EQUILIBRIO LIQUIDO VAPOR
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Transcript of EQUILIBRIO LIQUIDO VAPOR
EQUILIBRIO LIQUIDO - VAPOR CON LA CORRELACION DE HAYDEN
O’CONNELL Y ECUACION UNIFAC
LUZ DARY CHICAIZA REVELO
TERMODINAMICA QUIMICA
INGENIERIA QUIMICA
UNIVERSIDAD DEL VALLE
EQUILIBRIO LIQUIDO - VAPOR CON LA CORRELACION DE HAYDEN
O’CONNELL Y ECUACION UNIFAC
Sistema ciclohexano(1) / isopropanol (2)utilizando el lenguaje de programación
PASCAL para determinar la temperatura T en (ºC) en el punto de burbuja y la fracción
molar y1 del componente (1) en la fase de vapor e equilibrio con una fase liquida de
fracción molar x1 = 0, 0.05, 0.10, 0.15, 0.20, … , 1.00 y a una presión de 760 mmHg.
PROPIEDADES DEL COMPONENTE PURO:
CICLOHEXANO (1) ISOPROPANOL (2)
Tc (K) 553.54 508.32
Pc (bar) 40.75 47.64
RD (Å) 3.261 2.726
μ(Debye) 0.00 1.66
CONSTANTES GRUPOS CONSTITUYENTES:
GRUPO (CLASE #) RK QK
CH3(1) 0.9011 0.848
CH2 (2) 0.6744 0.5470
CH(3) 0.4469 0.228
OH (4) 1.0000 1.200
Parámetros de asociación y solvatación
η11 = 0.00 η22 = 1.32 η12 = 0.00
Parámetros de interacción
a1,2 = 0º K a3 = 0º K a1,4 = 986.5º K
a2,1 = 0º K a3 = 0º K a2,1 = 986.5º K
a13,1 = 0º K a2 = 0º K a3,1 = 986.5º K
a4,1= 156.4º K a2 = 156.4º K a4,1= 156.4º K
1. LISTADO DEL PROGRAMA
Program Termo_Hayden_OConnell;
{Programa para el calculo de los segundos coeficientes viriales con Hayden_Oconnell}
{Variables utilizadas en programa principal}
{Variables reales}
var n,z,O,P,Tsat1,Tsat2,Bij,T,y1,x1,O_1,O_2,gama_1,gama_2,Psat1,Psat2,Vsat1,Vsat2,
alfa11,alfa21,Omega_1,Omega_2,Er1,Er2,y1a,y2a,Td,Osat_1,Osat_2,B11,B22,y2:Real;
{Inicio del procedimiento que permite calcular los segundos coeficientes viriales}
{La funcion requiere valores iniciales dependiendiendo del coeficiente a calcular}
Procedure HOC(T,nii,njj,nij,Tci,Tcj,Pci,Pcj,Rdi,Rdj,ui,uj:Real);
{Variables del procedure HOC(Hayden_Oconnell)}
var
wii,wjj,oiip,ojjp,eiikp,ejjkp,c1i,c2i,ei,c1j,c2j,ej,oii,ojj,eiik,ejjk,wij,c1p,c2p,oijp,eijkp,ep,oij,eijk,Eij,uija,
Dhij,Aij,uijap,boij,Tija,invTijap,Bmetbouij,Bcheij,BijD,BFpolar,BFnonpolar,BijF:Real;
begin
{Codigo del programa}
{Calculo del factor acentrico para el componente puro }
wii := 0.006026*Rdi+0.02096*sqr(Rdi)-0.001366*sqr(Rdi)*Rdi;
wjj := 0.006026*Rdj+0.02096*sqr(Rdj)-0.001366*sqr(Rdj)*Rdj;
{Parametros del metodo _Hayden_Oconnell}
oiip := (2.44-wii)*exp((1/3)*ln(1.0133*Tci/Pci));
