Welcome to adsorption_isotherm_fitting’s documentation!

Installation

Docker

docker pull dejac001/isotherm-fitting-users:0.0.4
docker run -ti -v $PWD:/home/pyomo/shared/ dejac001/isotherm-fitting-users:0.0.4 # run interactively inside container (ubuntu-based)

Singularity

module load singularity
singularity pull docker://dejac001/isotherm-fitting-users:0.0.4
mv isotherm-fitting-users_0.0.4.sif /path/to/shared/directory/isotherm-fitting-users_0.0.4.sif
singularity exec -B $PWD:/home/pyomo/shared /path/to/shared/directory/isotherm-fitting-users_0.0.4.sif python3 path/to/input/file.py

Scipy Only

pip3 install Pyomo chem-util matplotlib pandas numpy realgas>=1.0.2
python3 -m pip3 install https://github.com/dejac001/adsorption_isotherm_fitting/archive/v0.0.4.tar.gz

CO2/N2 Unary Example

In this example, we fit temperature-dependent unary data from [PXSL14].

Initialization

We first load the necessary packages

>>> import pyomo.environ as pyo
>>> import matplotlib.pyplot as plt
>>> import pandas as pd
>>> from isotherm_models.unaryisotherm import LangmuirUnary

CO2

We first get the data from the data file

>>> data = pd.read_csv('data_sets/CO2_BEA.csv')

Using pandas, we can easily take a peek at the data we have input from our .csv file

>>> data.head()
    P [atm]  Q [mmol/g]  T [K] adsorbate
0  0.029814    0.096491  273.0       CO2
1  0.055856    0.175439  273.0       CO2
2  0.109177    0.328947  273.0       CO2
3  0.246821    0.719298  273.0       CO2
4  0.313781    0.903509  273.0       CO2

Before solving the model, we convert the partial pressures to si units

>>> P_i = data['P [atm]']*101325  # convert to Pa -- si units

so that we can create the model

>>> co2_model = LangmuirUnary(P_i, data['Q [mmol/g]'], data['T [K]'], name='CO2')

and solve it

>>> co2_model.solve()

We then take a look at the results

>>> co2_model.get_R2_pyomo()
0.99796
>>> co2_model.get_objective()
0.007229102
>>> co2_model.dH_i.display()
dH_i : Size=1
    Key  : Value
    None : -20780.90809523844
>>> co2_model.q_mi.display()
q_mi : Size=1
    Key  : Value
    None : 8.95582798469325
>>> co2_model.k_i_inf.display()
k_i_inf : Size=1
    Key  : Value
    None : 3.8656918601559114e-10

And save the results to a file

>>> fig = plt.figure()
>>> fig, ax = co2_model.plot_unary(fig=fig)
>>> _ = ax.legend()
>>> fig.savefig('docs/source/CO2_example.png')

which looks like

N2

We repeat a similar approach for the N2 isotherms, first formatting the data for input to the model

>>> data = pd.read_csv('data_sets/N2_BEA.csv')

Using pandas, we can easily take a peek at the data we have input from our .csv file

>>> data.head()
    P [atm]  Q [mmol/g]  T [K] adsorbate
0  0.525470    0.070175  303.0        N2
1  0.592387    0.078947  303.0        N2
2  0.656824    0.083333  303.0        N2
3  0.722502    0.092105  303.0        N2
4  0.788179    0.100877  303.0        N2

Before solving the model, we convert the partial pressures to si units

>>> P_i = data['P [atm]']*101325  # convert to Pa -- si units

Instantiating (creating) the model

>>> n2_model = LangmuirUnary(P_i, data['Q [mmol/g]'], data['T [K]'], name='N2')

Solving it

>>> n2_model.solve()

We then take a look at the results

>>> n2_model.get_R2_pyomo()
0.99262
>>> n2_model.get_objective()
0.00194249
>>> n2_model.dH_i.display()
dH_i : Size=1
    Key  : Value
    None : -12557.526993112784
>>> n2_model.q_mi.display()
q_mi : Size=1
    Key  : Value
    None : 0.45280441671269905
>>> n2_model.k_i_inf.display()
k_i_inf : Size=1
    Key  : Value
    None : 2.412336128388879e-08

