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 178 2007-03-05 13:41:51Z bicca $ |
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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 | * Model of a stream |
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57 | *--------------------------------------------------------------------*# |
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58 | |
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59 | Model stream |
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60 | |
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61 | PARAMETERS |
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62 | NComp as Integer (Brief="Number of components", Default=1); |
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63 | |
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64 | VARIABLES |
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65 | F(NComp) as flow_mol (Brief="Molar flow", Unit='mol/s'); |
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66 | X(NComp) as fraction (Brief="Molar conversion"); |
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67 | |
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68 | end |
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69 | |
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70 | #*--------------------------------------------------------------------- |
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71 | * Model of a steady-state, isotermic, and isobaric CSTR |
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72 | *--------------------------------------------------------------------*# |
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73 | |
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74 | Model cstr |
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75 | |
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76 | VARIABLES |
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77 | |
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78 | in Inlet as stream (Brief="Inlet stream"); |
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79 | out Outlet as stream (Brief="Outlet stream"); |
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80 | |
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81 | r as reaction_mol (Brief="Rate of reaction", Unit='mol/l/s'); |
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82 | V as volume (Brief="Volume", Unit='l', Upper=2e3); |
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83 | |
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84 | EQUATIONS |
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85 | |
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86 | "Component molar balance" |
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87 | Inlet.F - Outlet.F = (-r)*V; |
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88 | |
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89 | "Outlet molar flow" |
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90 | Outlet.F = Inlet.F*(1 - Outlet.X); |
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91 | |
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92 | end |
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93 | |
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94 | |
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95 | #*--------------------------------------------------------------------- |
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96 | * Model of a steady-state, isotermic, and isobaric PFR |
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97 | *--------------------------------------------------------------------*# |
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98 | |
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99 | Model pfr |
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100 | |
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101 | VARIABLES |
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102 | in Inlet as stream (Brief="Inlet stream"); |
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103 | out Outlet as stream (Brief="Outlet stream"); |
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104 | |
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105 | V as volume (Brief="Volume", Unit='l', Upper=2e3); |
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106 | r as reaction_mol (Brief="Rate of reaction", Unit='mol/l/s'); |
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107 | |
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108 | EQUATIONS |
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109 | |
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110 | "Molar balance" |
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111 | diff(V) = Inlet.F/(-r)*'1/s'; |
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112 | |
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113 | "Change time in X" |
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114 | Outlet.X = time*'1/s'; |
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115 | |
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116 | "Molar flow" |
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117 | Outlet.F = Inlet.F*(1 - Outlet.X); |
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118 | end |
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119 | |
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120 | |
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121 | #*--------------------------------------------------------------------- |
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122 | * Model of a discreted steady-state, isotermic, and isobaric PFR |
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123 | *--------------------------------------------------------------------*# |
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124 | |
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125 | Model pfr_d |
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126 | PARAMETERS |
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127 | N as Integer (Brief="Number of discrete points", Default=200); |
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128 | |
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129 | VARIABLES |
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130 | in Inlet as stream; # Inlet stream |
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131 | out Outlet as stream; # Outlet stream |
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132 | V(N) as volume (Brief="Volume", Unit='l', Upper=2e3); |
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133 | X(N) as fraction (Brief="Molar conversion"); |
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134 | dx as fraction (Brief="Conversion increment"); |
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135 | r(N) as reaction_mol (Brief="Rate of reaction", Unit='mol/l/s'); |
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136 | F(N) as flow_mol (Brief="Molar flow", Unit='mol/s'); |
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137 | |
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138 | EQUATIONS |
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139 | "Discrete interval" |
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140 | dx = X(N)/N; |
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141 | |
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142 | for i in [2:N] |
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143 | "Molar balance" |
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144 | V(i) - V(i-1) = Inlet.F*dx/(-r(i)); |
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145 | "Discrete molar conversion" |
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146 | X(i-1) = X(i) - dx; |
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147 | end |
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148 | |
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149 | "Molar flow" |
