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 | * 1. Thermodynamic properties from van der Waals equation |
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17 | *---------------------------------------------------------------------- |
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18 | * |
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19 | * Description: |
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20 | * This problem is part of a collection of 10 representative |
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21 | * problems in Chemical Engineering for solution by numerical methods |
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22 | * developed for Cutlip (1998). |
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23 | * |
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24 | * Subject: |
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25 | * * Introduction to Chemical Engineering |
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26 | * * Thermodynamics |
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27 | * |
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28 | * Concepts utilized: |
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29 | * Use of the van der Waals equation of state to calculate molar |
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30 | * volume and compressibility factor for a gas. |
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31 | * |
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32 | * Numerical method: |
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33 | * * Single nonlinear algebraic equation |
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34 | * |
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35 | * Reference: |
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36 | * * CUTLIP et al. A collection of 10 numerical problems in |
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37 | * chemical engineering solved by various mathematical software |
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38 | * packages. Comp. Appl. in Eng. Education. v. 6, 169-180, 1998. |
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39 | * * More informations and a detailed description of all problems |
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40 | * is available online in http://www.polymath-software.com/ASEE |
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41 | * |
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42 | *---------------------------------------------------------------------- |
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43 | * Author: Rodolfo Rodrigues |
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44 | * GIMSCOP/UFRGS - Group of Integration, Modeling, Simulation, |
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45 | * Control, and Optimization of Processes |
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46 | * $Id$ |
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47 | *--------------------------------------------------------------------*# |
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48 | using "types"; |
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49 | |
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50 | |
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51 | |
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52 | #*--------------------------------------------------------------------- |
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53 | * Equation of state |
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54 | *--------------------------------------------------------------------*# |
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55 | |
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56 | Model van_der_waals |
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57 | PARAMETERS |
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58 | outer Pc as pressure (Brief="Critical pressure"); |
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59 | outer Tc as temperature (Brief="Critical temperature"); |
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60 | R as Real (Brief="Gas constant", Default=0.08206, Unit='atm*l/mol/K'); |
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61 | |
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62 | |
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63 | VARIABLES |
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64 | P as pressure (Brief="Pressure"); |
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65 | V as volume_mol (Brief="Molar volume", DisplayUnit='l/mol'); |
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66 | T as temperature (Brief="Temperature"); |
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67 | |
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68 | a as Real (Brief="Parameter a of van der Waals equation", Unit='atm*(l/mol)^2'); |
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69 | b as volume_mol (Brief="Parameter b of van der Waals equation", DisplayUnit='l/mol'); |
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70 | |
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71 | |
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72 | EQUATIONS |
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73 | "Van der Waals equation" |
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74 | (P + a/V^2)*(V - b) = R*T; |
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75 | |
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76 | "Parameter a" |
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77 | a = (27/64)*(R^2*Tc^2)/Pc; |
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78 | |
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79 | "Parameter b" |
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80 | b = R*Tc/(8*Pc); |
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81 | end |
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82 | |
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83 | |
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84 | |
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85 | #*--------------------------------------------------------------------- |
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86 | * Thermodynamic properties calculation (question a) |
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87 | *--------------------------------------------------------------------*# |
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88 | |
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89 | FlowSheet properties |
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90 | PARAMETERS |
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91 | Pc as pressure; |
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92 | Tc as temperature; |
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93 | |
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94 | |
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95 | VARIABLES |
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96 | equation_of_state as van_der_waals; |
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97 | Pr as Real (Brief="Reduced pressure"); |
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98 | Z as Real (Brief="Compressibility factor"); |
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99 | |
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100 | |
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101 | EQUATIONS |
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102 | # Thermodynamic properties |
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103 | "Reduced pressure" |
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104 | Pr = equation_of_state.P/Pc; |
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105 | |
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106 | "Compressibility factor" |
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107 | Z = equation_of_state.P*equation_of_state.V/(equation_of_state.R*equation_of_state.T); |
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108 | |
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109 | |
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110 | SET |
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111 | Pc = 111.3*'atm'; # for ammonia |
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112 | Tc = 405.5*'K'; # for ammonia |
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113 | |
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114 | |
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115 | SPECIFY |
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116 | equation_of_state.P = 56*'atm'; |
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117 | equation_of_state.T = 450*'K'; |
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118 | |
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119 | |
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120 | OPTIONS |
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121 | Dynamic = false; |
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122 | end |
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123 | |
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124 | |
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125 | |
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126 | #*--------------------------------------------------------------------- |
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127 | * Variation of properties with Pr (question b and c) |
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128 | *--------------------------------------------------------------------*# |
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129 | |
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130 | FlowSheet variation_of_properties |
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131 | PARAMETERS |
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132 | Pc as pressure; |
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133 | Tc as temperature; |
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134 | |
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135 | |
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136 | VARIABLES |
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137 | equation_of_state as van_der_waals; |
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138 | Pr as Real (Brief="Reduced pressure"); |
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139 | Z as Real (Brief="Compressibility factor"); |
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140 | |
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141 | |
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142 | EQUATIONS |
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143 | "Change time in Pr" |
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144 | Pr = time/'s'; |
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145 | |
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146 | # Thermodynamic properties |
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147 | "Reduced pressure" |
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148 | Pr = equation_of_state.P/Pc; |
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149 | |
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150 | "Compressibility factor" |
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151 | Z = equation_of_state.P*equation_of_state.V/(equation_of_state.R*equation_of_state.T); |
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152 | |
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153 | |
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154 | SET |
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155 | Pc = 111.3*'atm'; # for ammonia |
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156 | Tc = 405.5*'K'; # for ammonia |
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157 | |
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158 | |
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159 | SPECIFY |
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160 | equation_of_state.T = 450*'K'; |
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161 | |
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162 | |
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163 | OPTIONS |
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164 | TimeStart = 1; |
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165 | TimeStep = 0.5; |
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166 | TimeEnd = 20; |
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167 | end |
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