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 | * Series of CSTR and PFR |
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17 | *---------------------------------------------------------------------- |
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18 | * Solved problem from Fogler (1999) |
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19 | * Problem number: 2-2 at 2-7 |
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20 | * Page: 38-49 (Brazilian edition, 2002) |
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21 | *---------------------------------------------------------------------- |
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22 | * |
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23 | * Description: |
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24 | * Sample to comparative between volumes to specific outlet molar |
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25 | * conversion of CSTR and PFR by means of several different |
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26 | * configurations |
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27 | * |
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28 | * Assumptions: |
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29 | * * steady-state |
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30 | * * isotermic and isobaric system |
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31 | * * gaseous phase |
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32 | * |
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33 | * Specify: |
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34 | * * the inlet stream (F,X) |
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35 | * * the expression of rate of reaction |
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36 | * * the initial volume |
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37 | * * the outlet conversion |
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38 | * |
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39 | * Configurations: |
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40 | * * only one CSTR |
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41 | * * only one PFR |
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42 | * * 2 CSTRs in series |
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43 | * * 2 PFRs in series |
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44 | * * one PFR followed for one CSTR |
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45 | * * one CSTR followed for one PFR |
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46 | * |
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47 | *---------------------------------------------------------------------- |
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48 | * Author: Rodolfo Rodrigues and Argimiro R. Secchi |
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49 | * $Id: series_reactors.mso 574 2008-07-25 14:18:50Z rafael $ |
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50 | *--------------------------------------------------------------------*# |
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51 | |
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52 | using "types"; |
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53 | |
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54 | |
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55 | #*--------------------------------------------------------------------- |
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56 | * Estimation of rate of reaction |
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57 | *--------------------------------------------------------------------*# |
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58 | |
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59 | FlowSheet rate |
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60 | PARAMETERS |
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61 | a1 as Real (Brief="Parameter to estimate", Default=0.01); |
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62 | a2 as Real (Brief="Parameter to estimate", Default=0.01); |
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63 | a3 as Real (Brief="Parameter to estimate", Default=0.01); |
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64 | a4 as Real (Brief="Parameter to estimate", Default=0.01); |
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65 | |
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66 | VARIABLES |
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67 | r as reaction_mol (Brief="Rate of reaction", DisplayUnit='mol/m^3/s'); |
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68 | X as fraction (Brief="Molar conversion", Unit='mol/mol'); |
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69 | |
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70 | EQUATIONS |
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71 | "Rate of reaction" # Attributed expression |
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72 | (-r) = (a4*X^3 + a3*X^2 + a2*X + a1)*'mol/l/s'; |
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73 | |
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74 | SPECIFY |
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75 | X = 0.5; |
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76 | |
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77 | OPTIONS |
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78 | Dynamic = false; |
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79 | end |
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80 | |
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81 | Estimation rate_of_reaction as rate |
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82 | ESTIMATE |
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83 | # PAR START LOWER UPPER |
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84 | a1 0.01 -1 1; |
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85 | a2 0.01 -1 1; |
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86 | a3 -0.01 -1 1; |
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87 | a4 0.01 -1 1; |
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88 | |
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89 | EXPERIMENTS |
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90 | # FILE WEIGTH |
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91 | "raw_data.dat" 1; # Table 2-1 (Fogler,1999) |
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92 | |
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93 | OPTIONS |
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94 | Dynamic = false; |
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95 | NLPSolver(File = "ipopt_emso", |
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96 | ObjTol = 1e-8 |
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97 | ); |
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98 | end |
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99 | |
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100 | |
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101 | #*--------------------------------------------------------------------- |
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102 | * Model of a simple stream |
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103 | *--------------------------------------------------------------------*# |
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104 | |
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105 | Model simple_stream |
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106 | VARIABLES |
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107 | F as flow_mol (Brief="Molar flow", DisplayUnit='mol/s'); |
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108 | X as fraction (Brief="Molar conversion"); |
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109 | end |
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110 | |
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111 | Model reactor_source |
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112 | ATTRIBUTES |
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113 | Pallete = true; |
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114 | Brief = "Simple inlet stream"; |
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115 | Icon = "icon/inlet"; |
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116 | |
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117 | VARIABLES |
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118 | out Outlet as simple_stream (Brief="Outlet stream", PosX=1, PosY=0.5); |
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119 | end |
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120 | |
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121 | Model reactor_sink |