ojjp := (2.44-wjj)*exp((1/3)*ln(1.0133*Tcj/Pcj));
eiikp := Tci*(0.748+0.91*wii-0.4*nii/(2+20*wii));
ejjkp := Tcj*(0.748+0.91*wjj-0.4*njj/(2+20*wjj));
c1i := (16+400*wii)/(10+400*wii);
c1j := (16+400*wjj)/(10+400*wjj);
c2i := 3/(10+400*wii);
c2j := 3/(10+400*wjj);
if (ui<1.45) then
begin
ei := 0;
end
else if (ui>=1.45) then
begin
ei := 1.7473e7*sqr(sqr(ui))/((2.882-1.882*wii/(0.03+wii))*Tci*sqr(oiip)*sqr(sqr(oiip))*eiikp);
end;
if (uj<1.45) then
begin
ej := 0;
end
else if (uj>=1.45) then
begin
ej := 1.7473e7*sqr(sqr(uj))/((2.882-1.882*wjj/(0.03+wjj))*Tcj*sqr(ojjp)*sqr(sqr(ojjp))*ejjkp);
end;
{Calculo de la energia caracteristica de interaccion y tamaño de la molecula para el componente puro }
oii := oiip*exp((1/3)*ln(1+ei*c2i));
ojj := ojjp*exp((1/3)*ln(1+ej*c2j));
eiik := eiikp*(1-ei*c1i*(1-ei*(1+c1i)/2));
ejjk := ejjkp*(1-ej*c1j*(1-ej*(1+c1j)/2));
{Parametros cruzando los componentes puros}
wij := 0.5*(wii+wjj);
c1p := (16+400*wij)/(10+400*wij);
c2p := 3/(10+400*wij);
oijp := exp((1/2)*ln(oii*ojj));
eijkp := 0.7*exp((1/2)*ln(eiik*ejjk))+0.6/(1/eiik+1/ejjk);
if (ui>=2) AND (uj=0) then
ep := sqr(ui)*(exp((2/3)*ln(ejjk)))*sqr(sqr(ojj))/(eijkp*sqr(oijp)*sqr(sqr(oijp)))
else
ep := 0;
if (uj>=2) AND (ui=0) then
ep := sqr(uj)*(exp((2/3)*ln(eiik)))*sqr(sqr(oii))/(eijkp*sqr(oijp)*sqr(sqr(oijp)))
else
ep := 0;
oij := oijp*exp((1/3)*ln(1-ep*c2p));
eijk := eijkp*(1+ep*c1p);
{Parametros independientes de la temperatura}
if (nij>=4.5) then
Eij := exp(nij*(42800/(eijk+22400)-4.27))
else
Eij := exp(nij*(650/(eijk+300)-4.27));
uija := 7243.8*ui*uj/(eijk*exp(3*ln(oij)));
Dhij := 1.99+0.2*sqr(uija);
Aij := -0.3-0.05*uija;
if (uija<0.04) then
begin
uijap := uija;
end
else if (uija>=0.04) AND (uija<0.25)then
begin
uijap := 0;
end
else if (uija>=0.25) then
begin
uijap := uija-0.25;
end;
boij := 1.26135*exp(3*ln(oij));
{Correalciones dependientes de la temperatura para el calculo de los segundos coeficientes viriales}
Tija := T/eijk;
invTijap := 1/Tija-1.6*wij;
Bcheij := boij*Eij*(1-exp(1500*nij/T));
Bmetbouij := boij*Aij*exp(Dhij/Tija);
BFpolar := -boij*uijap*(0.75-3.0*invTijap+2.1*sqr(invTijap)+2.1*exp(3*ln(invTijap)));
BFnonpolar := boij*(0.94-1.47*invTijap-0.85*sqr(invTijap)+1.015*exp(3*ln(invTijap)));
{Parametro que denota la relativa libertad de las moleculas}
BijD := Bmetbouij+Bcheij;
