#*------------------------------------------------------------------- * EMSO Model Library (EML) Copyright (C) 2004 - 2007 ALSOC. * * This LIBRARY is free software; you can distribute it and/or modify * it under the therms of the ALSOC FREE LICENSE as available at * http://www.enq.ufrgs.br/alsoc. * * EMSO Copyright (C) 2004 - 2007 ALSOC, original code * from http://www.rps.eng.br Copyright (C) 2002-2004. * All rights reserved. * * EMSO is distributed under the therms of the ALSOC LICENSE as * available at http://www.enq.ufrgs.br/alsoc. * *---------------------------------------------------------------------- * Author: Paula B. Staudt * $Id: tray.mso 522 2008-05-21 23:21:12Z arge $ *--------------------------------------------------------------------*# using "streams"; Model trayBasic ATTRIBUTES Pallete = false; Icon = "icon/Tray"; Brief = "Basic equations of a tray column model."; Info = "This model contains only the main equations of a column tray equilibrium model without the hidraulic equations. == Assumptions == * both phases (liquid and vapour) exists all the time; * thermodymanic equilibrium with Murphree plate efficiency; * no entrainment of liquid or vapour phase; * no weeping; * the dymanics in the downcomer are neglected. "; PARAMETERS outer PP as Plugin (Brief = "External Physical Properties", Type="PP"); outer NComp as Integer; VARIABLES Inlet as stream (Brief="Feed stream", Hidden=true, PosX=0, PosY=0.4932, Symbol="_{in}"); LiquidSideStream as liquid_stream (Brief="liquid Sidestream", Hidden=true, Symbol="_{outL}"); VapourSideStream as vapour_stream (Brief="vapour Sidestream", Hidden=true, Symbol="_{outV}"); in InletLiquid as stream (Brief="Inlet liquid stream", PosX=0.5195, PosY=0, Symbol="_{inL}"); in InletVapour as stream (Brief="Inlet vapour stream", PosX=0.4994, PosY=1, Symbol="_{inV}"); out OutletLiquid as liquid_stream (Brief="Outlet liquid stream", PosX=0.8277, PosY=1, Symbol="_{outL}"); out OutletVapour as vapour_stream (Brief="Outlet vapour stream", PosX=0.8043, PosY=0, Symbol="_{outV}"); M(NComp) as mol (Brief="Molar Holdup in the tray"); ML as mol (Brief="Molar liquid holdup"); MV as mol (Brief="Molar vapour holdup"); E as energy (Brief="Total Energy Holdup on tray"); vL as volume_mol (Brief="Liquid Molar Volume"); vV as volume_mol (Brief="Vapour Molar volume"); Level as length (Brief="Height of clear liquid on plate"); yideal(NComp) as fraction; EQUATIONS "Component Molar Balance" diff(M)=Inlet.F*Inlet.z + InletLiquid.F*InletLiquid.z + InletVapour.F*InletVapour.z- OutletLiquid.F*OutletLiquid.z - OutletVapour.F*OutletVapour.z- LiquidSideStream.F*LiquidSideStream.z-VapourSideStream.F*VapourSideStream.z; "Molar Holdup" M = ML*OutletLiquid.z + MV*OutletVapour.z; "Mol fraction normalisation" sum(OutletLiquid.z)= 1.0; sum(OutletLiquid.z)= sum(OutletVapour.z); "Liquid Volume" vL = PP.LiquidVolume(OutletLiquid.T, OutletLiquid.P, OutletLiquid.z); "Vapour Volume" vV = PP.VapourVolume(OutletVapour.T, OutletVapour.P, OutletVapour.z); "Chemical Equilibrium" PP.LiquidFugacityCoefficient(OutletLiquid.T, OutletLiquid.P, OutletLiquid.z)*OutletLiquid.z = PP.VapourFugacityCoefficient(OutletVapour.T, OutletVapour.P, yideal)*yideal; "Thermal Equilibrium" OutletVapour.T = OutletLiquid.T; "Mechanical Equilibrium" OutletVapour.P = OutletLiquid.P; "Thermal Equilibrium Vapour Side Stream" OutletVapour.T = VapourSideStream.T; "Thermal Equilibrium Liquid Side Stream" OutletLiquid.T = LiquidSideStream.T; "Mechanical Equilibrium Vapour Side Stream" OutletVapour.P= VapourSideStream.P; "Mechanical Equilibrium Liquid Side Stream" OutletLiquid.P = LiquidSideStream.P; "Composition Liquid Side Stream" OutletLiquid.z= LiquidSideStream.z; "Composition Vapour Side Stream" OutletVapour.z= VapourSideStream.z; end Model tray as trayBasic ATTRIBUTES Pallete = false; Icon = "icon/Tray"; Brief = "Complete model of a column tray."; Info = "== Specify == * the Feed stream * the Liquid inlet stream * the Vapour inlet stream * the Vapour outlet flow (OutletVapour.F) == Initial == * the plate temperature (OutletLiquid.T) * the liquid height (Level) OR the liquid flow OutletLiquid.F * (NoComps - 1) OutletLiquid compositions == Options == You can choose the equation for the liquid outlet flow and the vapour inlet flow calculation through the VapourFlowModel and LiquidFlowModel switchers. == References == * ELGUE, S.; PRAT, L.; CABASSUD, M.; LANN, J. L.; CéZERAC, J. Dynamic models for start-up operations of batch distillation columns with experimental validation. Computers and Chemical Engineering, v. 28, p. 2735-2747, 2004. * FEEHERY, W. F. Dynamic Optimization with Path Constraints. Tese (Doutorado) - Massachusetts Institute of Technology, June 1998. * KLINGBERG, A. Modeling and Optimization of Batch Distillation. Dissertação (Mestrado) - Department of Automatic Control, Lund Institute of Technology, Lund, Sweden, fev. 2000. * OLSEN, I.; ENDRESTOL, G. O.; SIRA, T. A rigorous and efficient distillation column model for engineering and training simulators. Computers and Chemical Engineering,v. 21, n. Suppl, p. S193-S198, 1997. * REEPMEYER, F.; REPKE, J.-U.; WOZNY, G. Analysis of the start-up process for reactive distillation. Chemical Engineering Technology, v. 26, p. 81-86, 2003. * ROFFEL, B.; BETLEM, B.; RUIJTER, J. de. First principles dynamic modeling and multivariable control of a cryogenic distillation column process. Computers and Chemical Engineering, v. 24, p. 111-123, 2000. * WANG, L.; LI, P.; WOZNY, G.; WANG, S. A start-up model for simulation of batch distillation starting from a cold state. Computers and Chemical Engineering, v. 27, p.1485-1497, 2003. "; VARIABLES rhoL as dens_mass; rhoV as dens_mass; EQUATIONS "Liquid Density" rhoL = PP.LiquidDensity(OutletLiquid.T, OutletLiquid.P, OutletLiquid.z); "Vapour Density" rhoV = PP.VapourDensity(InletVapour.T, InletVapour.P, InletVapour.z); end #*------------------------------------------------------------------- * Model of a tray with reaction *-------------------------------------------------------------------*# Model trayReac ATTRIBUTES Pallete = false; Icon = "icon/Tray"; Brief = "Model of a tray with reaction."; Info = "== Assumptions == * both phases (liquid and vapour) exists all the time; * thermodymanic equilibrium with Murphree plate efficiency; * no entrainment of liquid or vapour phase; * no weeping; * the dymanics in the downcomer are neglected. == Specify == * the Feed stream; * the Liquid inlet stream; * the Vapour inlet stream; * the Vapour outlet flow (OutletVapour.F); * the reaction related variables. == Initial == * the plate temperature (OutletLiquid.T) * the liquid height (Level) OR the liquid flow OutletLiquid.F * (NoComps - 1) OutletLiquid compositions "; PARAMETERS outer PP as Plugin(Type="PP"); outer NComp as Integer; VARIABLES Inlet as stream (Brief="Feed stream", PosX=0, PosY=0.4932, Symbol="_{in}"); LiquidSideStream as liquid_stream (Brief="liquid Sidestream", Hidden=true, Symbol="_{outL}"); VapourSideStream as vapour_stream (Brief="vapour Sidestream", Hidden=true, Symbol="_{outV}"); in InletLiquid as stream (Brief="Inlet liquid stream", PosX=0.5195, PosY=0, Symbol="_{inL}"); in InletVapour as stream (Brief="Inlet vapour stream", PosX=0.4994, PosY=1, Symbol="_{inV}"); out OutletLiquid as liquid_stream (Brief="Outlet liquid stream", PosX=0.8277, PosY=1, Symbol="_{outL}"); out OutletVapour as vapour_stream (Brief="Outlet vapour stream", PosX=0.8043, PosY=0, Symbol="_{outV}"); yideal(NComp) as fraction; M(NComp) as mol (Brief="Molar Holdup in the tray"); ML as mol (Brief="Molar liquid holdup"); MV as mol (Brief="Molar vapour holdup"); E as energy (Brief="Total Energy Holdup on tray"); vL as volume_mol (Brief="Liquid Molar Volume"); vV as volume_mol (Brief="Vapour Molar volume"); Level as length (Brief="Height of clear liquid on plate"); Vol as volume; rhoL as dens_mass; rhoV as dens_mass; r3 as reaction_mol (Brief = "Reaction resulting ethyl acetate", DisplayUnit = 'mol/l/s'); C(NComp) as conc_mol (Brief = "Molar concentration", Lower = -1); EQUATIONS "Molar Concentration" OutletLiquid.z = vL * C; "Reaction" r3 = exp(-7150*'K'/OutletLiquid.T)*(4.85e4*C(1)*C(2) - 1.23e4*C(3)*C(4))*'l/mol/s'; "Molar Holdup" M = ML*OutletLiquid.z + MV*OutletVapour.z; "Thermal Equilibrium Vapour Side Stream" OutletVapour.T = VapourSideStream.T; "Thermal Equilibrium Liquid Side Stream" OutletLiquid.T = LiquidSideStream.T; "Mechanical Equilibrium Vapour Side Stream" OutletVapour.P= VapourSideStream.P; "Mechanical Equilibrium Liquid Side Stream" OutletLiquid.P = LiquidSideStream.P; "Composition Liquid Side Stream" OutletLiquid.z= LiquidSideStream.z; "Composition Vapour Side Stream" OutletVapour.z= VapourSideStream.z; "Mol fraction normalisation" sum(OutletLiquid.z)= 1.0; "Liquid Volume" vL = PP.LiquidVolume(OutletLiquid.T, OutletLiquid.P, OutletLiquid.z); "Vapour Volume" vV = PP.VapourVolume(OutletVapour.T, OutletVapour.P, OutletVapour.z); "Thermal Equilibrium" OutletVapour.T = OutletLiquid.T; "Mechanical Equilibrium" OutletVapour.P = OutletLiquid.P; Vol = ML*vL; "Liquid Density" rhoL = PP.LiquidDensity(OutletLiquid.T, OutletLiquid.P, OutletLiquid.z); "Vapour Density" rhoV = PP.VapourDensity(InletVapour.T, InletVapour.P, InletVapour.z); "Chemical Equilibrium" PP.LiquidFugacityCoefficient(OutletLiquid.T, OutletLiquid.P, OutletLiquid.z)*OutletLiquid.z = PP.VapourFugacityCoefficient(OutletVapour.T, OutletVapour.P, yideal)*yideal; sum(OutletLiquid.z)= sum(OutletVapour.z); end #*------------------------------------- * Model of a packed column stage -------------------------------------*# Model packedStage ATTRIBUTES Pallete = false; Icon = "icon/PackedStage"; Brief = "Complete model of a packed column stage."; Info = "== Specify == * the Feed stream * the Liquid inlet stream * the Vapour inlet stream * the stage pressure drop (deltaP) == Initial == * the plate temperature (OutletLiquid.T) * the liquid molar holdup ML * (NoComps - 1) OutletLiquid compositions "; PARAMETERS outer PP as Plugin(Brief = "External Physical Properties", Type="PP"); outer NComp as Integer; PPwater