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122 | ATTRIBUTES |
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123 | Pallete = true; |
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124 | Brief = "Simple outlet stream"; |
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125 | Icon = "icon/outlet"; |
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126 | |
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127 | VARIABLES |
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128 | in Inlet as simple_stream (Brief="Inlet stream", PosX=0, PosY=0.5); |
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129 | end |
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130 | |
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131 | |
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132 | #*--------------------------------------------------------------------- |
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133 | * Model of a steady-state, isotermic, and isobaric CSTR |
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134 | *--------------------------------------------------------------------*# |
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135 | |
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136 | Model simple_cstr |
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137 | ATTRIBUTES |
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138 | Pallete = true; |
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139 | Brief = "Simple model of a steady-state CSTR"; |
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140 | Icon = "icon/simple_cstr"; |
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141 | |
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142 | PARAMETERS |
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143 | NT as Integer (Brief="Number of terms of reaction rate expression", Default=4); |
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144 | a(NT) as reaction_mol (Brief="Parameter of reaction rate expression", DisplayUnit='mol/l/s'); |
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145 | |
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146 | VARIABLES |
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147 | in Inlet as simple_stream(Brief="Inlet stream", Symbol="_{in}", PosX=0, PosY=0); |
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148 | out Outlet as simple_stream(Brief="Outlet stream", Symbol="_{out}", PosX=1, PosY=1); |
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149 | r as reaction_mol (Brief="Rate of reaction", DisplayUnit='mol/l/s'); |
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150 | V as volume (Brief="Volume", DisplayUnit='l', Upper=2e3); |
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151 | |
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152 | SET |
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153 | a = [0.00526629, 0.00133545, -0.0153342, 0.00921664]*'mol/l/s'; # Estimated |
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154 | |
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155 | EQUATIONS |
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156 | "Component molar balance" |
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157 | Inlet.F*(Outlet.X - Inlet.X) = (-r)*V; |
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158 | |
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159 | "Molar flow" |
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160 | Outlet.F = Inlet.F; |
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161 | |
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162 | "Rate of reaction" |
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163 | (-r) = sum(a*Outlet.X^[0:(NT-1)]); |
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164 | end |
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165 | |
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166 | |
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167 | #*--------------------------------------------------------------------- |
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168 | * Model of a steady-state, isotermic, and isobaric PFR |
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169 | *--------------------------------------------------------------------*# |
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170 | |
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171 | Model simple_pfr |
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172 | PARAMETERS |
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173 | NT as Integer (Brief="Number of terms of reaction rate expression", Default=4); |
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174 | a(NT) as reaction_mol (Brief="Parameter of reaction rate expression", DisplayUnit='mol/l/s'); |
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175 | |
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176 | VARIABLES |
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177 | in Inlet as simple_stream(Brief="Inlet stream", Symbol="_{in}"); |
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178 | out Outlet as simple_stream(Brief="Outlet stream", Symbol="_{out}"); |
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179 | V as volume (Brief="Volume", DisplayUnit='l', Upper=2e3); |
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180 | r as reaction_mol (Brief="Rate of reaction", DisplayUnit='mol/l/s'); |
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181 | |
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182 | SET |
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183 | a = [0.00526629, 0.00133545, -0.0153342, 0.00921664]*'mol/l/s'; # Estimated |
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184 | |
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185 | EQUATIONS |
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186 | "Molar balance" |
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187 | diff(V) = Inlet.F/(-r)/'s'; |
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188 | |
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189 | "Change time in X" |
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190 | Outlet.X = time/'s'; |
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191 | |
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192 | "Molar flow" |
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193 | Outlet.F = Inlet.F; |
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194 | |
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195 | "Rate of reaction" |
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196 | (-r) = sum(a*Outlet.X^[0:(NT-1)]); |
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197 | |
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198 | INITIAL |
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199 | "Reactor volume" |
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200 | V = 0.0*'l'; |
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201 | end |
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202 | |
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203 | |
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204 | #*--------------------------------------------------------------------- |
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205 | * Model of a discreted steady-state, isotermic, and isobaric PFR |
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206 | *--------------------------------------------------------------------*# |
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207 | |
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208 | Model simple_pfr_d |
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209 | ATTRIBUTES |
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210 | Pallete = true; |
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211 | Brief = "Simple model of a steady-state PFR"; |
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212 | Icon = "icon/simple_pfr"; |
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213 | |
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214 | PARAMETERS |
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215 | N as Integer (Brief="Number of discrete points", Lower=2, Default=150); |
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216 | NT as Integer (Brief="Number of terms of reaction rate expression", Default=4); |
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217 | a(NT) as reaction_mol (Brief="Parameter of reaction rate expression",DisplayUnit='mol/l/s'); |
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218 | |
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219 | VARIABLES |
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220 | in Inlet as simple_stream(Brief="Inlet stream", Symbol="_{in}", PosX=0, PosY=0.5); |
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221 | out Outlet as simple_stream(Brief="Outlet stream", Symbol="_{out}", PosX=1, PosY=0.5); |