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150 | F = Inlet.F*(1 - X); |
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151 | |
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152 | "Outlet molar flow" |
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153 | Outlet.F = F(N); |
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154 | |
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155 | "Outlet molar conversion" |
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156 | Outlet.X = X(N); |
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157 | end |
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158 | |
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159 | |
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160 | #*--------------------------------------------------------------------- |
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161 | * Example 2-2: Scale-up an isotermic CSTR in gaseous phase |
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162 | *--------------------------------------------------------------------*# |
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163 | |
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164 | FlowSheet cstr_sample |
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165 | PARAMETERS |
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166 | R as Real (Brief="Universal gas constant", Unit='atm*l/mol/K', Default=0.082); |
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167 | T as temperature (Brief="Temperatura in the reactor", Unit='K'); |
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168 | P as pressure (Brief="Pressure in the reactor", Unit='atm'); |
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169 | zin as fraction (Brief="Inlet molar fraction"); |
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170 | v0 as flow_vol (Brief="Volumetric flow"); |
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171 | |
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172 | VARIABLES |
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173 | Vt as volume (Brief="Total reactor volume", Unit='l'); |
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174 | |
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175 | DEVICES |
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176 | Inlet as stream; # Inlet stream |
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177 | R1 as cstr; |
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178 | |
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179 | CONNECTIONS |
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180 | Inlet to R1.Inlet; |
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181 | |
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182 | EQUATIONS |
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183 | "Inlet molar flow" |
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184 | Inlet.F = (zin*P/(R*T))*v0; |
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185 | |
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186 | "Rate of reaction" |
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187 | (-R1.r) = (0.0092*R1.Outlet.X^3 - 0.0153*R1.Outlet.X^2 + 0.0013*R1.Outlet.X + 0.0053)*'mol/l/s'; |
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188 | |
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189 | "Total reactor volume" |
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190 | Vt = R1.V; |
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191 | |
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192 | SPECIFY |
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193 | "Inlet conversion" |
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194 | Inlet.X = 0.0; |
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195 | "Required conversion" |
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196 | R1.Outlet.X = 0.8; |
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197 | |
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198 | SET |
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199 | v0 = 6.0*'l/s'; |
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200 | T = 422.2*'K'; |
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201 | P = 10*'atm'; |
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202 | zin = 0.5; |
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203 | |
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204 | OPTIONS |
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205 | Dynamic = false; |
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206 | end |
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207 | |
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208 | |
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209 | #*--------------------------------------------------------------------- |
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210 | * Example 2-3: Scale-up an isotermic PFR in gaseous phase |
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211 | *--------------------------------------------------------------------*# |
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212 | |
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213 | FlowSheet pfr_sample |
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214 | |
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215 | DEVICES |
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216 | Inlet as stream; |
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217 | R1 as pfr; |
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218 | |
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219 | CONNECTIONS |
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220 | Inlet to R1.Inlet; |
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221 | |
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222 | EQUATIONS |
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223 | |
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224 | "Rate of reaction" |
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225 | (-R1.r) = (0.0092*R1.Outlet.X^3 - 0.0153*R1.Outlet.X^2 + 0.0013*R1.Outlet.X + 0.0053)*'mol/l/s'; |
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226 | |
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227 | SPECIFY |
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228 | |
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229 | "Inlet molar flow" |
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230 | Inlet.F = 0.866541*'mol/s'; |
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231 | |
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232 | "Inlet conversion" |
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233 | Inlet.X = 0.0; |
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234 | |
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235 | INITIAL |
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236 | |
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237 | "Reactor volume" |
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238 | R1.V = 0.0*'l'; |
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239 | |
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240 | OPTIONS |
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241 | |
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242 | Dynamic = true; |
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243 | TimeStep = 0.004; |
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244 | TimeEnd = 0.8; |
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245 | TimeUnit = 's'; |
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246 | |
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247 | end |
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248 | |
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249 | |
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250 | #*--------------------------------------------------------------------- |