And save the results to a file

>>> fig = plt.figure()
>>> fig, ax = n2_model.plot_unary(fig=fig)
>>> _ = ax.legend()
>>> fig.savefig('docs/source/N2_example.png')

which looks like

Comparison to scipy

>>> import numpy as np
>>> popt, pcov = co2_model.solve_scipy()
>>> popt
array([  3.71939309, -10.14817759,  -7.28715595])
>>> popt - np.array(list(map(pyo.value, [co2_model.q_mi_star, co2_model.A_i, co2_model.H_i_star])))
array([3.28355311e-05, 3.67969745e-05, 3.88858220e-05])

H2S/CH4 Example

In this example, we fit temperature-dependent binary data from [STS15] and compare the results to using the extended Langmuir combining rule.

Initialization

First, we import the necessary packages

>>> import pyomo.environ as pyo
>>> import matplotlib.pyplot as plt
>>> import pandas as pd
>>> from isotherm_models.unaryisotherm import LangmuirUnary
>>> from isotherm_models.binaryisotherm import BinaryLangmuir

First, we grab the data for adsorption of H2S:

>>> df = pd.read_csv('data_sets/CH4_H2S_MFI_binary_with_fugacity.csv')
>>> hat_f_i, hat_f_j, q_i, T = df['fugacity H2S [Pa]'], df['fugacity CH4 [Pa]'], df['Q H2S [mmol/g]'], df['T [K]']

Here, we are going to fit the loading of H2S, q_i, as a function of the (mixture) fugacities of H2S, hat_f_i, and CH4, hat_f_j. Since the data file includes both binary and unary data (including CH4 unary data where H2S is not present), we need to find the data points where H2S is present. We can do this with a list comprehension as below

>>> all_points = [i for i in range(len(q_i)) if q_i[i] > 0.]

Now, we can create a model with all of these points. We choose the isotherm_models.binaryisotherm.BinaryLangmuir model.

>>> h2s_binary = BinaryLangmuir(
...     [hat_f_i[i] for i in all_points],
...     [hat_f_j[i] for i in all_points],
...     [q_i[i] for i in all_points],
...     [T[i] for i in all_points],
...     name='H2S_binary'
... )

Similarly, we can find the indices of points where only H2S is present (i.e., the unary points for H2S), using the following code

>>> unary_points = [i for i in range(len(q_i)) if hat_f_j[i] < 1e-12]
>>> f_i = [hat_f_i[i] for i in unary_points]

And we can create a unary model as

>>> h2s_unary = LangmuirUnary(
...     f_i,
...     [q_i[i] for i in unary_points],
...     [T[i] for i in unary_points],
...     name='H2S_unary'
... )

We can undertake a similar procedure for CH4, as below

>>> df = pd.read_csv('data_sets/CH4_H2S_MFI_binary_with_fugacity.csv')
>>> hat_f_i, hat_f_j, q_i, T = df['fugacity CH4 [Pa]'], df['fugacity H2S [Pa]'], df['Q CH4 [mmol/g]'], df['T [K]']
>>> all_points = [i for i in range(len(q_i)) if q_i[i] > 0.]
>>> unary_points = [i for i in range(len(q_i)) if hat_f_j[i] < 1e-12]
>>> f_i = [hat_f_i[i] for i in unary_points]
>>> ch4_unary = LangmuirUnary(f_i,
...     [q_i[i] for i in unary_points],
...     [T[i] for i in unary_points],
...     name='CH4_unary'
... )
>>> ch4_binary = BinaryLangmuir(
...     [hat_f_i[i] for i in all_points],
...     [hat_f_j[i] for i in all_points],
...     [q_i[i] for i in all_points],
...     [T[i] for i in all_points],
...     name='CH4_binary'
... )

Solution

We solve the ch4_unary model first

>>> ch4_unary.solve()

and observe that the fit is quite good.