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222 | V(N) as volume (Brief="Volume", DisplayUnit='l', Upper=2e3); |
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223 | r(N) as reaction_mol (Brief="Rate of reaction", DisplayUnit='mol/l/s'); |
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224 | X(N) as fraction (Brief="Molar conversion"); |
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225 | dx as fraction (Brief="Conversion increment"); |
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226 | |
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227 | SET |
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228 | a = [0.00526629, 0.00133545, -0.0153342, 0.00921664]*'mol/l/s'; # Estimated |
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229 | |
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230 | EQUATIONS |
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231 | |
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232 | "Outlet molar conversion" |
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233 | Outlet.X = X(N); |
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234 | |
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235 | "Discrete interval" |
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236 | dx = (Outlet.X - Inlet.X)/(N-1); |
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237 | |
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238 | "Initial reactor volume" |
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239 | V(1) = 0.0*'l'; |
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240 | |
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241 | for i in [2:N] do |
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242 | "Molar balance" |
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243 | V(i) - V(i-1) = -0.5*Inlet.F*dx*(1/r(i-1) + 1/r(i)); # second order |
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244 | # V(i) - V(i-1) = Inlet.F*dx/(-r(i)); # first order |
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245 | "Discrete molar conversion" |
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246 | X(i-1) = X(i) - dx; |
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247 | end |
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248 | |
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249 | "Molar flow" |
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250 | Outlet.F = Inlet.F; |
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251 | |
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252 | for i in [1:N] do |
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253 | "Rate of reaction" |
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254 | (-r(i)) = sum(a*X(i)^[0:(NT-1)]); |
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255 | end |
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256 | end |
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257 | |
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258 | |
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259 | #*--------------------------------------------------------------------- |
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260 | * Example 2-2: Scale-up an isotermic CSTR in gaseous phase |
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261 | *--------------------------------------------------------------------*# |
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262 | |
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263 | FlowSheet cstr_sample |
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264 | PARAMETERS |
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265 | R as Real (Brief="Universal gas constant", Unit='atm*l/mol/K', Default=0.082); |
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266 | T as temperature (Brief="Temperatura in the reactor"); |
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267 | P as pressure (Brief="Pressure in the reactor"); |
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268 | zin as fraction (Brief="Inlet molar fraction"); |
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269 | v0 as flow_vol (Brief="Volumetric flow"); |
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270 | |
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271 | VARIABLES |
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272 | Vt as volume (Brief="Total reactor volume", DisplayUnit='l'); |
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273 | |
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274 | DEVICES |
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275 | Inlet as simple_stream; |
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276 | R1 as simple_cstr; |
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277 | |
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278 | CONNECTIONS |
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279 | Inlet to R1.Inlet; |
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280 | |
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281 | EQUATIONS |
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282 | "Inlet molar flow" |
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283 | Inlet.F = (zin*P/(R*T))*v0; |
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284 | |
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285 | "Total reactor volume" |
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286 | Vt = R1.V; |
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287 | |
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288 | SET |
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289 | v0 = 6.0*'l/s'; |
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290 | T = 422.2*'K'; |
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291 | P = 10*'atm'; |
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292 | zin = 0.5; |
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293 | |
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294 | SPECIFY |
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295 | Inlet.X = 0.0; |
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296 | R1.Outlet.X = 0.8; |
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297 | |
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298 | OPTIONS |
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299 | Dynamic = false; |
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300 | end |
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301 | |
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302 | |
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303 | #*--------------------------------------------------------------------- |
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304 | * Example 2-3: Scale-up an isotermic PFR in gaseous phase |
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305 | *--------------------------------------------------------------------*# |
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306 | |
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307 | FlowSheet pfr_sample |
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308 | DEVICES |
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309 | Inlet as simple_stream; |
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310 | R1 as simple_pfr; |
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311 | |
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312 | CONNECTIONS |
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313 | Inlet to R1.Inlet; |
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314 | |
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315 | SPECIFY |
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316 | Inlet.F = 0.866541*'mol/s'; |
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317 | Inlet.X = 0.0; |
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318 | |
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319 | OPTIONS |
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320 | TimeStep = 0.008; |
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321 | TimeEnd = 0.8; |
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322 | end |
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323 | |
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324 | |
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325 | #*--------------------------------------------------------------------- |
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326 | * Example 2-3: (discreted) |
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327 | *--------------------------------------------------------------------*# |
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328 | |
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329 | FlowSheet pfr_d_sample |
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330 | VARIABLES |