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251 | * Example 2-3: (discreted) |
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252 | *--------------------------------------------------------------------*# |
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253 | |
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254 | FlowSheet pfr_d_sample |
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255 | VARIABLES |
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256 | Vt as volume (Brief="Total reactor volume", Unit='l'); |
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257 | |
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258 | DEVICES |
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259 | Inlet as stream; # Inlet stream |
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260 | R1 as pfr_d; |
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261 | |
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262 | CONNECTIONS |
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263 | Inlet to R1.Inlet; |
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264 | |
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265 | EQUATIONS |
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266 | "Rate of reaction" |
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267 | (-R1.r) = (0.0092*R1.X^3 - 0.0153*R1.X^2 + 0.0013*R1.X + 0.0053)*'mol/l/s'; |
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268 | |
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269 | "Total reactor volume" |
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270 | Vt = R1.V(R1.N); |
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271 | |
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272 | # SET |
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273 | # R1.N = 100; |
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274 | |
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275 | SPECIFY |
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276 | "Inlet molar flow" |
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277 | Inlet.F = 0.866541*'mol/s'; |
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278 | "Inlet conversion" |
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279 | Inlet.X = 0.0; |
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280 | |
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281 | "Required conversion" |
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282 | R1.Outlet.X = 0.8; |
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283 | "Initial volume" |
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284 | R1.V(1) = 0.0*'l'; |
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285 | |
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286 | OPTIONS |
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287 | Dynamic = false; |
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288 | end |
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289 | |
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290 | |
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291 | #*--------------------------------------------------------------------- |
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292 | * Example 2-4: Comparing volumes between one CSTR and one PFR |
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293 | *--------------------------------------------------------------------*# |
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294 | |
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295 | FlowSheet comparative |
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296 | VARIABLES |
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297 | V_cstr as volume (Brief="CSTR volume"); |
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298 | V_pfr as volume (Brief="PFR volume", Unit='l'); |
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299 | |
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300 | DEVICES |
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301 | Inlet as stream; # Inlet stream |
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302 | CSTR as cstr; |
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303 | PFR as pfr_d; |
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304 | |
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305 | CONNECTIONS |
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306 | Inlet to CSTR.Inlet; |
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307 | Inlet to PFR.Inlet; |
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308 | |
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309 | EQUATIONS |
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310 | "Rate of reaction in CSTR" |
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311 | (-CSTR.r) = (0.0092*CSTR.Outlet.X^3 - 0.0153*CSTR.Outlet.X^2 + 0.0013*CSTR.Outlet.X + 0.0053)*'mol/l/s'; |
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312 | "Rate of reaction in PFR" |
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313 | (-PFR.r) = (0.0092*PFR.X^3 - 0.0153*PFR.X^2 + 0.0013*PFR.X + 0.0053)*'mol/l/s'; |
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314 | |
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315 | "CSTR volume" |
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316 | V_cstr = CSTR.V; |
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317 | "PFR volume" |
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318 | V_pfr = PFR.V(PFR.N); |
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319 | |
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320 | # SET |
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321 | # PFR.N = 100; |
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322 | |
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323 | SPECIFY |
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324 | "Inlet molar flow" |
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325 | Inlet.F = 5.0*'mol/s'; |
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326 | "Inlet conversion" |
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327 | Inlet.X = 0.0; |
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328 | |
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329 | "Required CSTR conversion" |
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330 | CSTR.Outlet.X = 0.6; |
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331 | "Required PFR conversion" |
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332 | PFR.Outlet.X = 0.6; |
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333 | |
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334 | "Initial volume in PFR" |
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335 | PFR.V(1) = 0.0*'l'; |
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336 | |
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337 | OPTIONS |
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338 | Dynamic = false; |
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339 | end |
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340 | |
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341 | |
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342 | #*--------------------------------------------------------------------- |
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343 | * Example 2-5: two CSTRs in serie |
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344 | *--------------------------------------------------------------------*# |
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345 | |
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346 | FlowSheet cstr_cstr |
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347 | VARIABLES |
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348 | V1 as volume (Brief="1st reactor volume", Unit='l'); |
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349 | V2 as volume (Brief="2nd reactor volume", Unit='l'); |
