[82] | 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 | * Production of acetic anhydride |
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| 17 | *---------------------------------------------------------------------- |
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| 18 | * Solved problem from Fogler (1999) |
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| 19 | * Problem number: 8-7 |
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| 20 | * Page: 421 (Brazilian version, 2002) |
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| 21 | *---------------------------------------------------------------------- |
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| 22 | * |
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| 23 | * Description: |
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| 24 | * The acetic anhydride is produced for thermal craking of the |
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| 25 | * acetone in a PFR: |
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| 26 | * CH3COCH3 -> CH2CO + CH4 |
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| 27 | * This sample calculates the molar conversion and temperature |
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| 28 | * as function of the length in the tubular reactor. In the case I |
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| 29 | * the operation is adiabatic and in the case II the reactor is |
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| 30 | * jacketed. |
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| 31 | * |
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| 32 | * Assumptions |
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| 33 | * * first-order reaction with respect to acetone |
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| 34 | * * steady-state |
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| 35 | * * gaseous phase |
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| 36 | * |
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| 37 | * Specify: |
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| 38 | * * the inlet stream |
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| 39 | * * the kinetic parameters |
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| 40 | * * the parameters of components |
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| 41 | * |
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| 42 | *---------------------------------------------------------------------- |
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| 43 | * Author: Christiano D. W. Guerra and Rodolfo Rodrigues |
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| 44 | * $Id: acetic_anhydride.mso 82 2006-12-08 20:11:44Z paula $ |
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| 45 | *--------------------------------------------------------------------*# |
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| 46 | |
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| 47 | using "types"; |
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| 48 | |
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| 49 | |
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| 50 | #*--------------------------------------------------------------------- |
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| 51 | * Model of the thermal craking of acetone |
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| 52 | *--------------------------------------------------------------------*# |
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| 53 | |
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| 54 | Model thermal_cracking |
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| 55 | PARAMETERS |
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| 56 | NComp as Integer (Brief="Number of components", Lower=1); |
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| 57 | stoic(NComp)as Real (Brief="Stoichiometric number"); |
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| 58 | Pa0 as pressure (Brief="Input pressure of A"); |
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| 59 | Tr as temperature (Brief="Reference temperature"); |
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| 60 | T0 as temperature (Brief="Inlet temperature"); |
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| 61 | Ta as temperature (Brief="Internal temperature"); |
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| 62 | Hr(NComp) as enth_mol (Brief="Enthalpy of component"); |
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| 63 | R as Real (Brief="Universal gas constant", Unit="kPa*m^3/kmol/K", Default=8.314); |
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| 64 | U as Real (Brief="Heat transfer coefficient", Unit="J/m^2/K/s"); |
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| 65 | a as Real (Brief="Heat transfer area per volume of tube", Unit="1/m"); |
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| 66 | alpha(NComp)as cp_mol (Brief="Alpha term of Cp expression"); |
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| 67 | beta(NComp) as Real (Brief="Beta term of Cp expression", Unit="J/mol/K^2"); |
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| 68 | gamma(NComp)as Real (Brief="Gamma term of Cp expression", Unit="J/mol/K^3"); |
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| 69 | |
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| 70 | VARIABLES |
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| 71 | Ca as conc_mol (Brief="Molar concentration of A", Unit="kmol/m^3"); |
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| 72 | Ca0 as conc_mol (Brief="Inlet molar concentration of A", Unit="mol/m^3"); |
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| 73 | Fa0 as flow_mol (Brief="Inlet molar flow of A"); |
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| 74 | v0 as flow_vol (Brief="Volumetric flow", Unit="m^3/s"); |
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| 75 | r as reaction_mol (Brief="Rate of reaction", Unit="kmol/m^3/s"); |
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| 76 | k as Real (Brief="Specific rate of reaction", Unit="1/s"); |
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| 77 | T as temperature (Brief="Temperature of reactor", Unit="K"); |
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| 78 | X as fraction (Brief="Molar conversion", Lower=0); |
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| 79 | V as volume (Brief="Volume", Unit="m^3"); |
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| 80 | eps as Real (Brief="Parameter epsilon"); |
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| 81 | Cp(NComp) as cp_mol (Brief="Molar heat capacity", Unit="J/mol/K"); |
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| 82 | DHr as enth_mol (Brief="Enthalpy of reaction", Unit="kJ/mol"); |
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| 83 | |
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| 84 | EQUATIONS |
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| 85 | "Change time in V" |
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| 86 | V = time*"m^3/s"; |
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| 87 | |
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| 88 | "Molar balance" |
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| 89 | diff(X) = (-r)/Fa0*"m^3/s"; |
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| 90 | |
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| 91 | "Rate of reaction" |
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| 92 | r = -k*Ca; |
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| 93 | |
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| 94 | "Specific rate of reaction" |
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| 95 | k = exp(34.34)*exp(-34222*"K"/T)*"1/s"; |
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| 96 | |
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| 97 | "Concentration of component A" |
