| 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 | * Author: Rafael de P. Soares and Paula B. Staudt |
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| 17 | * $Id: pfr.mso 745 2009-03-20 19:59:07Z bicca $ |
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| 18 | *--------------------------------------------------------------------*# |
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| 19 | |
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| 20 | using "streams"; |
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| 21 | |
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| 22 | Model pfr |
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| 23 | |
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| 24 | ATTRIBUTES |
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| 25 | Pallete = true; |
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| 26 | Brief = "Model of a Generic PFR with constant mass holdup"; |
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| 27 | Icon = "icon/pfr"; |
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| 28 | Info = |
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| 29 | "== Requires the information of == |
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| 30 | * Reaction values |
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| 31 | * Heat of reaction |
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| 32 | * Pressure profile |
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| 33 | "; |
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| 34 | |
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| 35 | PARAMETERS |
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| 36 | |
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| 37 | outer PP as Plugin (Brief = "External Physical Properties", Type="PP"); |
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| 38 | outer NComp as Integer (Brief="Number of components"); |
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| 39 | |
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| 40 | NReac as Integer (Brief="Number of reactions"); |
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| 41 | stoic(NComp, NReac) as Real (Brief = "Stoichiometric Matrix"); |
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| 42 | NDisc as Integer (Brief="Number of points of discretization", Default=10); |
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| 43 | Mw(NComp) as molweight (Brief="Component Mol Weight"); |
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| 44 | L as length (Brief="Reactor Length"); |
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| 45 | Across as area (Brief="Cross section area"); |
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| 46 | Dpipe as length (Brief="Reactor Inner Diameter"); |
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| 47 | pi as Real (Brief="pi number",Default=3.141592, Symbol = "\pi"); |
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| 48 | dx as length (Brief = "Incremental Length"); |
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| 49 | dv as volume (Brief = "Incremental volume"); |
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| 50 | Roughness as length (Brief="Reactor Tube Roughness", Default = 4.572E-5, Symbol = "\varepsilon"); |
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| 51 | |
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| 52 | SET |
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| 53 | |
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| 54 | Mw = PP.MolecularWeight(); |
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| 55 | Across = 0.25*pi*Dpipe^2; |
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| 56 | dx = L/NDisc; |
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| 57 | dv = Across*dx; |
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| 58 | |
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| 59 | VARIABLES |
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| 60 | |
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| 61 | in Inlet as stream (Brief = "Inlet Stream", PosX=0, PosY=0.5076, Symbol="_{in}"); |
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| 62 | out Outlet as stream (Brief = "Outlet Stream", PosX=1, PosY=0.5236, Symbol="_{out}"); |
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| 63 | |
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| 64 | str(NDisc+1) as streamPH; |
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| 65 | vel(NDisc+1) as velocity; |
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| 66 | vol(NDisc+1) as vol_mol; |
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| 67 | rho(NDisc+1) as dens_mass; |
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| 68 | rhom(NDisc+1) as dens_mol; |
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| 69 | dP(NDisc+1) as press_delta (Brief = "Friction Pressure Drop"); |
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| 70 | Lincr(NDisc+1) as length (Brief = "Length Points", Symbol = "L_{incr}"); |
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| 71 | |
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| 72 | q(NDisc) as heat_rate; |
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| 73 | C(NComp, NDisc+1) as conc_mol (Brief="Components concentration"); |
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| 74 | E(NDisc) as energy (Brief="Total Energy Holdup on element"); |
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| 75 | r(NReac, NDisc) as reaction_mol; |
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| 76 | Hr(NReac, NDisc) as heat_reaction; |
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| 77 | Re(NDisc+1) as Real (Brief = "Reynolds Number Profile",Lower = 1E-6); |
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| 78 | mu(NDisc+1) as viscosity (Brief = "Viscosity Profile" , Symbol = "\mu"); |
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| 79 | fns(NDisc+1) as fricfactor (Brief = "No Slip Friction Factor"); |
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| 80 | |
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| 81 | EQUATIONS |
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| 82 | |
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| 83 | "Inlet boundary" |
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| 84 | str(1).F = Inlet.F; |
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| 85 | str(1).T = Inlet.T; |
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| 86 | str(1).P = Inlet.P; |
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| 87 | str(1).z = Inlet.z; |
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| 88 | |
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| 89 | "Outlet boundary" |
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| 90 | Outlet.F = str(NDisc+1).F; |
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| 91 | Outlet.T = str(NDisc+1).T; |
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| 92 | Outlet.P = str(NDisc+1).P; |
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| 93 | Outlet.z = str(NDisc+1).z; |
