mLdot=Kg*MWA*(dPlmAC)*area1

m1dot=m2dot-mLdot

m2dot=rhoAN2*QAN2

{Wagner Equation}

Pa2=xA2*P

xA1=xA2-(mLdot/m2dot)*(MWTA1/MWA)

Pa1=xA1*P

Pc=((exp(((-7.45514*J7)+(1.202*(J7^1.5))+(-2.43926*(J7^3))+(-3.3559*(J7^6)))/(Tc/508.1))*47))* 1e5

J7=1-(Tc/508.1)

{Thermodynamic Balance}

mLNdot*hLN+mLNdot*EnthN1=mLdot*hA+mLdot*EnthL+(rhoAN1*QAN1)*EnthAN

{Mass Transfer}

dPlmAC=((Pa2-Pc)-(Pa1-Pc))/ln((Pa2-Pc)/(Pa1-Pc))

Pa2n=Pa2-(1e-10)

xA2n=xA2-(1e-10)

Kg=(h1*((CpAN*VisAN/kAN)^(2/3)))/((CpAN*Pngf*MWANave)*(((VisAN/(rhoANave*kd))^(2/3))))

Pcn=Pc+(.001)

Kg=(h1*((CpAN*VisAN/kAN)^(2/3)))/((CpAN*Pngf*MWANave)*(((VisAN/(rhoANave*kd))^(2/3))))

kd=((0.0166*(((TA1+TA2)/2)^(3/2))*((1/MWN+1/MWA)^(1/2)))/((P/101325)*(NuN^(1/3)+

NuA^(1/3))^(2)){ft^2/hr}*0.0929/3600){m^2/sec}

Pngf=(PNc-PNb)/(ln(PNc/PNb))

PNc=P-Pc

PNb=P-((Pa1+Pa2)/2)

h1=1.86*(kAN/De)*((De*Gave/VisAN)*(CpAN*VisAN/kAN)*(De/dx))^(1/3)*(VisAN/VisANc)^(0.14)

{Correlations}

area1=3.14159*De*dx

area2=3.14159*Din*dx

area3=(3.14159*De^2)/4

MWANave=((MWTA1+MWTA2)/2)

rhoANave=((rhoAN1+rhoAN2)/2)

Gave=(rhoAN1*QAN1+rhoAN2*QAN2)/(2*area3)

De=(Dout^2-Din^2)/Din {m}

rhoAN1=P*MWTA1/(R*TA1)

rhoAN2=P*MWTA2/(R*TA2)

QAN1=m1dot/rhoAN1

MWTA1=xA1*MWA+xN1*MWN

MWTA2=xA2*MWA+xN2*MWN

xA1+xN1=1

xA2+xN2=1

{Specific Heats}

CpN2=(31.2+-0.0136*(TaveN2)+0.0000268*(TaveN2)^2+-0.0000000117*(TaveN2)^3)*(1/MWN) *(1000)

TaveN2=(TA1+TA2)/2

CpA=(6.301+0.261*TaveA-0.000125*(TaveA)^2+0.0000000204*(TaveA)^3)*(1/MWA)*(1000)

TaveA=(TA1+TA2)/2

CpAN=((xA1+xA2)/2)*CpA+((xN1+xN2)/2)*CpN2

CpL=(2.3388-0.0038942*Tc+1.1221e-05*(Tc)^2)*1000 {J/kg K} {correlation with experimental data}

{Enthalpies -- Integrated form of Specific Heats}

EnthN1=(31.2*(TN2-TN1)+-0.0136/2 * (TN2^2-TN1^2)^2+0.0000268 /3* (TN2^3-TN1^3)+ -0.0000000117/4*(TN2^4-TN1^4)) *(1/MWN)*(1000) {g-mol/kg-mol}

EnthN2=(31.2*(TA2-TA1)+-0.0136/2*(TA2^2-TA1^2)+0.0000268/3*(TA2^3-TA1^3)+ -0.0000000117/4*(TA2^4-TA1^4)) *(1/MWN)*(1000) {Reid 226}

EnthL=(2.3388*(TA2-TA1)-0.0038942/2*(TA2^2-TA1^2)+1.1221e-05/3*(TA2^3-TA1^3))*1000 {J/kg K} {correlation with experimental data}

EnthA=(6.301*(TA2-TA1)+0.261/2*(TA2^2-TA1^2)-0.000125/3*(TA2^3-TA1^3)+ 0.0000000204/4*(TA2^4-TA1^4))*(1/MWA)*(1000)

EnthAN=((xA1+xA2)/2)*EnthA+((xN1+xN2)/2)*EnthN2

{Viscosities}

{N2 Gas--Chapman-Enskog Method: Non-polar gas}

{Inner Tube}

sigmaN=3.798 {Ang.}

epskN=71.4 {K} {potential energy constant-epsilon/boltzmann's constant}

AAN=1.16145

BBN=0.14874

CCN=0.52487

DDN=0.77320

EEN=2.16178

FFN=2.43787

{Outer Tube}

VisNGO=26.69*(MWN*TaveN2)^(1/2)/(sigmaN^2*OMEGAvNO) {micro Poise}

OMEGAvNO=AAN/(TstarNO^(BBN))+CCN/(exp(DDN*TstarNO))+EEN/(exp(FFN*TstarNO))

