#*-------------------------------------------------------------------
* Models of tray with Efficiency Prediction
* Author: Josias J. Junges
*-------------------------------------------------------------------*#
using "streams";
using "tray";
Model trayEffEmp as tray
ATTRIBUTES
Pallete = false;
Icon = "icon/Tray";
Brief = "Tray with Efficiency Prediction - Empiric Model";
Info =
"==Description==
Prediciton based on Chan e Fair(1984) model, with entrainment correction.
Multicomponent mixture treated with pseudo-binary approach.
== References ==
*Clear Liquid Height: Bennett et al. (1983).
*Capacity Factor: Treybal(1968).
*Flood Velocity: Fair(1961).
*Liquid Mixing Models: Lewis(1936).
*Eddy Diffusivity: Molnar(1974).
*Entrainment Correction: Colburn(1936).
*Fraction of entrained liquid: Zuiderweg(1982).
General References:
*CHAN, H.;FAIR, J. R. Prediction of Point Efficiencies on Sieve Trays. 1. Binary Systems. Ind. Eng. Chem. Process Des. Dev., v.23, n.4, p.814-9, 1984.
*LOCKETT, M. J. Distillation Tray Fundamentals. Cambridge: Cambridge University Press, 1986.
";
PARAMETERS
z as length (Brief="Liquid flow path length");
d as length (Brief="Plate Diameter");
Aa as area (Brief="Active Area or Bubbling Area = Atray - 2*Adowncomer");
fi as fraction (Brief="Fractional perforated tray area(hole area/ bubbling area)");
Ts as length (Brief="Tray spacing");
outer iLK as Integer (Brief="Pseudo-binary ligth key index");
outer iHK as Integer (Brief="Pseudo-binary heavy key index");
VARIABLES
Qv as flow_vol (Brief="Vapour volumetric flow");
Ql as flow_vol (Brief="Liquid volumetric flow");
Mv as flow_mass (Brief="Vapour mass flow", Lower=0);
Ml as flow_mass (Brief="Liquid mass flow", Lower=0);
Dv as diffusivity (Brief="Diffusivity on Vapour Phase");
Dl as diffusivity (Brief="Diffusivity on Liquid Phase");
sigma as surf_tens (Brief="Surface Tension");
ua as velocity (Brief="Superficial velocity based on Aa");
fs as positive(Brief="Superficial factor", Unit='kg^.5/m^.5/s');
c as positive (Brief="Constant in eq. of Clear Liquid Height");
ae as fraction (Brief="Effective liquid volume fraction");
hcl as length (Brief="Clear Liquid Height");
tv as time_sec (Brief="Mean residence time of vapour in dispersion");
tl as time_sec (Brief="Mean residence time of liquid on tray");
us as velocity (Brief="Superficial velocity based on Ap");
fp as positive (Brief="Flow Parameter");
csb as positive (Brief="Capacity Factor");
uf as velocity (Brief="Flood velocity");
ff as positive (Brief="Flood factor");
lambda as Real (Brief="Stripping factor or ratio of slope of equilibrium line to slope of operating line");
m as Real (Brief="Slope of equilibrium line");
VinLK as Real (Brief="Pseudo-binary key ");
VoutLk as Real (Brief="Pseudo-binary key");
LinLK as Real (Brief="Pseudo-binary key");
LoutLk as Real (Brief="Pseudo-binary key");
NV as positive (Brief="Number of vapour phase transfer units");
NL as positive (Brief="Number of liquid phase transfer units");
NOG as positive (Brief="Number of overall vapour phase transfer units");