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| 94 | Outlet.h = str(NDisc+1).h; |
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| 95 | Outlet.v = str(NDisc+1).v; |
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| 96 | |
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| 97 | "Reactor Initial Length" |
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| 98 | Lincr(1) = 0*'m'; |
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| 99 | |
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| 100 | C(:,1)*vol(1) = Inlet.z; |
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| 101 | |
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| 102 | for i in [1:NDisc] do |
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| 103 | |
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| 104 | for c in [1:NComp] do |
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| 105 | |
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| 106 | "Component Molar Balance" |
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| 107 | #diff(M(c,i)) = str(i).F*str(i).z(c) - str(i+1).F*str(i+1).z(c) + sum(stoic(c,:)*r(:, i)) * dv; |
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| 108 | diff(C(c,i+1)*dv) = (vel(i)*C(c,i) - vel(i+1)*C(c,i+1) )*Across + sum(stoic(c,:)*r(:, i))*dv; |
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| 109 | |
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| 110 | end |
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| 111 | |
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| 112 | "Constraint" |
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| 113 | sum(str(i+1).z ) = 1; |
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| 114 | # Mt(i) = sum(M(:,i)); |
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| 115 | |
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| 116 | "Molar concentration" |
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| 117 | #C(:,i) = rhom(i)*str(i).z; |
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| 118 | str(i+1).z = C(:,i+1) * vol(i+1); |
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| 119 | |
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| 120 | #"Molar fraction" |
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| 121 | #str(i+1).z * Mt(i) = M(:,i); |
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| 122 | |
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| 123 | #"Geometrical constraint" |
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| 124 | #Mt(i) = dv * rhom(i); |
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| 125 | |
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| 126 | "Energy Balance" |
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| 127 | diff(E(i)) = str(i).F*str(i).h - str(i+1).F*str(i+1).h + sum(Hr(:,i)*r(:,i)) * dv - q(i); |
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| 128 | |
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| 129 | "Energy Holdup" |
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| 130 | #E(i) = Mt(i)*str(i+1).h - str(i+1).P*dv; |
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| 131 | E(i) = dv/vol(i+1) * str(i+1).h - str(i+1).P*dv; |
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| 132 | |
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| 133 | "Outlet Pressure" |
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| 134 | str(i+1).P =str(1).P - dP(i+1); |
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| 135 | |
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| 136 | "Incremental Length" |
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| 137 | Lincr(i+1) = i*dx; |
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| 138 | |
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| 139 | end |
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| 140 | |
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| 141 | for i in [1:NDisc+1] do |
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| 142 | |
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| 143 | "Incremental Pressure Drop" |
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| 144 | dP(i) = 0.5*fns(i)*Lincr(i)*rho(i)*vel(i)*vel(i)/Dpipe; # simple equation for pressure drop (Darcy Equation) |
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| 145 | |
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| 146 | "Specific Volume" |
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| 147 | vol(i) = PP.VapourVolume(str(i).T, str(i).P, str(i).z); |
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| 148 | |
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| 149 | "Specific Mass" |
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| 150 | rho(i) = PP.VapourDensity(str(i).T, str(i).P, str(i).z); |
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| 151 | |
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| 152 | "Molar Density" |
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| 153 | rhom(i)* vol(i) = 1; |
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| 154 | |
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| 155 | "Viscosity" |
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| 156 | mu(i) = 0.027*'cP';#PP.VapourViscosity(str(i).T,str(i).P,str(i).z); # VRTherm mu=16 cP !!!!!! |
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| 157 | |
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| 158 | "Reynolds Number" |
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| 159 | Re(i)*mu(i) = rho(i)*vel(i)*Dpipe; |
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| 160 | |
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| 161 | "Velocity" |
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| 162 | str(i).F = vel(i)*Across*rhom(i); |
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| 163 | |
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| 164 | if Re(i) > 2300 |
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| 165 | |
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| 166 | then |
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| 167 | "Friction Factor for Pressure Drop - Turbulent Flow" |
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| 168 | #1/sqrt(fns(i))= -2*log(abs(Roughness/Dpipe/3.7+2.51/Re(i)/sqrt(fns(i)))); |
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| 169 | 1/sqrt(fns(i))= -2*log(Roughness/Dpipe/3.7+2.51/Re(i)/sqrt(fns(i))); |
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| 170 | |
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| 171 | else |
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| 172 | "Friction Factor for Pressure Drop - laminar Flow" |
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| 173 | fns(i)*Re(i) = 16; |
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| 174 | |
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| 175 | end |
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| 176 | |
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| 177 | end |
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| 178 | |
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| 179 | end |
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