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
SOLUCION EN POLYMATH
LENGUAJE EN POLYMATH
# 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)
# Para i = 2K12 = exp(12.160 - 5473 / (T2 + 273.15))K22 = exp(-9.953 + 8619 / (T2 + 273.15))K32 = exp(-71.745 + 52596 / (T2 + 273.15))Kp2 = exp(11300 / (T2 + 273.15) - 10.68)Pa2 = Pao * (1 - x2)Pb2 = Pbo - 0.5 * Pao * x2Pc2 = Pao * x2R2 = (K12 * Pb2 * Pa2 * (1 - Pc2 / (Pa2 * Kp2 * (Pb2) ^ 0.5))) / (22.414 * (1 + K22 * Pa2 + K32 * Pc2) ^ 2)
# Para i = 3K13 = exp(12.160 - 5473 / (T3 + 273.15))K23 = exp(-9.953 + 8619 / (T3 + 273.15))K33 = exp(-71.745 + 52596 / (T3 + 273.15))Kp3 = exp(11300 / (T3 + 273.15) - 10.68)Pa3 = Pao * (1 - x3)Pb3 = Pbo - 0.5 * Pao * x3Pc3 = Pao * x3R3 = (K13 * Pb3 * Pa3 * (1 - Pc3 / (Pa3 * Kp3 * (Pb3) ^ 0.5))) / (22.414 * (1 + K23 * Pa3 + K33 * Pc3) ^ 2)
# Para i = 4K14 = exp(12.160 - 5473 / (T4 + 273.15))K24 = exp(-9.953 + 8619 / (T4 + 273.15))K34 = exp(-71.745 + 52596 / (T4 + 273.15))Kp4 = exp(11300 / (T4 + 273.15) - 10.68)Pa4 = Pao * (1 - x4)Pb4 = Pbo - 0.5 * Pao * x4Pc4 = Pao * x4R4 = (K14 * Pb4 * Pa4 * (1 - Pc4 / (Pa4 * Kp4 * (Pb4) ^ 0.5))) / (22.414 * (1 + K24 * Pa4 + K34 * Pc4) ^ 2)
# Para i = 5K15 = exp(12.160 - 5473 / (T5 + 273.15))K25 = exp(-9.953 + 8619 / (T5 + 273.15))K35 = exp(-71.745 + 52596 / (T5 + 273.15))Kp5 = exp(11300 / (T5 + 273.15) - 10.68)Pa5 = Pao * (1 - x5)Pb5 = Pbo - 0.5 * Pao * x5Pc5 = Pao * x5R5 = (K15 * Pb5 * Pa5 * (1 - Pc5 / (Pa5 * Kp5 * (Pb5) ^ 0.5))) / (22.414 * (1 + K25 * Pa5 + K35 * Pc5) ^ 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)
SOLUCION EN POLYMATH
LENGUAJE EN POLYMATH
# 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))
K111 = exp(12.16 - 5473 / (T11 + 273))K112 = exp(12.16 - 5473 / (T12 + 273))K113 = exp(12.16 - 5473 / (T13 + 273))K114 = exp(12.16 - 5473 / (T14 + 273))K115 = exp(12.16 - 5473 / (T15 + 273))K116 = exp(12.16 - 5473 / (T16 + 273))
K121 = exp(12.16 - 5473 / (T21 + 273))K122 = exp(12.16 - 5473 / (T22 + 273))K123 = exp(12.16 - 5473 / (T23 + 273))K124 = exp(12.16 - 5473 / (T24 + 273))K125 = exp(12.16 - 5473 / (T25 + 273))K126 = exp(12.16 - 5473 / (T26 + 273))
K131 = exp(12.16 - 5473 / (T31 + 273))K132 = exp(12.16 - 5473 / (T32 + 273))K133 = exp(12.16 - 5473 / (T33 + 273))K134 = exp(12.16 - 5473 / (T34 + 273))K135 = exp(12.16 - 5473 / (T35 + 273))K136 = exp(12.16 - 5473 / (T36 + 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))
K151 = exp(12.16 - 5473 / (T51 + 273))K152 = exp(12.16 - 5473 / (T52 + 273))K153 = exp(12.16 - 5473 / (T53 + 273))K154 = exp(12.16 - 5473 / (T54 + 273))K155 = exp(12.16 - 5473 / (T55 + 273))K156 = exp(12.16 - 5473 / (T56 + 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))
K211 = exp(-9.953 + 8619 / (T11 + 273))K212 = exp(-9.953 + 8619 / (T12 + 273))K213 = exp(-9.953 + 8619 / (T13 + 273))K214 = exp(-9.953 + 8619 / (T14 + 273))K215 = exp(-9.953 + 8619 / (T15 + 273))K216 = exp(-9.953 + 8619 / (T16 + 273))
K221 = exp(-9.953 + 8619 / (T21 + 273))K222 = exp(-9.953 + 8619 / (T22 + 273))K223 = exp(-9.953 + 8619 / (T23 + 273))K224 = exp(-9.953 + 8619 / (T24 + 273))K225 = exp(-9.953 + 8619 / (T25 + 273))K226 = exp(-9.953 + 8619 / (T26 + 273))
K231 = exp(-9.953 + 8619 / (T31 + 273))K232 = exp(-9.953 + 8619 / (T32 + 273))K233 = exp(-9.953 + 8619 / (T33 + 273))K234 = exp(-9.953 + 8619 / (T34 + 273))K235 = exp(-9.953 + 8619 / (T35 + 273))K236 = exp(-9.953 + 8619 / (T36 + 273))