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| 98 | Ca = Ca0*(1 - X)/(1 + eps*X)*T0/T; |
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| 99 | |
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| 100 | "Parameter epsilon" |
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| 101 | eps = sum(stoic); # yAo = 1 |
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| 102 | |
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| 103 | "Inlet molar concentration of A" |
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| 104 | Ca0 = Pa0/(R*T0); |
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| 105 | |
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| 106 | "Volumetric flow" |
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| 107 | Fa0 = Ca0*v0; |
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| 108 | |
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| 109 | "Energy balance" |
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| 110 | diff(T)*(Fa0*(Cp(1) + X*sumt(stoic*Cp))) = (U*a*(Ta - T) + (-r)*(-DHr))*"m^3/s"; |
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| 111 | |
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| 112 | "Enthalpy of reaction" |
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| 113 | DHr = sumt(stoic*Hr) + sumt(stoic*alpha)*(T - Tr) + sumt(stoic*beta)/2*(T^2 - Tr^2) |
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| 114 | + sumt(stoic*gamma)/3*(T^3 - Tr^3); |
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| 115 | |
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| 116 | "Molar heat capacity" |
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| 117 | Cp = alpha + beta*T + gamma*T^2; |
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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 | * Case I: In an adiabatic PFR |
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| 123 | *--------------------------------------------------------------------*# |
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| 124 | |
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| 125 | FlowSheet adiabatic_reactor |
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| 126 | DEVICES |
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| 127 | R as thermal_cracking; |
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| 128 | |
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| 129 | SET |
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| 130 | R.NComp = 3; # A: acetone, B: ketene and C: methane |
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| 131 | R.stoic = [-1.0, 1.0, 1.0]; # A -> B + C |
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| 132 | |
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| 133 | R.Pa0 = 162*"kPa"; |
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| 134 | |
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| 135 | R.alpha = [26.63, 20.04, 13.39]*"J/mol/K"; |
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| 136 | R.beta = [0.183, 0.0945, 0.077]*"J/mol/K^2"; |
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| 137 | R.gamma = [-45.86e-6, -30.95e-6, -18.71e-6]*"J/mol/K^3"; |
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| 138 | |
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| 139 | R.Hr = [-216.67, -61.09, -74.81]*"kJ/mol"; |
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| 140 | R.Tr = 298*"K"; |
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| 141 | R.T0 = 1035*"K"; |
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| 142 | R.Ta = 1150*"K"; |
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| 143 | R.U = 0.0*"J/m^2/K/s"; |
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| 144 | R.a = 150*"1/m"; |
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| 145 | |
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| 146 | SPECIFY |
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| 147 | "Inlet molar flow" |
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| 148 | R.Fa0 = (8000/58)*"kmol/h"; |
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| 149 | |
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| 150 | INITIAL |
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| 151 | "Molar conversion" |
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| 152 | R.X = 0.0; |
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| 153 | "Temperature" |
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| 154 | R.T = 1035*"K"; |
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| 155 | |
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| 156 | OPTIONS |
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| 157 | time = [0:0.05:5]; |
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| 158 | end |
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| 159 | |
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| 160 | |
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| 161 | #*--------------------------------------------------------------------- |
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| 162 | * Case II: In an jacketed PFR |
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| 163 | *--------------------------------------------------------------------*# |
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| 164 | |
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| 165 | FlowSheet jacketed_reactor |
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| 166 | DEVICES |
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| 167 | R as thermal_cracking; |
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| 168 | |
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| 169 | SET |
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| 170 | R.NComp = 3; # A: acetone, B: ketene and C: methane |
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| 171 | R.stoic = [-1.0, 1.0, 1.0]; # A -> B + C |
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| 172 | |
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| 173 | R.Pa0 = 162*"kPa"; |
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| 174 | |
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| 175 | R.alpha = [26.63, 20.04, 13.39]*"J/mol/K"; |
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| 176 | R.beta = [0.183, 0.0945, 0.077]*"J/mol/K^2"; |
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| 177 | R.gamma = [-45.86e-6, -30.95e-6, -18.71e-6]*"J/mol/K^3"; |
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| 178 | |
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| 179 | R.Hr = [-216.67, -61.09, -74.81]*"kJ/mol"; |
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| 180 | R.Tr = 298*"K"; |
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| 181 | R.T0 = 1035*"K"; |
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| 182 | R.Ta = 1150*"K"; |
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| 183 | R.U = 110*"J/m^2/K/s"; |
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| 184 | R.a = 150*"1/m"; |
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| 185 | |
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| 186 | SPECIFY |
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| 187 | "Inlet molar flow" |
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| 188 | R.Fa0 = (18.8*2e-3)*"mol/s"; |
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| 189 | |
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| 190 | INITIAL |
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| 191 | "Molar conversion" |
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| 192 | R.X = 0.0; |
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| 193 | "Temperature" |
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| 194 | R.T = 1035*"K"; |
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| 195 | |
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| 196 | OPTIONS |
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| 197 | time = [0:1e-5:1e-3]; |
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| 198 | end |
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