>>> ch4_unary.get_R2_pyomo()
0.9998
>>> ch4_unary.get_objective()
0.0007123352658190

We can take a look at the final parameters that were obtained

>>> ch4_unary.dH_i.display()
dH_i : Size=1
    Key  : Value
    None : -20205.7398278234

>>> ch4_unary.q_mi.display()
q_mi : Size=1
    Key  : Value
    None : 2.7226241284913613

>>> ch4_unary.k_i_inf.display()
k_i_inf : Size=1
    Key  : Value
    None : 6.61203298602151e-10

Then we can do the same thing with the H2S unary model

>>> h2s_unary.solve()
>>> h2s_unary.get_R2_pyomo()
0.998700
>>> h2s_unary.get_objective()
0.0053414

Alternatively, we can display results at once

>>> h2s_unary.display_results()
R2 : Size=1
    Key  : Value
    None : 0.9987002690496689
objective : Size=1, Index=None, Active=True
    Key  : Active : Value
    None :   True : 0.0053414186202173485
H_i_star : Size=1, Index=None
    Key  : Lower : Value               : Upper : Fixed : Stale : Domain
    None :  None : -10.976064382768586 :  None : False : False :  Reals
A_i : Size=1, Index=None
    Key  : Lower : Value              : Upper : Fixed : Stale : Domain
    None :  None : -7.365904878303015 :  None : False : False :  Reals
q_mi_star : Size=1, Index=None
    Key  : Lower : Value              : Upper : Fixed : Stale : Domain
    None :  None : 1.0109486926682547 :  None : False : False :  Reals
q_mi : Size=1
    Key  : Value
    None : 3.1127110247255563
k_i_inf : Size=1
    Key  : Value
    None : 1.6091644633767268e-10
dH_i : Size=1
    Key  : Value
    None : -31300.464752469943

Before solving the binary models, it is useful to have a good initial guess. One option is to initialize the binary variables from the Langmuir combining rule

>>> h2s_binary.H_i_star = pyo.value(h2s_unary.H_i_star)
>>> h2s_binary.A_i = pyo.value(h2s_unary.A_i)
>>> h2s_binary.q_mi_star = pyo.value(h2s_unary.q_mi_star)
>>> h2s_binary.A_j = pyo.value(ch4_unary.A_i)
>>> h2s_binary.H_j_star = pyo.value(ch4_unary.H_i_star)
>>> ch4_binary.H_i_star = pyo.value(ch4_unary.H_i_star)
>>> ch4_binary.A_i = pyo.value(ch4_unary.A_i)
>>> ch4_binary.q_mi_star = pyo.value(ch4_unary.q_mi_star)
>>> ch4_binary.A_j = pyo.value(h2s_unary.A_i)
>>> ch4_binary.H_j_star = pyo.value(h2s_unary.H_i_star)

And then solve them using the usual syntax

>>> h2s_binary.solve()
>>> ch4_binary.solve()
>>> h2s_binary.get_R2_pyomo()
0.9988281256
>>> h2s_binary.get_objective()
0.0186995038
>>> ch4_binary.get_R2_pyomo()
0.999329631
>>> ch4_binary.get_objective()
0.007515807

which demonstrates that the fits are again quite good. It is of interest to compare the binary fit parameters to the unary parameters

>>> pyo.value(h2s_binary.H_i_star)
-11.073113
>>> pyo.value(h2s_unary.H_i_star)
-10.97606
>>> pyo.value(h2s_binary.q_mi_star)
1.0189875
>>> pyo.value(h2s_unary.q_mi_star)
1.0109486
>>> pyo.value(h2s_binary.A_i)
-7.32572
>>> pyo.value(h2s_unary.A_i)
-7.36590