as Plugin(Brief="Physical Properties",Type="PP",Components = [ "water" ], LiquidModel = "PR", VapourModel = "PR" ); Mw(NComp) as molweight (Brief = "Component Mol Weight"); VARIABLES Inlet as stream (Brief="Feed stream", PosX=0, PosY=0.4932, Symbol="_{in}"); in InletLiquid as stream (Brief="Inlet liquid stream", PosX=0.5195, PosY=0, Symbol="_{inL}"); in InletVapour as stream (Brief="Inlet vapour stream", PosX=0.4994, PosY=1, Symbol="_{inV}"); out OutletLiquid as liquid_stream (Brief="Outlet liquid stream", PosX=0.8277, PosY=1, Symbol="_{outL}"); out OutletVapour as vapour_stream (Brief="Outlet vapour stream", PosX=0.8043, PosY=0, Symbol="_{outV}"); M(NComp) as mol (Brief="Molar Holdup in the tray", Default=0.01, Lower=0, Upper=100); ML as mol (Brief="Molar liquid holdup", Default=0.01, Lower=0, Upper=100); MV as mol (Brief="Molar vapour holdup", Default=0.01, Lower=0, Upper=100); E as energy (Brief="Total Energy Holdup on tray", Default=-500); vL as volume_mol (Brief="Liquid Molar Volume"); vV as volume_mol (Brief="Vapour Molar volume"); miL as viscosity (Brief="Liquid dynamic viscosity", DisplayUnit='kg/m/s'); miV as viscosity (Brief="Vapor dynamic viscosity", DisplayUnit='kg/m/s'); rhoL as dens_mass; rhoV as dens_mass; deltaP as pressure; uL as velocity (Brief="volume flow rate of liquid, m^3/m^2/s", Lower=-10, Upper=100); uV as velocity (Brief="volume flow rate of vapor, m^3/m^2/s", Lower=-10, Upper=100); dp as length (Brief="Particle diameter", Default=1e-3, Lower=0, Upper=10); invK as positive (Brief="Wall factor", Default=1, Upper=10); Rev as Real (Brief="Reynolds number of the vapor stream", Default=4000); Al as area (Brief="Area occupied by the liquid", Default=0.001, Upper=1); hl as positive (Brief="Column holdup", Unit='m^3/m^3', Default=0.01,Upper=10); SET Mw = PP.MolecularWeight(); EQUATIONS "Component Molar Balance" diff(M)=Inlet.F*Inlet.z + InletLiquid.F*InletLiquid.z + InletVapour.F*InletVapour.z- OutletLiquid.F*OutletLiquid.z - OutletVapour.F*OutletVapour.z; "Molar Holdup" M = ML*OutletLiquid.z + MV*OutletVapour.z; "Mol fraction normalisation" sum(OutletLiquid.z)= 1.0; "Liquid Volume" vL = PP.LiquidVolume(OutletLiquid.T, OutletLiquid.P, OutletLiquid.z); "Vapour Volume" vV = PP.VapourVolume(OutletVapour.T, OutletVapour.P, OutletVapour.z); "Chemical Equilibrium" PP.LiquidFugacityCoefficient(OutletLiquid.T, OutletLiquid.P, OutletLiquid.z)*OutletLiquid.z = PP.VapourFugacityCoefficient(OutletVapour.T, OutletVapour.P, OutletVapour.z)*OutletVapour.z; "Thermal Equilibrium" OutletVapour.T = OutletLiquid.T; "Mechanical Equilibrium" OutletLiquid.P = OutletVapour.P; "Liquid Density" rhoL = PP.LiquidDensity(OutletLiquid.T, OutletLiquid.P, OutletLiquid.z); "Vapour Density" rhoV = PP.VapourDensity(InletVapour.T, InletVapour.P, InletVapour.z); "Liquid viscosity" miL = PP.LiquidViscosity(OutletLiquid.T, OutletLiquid.P, OutletLiquid.z); "Vapour viscosity" miV = PP.VapourViscosity(InletVapour.T, InletVapour.P, InletVapour.z); "Volume flow rate of liquid, m^3/m^2/s" uL * Al = OutletLiquid.F * vL; deltaP = InletVapour.P - OutletVapour.P; end #*------------------------------------- * Nonequilibrium Model -------------------------------------* Model interfaceTeste ATTRIBUTES Pallete = false; Icon = "icon/Tray"; Brief = "Descrition of variables of the equilibrium interface."; Info = "This model contains only