{Parametro que denota los enlaces o la dimerizacion de las moleculas(fuerzas quimicas)}
BijF := BFpolar+BFnonpolar;
{Calculo de los segundos coeficientes viriales}
Bij := BijF+BijD;
end; {fin del procedimiento}
Procedure UNIFAC(x1,T:Real);
{Variables del procedure UNIFAC}
var
RCH3,RCH2,ROH,RCH,QCH3,QCH2,QOH,QCH,v1CH3,v1CH2,v1OH,v1CH,v2CH3,v2CH2,v2OH,v2
CH,r1,r2,q1,q2,J1,J2,L1,
L2,x2,G1CH3,G1CH2,G1OH,G1CH,G2CH3,G2CH2,G2OH,G2CH,tethaCH,tethaCH3,tethaCH2,tethaO
H,tCH3CH3,tCH3CH2,
tCH2CH3,tCH2CH2,aCH3CH3,aCH3CH2,aCH2CH3,aCH2CH2,aOHOH,aCH3OH,aCH2OH,aOHCH3,
aOHCH2,aCH3CH,aCH2CH,aCHCH,
aOHCH,aCHCH3,aCHCH2,aCHOH,tOHOH,tCH3OH,tCH2OH,tOHCH3,tCH3CH,tCH2CH,tCHCH,tO
HCH,tCHCH3,tCHCH2,tCHOH,tOHCH2,
s1CH3,s1CH2,s1OH,s1CH,s2CH3,s2CH2,s2OH,s2CH,nCH3,nCH2,nOH,nCH,lngamaC_1,lngamaC_2,ln
gamaR_1,lngamaR_2:Real;
begin
{Codigo del programa}
{Constantes conocidas}
{Parametro del volumen molecular relativo para los diferentes grupos}
RCH3 := 0.9011;
RCH2 := 0.6744;
ROH := 1.0000;
RCH := 0.4469;
{Parametro del area molecular relativo para los diferentes grupos}
QCH3 := 0.848;
QCH2 := 0.540;
QOH := 1.200;
QCH := 0.228;
{Numero de subgrupos del tipo k}
v1CH3 := 0;
v1CH2 := 6;
v1OH := 0;
v1CH := 0;
v2CH3 := 2;
v2CH2 := 0;
v2OH := 1;
v2CH := 1;
{Parametros de interaccion}
aCH3CH3 := 0;
aCH3CH2 := 0;
aCH2CH3 := 0;
aCH2CH2 := 0;
aOHOH := 0;
aCH3CH := 0;
aCH2CH := 0;
aCHCH := 0;
aCHCH3 := 0;
aCHCH2 := 0;
aCHOH := 986.5;
aCH3OH := 986.5;
aCH2OH := 986.5;
aOHCH3 := 156.4;
aOHCH2 := 156.4;
aOHCH := 156.4;
{Volumen molecular para el componente i}
r1 := v1CH3*RCH3+v1CH2*RCH2+v1OH*ROH+v1CH*RCH;
r2 := v2CH3*RCH3+v2CH2*RCH2+v2OH*ROH+v2CH*RCH;
{Area molecular para el componente i}
q1 := v1CH3*QCH3+v1CH2*QCH2+v1OH*QOH+v1CH*QCH;
q2 := v2CH3*QCH3+v2CH2*QCH2+v2OH*QOH+v2CH*QCH;
{Composicion del componente 2}
x2 := 1-x1;
{Parametros Ji y Li}
J1 := r1/(x1*r1+x2*r2);
J2 := r2/(x1*r1+x2*r2);
L1 := q1/(x1*q1+x2*q2);
L2 := q2/(x1*q1+x2*q2);
{Parametros Gik}
G1CH3 := v1CH3*QCH3;
G1CH2 := v1CH2*QCH2;
G1OH := v1OH*QOH;
G1CH := v1CH*QCH;
G2CH3 := v2CH3*QCH3;
G2CH2 := v2CH2*QCH2;
G2OH := v2OH*QOH;
G2CH := v2CH*QCH;
{Parametro tethak}
tethaCH3 := x1*G1CH3+x2*G2CH3;
tethaCH2 := x1*G1CH2+x2*G2CH2;
tethaOH := x1*G1OH+x2*G2OH;
tethaCH := x1*G1CH+x2*G2CH;
{Parametro de interaccion tkm}
tCH3CH3 := exp(-aCH3CH3/T);
tCH3CH2 := exp(-aCH3CH2/T);
tCH2CH3 := exp(-aCH2CH3/T);
tCH2CH2 := exp(-aCH2CH2/T);
tOHOH := exp(-aOHOH/T);
