Redlich Kwong

In [17]:

## Redlich_Kwong Equation - for Mixtures
import pandas as pd
import numpy as np
from pvtpy.compositional import Chromatography, Component, properties_df
from pvtpy.units import Pressure, Temperature

## Redlich_Kwong Equation - for Mixtures import pandas as pd import numpy as np from pvtpy.compositional import Chromatography, Component, properties_df from pvtpy.units import Pressure, Temperature

Liquid Hydrocarbon Mixture¶

In [18]:

d1 = {
    'comp': ['methane','ethane','propane','butane','pentane','n-hexane'],
    'mole_fraction':[0.45,0.05,0.05,0.03,0.01,0.01]
}

c7_plus = Component(
    name = 'C7+', 
    molecular_weight=215,
    mole_fraction=0.4,   
    critical_pressure=285,
    critical_pressure_unit='psi',
    critical_temperature=1287,
    critical_temperature_unit='rankine',

)

ch1 = Chromatography()
ch1.from_df(pd.DataFrame(d1),name='comp')
ch1.plus_fraction = c7_plus

ch1.df()['mole_fraction']

d1 = { 'comp': ['methane','ethane','propane','butane','pentane','n-hexane'], 'mole_fraction':[0.45,0.05,0.05,0.03,0.01,0.01] } c7_plus = Component( name = 'C7+', molecular_weight=215, mole_fraction=0.4, critical_pressure=285, critical_pressure_unit='psi', critical_temperature=1287, critical_temperature_unit='rankine', ) ch1 = Chromatography() ch1.from_df(pd.DataFrame(d1),name='comp') ch1.plus_fraction = c7_plus ch1.df()['mole_fraction']

Out[18]:

methane     0.45
ethane      0.05
propane     0.05
butane      0.03
pentane     0.01
n-hexane    0.01
C7+         0.40
Name: mole_fraction, dtype: float64

In [19]:

ch1.redlich_kwong_components_coef()

ch1.df(columns=['mole_fraction','rk_a','rk_b'])

ch1.redlich_kwong_components_coef() ch1.df(columns=['mole_fraction','rk_a','rk_b'])

Out[19]:

	mole_fraction	rk_a	rk_b
methane	0.45	1.609183e+05	0.478495
ethane	0.05	4.932760e+05	0.723177
propane	0.05	9.136286e+05	1.004698
butane	0.03	1.448218e+06	1.292135
pentane	0.01	2.093616e+06	1.608655
n-hexane	0.01	2.839364e+06	1.943280
C7+	0.40	1.026140e+07	4.198091

In [20]:

ch1.redlich_kwong_mix_coef()

ch1.redlich_kwong_mix_coef()

Out[20]:

(2599136.1341489274, 2.0552362922703455)

In [21]:

p1 = Pressure(value = 4000, unit='psi')
t1 = Temperature(value = 160, unit='farenheit')

ma = ch1.apparent_molecular_weight()
ma

p1 = Pressure(value = 4000, unit='psi') t1 = Temperature(value = 160, unit='farenheit') ma = ch1.apparent_molecular_weight() ma

Out[21]:

100.264435

In [22]:

df1 = ch1.df(columns=['mole_fraction','molecular_weight'])
print(df1)

df1 = ch1.df(columns=['mole_fraction','molecular_weight']) print(df1)

          mole_fraction  molecular_weight
methane            0.45           16.0425
ethane             0.05           30.0700
propane            0.05           44.0970
butane             0.03           58.1230
pentane            0.01           73.1500
n-hexane           0.01           86.1770
C7+                0.40          215.0000

In [23]:

A,B = ch1.redlich_kwong.coef_AB(p1,t1)

print(A,B)

A,B = ch1.redlich_kwong.coef_AB(p1,t1) print(A,B)

9.446879948552613 1.2364072939404886

In [24]:

poly = ch1.redlich_kwong.cubic_poly(p1,t1)
print(type(poly))
print(poly)

poly = ch1.redlich_kwong.cubic_poly(p1,t1) print(type(poly)) print(poly)

