Simulacion Del Reactor de Lecho Fijo[1]

POR EL MODELO DE DOS DIMENSIONES PARA LA OXIDACION DEL

ANHIDRIDO SULFUROSO

Índice

Presentación

CASO I: REACTOR HOMOGENEO

CASO II: CONSIDERANDO DIFUSION RADIAL

CASO III: CON DIFUSION AXIAL Y RADIAL

COMPARACION DEL CASO I, II YIII

PUNTOS CALIENTES

Conclusiones

PRESENTACION

Los reactores de lecho fijo consisten en uno o más tubos empacados con partículas

de catalizador, que operan en posición vertical. Las partículas catalíticas pueden

variar de tamaño y forma: granulares, cilíndricas, esféricas, etc. En algunos casos,

especialmente con catalizadores metálicos como el platino, no se emplean partículas

de metal, sino que éste se presenta en forma de mallas de alambre. El lecho

vatalizador está constituído por un conjunto de capas de este material. Estas mallas

catalíticas se emplean en procesos comerciales para la oxidación de amoniaco y para

la oxidación del acetaldehídico a ácido acético.

Debido a la necesidad de eliminar o añadir calor, no es posible usar un solo tubo

de gran diámetro empacado con el catalizador. En su lugar, el reactor deberá

construirse con cierto número de tubos engarzados en un solo cuerpo. El intercambio

energético con los alrededores se obtiene circulando, algunas veces hirviendo un

fluido en el espacio que hay entre los tubos. Si el efecto calorífico es considerable, los

tubos de catalizador deben de ser pequeños (de hasta 1 plg de diámetro) para evitar

temperaturas excesivas en la mezcla reaccionante. El problema de la decisión del

diámetro del tubo y, por tanto, cuántos tubos son necesarios para una producción

dada, constituye un obstáculo importante en el diseño de estos reactores.

ECUACIÓN GENERAL DE BALANCE DE MATERIA Y ENERGÍA

Conservación de materia

ε Der ( ∂2 CA

∂ r2+ 1

r∂C A

∂r )−υs

∂ C A

∂ z−ρb νA r=0…….(1)

Conservación de energía

K er ( ∂2T∂r 2 + 1

r∂ T∂ r )−υs ρg C pg

∂ T∂ z

+ρb r (−ΔH r )=0…… ..(2)

Donde:

ε: Porosidad del lecho

Ker: Conductividad efectiva radial

Der: Difusividad efectiva radial

CA: Concentración en cada r, z

T: Temperatura en cada r, z𝜐S: Velocidad superficial𝜌b: Densidad del catalizador𝝂A: Coeficiente estequiometrico𝜌g: Densidad del fluido

Cpg: Calor especifico del fluido

CASO I

REACTOR HOMOGENEO

CASO I: REACTOR HOMOGENEO

No se considera difusión radial ni axial:

Esto quiere decir que tanto la concentración como la temperatura se mantienen

constantes en el eje “r” (eje radial)

De la figura se cumple lo siguiente:

En el eje radial: C An=CAm⟹CAn−C Am=0

T n=T m⟹T n−T m=0

Sabemos que la derivada se define coma la pendiente de la función:

∂ CA

∂ r=

C Am−CAn

r2−r1

=CAm−CAm

r2−r1

= 0r2−r1

=0

∂ CA

∂ r=0

De la misma manera se tiene lo siguiente:

∂2C A

∂ r2 =0 ∂ CA

∂ r=0 …………(α)

∂2T∂r 2 =0

∂ T∂r

=0 …………(β)

Reemplazando la condición (α) en la ecuación (1) y la condición (β) ecuación 2 se tiene

lo siguiente:

−υs

∂ C A

∂ z−ρb ν A r=0 ……… (3)

-υs ρg C pg∂T∂ z

+ρb r ( – ΔH r )=0 ……… (4 )

Despejando el término diferencial

∂ CA

∂ z=

−ρb ν A r

υs ……(5)

∂ T∂ z

=ρb r (−ΔH r )

υs ρgC pg

……..(6)

La ecuación (5) lo ponemos en función de la conversión

Se sabe que:

C A=C A0−CA 0 X

Derivando

∂ C A=−C A0 ∂ X

Reemplazando en la ecuación (5) y que υ A=−1,se tiene:

∂ X∂ z

=−ρbr

υsC A0 ……. (7)

La ecuación de velocidad para la oxidación del anhídrido sulfuroso:

SO2+12

O2⇄ SO3

Donde:

Datos del Reactor y de la

operación:

Oxidación del Anhídrido

Sulfuroso

Composición del alimento

6,5% mol de SO2 93,5% mol de aire seco

Catalizador del lecho

Pt/Al2O3(esferas) dp= 0,3175cm 𝜌b =

1025Kg cat/m3 εL = 0,5

Propiedades del Flujo y fase fluida

CPg=1,09KJ

Kgº C

ρg= 0,5864kg

m3

G=1709kg

m3h

Temperatura de alimentación, To

400ºC

Temperatura de la pared, Tw

197ºC

Diámetro del tubo, Dt 5,23cm

Longitud del tubo 9,14cm

Numero de Peclet de transferencia de

calor radial, PeHr4,4

Numero de Peclet de transferencia de

masa radial, PeHr

9,6

Numero de Biot en la pared Biw

6,67

SOLUCION EN POLYMATH

LENGUAJE EN POLYMATH

# Distancia de reactorz(0) = 0z(f) = 0.1524

# Balance de Materia y Energiad(X)/d(z) = db * Rx / (Cao * Us)d(T)/d(z) = db * (-dH) * Rx / (Us * df * Cpf) # Temperatura obtenida en C

# Condiciones InicialesX(0) = 0 # Conversion a la entrada del reactorT(0) = 400 # Temperatura a la entrada del reactor

# Velocidad de la reaccion en funcion de la Conversion y Presion R = funcion(x,T), donde T debe ser usada en Kelvin

Rx = (K1 * Po2 * Pso2 * (1 - Pso3 / (Pso2 * Kp * (Po2) ^ 0.5))) / (22.414 * (1 + K2 * Pso2 + K3 * Pso3) ^ 2)Trx = T + 273.15K1 = exp(12.160 - 5473 / (Trx))K2 = exp(-9.953 + 8619 / (Trx))K3 = exp(-71.745 + 52596 / (Trx))Kp = exp(11300 / (Trx) - 10.68)

# Calculo de las PresionesPso2 = Pao * (1 - X)Po2 = Pbo - 0.5 * Pao * XPso3 = Pao * X

# Propiedades del Fluido

P = 1.6 # Presion del sistemaR = 0.082 # Constante universal de los gasesdb = 1025 # Densidad del Lecho cataliticoCpf = 1.09 # Capacidad Calorifica del FluidoUs = 2914.393 # Velocidad del Fluido G/dfG = 1709 # Flujo masicodf = 0.5864 # Densidad del FluidodH = -94886 # Entalpia de la Reaccion

# Calculo de la Concetracion InicialCao = Pao / (R * Tin)Tin = (400 + 273.15)

# Calculo de la Presion inicialya = 0.065Pao = ya * PPbo = (1 - ya) * P * 0.21

Con las tablas obtenidas por polymath, procedemos a graficar

Z X T

0.000 0.0000 400.00

0.015 0.0245257 406.8598

0.030 0.0505842 414.1483

0.046 0.0886139 424.7851

0.061 0.1599124 444.7272

0.076 0.3207904 489.7244

0.091 0.624388 574.6401

0.107 0.7754533 616.8927

0.122 0.7878356 620.356

0.137 0.788415 620.5181

0.152 0.788441 620.5253

CONVERSION vs. LONGITUD DEL REACTOR

0.000 0.015 0.030 0.046 0.061 0.076 0.091 0.107 0.122 0.137 0.1520.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

X vs Z

P=1.6

Z en metros

Conv

ersio

n

TEMPERATURA vs. LONGITUD DEL REACTOR

0.000 0.015 0.030 0.046 0.061 0.076 0.091 0.107 0.122 0.137 0.152400420440460480500520540560580600620640

T vs Z

P= 1.6 atm

Z en metros

Tem

pera

tura

CASO IICON DIFUSION RADIAL

CASO II: CON DIFUSION RADIAL

Balance de materia:

Se sabe que: C = CA0 - CAoX

Derivando tenemos:

∂C=−CAo∂ X

Dividiendo entre (-CAo)

ε Der [∂2 C∂r2

+ 1r

∂C∂ r ]−Us

∂ C∂ z

−ρb ν A γ(X , T )=0

ε Der [−C Ao ∂2 X

∂ r2+1

r

(−C Ao)∂ X

∂ r ]−Us(−C Ao )∂ X

∂ z−ρb ν A γ (X ,T )=0

ε Der [∂2 X∂ r2

+ 1r

∂ X∂ r ]−Us

∂ X∂ z

+ρb ν A γ( X ,T )

C Ao

=0

Despejando tenemos:

Luego: ν A=1 ;

ρb

C Ao Us=C 1 ;

ε DerUs

=C 2

Reemplazando:

∂ X∂ z

=C 2[∂2 X∂r 2

+ 1r

∂ X∂ r ]+C 1 γ( X ,T )=0

Balance de energía:

Despejando:

Haciendo: −

ρb(−ΔΗ r )ρ f C pf Us

=C 3 ;Ker

Us ρ f C pf

=C 4

Finalmente tenemos:

∂ X∂ z

=ε . d P

PEMr . (∂2 X

∂r2+1

r∂ X∂r )+ ρb . ν A . r A( X ,T )

C A 0 .U S

Ker [∂2 T∂ r2

+ 1r

∂T∂r ]−Us ρf C pf

∂T∂ z

−ρb (−Δ Hr )γ( X , T )=0

∂T∂ z

= KerUs ρ f C pf

(∂2T

∂ r2+ 1

r∂T∂r )−

ρb . (−Δ Hr ) . r A(X ,T )

U S . ρf .C Pf

∂ X∂ z

=C 2(∂2 X∂ r2

+1r

∂ X∂ r )+C 1 .r A( X ,T )

∂T∂ z

=C 4 (∂2T∂ r2

+1r

∂T∂r )+C 3 .r A( X , T )

Condiciones iníciales:

X(o) = 0

T(o) = 400oC

El radio del reactor se divide en cinco partes iguales:

Radio del reactor:

ri=Δr i ; i={0,1,2,3,4,5 }Δr⇒ es la fraccion del radio

Los puntos máximos y mínimos:

∂ Xo∂ z

=0 ;∂ To∂ z

=0

Para r = 0

limr →0

(1r ∂ X∂ r )=(∂2 X

∂r2 )lim

r →0(1r ∂T

∂r )=(∂2T∂r2 )

Reemplazando en estas ecuaciones:

∂ X∂ z

=C 2(∂2 X∂ r2

+1r

∂ X∂ r )+C 1 .r A( X ,T )

∂T∂ z

=C 4 (∂2T∂ r2

+1r

∂T∂r )+C 3 .r A( X , T )

Tenemos:

∂ X∂ z

=2C 2(∂2 X∂r2 )+C 1 .r A( X , T )

∂T∂ z

=2C 4 (∂2 T∂r 2 )+C 3 . r A(X , T )

∂ X i

∂ z=2C 2.(X i+1−2 X i+ X i−1

Δr2 )+C 1 . r A( Xi , T i )

∂T i

∂ z=2C 4 .(T i+1−2T i+T i−1

Δr2 )+C 3 . r A( Xi , T i )

i = 0

∂ X0

∂ z=2C 2 .(X1−2 X0+ X−1

Δr2 )+C 1 . r A( Xi , T i )

∂T 0

∂ z=2C 4 .(T 1−2T 0+T−1

Δr2 )+C 3 . r A( Xi , T i )

Estos puntos no existen: X-1; T-1

Por discretizacion regresiva:

∂ X i

∂r=

X i−X i−1

Δr

Cuando i = 0; reemplazando: Xo = X-1, To = T-1

Para r ≠0

∂ X i

∂ z=C 2 .(X i+1−2 X i+X i−1

Δr2+

1iΔr (X i−X i−1

Δr ))+C 1. r A( Xi , T i )

∂T i

∂ z=C 4 .(T i+1−2T i+T i−1

Δr2+1

iΔr (T i−T i−1

Δr ))+C 3 .r A ( X i , T i )

Cuando i = 1

∂ X1

∂ z=C 2 .(X2−2 X1+ X0

Δr2+

11 Δr (X1−X0

Δr ))+C 1 . r A( X1 , T1 )

∂T 1

∂ z=C 4 .(T 2−2T 1+T 0

Δr2+1

1 Δr (T 1−T0

Δr ))+C 3. r A( X 1 , T1)

Cuando i = 2

∂ X2

∂ z=C 2 .(X3−2 X2+X1

Δr2+

12 Δr (X2−X1

Δr ))+C 1 .r A( X2 , T2 )

∂T 2

∂ z=C 4 .(T 3−2T 2+T 1

Δr2+1

2 Δr (T 2−T1

Δr ))+C 3 . r A( X 2 , T2)

Cuando i = 3

∂ X3

∂ z=C 2 .(X 4−2 X3+ X2

Δr2+

13 Δr (X3−X2

Δr ))+C 1 . r A( X3 ,T3 )

∂T 3

∂ z=C 4 .(T 4−2T 3+T 2

Δr2+1

3 Δr (T 3−T 2

Δr ))+C 3. r A(X 3 , T3 )

Cuando i = 4

∂ X4

∂ z=C 2.(X5−2 X4+X 3

Δr2+

14 Δr (X 4−X3

Δr ))+C 1 . r A( X 4 , T4 )

∂T 4

∂ z=C 4 .(T5−2T 4+T3

Δr2+1

4 Δr (T 4−T 3

Δr ))+C 3 .r A( X4 ,T 4 )

Cuando i = 5

∂ X5

∂ z=C 2 .(X 6−2X 5+X 4

Δr2+

15 Δr (X5−X 4

Δr ))+C 1 .r A( X5 , T5 )

∂T 5

∂ z=C 4 .(T 6−2T5+T 4

Δr2+1

5 Δr (T5−T 4

Δr ))+C 3 . r A( X 5 , T5 )

Condiciones de Frontera:

Para el balance de materia:

Para r = R = ri=iΔr

∂C A

∂ r=0

ó

∂ X∂ r

=0

X i+1−X i=0 ; i=5→X 6=X5

r=R ; →∂C A

∂ r=0

ó

∂ x∂ r

=0

Reemplazando:

∂X5

∂ z=C 2 .( X5−2 X5+ X4

Δr2+ 1

5 Δr ( X 5−X4

Δr ))+C 1 .r A(X 5 , T5 )

Para el Balance de Energía:

Para: r = R;

Transferencia de calor:

−k∂T∂r

=h (T i−T w )→ ∂T∂ r

=−hk (T i−T w )

T i+1−T i

Δr=−h

kT i+

hk

T w

Entonces:

Para i = 5

T 6=T5−hΔr

kT5+

hΔrk

T w

T 6=(1−hΔrk )T5+

hΔrk

T w

Además se sabe que:

ri=iΔr

Biw=rhK

Biw=iΔ rhK

Reemplazando:

∂ X5

∂ z=C 2 .(−X 5+X 4

Δr2+

15 Δr (X5−X 4

Δr ))+C 1 .r A( X5 , T5 )

∂T 5

∂ z=C 4 .((1−Biw

5 )T5+Biw

5T w−2T 5+T 4

Δr2+1

5 Δr (T 5−T 4

Δr ))+C 3 . r A( X5 ,T5 )

Condiciones iníciales:

Cuando Z = 0

conversión temperatura

Xo(0) = 0 T0(0) = 0

X1 (0) = 0 T1(0) = 0

X2 (0) = 0 T2(0) = 0

X3 (0) = 0 T3(0) = 0

X4 (0) = 0 T4(0) = 0

X5 (0) = 0 T5(0) = 0



# Distancia del Reactor

z(0) = 0z(f) = 0.1524

# Propiedades del Fluido

P = 1.60 # Presion del sistemaR = 0.082 # Constante Universl de los gasesdf = 0.5864 # Densidad del fluidoTw = 197 # Temperatura de la paredPhr = 4.4 # Peclet Calor RadialPmr = 9.6 # Peclet Masa RadialBi = 6.67 # Numero de Biot de la pareddp = 0.003175 # Densidad del CatalizadorE = 0.5 # Porosidad del Lecho cataliticodb = 1025 # Densidad del lechoG = 1709 # Flujo masicoUs = 2914.393 # VelocidaddH = -94886 # EntalpiaCpf = 1.09 # Capacidad Calorifica del Fluidodr = (0.02615) / 5 # Espaciamiento Radial 5*dr=Radio

# Calculo de la Concetracion InicialCao = Pao / (R * (Tin))Tin = 400 + 273.15

# Calculo de la Presion inicialya = 0.065Pao = P * yaPbo = (1 - ya) * P * 0.21

# Definicion de Parametros de las Ecuaciones Diferenciales de Materia y Energia# Para EDB Materiapi1 = E * Us * dp / (Us * Pmr)pi2 = db / (Us * Cao)# Para EDB Energiapi3 = dp / Phrpi4 = -dH * db / (Us * df * Cpf)

# Balance de Materia para 5 divisiones del Radio

d(x0)/d(z) = 2 * pi1 * (x1 - 2 * x0 + x0) / dr ^ 2 + pi2 * R0d(x1)/d(z) = pi1 * ((x2 - 2 * x1 + x0) + (x1 - x0) / 1) / dr ^ 2 + pi2 * R1d(x2)/d(z) = pi1 * ((x3 - 2 * x2 + x1) + (x2 - x1) / 2) / dr ^ 2 + pi2 * R2d(x3)/d(z) = pi1 * ((x4 - 2 * x3 + x2) + (x3 - x2) / 3) / dr ^ 2 + pi2 * R3d(x4)/d(z) = pi1 * ((x5 - 2 * x4 + x3) + (x4 - x3) / 4) / dr ^ 2 + pi2 * R4d(x5)/d(z) = pi1 * ((x6 - 2 * x5 + x4) + (x5 - x4) / 5) / dr ^ 2 + pi2 * R5

# Valores iniciales de conversion y Temperaturax0(0) = 0x1(0) = 0x2(0) = 0x3(0) = 0x4(0) = 0x5(0) = 0

# Balance de Energia para 5 divisiones del Radio

d(T0)/d(z) = 2 * pi3 * (T1 - 2 * T0 + T0) / dr ^ 2 + pi4 * R0d(T1)/d(z) = pi3 * ((T2 - 2 * T1 + T0) + (T1 - T0) / 1) / dr ^ 2 + pi4 * R1d(T2)/d(z) = pi3 * ((T3 - 2 * T2 + T1) + (T2 - T1) / 2) / dr ^ 2 + pi4 * R2d(T3)/d(z) = pi3 * ((T4 - 2 * T3 + T2) + (T3 - T2) / 3) / dr ^ 2 + pi4 * R3d(T4)/d(z) = pi3 * ((T5 - 2 * T4 + T3) + (T4 - T3) / 4) / dr ^ 2 + pi4 * R4d(T5)/d(z) = pi3 * ((T6 - 2 * T5 + T4) + (T5 - T4) / 5) / dr ^ 2 + pi4 * R5

# Valores iniciales de conversion y TemperaturaT0(0) = 400T1(0) = 400T2(0) = 400T3(0) = 400T4(0) = 400T5(0) = 400

# Para i = 0K10 = exp(12.160 - 5473 / (T0 + 273.15))K20 = exp(-9.953 + 8619 / (T0 + 273.15))K30 = exp(-71.745 + 52596 / (T0 + 273.15))Kp0 = exp(11300 / (T0 + 273.15) - 10.68)Pa0 = Pao * (1 - x0)Pb0 = Pbo - 0.5 * Pao * x0Pc0 = Pao * x0

R0 = (K10 * Pb0 * Pa0 * (1 - Pc0 / (Pa0 * Kp0 * (Pb0) ^ 0.5))) / (22.414 * (1 + K20 * Pa0 + K30 * Pc0) ^ 2)

# Para i = 1K11 = exp(12.160 - 5473 / (T1 + 273.15))K21 = exp(-9.953 + 8619 / (T1 + 273.15))K31 = exp(-71.745 + 52596 / (T1 + 273.15))Kp1 = exp(11300 / (T1 + 273.15) - 10.68)Pa1 = Pao * (1 - x1)Pb1 = Pbo - 0.5 * Pao * x1Pc1 = Pao * x1R1 = (K11 * Pb1 * Pa1 * (1 - Pc1 / (Pa1 * Kp1 * (Pb1) ^ 0.5))) / (22.414 * (1 + K21 * Pa1 + K31 * Pc1) ^ 2)





# en i= 5 hay intercambio de calor con el exteriorT6 = T5 - Bi * (T5 - Tw) / 5

# para x valor minimo dx/dr = 0 en i =5x6 = x5

Con las tablas obtenidas por polymath, procedemos a graficarDATOS OBTENIDOS EN POLYMATH

ro r1 r2 r3 r4 r5

Radio 0 0.00523 0.01046 0.01569 0.02092 0.02615

z x0 x1 x2 x3 x4 x5 xprom

0.0000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

0.0152 0.025 0.0245188 0.0244299 0.023 0.017 0.004 0.020

0.0305 0.0504852 0.0501527 0.0478677 0.0377272 0.0177939 0.0051528 0.035

0.0457 0.0868168 0.0835159 0.0701128 0.0420615 0.0182194 0.0060648 0.051

0.0610 0.1446385 0.1283229 0.0864383 0.0428475 0.0187751 0.0069482 0.071

0.0762 0.2391598 0.1861042 0.0951262 0.0436372 0.0193669 0.0078096 0.099

0.0914 0.3793842 0.2557484 0.0996847 0.0446674 0.0200022 0.0086534 0.135

0.1067 0.5419311 0.3333168 0.1044463 0.0458546 0.020685 0.0094841 0.176

0.1219 0.6736494 0.4116675 0.1113297 0.0472624 0.0214188 0.0103061 0.213

0.1372 0.7541042 0.4808613 0.1204608 0.0489946 0.022213 0.0111239 0.240

0.1524 0.7980479 0.5299375 0.1310985 0.0511199 0.0230818 0.0119426 0.258

ro r1 r2 r3 r4 r5

Radio 0 0.00523 0.01046 0.01569 0.02092 0.02615

z T0 T1 T2 T3 T4 T5 Tprom

0.0000 400.000 400.000 400.000 400.000 400.000 400.000 400.000

0.0152 406.8572 406.8403 406.6297 404.6377 390.7559 326.7332 390.409

0.0305 414.0097 413.615 411.223 400.9677 368.9261 291.1729 383.319

0.0457 423.3305 421.0735 412.5478 391.4339 348.9197 271.5301 378.139

0.0610 436.3372 428.8973 410.0592 380.2471 332.3455 259.3035 374.532

0.0762 454.6058 436.5931 404.7496 369.2411 318.8762 250.9334 372.500

0.0914 477.6067 443.7096 398.4598 358.8974 307.8717 244.791 371.889

0.1067 498.1099 449.692 392.4978 349.4955 298.764 240.0527 371.435

0.1219 505.9351 453.4905 387.151 341.1703 291.1446 236.2663 369.193

0.1372 501.659 453.5445 382.1258 333.8768 284.7215 233.1675 364.849

0.1524 491.3662 448.2249 376.8912 327.4304 279.2634 230.5893 358.961

0.0000 0.0152 0.0305 0.0457 0.0610 0.0762 0.0914 0.1067 0.1219 0.1372 0.15240.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

X vs Z

T0T1T2T3T4T5

Z en metros

Conv

ersio

n

0.0000 0.0152 0.0305 0.0457 0.0610 0.0762 0.0914 0.1067 0.1219 0.1372 0.1524220.0

270.0

320.0

370.0

420.0

470.0

520.0

T vs Z

T0T1T2T3T4T5

Z en metros

Tem

pera

tura

0

0.00523000000000001

0.01046

0.01569

0.02092

0.026150.00.10.20.30.40.50.60.70.8

Perfil de conversion

0.00000.01520.03050.04570.06100.07620.09140.10670.12190.13720.1524

Radio en Metros

Conv

ersio

n

0

0.005230000000000010.01046

0.01569

0.02092

0.02615230.0270.0310.0350.0390.0430.0470.0510.0

Perfil de Temperatura

0.00000.01520.03050.04570.06100.07620.09140.10670.12190.13720.1524

Radio en Metros

Tem

pera

tura

0.0000 0.0200 0.0400 0.0600 0.0800 0.1000 0.1200 0.1400 0.1600 0.18000.000

0.050

0.100

0.150

0.200

0.250

0.300

X promedio

Z en metros

Conv

ersio

n Pr

omed

io

0.0000 0.0200 0.0400 0.0600 0.0800 0.1000 0.1200 0.1400 0.1600 0.1800330.000

340.000

350.000

360.000

370.000

380.000

390.000

400.000

410.000

T promedio

Z en metros

Tmep

erat

ura P

rom

edio

CASO IIICON DIFUSION AXIAL Y

RADIAL

CASO III: CON DIFUSION AXIAL Y RADIAL

1. BALANCE DE MATERIA:

Ecuación de conservación de cantidad de materia

EDer (∂2 C A

∂r2+1

r

∂ CA

∂r )+ EDeZ

∂2 C A

∂ z2−U S

∂C A

∂ z+

ρb .ν A . r A ( X ,T )=0

………….(1)

Donde:

CA= CA0- CA0X ,dCA = –CAo.dx

Pemr=US . dp

Der

Pehz=U S. dp

Dez

Reemplazando en (1) se obtiene:

Donde:

Se obtiene:

Luego discretizando

Si: i = 0

limi→ 0 ( 1

rdxdr )=d2 x

d r2

X i+1, j−2 X i , j+ X i−1 , j

Δr2+

φ1

2

( X i , j+1−2 X i , j+ X i , j−1 )

Δz2+

φ2

2

( X i , j−X i , j−1 )Δz

+φ3

2r A( X i , j+1 ,T i , j+1 )=0. . .. .. (4 )

Si : i≠0

∂2 X

∂ r2+ 1

r∂ X∂r

+Pe Mr

Pemz∂2 X

∂ z2−

PeMr

ε .d P

∂ X∂ z

+ρb . ν A PeMr .r A( X ,T )

ε .C A 0 . US .dP

=0. . .. .. . .. .. .(2)

φ3=ρb .ν A PeMr

ε .C A 0 .US .d P

φ2=−PeMr

ε .dP

φ1=PeMr

Pemz

∂2 X∂ r2

+ 1r

∂ X∂r

+φ1∂2 X∂ z2

+φ2∂ X∂ z

+φ3 r A( X ,T )=0 . .. . .. .. . .. ..(3 )

∂2 X∂ r2

+φ1

2∂2 X∂ z2

+φ2

2∂ X∂ z

+φ3

2r A( X , T )=0

X i+1, j−2 X i , j+ X i−1,, j

Δr2+ 1

iΔr(X i , j−X i−1 , j )

Δr+φ1

( X i , j+1−2 X i , j+X i , j−1 )

Δz2+φ2

( X i , j−X i , j−1)Δz

+φ3 r A( X i , j+1 , T i , j+1 )=0 .. . .. .. .. . ..(5 )

Entonces:

Para los valores:

i=0, j=1,…,6 ; se aplicara la fórmula (4)

Para los valores:

i=1,…,5 y j=1,…,6; se aplicara la fórmula (5)

Para los valores:

i=0,….,5 y j=0 son valores iniciales de x = 0

Para los valores:

i= 5 y j=0,….,6 por ser valor mínimo : dx/dr = 0 x6 , j=x5 , j

Para los valores:

j = 6 , i = 0,…..,5 por ser valor máximo: dx/dz = 0 x i ,7=x i , 6

2. BALANCE ENERGIA:

Ecuación de conservación de Energía

Ker (∂2T∂ r2

+1r

∂ T∂r )+K ez

∂2T∂ z2

−US ρbC P∂T∂ z

+ρb .(−Δ Hr )r A ( X ,T )

=0………..( 6 )

Donde:

Ker=GdpC Pg

PeHr

Kez=GdpC Pg

PeHZ

Reemplazando en (5) se obtiene:

∂2T∂ r2

+1r

∂T∂r

+PEHr

PEHa

∂2 T∂ z2

−U s PEHr . ρg

G .dP

∂ T∂ z

+ρb . PEHr (−Δ HR ) . r A( X , T )

dP .G . CPg

=0 .. . .. .. . .. .. .(7 )

Donde:

Se obtiene:

Luego discretizando

Si: i = 0

lim r→0 (1r

.∂T∂r

)≡∂2 T∂r2

∂2T∂ r2

+φ4

2∂2 T∂ z2

+φ5

2∂ T∂ z

+φ6

2r A( X ,T )=0

T i+1, j+1−2 T i , j+1+T i−1 , j+1

Δr2+

φ4

2

(T i , j+1−2T i , j+T i , j−1 )