We can also plot all the results to a figure, and save it to a file

>>> fig = plt.figure()
>>> fig, ax = h2s_unary.plot_comparison_dimensionless(fig=fig, color='red', marker='o', markerfacecolor='None', label='H2S unary')
>>> fig, ax = ch4_unary.plot_comparison_dimensionless(fig=fig, ax=ax, color='blue', marker='x', markerfacecolor='None', label='CH4 unary')
>>> fig, ax = h2s_binary.plot_comparison_dimensionless(fig=fig, ax=ax, color='purple', marker='d', markerfacecolor='None', label='H2S binary')
>>> fig, ax = ch4_binary.plot_comparison_dimensionless(fig=fig, ax=ax, color='cyan', marker='s', markerfacecolor='None', label='CH4 binary')
>>> _ = ax.legend()
>>> fig.savefig('docs/source/h2s_ch4_example.png')

Which looks like

Having fit the isotherms, we can now evaluate them at arbitrary fugacities and temperatures. We get the same answer whether we use units or dimensional quantities

>>> pyo.value(h2s_unary.eval_pyomo(h2s_unary.f_ref, h2s_unary.T_ref) - h2s_unary.q_ref*h2s_unary.eval_dimensionless_pyomo(1., 1.))
0.0

>>> pyo.value(
... h2s_binary.eval_pyomo(h2s_binary.f_ref, h2s_binary.f_ref, h2s_binary.T_ref)
... - h2s_binary.q_ref*h2s_binary.eval_dimensionless_pyomo(1., 1., 1.)
... )
0.0

Comparison to scipy

>>> import numpy as np
>>> popt, pcov = h2s_binary.solve_scipy()
>>> popt
array([  1.01898639, -11.07321779,  -8.15011325,  -7.32582652,
        -7.11673647])
>>> popt - np.array(list(map(pyo.value,
...         [h2s_binary.q_mi_star, h2s_binary.H_i_star, h2s_binary.H_j_star, h2s_binary.A_i, h2s_binary.A_j])))
array([-1.12501256e-06, -1.04698086e-04, -1.76342848e-04, -1.04982550e-04,
       -1.81042032e-04])
>>> h2s_binary.get_R2_scipy()
0.998828

which is nearly the same as the pyomo/ipopt result.

Unary Isotherms

Langmuir

The temperature-dependent unary Langmuir isotherm is expressed as

(1)\[q_i = \frac{q_{\text{m},i}k_if_i}{1 + k_i f_i}\]

where \(f_i\), is the fugacity of component i, can be calculated assuming ideal gas

\[f_i^\text{IG} = y_i P\]

or, using the RealGas package to calculate \(\phi_i\) from \(y_i,P,T\) data,

\[f_i = \phi_i y_i P\]

An Arrhenius relationship for \(k_i\) is assumed as

\[k_i = k_{i,\infty}\exp\left(\frac{-\Delta H_i}{RT}\right)\]

Introducing the dimensionless parameters

(2)\[\theta_i = \frac{q_i}{q_\text{ref}}\]

(3)\[f_i^\star = \frac{f_i}{f_\text{ref}}\]

(4)\[T^\star = \frac{T}{T_\text{ref}}\]

The variables to be fit in dimensionless form are

(5)\[H_i^\star = \frac{\Delta H_i}{R T_\text{ref}}\]

(6)\[q_{\text{m},i}^\star = \frac{q_{\text{m},i}}{q_\text{ref}}\]

(7)\[A_i = \ln\left(k_{i,\infty} f_\text{ref}\right)\]

So that Equation (1) becomes

(8)\[\theta_i = \frac{q_{\text{m},i}^\star\exp\left(A_i - \frac{H_i^\star}{T^\star}\right)f_i^\star}{1 + \exp\left(A_i - \frac{H_i^\star}{T^\star}\right)f_i^\star}\]

Modules

class isotherm_models.unaryisotherm.UnaryIsotherm(f_i, q_i, T, q_ref=None, f_ref=None, T_ref=None, **kwargs)

Base class for Unary Isotherms

Parameters

• f_i (list) – fugacities of component i (can be calculated assuming ideal gas or real gas)