TstarNO=TaveN2/epskN

{Outer Tube at Condensate Film}

VisNGOc=26.69*(MWN*Tc)^(1/2)/(sigmaN^2*OMEGAvNOc) {micro Poise}

OMEGAvNOc=AAN/(TstarNOc^(BBN))+CCN/(exp(DDN*TstarNOc))+EEN/(exp(FFN*TstarNOc))

TstarNOc=Tc/epskN

{Acetone Gas Viscosity--Reichenberg Method: Polar Gas}

VisAce=(Astar*(TrAce)/((1+0.36*TrAce*(TrAce-1))^(1/6)))

TrAce=TaveN2/508.1

Astar=MWA^(1/2)*508.1/(30.1) {30.1 from molecular bond structure of Acetone--see notes}

{Acetone Gas Viscosity at Condensate Film--Reichenberg Method: Polar Gas}

VisAcec=(Astar*(TrAc)/((1+0.36*TrAc*(TrAc-1))^(1/6)))

TrAc=Tc/508.1

{Combined Gas Viscosity--Brokaw Approximation of PHIij}

VisAN=((xAave*VisAce/(xAave+xNave*PHI12))+(xNave*VisNGO/(xNave+xAave*PHI21)))*1e-7

xAave=(xA1+xA2)/2

xNave=(xN1+xN2)/2

PHI12=(VisAce/VisNGO)^(1/2)*Souter12*Aouter12

Aouter12=mwx12*MWy12^(-1/2)*(1+((MWy12-MWy12^(0.45)))/(2*(1+MWy12)+((1+MWy12^(0.45))*mwx12^(-1/2)/(1+mwx12))))

mwx12=(4/((1+MWy12^(-1))*(1+MWy12)))^(0.25)

MWy12=MWA/MWN

PHI21=(VisNGO/VisAce)^(1/2)*Souter21*Aouter21

Souter21=Souter12

Aouter21=(MWN/MWA)^(-0.37) {since 0.4 < (MWN/MWA) < 1.33}

Souter12=(1+(TstarAce*TstarNO)^(1/2))/(((1+TstarAce+deltaAce^2/4)^(1/2))*((1+TstarNO)^(1/2)))

TstarAce=TaveA/epskA

epskA=560.2 {K}

deltaAce=(1.94e03*dipoleAce^2)/(VboilingA*TboilingA)

dipoleAce=2.9 {debyes}

VboilingA=82.6 {cm³/g-mol}

TboilingA=329.4 {K}

TboilingN=77.4 {K}

{Combined Gas Viscosity at Condensate Film--Brokaw Approximation of PHIij}

VisANc=((xAc*VisAcec/(xAc+xNc*PHI12c))+(xNc*VisNGOc/(xNc+xAc*PHI21c)))*1e-7

xAc=(Pc/P)

xNc=(1-Pc/P)

PHI12c=(VisAcec/VisNGOc)^(1/2)*Souter12c*Aouter12

PHI21c=(VisNGOc/VisAcec)^(1/2)*Souter21c*Aouter21

Souter21c=Souter12c

Souter12c=(1+(TstarAc*TstarNc)^(1/2))/(((1+TstarAc+deltaAce^2/4)^(1/2))*((1+TstarNc)^(1/2)))

TstarAc=Tc/epskA

TstarNc=Tc/epskN

{Conductivity of Acetone Gas}

kAce=(TaveA/TrefA)^(1.786)*kAceref

TrefA=373 {K}

kAceref=17.3e-3 {W/m K}

{Conductivity of Gas Mixture--Wassiljewa Eq. modified with the Lindsay and Bromley Modification}

kAN=(xAave*kAce/(xAave+Ak12*xNave))+(xNave*kNG2/(xNave+Ak21*xAave))

Ak12=(1/4)*(1+(VisAce*1e7/(VisNGO*1e7)*((MWN/MWA)^(3/4))*(TaveA+Sace) /(TaveA+Snit))^(1/2))^2*(TaveA+Sacenit)/(TaveA+Sace)

Ak21=(1/4)*(1+(VisNGO*1e7/(VisAce*1e7)*((MWA/MWN)^(3/4))*(TaveA+Snit) /(TaveA+Sace))^(1/2))^2*(TaveA+Sacenit)/(TaveA+Snit)

Sace=1.5*TboilingA

Snit=1.5*TboilingN

Sacenit=Cs*((Sace*Snit)^(1/2))

Cs=0.73 {If one of the gases is very polar, otherwise-->Cs=1.0}

{Parameters}

{dx=.1}

Dout=0.0191 {m}

Din=0.0127 {m}

P=101325 {N/m^2}

R=8314 {N m/K kg-mol}

TA2=294.1 {K}

TA1=200 {K}

T1=77 {K}

MWA=58.1 {kg/kg-mol}

MWN=28.02 {kg/kg-mol}

NuN=2*15.6 {2*N}

NuA=3*14.8+6*3.7+7.4 {3*C+6*H+O}

QAN2=(1{Lpm}/(1000*60)) {m³/sec}

xA2=0.8

kNG2=1.8e-2

hA=524000*((1-Tc/508.1)/(1-329.2/508.1))^0.27 {J/Kg}{Reid pg.228}

hLN=199106 {J/Kg}