Δz2+

φ5

2

(T i , j+1−T i , j )Δz

+φ6

2r A( X i , j+1 , T i , j+1)=0 .. ..( 8)

Si : i≠1

T i+1, j−2 T i , j+T i−1,, j

Δr2+ 1

iΔr(T i , j−T i−1, j )

Δr+φ4

(T i , j+1−2T i , j+T i , j−1 )

Δz2+φ5

(T i , j−T i , j−1)Δz

+φ6 r A( X i , j+1 , T i , j+1 )=0 . .. .(9 )

Entonces:

Para los valores:

i=0 j=1,…,6 ; se aplicara la fórmula (8)

Para los valores:

i=1,…,5 y j=1,…,6; se aplicara la fórmula (9)

Para los valores:

i=0,….,5 y j=0 su temperatura inicial es: 400ªC

Para los valores:

φ6=ρb .PEHr(−Δ Hr )

d P . G . CPgφ5=−

U s PEHr . ρg

G .d P

φ4=PeHr

PeHZ

∂2T∂ r2

+1r

∂T∂r

+φ4∂2T∂ z2

+φ5∂T∂ z

+φ6 r A( X , T )=0 .

i= 5 y j=0,….,6 existe intercambio de calor en sector externo

Se utiliza:

T 6 , j=T5 , j−Bi5

(T 5 , j−T w)

Para los valores:

j = 6 , i = 0,…..,5 por ser valor máximo: dT/dz = 0 T i ,7=T i ,6

Para la Ecuación de velocidad:

Para valores de i=0,..,5 y j=0,..,6

ri , j=8.314 ×1027e

( −38834Ti , j+273 )× P Ao

2 (1− xi , j)2

1+3.41× 1015 e( −21046

T i, j+273)× P Ao(1−x i , j)



# Constantes de las Ecuaciones de Balance Materia

pi1 = ( Us * dp / Pmz) / (Us * dp / Pmr)pi2 = -Us/(E * (Us * dp / Pmr))pi3 = db / (Cao * E * (Us * dp / Pmr))

# Constantes de las Ecuaciones de Balance de Energia

pi4 = (dp * G * Cpf / Phz) / (dp * G * Cpf / Phr)pi5 = -Us * df * Cpf / (dp * G * Cpf / Phr)pi6 = db * (-dH) / (dp * G * Cpf / Phr)

# Datos del problema

db = 1025 # Densidad del lechoG = 1709 # Flujo masicoUs = 2914.393 # Velocidad dH = -94886 # EntalpiaCpf = 1.09 # Capacidad Calorifica del Fluido df = 0.5864 # Densidad del Fluido

Tw = 197 # Temperatura de la pared Phr = 4.4 # Peclet de calor en direccion radial Pmr = 9.6 # Peclet de masa en direccion radialPhz = 4.4 # Peclet de Calor en Direccion AxialPmz = 9.6 # Peclet de Masa en Direccion AxialBi = 6.67 # Numero de Biotdp = 0.003175E = 0.5 # Porosidad del lecho

dz = (0.1524)/6dr = 0.02615 / 5

# Calculo de la Concetracion inicial

Tin = 400 +273Cao = Pao / (R * Tin )R = 0.082

# Calculo de la Presiones inicialesP = 1.6ya = 0.065Pao = 1.7 * 0.065Pbo = (1 - ya) * P * 0.21

K101 = exp(12.16 - 5473 / (T01 + 273))K102 = exp(12.16 - 5473 / (T02 + 273))K103 = exp(12.16 - 5473 / (T03 + 273))K104 = exp(12.16 - 5473 / (T04 + 273))K105 = exp(12.16 - 5473 / (T05 + 273))K106 = exp(12.16 - 5473 / (T06 + 273))




K141 = exp(12.16 - 5473 / (T41 + 273))K142 = exp(12.16 - 5473 / (T42 + 273))

K143 = exp(12.16 - 5473 / (T43 + 273))K144 = exp(12.16 - 5473 / (T44 + 273))K145 = exp(12.16 - 5473 / (T45 + 273))K146 = exp(12.16 - 5473 / (T46 + 273))


K201 = exp(-9.953 + 8619 / (T01 + 273))K202 = exp(-9.953 + 8619 / (T02 + 273))K203 = exp(-9.953 + 8619 / (T03 + 273))K204 = exp(-9.953 + 8619 / (T04 + 273))K205 = exp(-9.953 + 8619 / (T05 + 273))K206 = exp(-9.953 + 8619 / (T06 + 273))






K301 = exp(-71.745 + 52596 / (T01 + 273))

K302 = exp(-71.745 + 52596 / (T02 + 273))K303 = exp(-71.745 + 52596 / (T03 + 273))K304 = exp(-71.745 + 52596 / (T04 + 273))K305 = exp(-71.745 + 52596 / (T05 + 273))K306 = exp(-71.745 + 52596 / (T06 + 273))






Kp01 = exp(11300 / (T01 + 273) - 10.68)Kp02 = exp(11300 / (T02 + 273) - 10.68)Kp03 = exp(11300 / (T03 + 273) - 10.68)Kp04 = exp(11300 / (T04 + 273) - 10.68)Kp05 = exp(11300 / (T05 + 273) - 10.68)Kp06 = exp(11300 / (T06 + 273) - 10.68)


Kp21 = exp(11300 / (T21 + 273) - 10.68)Kp22 = exp(11300 / (T22 + 273) - 10.68)

Kp23 = exp(11300 / (T23 + 273) - 10.68)Kp24 = exp(11300 / (T24 + 273) - 10.68)Kp25 = exp(11300 / (T25 + 273) - 10.68)Kp26 = exp(11300 / (T26 + 273) - 10.68)




Pa01 = Pao * (1 - x01)Pa02 = Pao * (1 - x02)Pa03 = Pao * (1 - x03)Pa04 = Pao * (1 - x04)Pa05 = Pao * (1 - x05)Pa06 = Pao * (1 - x06)




Pa41 = Pao * (1 - x41)Pa42 = Pao * (1 - x42)Pa43 = Pao * (1 - x43)

Pa44 = Pao * (1 - x44)Pa45 = Pao * (1 - x45)Pa46 = Pao * (1 - x46)


Pb01 = Pbo - 0.5 * Pao * x01Pb02 = Pbo - 0.5 * Pao * x02Pb03 = Pbo - 0.5 * Pao * x03Pb04 = Pbo - 0.5 * Pao * x04Pb05 = Pbo - 0.5 * Pao * x05Pb06 = Pbo - 0.5 * Pao * x06






Pr01 = Pao * x01Pr02 = Pao * x02

Pr03 = Pao * x03Pr04 = Pao * x04Pr05 = Pao * x05Pr06 = Pao * x06

Pr11 = Pao * x11Pr12 = Pao * x12Pr13 = Pao * x13Pr14 = Pao * x14Pr15 = Pao * x15Pr16 = Pao * x16





f(x01) = 2 * (x11 - 2 * x01 + x01) / dr ^ 2 + pi1 * (x02 - 2 * x01 + x00) / dz ^ 2 + pi2 * (x01 - x00) / dz + pi3 * (K101 * Pb01 * Pa01 * (1 - Pr01 / (Pa01 * (Pb01 ^ 0.5) * Kp01))) / (22.414 * (1 + K201 * Pa01 + K301 * Pr01) ^ 2)f(x02) = 2 * (x12 - 2 * x02 + x02) / dr ^ 2 + pi1 * (x03 - 2 * x02 + x01) / dz ^ 2 + pi2 * (x02 - x01) / dz + pi3 * (K102 * Pb02 * Pa02 * (1 - Pr02 / (Pa02 * (Pb02 ^ 0.5) * Kp02))) / (22.414 * (1 + K202 * Pa02 + K302 * Pr02) ^ 2)f(x03) = 2 * (x13 - 2 * x03 + x03) / dr ^ 2 + pi1 * (x04 - 2 * x03 + x02) / dz ^ 2 + pi2 * (x03 - x02) / dz + pi3 * (K103 * Pb03 * Pa03 * (1 - Pr03 / (Pa03 * (Pb03 ^ 0.5) * Kp03))) / (22.414 * (1 + K203 * Pa03 + K303 * Pr03) ^ 2)f(x04) = 2 * (x14 - 2 * x04 + x04) / dr ^ 2 + pi1 * (x05 - 2 * x04 + x03) / dz ^ 2 + pi2 * (x04 - x03) / dz + pi3 * (K104 * Pb04 * Pa04 * (1 - Pr04 / (Pa04 * (Pb04 ^ 0.5) * Kp04))) / (22.414 * (1 + K204 * Pa04 + K304 * Pr04) ^ 2)

f(x05) = 2 * (x15 - 2 * x05 + x05) / dr ^ 2 + pi1 * (x06 - 2 * x05 + x04) / dz ^ 2 + pi2 * (x05 - x04) / dz + pi3 * (K105 * Pb05 * Pa05 * (1 - Pr05 / (Pa05 * (Pb05 ^ 0.5) * Kp05))) / (22.414 * (1 + K205 * Pa05 + K305 * Pr05) ^ 2)f(x06) = 2 * (x16 - 2 * x06 + x06) / dr ^ 2 + pi1 * (x06 - 2 * x06 + x05) / dz ^ 2 + pi2 * (x06 - x05) / dz + pi3 * (K106 * Pb06 * Pa06 * (1 - Pr06 / (Pa06 * (Pb06 ^ 0.5) * Kp06))) / (22.414 * (1 + K206 * Pa06 + K306 * Pr06) ^ 2)f(T01) = 2 * (T11 - 2 * T01 + T01) / dr ^ 2 + pi4 * (T02 - 2 * T01 + T00) / dz ^ 2 + pi5 * (T01 - T00) / dz + pi6 * (K101 * Pb01 * Pa01 * (1 - Pr01 / (Pa01 * (Pb01 ^ 0.5) * Kp01))) / (22.414 * (1 + K201 * Pa01 + K301 * Pr01) ^ 2)f(T02) = 2 * (T12 - 2 * T02 + T02) / dr ^ 2 + pi4 * (T03 - 2 * T02 + T01) / dz ^ 2 + pi5 * (T02 - T01) / dz + pi6 * (K102 * Pb02 * Pa02 * (1 - Pr02 / (Pa02 * (Pb02 ^ 0.5) * Kp02))) / (22.414 * (1 + K202 * Pa02 + K302 * Pr02) ^ 2)f(T03) = 2 * (T13 - 2 * T03 + T03) / dr ^ 2 + pi4 * (T04 - 2 * T03 + T02) / dz ^ 2 + pi5 * (T03 - T02) / dz + pi6 * (K103 * Pb03 * Pa03 * (1 - Pr03 / (Pa03 * (Pb03 ^ 0.5) * Kp03))) / (22.414 * (1 + K203 * Pa03 + K303 * Pr03) ^ 2)f(T04) = 2 * (T14 - 2 * T04 + T04) / dr ^ 2 + pi4 * (T05 - 2 * T04 + T03) / dz ^ 2 + pi5 * (T04 - T03) / dz + pi6 * (K104 * Pb04 * Pa04 * (1 - Pr04 / (Pa04 * (Pb04 ^ 0.5) * Kp04))) / (22.414 * (1 + K204 * Pa04 + K304 * Pr04) ^ 2)f(T05) = 2 * (T15 - 2 * T05 + T05) / dr ^ 2 + pi4 * (T06 - 2 * T05 + T04) / dz ^ 2 + pi5 * (T05 - T04) / dz + pi6 * (K105 * Pb05 * Pa05 * (1 - Pr05 / (Pa05 * (Pb05 ^ 0.5) * Kp05))) / (22.414 * (1 + K205 * Pa05 + K305 * Pr05) ^ 2)f(T06) = 2 * (T16 - 2 * T06 + T06) / dr ^ 2 + pi4 * (T06 - 2 * T06 + T05) / dz ^ 2 + pi5 * (T06 - T05) / dz + pi6 * (K106 * Pb06 * Pa06 * (1 - Pr06 / (Pa06 * (Pb06 ^ 0.5) * Kp06))) / (22.414 * (1 + K206 * Pa06 + K306 * Pr06) ^ 2)