tCH3OH := exp(-aCH3OH/T);
tCH2OH := exp(-aCH2OH/T);
tOHCH3 := exp(-aOHCH3/T);
tOHCH2 := exp(-aOHCH2/T);
tCH3CH := exp(-aCH3CH/T);
tCH2CH := exp(-aCH2CH/T);
tCHCH := exp(-aCHCH/T);
tOHCH := exp(-aOHCH/T);
tCHCH3 := exp(-aCHCH3/T);
tCHCH2 := exp(-aCHCH2/T);
tCHOH := exp(-aCHOH/T);
{Parametro sik}
s1CH3 := G1CH3*tCH3CH3+G1CH2*tCH2CH3+G1OH*tOHCH3+G1CH*tCHCH3;
s1CH2 := G1CH3*tCH3CH2+G1CH2*tCH2CH2+G1OH*tOHCH2+G1CH*tCHCH2;
s1OH := G1CH3*tCH3OH+G1CH2*tCH2OH+G1OH*tOHOH+G1CH*tCHOH;
s1CH := G1CH3*tCH3CH+G1CH2*tCH2CH+G1OH*tOHCH+G1CH*tCHCH;
s2CH3 := G2CH3*tCH3CH3+G2CH2*tCH2CH3+G2OH*tOHCH3+G2CH*tCHCH3;
s2CH2 := G2CH3*tCH3CH2+G2CH2*tCH2CH2+G2OH*tOHCH2+G2CH*tCHCH2;
s2OH := G2CH3*tCH3OH+G2CH2*tCH2OH+G2OH*tOHOH+G2CH*tCHOH;
s2CH := G2CH3*tCH3CH+G2CH2*tCH2CH+G2OH*tOHCH+G2CH*tCHCH;
{Parametro nk}
nCH3 := x1*s1CH3+x2*s2CH3;
nCH2 := x1*s1CH2+x2*s2CH2;
nOH := x1*s1OH+x2*s2OH;
nCH := x1*s1CH+x2*s2CH;
{Calculo de gama combinatoria que toma en cuenta las diferencia en forma y tamaño}
lngamaC_1 := 1-J1+ln(J1)-5*q1*(1-J1/L1+ln(J1/L1));
lngamaC_2 := 1-J2+ln(J2)-5*q2*(1-J2/L2+ln(J2/L2));
{Calculo de gama residual que estima las interacciones moleculares}
lngamaR_1 := q1*(1-ln(L1))-((tethaCH3*s1CH3/nCH3-
G1CH3*ln(s1CH3/nCH3))+(tethaCH2*s1CH2/nCH2-G1CH2*ln(s1CH2/nCH2))+(tethaOH*s1OH/nOH-
G1OH*ln(s1OH/nOH))+(tethaCH*s1CH/nCH-G1CH*ln(s1CH/nCH)));
lngamaR_2 := q2*(1-ln(L2))-((tethaCH3*s2CH3/nCH3-
G2CH3*ln(s2CH3/nCH3))+(tethaCH2*s2CH2/nCH2-G2CH2*ln(s2CH2/nCH2))+(tethaOH*s2OH/nOH-
G2OH*ln(s2OH/nOH))+(tethaCH*s2CH/nCH-G2CH*ln(s2CH/nCH)));
{calculo de los coeficientes de actividad para los componentes i}
gama_1 := exp(lngamaC_1+lngamaR_1);
gama_2 := exp(lngamaC_2+lngamaR_2);
end; {fin del procedure UNIFAC}
Procedure ANTOINET(T:Real);
{Variables del procedure ANTOINE}
var
a1,b1,c1,a2,b2,c2:Real;
begin
{Codigo del programa}
{Constantes conocidas}
a1 := 6.84498;
b1 := 1203.526;
c1 := 222.863;
a2 := 7.75634;
b2 := 1366.142;
c2 := 197.970;
Psat1 := exp((a1-b1/(T+c1))*ln(10));
Psat2 := exp((a2-b2/(T+c2))*ln(10));
end; {fin del procedure AntoineT}
Procedure ANTOINEP(P:Real);
{Variables del procedure ANTOINE}
var
a1,b1,c1,a2,b2,c2:Real;
begin
{Codigo del programa}
{Constantes conocidas}
a1 := 6.84498;
b1 := 1203.526;
c1 := 222.863;
a2 := 7.75634;
b2 := 1366.142;
c2 := 197.970;
Tsat1 := b1/(a1-log(P))-c1;
Tsat2 := b2/(a2-log(P))-c2;
end; {fin del procedure AntoineP}
Procedure SDOC(T:Real);
