5. Modelos y parametros para sustancia puras¶
En todos los casos se realiza el calculo (o el reclaculo) del parametro rk de la ecuación RKPR.
Se tiene la posibilidad de especificar un par (presión de vapor, temperatura) para realizar los calculos, en caso contrario de no hacer esta especificación, se toma por defecto el valor de la presión de vapor correspondiente a una temperatura reducida Tr = 0.7 junto con el correspondiente valor del factor acentrico según cada sustancia pura.
- Temperatura critica
- Presión critica
- factor acentrico Omega
- Volumen critico
En esta sección se presenta la forma de obtener los parámetros correspondientes para las ecuaciones de estado SRK, PR y RKPR con las diferentes especificaciones que se pueden realizar.
Para el caso de las ecuaciones de estado SRK y PR se tienen como parámetros a las constantes a_c y b. Estos parámetros se determinan a partir de las constantes criticas para cada sustancia pura.
En el caso de la ecuación de estado RKPR se tiene 2 parámetros adicionales a los ya mencionados ac y b. Son los parámetros d1 y k, que se muestran en las siguientes ecuaciones:
importar las linrerías requeridas, en este caso se trata de las librerías numpy, pandas junto con pyther
import numpy as np
import pandas as pd
import pyther as pt
En los ejemplos siguientes se utilizan los datos termodísicos de la base de datos DPPR. Para el caso se tiene como especificación la ecuación de estado RKPR y las constantes criticas para el componente 3-METHYLHEPTANE a continuación.
properties_data = pt.Data_parse()
dppr_file = "PureFull.xls"
component = "3-METHYLHEPTANE"
NMODEL = "RKPR"
ICALC = "constants_eps"
properties_component = properties_data.selec_component(dppr_file, component)
pt.print_properties_component(component, properties_component)
dinputs = np.array([properties_component[1]['Tc'], properties_component[1]['Pc'],
properties_component[1]['Omega'], properties_component[1]['Vc']])
component_eos = pt.models_eos_cal(NMODEL, ICALC, dinputs)
#ac = component_eos[0]
print(component_eos)
Component = 3-METHYLHEPTANE
Acentric_factor = 0.3718
Critical_Temperature = 563.67 K
Critical_Pressure = 25.127 Bar
Critical_Volume = 0.464 cm3/mol
Compressibility_factor_Z = 0.252
del1ini = 6.038268203938681
Zc = 0.24877058378575795
The NMODEL is eos_RKPR and method ICALC is constants_eps
params = [ac, b, rm, del1]
[46.430578671675555, 0.10935115096084358, 2.5860921512475117, 6.0431253541984447]
De esta forma se observa el calculo simple de los parámetros para la sustancia pura 3-METHYLHEPTANE_RKPR
A continuación se realiza el mismo tipo de calculo pero tomando una serie de 9 sustancias puras, que se pueden extender facilmente a n sustancias, para obtener sus parámetros de nuevo con la ecuación de estado RKPR.
properties_data = pt.Data_parse()
dppr_file = "PureFull.xls"
components = ["ISOBUTANE", "CARBON DIOXIDE", 'METHANE', "ETHANE", "3-METHYLHEPTANE", "n-PENTACOSANE",
"NAPHTHALENE", "m-ETHYLTOLUENE", "2-METHYL-1-HEXENE"]
NMODEL = "RKPR"
ICALC = "constants_eps"
component_eos_list = np.zeros( (len(components),4) )
for index, component in enumerate(components):
properties_component = properties_data.selec_component(dppr_file, component)
pt.print_properties_component(component, properties_component)
dinputs = np.array([properties_component[1]['Tc'], properties_component[1]['Pc'],
properties_component[1]['Omega'], properties_component[1]['Vc']])
component_eos = pt.models_eos_cal(NMODEL, ICALC, dinputs)
component_eos_list[index] = component_eos
components_table = pd.DataFrame(component_eos_list, index=components, columns=['ac', 'b', 'rm', 'del1'])
print(components_table)
Component = ISOBUTANE
Acentric_factor = 0.18080000000000002
Critical_Temperature = 408.14 K
Critical_Pressure = 36.003 Bar
Critical_Volume = 0.2627 cm3/mol
Compressibility_factor_Z = 0.28200000000000003
del1ini = 3.9722378008963446
Zc = 0.27871152548257544
The NMODEL is eos_RKPR and method ICALC is constants_eps
params = [ac, b, rm, del1]
Component = CARBON DIOXIDE
Acentric_factor = 0.22360000000000002
Critical_Temperature = 304.21 K
Critical_Pressure = 72.865 Bar
Critical_Volume = 0.094 cm3/mol
Compressibility_factor_Z = 0.274
del1ini = 4.462908059336361
Zc = 0.2707937660977233
The NMODEL is eos_RKPR and method ICALC is constants_eps
params = [ac, b, rm, del1]
Component = METHANE
Acentric_factor = 0.0115
Critical_Temperature = 190.564 K
Critical_Pressure = 45.389 Bar
Critical_Volume = 0.09860000000000001 cm3/mol
Compressibility_factor_Z = 0.28600000000000003
del1ini = 3.7519407434981633
Zc = 0.2824567739174239