• q_i (list) – loadings of component i

• T (list, optional) – temperatures in [K], defaults to None

• q_ref (float, optional) – reference loading, defaults to maximum loading in q_i

• f_ref (float, optional) – reference fugacity, defaults to maximum fugacity in f_j

• T_ref (float, optional) – reference temperature, defaults to maximum temperature in T

• points (list, derived from input) – state points at which a pressure and temperature are provided

• f_i_star (list, derived) – dimensionless fugacitities, calculated by Equation (3)

• theta (list, derived) – dimensionless loadings, calculated by Equation (2)

• T_star (list, derived) – dimensionless temperatures, calculated by Equation (4)

• theta_calc (pyo.Var, derived from input) – calculated dimensionless at each state point

• objective (pyo.Objective, derived from input) – objective function to be minimized for isotherm fitting, calculated from isotherm_models.unaryisotherm.UnaryIsotherm.objective_rule_pyomo()

• R2 (pyo.Expression, derived) – coefficient of determination, see isotherm_models.unaryisotherm.UnaryIsotherm.R2_rule()

• q_calc (pyo.Expression, derived) – calculated loading in units

R2_rule()

Calculate coefficient of determination squared, \(R^2\)

isotherm_eq_rule(point)

Constraint for dimensionless expression

objective_rule_pyomo()

Sum of squared errors between calculated loading and predicted loading

\[\sum_i \left(\theta_i^{\text{raw}}-\theta_i^{\text{calc}}\right)^2\]

where raw denotes the raw data obtained by experiment or molecular simulation and calc denotes the data calculated from the isotherm function

solve(solver=<pyomo.solvers.plugins.solvers.IPOPT.IPOPT object>, **kwargs)

Solve constraints subject to objective function

Parameters

• solver (pyo.SolverFactory, optional) – solver for solving model equations, defaults to pyo.SolverFactory(‘ipopt’)

• kwargs – for solve argument

class isotherm_models.unaryisotherm.LangmuirUnary(*args, **kwargs)

Langmuir isotherm for unary mixture

Isotherm is Equation (1). Dimensionless isotherm is Equation (8). Dimensionless variables to be fit are \(H_i^\star\), \(A_i\), and \(q_{\text{m},i}^\star\), as defined in Equations (5), (6), and (7), respectively.

Parameters

• H_i_star (pyo.Var) – \(H_i^\star\), dimensionless heat of adsorption of component i

• A_i (pyo.Var) – \(A_i\), dimensionless langmuir constant in logarithmic space

• q_mi_star (pyo.Var) – \(q_{\text{m}i}^\star\), dimensionless saturation loading

• q_mi (pyo.Expression) – langmuir saturaiton loading

• k_i_inf (pyo.Expression) – langmuir adsorption constant independent of temperature

• dH_i (pyo.Expression) – heat of adsorption of component i

dimensionless_isotherm_expression(point)

Dimensionless isotherm expression, see Equation (8)

eval(f_i, T, q_mi, k_i_inf, dH_i)

evaluate using generic types (any type)

eval_pyomo(f_i, T)

evaluate using pyomo types (any type)

initial_guess_A_i()

Initial guess for \(A_i\) variable

Todo

Come up with logical initial guess

initial_guess_H_i_star()

Initial guess for \(H_i^\star\) variable

This value of 10 corresponds to an absolute value for heat of adsorption of \(10RT\) which is approximately 25 kJ/mol

initial_guess_q_mi_star()

Initial guess for \(q_mi^\star\) variable

If \(q_\text{ref}\) is chosen to be the saturation loading, \(q_mi^\star\) will be 1. Thus, we return 1 as initial guess

initial_guess_vector()

p0 in scipy curve fit; initial guess for dimensionless parameters

Note

order here must be the same as last args in LangmuirUnary.eval_dimensionless()

isotherm_expression(point)

Isotherm expression in unit quantities, see Equation (1)

Binary Isotherms

Binary Langmuir

(9)\[q_i = \frac{q_{\text{m},i}k_i\hat{f}_i}{1 + k_i \hat{f}_i + k_j \hat{f}_j}\]

Arrhenius relationships are used for \(k_i\) and \(k_j\), and dimensionless variables are used as illustrated in isotherm_models.unaryisotherm.LangmuirUnary

Note

This isotherm is not equivalent to the conventional extended langmuir isotherm, because both \(k_i\) and \(k_j\) are fit simultaneously to binary data.