var
tao1,tao2,Za1,Za2,Tc1,Tc2,Tr1,Tr2,Pc1,Pc2,R:Real;
begin
{Codigo del programa}
{Constante conocidas}
R := 83.1434; {cm3*bar/(mol*K)}
Za1 := 0.2729;
Za2 := 0.2540;
Tc1 := 553.54;
Tc2 := 508.32;
Pc1 := 40.75;
Pc2 := 47.64;
Tr1 := T/Tc1;
Tr2 := T/Tc2;
if (Tr1<=0.75) OR (Tr2<=0.75) then
begin
tao1 := 1+exp((2/7)*ln(1-Tr1));
tao2 := 1+exp((2/7)*ln(1-Tr2));
end
else if (Tr1>0.75) OR (Tr2>0.75) then
begin
tao1 := 1.6+0.00693026/(Tr1-0.655);
tao2 := 1.6+0.00693026/(Tr2-0.655);
end;
Vsat1 := (83.1434*Tc1/Pc1)*exp(tao1*ln(Za1));
Vsat2 := (83.1434*Tc2/Pc2)*exp(tao2*ln(Za2));
end; {fin procedure SDOC}
Procedure Fugacidad(T,P,y1:Real);
var
B12,d12,R:Real;
begin
HOC(T,0,0,0,553.54,553.54,40.75,40.75,3.261,3.261,0,0);
B11 := Bij;
{Se llama la funcion HOC para B11 cuando i=1 j=2 a 360K}
HOC(T,0,1.32,0,553.54,508.32,40.75,47.64,3.261,2.726,0,1.66);
B12 := Bij;
{Se llama la funcion HOC para B11 cuando i=2 j=2 a 360K}
HOC(T,1.32,1.32,1.32,508.32,508.32,47.64,47.64,2.726,2.726,1.66,1.66);
B22 := Bij;
R := 83.1434; {cm3*bar/(mol*K)}
d12 := 2*B12-B11-B22;
O_1 := exp((P/(R*T))*(B11+sqr(1-y1)*d12));
O_2 := exp((P/(R*T))*(B22+sqr(y1)*d12));
end;
begin {inicio del programa principal}
{Inicio de las constanes}
P := 1.01325;
{Inicio del ciclo que permite calcular los coeficientes de fugacidad a distintas composiciones teniendo la
temperatura a 360K}
{Calculo de los coeficientes de fugacidad parcial}
{Se llama la funcion HOC para B11 cuando i=j=1 a 360K}
writeln('PROGRAMA QUE CALCULA EL PUNTO DE BURBUJA DE lA MEZCLA BINARIA
CICLOHEXANO(1) E ISOPROPANOL(2) MEDIANTE');
writeln(' LA CORRELACION DE HAYDEN-OCONNELL Y UNIFAC A UNA PRESION DE
760 mmHg');
writeln(' ');
writeln('******************************************************************************
*************************** ');
writeln(' ');
writeln('DIGITE LA OPCION QUE MAS LE CONVENGA: ');
writeln('(1) GENERA UNA TABLA DONDE X1 VARIA DESDE 0 A 1.0 ACUMULANDO 0.05 ');
writeln('(2) GENERA LA RESPUESTA SEGUN LA COMPOSICION DESEADA: ');
read(O);
while (O=1) OR (O=2) do
begin
if O=1 then
begin
z:=21;
end;
if O=2 then
begin
z:=1;
end;
n:=1;
while n<=z do
begin
x1 := 0.05*(n-1);
if (O=2) then
begin
writeln('DIGITE LA COMPOSICION DESEADA: ');
read(x1);
end;
Er2 :=1;
{PASO 1}
ANTOINEP(P*750.0617);
T := x1*(Tsat1+273.15)+(1-x1)*(Tsat2+273.15);
{PASO 2}
ANTOINET(T-273.15);
UNIFAC(x1,T);
{PASO 3}