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331 | Vt as volume (Brief="Total reactor volume", DisplayUnit='l'); |
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332 | |
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333 | DEVICES |
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334 | Inlet as simple_stream; |
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335 | R1 as simple_pfr_d; |
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336 | |
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337 | CONNECTIONS |
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338 | Inlet to R1.Inlet; |
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339 | |
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340 | EQUATIONS |
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341 | "Total reactor volume" |
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342 | Vt = R1.V(R1.N); |
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343 | |
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344 | SET |
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345 | R1.N = 150; |
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346 | |
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347 | SPECIFY |
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348 | Inlet.F = 0.866541*'mol/s'; |
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349 | Inlet.X = 0.0; |
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350 | |
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351 | R1.Outlet.X = 0.8; |
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352 | |
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353 | OPTIONS |
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354 | Dynamic = false; |
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355 | end |
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356 | |
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357 | |
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358 | #*--------------------------------------------------------------------- |
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359 | * Example 2-4: Comparing volumes between one CSTR and one PFR |
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360 | *--------------------------------------------------------------------*# |
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361 | |
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362 | FlowSheet comparative |
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363 | VARIABLES |
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364 | V_cstr as volume (Brief="CSTR volume", DisplayUnit='l'); |
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365 | V_pfr as volume (Brief="PFR volume", DisplayUnit='l'); |
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366 | |
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367 | DEVICES |
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368 | Inlet as simple_stream; |
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369 | CSTR as simple_cstr; |
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370 | PFR as simple_pfr_d; |
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371 | |
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372 | CONNECTIONS |
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373 | Inlet to CSTR.Inlet; |
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374 | Inlet to PFR.Inlet; |
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375 | |
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376 | EQUATIONS |
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377 | "CSTR volume" |
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378 | V_cstr = CSTR.V; |
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379 | |
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380 | "PFR volume" |
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381 | V_pfr = PFR.V(PFR.N); |
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382 | |
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383 | SET |
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384 | PFR.N = 100; |
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385 | |
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386 | SPECIFY |
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387 | Inlet.F = 5.0*'mol/s'; |
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388 | Inlet.X = 0.0; |
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389 | |
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390 | CSTR.Outlet.X = 0.6; |
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391 | PFR.Outlet.X = 0.6; |
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392 | |
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393 | OPTIONS |
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394 | Dynamic = false; |
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395 | end |
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396 | |
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397 | |
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398 | #*--------------------------------------------------------------------- |
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399 | * Example 2-5: two CSTRs in serie |
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400 | *--------------------------------------------------------------------*# |
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401 | |
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402 | FlowSheet cstr_cstr |
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403 | VARIABLES |
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404 | V1 as volume (Brief="1st reactor volume", DisplayUnit='l'); |
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405 | V2 as volume (Brief="2nd reactor volume", DisplayUnit='l'); |
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406 | Vt as volume (Brief="Total reactor volumes", DisplayUnit='l'); |
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407 | |
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408 | DEVICES |
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409 | Inlet as simple_stream; |
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410 | R1 as simple_cstr; |
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411 | R2 as simple_cstr; |
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412 | |
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413 | CONNECTIONS |
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414 | Inlet to R1.Inlet; |
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415 | R1.Outlet to R2.Inlet; |
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416 | |
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417 | EQUATIONS |
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418 | "1st volume reactor" |
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419 | V1 = R1.V; |
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420 | "1st volume reactor" |
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421 | V2 = R2.V; |
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422 | "Total volume of reactors" |
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423 | Vt = V1 + V2; |
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424 | |
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425 | SPECIFY |
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426 | Inlet.F = 0.866541*'mol/s'; |
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427 | Inlet.X = 0.0; |
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428 | |
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429 | R1.Outlet.X = 0.4; |
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430 | R2.Outlet.X = 0.8; |
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431 | |
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432 | OPTIONS |
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433 | Dynamic = false; |
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434 | end |
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435 | |
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436 | |
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437 | #*--------------------------------------------------------------------- |
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438 | * Example 2-6: two PFRs in series (discreted) |
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439 | *--------------------------------------------------------------------*# |
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440 | |
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441 | FlowSheet pfr_pfr |
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442 | VARIABLES |
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443 | V1 as volume (Brief="1st reactor volume", DisplayUnit='l'); |
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444 | V2 as volume (Brief="2nd reactor volume", DisplayUnit='l'); |