the variables of the equilibrium interface."; PARAMETERS outer PP as Plugin(Brief = "External Physical Properties", Type="PP"); outer NComp as Integer; outer NC1 as Integer; VARIABLES NL(NComp) as flow_mol_delta (Brief = "Stream Molar Rate on Liquid Phase"); NV(NComp) as flow_mol_delta (Brief = "Stream Molar Rate on Vapour Phase"); T as temperature (Brief = "Stream Temperature"); P as pressure (Brief = "Stream Pressure"); x(NComp) as fraction (Brief = "Stream Molar Fraction on Liquid Phase"); y(NComp) as fraction (Brief = "Stream Molar Fraction on Vapour Phase"); a as area (Brief = "Interface Area"); htL as heat_trans_coeff (Brief = "Heat Transference Coefficient on Liquid Phase"); htV as heat_trans_coeff (Brief = "Heat Transference Coefficient on Vapour Phase"); E_liq as heat_rate (Brief = "Liquid Energy Rate at interface"); E_vap as heat_rate (Brief = "Vapour Energy Rate at interface"); hL as enth_mol (Brief = "Liquid Molar Enthalpy"); hV as enth_mol (Brief = "Vapour Molar Enthalpy"); kL(NC1,NC1) as velocity (Brief = "Mass Transfer Coefficients"); kV(NC1,NC1) as velocity (Brief = "Mass Transfer Coefficients"); EQUATIONS "Liquid Enthalpy" hL = PP.LiquidEnthalpy(T, P, x); "Vapour Enthalpy" hV = PP.VapourEnthalpy(T, P, y); end Model trayRateBasicTeste ATTRIBUTES Pallete = false; Icon = "icon/Tray"; Brief = "Basic equations of a tray rate column model."; Info = "This model contains only the main equations of a column tray nonequilibrium model without the hidraulic equations. == Assumptions == * both phases (liquid and vapour) exists all the time; * no entrainment of liquid or vapour phase; * no weeping; * the dymanics in the downcomer are neglected. "; PARAMETERS outer PP as Plugin(Brief = "External Physical Properties", Type="PP"); outer NComp as Integer; NC1 as Integer; V as volume(Brief="Total Volume of the tray"); Q as heat_rate (Brief="Rate of heat supply"); Ap as area (Brief="Plate area = Atray - Adowncomer"); VARIABLES in Inlet as stream (Brief="Feed stream", PosX=0, PosY=0.4932, Symbol="_{in}"); in InletFV as stream (Brief="Feed stream", PosX=0, PosY=0.4932, Symbol="_{in}"); in InletLiquid as stream (Brief="Inlet liquid stream", PosX=0.5195, PosY=0, Symbol="_{inL}"); in InletVapour as stream (Brief="Inlet vapour stream", PosX=0.4994, PosY=1, Symbol="_{inV}"); out OutletLiquid as liquid_stream (Brief="Outlet liquid stream", PosX=0.8277, PosY=1, Symbol="_{outL}"); out OutletVapour as vapour_stream (Brief="Outlet vapour stream", PosX=0.8043, PosY=0, Symbol="_{outV}"); M_liq(NComp) as mol (Brief="Liquid Molar Holdup in the tray"); M_vap(NComp) as mol (Brief="Vapour Molar Holdup in the tray"); ML as mol (Brief="Molar liquid holdup"); MV as mol (Brief="Molar vapour holdup"); E_liq as energy (Brief="Total Liquid Energy Holdup on tray"); E_vap as energy (Brief="Total Vapour Energy Holdup on tray"); vL as volume_mol (Brief="Liquid Molar Volume"); vV as volume_mol (Brief="Vapour Molar volume"); Level as length (Brief="Height of clear liquid on plate"); interf as interfaceTeste; SET NC1=NComp-1; EQUATIONS "Component Molar Balance" diff(M_liq)=Inlet.F*Inlet.z + InletLiquid.F*InletLiquid.z - OutletLiquid.F*OutletLiquid.z + interf.NL; diff(M_vap)=InletFV.F*InletFV.z + InletVapour.F*InletVapour.z - OutletVapour.F*OutletVapour.z - interf.NV; "Energy Balance" diff(E_liq) = Inlet.F*Inlet.h + InletLiquid.F*InletLiquid.h - OutletLiquid.F*OutletLiquid.h + Q + interf.E_liq; diff(E_vap) = InletFV.F*InletFV.h + InletVapour.F*InletVapour.h - OutletVapour.F*OutletVapour.h - interf.E_vap; "Molar Holdup" M_liq = ML*OutletLiquid.z; M_vap = MV*OutletVapour.z; "Energy Holdup" E_liq = ML*(OutletLiquid.h - OutletLiquid.P*vL); E_vap = MV*(OutletVapour.h - OutletVapour.P*vV); "Energy Rate through the interface" interf.E_liq = interf.htL*interf.a*(interf.T-OutletLiquid.T)+sum(interf.NL)*interf.hL; interf.E_vap = interf.htV*interf.a*(OutletVapour.T-interf.T)+sum(interf.NV)*interf.hV; "Mass Conservation" interf.NL = interf.NV; "Energy Conservation" interf.E_liq = interf.E_vap; "Mol fraction normalisation" sum(OutletLiquid.z)= 1.0; sum(OutletLiquid.z)= sum(OutletVapour.z); sum(interf.x)=1.0; sum(interf.x)=sum(interf.y); "Liquid Volume" vL = PP.LiquidVolume(OutletLiquid.T, OutletLiquid.P, OutletLiquid.z); "Vapour Volume" vV = PP.VapourVolume(OutletVapour.T, OutletVapour.P, OutletVapour.z); "Chemical Equilibrium" PP.LiquidFugacityCoefficient(interf.T, interf.P, interf.x)*interf.x = PP.VapourFugacityCoefficient(interf.T, interf.P, interf.y)*interf.y; "Geometry Constraint" V = ML*vL + MV*vV; "Level of clear liquid over the weir" Level = ML*vL/Ap; "Total Mass Transfer Rates" interf.NL(1:NC1)=interf.a*sumt(interf.kL*(interf.x(1:NC1)-OutletLiquid.z(1:NC1)))/vL+ OutletLiquid.z(1:NC1)*sum(interf.NL); # interf.NL(1:NC1)=0.01*'kmol/s'; interf.NV(1:NC1)=interf.a*sumt(interf.kV*(OutletVapour.z(1:NC1)-interf.y(1:NC1)))/vV+ OutletVapour.z(1:NC1)*sum(interf.NV); "Mechanical Equilibrium" OutletVapour.P = OutletLiquid.P; interf.P=OutletLiquid.P; end Model trayRateTeste as trayRateBasicTeste ATTRIBUTES Pallete = false; Icon = "icon/Tray"; Brief = "Complete rate model of a column tray."; Info = "== Specify == * the Feed stream * the Liquid inlet stream * the Vapour inlet stream * the Vapour outlet flow (OutletVapour.F) == Initial == * the plate temperature of both phases (OutletLiquid.T and OutletVapour.T) * the liquid height (Level) OR the liquid flow holdup (ML) * the vapor holdup (MV) * (NoComps - 1) OutletLiquid compositions "; PARAMETERS Ah as area (Brief="Total holes area"); lw as length (Brief="Weir length"); g as acceleration (Default=9.81); hw as length (Brief="Weir height"); beta as fraction (Brief="Aeration fraction"); alfa as fraction (Brief="Dry pressure drop coefficient"); VapourFlow as Switcher(Valid = ["on", "off"], Default = "on"); LiquidFlow as Switcher(Valid = ["on", "off"], Default = "on"); VARIABLES rhoL as dens_mass; rhoV as dens_mass; EQUATIONS "Liquid Density" rhoL = PP.LiquidDensity(OutletLiquid.T, OutletLiquid.P, OutletLiquid.z); "Vapour Density" rhoV = PP.VapourDensity(InletVapour.T, InletVapour.P, InletVapour.z); switch LiquidFlow case "on": "Francis Equation" # OutletLiquid.F*vL = 1.84*'m^0.5/s'*lw*((Level-(beta*hw))/(beta))^1.5; OutletLiquid.F*vL = 1.84*'1/s'*lw*((Level-(beta*hw))/(beta))^2; when Level < (beta * hw) switchto "off"; case "off": "Low level" OutletLiquid.F = 0 * 'mol/h'; when Level > (beta * hw) + 1e-6*'m' switchto "on"; end switch VapourFlow case "on": InletVapour.F*vV = sqrt((InletVapour.P - OutletVapour.P)/(rhoV*alfa))*Ah; when InletVapour.F < 1e-6 * 'kmol/h' switchto "off"; case "off": InletVapour.F = 0 * 'mol/s'; when InletVapour.P > OutletVapour.P + Level*g*rhoL + 1e-1 * 'atm' switchto "on"; end end *#