alfa11 := Psat1/Psat1;
alfa21 := Psat2/Psat1;
{PASO 4}
Omega_1 := 1;
Omega_2 := 1;
y1a := x1*gama_1*Psat1*0.001333224/(Omega_1*P);
y2a := (1-x1)*gama_2*Psat2*0.001333224/(Omega_2*P);
y1a := y1a/(y1a+y2a);
while (Er2>1e-6) do
begin
{PASO 5}
Fugacidad(T,P,y1a);
Osat_1 :=exp(B11*Psat1*0.001333224/(83.1434*T));
Osat_2 :=exp(B22*Psat2*0.001333224/(83.1434*T));
SDOC(T);
Omega_1 := O_1/(Osat_1*exp(Vsat1*(P-Psat1*0.001333224)/(83.1434*T)));
Omega_2 := O_2/(Osat_2*exp(Vsat2*(P-Psat2*0.001333224)/(83.1434*T)));
Er1 := 1;
while (Er1>1e-6) do
begin
{PASO 6}
y1 := x1*gama_1*Psat1*0.001333224/(Omega_1*P);
y2 := (1-x1)*gama_2*Psat2*0.001333224/(Omega_2*P);
y1 := y1/(y1+y2);
Fugacidad(T,P,y1);
Osat_1 :=exp(B11*Psat1*0.001333224/(83.1434*T));
Osat_2 :=exp(B22*Psat2*0.001333224/(83.1434*T));
Omega_1 := O_1/(Osat_1*exp(Vsat1*(P-Psat1*0.001333224)/(83.1434*T)));
Omega_2 := O_2/(Osat_2*exp(Vsat2*(P-Psat2*0.001333224)/(83.1434*T)));
{PASO 7}
Er1 := abs(y1-y1a);
y1a := y1;
end;
{PASO 8}
Psat1 :=P/((x1*alfa11)*gama_1/Omega_1+((1-x1)*alfa21)*gama_2/Omega_2);
Td := 1203.526/(6.84498-log(Psat1*750.0617))-222.863+273.15;
{PASO 9}
ANTOINET(Td-273.15);
alfa11 := Psat1/Psat1;
alfa21 := Psat2/Psat1;
UNIFAC(x1,Td);
{PASO 10}
Er2 := abs(Td-T);
T := Td;
end;
{PASO 11}
ANTOINET(T-273.15);
UNIFAC(x1,T);
Fugacidad(T,P,y1a);
Osat_1 :=exp(B11*Psat1*0.001333224/(83.1434*T));
Osat_2 :=exp(B22*Psat2*0.001333224/(83.1434*T));
SDOC(T);
Omega_1 := O_1/(Osat_1*exp(Vsat1*(P-Psat1*0.001333224)/(83.1434*T)));
Omega_2 := O_2/(Osat_2*exp(Vsat2*(P-Psat2*0.001333224)/(83.1434*T)));
y1 := x1*gama_1*Psat1*0.001333224/(Omega_1*P);
y2 := (1-x1)*gama_2*Psat2*0.001333224/(Omega_2*P);
y1 := y1/(y1+y2);
if (n=1) then
begin
write(' ');
write('x1 ');
write(' ');
write('y1 ');
write(' ');
write('PhiMini_1 ');
write('');
write('PhiMini_2 ');
write(' ');
write('PhiMayu_1 ');
write(' ');
write('PhiMayu_2 ');
write(' ');
write('Gama_1 ');
write(' ');
write('Gama_2 ');
write(' ');
write('T ,ºC ');
writeln(' ');
end;
write(' ');
write(x1:1:4);
write(' ');
write(y1:2:4);
write(' ');
write(' ');
write(O_1:2:4);
write(' ');
write(O_2:2:4);
write(' ');
write(Omega_1:2:4);
write(' ');
write(Omega_2:2:4);
write(' ');
write(gama_1:2:4);
write(' ');
write(gama_2:2:4);
write(' ');
write(T-273.15:2:4);
writeln(' ');
n:=n+1;
end;
writeln('DIGITE NUEVA OPCION ENTRE (1) O (2) O (3) PARA SALIR ');
read(O);
end;
end.