f(x11) = (x21 - 2 * x11 + x01) / dr ^ 2 + (x11 - x01) / (1 * dr ^ 2) + pi1 * (x12 - 2 * x11 + x10) / dz ^ 2 + pi2 * (x11 - x10) / dz + pi3 * (K111 * Pb11 * Pa11 * (1 - Pr11 / (Pa11 * (Pb11 ^ 0.5) * Kp11))) / (22.414 * (1 + K211 * Pa11 + K311 * Pr11) ^ 2)f(x12) = (x22 - 2 * x12 + x02) / dr ^ 2 + (x12 - x02) / (1 * dr ^ 2) + pi1 * (x13 - 2 * x12 + x11) / dz ^ 2 + pi2 * (x12 - x11) / dz + pi3 * (K112 * Pb12 * Pa12 * (1 - Pr12 / (Pa12 * (Pb12 ^ 0.5) * Kp12))) / (22.414 * (1 + K212 * Pa12 + K312 * Pr12) ^ 2)f(x13) = (x23 - 2 * x13 + x03) / dr ^ 2 + (x13 - x03) / (1 * dr ^ 2) + pi1 * (x14 - 2 * x13 + x12) / dz ^ 2 + pi2 * (x13 - x12) / dz + pi3 * (K113 * Pb13 * Pa13 * (1 - Pr13 / (Pa13 * (Pb13 ^ 0.5) * Kp13))) / (22.414 * (1 + K213 * Pa13 + K313 * Pr13) ^ 2)f(x14) = (x24 - 2 * x14 + x04) / dr ^ 2 + (x14 - x04) / (1 * dr ^ 2) + pi1 * (x15 - 2 * x14 + x13) / dz ^ 2 + pi2 * (x14 - x13) / dz + pi3 * (K114 * Pb14 * Pa14 * (1 - Pr14 / (Pa14 * (Pb14 ^ 0.5) * Kp14))) / (22.414 * (1 + K214 * Pa14 + K314 * Pr14) ^ 2)f(x15) = (x25 - 2 * x15 + x05) / dr ^ 2 + (x15 - x05) / (1 * dr ^ 2) + pi1 * (x16 - 2 * x15 + x14) / dz ^ 2 + pi2 * (x15 - x14) / dz + pi3 * (K115 * Pb15 * Pa15 * (1 - Pr15 / (Pa15 * (Pb15 ^ 0.5) * Kp15))) / (22.414 * (1 + K215 * Pa15 + K315 * Pr15) ^ 2)f(x16) = (x26 - 2 * x16 + x06) / dr ^ 2 + (x16 - x06) / (1 * dr ^ 2) + pi1 * (x16 - 2 * x16 + x15) / dz ^ 2 + pi2 * (x16 - x15) / dz + pi3 * (K116 * Pb16 * Pa16 * (1 - Pr16 / (Pa16 * (Pb16 ^ 0.5) * Kp16))) / (22.414 * (1 + K216 * Pa16 + K316 * Pr16) ^ 2)f(T11) = (T21 - 2 * T11 + T01) / dr ^ 2 + (T11 - T01) / (1 * dr ^ 2) + pi4 * (T12 - 2 * T11 + T10) / dz ^ 2 + pi5 * (T11 - T10) / dz + pi6 * (K111 * Pb11 * Pa11 * (1 - Pr11 / (Pa11 * (Pb11 ^ 0.5) * Kp11))) / (22.414 * (1 + K211 * Pa11 + K311 * Pr11) ^ 2)f(T12) = (T22 - 2 * T12 + T02) / dr ^ 2 + (T12 - T02) / (1 * dr ^ 2) + pi4 * (T13 - 2 * T12 + T11) / dz ^ 2 + pi5 * (T12 - T11) / dz + pi6 * (K112 * Pb12 * Pa12 * (1 - Pr12 / (Pa12 * (Pb12 ^ 0.5) * Kp12))) / (22.414 * (1 + K212 * Pa12 + K312 * Pr12) ^ 2)f(T13) = (T23 - 2 * T13 + T03) / dr ^ 2 + (T13 - T03) / (1 * dr ^ 2) + pi4 * (T14 - 2 * T13 + T12) / dz ^ 2 + pi5 * (T13 - T12) / dz + pi6 * (K113 * Pb13 * Pa13 * (1 - Pr13 / (Pa13 * (Pb13 ^ 0.5) * Kp13))) / (22.414 * (1 + K213 * Pa13 + K313 * Pr13) ^ 2)f(T14) = (T24 - 2 * T14 + T04) / dr ^ 2 + (T14 - T04) / (1 * dr ^ 2) + pi4 * (T15 - 2 * T14 + T13) / dz ^ 2 + pi5 * (T14 - T13) / dz + pi6 * (K114 * Pb14 * Pa14 * (1 - Pr14 / (Pa14 * (Pb14 ^ 0.5) * Kp14))) / (22.414 * (1 + K214 * Pa14 + K314 * Pr14) ^ 2)

f(T15) = (T25 - 2 * T15 + T05) / dr ^ 2 + (T15 - T05) / (1 * dr ^ 2) + pi4 * (T16 - 2 * T15 + T14) / dz ^ 2 + pi5 * (T15 - T14) / dz + pi6 * (K115 * Pb15 * Pa15 * (1 - Pr15 / (Pa15 * (Pb15 ^ 0.5) * Kp15))) / (22.414 * (1 + K215 * Pa15 + K315 * Pr15) ^ 2)f(T16) = (T26 - 2 * T16 + T06) / dr ^ 2 + (T16 - T06) / (1 * dr ^ 2) + pi4 * (T16 - 2 * T16 + T15) / dz ^ 2 + pi5 * (T16 - T15) / dz + pi6 * (K116 * Pb16 * Pa16 * (1 - Pr16 / (Pa16 * (Pb16 ^ 0.5) * Kp16))) / (22.414 * (1 + K216 * Pa16 + K316 * Pr16) ^ 2)

f(x21) = (x31 - 2 * x21 + x11) / dr ^ 2 + (x21 - x11) / (2 * dr ^ 2) + pi1 * (x22 - 2 * x21 + x20) / dz ^ 2 + pi2 * (x21 - x20) / dz + pi3 * (K121 * Pb21 * Pa21 * (1 - Pr21 / (Pa21 * (Pb21 ^ 0.5) * Kp21))) / (22.414 * (1 + K221 * Pa21 + K321 * Pr21) ^ 2)f(x22) = (x32 - 2 * x22 + x12) / dr ^ 2 + (x22 - x12) / (2 * dr ^ 2) + pi1 * (x23 - 2 * x22 + x21) / dz ^ 2 + pi2 * (x22 - x21) / dz + pi3 * (K122 * Pb22 * Pa22 * (1 - Pr22 / (Pa22 * (Pb22 ^ 0.5) * Kp22))) / (22.414 * (1 + K222 * Pa22 + K322 * Pr22) ^ 2)f(x23) = (x33 - 2 * x23 + x13) / dr ^ 2 + (x23 - x13) / (2 * dr ^ 2) + pi1 * (x24 - 2 * x23 + x22) / dz ^ 2 + pi2 * (x23 - x22) / dz + pi3 * (K123 * Pb23 * Pa23 * (1 - Pr23 / (Pa23 * (Pb23 ^ 0.5) * Kp23))) / (22.414 * (1 + K223 * Pa23 + K323 * Pr23) ^ 2)f(x24) = (x34 - 2 * x24 + x14) / dr ^ 2 + (x24 - x14) / (2 * dr ^ 2) + pi1 * (x25 - 2 * x24 + x23) / dz ^ 2 + pi2 * (x24 - x23) / dz + pi3 * (K124 * Pb24 * Pa24 * (1 - Pr24 / (Pa24 * (Pb24 ^ 0.5) * Kp24))) / (22.414 * (1 + K224 * Pa24 + K324 * Pr24) ^ 2)f(x25) = (x35 - 2 * x25 + x15) / dr ^ 2 + (x25 - x15) / (2 * dr ^ 2) + pi1 * (x26 - 2 * x25 + x24) / dz ^ 2 + pi2 * (x25 - x24) / dz + pi3 * (K125 * Pb25 * Pa25 * (1 - Pr25 / (Pa25 * (Pb25 ^ 0.5) * Kp25))) / (22.414 * (1 + K225 * Pa25 + K325 * Pr25) ^ 2)f(x26) = (x36 - 2 * x26 + x16) / dr ^ 2 + (x26 - x16) / (2 * dr ^ 2) + pi1 * (x26 - 2 * x26 + x25) / dz ^ 2 + pi2 * (x26 - x25) / dz + pi3 * (K126 * Pb26 * Pa26 * (1 - Pr26 / (Pa26 * (Pb26 ^ 0.5) * Kp26))) / (22.414 * (1 + K226 * Pa26 + K326 * Pr26) ^ 2)f(T21) = (T31 - 2 * T21 + T11) / dr ^ 2 + (T21 - T11) / (2 * dr ^ 2) + pi4 * (T22 - 2 * T21 + T20) / dz ^ 2 + pi5 * (T21 - T20) / dz + pi6 * (K121 * Pb21 * Pa21 * (1 - Pr21 / (Pa21 * (Pb21 ^ 0.5) * Kp21))) / (22.414 * (1 + K221 * Pa21 + K321 * Pr21) ^ 2)f(T22) = (T32 - 2 * T22 + T12) / dr ^ 2 + (T22 - T12) / (2 * dr ^ 2) + pi4 * (T23 - 2 * T22 + T21) / dz ^ 2 + pi5 * (T22 - T21) / dz + pi6 * (K122 * Pb22 * Pa22 * (1 - Pr22 / (Pa22 * (Pb22 ^ 0.5) * Kp22))) / (22.414 * (1 + K222 * Pa22 + K322 * Pr22) ^ 2)f(T23) = (T33 - 2 * T23 + T13) / dr ^ 2 + (T23 - T13) / (2 * dr ^ 2) + pi4 * (T24 - 2 * T23 + T22) / dz ^ 2 + pi5 * (T23 - T22) / dz + pi6 * (K123 * Pb23 * Pa23 * (1 - Pr23 / (Pa23 * (Pb23 ^ 0.5) * Kp23))) / (22.414 * (1 + K223 * Pa23 + K323 * Pr23) ^ 2)f(T24) = (T34 - 2 * T24 + T14) / dr ^ 2 + (T24 - T14) / (2 * dr ^ 2) + pi4 * (T25 - 2 * T24 + T23) / dz ^ 2 + pi5 * (T24 - T23) / dz + pi6 * (K124 * Pb24 * Pa24 * (1 - Pr24 / (Pa24 * (Pb24 ^ 0.5) * Kp24))) / (22.414 * (1 + K224 * Pa24 + K324 * Pr24) ^ 2)f(T25) = (T35 - 2 * T25 + T15) / dr ^ 2 + (T25 - T15) / (2 * dr ^ 2) + pi4 * (T26 - 2 * T25 + T24) / dz ^ 2 + pi5 * (T25 - T24) / dz + pi6 * (K125 * Pb25 * Pa25 * (1 - Pr25 / (Pa25 * (Pb25 ^ 0.5) * Kp25))) / (22.414 * (1 + K225 * Pa25 + K325 * Pr25) ^ 2)f(T26) = (T36 - 2 * T26 + T16) / dr ^ 2 + (T26 - T16) / (2 * dr ^ 2) + pi4 * (T26 - 2 * T26 + T25) / dz ^ 2 + pi5 * (T26 - T25) / dz + pi6 * (K126 * Pb26 * Pa26 * (1 - Pr26 / (Pa26 * (Pb26 ^ 0.5) * Kp26))) / (22.414 * (1 + K226 * Pa26 + K326 * Pr26) ^ 2)

f(x31) = (x41 - 2 * x31 + x21) / dr ^ 2 + (x31 - x21) / (3 * dr ^ 2) + pi1 * (x32 - 2 * x31 + x30) / dz ^ 2 + pi2 * (x31 - x30) / dz + pi3 * (K131 * Pb31 * Pa31 * (1 - Pr31 / (Pa31 * (Pb31 ^ 0.5) * Kp31))) / (22.414 * (1 + K231 * Pa31 + K331 * Pr31) ^ 2)f(x32) = (x42 - 2 * x32 + x22) / dr ^ 2 + (x32 - x22) / (3 * dr ^ 2) + pi1 * (x33 - 2 * x32 + x31) / dz ^ 2 + pi2 * (x32 - x31) / dz + pi3 * (K132 * Pb32 * Pa32 * (1 - Pr32 / (Pa32 * (Pb32 ^ 0.5) * Kp32))) / (22.414 * (1 + K232 * Pa32 + K332 * Pr32) ^ 2)f(x33) = (x43 - 2 * x33 + x23) / dr ^ 2 + (x33 - x23) / (3 * dr ^ 2) + pi1 * (x34 - 2 * x33 + x32) / dz ^ 2 + pi2 * (x33 - x32) / dz + pi3 * (K133 * Pb33 * Pa33 * (1 - Pr33 / (Pa33 * (Pb33 ^ 0.5) * Kp33))) / (22.414 * (1 + K233 * Pa33 + K333 * Pr33) ^ 2)

f(x34) = (x44 - 2 * x34 + x24) / dr ^ 2 + (x34 - x24) / (3 * dr ^ 2) + pi1 * (x35 - 2 * x34 + x33) / dz ^ 2 + pi2 * (x34 - x33) / dz + pi3 * (K134 * Pb34 * Pa34 * (1 - Pr34 / (Pa34 * (Pb34 ^ 0.5) * Kp34))) / (22.414 * (1 + K234 * Pa34 + K334 * Pr34) ^ 2)f(x35) = (x45 - 2 * x35 + x25) / dr ^ 2 + (x35 - x25) / (3 * dr ^ 2) + pi1 * (x36 - 2 * x35 + x34) / dz ^ 2 + pi2 * (x35 - x34) / dz + pi3 * (K135 * Pb35 * Pa35 * (1 - Pr35 / (Pa35 * (Pb35 ^ 0.5) * Kp35))) / (22.414 * (1 + K235 * Pa35 + K335 * Pr35) ^ 2)f(x36) = (x46 - 2 * x36 + x26) / dr ^ 2 + (x36 - x26) / (3 * dr ^ 2) + pi1 * (x36 - 2 * x36 + x35) / dz ^ 2 + pi2 * (x36 - x35) / dz + pi3 * (K136 * Pb36 * Pa36 * (1 - Pr36 / (Pa36 * (Pb36 ^ 0.5) * Kp36))) / (22.414 * (1 + K236 * Pa36 + K336 * Pr36) ^ 2)f(T31) = (T41 - 2 * T31 + T21) / dr ^ 2 + (T31 - T21) / (3 * dr ^ 2) + pi4 * (T32 - 2 * T31 + T30) / dz ^ 2 + pi5 * (T31 - T30) / dz + pi6 * (K131 * Pb31 * Pa31 * (1 - Pr31 / (Pa31 * (Pb31 ^ 0.5) * Kp31))) / (22.414 * (1 + K231 * Pa31 + K331 * Pr31) ^ 2)f(T32) = (T42 - 2 * T32 + T22) / dr ^ 2 + (T32 - T22) / (3 * dr ^ 2) + pi4 * (T33 - 2 * T32 + T31) / dz ^ 2 + pi5 * (T32 - T31) / dz + pi6 * (K132 * Pb32 * Pa32 * (1 - Pr32 / (Pa32 * (Pb32 ^ 0.5) * Kp32))) / (22.414 * (1 + K232 * Pa32 + K332 * Pr32) ^ 2)f(T33) = (T43 - 2 * T33 + T23) / dr ^ 2 + (T33 - T23) / (3 * dr ^ 2) + pi4 * (T34 - 2 * T33 + T32) / dz ^ 2 + pi5 * (T33 - T32) / dz + pi6 * (K133 * Pb33 * Pa33 * (1 - Pr33 / (Pa33 * (Pb33 ^ 0.5) * Kp33))) / (22.414 * (1 + K233 * Pa33 + K333 * Pr33) ^ 2)f(T34) = (T44 - 2 * T34 + T24) / dr ^ 2 + (T34 - T24) / (3 * dr ^ 2) + pi4 * (T35 - 2 * T34 + T33) / dz ^ 2 + pi5 * (T34 - T33) / dz + pi6 * (K134 * Pb34 * Pa34 * (1 - Pr34 / (Pa34 * (Pb34 ^ 0.5) * Kp34))) / (22.414 * (1 + K234 * Pa34 + K334 * Pr34) ^ 2)f(T35) = (T45 - 2 * T35 + T25) / dr ^ 2 + (T35 - T25) / (3 * dr ^ 2) + pi4 * (T36 - 2 * T35 + T34) / dz ^ 2 + pi5 * (T35 - T34) / dz + pi6 * (K135 * Pb35 * Pa35 * (1 - Pr35 / (Pa35 * (Pb35 ^ 0.5) * Kp35))) / (22.414 * (1 + K235 * Pa35 + K335 * Pr35) ^ 2)f(T36) = (T46 - 2 * T36 + T26) / dr ^ 2 + (T36 - T26) / (3 * dr ^ 2) + pi4 * (T36 - 2 * T36 + T35) / dz ^ 2 + pi5 * (T36 - T35) / dz + pi6 * (K136 * Pb36 * Pa36 * (1 - Pr36 / (Pa36 * (Pb36 ^ 0.5) * Kp36))) / (22.414 * (1 + K236 * Pa36 + K336 * Pr36) ^ 2)