K241 = exp(-9.953 + 8619 / (T41 + 273))K242 = exp(-9.953 + 8619 / (T42 + 273))K243 = exp(-9.953 + 8619 / (T43 + 273))K244 = exp(-9.953 + 8619 / (T44 + 273))K245 = exp(-9.953 + 8619 / (T45 + 273))K246 = exp(-9.953 + 8619 / (T46 + 273))
K251 = exp(-9.953 + 8619 / (T51 + 273))K252 = exp(-9.953 + 8619 / (T52 + 273))K253 = exp(-9.953 + 8619 / (T53 + 273))K254 = exp(-9.953 + 8619 / (T54 + 273))K255 = exp(-9.953 + 8619 / (T55 + 273))K256 = exp(-9.953 + 8619 / (T56 + 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))
K311 = exp(-71.745 + 52596 / (T11 + 273))K312 = exp(-71.745 + 52596 / (T12 + 273))K313 = exp(-71.745 + 52596 / (T13 + 273))K314 = exp(-71.745 + 52596 / (T14 + 273))K315 = exp(-71.745 + 52596 / (T15 + 273))K316 = exp(-71.745 + 52596 / (T16 + 273))
K321 = exp(-71.745 + 52596 / (T21 + 273))K322 = exp(-71.745 + 52596 / (T22 + 273))K323 = exp(-71.745 + 52596 / (T23 + 273))K324 = exp(-71.745 + 52596 / (T24 + 273))K325 = exp(-71.745 + 52596 / (T25 + 273))K326 = exp(-71.745 + 52596 / (T26 + 273))
K331 = exp(-71.745 + 52596 / (T31 + 273))K332 = exp(-71.745 + 52596 / (T32 + 273))K333 = exp(-71.745 + 52596 / (T33 + 273))K334 = exp(-71.745 + 52596 / (T34 + 273))K335 = exp(-71.745 + 52596 / (T35 + 273))K336 = exp(-71.745 + 52596 / (T36 + 273))
K341 = exp(-71.745 + 52596 / (T41 + 273))K342 = exp(-71.745 + 52596 / (T42 + 273))K343 = exp(-71.745 + 52596 / (T43 + 273))K344 = exp(-71.745 + 52596 / (T44 + 273))K345 = exp(-71.745 + 52596 / (T45 + 273))K346 = exp(-71.745 + 52596 / (T46 + 273))
K351 = exp(-71.745 + 52596 / (T51 + 273))K352 = exp(-71.745 + 52596 / (T52 + 273))K353 = exp(-71.745 + 52596 / (T53 + 273))K354 = exp(-71.745 + 52596 / (T54 + 273))K355 = exp(-71.745 + 52596 / (T55 + 273))K356 = exp(-71.745 + 52596 / (T56 + 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)
Kp11 = exp(11300 / (T11 + 273) - 10.68)Kp12 = exp(11300 / (T12 + 273) - 10.68)Kp13 = exp(11300 / (T13 + 273) - 10.68)Kp14 = exp(11300 / (T14 + 273) - 10.68)Kp15 = exp(11300 / (T15 + 273) - 10.68)Kp16 = exp(11300 / (T16 + 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)
Kp31 = exp(11300 / (T31 + 273) - 10.68)Kp32 = exp(11300 / (T32 + 273) - 10.68)Kp33 = exp(11300 / (T33 + 273) - 10.68)Kp34 = exp(11300 / (T34 + 273) - 10.68)Kp35 = exp(11300 / (T35 + 273) - 10.68)Kp36 = exp(11300 / (T36 + 273) - 10.68)
Kp41 = exp(11300 / (T41 + 273) - 10.68)Kp42 = exp(11300 / (T42 + 273) - 10.68)Kp43 = exp(11300 / (T43 + 273) - 10.68)Kp44 = exp(11300 / (T44 + 273) - 10.68)Kp45 = exp(11300 / (T45 + 273) - 10.68)Kp46 = exp(11300 / (T46 + 273) - 10.68)
Kp51 = exp(11300 / (T51 + 273) - 10.68)Kp52 = exp(11300 / (T52 + 273) - 10.68)Kp53 = exp(11300 / (T53 + 273) - 10.68)Kp54 = exp(11300 / (T54 + 273) - 10.68)Kp55 = exp(11300 / (T55 + 273) - 10.68)Kp56 = exp(11300 / (T56 + 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)
Pa11 = Pao * (1 - x11)Pa12 = Pao * (1 - x12)Pa13 = Pao * (1 - x13)Pa14 = Pao * (1 - x14)Pa15 = Pao * (1 - x15)Pa16 = Pao * (1 - x16)
Pa21 = Pao * (1 - x21)Pa22 = Pao * (1 - x22)Pa23 = Pao * (1 - x23)Pa24 = Pao * (1 - x24)Pa25 = Pao * (1 - x25)Pa26 = Pao * (1 - x26)
Pa31 = Pao * (1 - x31)Pa32 = Pao * (1 - x32)Pa33 = Pao * (1 - x33)Pa34 = Pao * (1 - x34)Pa35 = Pao * (1 - x35)Pa36 = Pao * (1 - x36)
Pa41 = Pao * (1 - x41)Pa42 = Pao * (1 - x42)Pa43 = Pao * (1 - x43)
