We test the IAST code with a binary mixture of methane (CH$_4$) and ethane (C$_2$H$_6$) adsorbed in metal-organic framework IRMOF-1.
Simulated pure-component adsorption isotherms at 298 K are present in the files:
IRMOF-1_methane_isotherm_298K.csvIRMOF-1_ethane_isotherm_298K.csvWe ran dual component GCMC mixture isotherms of methane/ethane in IRMOF-1 at 65 bar total pressure and 298 K at different mixture compositions. This data is present in IRMOF-1_methane_ethane_mixture_isotherm_65bar_298K.csv.
The goal of this test is to use pyIAST to predict the mixture isotherms from the pure-component isotherms and compare to the binary GCMC mixture simulations.
In [1]:
import pyiast
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
# Matplotlib settings
plt.style.use('bmh')
%matplotlib inline
%config InlineBackend.rc = {'font.size': 15, 'lines.linewidth':3, 'axes.facecolor':'w', 'legend.numpoints':1}
# colors to use for plots
color_key = {'methane':'g', 'ethane':'r'}
In [2]:
df_ch4 = pd.read_csv("IRMOF-1_methane_isotherm_298K.csv")
df_ch4.head()
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In [3]:
df_ch3ch3 = pd.read_csv("IRMOF-1_ethane_isotherm_298K.csv")
df_ch3ch3 = df_ch3ch3[df_ch3ch3['Pressure(bar)'] < 55]
df_ch3ch3.head()
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In [4]:
fig, ax = plt.subplots()
plt.scatter(df_ch3ch3['Pressure(bar)'], df_ch3ch3['Loading(mmol/g)'],
label='Ethane', color=color_key['ethane'], s=50)
plt.scatter(df_ch4['Pressure(bar)'], df_ch4['Loading(mmol/g)'],
label='Methane', color=color_key['methane'], s=50, marker='s')
plt.xlabel('Pressure (bar)')
plt.ylabel('Gas uptake (mmol/g)')
plt.xlim([0, 100])
plt.ylim(ymin=0)
plt.legend(loc='lower right')
plt.tight_layout()
plt.savefig("pure_component_isotherms.pdf", format='pdf')
plt.savefig("pure_component_isotherms.png", format='png', dpi=250)
plt.show()
This data has the component uptakes in IRMOF-1 at 298 K immersed in a methane/ethane mixture at 65.0 bar total pressure. The column y_ethane in the data is the mole fraction of ethane in the mixture.
In [5]:
df_mixture = pd.read_csv("IRMOF-1_methane_ethane_mixture_isotherm_65bar_298K.csv")
df_mixture.head()
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In [6]:
fig = plt.figure()
plt.scatter(df_mixture['y_ethane'], df_mixture['EthaneLoading(mmol/g)'],
color=color_key["ethane"], label='Ethane', s=50)
plt.scatter(df_mixture['y_ethane'], df_mixture['MethaneLoading(mmol/g)'],
color=color_key["methane"], label='Methane', s=50)
plt.xlabel('Mole fraction ethane in gas phase, $y_{C_2H_6}$')
plt.ylabel('Gas uptake (mmol/g)')
plt.ylim(ymin=0)
plt.xlim([0, .12])
plt.legend(loc='center left')
plt.show()
Construct isotherm objects. Use the interpolator isotherm here, as Langmuir and Quadratic isotherms do not fit well.
We use fill_value = largest loading so that, when the linear interpolation routine calls a pressure beyond our data, it will yield this value. Essentially, the assumption is that the saturation loading = the highest loading observed in the data.
In [7]:
ch4_isotherm = pyiast.InterpolatorIsotherm(df_ch4, loading_key="Loading(mmol/g)",
pressure_key="Pressure(bar)",
fill_value=df_ch4['Loading(mmol/g)'].max())
pyiast.plot_isotherm(ch4_isotherm)
In [8]:
ch3ch3_isotherm = pyiast.InterpolatorIsotherm(df_ch3ch3, loading_key="Loading(mmol/g)",
pressure_key="Pressure(bar)",
fill_value=df_ch3ch3["Loading(mmol/g)"].max())
pyiast.plot_isotherm(ch3ch3_isotherm)
In [9]:
n_mixtures = df_mixture.shape[0]
iast_component_loadings = np.zeros((2, n_mixtures)) # store component loadings here
for i in range(n_mixtures):
y_ethane = df_mixture['y_ethane'].iloc[i]
partial_pressures = 65.0 * np.array([y_ethane, 1.0 - y_ethane])
iast_component_loadings[:, i] = pyiast.iast(partial_pressures,
[ch3ch3_isotherm, ch4_isotherm],
verboseflag=False)
In the following plot, the points are the dual component GCMC simulation loadings at the respective ethane mole fraction in the gas phase. The lines are the result of the IAST calculation. The IAST calculations match the binary GCMC simulations very well.