f(x41) = (x51 - 2 * x41 + x31) / dr ^ 2 + (x41 - x31) / (4 * dr ^ 2) + pi1 * (x42 - 2 * x41 + x40) / dz ^ 2 + pi2 * (x41 - x40) / dz + pi3 * (K141 * Pb41 * Pa41 * (1 - Pr41 / (Pa41 * (Pb41 ^ 0.5) * Kp41))) / (22.414 * (1 + K241 * Pa41 + K341 * Pr41) ^ 2)f(x42) = (x52 - 2 * x42 + x32) / dr ^ 2 + (x42 - x32) / (4 * dr ^ 2) + pi1 * (x43 - 2 * x42 + x41) / dz ^ 2 + pi2 * (x42 - x41) / dz + pi3 * (K142 * Pb42 * Pa42 * (1 - Pr42 / (Pa42 * (Pb42 ^ 0.5) * Kp42))) / (22.414 * (1 + K242 * Pa42 + K342 * Pr42) ^ 2)f(x43) = (x53 - 2 * x43 + x33) / dr ^ 2 + (x43 - x33) / (4 * dr ^ 2) + pi1 * (x44 - 2 * x43 + x42) / dz ^ 2 + pi2 * (x43 - x42) / dz + pi3 * (K143 * Pb43 * Pa43 * (1 - Pr43 / (Pa43 * (Pb43 ^ 0.5) * Kp43))) / (22.414 * (1 + K243 * Pa43 + K343 * Pr43) ^ 2)f(x44) = (x54 - 2 * x44 + x34) / dr ^ 2 + (x44 - x34) / (4 * dr ^ 2) + pi1 * (x45 - 2 * x44 + x43) / dz ^ 2 + pi2 * (x44 - x43) / dz + pi3 * (K144 * Pb44 * Pa44 * (1 - Pr44 / (Pa44 * (Pb44 ^ 0.5) * Kp44))) / (22.414 * (1 + K244 * Pa44 + K344 * Pr44) ^ 2)f(x45) = (x55 - 2 * x45 + x35) / dr ^ 2 + (x45 - x35) / (4 * dr ^ 2) + pi1 * (x46 - 2 * x45 + x44) / dz ^ 2 + pi2 * (x45 - x44) / dz + pi3 * (K145 * Pb45 * Pa45 * (1 - Pr45 / (Pa45 * (Pb45 ^ 0.5) * Kp45))) / (22.414 * (1 + K245 * Pa45 + K345 * Pr45) ^ 2)f(x46) = (x56 - 2 * x46 + x36) / dr ^ 2 + (x46 - x36) / (4 * dr ^ 2) + pi1 * (x46 - 2 * x46 + x45) / dz ^ 2 + pi2 * (x46 - x45) / dz + pi3 * (K146 * Pb46 * Pa46 * (1 - Pr46 / (Pa46 * (Pb46 ^ 0.5) * Kp46))) / (22.414 * (1 + K246 * Pa46 + K346 * Pr46) ^ 2)f(T41) = (T51 - 2 * T41 + T31) / dr ^ 2 + (T41 - T31) / (4 * dr ^ 2) + pi4 * (T42 - 2 * T41 + T40) / dz ^ 2 + pi5 * (T41 - T40) / dz + pi6 * (K141 * Pb41 * Pa41 * (1 - Pr41 / (Pa41 * (Pb41 ^ 0.5) * Kp41))) / (22.414 * (1 + K241 * Pa41 + K341 * Pr41) ^ 2)f(T42) = (T52 - 2 * T42 + T32) / dr ^ 2 + (T42 - T32) / (4 * dr ^ 2) + pi4 * (T43 - 2 * T42 + T41) / dz ^ 2 + pi5 * (T42 - T41) / dz + pi6 * (K142 * Pb42 * Pa42 * (1 - Pr42 / (Pa42 * (Pb42 ^ 0.5) * Kp42))) / (22.414 * (1 + K242 * Pa42 + K342 * Pr42) ^ 2)f(T43) = (T53 - 2 * T43 + T33) / dr ^ 2 + (T43 - T33) / (4 * dr ^ 2) + pi4 * (T44 - 2 * T43 + T42) / dz ^ 2 + pi5 * (T43 - T42) / dz + pi6 * (K143 * Pb43 * Pa43 * (1 - Pr43 / (Pa43 * (Pb43 ^ 0.5) * Kp43))) / (22.414 * (1 + K243 * Pa43 + K343 * Pr43) ^ 2)

f(T44) = (T54 - 2 * T44 + T34) / dr ^ 2 + (T44 - T34) / (4 * dr ^ 2) + pi4 * (T45 - 2 * T44 + T43) / dz ^ 2 + pi5 * (T44 - T43) / dz + pi6 * (K144 * Pb44 * Pa44 * (1 - Pr44 / (Pa44 * (Pb44 ^ 0.5) * Kp44))) / (22.414 * (1 + K244 * Pa44 + K344 * Pr44) ^ 2)f(T45) = (T55 - 2 * T45 + T35) / dr ^ 2 + (T45 - T35) / (4 * dr ^ 2) + pi4 * (T46 - 2 * T45 + T44) / dz ^ 2 + pi5 * (T45 - T44) / dz + pi6 * (K145 * Pb45 * Pa45 * (1 - Pr45 / (Pa45 * (Pb45 ^ 0.5) * Kp45))) / (22.414 * (1 + K245 * Pa45 + K345 * Pr45) ^ 2)f(T46) = (T56 - 2 * T46 + T36) / dr ^ 2 + (T46 - T36) / (4 * dr ^ 2) + pi4 * (T46 - 2 * T46 + T45) / dz ^ 2 + pi5 * (T46 - T45) / dz + pi6 * (K146 * Pb46 * Pa46 * (1 - Pr46 / (Pa46 * (Pb46 ^ 0.5) * Kp46))) / (22.414 * (1 + K246 * Pa46 + K346 * Pr46) ^ 2)

f(x51) = (x51 - 2 * x51 + x41) / dr ^ 2 + (x51 - x41) / (5 * dr ^ 2) + pi1 * (x52 - 2 * x51 + x50) / dz ^ 2 + pi2 * (x51 - x50) / dz + pi3 * (K151 * Pb51 * Pa51 * (1 - Pr51 / (Pa51 * (Pb51 ^ 0.5) * Kp51))) / (22.414 * (1 + K251 * Pa51 + K351 * Pr51) ^ 2)f(x52) = (x52 - 2 * x52 + x42) / dr ^ 2 + (x52 - x42) / (5 * dr ^ 2) + pi1 * (x53 - 2 * x52 + x51) / dz ^ 2 + pi2 * (x52 - x51) / dz + pi3 * (K152 * Pb52 * Pa52 * (1 - Pr52 / (Pa52 * (Pb52 ^ 0.5) * Kp52))) / (22.414 * (1 + K252 * Pa52 + K352 * Pr52) ^ 2)f(x53) = (x53 - 2 * x53 + x43) / dr ^ 2 + (x53 - x43) / (5 * dr ^ 2) + pi1 * (x54 - 2 * x53 + x52) / dz ^ 2 + pi2 * (x53 - x52) / dz + pi3 * (K153 * Pb53 * Pa53 * (1 - Pr53 / (Pa53 * (Pb53 ^ 0.5) * Kp53))) / (22.414 * (1 + K253 * Pa53 + K353 * Pr53) ^ 2)f(x54) = (x54 - 2 * x54 + x44) / dr ^ 2 + (x54 - x44) / (5 * dr ^ 2) + pi1 * (x55 - 2 * x54 + x53) / dz ^ 2 + pi2 * (x54 - x53) / dz + pi3 * (K154 * Pb54 * Pa54 * (1 - Pr54 / (Pa54 * (Pb54 ^ 0.5) * Kp54))) / (22.414 * (1 + K254 * Pa54 + K354 * Pr54) ^ 2)f(x55) = (x55 - 2 * x55 + x45) / dr ^ 2 + (x55 - x45) / (5 * dr ^ 2) + pi1 * (x56 - 2 * x55 + x54) / dz ^ 2 + pi2 * (x55 - x54) / dz + pi3 * (K155 * Pb55 * Pa55 * (1 - Pr55 / (Pa55 * (Pb55 ^ 0.5) * Kp55))) / (22.414 * (1 + K255 * Pa55 + K355 * Pr55) ^ 2)f(x56) = (x56 - 2 * x56 + x46) / dr ^ 2 + (x56 - x46) / (5 * dr ^ 2) + pi1 * (x56 - 2 * x56 + x55) / dz ^ 2 + pi2 * (x56 - x55) / dz + pi3 * (K156 * Pb56 * Pa56 * (1 - Pr56 / (Pa56 * (Pb56 ^ 0.5) * Kp56))) / (22.414 * (1 + K256 * Pa56 + K356 * Pr56) ^ 2)f(T51) = (T61 - 2 * T51 + T41) / dr ^ 2 + (T51 - T41) / (5 * dr ^ 2) + pi4 * (T52 - 2 * T51 + T50) / dz ^ 2 + pi5 * (T51 - T50) / dz + pi6 * (K151 * Pb51 * Pa51 * (1 - Pr51 / (Pa51 * (Pb51 ^ 0.5) * Kp51))) / (22.414 * (1 + K251 * Pa51 + K351 * Pr51) ^ 2)f(T52) = (T62 - 2 * T52 + T42) / dr ^ 2 + (T52 - T42) / (5 * dr ^ 2) + pi4 * (T53 - 2 * T52 + T51) / dz ^ 2 + pi5 * (T52 - T51) / dz + pi6 * (K152 * Pb52 * Pa52 * (1 - Pr52 / (Pa52 * (Pb52 ^ 0.5) * Kp52))) / (22.414 * (1 + K252 * Pa52 + K352 * Pr52) ^ 2)f(T53) = (T63 - 2 * T53 + T43) / dr ^ 2 + (T53 - T43) / (5 * dr ^ 2) + pi4 * (T54 - 2 * T53 + T52) / dz ^ 2 + pi5 * (T53 - T52) / dz + pi6 * (K153 * Pb53 * Pa53 * (1 - Pr53 / (Pa53 * (Pb53 ^ 0.5) * Kp53))) / (22.414 * (1 + K253 * Pa53 + K353 * Pr53) ^ 2)f(T54) = (T64 - 2 * T54 + T44) / dr ^ 2 + (T54 - T44) / (5 * dr ^ 2) + pi4 * (T55 - 2 * T54 + T53) / dz ^ 2 + pi5 * (T54 - T53) / dz + pi6 * (K154 * Pb54 * Pa54 * (1 - Pr54 / (Pa54 * (Pb54 ^ 0.5) * Kp54))) / (22.414 * (1 + K254 * Pa54 + K354 * Pr54) ^ 2)f(T55) = (T65 - 2 * T55 + T45) / dr ^ 2 + (T55 - T45) / (5 * dr ^ 2) + pi4 * (T56 - 2 * T55 + T54) / dz ^ 2 + pi5 * (T55 - T54) / dz + pi6 * (K155 * Pb55 * Pa55 * (1 - Pr55 / (Pa55 * (Pb55 ^ 0.5) * Kp55))) / (22.414 * (1 + K255 * Pa55 + K355 * Pr55) ^ 2)f(T56) = (T66 - 2 * T56 + T46) / dr ^ 2 + (T56 - T46) / (5 * dr ^ 2) + pi4 * (T56 - 2 * T56 + T55) / dz ^ 2 + pi5 * (T56 - T55) / dz + pi6 * (K156 * Pb56 * Pa56 * (1 - Pr56 / (Pa56 * (Pb56 ^ 0.5) * Kp56))) / (22.414 * (1 + K256 * Pa56 + K356 * Pr56) ^ 2)

T61 = T51 - Bi*(T51 - Tw)/5T62 = T52 - Bi*(T52 - Tw)/5T63 = T53 - Bi*(T53 - Tw)/5T64 = T54 - Bi*(T54 - Tw)/5T65 = T55 - Bi*(T55 - Tw)/5T66 = T56 - Bi*(T56 - Tw)/5

x00 = 0x10 = 0x20 = 0x30 = 0x40 = 0x50 = 0x01(0) = 0x02(0) = 0x03(0) = 0x04(0) = 0x05(0) = 0x06(0) = 0x11(0) = 0x12(0) = 0x13(0) = 0x14(0) = 0x15(0) = 0x16(0) = 0x21(0) = 0x22(0) = 0x23(0) = 0x24(0) = 0x25(0) = 0x26(0) = 0x31(0) = 0x32(0) = 0x33(0) = 0x34(0) = 0x35(0) = 0x36(0) = 0x41(0) = 0x42(0) = 0x43(0) = 0x44(0) = 0x45(0) = 0x46(0) = 0x51(0) = 0x52(0) = 0x53(0) = 0x54(0) = 0x55(0) = 0x56(0) = 0

T00 = 400T10 = 400T20 = 400T30 = 400T40 = 400T50 = 400T01(0) = 400T02(0) = 400T03(0) = 400T04(0) = 400T05(0) = 400T06(0) = 400

T11(0) = 400T12(0) = 400T13(0) = 400T14(0) = 400T15(0) = 400T16(0) = 400T21(0) = 400T22(0) = 400T23(0) = 400T24(0) = 400T25(0) = 400T26(0) = 400T31(0) = 400T32(0) = 400T33(0) = 400T34(0) = 400T35(0) = 400T36(0) = 400T41(0) = 400T42(0) = 400T43(0) = 400T44(0) = 400T45(0) = 400T46(0) = 400T51(0) = 400T52(0) = 400T53(0) = 400T54(0) = 400T55(0) = 400T56(0) = 400

Con las tablas obtenidas por polymath, procedemos a graficar

DATOS OBTENIDOS EN POLYMATH

ro r1 r2 r3 r4 r5

Radio 0 0.00523 0.01046 0.01569 0.02092 0.02615

Z x0 x1 x2 x3 x4 x5 xprom

0 0 0 0 0 0 0 0

0.0254 0.033205 0.0304528 0.0241723 0.0141693 0.0037283 0.0004082 0.01768932

0.0508 0.0621238 0.0510427 0.0331441 0.0156018 0.0044601 0.0008516 0.02787068

0.0762 0.0743783 0.0565632 0.0337676 0.0158213 0.0051107 0.0013177 0.0311598

0.1016 0.0730974 0.0547159 0.0329347 0.0159783 0.0056959 0.0017967 0.03070315

0.127 0.0684806 0.0517973 0.0320125 0.0160927 0.0062261 0.0022813 0.02948175

0.1524 0.0639686 0.0490635 0.031104 0.0161683 0.006707 0.0027627 0.02829568

ro r1 r2 r3 r4 r5

Radio 0 0.00523 0.01046 0.01569 0.02092 0.02615


0 400 400 400 400 400 400 400

0.0254 408.0895 406.6659 402.9154 394.5097 374.5033 320.175 384.476467

0.0508 411.5191 407.0443 397.5037 380.2837 347.0625 281.0043 370.736267

0.0762 407.4392 400.5537 387.003 363.9168 324.0797 259.7039 357.11605

0.1016 398.1714 390.3222 374.4462 347.7533 305.7875 246.8546 343.8892

0.127 387.0574 378.6604 361.2166 332.7341 291.2583 238.3402 331.5445

0.1524 375.5467 366.7055 348.3545 319.4386 279.7556 232.3394 320.356717

0

0.01524

0.03048

0.04572

0.060960.0762

0.09144

0.10668

0.12192

0.137160.1524

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

X vs Z

T0T1T2T3T4T5

Z en metros

Conv

ersio

n

0

0.01524

0.03048

0.04572

0.060960.0762

0.09144

0.10668

0.12192

0.137160.1524

220.0240.0260.0280.0300.0320.0340.0360.0380.0400.0420.0

T vs Z

T0T1T2T3T4T5

Z en metros

Tem

pera

tura

0

0.005230000000000010.01046

0.01569

0.02092

0.026150.000.010.020.030.040.050.060.070.08


00.02540.05080.07620.10160.1270.1524

Radio en Metros

Conv

ersio

n

0

0.005230000000000010.01046

0.01569

0.02092

0.02615230.0

270.0

310.0

350.0

390.0

430.0


00.02540.05080.07620.10160.1270.1524

Radio en Metros

Tem

pera

tura

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.180

0.005

0.01

0.015

0.02

0.025

0.03

0.035

X promedio

Z en metros

Conv

ersio

n Pr

omed

io

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18300

310

320

330

340

350

360

370

380

390

400

T promedio

Z en metros

Tmep

erat

ura

Prom

edio



Se obtuvo las siguientes tablas

CASO I CASO II CASO III

Z Xprom z xprom z xprom0.000 0.0000 0.0000 0.000 0 0

0.0150.024525

7 0.0152 0.000 0.0254 0

0.0300.050584

2 0.0305 0.000 0.0508 0

0.0460.088613

9 0.0457 0.000 0.0762 0

0.0610.159912

4 0.0610 0.000 0.1016 0

0.0760.320790

4 0.0762 0.000 0.127 0

0.091 0.624388 0.0914 0.000 0.1524 0

0.1070.775453

3 0.1067 0.000

0.1220.787835

6 0.1219 0.000

0.137 0.788415 0.1372 0.000

0.152 0.788441 0.1524 0.000

-0.015 0.000 0.015 0.030 0.046 0.061 0.076 0.091 0.107 0.122 0.137 0.1520.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

X vs Z

Caso 1Caso 2Caso 3

Longitud del reactor metros

Conv

ersio

n

Se obtuvo las siguientes tablas

CASO I CASO II CASO III

Z Tprom z Tprom z Tprom0.000 400.00 0.0000 0 0 0

0.015 406.8598 0.0152 0 0.0254 0

0.030 414.1483 0.0305 0 0.0508 0

0.046 424.7851 0.0457 0 0.0762 0

0.061 444.7272 0.0610 0 0.1016 0

0.076 489.7244 0.0762 0 0.127 0

0.091 574.6401 0.0914 0 0.1524 0

0.107 616.8927 0.1067 0

0.122 620.356 0.1219 0

0.137 620.5181 0.1372 0

0.152 620.5253 0.1524 0

-0.015 0.000 0.015 0.030 0.046 0.061 0.076 0.091 0.107 0.122 0.137 0.1520.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

X vs Z

Caso 1Caso 2Caso 3

Longitud del reactor metros

Conv

ersio

n

PUNTOS CALIENTES

PUNTOS CALIENTES

TABLAS OBTENIDAS EN POLYMATH

390ºC 400ºC 410ºC r z r z r z

10 0.002 0 0 0 0.0239 0.008 1 0 1 0.0238 0.02 2 0 2 0.0237 0.035 3 0 3 0.0236 0.055 4 0 4 0.0255 0.08 5 0 4 0.054 0.12 6 0 3 0.0883 0.135 7 0 2 0.1162 0.151 8 0 1 0.129

9 0 0 0.134420ºC 10 0r z 10 0

0 0.041 9 01 0.042 8 0.0052 0.045 7 0.0152 0.101 6 0.029

1 0.12 5 0.0470 0.126 4 0.074

3 0.105430ºC 2 0.126 440ºC r z 1 0.138 r z

0 0.056 0 0.143 0 0.0681 0.058 1 0.0791 0.11 1 0.0960 0.119 0 0.11

GRAFICA DE PUNTOS CALIENTES

CONCLUSIONES

La presión que utilizamos para el trabajo fue de 1.6 atm. Estuvimos probando con

varias presiones, y esta fue la que mejor se adecuo a las graficas dadas por el

profesor.

Comparando los tres casos, concluimos que el caso que mejor se ajusta al trabajo es

el caso II. Del cual se obtiene una conversión de 0.798 a la presión de 1.6 atm.

En el caso III se observo una conversión mínima (muy baja) esto se debía al igualar

el peclet axial con el peclet radial, (no teníamos datos del peclet radial de masa y

calor).

Los valores mas altos en el caso III son los valores centrales, tal como se observa en

la grafica.

FIN…

CASO IIIMODIFICADO

CON DIFUSION AXIAL Y RADIAL



Calculated values of NLE variables

Variable

Value f(x) Initial Guess

1 x01 0.0736259

6.149E-07 0

2 x02 0.1577011

6.391E-07 0

3 x03 0.2533425

-3.403E-08

0

4 x04 0.3513065

-5.805E-08

0

5 x05 0.4294447

-3.635E-06

0

6 x06 0.4663684

-4.697E-06

0

7 T01 408.209 4.188E-05 400.

8 T02 419.8046 4.35E-05 400.

9 T03 441.2436 -2.367E-06

400.

10

T04 475.2143 -4.003E-06

400.

11 T05 506.0725

-0.0002476

400.

12 T06 499.5153

-0.0003198

400.

13

x11 0.0362447

1.555E-08 0

14

x12 0.0727259

8.195E-09 0

15

x13 0.1066693

3.7E-09 0

16

x14 0.1333403

1.401E-09 0

17

x15 0.1471837

3.765E-09 0

18

x16 0.1474863

-2.762E-08

0

19

T11 409.9081 1.057E-06 400.

20

T12 419.9525 5.617E-07 400.

21

T13 429.1264 2.454E-07 400.

22

T14 436.5353 1.001E-07 400.

23

T15 435.7941 2.489E-07 400.

24

T16 413.4572 -1.906E-06

400.

25

x21 0.0150895

9.863E-09 0

26

x22 0.0253191

1.312E-08 0

27

x23 0.0306477

2.094E-08 0

28

x24 0.0331322

1.616E-08 0

29

x25 0.0344738

3.405E-09 0

30

x26 0.0351303

1.471E-10 0

31

T21 407.8283 6.716E-07 400.

32

T22 408.5118 8.976E-07 400.

33

T23 402.4555 1.428E-06 400.

34

T24 393.5392 1.103E-06 400.

35

T25 383.775 2.274E-07 400.

36

T26 371.0321 1.168E-08 400.

37

x31 0.0060563

3.242E-08 0

38

x32 0.0079257

7.98E-08 0

39

x33 0.0086074

1.466E-08 0

40

x34 0.0091252

4.258E-10 0

41

x35 0.0095016

9.255E-12 0

42

x36 0.0097058

2.187E-13 0

43

T31 398.5568 2.209E-06 400.

44

T32 386.2546 5.432E-06 400.

45

T33 370.9801 9.97E-07 400.

46

T34 356.2591 2.592E-08 400.

47

T35 342.8984 4.634E-09 400.

48

T36 330.5216 -1.519E-09

400.

49

x41 0.0014707

2.232E-06 0

50

x42 0.0017463

6.058E-08 0

51

x43 0.0019836

6.279E-11 0

52

x44 0.0021775

-1.435E-13

0

53

x45 0.0023179

1.022E-12 0

54

x46 0.0023939

-6.128E-13

0

55

T41 376.2505 0.0001521

400.

56

T42 349.3648 4.13E-06 400.

57

T43 326.983 8.268E-09 400.

58

T44 309.4037 1.234E-09 400.

59

T45 295.6876 -9.838E-10

400.

60

T46 284.7872 1.332E-09 400.

61

x51 0.000118 4.238E-08 0

62

x52 0.0002281

-4.72E-14 0

63

x53 0.000326 9.864E-14 0

64

x54 0.0004069

-1.167E-13

0

65

x55 0.0004659

4.008E-14 0

66

x56 0.0004981

3.054E-14 0

67

T51 320.3186 2.889E-06 400.

68

T52 281.4645 -5.52E-09 400.

69

T53 260.4833 -4.2E-09 400.

70

T54 247.9473 2.224E-09 400.

71

T55 239.7515 5.852E-11 400.

72

T56 233.993 1.339E-09 400.

Variable

Value

1 Pmz 0.01

2 E 0.5

3 R 0.082

4 Phz 9.

5 Phr 4.4

6 dp 0.003175

7 db 1025.

8 G 1709.

9 Us 2914.393

10 dH -9.489E+04

11 Cpf 1.09

12 df 0.5864

13 Tw 197.

14 pi5 -1385.827

15 Pmr 9.6

16 pi4 0.4888889

17 pi1 960.

