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Comparación del Metodo de Euler vs Rugen Kutta en un Reactor Batch
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Este es un ejercicio del Metodo de Euler vs Rugen Kutta en un Reactor Batch, reacción homogénea fase liquida
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El caso consiste en una reacción homogénea en fase líquida de segundo orden respecto a A, con las siguientcaracterísticas:
Reacción: A + B → C
Concentración inicial de los reactivos A y B, 1.65 mol/L y 5.5 mol/L, respectivamente.
Temeperatura de alimentación 315 K, para ambos reactivos.
Flujo volumétrico total 14.4 L/min.
Coeficiente cinético ka = 5.044 x10^9 e(-10,270/T) L/mol*seg, con T en K.
Calor de reacción -DHRxn = 36.35 KJ/mol.
Capacidad calorífica de las especies A, B y C, en J/mol*K: 138.5, 117.5 y 95, respectivamente.
Coeficiente global de trasnferencia de calor entre el sistema de reacción y el fluido de servicio: 32.3 Watts/m
Temperatura promedio de los alrededores: K. Conversión esperada para el reactivo A 303 %70
Configuración de tubos y coraza 1 -1, con 274 tubos de tubería IPS de 1 1/2 pulg., Ced. 40, en arreglo triangu
paso de 1 7/8 Reactor batch.
Tanque de 0.78 m de diámetro y 2.39 m de altura, para la mezcla de reacción.
DATOS DEL REACTOR BATCH
CA0 1.65 mol/L kA 5.044x109e(-10270/T) L/mol*seg
CB0 5.5 mol/L kA 3.4946E-05 L/mol*seg
T0 315 K ntubos 247 tubos
uTOTAL 14.4 L/min PT 1.875 plgtriangular
DHRxn 36.35 KJ/mol
CpA 138.5 J/mol*K Tuberia 1 1/2 plg IPS Cédula No. 40 (KERN. Apendice Tabla 11)
CpB 117.5 J/mol*K Dinterior 1.61 plg
CpC 95 J/mol*K Dexterior 1.9 plg
U 35.3 Watts/m *K2
XA 0.7 Balance Molar
𝒅𝒕/(𝒅𝑿_𝑨 )=𝟏/(𝒌_𝑨 𝑪_𝑨𝟎 (𝟏−𝑿_𝑨
METODO RUNGE KUTTA 4° ORDEN )(𝑪_𝑩𝟎/𝑪_𝑨𝟎 −𝑿_𝑨 ) )
Xinicial 0
Xfinal 0.7
yinicial 0
h 0.05
XA yA1 yA2 k1 xA + h/2 yA1 +h* k11/2 yA2 +h* k12/2
0.00 1.65 5.5 5.2028E+03 0.025 1.3172E+02 1.3557E+02
0.05 9.5595E+01 9.9445E+01 3.1819E+02 0.075 1.0355E+02 1.0740E+02
0.10 1.1116E+02 1.1501E+02 3.0604E+02 0.125 1.1881E+02 1.2266E+02
0.15 1.2634E+02 1.3019E+02 3.0263E+02 0.175 1.3391E+02 1.3776E+02
0.20 1.4152E+02 1.4537E+02 3.0554E+02 0.225 1.4916E+02 1.5301E+02
0.25 1.5699E+02 1.6084E+02 3.1379E+02 0.275 1.6483E+02 1.6868E+02
, 0.30 1.7299E+02 1.7684E+02 3.2719E+02 0.325 1.8117E+02 1.8502E+02
0.35 1.8980E+02 1.9365E+02 3.4605E+02 0.375 1.9845E+02 2.0230E+02
0.40 2.0770E+02 2.1155E+02 3.7124E+02 0.425 2.1698E+02 2.2083E+02
0.45 2.2705E+02 2.3090E+02 4.0418E+02 0.475 2.3715E+02 2.4100E+02
0.50 2.4828E+02 2.5213E+02 4.4715E+02 0.525 2.5946E+02 2.6331E+02
0.55 2.7199E+02 2.7584E+02 5.0371E+02 0.575 2.8458E+02 2.8843E+02
0.60 2.9897E+02 3.0282E+02 5.7955E+02 0.625 3.1346E+02 3.1731E+02
0.65 3.3042E+02 3.3427E+02 6.8419E+02 0.675 3.4753E+02 3.5138E+02
0.70 3.6815E+02 3.7200E+02 8.3456E+02 0.725 3.8901E+02 3.9286E+02
METODO DE EULER
M
𝒚_(𝟏+𝟏,𝒋)=𝒚_𝒊𝒋+𝒉𝒇_𝒋 (𝒙_𝒊,𝒚_𝒊𝟏,𝒚_𝒊𝟐 ) 5.0000E+02
𝒙_(𝒊+𝟏)=𝒙_𝒊+𝒉
4.5000E+02
4.0000E+02
3.5000E+02
XA yA1 yA2 f (XA, yA1, yA2)
0.00 1.65 5.5 5.2028E+03 3.0000E+02
Concentración
0.05 2.6179E+02 2.6564E+02 1.1927E+02 2.5000E+02
0.10 2.6776E+02 2.7161E+02 1.2987E+02
2.0000E+02
0.15 2.7425E+02 2.7810E+02 1.4207E+02
0.20 2.8135E+02 2.8520E+02 1.5625E+02 1.5000E+02
0.25 2.8916E+02 2.9301E+02 1.7286E+02 1.0000E+02
0.30 2.9781E+02 3.0166E+02 1.9254E+02 5.0000E+01
0.35 3.0743E+02 3.1128E+02 2.1614E+02
0.0000E+00
0.40 3.1824E+02 3.2209E+02 2.4484E+02 0.00 0.10 0.20 0.30
0.45 3.3048E+02 3.3433E+02 2.8030E+02 Conv
0.50 3.4450E+02 3.4835E+02 3.2499E+02
0.55 3.6075E+02 3.6460E+02 3.8264E+02
0.60 3.7988E+02 3.8373E+02 4.5917E+02
0.65 4.0284E+02 4.0669E+02 5.6446E+02
0.70 4.3106E+02 4.3491E+02 7.1628E+02 COM
5.0000E+02
4.5000E+02
AREA DE TRANSFERENCIA DE CALOR
4.0000E+02
𝐴_𝐵𝐴𝑇𝐶𝐻=𝜋𝑑_𝑡𝑞𝑒 ℎ_𝑡𝑞𝑒=π(0.55 𝑚)(1.65 𝑚)=3.37 𝑚^2
3.5000E+02
3.0000E+02
Concentración
VOLUMEN DE LA MEZCLA DE REACCION
2.5000E+02
𝑉_𝐵𝐴𝑇𝐶𝐻=𝜋 〖 (𝑑_𝑡𝑞𝑒) 〗 ^2/4 ℎ_𝑡𝑞𝑒=𝜋 (0.55 𝑚)^2/4 2.0000E+02
(1.65 𝑚)=0.39 𝑚^2
1.5000E+02
1.0000E+02
5.0000E+01
0.0000E+00
0.00 0.10 0.20
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