For completeness, the relationships are repeated for the binary case below

\[\begin{split}\begin{align} k_i &= k_{i,\infty}\exp\left(\frac{-\Delta H_i}{RT}\right)\\ k_j &= k_{j,\infty}\exp\left(\frac{-\Delta H_j}{RT}\right)\\ \end{align}\end{split}\]

The dimensionless parameters \(\theta_i\) and \(T^\star\) are calculated as the unary case, as shown in Equations (2) and (4), respectively. The other dimensionless parameters are

(10)\[\hat{f}_i^\star = \frac{\hat{f}_i}{f_\text{ref}}\]

(11)\[\hat{f}_j^\star = \frac{\hat{f}_j}{f_\text{ref}}\]

The dimensionless variables to be fit include \(H_i^\star\), \(q_{\text{m},i}^\star\), \(A_i\), \(H_j^\star\), \(q_{\text{m},j}^\star\), and \(A_j\). The former three (\(H_i^\star\), \(q_{\text{m},i}^\star\), and \(A_i\)) have the same expression as the unary case, as shown in Equations (5), (6), and (7), respectively. The latter two are expressed as

(12)\[H_j^\star = \frac{\Delta H_j}{R T_\text{ref}}\]

(13)\[A_j = \ln\left(k_{j,\infty} f_\text{ref}\right)\]

So that Equation (9) becomes

(14)\[\theta_i = \frac{ q_{\text{m},i}^\star\exp\left(A_i - \frac{H_i^\star}{T^\star}\right)\hat{f}_i^\star }{ 1 + \exp\left(A_i - \frac{H_i^\star}{T^\star}\right)\hat{f}_i^\star + \exp\left(A_j - \frac{H_j^\star}{T^\star}\right)\hat{f}_j^\star }\]

Modules

class isotherm_models.binaryisotherm.BinaryIsotherm(hat_f_i, hat_f_j, q_i, T, f_ref=None, **kwargs)

Base class for Binary Isotherms, inherits from UnaryIsotherm

The following additional dimensionless variables are used in computations

Parameters

• hat_f_j (list) – mixture fugacities of component i

• hat_f_j – mixture fugacities of component j

• q_i (list) – loadings of component i

• T (list, optional) – temperatures in [K], defaults to None

• points (list, derived from input) – state points at which a pressure and temperature are provided

• hat_f_i_star (list, derived) – dimensionless fugacitities of component i, calculated by Equation (10)

• hat_f_j_star (list, derived) – dimensionless fugacitities of component j, calculated by Equation (11)

• theta (list, derived) – dimensionless loadings, calculated by Equation (2)

• T_star (list, derived) – dimensionless temperatures, calculated by Equation (4)

• theta_calc (pyo.Var, derived from input) – calculated dimensionless at each state point

• objective (pyo.Objective, derived from input) – objective function to be minimized for isotherm fitting, calculated from isotherm_models.unaryisotherm.UnaryIsotherm.objective_rule_pyomo()

• R2 (pyo.Expression, derived) – coefficient of determination, see isotherm_models.unaryisotherm.UnaryIsotherm.R2_rule()

• q_calc (pyo.Expression, derived) – calculated loading in units

• unary_points (list, derived) – points where only i is present, derived from where \(\hat{f}_j < 1\times10^{-12}\)

plot_adsorption_surface()

plot surface of adsorption data

Todo

implement this helpful for debugging

class isotherm_models.binaryisotherm.BinaryLangmuir(*args, **kwargs)

Temperature-dependent extended unary Langmuir isotherm, expressed as

Isotherm is Equation (9). Dimensionless isotherm is Equation (14). Dimensionless variables to be fit are \(H_i^\star\), \(A_i\), \(q_{\text{m},i}^\star\), \(H_j_star\), and \(A_j\), as defined in Equations (5), (6), (7), (12), and (13), respectively.

