source: mso/eml/stage_separators/tray.mso @ 4

#*-------------------------------------------------------------------
* Model of a tray
*-------------------------------------------------------------------- 
*       - Streams
*               * a liquid outlet stream
*               * a liquid inlet stream
*               * a vapour outlet stream
*               * a vapour inlet stream
*               * a feed stream
*
*       - Assumptions
*               * both phases (liquid and vapour) exists all the time
*               * thermodymanic equilibrium (Murphree plate efficiency=1)
*               * no entrainment of liquid or vapour phase
*               * no weeping
*               * the dymanics in the downcomer are neglected
* 
*       - Tray hydraulics: Roffel B.,Betlem B.H.L.,Ruijter J.A.F. (2000)
*                                               Computers and Chemical Engineering and
*                                          The gPROMS Model Library
*
*       Specify:
*               * the Feed stream
*               * the Liquid inlet stream
*               * the Vapour inlet stream excluding its flow
*               * the Vapour outlet flow (Outlet.F)
*
*       Initial:
*               * the plate temperature (OutletL.T)
*               * the liquid height (hl)
*               * (NoComps - 1) OutletL (or OutletV) compositions
*
*----------------------------------------------------------------------
* Author: Paula B. Staudt
* $Id: tray.mso 1 2006-06-20 17:33:53Z rafael $
*--------------------------------------------------------------------*#

using "streams";

Model trayBasic

        PARAMETERS
ext PP as CalcObject;
ext 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;
in      InletL as stream;
in      InletV as stream;
out     OutletL as stream_therm;
out     OutletV as stream_therm;

        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, OutletV.z)*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;
        
        "vaporization fraction "
        OutletV.v = 1.0;
        OutletL.v = 0.0;
        
        "Level of clear liquid over the weir"
        Level = ML*vL/Ap;
end

Model tray as trayBasic

        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");
        
        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);

        if (Level > (beta * hw)) then
                "Francis Equation"
                OutletL.F = 1.84*lw*((Level-(beta*hw))/(beta))^1.5/vL;
        else
                "Low level"
                OutletL.F = 0 * "mol/h";
        end

end