Corriendo el programa se obtiene:
PROGRAMA QUE CALCULA EL PUNTO DE BURBUJA DE lA MEZCLA BINARIA
CICLOHEXANO(1) E I
SOPROPANOL(2) MEDIANTE
LA CORRELACION DE HAYDEN-OCONNELL Y UNIFAC A UNA PRESION DE 760
mmHg
********************************************************************************
*************************
DIGITE LA OPCION QUE MAS LE CONVENGA:
(1) GENERA UNA TABLA DONDE X1 VARIA DESDE 0 A 1.0 ACUMULANDO 0.05
(2) GENERA LA RESPUESTA SEGUN LA COMPOSICION DESEADA:
Digitando 1 y enter programa la siguiente tabla:
x1 y1 PhiMini_1 PhiMini_2 PhiMayu_1 PhiMayu_
2 Gama_1 Gama_2 T ,║C
0.0000 0.0000 0.9890 0.9638 1.0292 1.0000
4.4106 1.0000 82.2340
0.0500 0.1820 0.9800 0.9627 1.0163 0.9949
3.9758 1.0028 78.3559
0.1000 0.3036 0.9744 0.9629 1.0081 0.9923
3.5901 1.0115 75.5190
0.1500 0.3882 0.9707 0.9635 1.0025 0.9911
3.2491 1.0266 73.4343
0.2000 0.4490 0.9681 0.9643 0.9987 0.9905
2.9481 1.0485 71.9010
0.2500 0.4940 0.9663 0.9650 0.9960 0.9903
2.6823 1.0782 70.7779
0.3000 0.5279 0.9650 0.9657 0.9940 0.9904
2.4474 1.1169 69.9635
0.3500 0.5539 0.9641 0.9664 0.9926 0.9906
2.2395 1.1661 69.3832
0.4000 0.5740 0.9634 0.9669 0.9915 0.9908
2.0553 1.2282 68.9808
0.4500 0.5897 0.9628 0.9674 0.9908 0.9911
1.8920 1.3062 68.7135
0.5000 0.6020 0.9625 0.9678 0.9903 0.9914
1.7468 1.4044 68.5477
0.5500 0.6117 0.9622 0.9682 0.9899 0.9916
1.6177 1.5291 68.4569
0.6000 0.6193 0.9620 0.9684 0.9897 0.9919
1.5029 1.6896 68.4201
0.6500 0.6255 0.9618 0.9687 0.9895 0.9922
1.4008 1.9001 68.4214
0.7000 0.6307 0.9617 0.9689 0.9894 0.9924
1.3102 2.1836 68.4510
0.7500 0.6357 0.9616 0.9692 0.9894 0.9927
1.2302 2.5788 68.5087
0.8000 0.6418 0.9615 0.9695 0.9894 0.9931
1.1602 3.1564 68.6152
0.8500 0.6515 0.9614 0.9700 0.9894 0.9938
1.1002 4.0560 68.8457
0.9000 0.6718 0.9611 0.9711 0.9896 0.9955
1.0509 5.5878 69.4497
0.9500 0.7286 0.9608 0.9744 0.9908 1.0005
1.0150 8.5286 71.4035
1.0000 1.0000 0.9623 0.9899 1.0000 1.0255
1.0000 14.5633 80.7383
DIGITE NUEVA OPCION ENTRE (1) O (2) O (3) PARA SALIR
Al digitar la opción 2 se puede obtener los resultados a una composición distinta a la
dadas en el problema.