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445 | Vt as volume (Brief="Total reactor volumes", DisplayUnit='l'); |
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446 | |
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447 | DEVICES |
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448 | Inlet as simple_stream; |
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449 | R1 as simple_pfr_d; |
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450 | R2 as simple_pfr_d; |
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451 | |
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452 | CONNECTIONS |
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453 | Inlet to R1.Inlet; |
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454 | R1.Outlet to R2.Inlet; |
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455 | |
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456 | EQUATIONS |
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457 | "1st reactor volume" |
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458 | V1 = R1.V(R1.N); |
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459 | "1st reactor volume" |
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460 | V2 = R2.V(R2.N); |
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461 | "Total reactor volumes" |
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462 | Vt = V1 + V2; |
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463 | |
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464 | SPECIFY |
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465 | Inlet.F = 0.866541*'mol/s'; |
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466 | Inlet.X = 0.0; |
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467 | |
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468 | R1.Outlet.X = 0.4; |
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469 | R2.Outlet.X = 0.8; |
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470 | |
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471 | OPTIONS |
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472 | Dynamic = false; |
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473 | end |
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474 | |
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475 | |
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476 | #*--------------------------------------------------------------------- |
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477 | * Example 2-7a: one PFR and one CSTR in series |
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478 | *--------------------------------------------------------------------*# |
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479 | |
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480 | FlowSheet pfr_cstr |
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481 | VARIABLES |
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482 | V1 as volume (Brief="1st reactor volume", DisplayUnit='l'); |
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483 | V2 as volume (Brief="2nd reactor volume", DisplayUnit='l'); |
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484 | Vt as volume (Brief="Total reactor volumes", DisplayUnit='l'); |
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485 | |
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486 | DEVICES |
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487 | Inlet as simple_stream; |
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488 | R1 as simple_pfr_d; |
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489 | R2 as simple_cstr; |
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490 | |
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491 | CONNECTIONS |
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492 | Inlet to R1.Inlet; |
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493 | R1.Outlet to R2.Inlet; |
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494 | |
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495 | EQUATIONS |
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496 | "1st reactor volume" |
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497 | V1 = R1.V(R1.N); |
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498 | "1st reactor volume" |
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499 | V2 = R2.V; |
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500 | "Total reactor volumes" |
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501 | Vt = V1 + V2; |
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502 | |
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503 | SET |
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504 | R1.N = 100; |
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505 | |
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506 | SPECIFY |
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507 | Inlet.F = 0.866541*'mol/s'; |
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508 | Inlet.X = 0.0; |
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509 | |
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510 | R1.Outlet.X = 0.5; |
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511 | R2.Outlet.X = 0.8; |
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512 | |
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513 | OPTIONS |
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514 | Dynamic = false; |
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515 | end |
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516 | |
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517 | |
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518 | #*--------------------------------------------------------------------- |
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519 | * Example 2-7b: one CSTR and one PFR in series |
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520 | *--------------------------------------------------------------------*# |
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521 | |
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522 | FlowSheet cstr_pfr |
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523 | VARIABLES |
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524 | V1 as volume (Brief="1st reactor volume", DisplayUnit='l'); |
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525 | V2 as volume (Brief="2nd reactor volume", DisplayUnit='l'); |
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526 | Vt as volume (Brief="Total reactor volumes", DisplayUnit='l'); |
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527 | |
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528 | DEVICES |
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529 | Inlet as simple_stream; |
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530 | R1 as simple_cstr; |
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531 | R2 as simple_pfr_d; |
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532 | |
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533 | CONNECTIONS |
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534 | Inlet to R1.Inlet; |
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535 | R1.Outlet to R2.Inlet; |
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536 | |
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537 | EQUATIONS |
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538 | "1st reactor volume" |
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539 | V1 = R1.V; |
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540 | "1st reactor volume" |
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541 | V2 = R2.V(R2.N); |
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542 | "Total reactor volumes" |
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543 | Vt = V1 + V2; |
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544 | |
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545 | SET |
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546 | R2.N = 100; |
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547 | |
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548 | SPECIFY |
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549 | Inlet.F = 0.866541*'mol/s'; |
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550 | Inlet.X = 0.0; |
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551 | |
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552 | R1.Outlet.X = 0.5; |
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553 | R2.Outlet.X = 0.8; |
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554 | |
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555 | OPTIONS |
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556 | Dynamic = false; |
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557 | end |
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