18 Bi 6.67

19 pi6 7.235E+07

20 pi2 -6047.244

21 dz 0.0254

22 dr 0.00523

23 Tin 673.

24 Pao 0.1105

25 Cao 0.0020023

26 P 1.6

27 ya 0.065

28 pi3 1.062E+06

29 Pbo 0.31416

30 K101 61.91454

31 K102 70.826

32 K103 89.77875

33 K104 127.1352

34 K105 169.8609

35 K106 160.0284

36 K111 63.16464

37 K112 70.94545

38 K113 78.65786

39 K114 85.32788

40 K115 84.64238

41 K116 65.8368

42 K121 61.63703

43 K122 62.13592

44 K123 57.81914

45 K124 51.87981

46 K125 45.91801

47 K126 38.9382

48 K131 55.16234

49 K132 47.37996

50 K133 38.91154

51 K134 31.89568

52 K135 26.41136

53 K136 22.01137

54 K141 41.69075

55 K142 28.966

56 K143 20.86502

57 K144 15.84317

58 K145 12.63015

59 K146 10.46477

60 K151 18.83306

61 K152 9.867191

62 K153 6.692647

63 K154 5.228571

64 K155 4.420328

65 K156 3.915641

66 K201 14.87236

67 K202 12.03401

68 K203 8.283879

69 K204 4.789504

70 K205 3.034829

71 K206 3.333624

72 K211 14.41147

73 K212 12.00211

74 K213 10.20183

75 K214 8.974493

76 K215 9.089221

77 K216 13.50112

78 K221 14.97795

79 K222 14.789

80 K223 16.56477

81 K224 19.64795

82 K225 23.81261

83 K226 30.87275

84 K231 17.83845

85 K232 22.6658

86 K233 30.90608

87 K234 42.26924

88 K235 56.89405

89 K236 75.80611

90 K241 27.72428

91 K242 49.1949

92 K243 82.4678

93 K244 127.232

94 K245 181.8075

95 K246 244.4789

96 K251 96.90825

97 K252 268.1985

98 K253 494.2702

99 K254 729.1366

100

K255 949.8571

101

K256 1149.675

102

K301 236.225

103

K302 64.87775

104

K303 6.644177

105

K304 0.2346565

10 K305 0.014495

6

107

K306 0.025709

108

K311 194.9381

109

K312 63.83557

110

K313 23.67893

111

K314 10.83071

112

K315 11.70366

113

K316 130.9079

114

K321 246.6463

115

K322 228.2596

116

K323 455.9817

117

K324 1292.186

118

K325 4176.448

119

K326 2.037E+04

120

K331 716.5909

121

K332 3090.28

122

K333 2.05E+04

123

K334 1.386E+05

124

K335 8.493E+05

125

K336 4.894E+06

126

K341 1.057E+04

127

K342 3.497E+05

128

K343 8.182E+06

12 K344 1.154E+0

9 8

130

K345 1.019E+09

131

K346 6.207E+09

132

K351 2.19E+07

133

K352 1.092E+10

134

K353 4.556E+11

135

K354 4.885E+12

136

K355 2.453E+13

137

K356 7.865E+13

138

Kp01 368.0263

139

Kp02 278.8054

140

Kp03 170.8751

141

Kp04 83.31468

142

Kp05 45.80652

143

Kp06 51.80783

144

Kp11 353.1462

145

Kp12 277.8371

146

Kp13 224.5206

147

Kp14 189.7895

148

Kp15 192.9767

149

Kp16 324.1911

150

Kp21 371.4556

151

Kp22 365.3241

15 Kp23 423.8803

2

153

Kp24 530.1936

154

Kp25 682.1725

155

Kp26 958.8266

156

Kp31 467.1136

157

Kp32 639.4263

158

Kp33 960.1839

159

Kp34 1447.547

160

Kp35 2137.049

161

Kp36 3113.302

162

Kp41 832.7102

163

Kp42 1766.141

164

Kp43 3476.802

165

Kp44 6138.577

166

Kp45 9801.704

167

Kp46 1.445E+04

168

Kp51 4295.899

169

Kp52 1.632E+04

170

Kp53 3.637E+04

171

Kp54 6.055E+04

172

Kp55 8.564E+04

173

Kp56 1.1E+05

174

Pa01 0.1023643

17 Pa02 0.093074

5

176

Pa03 0.0825057

177

Pa04 0.0716806

178

Pa05 0.0630464

179

Pa06 0.0589663

180

Pa11 0.106495

181

Pa12 0.1024638

182

Pa13 0.098713

183

Pa14 0.0957659

184

Pa15 0.0942362

185

Pa16 0.0942028

186

Pa21 0.1088326

187

Pa22 0.1077022

188

Pa23 0.1071134

189

Pa24 0.1068389

190

Pa25 0.1066906

191

Pa26 0.1066181

192

Pa31 0.1098308

193

Pa32 0.1096242

194

Pa33 0.1095489

195

Pa34 0.1094917

196

Pa35 0.1094501

197

Pa36 0.1094275

19 Pa41 0.110337

8 5

199

Pa42 0.110307

200

Pa43 0.1102808

201

Pa44 0.1102594

202

Pa45 0.1102439

203

Pa46 0.1102355

204

Pa51 0.110487

205

Pa52 0.1104748

206

Pa53 0.110464

207

Pa54 0.110455

208

Pa55 0.1104485

209

Pa56 0.110445

210

Pb01 0.3100922

211

Pb02 0.305447

212

Pb03 0.3001628

213

Pb04 0.2947503

214

Pb05 0.2904332

215

Pb06 0.2883931

216

Pb11 0.3121575

217

Pb12 0.3101419

218

Pb13 0.3082665

219

Pb14 0.306793

220

Pb15 0.3060281

22 Pb16 0.306011

1 4

222

Pb21 0.3133263

223

Pb22 0.3127611

224

Pb23 0.3124667

225

Pb24 0.3123294

226

Pb25 0.3122553

227

Pb26 0.3122191

228

Pb31 0.3138254

229

Pb32 0.3137221

230

Pb33 0.3136844

231

Pb34 0.3136558

232

Pb35 0.313635

233

Pb36 0.3136238

234

Pb41 0.3140787

235

Pb42 0.3140635

236

Pb43 0.3140504

237

Pb44 0.3140397

238

Pb45 0.3140319

239

Pb46 0.3140277

240

Pb51 0.3141535

241

Pb52 0.3141474

242

Pb53 0.314142

243

Pb54 0.3141375

24 Pb55 0.314134

4 3

245

Pb56 0.3141325

246

Pr01 0.0081357

247

Pr02 0.017426

248

Pr03 0.0279943

249

Pr04 0.0388194

250

Pr05 0.0474536

251

Pr06 0.0515337

252

Pr11 0.004005

253

Pr12 0.0080362

254

Pr13 0.011787

255

Pr14 0.0147341

256

Pr15 0.0162638

257

Pr16 0.0162972

258

Pr21 0.0016674

259

Pr22 0.0027978

260

Pr23 0.0033866

261

Pr24 0.0036611

262

Pr25 0.0038094

263

Pr26 0.0038819

264

Pr31 0.0006692

265

Pr32 0.0008758

266

Pr33 0.0009511

26 Pr34 0.001008

7 3

268

Pr35 0.0010499

269

Pr36 0.0010725

270

Pr41 0.0001625

271

Pr42 0.000193

272

Pr43 0.0002192

273

Pr44 0.0002406

274

Pr45 0.0002561

275

Pr46 0.0002645

276

Pr51 1.304E-05

277

Pr52 2.52E-05

278

Pr53 3.602E-05

279

Pr54 4.496E-05

280

Pr55 5.149E-05

281

Pr56 5.504E-05

282

T61 155.8116

283

T62 168.7888

284

T63 175.7966

285

T64 179.9836

286

T65 182.721

287

T66 184.6443

288

x00 0

289

x10 0

29 x20 0

0

291

x30 0

292

x40 0

293

x50 0

294

T00 400.

295

T10 400.

296

T20 400.

297

T30 400.

298

T40 400.

299

T50 400.

Nonlinear equations

1 f(x01) = 2 * (x11 - 2 * x01 + x01) / dr ^ 2 + pi1 * (x02 - 2 * x01 + x00) / dz ^ 2 + pi2 * (x01 - x00) / dz + pi3 * (K101 * Pb01 * Pa01 * (1 - Pr01 / (Pa01 * (Pb01 ^ 0.5) * Kp01))) / (22.414 * (1 + K201 * Pa01 + K301 * Pr01) ^ 2) = 0






7 f(T01) = 2 * (T11 - 2 * T01 + T01) / dr ^ 2 + pi4 * (T02 - 2 * T01 + T00) / dz ^ 2 + pi5 * (T01 - T00) / dz + pi6 * (K101 * Pb01 * Pa01 * (1 - Pr01 / (Pa01 * (Pb01 ^ 0.5) * Kp01))) / (22.414 * (1 + K201 * Pa01 + K301 * Pr01) ^ 2) = 0



10 f(T04) = 2 * (T14 - 2 * T04 + T04) / dr ^ 2 + pi4 * (T05 - 2 * T04 + T03) / dz ^ 2 +

pi5 * (T04 - T03) / dz + pi6 * (K104 * Pb04 * Pa04 * (1 - Pr04 / (Pa04 * (Pb04 ^ 0.5) * Kp04))) / (22.414 * (1 + K204 * Pa04 + K304 * Pr04) ^ 2) = 0



13 f(x11) = (x21 - 2 * x11 + x01) / dr ^ 2 + (x11 - x01) / (1 * dr ^ 2) + pi1 * (x12 - 2 * x11 + x10) / dz ^ 2 + pi2 * (x11 - x10) / dz + pi3 * (K111 * Pb11 * Pa11 * (1 - Pr11 / (Pa11 * (Pb11 ^ 0.5) * Kp11))) / (22.414 * (1 + K211 * Pa11 + K311 * Pr11) ^ 2) = 0






19 f(T11) = (T21 - 2 * T11 + T01) / dr ^ 2 + (T11 - T01) / (1 * dr ^ 2) + pi4 * (T12 - 2 * T11 + T10) / dz ^ 2 + pi5 * (T11 - T10) / dz + pi6 * (K111 * Pb11 * Pa11 * (1 - Pr11 / (Pa11 * (Pb11 ^ 0.5) * Kp11))) / (22.414 * (1 + K211 * Pa11 + K311 * Pr11) ^ 2) = 0








27 f(x23) = (x33 - 2 * x23 + x13) / dr ^ 2 + (x23 - x13) / (2 * dr ^ 2) + pi1 * (x24 - 2 *

x23 + x22) / dz ^ 2 + pi2 * (x23 - x22) / dz + pi3 * (K123 * Pb23 * Pa23 * (1 - Pr23 / (Pa23 * (Pb23 ^ 0.5) * Kp23))) / (22.414 * (1 + K223 * Pa23 + K323 * Pr23) ^ 2) = 0

















44 f(T32) = (T42 - 2 * T32 + T22) / dr ^ 2 + (T32 - T22) / (3 * dr ^ 2) + pi4 * (T33 - 2 *

T32 + T31) / dz ^ 2 + pi5 * (T32 - T31) / dz + pi6 * (K132 * Pb32 * Pa32 * (1 - Pr32 / (Pa32 * (Pb32 ^ 0.5) * Kp32))) / (22.414 * (1 + K232 * Pa32 + K332 * Pr32) ^ 2) = 0

















61 f(x51) = (x51 - 2 * x51 + x41) / dr ^ 2 + (x51 - x41) / (5 * dr ^ 2) + pi1 * (x52 - 2 *

x51 + x50) / dz ^ 2 + pi2 * (x51 - x50) / dz + pi3 * (K151 * Pb51 * Pa51 * (1 - Pr51 / (Pa51 * (Pb51 ^ 0.5) * Kp51))) / (22.414 * (1 + K251 * Pa51 + K351 * Pr51) ^ 2) = 0












Explicit equations 1 Pmz = 0.01

Peclet de Masa en Direccion Axial

2 E = 0.5

Porosidad del lecho

3 R = 0.082

4 Phz = 9

Peclet de Calor en Direccion Axial

5 Phr = 4.4

Peclet de calor en direccion radial

6 dp = 0.003175

7 db = 1025

Densidad del lecho

8 G = 1709

Flujo masico

9 Us = 2914.393

Velocidad

10 dH = -94886

Entalpia

11 Cpf = 1.09

Capacidad Calorifica del Fluido

12 df = 0.5864

Densidad del Fluido

13 Tw = 197

Temperatura de la pared

14 pi5 = -Us * df * Cpf / (dp * G * Cpf / Phr)

15 Pmr = 9.6

Peclet de masa en direccion radial

16 pi4 = (dp * G * Cpf / Phz) / (dp * G * Cpf / Phr)

17 pi1 = ( Us * dp / Pmz) / (Us * dp / Pmr)

18 Bi = 6.67

Numero de Biot

19 pi6 = db * (-dH) / (dp * G * Cpf / Phr)

20 pi2 = -Us/(E * (Us * dp / Pmr))

21 dz = (0.1524)/6

22 dr = 0.02615 / 5

23 Tin = 400 +273

24 Pao = 1.7 * 0.065

25 Cao = Pao / (R * Tin )

26 P = 1.6

27 ya = 0.065

28 pi3 = db / (Cao * E * (Us * dp / Pmr))

29 Pbo = (1 - ya) * P * 0.21

30 K101 = exp(12.16 - 5473 / (T01 + 273))

31 K102 = exp(12.16 - 5473 / (T02 + 273))

32 K103 = exp(12.16 - 5473 / (T03 + 273))

33 K104 = exp(12.16 - 5473 / (T04 + 273))

34 K105 = exp(12.16 - 5473 / (T05 + 273))

35 K106 = exp(12.16 - 5473 / (T06 + 273))

36 K111 = exp(12.16 - 5473 / (T11 + 273))

37 K112 = exp(12.16 - 5473 / (T12 + 273))

38 K113 = exp(12.16 - 5473 / (T13 + 273))

39 K114 = exp(12.16 - 5473 / (T14 + 273))

40 K115 = exp(12.16 - 5473 / (T15 + 273))

41 K116 = exp(12.16 - 5473 / (T16 + 273))

42 K121 = exp(12.16 - 5473 / (T21 + 273))

43 K122 = exp(12.16 - 5473 / (T22 + 273))

44 K123 = exp(12.16 - 5473 / (T23 + 273))

45 K124 = exp(12.16 - 5473 / (T24 + 273))

46 K125 = exp(12.16 - 5473 / (T25 + 273))

47 K126 = exp(12.16 - 5473 / (T26 + 273))

48 K131 = exp(12.16 - 5473 / (T31 + 273))

49 K132 = exp(12.16 - 5473 / (T32 + 273))

50 K133 = exp(12.16 - 5473 / (T33 + 273))

51 K134 = exp(12.16 - 5473 / (T34 + 273))

52 K135 = exp(12.16 - 5473 / (T35 + 273))

53 K136 = exp(12.16 - 5473 / (T36 + 273))

54 K141 = exp(12.16 - 5473 / (T41 + 273))

55 K142 = exp(12.16 - 5473 / (T42 + 273))

56 K143 = exp(12.16 - 5473 / (T43 + 273))

57 K144 = exp(12.16 - 5473 / (T44 + 273))

58 K145 = exp(12.16 - 5473 / (T45 + 273))

59 K146 = exp(12.16 - 5473 / (T46 + 273))

60 K151 = exp(12.16 - 5473 / (T51 + 273))

61 K152 = exp(12.16 - 5473 / (T52 + 273))

62 K153 = exp(12.16 - 5473 / (T53 + 273))

63 K154 = exp(12.16 - 5473 / (T54 + 273))

64 K155 = exp(12.16 - 5473 / (T55 + 273))

65 K156 = exp(12.16 - 5473 / (T56 + 273))

66 K201 = exp(-9.953 + 8619 / (T01 + 273))

67 K202 = exp(-9.953 + 8619 / (T02 + 273))

68 K203 = exp(-9.953 + 8619 / (T03 + 273))

69 K204 = exp(-9.953 + 8619 / (T04 + 273))

70 K205 = exp(-9.953 + 8619 / (T05 + 273))

71 K206 = exp(-9.953 + 8619 / (T06 + 273))

72 K211 = exp(-9.953 + 8619 / (T11 + 273))

73 K212 = exp(-9.953 + 8619 / (T12 + 273))

74 K213 = exp(-9.953 + 8619 / (T13 + 273))

75 K214 = exp(-9.953 + 8619 / (T14 + 273))

76 K215 = exp(-9.953 + 8619 / (T15 + 273))

77 K216 = exp(-9.953 + 8619 / (T16 + 273))

78 K221 = exp(-9.953 + 8619 / (T21 + 273))

79 K222 = exp(-9.953 + 8619 / (T22 + 273))

80 K223 = exp(-9.953 + 8619 / (T23 + 273))

81 K224 = exp(-9.953 + 8619 / (T24 + 273))

82 K225 = exp(-9.953 + 8619 / (T25 + 273))

83 K226 = exp(-9.953 + 8619 / (T26 + 273))

84 K231 = exp(-9.953 + 8619 / (T31 + 273))

85 K232 = exp(-9.953 + 8619 / (T32 + 273))

86 K233 = exp(-9.953 + 8619 / (T33 + 273))

87 K234 = exp(-9.953 + 8619 / (T34 + 273))

88 K235 = exp(-9.953 + 8619 / (T35 + 273))

89 K236 = exp(-9.953 + 8619 / (T36 + 273))

90 K241 = exp(-9.953 + 8619 / (T41 + 273))

91 K242 = exp(-9.953 + 8619 / (T42 + 273))

92 K243 = exp(-9.953 + 8619 / (T43 + 273))

93 K244 = exp(-9.953 + 8619 / (T44 + 273))

94 K245 = exp(-9.953 + 8619 / (T45 + 273))

95 K246 = exp(-9.953 + 8619 / (T46 + 273))

96 K251 = exp(-9.953 + 8619 / (T51 + 273))

97 K252 = exp(-9.953 + 8619 / (T52 + 273))

98 K253 = exp(-9.953 + 8619 / (T53 + 273))

99 K254 = exp(-9.953 + 8619 / (T54 + 273))

100

K255 = exp(-9.953 + 8619 / (T55 + 273))

101

K256 = exp(-9.953 + 8619 / (T56 + 273))

102

K301 = exp(-71.745 + 52596 / (T01 + 273))

103

K302 = exp(-71.745 + 52596 / (T02 + 273))

104

K303 = exp(-71.745 + 52596 / (T03 + 273))

105

K304 = exp(-71.745 + 52596 / (T04 + 273))