Pa44 = Pao * (1 - x44)Pa45 = Pao * (1 - x45)Pa46 = Pao * (1 - x46)
Pa51 = Pao * (1 - x51)Pa52 = Pao * (1 - x52)Pa53 = Pao * (1 - x53)Pa54 = Pao * (1 - x54)Pa55 = Pao * (1 - x55)Pa56 = Pao * (1 - x56)
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
Pb11 = Pbo - 0.5 * Pao * x11Pb12 = Pbo - 0.5 * Pao * x12Pb13 = Pbo - 0.5 * Pao * x13Pb14 = Pbo - 0.5 * Pao * x14Pb15 = Pbo - 0.5 * Pao * x15Pb16 = Pbo - 0.5 * Pao * x16
Pb21 = Pbo - 0.5 * Pao * x21Pb22 = Pbo - 0.5 * Pao * x22Pb23 = Pbo - 0.5 * Pao * x23Pb24 = Pbo - 0.5 * Pao * x24Pb25 = Pbo - 0.5 * Pao * x25Pb26 = Pbo - 0.5 * Pao * x26
Pb31 = Pbo - 0.5 * Pao * x31Pb32 = Pbo - 0.5 * Pao * x32Pb33 = Pbo - 0.5 * Pao * x33Pb34 = Pbo - 0.5 * Pao * x34Pb35 = Pbo - 0.5 * Pao * x35Pb36 = Pbo - 0.5 * Pao * x36
Pb41 = Pbo - 0.5 * Pao * x41Pb42 = Pbo - 0.5 * Pao * x42Pb43 = Pbo - 0.5 * Pao * x43Pb44 = Pbo - 0.5 * Pao * x44Pb45 = Pbo - 0.5 * Pao * x45Pb46 = Pbo - 0.5 * Pao * x46
Pb51 = Pbo - 0.5 * Pao * x51Pb52 = Pbo - 0.5 * Pao * x52Pb53 = Pbo - 0.5 * Pao * x53Pb54 = Pbo - 0.5 * Pao * x54Pb55 = Pbo - 0.5 * Pao * x55Pb56 = Pbo - 0.5 * Pao * x56
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
Pr21 = Pao * x21Pr22 = Pao * x22Pr23 = Pao * x23Pr24 = Pao * x24Pr25 = Pao * x25Pr26 = Pao * x26
Pr31 = Pao * x31Pr32 = Pao * x32Pr33 = Pao * x33Pr34 = Pao * x34Pr35 = Pao * x35Pr36 = Pao * x36
Pr41 = Pao * x41Pr42 = Pao * x42Pr43 = Pao * x43Pr44 = Pao * x44Pr45 = Pao * x45Pr46 = Pao * x46
Pr51 = Pao * x51Pr52 = Pao * x52Pr53 = Pao * x53Pr54 = Pao * x54Pr55 = Pao * x55Pr56 = Pao * x56
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
z T0 T1 T2 T3 T4 T5 Tprom
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
Perfil de conversion
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
Perfil de Temperatura
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
COMPARACION DEL CASO I, II YIII
COMPARACION DEL CASO I, II YIII
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
SOLUCION EN POLYMATH
LENGUAJE EN POLYMATH
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
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) = 0
3 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) = 0
4 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) = 0
5 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) = 0
6 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) = 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
8 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) = 0
9 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) = 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
11 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) = 0
12 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) = 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
14 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) = 0
15 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) = 0
16 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) = 0
17 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) = 0
18 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) = 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
20 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) = 0
21 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) = 0
22 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) = 0
23 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) = 0
24 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) = 0
25 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) = 0
26 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) = 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
28 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) = 0
29 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) = 0
30 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) = 0
31 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) = 0
32 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) = 0
33 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) = 0
34 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) = 0
35 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) = 0
36 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) = 0
37 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) = 0
38 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) = 0
39 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) = 0
40 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) = 0
41 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) = 0
42 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) = 0
43 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) = 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
45 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) = 0
46 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) = 0
47 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) = 0
48 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) = 0
49 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) = 0
50 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) = 0
51 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) = 0
52 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) = 0
53 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) = 0
54 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) = 0
55 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) = 0
56 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) = 0
57 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) = 0
58 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) = 0
59 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) = 0
60 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) = 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
62 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) = 0
63 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) = 0
64 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) = 0
65 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) = 0
66 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) = 0
67 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) = 0
68 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) = 0
69 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) = 0
70 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) = 0
71 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) = 0
72 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) = 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
z T0 T1 T2 T3 T4 T5 Tprom
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
Perfil de conversion
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
Perfil de Temperatura
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