source: trunk/eml/stage_separators/tray.mso @ 419

#*-------------------------------------------------------------------
* 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 398 2007-10-26 14:44:56Z paula $
*--------------------------------------------------------------------*#

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;
        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      InletL as stream (Brief="Inlet liquid stream", PosX=0.5195, PosY=0, Symbol="_{inL}");
in      InletV as stream (Brief="Inlet vapour stream", PosX=0.4994, PosY=1, Symbol="_{inV}");
out     OutletL as liquid_stream (Brief="Outlet liquid stream", PosX=0.8277, PosY=1, Symbol="_{outL}");
out     OutletV 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;
        Emv as Real (Brief = "Murphree efficiency");
        
        EQUATIONS
        "Component Molar Balance"
        diff(M)=Inlet.F*Inlet.z + InletL.F*InletL.z + InletV.F*InletV.z
                - OutletL.F*OutletL.z - OutletV.F*OutletV.z;
        
        "Energy Balance"
        diff(E) = ( Inlet.F*Inlet.h + InletL.F*InletL.h + InletV.F*InletV.h
                - OutletL.F*OutletL.h - OutletV.F*OutletV.h + Q );
        
        "Molar Holdup"
        M = ML*OutletL.z + MV*OutletV.z;
        
        "Energy Holdup"
        E = ML*OutletL.h + MV*OutletV.h - OutletL.P*V;
        
        "Mol fraction normalisation"
        sum(OutletL.z)= 1.0;
        sum(OutletL.z)= sum(OutletV.z);
        
        "Liquid Volume"
        vL = PP.LiquidVolume(OutletL.T, OutletL.P, OutletL.z);
        "Vapour Volume"
        vV = PP.VapourVolume(OutletV.T, OutletV.P, OutletV.z);
        
        "Chemical Equilibrium"
        PP.LiquidFugacityCoefficient(OutletL.T, OutletL.P, OutletL.z)*OutletL.z = 
                PP.VapourFugacityCoefficient(OutletV.T, OutletV.P, yideal)*yideal;

        "Murphree Efficiency"
        OutletV.z = Emv * (yideal - InletV.z) + InletV.z;
        
        "Thermal Equilibrium"
        OutletV.T = OutletL.T;
        
        "Mechanical Equilibrium"
        OutletV.P = OutletL.P;
        
        "Geometry Constraint"
        V = ML* vL + MV*vV;
        
        "Level of clear liquid over the weir"
        Level = ML*vL/Ap;
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 (OutletV.F)
        
== Initial ==
* the plate temperature (OutletL.T)
* the liquid height (Level) OR the liquid flow OutletL.F
* (NoComps - 1) OutletL 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(OutletL.T, OutletL.P, OutletL.z);
        "Vapour Density"
        rhoV = PP.VapourDensity(InletV.T, InletV.P, InletV.z);

        switch LiquidFlow
                case "on":
                "Francis Equation"
#               OutletL.F*vL = 1.84*'m^0.5/s'*lw*((Level-(beta*hw))/(beta))^1.5;
                OutletL.F*vL = 1.84*'1/s'*lw*((Level-(beta*hw))/(beta))^2;
                when Level < (beta * hw) switchto "off";
                
                case "off":
                "Low level"
                OutletL.F = 0 * 'mol/h';
                when Level > (beta * hw) + 1e-6*'m' switchto "on";
        end

        switch VapourFlow
                case "on":
                InletV.F*vV = sqrt((InletV.P - OutletV.P)/(rhoV*alfa))*Ah;
                when InletV.F < 1e-6 * 'kmol/h' switchto "off";
                
                case "off":
                InletV.F = 0 * 'mol/s';
                when InletV.P > OutletV.P + Level*g*rhoL + 1e-1 * 'atm' switchto "on";
        end

end

#*-------------------------------------------------------------------
* Model of a tray with reaction
*-------------------------------------------------------------------*#
Model trayReact
        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 (OutletV.F);
* the reaction related variables.
        