In [10]:
fig = plt.figure()
plt.scatter(df_mixture['y_ethane'], df_mixture['EthaneLoading(mmol/g)'],
color=color_key["ethane"], label='Ethane', s=50)
plt.scatter(df_mixture['y_ethane'], df_mixture['MethaneLoading(mmol/g)'],
color=color_key["methane"], label='Methane', s=50)
plt.plot(df_mixture['y_ethane'], iast_component_loadings[0, :],
color=color_key['ethane'], label='Ethane, IAST')
plt.plot(df_mixture['y_ethane'], iast_component_loadings[1, :],
color=color_key['methane'], label='Methane, IAST')
plt.xlabel('Mole fraction ethane in gas phase, $y_{C_2H_6}$')
plt.ylabel('Gas uptake (mmol/g)')
plt.ylim(ymin=0)
plt.xlim([0, .12])
plt.legend(loc='center left', prop={'size':12})
plt.tight_layout()
plt.savefig("IAST_validation.pdf", format='pdf')
plt.savefig("IAST_validation.png", format='png', dpi=250)
plt.show()
We use IAST for a three-component mixture of 5 bar methane (all the same!). This should yield the loading at 15 bar.
In [11]:
iast_component_loadings = pyiast.iast([5., 5., 5.],
[ch4_isotherm, ch4_isotherm, ch4_isotherm])
print("Sum of loadings: ", np.sum(iast_component_loadings))
print("Loading at 15 bar: ", ch4_isotherm.loading(15.))
np.testing.assert_almost_equal(np.sum(iast_component_loadings), ch4_isotherm.loading(15.))
In reverse IAST, we specify the mole fraction in the adsorbed phase and calculate the mole fractions in the gas phase that will yield these adsorbed phase mole fractions. We will test this using the binary component GCMC methane/ethane simulations in df_mixture. We define the mole fraction of ethane in the adsorbed phase, $x_{ethane}$, below. ($x_{methane} = 1- x_{ethane}$).
In [12]:
df_mixture['x_ethane'] = df_mixture['EthaneLoading(mmol/g)'] / (
df_mixture['EthaneLoading(mmol/g)'] + df_mixture['MethaneLoading(mmol/g)'])
df_mixture.head()
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Perform reverse IAST at same adsorbed phase composition as in the binary GCMC simulations.
In [13]:
n_mixtures = df_mixture.shape[0]
gas_mole_fractions = np.zeros((2, n_mixtures)) # store bulk gas mole fractions here
component_loadings = np.zeros((2, n_mixtures)) # store component loadings here
P_total = 65.0 # bar, same units as in xe_isotherm and kr_isotherm
for i in range(n_mixtures):
x_ethane = df_mixture['x_ethane'].iloc[i]
gas_mole_fractions[:, i], component_loadings[:, i] =\
pyiast.reverse_iast([x_ethane, 1.0 - x_ethane],
P_total,
[ch3ch3_isotherm, ch4_isotherm])
Relationship between mole fraction of ethane in the bulk gas phase and the resulting mole fraction of ethane in the adsorbed phase.
In [14]:
plt.figure()
plt.scatter(df_mixture['x_ethane'], df_mixture['y_ethane'],
color='b', label='binary GCMC simulations', s=50)
plt.plot(df_mixture['x_ethane'].values, gas_mole_fractions[0, :],
color='b', label='pyIAST')
plt.xlabel('$x_{C_2H_6}$')
plt.ylabel('$y_{C_2H_6}$')
plt.xlim([0, .4])
plt.ylim([0, .4])
plt.legend(loc='upper left')
plt.tight_layout()
plt.savefig("y_vs_x.pdf", format='pdf')
plt.show()
In [15]:
ch3ch3_interpolated = pyiast.InterpolatorIsotherm(df_ch3ch3, loading_key="Loading(mmol/g)",
pressure_key="Pressure(bar)",
fill_value=df_ch3ch3["Loading(mmol/g)"].max())
ch3ch3_langmuir = pyiast.ModelIsotherm(df_ch3ch3, loading_key="Loading(mmol/g)",
pressure_key="Pressure(bar)",
model="Langmuir")
p_plot = np.logspace(np.log(df_ch3ch3['Pressure(bar)'].min()), np.log(80), num=200)
fig = plt.figure()
plt.xlabel("Pressure (bar)")
plt.ylabel("Ethane uptake (mmol/g)")
plt.scatter(df_ch3ch3['Pressure(bar)'], df_ch3ch3['Loading(mmol/g)'],
marker='o', color='r', s=40, label='Data', clip_on=False)
plt.plot(p_plot, ch3ch3_interpolated.loading(p_plot), color='k', linewidth=1,
label='Linear interpolation', linestyle='--')
plt.plot(p_plot, ch3ch3_langmuir.loading(p_plot), color='k', linewidth=1,
label='Langmuir fit')
plt.xscale("log")
plt.xlim(10**-4, 10**2)
plt.ylim(0, 22)
plt.legend(loc='upper left')
plt.tight_layout()
plt.savefig("Ethane_isotherm.pdf", format='pdf')
plt.show()
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pyiast._MODELS
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pyiast._VERSION
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