#*-------------------------------------------------------------------
* 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 613 2008-09-01 22:45:47Z bicca $
*--------------------------------------------------------------------*#
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
== 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.
";
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");
w as Real (Brief="Feehery's correlation coefficient", Unit='1/m^4', Default=1);
btray as Real (Brief="Elgue's correlation coefficient", Unit='kg/m/mol^2', Default=1);
fw as Real (Brief = "Olsen's correlation coefficient", Default=1);
Np as Real (Brief = "Number of liquid passes in the tray", Default=1);
Mw(NComp) as molweight (Brief = "Component Mol Weight");
VapourFlow as Switcher(Valid = ["on", "off"], Default = "on");
LiquidFlow as Switcher(Valid = ["on", "off"], Default = "on");
VapourFlowModel as Switcher(Valid = ["Reepmeyer", "Feehery_Fv", "Roffel_Fv", "Klingberg", "Wang_Fv", "Elgue"], Default = "Reepmeyer");
LiquidFlowModel as Switcher(Valid = ["default", "Wang_Fl", "Olsen", "Feehery_Fl", "Roffel_Fl"], Default = "default");
SET
Mw = PP.MolecularWeight();
VARIABLES
rhoL as dens_mass;
rhoV as dens_mass;
btemp as Real (Brief="Temporary variable of Roffel's liquid flow equation");
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":
switch LiquidFlowModel
case "default":
"Francis Equation"
OutletL.F*vL = 1.84*'1/s'*lw*((Level-(beta*hw))/(beta))^2;
case "Wang_Fl":
OutletL.F*vL = 1.84*'m^0.5/s'*lw*((Level-(beta*hw))/(beta))^1.5;
case "Olsen":
OutletL.F / 'mol/s'= lw*Np*rhoL/sum(Mw*OutletV.z)/(0.665*fw)^1.5 * ((ML*sum(Mw*OutletL.z)/rhoL/Ap)-hw)^1.5 * 'm^0.5/mol';
case "Feehery_Fl":
OutletL.F = lw*rhoL/sum(Mw*OutletL.z) * ((Level-hw)/750/'mm')^1.5 * 'm^2/s';
case "Roffel_Fl":
OutletL.F = 2/3*sqrt(2*g)*rhoL/sum(Mw*OutletL.z)*lw*(2*btemp-1)*(ML*sum(Mw*OutletL.z)/(Ap*1.3)/rhoL/(2*btemp-1))^1.5;
end
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
btemp = 1 - 0.3593/'Pa^0.0888545'*abs(OutletV.F*sum(Mw*OutletV.z)/(Ap*1.3)/sqrt(rhoV))^0.177709; #/'(kg/m)^0.0888545/s^0.177709';
switch VapourFlow
case "on":
switch VapourFlowModel
case "Reepmeyer":
InletV.F*vV = sqrt((InletV.P - OutletV.P)/(rhoV*alfa))*Ah;
case "Feehery_Fv":
InletV.F = rhoV/Ap/w/sum(Mw*OutletV.z) * sqrt(((InletV.P - OutletV.P)-(rhoV*g*ML*vL/Ap))/rhoV);
case "Roffel_Fv":
InletV.F^1.08 * 0.0013 * 'kg/m/mol^1.08/s^0.92*1e5' = (InletV.P - OutletV.P)*1e5 - (beta*sum(M*Mw)/(Ap*1.3)*g*1e5) * (rhoV*Ah/sum(Mw*OutletV.z))^1.08 * 'm^1.08/mol^1.08';
case "Klingberg":
InletV.F * vV = Ap * sqrt(((InletV.P - OutletV.P)-rhoL*g*Level)/rhoV);
case "Wang_Fv":
InletV.F * vV = Ap * sqrt(((InletV.P - OutletV.P)-rhoL*g*Level)/rhoV*alfa);
case "Elgue":
InletV.F = sqrt((InletV.P - OutletV.P)/btray);
end
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
#*-------------------------------------
* 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 (OutletL.T)
* the liquid molar holdup ML
* (NoComps - 1) OutletL 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"
);
V as volume(Brief="Total Volume of the tray");
Q as heat_rate (Brief="Rate of heat supply");
d as length (Brief="Column diameter");
a as Real (Brief="surface area per packing volume", Unit='m^2/m^3');
g as acceleration;
e as Real (Brief="Void fraction of packing, m^3/m^3");
Cpo as Real (Brief="Constant for resitance equation"); # Billet and Schultes, 1999.