106

K305 = exp(-71.745 + 52596 / (T05 + 273))

107

K306 = exp(-71.745 + 52596 / (T06 + 273))

108

K311 = exp(-71.745 + 52596 / (T11 + 273))

109

K312 = exp(-71.745 + 52596 / (T12 + 273))

110

K313 = exp(-71.745 + 52596 / (T13 + 273))

111

K314 = exp(-71.745 + 52596 / (T14 + 273))

112

K315 = exp(-71.745 + 52596 / (T15 + 273))

113

K316 = exp(-71.745 + 52596 / (T16 + 273))

114

K321 = exp(-71.745 + 52596 / (T21 + 273))

115

K322 = exp(-71.745 + 52596 / (T22 + 273))

116

K323 = exp(-71.745 + 52596 / (T23 + 273))

117

K324 = exp(-71.745 + 52596 / (T24 + 273))

118

K325 = exp(-71.745 + 52596 / (T25 + 273))

119

K326 = exp(-71.745 + 52596 / (T26 + 273))

120

K331 = exp(-71.745 + 52596 / (T31 + 273))

121

K332 = exp(-71.745 + 52596 / (T32 + 273))

122

K333 = exp(-71.745 + 52596 / (T33 + 273))

123

K334 = exp(-71.745 + 52596 / (T34 + 273))

124

K335 = exp(-71.745 + 52596 / (T35 + 273))

125

K336 = exp(-71.745 + 52596 / (T36 + 273))

126

K341 = exp(-71.745 + 52596 / (T41 + 273))

127

K342 = exp(-71.745 + 52596 / (T42 + 273))

128

K343 = exp(-71.745 + 52596 / (T43 + 273))

129

K344 = exp(-71.745 + 52596 / (T44 + 273))

130

K345 = exp(-71.745 + 52596 / (T45 + 273))

131

K346 = exp(-71.745 + 52596 / (T46 + 273))

132

K351 = exp(-71.745 + 52596 / (T51 + 273))

133

K352 = exp(-71.745 + 52596 / (T52 + 273))

134

K353 = exp(-71.745 + 52596 / (T53 + 273))

135

K354 = exp(-71.745 + 52596 / (T54 + 273))

136

K355 = exp(-71.745 + 52596 / (T55 + 273))

137

K356 = exp(-71.745 + 52596 / (T56 + 273))

138

Kp01 = exp(11300 / (T01 + 273) - 10.68)

139

Kp02 = exp(11300 / (T02 + 273) - 10.68)

140

Kp03 = exp(11300 / (T03 + 273) - 10.68)

141

Kp04 = exp(11300 / (T04 + 273) - 10.68)

14 Kp05 = exp(11300 / (T05 + 273) - 10.68)

2

143

Kp06 = exp(11300 / (T06 + 273) - 10.68)

144

Kp11 = exp(11300 / (T11 + 273) - 10.68)

145

Kp12 = exp(11300 / (T12 + 273) - 10.68)

146

Kp13 = exp(11300 / (T13 + 273) - 10.68)

147

Kp14 = exp(11300 / (T14 + 273) - 10.68)

148

Kp15 = exp(11300 / (T15 + 273) - 10.68)

149

Kp16 = exp(11300 / (T16 + 273) - 10.68)

150

Kp21 = exp(11300 / (T21 + 273) - 10.68)

151

Kp22 = exp(11300 / (T22 + 273) - 10.68)

152

Kp23 = exp(11300 / (T23 + 273) - 10.68)

153

Kp24 = exp(11300 / (T24 + 273) - 10.68)

154

Kp25 = exp(11300 / (T25 + 273) - 10.68)

155

Kp26 = exp(11300 / (T26 + 273) - 10.68)

156

Kp31 = exp(11300 / (T31 + 273) - 10.68)

157

Kp32 = exp(11300 / (T32 + 273) - 10.68)

158

Kp33 = exp(11300 / (T33 + 273) - 10.68)

159

Kp34 = exp(11300 / (T34 + 273) - 10.68)

160

Kp35 = exp(11300 / (T35 + 273) - 10.68)

161

Kp36 = exp(11300 / (T36 + 273) - 10.68)

162

Kp41 = exp(11300 / (T41 + 273) - 10.68)

163

Kp42 = exp(11300 / (T42 + 273) - 10.68)

164

Kp43 = exp(11300 / (T43 + 273) - 10.68)

165

Kp44 = exp(11300 / (T44 + 273) - 10.68)

166

Kp45 = exp(11300 / (T45 + 273) - 10.68)

167

Kp46 = exp(11300 / (T46 + 273) - 10.68)

168

Kp51 = exp(11300 / (T51 + 273) - 10.68)

169

Kp52 = exp(11300 / (T52 + 273) - 10.68)

170

Kp53 = exp(11300 / (T53 + 273) - 10.68)

171

Kp54 = exp(11300 / (T54 + 273) - 10.68)

172

Kp55 = exp(11300 / (T55 + 273) - 10.68)

173

Kp56 = exp(11300 / (T56 + 273) - 10.68)

174

Pa01 = Pao * (1 - x01)

175

Pa02 = Pao * (1 - x02)

176

Pa03 = Pao * (1 - x03)

177

Pa04 = Pao * (1 - x04)

178

Pa05 = Pao * (1 - x05)

179

Pa06 = Pao * (1 - x06)

180

Pa11 = Pao * (1 - x11)

181

Pa12 = Pao * (1 - x12)

182

Pa13 = Pao * (1 - x13)

183

Pa14 = Pao * (1 - x14)

184

Pa15 = Pao * (1 - x15)

185

Pa16 = Pao * (1 - x16)

186

Pa21 = Pao * (1 - x21)

187

Pa22 = Pao * (1 - x22)

188

Pa23 = Pao * (1 - x23)

189

Pa24 = Pao * (1 - x24)

190

Pa25 = Pao * (1 - x25)

19 Pa26 = Pao * (1 - x26)

1

192

Pa31 = Pao * (1 - x31)

193

Pa32 = Pao * (1 - x32)

194

Pa33 = Pao * (1 - x33)

195

Pa34 = Pao * (1 - x34)

196

Pa35 = Pao * (1 - x35)

197

Pa36 = Pao * (1 - x36)

198

Pa41 = Pao * (1 - x41)

199

Pa42 = Pao * (1 - x42)

200

Pa43 = Pao * (1 - x43)

201

Pa44 = Pao * (1 - x44)

202

Pa45 = Pao * (1 - x45)

203

Pa46 = Pao * (1 - x46)

204

Pa51 = Pao * (1 - x51)

205

Pa52 = Pao * (1 - x52)

206

Pa53 = Pao * (1 - x53)

207

Pa54 = Pao * (1 - x54)

208

Pa55 = Pao * (1 - x55)

209

Pa56 = Pao * (1 - x56)

210

Pb01 = Pbo - 0.5 * Pao * x01

211

Pb02 = Pbo - 0.5 * Pao * x02

212

Pb03 = Pbo - 0.5 * Pao * x03

213

Pb04 = Pbo - 0.5 * Pao * x04

214

Pb05 = Pbo - 0.5 * Pao * x05

215

Pb06 = Pbo - 0.5 * Pao * x06

216

Pb11 = Pbo - 0.5 * Pao * x11

217

Pb12 = Pbo - 0.5 * Pao * x12

218

Pb13 = Pbo - 0.5 * Pao * x13

219

Pb14 = Pbo - 0.5 * Pao * x14

220

Pb15 = Pbo - 0.5 * Pao * x15

221

Pb16 = Pbo - 0.5 * Pao * x16

222

Pb21 = Pbo - 0.5 * Pao * x21

223

Pb22 = Pbo - 0.5 * Pao * x22

224

Pb23 = Pbo - 0.5 * Pao * x23

225

Pb24 = Pbo - 0.5 * Pao * x24

226

Pb25 = Pbo - 0.5 * Pao * x25

227

Pb26 = Pbo - 0.5 * Pao * x26

228

Pb31 = Pbo - 0.5 * Pao * x31

229

Pb32 = Pbo - 0.5 * Pao * x32

230

Pb33 = Pbo - 0.5 * Pao * x33

231

Pb34 = Pbo - 0.5 * Pao * x34

232

Pb35 = Pbo - 0.5 * Pao * x35

233

Pb36 = Pbo - 0.5 * Pao * x36

234

Pb41 = Pbo - 0.5 * Pao * x41

235

Pb42 = Pbo - 0.5 * Pao * x42

236

Pb43 = Pbo - 0.5 * Pao * x43

237

Pb44 = Pbo - 0.5 * Pao * x44

238

Pb45 = Pbo - 0.5 * Pao * x45

239

Pb46 = Pbo - 0.5 * Pao * x46

24 Pb51 = Pbo - 0.5 * Pao * x51

0

241

Pb52 = Pbo - 0.5 * Pao * x52

242

Pb53 = Pbo - 0.5 * Pao * x53

243

Pb54 = Pbo - 0.5 * Pao * x54

244

Pb55 = Pbo - 0.5 * Pao * x55

245

Pb56 = Pbo - 0.5 * Pao * x56

246

Pr01 = Pao * x01

247

Pr02 = Pao * x02

248

Pr03 = Pao * x03

249

Pr04 = Pao * x04

250

Pr05 = Pao * x05

251

Pr06 = Pao * x06

252

Pr11 = Pao * x11

253

Pr12 = Pao * x12

254

Pr13 = Pao * x13

255

Pr14 = Pao * x14

256

Pr15 = Pao * x15

257

Pr16 = Pao * x16

258

Pr21 = Pao * x21

259

Pr22 = Pao * x22

260

Pr23 = Pao * x23

261

Pr24 = Pao * x24

262

Pr25 = Pao * x25

263

Pr26 = Pao * x26

264

Pr31 = Pao * x31

265

Pr32 = Pao * x32

266

Pr33 = Pao * x33

267

Pr34 = Pao * x34

268

Pr35 = Pao * x35

269

Pr36 = Pao * x36

270

Pr41 = Pao * x41

271

Pr42 = Pao * x42

272

Pr43 = Pao * x43

273

Pr44 = Pao * x44

274

Pr45 = Pao * x45

275

Pr46 = Pao * x46

276

Pr51 = Pao * x51

277

Pr52 = Pao * x52

278

Pr53 = Pao * x53

279

Pr54 = Pao * x54

280

Pr55 = Pao * x55

281

Pr56 = Pao * x56

282

T61 = T51 - Bi*(T51 - Tw)/5

283

T62 = T52 - Bi*(T52 - Tw)/5

284

T63 = T53 - Bi*(T53 - Tw)/5

285

T64 = T54 - Bi*(T54 - Tw)/5

286

T65 = T55 - Bi*(T55 - Tw)/5

287

T66 = T56 - Bi*(T56 - Tw)/5

288

x00 = 0

28 x10 = 0

9

290

x20 = 0

291

x30 = 0

292

x40 = 0

293

x50 = 0

294

T00 = 400

295

T10 = 400

296

T20 = 400

297

T30 = 400

298

T40 = 400

299

T50 = 400

Con las tablas obtenidas por polymath procedemos a graficar

DATOS OBTENIDOS EN POLYMATH

ro r1 r2 r3 r4 r5

Radio 0 0.00523 0.01046 0.01569 0.02092 0.02615

z x0 x1 x2 x3 x4 x5 xprom

0 0 0 0 0 0 0 0

0.02540.073625

90.036244

70.015089

50.006056

30.001470

7 0.000118 0.02210085

0.05080.157701

10.072725

90.025319

10.007925

70.001746

30.000228

1 0.04427437

0.07620.253342

50.106669

30.030647

70.008607

40.001983

6 0.000326 0.06692942

0.10160.351306

50.133340

30.033132

20.009125

20.002177

50.000406

9 0.0882481

0.1270.429444

70.147183

70.034473

80.009501

60.002317

90.000465

9 0.10389793

0.15240.466368

40.147486

30.035130

30.009705

80.002393

90.000498

1 0.1102638

ro r1 r2 r3 r4 r5

Radio 0 0.00523 0.01046 0.01569 0.02092 0.02615


0 400 400 400 400 400 400 400

0.0254 408.209 409.9081 407.8283 398.5568 376.2505 320.3186 386.845217

0.0508 419.8046 419.9525 408.5118 386.2546 349.3648 281.4645 377.5588

0.0762 441.2436 429.1264 402.4555 370.9801 326.983 260.4833 371.87865

0.1016 475.2143 436.5353 393.5392 356.2591 309.4037 247.9473 369.816483

0.127 506.0725 435.7941 383.775 342.8984 295.6876 239.7515 367.32985

0.1524 499.5153 413.4572 371.0321 330.5216 284.7872 233.993 355.551067

0

0.01524

0.03048

0.04572

0.06096

0.0762

0.09144

0.10668

0.12192

0.13716

0.15240.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50 X vs Z

T0T1T2T3T4T5

Z en metros

Conv

ersio

n

0

0.01524

0.03048

0.04572

0.060960.0762

0.09144

0.10668

0.12192

0.137160.1524

220.0

270.0

320.0

370.0

420.0

470.0

520.0

570.0

T vs Z

T0T1T2T3T4T5

Z en metros

Tem

pera

tura

0

0.00523000000000001

0.01046

0.01569

0.02092

0.026150.00

0.10

0.20

0.30

0.40

0.50


00.02540.05080.07620.10160.1270.1524

Radio en Metros

Conv

ersio

n

0

0.005230000000000010.01046

0.01569

0.02092

0.02615230.0270.0310.0350.0390.0430.0470.0510.0


00.02540.05080.07620.10160.1270.1524

Radio en Metros

Tem

pera

tura

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.180

0.02

0.04

0.06

0.08

0.1

0.12

X promedio

Z en metros

Conv

ersio

n Pr

omed

io

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18300

310

320

330

340

350

360

370

380

390

400

T promedio

Z en metros

Tmep

erat

ura P

rom

edio

HALLANDO EL PESO DEL CATALIZADOR

W =V∗ε∗D . .. .. . .. ..(1 )

V= π4∗Z∗d2

Donde:

ε = 0.5 (porosidad)

D = 800Kg/m3 (densidad del catalizador)

Z= 0.1524m (longitud del catalizador)

d = 0.0523m (diámetro del catalizador)

Reemplazando datos en (1)

W =π4∗0 . 1524∗0 . 05232∗0 .5∗800

W =0 .1309 Kg

Simulacion Del Reactor de Lecho Fijo[1]

Documents

Transcript of Simulacion Del Reactor de Lecho Fijo[1]