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350 | Vt as volume (Brief="Total reactor volumes", Unit='l'); |
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351 | |
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352 | DEVICES |
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353 | Inlet as stream; |
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354 | R1 as cstr; |
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355 | R2 as cstr; |
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356 | |
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357 | CONNECTIONS |
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358 | Inlet to R1.Inlet; |
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359 | R1.Outlet to R2.Inlet; |
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360 | |
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361 | EQUATIONS |
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362 | "Rate of reaction in 1st reactor" |
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363 | (-R1.r) = (0.0092*R1.Outlet.X^3 - 0.0153*R1.Outlet.X^2 + 0.0013*R1.Outlet.X + 0.0053)*'mol/l/s'; |
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364 | "Rate of reaction in 2nd reactor" |
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365 | (-R2.r) = (0.0092*R2.Outlet.X^3 - 0.0153*R2.Outlet.X^2 + 0.0013*R2.Outlet.X + 0.0053)*'mol/l/s'; |
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366 | |
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367 | "1st volume reactor" |
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368 | V1 = R1.V; |
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369 | "1st volume reactor" |
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370 | V2 = R2.V; |
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371 | "Total volume of reactors" |
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372 | Vt = V1 + V2; |
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373 | |
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374 | SPECIFY |
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375 | "Inlet molar flow" |
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376 | Inlet.F = 0.866541*'mol/s'; |
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377 | "Inlet conversion" |
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378 | Inlet.X = 0.0; |
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379 | |
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380 | "Required 1st reactor conversion" |
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381 | R1.Outlet.X = 0.4; |
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382 | "Required 2nd reactor conversion" |
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383 | R2.Outlet.X = 0.8; |
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384 | |
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385 | OPTIONS |
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386 | Dynamic=false; |
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387 | |
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388 | end |
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389 | |
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390 | |
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391 | #*--------------------------------------------------------------------- |
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392 | * Example 2-6: two PFRs in series (discreted) |
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393 | *--------------------------------------------------------------------*# |
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394 | |
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395 | FlowSheet pfr_pfr |
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396 | VARIABLES |
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397 | V1 as volume (Brief="1st reactor volume", Unit='l'); |
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398 | V2 as volume (Brief="2nd reactor volume", Unit='l'); |
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399 | Vt as volume (Brief="Total reactor volumes", Unit='l'); |
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400 | |
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401 | DEVICES |
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402 | Inlet as stream; |
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403 | R1 as pfr_d; |
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404 | R2 as pfr_d; |
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405 | |
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406 | CONNECTIONS |
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407 | Inlet to R1.Inlet; |
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408 | R1.Outlet to R2.Inlet; |
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409 | |
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410 | EQUATIONS |
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411 | "Rate of reaction in 1st reactor" |
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412 | (-R1.r) = (0.0092*R1.X^3 - 0.0153*R1.X^2 + 0.0013*R1.X + 0.0053)*'mol/l/s'; |
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413 | "Rate of reaction in 2nd reactor" |
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414 | (-R2.r) = (0.0092*R2.X^3 - 0.0153*R2.X^2 + 0.0013*R2.X + 0.0053)*'mol/l/s'; |
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415 | |
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416 | "1st reactor volume" |
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417 | V1 = R1.V(R1.N); |
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418 | "1st reactor volume" |
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419 | V2 = R2.V(R2.N); |
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420 | "Total reactor volumes" |
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421 | Vt = V1 + V2; |
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422 | |
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423 | SPECIFY |
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424 | "Inlet molar flow" |
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425 | Inlet.F = 0.866541*'mol/s'; |
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426 | "Inlet conversion" |
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427 | Inlet.X = 0.0; |
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428 | |
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429 | "Required 1st reactor conversion" |
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430 | R1.Outlet.X = 0.4; |
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431 | "Required 2nd reactor conversion" |
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432 | R2.Outlet.X = 0.8; |
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433 | |
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434 | "Initial 1st reactor volume" |
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435 | R1.V(1) = 0.0*'l'; |
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436 | "Initial 2nd reactor volume" |
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437 | R2.V(1) = 0.0*'l'; |
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438 | |
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439 | OPTIONS |
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440 | Dynamic = false; |
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441 | end |
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442 | |
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443 | |
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444 | #*--------------------------------------------------------------------- |
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445 | * Example 2-7a: one PFR and one CSTR in series |
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446 | *--------------------------------------------------------------------*# |
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447 | |