2
DIGITE LA COMPOSICION DESEADA:
0.17
x1 y1 PhiMini_1 PhiMini_2 PhiMayu_1 PhiMayu_
2 Gama_1 Gama_2 T ,║C
0.1700 0.4149 0.9695 0.9638 1.0008 0.9908
3.1242 1.0345 72.7638
DIGITE NUEVA OPCION ENTRE (1) O (2) O (3) PARA SALIR
Tabla No. 1 resultado de la ejecución del programa
x1 y1 T (ºC) 1̂ 2̂ Φ1 Φ2 γ1 γ2
0.00 0.0000 82.2340 0.9890 0.9638 1.0292 1.0000 4.4106 1.00000
0.05 0.1820 78.3559 0.9800 0.9627 1.0163 0.9949 3.9758 1.00280
0.10 0.3036 75.5190 0.9744 0.9629 1.0081 0.9923 3.5901 1.01150
0.15 0.3882 73.4343 0.9707 0.9635 1.0025 0.9911 3.2491 1.02660
0.20 0.4490 71.9010 0.9681 0.9643 0.9987 0.9905 2.9481 1.04850
0.25 0.4940 70.7779 0.9663 0.9650 0.9960 0.9903 2.6823 1.07820
0.30 0.5279 69.9635 0.9650 0.9657 0.9940 0.9904 2.4474 1.11690
0.35 0.5539 69.3832 0.9641 0.9664 0.9926 0.9906 2.2395 1.16610
0.40 0.5740 68.9808 0.9634 0.9669 0.9915 0.9908 2.0553 1.22820
0.45 0.5897 68.7135 0.9628 0.9674 0.9908 0.9911 1.8920 1.30620
0.50 0.6020 68.5477 0.9625 0.9678 0.9903 0.9914 1.7468 1.40440
0.55 0.6117 68.4569 0.9622 0.9682 0.9899 0.9916 1.6177 1.52910
0.60 0.6193 68.4201 0.9620 0.9684 0.9897 0.9919 1.5029 1.68960
0.65 0.6255 68.4214 0.9618 0.9687 0.9895 0.9922 1.4008 1.90010
0.70 0.6307 68.4510 0.9617 0.9689 0.9894 0.9924 1.3102 2.18360
0.75 0.6357 68.5087 0.9616 0.9692 0.9894 0.9927 1.2302 2.57880
0.80 0.6418 68.6152 0.9615 0.9695 0.9894 0.9931 1.1602 3.15640
0.85 0.6515 68.8457 0.9614 0.9700 0.9894 0.9938 1.1002 4.05600
0.90 0.6718 69.4497 0.9611 0.9711 0.9896 0.9955 1.0509 5.58780
0.95 0.7286 71.4035 0.9608 0.9744 0.9908 1.0005 1.0150 8.52860
1.00 1.0000 80.7383 0.9623 0.9899 1.0000 1.0255 1.0000 14.5633
A partir de la tabla anterior se construyeron los siguientes graficos
Fig No. 1Diagrama de equilibrio TXY
60
65
70
75
80
85
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x1 y1
Tem
pera
tura
(ºC
)
y1
x1
x1experimental
y1experimental
Fig No. 2Coeficiente de Fugacidad vs. Fracción (y1)
0.955
0.960
0.965
0.970
0.975
0.980
0.985
0.990
0.995
0.00 0.20 0.40 0.60 0.80 1.00 1.20
y1
Co
efi
cie
nte
de f
ug
acid
ad
parc
ial
(φi)
φ1
φ2
Fig No. 3 Фi Vs y1
0.985
0.990
0.995
1.000
1.005
1.010
1.015
1.020
1.025
1.030
1.035
0.00 0.20 0.40 0.60 0.80 1.00 1.20
Composición fase vapor y1
Фi
PhiMayu_1
PhiMayu_2
Fig No. 4Coeficiente de actividad vs. X1
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Composición fase líquida ( X1)
Co
ef.
acti
vid
ad
(γi)
Gama_1
Gama_2
Fig No. 5 Diagrama de equilibrio XY
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Fraciones molares fase líquida (X1)
Fra
cio
nes m
ola
res f
ase g
aseo
sa (
Y1)
x1 = y1
Experimentales
x1 = y1=
BIBLIOGRAFIA
M. A. Llano, Conferencias de clase del curso de Termodinámica Química,
Departamento de Procesos Químicos y Biológicos, Facultad de Ingeniería,
Universidad del Valle, Cali (1996)
L. J. Agular. Turbo pascal 7.0 manual de bolsillo, McGraw-Hill, Madrid -
España, 1995
C. R. Joyanes. Programación en Turbo Pascal versiones 4.0, 5.0, 5.5, McGraw -
Hill, Madrid - España, 1995
Hirata et all, Computer aided data book of vapor-liquid equilibria. Kodansha
Internacional, Tokio Japon, 1975
J. M. Smith, H.C. van ness, Ande M.M. Abbot. Introduction to Chemical
Engeneering Thermodynamics. Sixth Edition, McGraw Hill, (2000)