[403] | 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 | * Model of a Gibbs reactor |
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| 17 | *---------------------------------------------------------------------- |
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| 18 | * |
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[421] | 19 | * Description: |
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[414] | 20 | * Thermodynamic equilibrium modeling of a reactor using Gibbs |
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[421] | 21 | * free energy minimization approach. |
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| 22 | * |
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| 23 | * Assumptions: |
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| 24 | * * single- and two-phases involved |
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| 25 | * * thermodynamic equilibrium |
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| 26 | * * steady-state |
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| 27 | * |
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| 28 | * Specify: |
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[414] | 29 | * * inlet stream |
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[421] | 30 | * * number of elements related to components |
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| 31 | * * matrix of elements by components |
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[414] | 32 | * * equilibrium temperature |
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[403] | 33 | * |
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| 34 | *---------------------------------------------------------------------- |
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| 35 | * Author: Rodolfo Rodrigues |
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| 36 | * $Id$ |
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| 37 | *--------------------------------------------------------------------*# |
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| 38 | |
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| 39 | using "tank_basic"; |
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| 40 | |
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| 41 | |
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| 42 | #*--------------------------------------------------------------------- |
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| 43 | * only vapour phase |
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| 44 | *--------------------------------------------------------------------*# |
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| 45 | Model gibbs_vap as tank_vap |
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| 46 | ATTRIBUTES |
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[414] | 47 | Pallete = true; |
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| 48 | Icon = "icon/cstr"; |
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| 49 | Brief = "Model of a generic vapour-phase Gibbs CSTR"; |
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| 50 | Info = " |
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[421] | 51 | == Assumptions == |
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| 52 | * thermodynamic equilibrium |
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| 53 | * steady-state |
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| 54 | |
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| 55 | == Specify == |
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| 56 | * inlet stream |
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| 57 | * number of elements related to components |
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| 58 | * matrix of elements by components |
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| 59 | * equilibrium temperature |
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[403] | 60 | "; |
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| 61 | |
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| 62 | PARAMETERS |
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| 63 | outer NElem as Integer (Brief="Number of elements", Default=1); |
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| 64 | Rg as Real (Brief="Universal gas constant", Unit='J/mol/K', Default=8.314); |
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| 65 | na(NElem,NComp) as Real (Brief="Number of elements per component"); |
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| 66 | fs(NComp) as pressure (Brief="Fugacity in standard state", Default=1, DisplayUnit='atm'); |
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[414] | 67 | To as temperature (Brief="Reference temperature", Default=298.15); |
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[403] | 68 | |
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| 69 | VARIABLES |
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[421] | 70 | out Outlet as vapour_stream(Brief="Outlet stream", PosX=1, PosY=1, Symbol="_{out}"); |
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[403] | 71 | |
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[414] | 72 | G(NComp) as energy_mol (Brief="Gibbs free-energy change of formation"); |
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[421] | 73 | lambda(NElem) as energy_mol (Brief="Lagrangian multiplier", Symbol="\lambda"); |
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[426] | 74 | activ(NComp) as Real (Brief="Activity", Symbol="\hat{a}", Lower=0); |
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[414] | 75 | |
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[403] | 76 | rate(NComp) as reaction_mol (Brief="Overall component rate of reaction"); |
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[421] | 77 | conv(NComp) as Real (Brief="Fractional conversion of component", Symbol="X", Default=0); |
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[403] | 78 | Fi(NComp) as flow_mol (Brief="Component molar flow rate"); |
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| 79 | |
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| 80 | EQUATIONS |
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| 81 | "Outlet stream" |
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[426] | 82 | Outlet.F*Outlet.z = Outletm.F*Outletm.z + rate*Tank.V; |
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[403] | 83 | |
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| 84 | "Mechanical equilibrium" |
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| 85 | Outlet.P = Outletm.P; |
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| 86 | |
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| 87 | "Steady-state" |
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| 88 | Outlet.F = sum(Fi); |
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| 89 | |
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| 90 | "Component molar flow rate" |
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| 91 | Fi = Outlet.F*Outlet.z; |
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| 92 | |
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| 93 | "Energy balance" |
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| 94 | Outlet.F*Outlet.h = Outletm.F*Outletm.h; |
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| 95 | |
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| 96 | "Element balance" |
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| 97 | sumt(Fi*na) = sumt(Outletm.F*Outletm.z*na); |
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| 98 | |
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[414] | 99 | "Gibbs free-energy of formation" |
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| 100 | G = PP.IdealGasGibbsOfFormation(Outlet.T); |
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[403] | 101 | |
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[414] | 102 | # "Gibbs free-energy of formation without Cp correction" |
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[421] | 103 | # G = PP.IdealGasGibbsOfFormationAt25C()*Outlet.T/To |
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| 104 | # + PP.IdealGasEnthalpyOfFormationAt25C()*(1 - Outlet.T/To); |
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[403] | 105 | |
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| 106 | for i in [1:NComp] |
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| 107 | "Lagrangian multiplier" |
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[414] | 108 | G(i) + sumt(lambda*na(:,i)) = -Rg*Outlet.T*ln(activ(i)); |
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[403] | 109 | |
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| 110 | if (Outletm.z(i) > 0) then |
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| 111 | "Molar conversion" |
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| 112 | Fi(i) = Outletm.F*Outletm.z(i)*(1 - conv(i)); |
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| 113 | else if (Outlet.z(i) > 0) then |