<class 'numpy.polynomial.polynomial.Polynomial'>
-11.6801912733706 + 6.681769658102883·x¹ - 1.0·x² + 1.0·x³

In [25]:

roots = poly.roots()

roots[np.isreal(roots)].real

roots = poly.roots() roots[np.isreal(roots)].real

Out[25]:

array([1.55019215])

In [26]:

ch1.redlich_kwong.estimate_densities(p1,t1, ma)

ch1.redlich_kwong.estimate_densities(p1,t1, ma)

Out[26]:

{'rho': array([38.90999504])}

Gas Hydrocarbon Mixture¶

In [27]:

d2 = {
    'comp': ['methane','ethane','propane','butane','pentane','n-hexane'],
    'mole_fraction':[0.86,0.05,0.05,0.02,0.01,0.005]
}

c7_plus2 = Component(
    name = 'C7+', 
    molecular_weight=215,
    mole_fraction=0.005,   
    critical_pressure=285,
    critical_pressure_unit='psi',
    critical_temperature=1287,
    critical_temperature_unit='rankine'
)

ch2 = Chromatography()
ch2.from_df(pd.DataFrame(d2),name='comp')
ch2.plus_fraction = c7_plus2

ch2.df(columns=['mole_fraction'], normalize=False)

d2 = { 'comp': ['methane','ethane','propane','butane','pentane','n-hexane'], 'mole_fraction':[0.86,0.05,0.05,0.02,0.01,0.005] } c7_plus2 = Component( name = 'C7+', molecular_weight=215, mole_fraction=0.005, critical_pressure=285, critical_pressure_unit='psi', critical_temperature=1287, critical_temperature_unit='rankine' ) ch2 = Chromatography() ch2.from_df(pd.DataFrame(d2),name='comp') ch2.plus_fraction = c7_plus2 ch2.df(columns=['mole_fraction'], normalize=False)

Out[27]:

	mole_fraction
methane	0.860
ethane	0.050
propane	0.050
butane	0.020
pentane	0.010
n-hexane	0.005
C7+	0.005

In [28]:

ch2.redlich_kwong_components_coef()

ch2.df(columns=['mole_fraction','rk_a','rk_b'])

ch2.redlich_kwong_components_coef() ch2.df(columns=['mole_fraction','rk_a','rk_b'])

Out[28]:

	mole_fraction	rk_a	rk_b
methane	0.860	1.609183e+05	0.478495
ethane	0.050	4.932760e+05	0.723177
propane	0.050	9.136286e+05	1.004698
butane	0.020	1.448218e+06	1.292135
pentane	0.010	2.093616e+06	1.608655
n-hexane	0.005	2.839364e+06	1.943280
C7+	0.005	1.026140e+07	4.198091

In [29]:

ma2 = ch2.apparent_molecular_weight()
ma2

ma2 = ch2.apparent_molecular_weight() ma2

Out[29]:

20.904745

In [30]:

ch2.redlich_kwong_mix_coef()

ch2.redlich_kwong_mix_coef()

Out[30]:

(240957.42827545686, 0.570535481591962)

In [ ]:

In [31]:

p2 = Pressure(value = 4000, unit='psi')
t2 = Temperature(value = 160, unit='farenheit')
ch2.redlich_kwong.estimate_densities(p2,t2, ma2)

p2 = Pressure(value = 4000, unit='psi') t2 = Temperature(value = 160, unit='farenheit') ch2.redlich_kwong.estimate_densities(p2,t2, ma2)

Out[31]:

{'rho': array([13.85246264])}

In [32]:

ch2.redlich_kwong.cubic_poly(p2,t2)

ch2.redlich_kwong.cubic_poly(p2,t2)

Out[32]:

$x \mapsto \text{-0.3005952718766425} + \text{0.4147562859938712}\,x - \text{1.0}\,x^{2} + \text{1.0}\,x^{3}$

In [ ]: