| 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 | * Multiple reactions in a CSTR |
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| 17 | *---------------------------------------------------------------------- |
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| 18 | * Solved problem from Fogler (1999) |
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| 19 | * Problem number: 8-12 |
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| 20 | * Page: 460 (Brazilian version) |
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| 21 | *---------------------------------------------------------------------- |
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| 22 | * |
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| 23 | * Description: |
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| 24 | * There are these reactions in series: |
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| 25 | * A -> B -> C |
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| 26 | * This sample calculates the outlet molar concentration as |
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| 27 | * function of the time in a CSTR. It is possible to identify the MSS |
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| 28 | * (Multiple Steady-State). |
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| 29 | * |
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| 30 | * Assumptions |
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| 31 | * * elementary reactions |
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| 32 | * * steady-state |
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| 33 | * * isobaric system |
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| 34 | * * gaseous phase |
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| 35 | * |
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| 36 | * Specify: |
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| 37 | * * the inlet stream |
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| 38 | * * the kinetic parameters |
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| 39 | * * the parameters of components |
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| 40 | * |
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| 41 | *---------------------------------------------------------------------- |
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| 42 | * Author: Christiano D. W. Guerra and Rodolfo Rodrigues |
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| 43 | * $Id: series_reactions.mso 574 2008-07-25 14:18:50Z rafael $ |
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| 44 | *--------------------------------------------------------------------*# |
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| 45 | |
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| 46 | using "types"; |
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| 47 | |
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| 48 | |
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| 49 | FlowSheet multiple_reactions |
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| 50 | PARAMETERS |
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| 51 | NComp as Integer (Brief="Number of components", Lower=1); |
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| 52 | NReac as Integer (Brief="Number of reactions"); |
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| 53 | stoic(NComp,NReac)as Real (Brief="Stoichiometric coefficients"); |
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| 54 | |
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| 55 | DH(NReac) as enth_mol (Brief="Enthapy of formation in reaction"); |
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| 56 | vo as flow_vol (Brief="Volumetric flow"); |
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| 57 | Cp as cp_mol (Brief="Heat capacity"); |
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| 58 | UA as Real (Brief="Heat change", Unit='J/min/K'); |
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| 59 | tau as time_min (Brief="Residence time"); |
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| 60 | |
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| 61 | Ta as temperature (Brief="Surface temperature"); |
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| 62 | Tr_ko(NReac)as temperature (Brief="Reference temperature for ko"); |
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| 63 | |
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| 64 | ko(NReac) as Real (Brief="Frequency factor", Unit='1/min'); |
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| 65 | E(NReac) as energy_mol (Brief="Activation energy"); |
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| 66 | R as Real (Brief="Universal gas constant", Unit='cal/mol/K', Default=1.987); |
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| 67 | |
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| 68 | VARIABLES |
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| 69 | C(NComp) as conc_mol (Brief="Molar concentration", Lower=-1e-6); |
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| 70 | Generated as energy_mol (Brief="Generated heat"); |
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| 71 | Removed as energy_mol (Brief="Removed heat"); |
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| 72 | T as temperature (Brief="Temperature of the Reactor"); |
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| 73 | kappa as Real (Brief="Kappa parameter"); |
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| 74 | Tc as temperature (Brief="Temperature of reactor surface"); |
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| 75 | k(NReac) as Real (Brief="Specific rate of reaction", Unit='1/min'); |
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| 76 | Co as conc_mol (Brief="Initial concentration of A"); |
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| 77 | To as temperature (Brief="Initial temperature"); |
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| 78 | |
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| 79 | EQUATIONS |
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| 80 | "Temperature profile" |
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| 81 | diff(T) = 2*'K/min'; |
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| 82 | |
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| 83 | "Parameter kappa" |
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| 84 | kappa = UA/(vo*Co)/Cp; |
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| 85 | |
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| 86 | "Specific rate of reaction" |
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| 87 | k = ko*exp(E/R*(1/Tr_ko - 1/T)); |
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| 88 | |
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| 89 | "Molar concentration of A" |
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| 90 | C(1) = Co/(1+tau*k(1)); |
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| 91 | |
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| 92 | "Generated term" |
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| 93 | Generated = (-DH(1))*k(1)*tau/(1 + k(1)*tau) + |
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| 94 | (-DH(2))*k(1)*k(2)*tau^2/(1 + tau*k(1))/(1 + tau*k(2)); |
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| 95 | |
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| 96 | "Temperature of reactor surface" |
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| 97 | Tc = (To + kappa * Ta)/(1 + kappa); |
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| 98 | |
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| 99 | "Molar concentration of B" |
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| 100 | C(2) = tau*k(1)*C(1)/(1 + tau*k(2)); |
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| 101 | |
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| 102 | "Molar concentration of C" |
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| 103 | Co = sum(C); |
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| 104 | |
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| 105 | "Removed term" |
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| 106 | Removed = Cp*(1 + kappa)*(T - Tc); |
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| 107 | |
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| 108 | SET |
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| 109 | NComp = 3; # A, B, and C |
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| 110 | NReac = 2; # A->B->C |
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| 111 | |
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| 112 | DH = [-5.50e4, -7.15e4]*'J/mol'; |
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| 113 | vo = 1000*'m^3/min'; |
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| 114 | |
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| 115 | ko = [ 3.30, 4.58]/'min'; |
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| 116 | E = [9.9e3, 2.7e4]*'cal/mol'; |
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| 117 | Tr_ko = [300, 500]*'K'; |
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| 118 | |
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| 119 | Cp = 200*'J/mol/K'; |
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| 120 | UA = 4e4*'J/min/K'; |
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| 121 | tau = 0.01*'min'; |
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| 122 | Ta = 330*'K'; |
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| 123 | |
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| 124 | SPECIFY |
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| 125 | To = 283*'K'; |
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| 126 | Co= 0.3*'mol/m^3'; |
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| 127 | |
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| 128 | INITIAL |
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| 129 | "Temperature" |
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| 130 | T = 283*'K'; |
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| 131 | |
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| 132 | OPTIONS |
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| 133 | TimeStep = 2; |
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| 134 | TimeEnd = 225; |
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| 135 | TimeUnit = 'min'; |
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| 136 | end |
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