EOG as positive (Brief="Point Efficiency");
De as Real (Brief="Eddy diffusivity for liquid mixing");
Pe as positive (Brief="Peclet Number");
n as Real (Brief="Constant");
Emv1 as positive (Brief="Murphree tray efficiency");
hb as length (Brief="Height on spray regime");
l as positive (Brief="Fraction of entrained liquid");
uh as velocity (Brief="Gas velocity through holes");
Emv2 as positive (Brief="Apparent Murphree tray efficiency");
EQUATIONS
"Vapour Volumetric Flow"
Qv=OutletV.F*vV;
"Liquid Volumetric Flow"
Ql=OutletL.F*vL;
"Vapour Mass Flow"
Mv=Qv*rhoV;
"Liquid Mass Flow"
Ml=Ql*rhoL;
"Superficial Velocity"
ua=Qv/Aa;
"Superficial Factor"
fs=ua*rhoV^.5;
"Constant c"
c=.5+0.438*exp(-137.8*'1/m'*hw);
"Effective liquid volume fraction"
ae=exp(-12.55*(ua*'s/m'*(rhoV/(rhoL-rhoV))^0.5)^0.91);
"Clear Liquid Height"
hcl=ae*(hw*'1/m'+c*((Ql*'s/m^3')/(lw*'1/m'*ae))^.67)*'m';
"Mean residence time of vapour in dispersion"
tv=(1-ae)*hcl/(ae*ua);
"Mean residence time of liquid on tray"
tl=hcl*z*lw/Ql;
"Superficial velocity based on Ap"
us*Ap=Qv;
"Flow Parameter"
(fp*Mv)^2*rhoL=Ml^2*rhoV;
"Capacity Factor"
csb=(0.0744*Ts*'1/m'+0.0117)*(log(abs(1/fp)))+0.0304*Ts*'1/m'+0.0153;
"Flood velocity"
uf = csb*(sigma*'1/(N/m)'/0.02)^.2*(abs((rhoL-rhoV)/rhoV))^.5*(fi/.1)^.44*'m/s';
"Flood Factor"
ff*uf=us;
if NComp > 2 then
"Pseudo-binary Approach"
VinLK=InletV.z(iLK)/(InletV.z(iLK)+InletV.z(iHK));
VoutLk=OutletV.z(iLK)/(OutletV.z(iLK)+OutletV.z(iHK));
LinLK=InletL.z(iLK)/(InletL.z(iLK)+InletL.z(iHK));
LoutLk=OutletL.z(iLK)/(OutletL.z(iLK)+OutletL.z(iHK));
else
VinLK=1;
VoutLk=1;
LinLK=1;
LoutLk=1;
end
"Stripping factor or ratio of slope of equilibrium line to slope of operating line"
lambda=m*(OutletV.F/OutletL.F);
#Chan e Fair(1984) Model#
"Number of vapour phase transfer units"
NV*(abs(hcl)*'1/m')^.5=(10300-8670*ff)*ff*(Dv*'s/m^2')^0.5*tv*'1/s';
"Number of liquid phase transfer units"
NL=19700*((Dl*'s/m^2')^.5)*(.4*fs*'1/(kg^.5/m^.5/s)'+.17)*tl*'1/s';
"Number of overall vapour phase transfer units"
NV*NL=NOG*(NL+lambda*NV);
"Point Efficiency"
EOG=1-exp(-NOG);
#Liquid Mixing Models#
"Eddy diffusivity for liquid mixing"
De=(0.0005+0.01285*ua*'s/m'+6.32*(Ql*'s/m^3'/(lw*'1/m'))+0.312*hw*'1/m')^2;
"Peclet Number"
Pe=(OutletL.F*d)/(lw*hcl*(1/vL)*De*'m^2/s');
"Constant n"
n=Pe/2*((1+4*lambda*EOG/Pe)^.5-1);
if Pe equal 0 then
Emv1=EOG;
else
if Pe < 20 then
Emv1/EOG=(1-exp(-(n+Pe)))/((n+Pe)*(1+(n+Pe)/n))+(exp(n)-1)/(n*(1+n/(n+Pe)));
else
lambda*Emv1=(exp(lambda*EOG)-1);
end
end
#Entrainment Correction#
"Height on spray regime"
hb=hcl*(265*((ua/(g*hcl)^.5)*(rhoV/rhoL)^.5)^1.7+1);
"Gas velocity through hole"
uh=Qv/Ah;
"Fraction of entrained liquid"
l=1e-8*(hb/Ts)^3*(uh/(Ql/Aa))^2;
"Apparent Murphree tray efficiency"
Emv1=Emv2*(1+l*Emv1);
Emv=Emv2;
end
Model trayEffFund as tray
ATTRIBUTES
Pallete = false;
Icon = "icon/Tray";
Brief = "Tray with Efficiency Prediction - Fundamental Model";
Info =
"==Description==
Prediciton based on Prado(1986), Gracia and Fair(2000,2002) model, with entrainment and weeping correction.