== Initial ==
* the plate temperature (OutletL.T)
* the liquid height (Level) OR the liquid flow OutletL.F
* (NoComps - 1) OutletL compositions
";

        PARAMETERS
        outer PP as Plugin(Type="PP");
        outer NComp as Integer;
        V as volume(Brief="Total Volume of the tray");
        Q as power (Brief="Rate of heat supply"); 
        Ap as area (Brief="Plate area = Atray - Adowncomer");
        
        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");

        stoic(NComp) as Real(Brief="Stoichiometric matrix");
        Hr as energy_mol;
        Pstartup as pressure;
        
        VapourFlow as Switcher(Valid = ["on", "off"], Default = "off");
        LiquidFlow as Switcher(Valid = ["on", "off"], Default = "off");
        
        VARIABLES
in      Inlet as stream (Brief="Feed stream", PosX=0, PosY=0.4932, Symbol="_{in}");
in      InletL as stream (Brief="Inlet liquid stream", PosX=0.5195, PosY=0, Symbol="_{inL}");
in      InletV as stream (Brief="Inlet vapour stream", PosX=0.4994, PosY=1, Symbol="_{inV}");
out     OutletL as liquid_stream (Brief="Outlet liquid stream", PosX=0.8277, PosY=1, Symbol="_{outL}");
out     OutletV as vapour_stream (Brief="Outlet vapour stream", PosX=0.8043, PosY=0, Symbol="_{outV}");

        yideal(NComp) as fraction;
        Emv as Real (Brief = "Murphree efficiency");

        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); #, Unit = "mol/l");
        
        EQUATIONS
        "Molar Concentration"
        OutletL.z = vL * C;
        
        "Reaction"
        r3 = exp(-7150*'K'/OutletL.T)*(4.85e4*C(1)*C(2) - 1.23e4*C(3)*C(4))*'l/mol/s';
        
        "Component Molar Balance"
        diff(M)=Inlet.F*Inlet.z + InletL.F*InletL.z + InletV.F*InletV.z
                - OutletL.F*OutletL.z - OutletV.F*OutletV.z + stoic*r3*ML*vL;
        
        "Energy Balance"
        diff(E) = ( Inlet.F*Inlet.h + InletL.F*InletL.h + InletV.F*InletV.h
                - OutletL.F*OutletL.h - OutletV.F*OutletV.h + Q ) + Hr * r3 * vL*ML;
        
        "Molar Holdup"
        M = ML*OutletL.z + MV*OutletV.z;
        
        "Energy Holdup"
        E = ML*OutletL.h + MV*OutletV.h - OutletL.P*V;
        
        "Mol fraction normalisation"
        sum(OutletL.z)= 1.0;
        
        "Liquid Volume"
        vL = PP.LiquidVolume(OutletL.T, OutletL.P, OutletL.z);
        "Vapour Volume"
        vV = PP.VapourVolume(OutletV.T, OutletV.P, OutletV.z);

        "Thermal Equilibrium"
        OutletV.T = OutletL.T;
        
        "Mechanical Equilibrium"
        OutletV.P = OutletL.P;
        
        "Level of clear liquid over the weir"
        Level = ML*vL/Ap;

        Vol = ML*vL;
        
        "Liquid Density"
        rhoL = PP.LiquidDensity(OutletL.T, OutletL.P, OutletL.z);
        "Vapour Density"
        rhoV = PP.VapourDensity(InletV.T, InletV.P, InletV.z);

        switch LiquidFlow
                case "on":
                "Francis Equation"
                OutletL.F*vL = 1.84*'1/s'*lw*((Level-(beta*hw)+1e-6*'m')/(beta))^2;
                when Level < (beta * hw) switchto "off";
                
                case "off":
                "Low level"
                OutletL.F = 0 * 'mol/h';
                when Level > (beta * hw) + 1e-6*'m' switchto "on";
        end

        switch VapourFlow
                case "on":
                #InletV.P = OutletV.P + Level*g*rhoL + rhoV*alfa*(InletV.F*vV/Ah)^2;
                InletV.F*vV = sqrt((InletV.P - OutletV.P - Level*g*rhoL + 1e-8 * 'atm')/(rhoV*alfa))*Ah;
                when InletV.P < OutletV.P + Level*g*rhoL switchto "off";
                
                case "off":
                InletV.F = 0 * 'mol/s';
                when InletV.P > OutletV.P + Level*g*rhoL + 3e-2 * 'atm' switchto "on";
                #when InletV.P > OutletV.P + Level*beta*g*rhoL + 1e-2 * 'atm' switchto "on";
        end

        "Chemical Equilibrium"
        PP.LiquidFugacityCoefficient(OutletL.T, OutletL.P, OutletL.z)*OutletL.z = 
                PP.VapourFugacityCoefficient(OutletV.T, OutletV.P, yideal)*yideal;
        
        OutletV.z = Emv * (yideal - InletV.z) + InletV.z;
        
        sum(OutletL.z)= sum(OutletV.z);
        
        "Geometry Constraint"
        V = ML* vL + MV*vV;
end