
745 | when Level > (beta * hw) + 1e-6*'m' switchto "on"; |
---|
746 | end |
---|
747 | |
---|
748 | switch VapourFlow |
---|
749 | case "on": |
---|
750 | InletV.F*vV = sqrt((InletV.P - OutletV.P)/(rhoV*alfa))*Ah; |
---|
751 | when InletV.F < 1e-6 * 'kmol/h' switchto "off"; |
---|
752 | |
---|
753 | case "off": |
---|
754 | InletV.F = 0 * 'mol/s'; |
---|
755 | when InletV.P > OutletV.P + Level*g*rhoL + 1e-1 * 'atm' switchto "on"; |
---|
756 | end |
---|
757 | end |
---|