The NMODEL is eos_RKPR and method ICALC is constants_eps
params = [ac, b, rm, del1]
Component = ETHANE
Acentric_factor = 0.0995
Critical_Temperature = 305.32 K
Critical_Pressure = 48.083 Bar
Critical_Volume = 0.14550000000000002 cm3/mol
Compressibility_factor_Z = 0.279
del1ini = 4.161423913263858
Zc = 0.2755907402334964
The NMODEL is eos_RKPR and method ICALC is constants_eps
params = [ac, b, rm, del1]
Component = 3-METHYLHEPTANE
Acentric_factor = 0.3718
Critical_Temperature = 563.67 K
Critical_Pressure = 25.127 Bar
Critical_Volume = 0.464 cm3/mol
Compressibility_factor_Z = 0.252
del1ini = 6.038268203938681
Zc = 0.24877058378575795
The NMODEL is eos_RKPR and method ICALC is constants_eps
params = [ac, b, rm, del1]
Component = n-PENTACOSANE
Acentric_factor = 1.1053
Critical_Temperature = 812 K
Critical_Pressure = 9.376 Bar
Critical_Volume = 1.46 cm3/mol
Compressibility_factor_Z = 0.20500000000000002
del1ini = 10.600246415857843
Zc = 0.20275882073834256
The NMODEL is eos_RKPR and method ICALC is constants_eps
params = [ac, b, rm, del1]
Component = NAPHTHALENE
Acentric_factor = 0.3022
Critical_Temperature = 748.35 K
Critical_Pressure = 39.98 Bar
Critical_Volume = 0.41300000000000003 cm3/mol
Compressibility_factor_Z = 0.269
del1ini = 4.8204311891035925
Zc = 0.2653709654843225
The NMODEL is eos_RKPR and method ICALC is constants_eps
params = [ac, b, rm, del1]
Component = m-ETHYLTOLUENE
Acentric_factor = 0.3226
Critical_Temperature = 637.15 K
Critical_Pressure = 28.029 Bar
Critical_Volume = 0.49 cm3/mol
Compressibility_factor_Z = 0.263
del1ini = 5.246526144851435
Zc = 0.2592551086535563
The NMODEL is eos_RKPR and method ICALC is constants_eps
params = [ac, b, rm, del1]
Component = 2-METHYL-1-HEXENE
Acentric_factor = 0.3094
Critical_Temperature = 538 K
Critical_Pressure = 28.325 Bar
Critical_Volume = 0.398 cm3/mol
Compressibility_factor_Z = 0.255
del1ini = 5.784189965441039
Zc = 0.2520206003977051
The NMODEL is eos_RKPR and method ICALC is constants_eps
params = [ac, b, rm, del1]
ac b rm del1
ISOBUTANE 15.743219 0.064343 2.205509 4.000470
CARBON DIOXIDE 4.409808 0.022801 2.280728 4.492210
METHANE 2.696405 0.024259 1.282178 3.777713
ETHANE 6.649597 0.035503 1.673541 4.190762
3-METHYLHEPTANE 46.430579 0.109351 2.586092 6.043125
n-PENTACOSANE 289.947431 0.320522 4.581358 10.628260
NAPHTHALENE 49.312554 0.099495 2.591582 4.847168
m-ETHYLTOLUENE 51.786960 0.117115 2.565531 5.267361
2-METHYL-1-HEXENE 37.214555 0.094214 2.338038 5.794610
Como se observa, los resultados obtenidos son organizados en un DataFrame permitiendo agilizar la manipulación de los datos de una serie de sustancias puras.
components_table
| ac | b | rm | del1 | |
|---|---|---|---|---|
| ISOBUTANE | 15.743219 | 0.064343 | 2.205509 | 4.000470 |
| CARBON DIOXIDE | 4.409808 | 0.022801 | 2.280728 | 4.492210 |
| METHANE | 2.696405 | 0.024259 | 1.282178 | 3.777713 |
| ETHANE | 6.649597 | 0.035503 | 1.673541 | 4.190762 |
| 3-METHYLHEPTANE | 46.430579 | 0.109351 | 2.586092 | 6.043125 |
| n-PENTACOSANE | 289.947431 | 0.320522 | 4.581358 | 10.628260 |
| NAPHTHALENE | 49.312554 | 0.099495 | 2.591582 | 4.847168 |
| m-ETHYLTOLUENE | 51.786960 | 0.117115 | 2.565531 | 5.267361 |
| 2-METHYL-1-HEXENE | 37.214555 | 0.094214 | 2.338038 | 5.794610 |
En el siguiente ejemplo se utiliza la ecuación RKPR pero esta vez con la especificación de la temperatura y densidad de líquido saturado para el CARBON DIOXIDE y de esta forma encontrar el valor del parámetro delta que verifica la especificación realizada para la densidad de líquido saturado.
properties_data = pt.Data_parse()
dppr_file = "PureFull.xls"
component = "CARBON DIOXIDE"
NMODEL = "RKPR"
ICALC = "density"
properties_component = properties_data.selec_component(dppr_file, component)
pt.print_properties_component(component, properties_component)
#dinputs = np.array([properties_component[1]['Tc'], properties_component[1]['Pc'],
# properties_component[1]['Omega'], properties_component[1]['Vc']])
T_especific = 270.0
RHOLSat_esp = 21.4626
# valor initial of delta_1
delta_1 = 1.5
dinputs = np.array([properties_component[1]['Tc'], properties_component[1]['Pc'],
properties_component[1]['Omega'], delta_1, T_especific, RHOLSat_esp])
component_eos = pt.models_eos_cal(NMODEL, ICALC, dinputs)
print(component_eos)
Component = CARBON DIOXIDE
Acentric_factor = 0.22360000000000002
Critical_Temperature = 304.21 K
Critical_Pressure = 72.865 Bar
Critical_Volume = 0.094 cm3/mol
Compressibility_factor_Z = 0.274
The NMODEL is eos_RKPR and method ICALC is density
The parameter delta1(rho,T) = [ 2.65756708]
[ 2.65756708]