Multicomponent mixture treated with pseudo-binary approach.
== Options ==
You can select the tray type: with downcomer or dualflow.
== References ==
*Clear Liquid Height (Downcomer): Dhulesia (1984).
*Clear Liquid Height (Dualflow): Garcia e Fair(2002).
*Froth Height: Todd & Van Winkle (1972).
*Fraction of holes with vapour flow (Downcomer): Prado (1990).
*Fraction of holes with vapour flow (Dualflow): Garcia e Fair (2002).
*Fraction of active holes that are in jetting: Prado (1987), considering fj=60% when ua=uatp.
*Capacity Factor (Downcomer): Treybal(1968).
*Capacity Factor (Dualflow): Garcia e Fair(2002).
*Flood Velocity: Fair(1961).
*Liquid Mixing Models: Lewis(1936).
*Eddy Diffusivity: Molnar(1974).
*Entrainment Correction (Downcomer): Colburn(1936).
*Fraction of entrained liquid (Downcomer): Zuiderweg(1982).
General References:
*GARCIA, J. A.; FAIR, J. R. A Fundamental Model for the Prediction of Distillation Sieve Tray Efficiency. 1. Database Development. Ind. Eng. Chem. Res., v.39, n.6, p. 1809-17,2000.
*GARCIA, J. A.; FAIR, J. R. A Fundamental Model for the Prediction of Distillation Sieve Tray Efficiency. 2. Model Development and Validation. Ind. Eng. Chem. Res., v.39, n.6, p. 1818-25,2000.
*GARCIA, J. A.; FAIR, J. R. Distillation Sieve Trays without Downcomers: Prediction of Performance Characteristics. Ind. Eng. Chem. Res., v.41, n.6, p. 1632-40,2002.
*LOCKETT, M. J. Distillation Tray Fundamentals. Cambridge: Cambridge University Press, 1986.
*PRADO, M.; FAIR, J. R. Fundamental Model for the Prediction of Sieve Tray Efficiency. Ind. Eng. Chem. Res., v.29, n.6, p. 1031-42,1990.
";
PARAMETERS
d as length (Brief="Tray Diameter");
dh as length (Brief="Hole Diameter");
Aa as area (Brief="Case Downcomer: Active Area or Bubbling Area = Atray - 2*Adowncomer. Case dualflow: total tray area");
Ah as area (Brief="Area of Holes");
fi as fraction (Brief="Fractional perforated tray area(hole area/ bubbling area)");
Ts as length (Brief="Tray spacing");
T as length (Brief="Tray thickness");
tray_type as Switcher (Valid = ["Dualflow", "Downcomer"], Default= "Downcomer");
outer iLK as Integer (Brief="Pseudo-binary ligth key index");
outer iHK as Integer (Brief="Pseudo-binary heavy key index");
VARIABLES
Qv as flow_vol (Brief="Vapour volumetric flow");
Ql as flow_vol (Brief="Liquid volumetric flow");
Mv as flow_mass (Brief="Vapour mass flow");
Ml as flow_mass (Brief="Liquid mass flow");
Miv as viscosity (Brief="Vapour viscosity");
Mil as viscosity (Brief="Liquid viscosity");
Dl as diffusivity (Brief="Diffusivity on Liquid Phase");
Dv as diffusivity (Brief="Diffusivity on Vapour Phase");
lambda as Real (Brief="Stripping factor or ratio of slope of equilibrium line to slope of operating line");
m as Real (Brief="Slope of equilibrium line");
VinLK as Real (Brief="Pseudo-binary key ");
VoutLk as Real (Brief="Pseudo-binary key");
LinLK as Real (Brief="Pseudo-binary key");
LoutLk as Real (Brief="Pseudo-binary key");
us as velocity (Brief="Superficial velocity based on Ap");