Mw(NComp) as molweight (Brief = "Component Mol Weight");
hs as length (Brief="Height of the packing stage");
Qsil as positive (Brief="Resistance coefficient on the liquid load", Default=1);
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", 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 + 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;
"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)*OutletV.z;
"Thermal Equilibrium"
OutletV.T = OutletL.T;
"Mechanical Equilibrium"
OutletL.P = OutletV.P;
"Geometry Constraint"
V*e = ML*vL + MV*vV;
"Liquid Density"
rhoL = PP.LiquidDensity(OutletL.T, OutletL.P, OutletL.z);
"Vapour Density"
rhoV = PP.VapourDensity(InletV.T, InletV.P, InletV.z);
"Liquid viscosity"
miL = PP.LiquidViscosity(OutletL.T, OutletL.P, OutletL.z);
"Vapour viscosity"
miV = PP.VapourViscosity(InletV.T, InletV.P, InletV.z);
"Area occupied by the liquid"
Al = ML*vL/hs;
"Volume flow rate of liquid, m^3/m^2/s"
uL * Al = OutletL.F * vL;
"Volume flow rate of vapor, m^3/m^2/s"
uV * ((d^2*3.14159/4)*e - Al) = OutletV.F * vV;
"Liquid holdup"
hl = ML*vL/V/e;
"Particle diameter"
dp = 6 * (1-e)/a;
"Wall Factor"
invK = (1 + (2*dp/(3*d*(1-e))));
"Reynolds number of the vapor stream"
Rev*invK = dp*uV*rhoV / (miV*(1-e));
deltaP = InletV.P - OutletV.P;
"Pressure drop and Vapor flow"
deltaP/hs = Qsil*a*uV^2*rhoV*invK / (2*(e-hl)^3);
"Liquid holdup"
hl = (12*miL*a^2*uL/rhoL/g)^1/3;
end
#*-------------------------------------
* Nonequilibrium Model
-------------------------------------*#
Model interface
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 trayRateBasic
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 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_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 interface;
SET
NC1=NComp-1;
EQUATIONS
"Component Molar Balance"
diff(M_liq)=Inlet.F*Inlet.z + InletL.F*InletL.z
- OutletL.F*OutletL.z + interf.NL;
diff(M_vap)=InletFV.F*InletFV.z + InletV.F*InletV.z
- OutletV.F*OutletV.z - interf.NV;
"Energy Balance"
diff(E_liq) = Inlet.F*Inlet.h + InletL.F*InletL.h
- OutletL.F*OutletL.h + Q + interf.E_liq;
diff(E_vap) = InletFV.F*InletFV.h + InletV.F*InletV.h
- OutletV.F*OutletV.h - interf.E_vap;
"Molar Holdup"
M_liq = ML*OutletL.z;
M_vap = MV*OutletV.z;
"Energy Holdup"
E_liq = ML*(OutletL.h - OutletL.P*vL);
E_vap = MV*(OutletV.h - OutletV.P*vV);
"Energy Rate through the interface"
interf.E_liq = interf.htL*interf.a*(interf.T-OutletL.T)+sum(interf.NL)*interf.hL;
interf.E_vap = interf.htV*interf.a*(OutletV.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(OutletL.z)= 1.0;
sum(OutletL.z)= sum(OutletV.z);
sum(interf.x)=1.0;
sum(interf.x)=sum(interf.y);
"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(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)-OutletL.z(1:NC1)))/vL+
OutletL.z(1:NC1)*sum(interf.NL);
# interf.NL(1:NC1)=0.01*'kmol/s';
interf.NV(1:NC1)=interf.a*sumt(interf.kV*(OutletV.z(1:NC1)-interf.y(1:NC1)))/vV+
OutletV.z(1:NC1)*sum(interf.NV);
"Mechanical Equilibrium"
OutletV.P = OutletL.P;
interf.P=OutletL.P;
end
Model trayRate as trayRateBasic
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 (OutletV.F)
== Initial ==
* the plate temperature of both phases (OutletL.T and OutletV.T)
* the liquid height (Level) OR the liquid flow holdup (ML)
* the vapor holdup (MV)
* (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