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| 114 | "Molar conversion" |
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| 115 | conv(i) = 1; # ? |
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| 116 | else |
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| 117 | "Molar conversion" |
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| 118 | conv(i) = 0; # ? |
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| 119 | end |
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| 120 | end |
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| 121 | end |
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| 122 | |
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| 123 | "Activity" |
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[421] | 124 | activ = PP.VapourFugacityCoefficient(Outlet.T,Outlet.P,Outlet.z) |
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| 125 | *Outlet.P*Outlet.z/fs; |
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[403] | 126 | end |
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[414] | 127 | |
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| 128 | |
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| 129 | #*--------------------------------------------------------------------- |
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| 130 | * only liquid phase |
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| 131 | *--------------------------------------------------------------------*# |
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| 132 | Model gibbs_liq as tank_liq |
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| 133 | ATTRIBUTES |
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| 134 | Pallete = true; |
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| 135 | Icon = "icon/cstr"; |
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| 136 | Brief = "Model of a generic liquid-phase Gibbs CSTR"; |
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| 137 | Info = " |
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[421] | 138 | == Assumptions == |
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| 139 | * thermodynamic equilibrium |
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| 140 | * steady-state |
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| 141 | |
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| 142 | == Specify == |
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| 143 | * inlet stream |
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| 144 | * number of elements related to components |
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| 145 | * matrix of elements by components |
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| 146 | * equilibrium temperature |
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[414] | 147 | "; |
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| 148 | |
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| 149 | PARAMETERS |
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| 150 | outer NElem as Integer (Brief="Number of elements", Default=1); |
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| 151 | Rg as Real (Brief="Universal gas constant", Unit='J/mol/K', Default=8.314); |
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| 152 | na(NElem,NComp) as Real (Brief="Number of elements per component"); |
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| 153 | Ps as pressure (Brief="Pressure of standard state", Default=1, DisplayUnit='atm'); |
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| 154 | To as temperature (Brief="Reference temperature", Default=298.15); |
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| 155 | |
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| 156 | VARIABLES |
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[421] | 157 | out Outlet as liquid_stream(Brief="Outlet stream", PosX=1, PosY=1, Symbol="_{out}"); |
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[414] | 158 | |
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| 159 | G(NComp) as energy_mol (Brief="Gibbs free-energy change of formation"); |
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[421] | 160 | lambda(NElem) as energy_mol (Brief="Lagrangian multiplier", Symbol="\lambda"); |
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| 161 | activ(NComp) as Real (Brief="Activity", Symbol="\hat{a}", Lower=0); |
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| 162 | |
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[414] | 163 | rate(NComp) as reaction_mol (Brief="Overall component rate of reaction"); |
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[421] | 164 | conv(NComp) as Real (Brief="Fractional conversion of component", Symbol="X", Default=0); |
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[414] | 165 | Fi(NComp) as flow_mol (Brief="Component molar flow rate"); |
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| 166 | |
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| 167 | EQUATIONS |
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| 168 | "Outlet stream" |
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[426] | 169 | Outlet.F*Outlet.z = Outletm.F*Outletm.z + rate*Tank.V; |
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[414] | 170 | |
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| 171 | "Mechanical equilibrium" |
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| 172 | Outlet.P = Outletm.P; |
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| 173 | |
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| 174 | "Steady-state" |
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| 175 | Outlet.F = sum(Fi); |
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| 176 | |
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| 177 | "Component molar flow rate" |
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| 178 | Fi = Outlet.F*Outlet.z; |
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| 179 | |
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| 180 | "Energy balance" |
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| 181 | Outlet.F*Outlet.h = Outletm.F*Outletm.h; |
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| 182 | |
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| 183 | "Element balance" |
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| 184 | sumt(Fi*na) = sumt(Outletm.F*Outletm.z*na); |
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| 185 | |
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| 186 | "Gibbs free-energy of formation" |
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| 187 | G = PP.IdealGasGibbsOfFormation(Outlet.T); |
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| 188 | |
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| 189 | # "Gibbs free-energy of formation without Cp correction" |
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[421] | 190 | # G = PP.IdealGasGibbsOfFormationAt25C()*Outlet.T/To |
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| 191 | # + PP.IdealGasEnthalpyOfFormationAt25C()*(1 - Outlet.T/To); |
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[414] | 192 | |
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| 193 | for i in [1:NComp] |
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| 194 | "Lagrangian multiplier" |
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| 195 | G(i) + sumt(lambda*na(:,i)) = -Rg*Outlet.T*ln(activ(i)); |
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| 196 | |
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| 197 | if (Outletm.z(i) > 0) then |
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| 198 | "Molar conversion" |
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| 199 | Fi(i) = Outletm.F*Outletm.z(i)*(1 - conv(i)); |
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| 200 | else if (Outlet.z(i) > 0) then |
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| 201 | "Molar conversion" |
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| 202 | conv(i) = 1; # ? |
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| 203 | else |
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| 204 | "Molar conversion" |
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| 205 | conv(i) = 0; # ? |
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| 206 | end |
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| 207 | end |
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| 208 | end |
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| 209 | |
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| 210 | "Activity" |
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[421] | 211 | activ = PP.LiquidFugacityCoefficient(Outlet.T,Outlet.P,Outlet.z)*Outlet.z |
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| 212 | *exp(PP.LiquidVolume(Outlet.T,Outlet.P,Outlet.z)*(Outlet.P - Ps)/Rg/Outlet.T); |
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[414] | 213 | end |
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