ua as velocity (Brief="Superficial velocity based on Aa");
fs as positive (Brief="Superficial factor", Unit='kg^.5/m^.5/s');
uh as velocity (Brief="Vapour velocity through holes");
fp as positive (Brief="Flow Parameter");
hcl as length (Brief="Clear Liquid Height");
hcld as length (Brief="Dynamic liquid head at tray floor");
hf as length (Brief="Froth Height");
e as positive (Brief="Porosity");
csb as positive(Brief="Capacity Factor");
uf as velocity (Brief="Flood velocity");
ff as positive (Brief="Flood factor");
sigma as surf_tens (Brief="Surface Tension");
ftm as Real (Brief="General Factor in equations of Units of Mass Transfer", Unit='cm/s^.5');
xf as fraction (Brief="Fraction of holes with vapour flow");
dj as length (Brief="Jet Diameter");
uj as velocity (Brief="Jet velocity");
Reh as positive (Brief="Reynolds number for vapour flow through hole");
hj as length (Brief="Jet lenght");
tg1 as time_sec (Brief="Residence time in Zone One");
NL1 as positive (Brief="Number of liquid phase transfer units in Zone One");
dbs as length (Brief="Small bubble diameter");
dbl as length (Brief="Large bubble diameter");
sigCSB as positive (Brief="Surface tension correction");
MilCSB as positive (Brief="Liquid viscosity correction");
fi3 as positive;
dbss as length (Brief="Small bubble Sauter diameter");
dbls as length (Brief="Large bubble Sauterdiameter");
eo as positive (Brief="Etvos number");
mo as positive (Brief="Morton number");
h as positive (Brief="Constant h");
j as positive (Brief="Constant j");
usb as velocity (Brief="Terminal velocity of small bubbles");
ubss as velocity (Brief="Terminal velocity of small bubbles using Sauter diameter");
aj as fraction (Brief="Fraction of small bubbles in froth");
ulb as velocity (Brief="Terminal velocity of large bubbles");
tg2s as time_sec (Brief="Residence time of small bubbles in Zone Two");
tg2l as time_sec (Brief="Residence time of large bubbles in Zone Two");
NL2S as positive (Brief="Number of liquid phase transfer units of small bubbles in Zone Two");
NL2L as positive (Brief="Number of liquid phase transfer units of large bubbles in Zone Two");
tg3 as time_sec (Brief="Residence time in Zone Three");
NL3 as positive (Brief="Number of liquid phase transfer units in Zone Three");
ulb3 as velocity (Brief="Terminal velocity of large bubbles in Zone Three");
tg4s as time_sec (Brief="Residence time of small bubbles in Zone Four");
tg4l as time_sec (Brief="Residence time of large bubbles in Zone Four");
NL4S as positive (Brief="Number of liquid phase transfer units of small bubbles in Zone Four");
NL4L as positive (Brief="Number of liquid phase transfer units of large bubbles in Zone Four");
tg5 as time_sec (Brief="Residence time in Zone Five");
NL5 as positive (Brief="Number of liquid phase transfer units in Zone Five");
uatp as velocity (Brief="Superficial velocity based on Aa in the transition point of froth regime to spay regime");
fj as positive (Brief="Fraction of active holes that are in jetting");