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448 | FlowSheet pfr_cstr |
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449 | VARIABLES |
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450 | V1 as volume (Brief="1st reactor volume", Unit='l'); |
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451 | V2 as volume (Brief="2nd reactor volume", Unit='l'); |
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452 | Vt as volume (Brief="Total reactor volumes", Unit='l'); |
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453 | |
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454 | DEVICES |
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455 | Inlet as stream; |
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456 | R1 as pfr_d; |
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457 | R2 as cstr; |
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458 | |
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459 | CONNECTIONS |
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460 | Inlet to R1.Inlet; |
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461 | R1.Outlet to R2.Inlet; |
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462 | |
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463 | EQUATIONS |
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464 | "Rate of reaction in 1st reactor" |
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465 | (-R1.r) = (0.0092*R1.X^3 - 0.0153*R1.X^2 + 0.0013*R1.X + 0.0053)*'mol/l/s'; |
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466 | "Rate of reaction in 2nd reactor" |
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467 | (-R2.r) = (0.0092*R2.Outlet.X^3 - 0.0153*R2.Outlet.X^2 + 0.0013*R2.Outlet.X + 0.0053)*'mol/l/s'; |
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468 | |
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469 | "1st reactor volume" |
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470 | V1 = R1.V(R1.N); |
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471 | "1st reactor volume" |
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472 | V2 = R2.V; |
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473 | "Total reactor volumes" |
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474 | Vt = V1 + V2; |
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475 | |
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476 | # SET |
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477 | # R1.N = 100; |
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478 | |
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479 | SPECIFY |
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480 | "Inlet molar flow" |
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481 | Inlet.F = 0.866541*'mol/s'; |
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482 | "Inlet conversion" |
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483 | Inlet.X = 0.0; |
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484 | |
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485 | "Required 1st reactor conversion" |
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486 | R1.Outlet.X = 0.5; |
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487 | "Required 2nd reactor conversion" |
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488 | R2.Outlet.X = 0.8; |
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489 | |
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490 | "Initial 1st reactor volume" |
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491 | R1.V(1) = 0.0*'l'; |
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492 | |
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493 | OPTIONS |
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494 | Dynamic= false; |
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495 | end |
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496 | |
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497 | |
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498 | #*--------------------------------------------------------------------- |
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499 | * Example 2-7b: one CSTR and one PFR in series |
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500 | *--------------------------------------------------------------------*# |
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501 | |
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502 | FlowSheet cstr_pfr |
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503 | VARIABLES |
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504 | V1 as volume (Brief="1st reactor volume", Unit='l'); |
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505 | V2 as volume (Brief="2nd reactor volume", Unit='l'); |
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506 | Vt as volume (Brief="Total reactor volumes", Unit='l'); |
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507 | |
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508 | DEVICES |
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509 | Inlet as stream; # Inlet stream |
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510 | R1 as cstr; |
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511 | R2 as pfr_d; |
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512 | |
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513 | CONNECTIONS |
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514 | Inlet to R1.Inlet; |
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515 | R1.Outlet to R2.Inlet; |
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516 | |
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517 | EQUATIONS |
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518 | "Rate of reaction in 1st reactor" |
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519 | (-R1.r) = (9.2*R1.Outlet.X^3 - 15.3*R1.Outlet.X^2 + 1.3*R1.Outlet.X + 5.3)*1e-3*'mol/l/s'; |
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520 | "Rate of reaction in 2nd reactor" |
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521 | (-R2.r) = (9.2*R2.X^3 - 15.3*R2.X^2 + 1.3*R2.X + 5.3)*1e-3*'mol/l/s'; |
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522 | |
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523 | "1st reactor volume" |
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524 | V1 = R1.V; |
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525 | "1st reactor volume" |
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526 | V2 = R2.V(R2.N); |
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527 | "Total reactor volumes" |
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528 | Vt = V1 + V2; |
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529 | |
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530 | # SET |
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531 | # R2.N = 100; |
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532 | |
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533 | SPECIFY |
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534 | "Inlet molar flow" |
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535 | Inlet.F = 0.866541*'mol/s'; |
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536 | "Inlet conversion" |
---|
537 | Inlet.X = 0.0; |
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538 | |
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539 | "Required 1st reactor conversion" |
---|
540 | R1.Outlet.X = 0.5; |
---|
541 | "Required 2nd reactor conversion" |
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542 | R2.Outlet.X = 0.8; |
---|
543 | |
---|
544 | "Initial 2nd reactor volume" |
---|
545 | R2.V(1) = 0.0*'l'; |
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546 | |
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547 | OPTIONS |
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548 | Dynamic = false; |
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549 | end |
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