flb as positive (Brief="Fraction of active holes that are producing small bubbles");
fsb as positive (Brief="Fraction of active holes that are producing large bubbles");
ftmg as positive (Brief="General Factor in equations of Units of Mass Transfer");
Rej as positive (Brief="Reynolds number of jet");
Scg as positive (Brief="Schmidt number of vapour phase");
kl1 as positive (Brief="Liquid phase mass transfer coefficient in Zone One");
kg1 as positive (Brief="Vapour phase mass transfer coefficient in Zone One");
NG1 as positive (Brief="Number of vapour phase transfer units in Zone One");
Peg2s as positive (Brief="Peclet number of small bubbles in Zone Two");
Peg2l as positive (Brief="Peclet number of large bubbles in Zone Two");
Peg3 as positive (Brief="Peclet number in Zone Three");
Peg4s as positive (Brief="Peclet number of small bubbles in Zone Four");
Peg4l as positive (Brief="Peclet number of large bubbles in Zone Four");
Peg5 as positive (Brief="Peclet number in Zone Five");
Sh2s as positive (Brief="Sherwood number of small bubbles in Zone Two");
Sh2l as positive (Brief="Sherwood number of large bubbles in Zone Two");
Sh3 as positive (Brief="Sherwood number in Zone Three");
Sh4s as positive (Brief="Sherwood number of small bubbles in Zone Four");
Sh4l as positive (Brief="Sherwood number of large bubbles in Zone Four");
Sh5 as positive (Brief="Sherwood number in Zone Five");
kg2s as positive (Brief="Vapour phase mass transfer coefficient of small bubbles in Zone Two");
kg2l as positive (Brief="Vapour phase mass transfer coefficient of large bubbles in Zone Two");
kg3 as positive (Brief="Vapour phase mass transfer coefficient in Zone Three");
kg4s as positive (Brief="Vapour phase mass transfer coefficient of small bubbles in Zone Four");
kg4l as positive (Brief="Vapour phase mass transfer coefficient of large bubbles in Zone Four");
kg5 as positive (Brief="Vapour phase mass transfer coefficient in Zone Five");
kl2s as positive (Brief="Liquid phase mass transfer coefficient of small bubbles in Zone Two");
kl2l as positive (Brief="Liquid phase mass transfer coefficient of large bubbles in Zone Two");
kl3 as positive (Brief="Liquid phase mass transfer coefficient in Zone Three");
kl4s as positive (Brief="Liquid phase mass transfer coefficient of small bubbles in Zone Four");
kl4l as positive (Brief="Liquid phase mass transfer coefficient of large bubbles in Zone Four");
kl5 as positive (Brief="Liquid phase mass transfer coefficient in Zone Five");
NG2S as positive (Brief="Number of Vapour phase transfer units of small bubbles in Zone Two");
NG2L as positive (Brief="Number of Vapour phase transfer units of large bubbles in Zone Two");
NG3 as positive (Brief="Number of Vapour phase transfer units in Zone Three");
NG4S as positive (Brief="Number of Vapour phase transfer units of small bubbles in Zone Four");
NG4L as positive (Brief="Number of Vapour phase transfer units of large bubbles in Zone Four");
NG5 as positive (Brief="Number of Vapour phase transfer units in Zone Five");
NGFJ as positive (Brief="Number of Vapour phase transfer units of jetting");
NGFLB as positive (Brief="Number of Vapour phase transfer units of large bubbles");
EOG as positive (Brief="Point Efficiency");
De as Real (Brief="Eddy diffusivity for liquid mixing");
Pe as positive (Brief="Peclet Number");
n as Real (Brief="Constant");
Emv1 as positive (Brief="Murphree tray efficiency");
psi as Real (Brief="Correction factor of liquid entrainment in dualflow trays");
psi1 as Real (Brief="Correction factor of weeping in dualflow trays");
hb as length (Brief="Height on spray regime");
l as positive (Brief="Fraction of entrained liquid");
Emv2 as positive (Brief="Apparent Murphree tray efficiency");
Emv3 as positive (Brief="Apparent Murphree tray efficiency");
EQUATIONS
"Vapour volumetric flow"
Qv=OutletV.F*vV;
"Liquid volumetric flow"
Ql=OutletL.F*vL;
"Vapour mass flow"
Mv=Qv*rhoV;
"Liquid mass flow"
Ml=Ql*rhoL;
"Vapour viscosity"
Miv=PP.VapourViscosity(OutletL.T, OutletL.P, OutletL.z);
"Liquid viscosity"
Mil=PP.LiquidViscosity(OutletL.T, OutletL.P, OutletL.z);
if NComp > 2 then
"Pseudo-binary Approach"
VinLK=InletV.z(iLK)/(InletV.z(iLK)+InletV.z(iHK));
VoutLk=OutletV.z(iLK)/(OutletV.z(iLK)+OutletV.z(iHK));
LinLK=InletL.z(iLK)/(InletL.z(iLK)+InletL.z(iHK));
LoutLk=OutletL.z(iLK)/(OutletL.z(iLK)+OutletL.z(iHK));
else
VinLK=1;
VoutLk=1;
LinLK=1;
LoutLk=1;
end
"Stripping factor or ratio of slope of equilibrium line to slope of operating line"
lambda=m*(OutletV.F/OutletL.F);
"Superficial velocity based on Ap"
us=Qv/Ap;
"Superficial velocity based on Aa"
ua=Qv/Aa;
"Superficial factor"
fs=ua*rhoV^.5;
"Vapour velocity through holes"
uh=Qv/Ah;
"Flow parameter"
(fp*Mv)^2*rhoL=Ml^2*rhoV;
switch tray_type
case "Downcomer":
"Clear Liquid Height"
hcl=0.42*(Ql*'1/m'/(lw*ua)*(rhoL/rhoV)^.5)^.33*(hw*'1/m')^.67*'m';
case "Dualflow":
"Clear Liquid Height"
hcl=(0.01728*((Ml*'1/(kg/s)')^(4.3*(fi^1.5))*(ua*'1/(m/s)'*(rhoV/rhoL)^.5)^1))/(rhoL*'1/(kg/m^3)'*fi^1.5*(T/(dh*1000*1000))^.42)*'m';
end
"Dynamic liquid head at tray floor"
hcld=hcl-ua*rhoV*(uh-ua)/(rhoL*g);
"Froth Height"
hf=0.076*'m'+32.6*'m'*(fs*'1/(kg^.5/m^.5/s)')^2/((rhoL-rhoV)*'m^3/kg')+0.82*hcld;
"Porosity"
e=1-hcl/hf;
switch tray_type
case "Downcomer":
"Capacity factor"
csb=(0.0744*Ts*'1/m'+0.0117)*(log(abs(1/fp)))+0.0304*Ts*'1/m'+0.0153;
case "Dualflow":
"Capacity factor"
csb=(0.1317*fp^2-0.1747*fp+0.1124)*(0.6649*Ts*'1/m'+0.5667);
end
"Flood velocity"
uf = csb*(sigma*'1/(N/m)'/0.02)^.2*(abs((rhoL-rhoV)/rhoV))^.5*(fi/.1)^.44*'m/s';
switch tray_type
case "Downcomer":
"Flood Factor"
ff=us/uf;
case "Dualflow":
"Flood Factor"
ff=ua/uf;
end
#Prado, Garcia and Fair Model#
#Liquid Phase#
"General Factor in equations of Units of Mass Transfer"
ftm=(rhoL*Mv*Dl^.5)/(3.1416^.5*rhoV*Ml);
#Zone One#
switch tray_type
case "Downcomer":
"Fraction of holes with vapour flow"
xf=0.9;
case "Dualflow":
"Fraction of holes with vapour flow"
xf=0.4668*(fi/0.2)^.8*(Ts*'1/m'/0.61)^.2*exp(-0.35*(abs(ff*100-90)/45));
end
"Jet diameter"
dj=1.1*dh+0.25*hcl;
"Jet velocity"
uj=(uh*dh^2)/(xf*dj^2);
"Reynolds number for vapour flow through hole"
Reh=dh*uh*rhoV/Miv;
"Jet Height"
hj=1.1e-3*(dh*'1/m')^.2*Reh^.46*'m';
"Residence time in Zone One"
tg1=hj/uj;
"Number of vapour phase transfer units in Zone One"
NL1=(8*ftm*tg1^.5)/dj;
#Zone Two#
"Small Bubble Diameter"
dbs=3.34/(ua*'s/m'*9.8)^.4*(sigma*'m/N'/(rhoL*'m^3/kg'))^.6*(Mil/Miv)^.1*'m';
"Large Bubble Diameter"
dbl=dbs*(0.83+41.5*((sigma*'m/N')^.6*(Mil*'1/cP'/(rhoV*'m^3/kg'))^.1));
if sigma > 5e-3 then
sigCSB=1;
else
sigCSB=3*(sigma*'m/N')^.6;
end
if Mil > .6e-3 then
MilCSB=4.13*(Mil*'1/cP')^1.5;
else
MilCSB=1;
end
fi3=1*MilCSB*sigCSB;
"Sauter diameters"
dbls=fi3*.605*(dh*'1/m')^.84*(uh*'s/m')^.18/((Ql*'s/m^3')/(lw*'1/m')^.07)*'m';
dbss=fi3*.660*(dh*'1/m')^.84*(uh*'s/m')^.085/((Ql*'s/m^3')/(lw*'1/m')^.08)*'m';
"Eotvos Number"
eo=g*(rhoL-rhoV)*dbs^2/sigma;
"Morton Number"
mo=g*Mil^4*(rhoL-rhoV)/(rhoL^2*sigma^3);
"Constant h"
h=4/3*eo*mo^-0.149*((Mil*'1/cP')/9.12e-4)^-.14;
if h > 59.3 then
j=3.42*h^.441;
else
j=0.94*h^.757;
end
"Terminal velocity of small bubbles"
usb=Mil/(rhoL*dbs)*mo^-.149*(j-0.857);
"Terminal velocity of small bubbles using Sauter diameter"
ubss=Mil/(rhoL*dbs)*mo^-.149*(j-0.857);
"Fraction of small bubbles in froth"
aj=1-0.463*((sigma*'m/N')/0.07282)^0.6*((Mil/9.12e-4)*(1.845e-5/Miv))^0.1*(994.7/(rhoL*'m^3/kg'))^0.6*(1.183/(rhoV*'m^3/kg'))^0.1;
"Terminal velocity of large bubbles"
ulb = us/((1 - aj)*e) - usb*aj/(1-aj);
if hf > hj then
tg2s = (hf-hj)/usb;
tg2l = (hf-hj)/ulb;
else
tg2s = hf/usb;
tg2l = hf/ulb;
end
"Number of liquid phase transfer units in Zone Two"
NL2S = 12*ftm*tg2s^0.5/dbs;
NL2L = 12*ftm*tg2l^0.5/dbl;
#Zone Three#
"Terminal velocity of large bubbles in Zone Three"
ulb3 = us/e;
"Residence time in Zone Three"
tg3 = dbls/ulb3;
"Number of liquid phase transfer units in Zone Three"
NL3 = 12*ftm*tg3^0.5/dbls;
#Zone Four#
if hf > dbls then
tg4s = (hf-dbls)/usb;
tg4l = (hf-dbls)/ulb;
else
tg4s = hf/usb;
tg4l = hf/ulb;
end
"Number of liquid phase transfer units in Zone Four"
NL4S=12*ftm*tg4s^0.5/dbs;
NL4L=12*ftm*tg4l^0.5/dbl;
#Zone Five#
"Residence time in Zone Five"
tg5=hf/ulb3;
"Number of liquid phase transfer units in Zone Five"
NL5=12*ftm*tg5^0.5/dbss;
#Fraction of holes in jet regime estimation
"Superficial velocity based on Aa in the transition point of froth regime to spay regime"
uatp=((0.04302*(rhoV*'m^3/kg')^(-0.5)*(rhoL*'m^3/kg')^0.692*(sigma*'m/N')^0.06*fi^0.25*((Ql*'s/m^3')/(lw*'1/m'))^.05*(dh*'1/m')^(-0.1))*(2.58717*(hw*'1/m')+0.86))*'m/s';
"Fraction of active holes that are in jetting"
fj=ua*0.6/uatp;
"Fraction of active holes that are producing small bubbles"
fsb=165.65*(dh*'1/m')^1.32*fi^1.33;
"Fraction of active holes that are producing large bubbles"
flb=1-fj-fsb;
#Vapour Phase#
"General Factor in equations of Units of Mass Transfer"
ftmg=(Ml*rhoV)/(Mv*rhoL);
#Zone One#
"Reynolds number of jet"
Rej=uj*dj*rhoV/Miv;
"Schimdt number on vapour phase"
Scg=Miv/(rhoV*Dv);
"Vapour phase mass transfer coefficient in Zone One"
kg1=0.046*((Dv*'s/m^2')/(dj*'1/m'))*Rej^0.96*Scg^0.44;
"Liquid phase mass transfer coefficient in Zone One"
kl1=1.13*((Dl*'s/m^2')/(tg1*'1/s'))^0.5;
"Number of vapour phase transfer units in Zone One"
NG1=ftmg*kg1*NL1/kl1;
#Zones Two,Three, Four and Five#
"Peclet number"
Peg2s=dbs*usb/Dv;
Peg2l=dbl*ulb/Dv;
Peg3=dbls*ulb3/Dv;
Peg4s=dbs*usb/Dv;
Peg4l=dbl*ulb/Dv;
Peg5=dbss*ubss/Dv;
if Peg2s > 200 then
Sh2s=17.9;
else
Sh2s=-11.878+25.879*log(Peg2s)-5.640*(log(Peg2s))^2;
end
if Peg2l > 200 then
Sh2l=17.9;
else
Sh2l=-11.878+25.879*log(Peg2l)-5.640*(log(Peg2l))^2;
end
if Peg3 > 200 then
Sh3=17.9;
else
Sh3=-11.878+25.879*log(Peg3)-5.640*(log(Peg3))^2;
end
if Peg4s > 200 then
Sh4s=17.9;
else
Sh4s=-11.878+25.879*log(Peg4s)-5.640*(log(Peg4s))^2;
end
if Peg4l > 200 then
Sh4l=17.9;
else
Sh4l=-11.878+25.879*log(Peg4l)-5.640*(log(Peg4l))^2;
end
if Peg5 > 200 then
Sh5=17.9;
else
Sh5=-11.878+25.879*log(Peg5)-5.640*(log(Peg5))^2;
end
"Vapour phase mass transfer coefficient"
kg2s=Sh2s*(Dv*'s/m^2')/(dbs*'1/m');
kg2l=Sh2l*(Dv*'s/m^2')/(dbl*'1/m');
kg3=Sh3*(Dv*'s/m^2')/(dbls*'1/m');
kg4s=Sh4s*(Dv*'s/m^2')/(dbs*'1/m');
kg4l=Sh4l*(Dv*'s/m^2')/(dbl*'1/m');
kg5=Sh5*(Dv*'s/m^2')/(dbss*'1/m');
"Liquid phase mass transfer coefficient"
kl2s=1.13*((Dl*'s/m^2')/(tg2s*'1/s'))^0.5;
kl2l=1.13*((Dl*'s/m^2')/(tg2l*'1/s'))^0.5;
kl3=1.13*((Dl*'s/m^2')/(tg3*'1/s'))^0.5;
kl4s=1.13*((Dl*'s/m^2')/(tg4s*'1/s'))^0.5;
kl4l=1.13*((Dl*'s/m^2')/(tg4l*'1/s'))^0.5;
kl5=1.13*((Dl*'s/m^2')/(tg5*'1/s'))^0.5;
"Number of vapour phase transfer units"
NG2S=ftmg*kg2s*NL2S/kl2s;
NG2L=ftmg*kg2l*NL2L/kl2l;
NG3=ftmg*kg3*NL3/kl3;
NG4S=ftmg*kg4s*NL4S/kl4s;
NG4L=ftmg*kg4l*NL4L/kl4l;
NG5=ftmg*kg5*NL5/kl5;
"Number of Vapour phase transfer units of jetting"
NGFJ=NG1-ln(1e-8+abs(1-(aj*(1-exp(-NG2S))+(1-aj)*(1-exp(-NG2L)))));
"Number of Vapour phase transfer units of large bubbles"
NGFLB= NG3-ln(1e-8+abs(1-(aj*(1-exp(-NG4S))+(1-aj)*(1-exp(-NG4L)))));
"Point Efficiency"
EOG=fj*(1-exp(-NGFJ))+flb*(1-exp(-NGFLB))+fsb*(1-exp(-NG5));
#Liquid Mixing Models#
"Eddy diffusivity for liquid mixing"
De=(0.0005+0.01285*ua*'s/m'+6.32*(Ql*'s/m^3'/(lw*'1/m'))+0.312*hw*'1/m')^2;
"Peclet Number"
Pe=(OutletL.F*d)/(lw*hcl*(1/vL)*De*'m^2/s');
"Constant n"
n=Pe/2*((1+4*lambda*EOG/Pe)^.5-1);
if Pe equal 0 then
Emv1=EOG;
else
if Pe < 20 then
Emv1/EOG=(1-exp(-(n+Pe)))/((n+Pe)*(1+(n+Pe)/n))+(exp(n)-1)/(n*(1+n/(n+Pe)));
else
lambda*Emv1=(exp(lambda*EOG)-1);
end
end
#Entrainment and Weeping Correction#
"Height on spray regime"
hb=hcl*(265*((ua/(g*hcl)^.5)*(rhoV/rhoL)^.5)^1.7+1);
"Fraction of entrained liquid"
l=1e-8*(hb/Ts)^3*(uh/(Ql/Aa))^2;
switch tray_type
case "Downcomer":
"Apparent Murphree tray efficiency"
Emv1=Emv2*(1+l*Emv1);
case "Dualflow":
"Apparent Murphree tray efficiency"
Emv1=Emv2*(1+Emv1*psi/(1-psi));
end
switch tray_type
case "Downcomer":
"Apparent Murphree tray efficiency"
Emv2=Emv3;
case "Dualflow":
"Apparent Murphree tray efficiency"
Emv2=Emv3*(1+Emv2*psi1/(1-psi1));
end
Emv=Emv3;
end