Parameters

• H_i_star (pyo.Var) – \(H_i^\star\), dimensionless heat of adsorption of component i

• A_i (pyo.Var) – \(A_i\), dimensionless langmuir constant in logarithmic space

• H_j_star (pyo.Var) – \(H_j^\star\), dimensionless heat of adsorption of component j

• A_j (pyo.Var) – \(A_j\), dimensionless langmuir constant in logarithmic space

• q_mi_star (pyo.Var) – \(q_{\text{m},i}^\star\), dimensionless saturation loading

• q_mi (pyo.Expression) – langmuir saturation loading

• k_i_inf (pyo.Expression) – langmuir adsorption constant independent of temperature

• dH_i (pyo.Expression) – heat of adsorption of component i

• k_j_inf (pyo.Expression) – langmuir adsorption constant independent of temperature

• dH_j (pyo.Expression) – heat of adsorption of component j

dimensionless_isotherm_expression(point)

Dimensionless isotherm expression, see Equation (14)

eval(x, q_mi, dH_i, dH_j, k_i_inf, k_j_inf)

evaluate using generic types (any type)

eval_pyomo(hat_f_i, hat_f_j, T)

Evaluate isotherm in dimensional form

initial_guess_vector()

p0 in scipy curve fit; initial guess for dimensionless parameters

Note

order here must be the same as last args in LangmuirUnary.eval_dimensionless()

isotherm_expression(point)

Isotherm expression in unit quantities, see Equation (9)

Adsorption Equilibria Rules

For gases and their mixtures, the rules, limits, and consistency tests are [TM88]

1. Unary isotherms should reduce to Henry’s law at the limit of zero pressure.

2. In spite of incorrect limits at zero pressure, both the Toth and DR equations are accurate for calculating spreading pressure provided the pressure is sufficiently high.

3. At fixed temperature and pressure, thermodynamically consistent \(x\)-\(y\) diagrams intersect each other at least once. This can be derived by considering the Gibbs adsorption isotherm at constant spreading pressure.

4. Mixed gas isotherms should display continuity with single-gas isotherms. That is,

   \[\lim_{y_i\to 1} q_\text{t} = q_i \;(\text{constant}\; P, T)\]

   where \(q_\text{t}=\sum_iq_i\) is the total loading. Discontinuities generate inaccurate values of adsorbate vapor pressure that lower the quality of calculations of mixed-gas adsorption.

5. Isothermal selectivity curves for different vapor compositions should intersect at the limit of zero pressure.

6. Activity coefficients in the adsorbed phase are functions of spreading pressure as well as composition.

7. Imperfections in the gas phase led to corrections in fugacity that are small compared to the effect of nonidealities in the adsorbed phase. In most cases, vapor-phase imperfections may be ignored unless the pressure is above 500 kPa and experimental error is less than a few percent.

Real Adsorbed Solution Theory

Todo

implement this into the code

The Gibbs adsorption isotherm is

(1)\[-a \mathrm{d}\Pi + \sum_i x_i \mathrm{d}\mu_i = 0\]

where \(a\) is the surface area per mole of adsorbate, \(\Pi\) is the spreading pressure, \(x_i\) is the adsorbed mole fraction of component i, and \(\mu_i\) is the adsorbed-phase chemical potential of component i.

For change in equilibrium conditions,

(2)\[\mathrm{d}\mu_i = \mathrm{d}\mu_i^\text{g} = RT \mathrm{d} \ln{\hat{f}_i^\text{g}}\]

where \(\hat{f}_i^\text{g}\) is the fugacity of component i in the gas phase. And the substituting surface area of the adsorbent is

(3)\[A = a \sum_i q_i\]

where \(q_i\) is the loading of component i. Substituting Equations (2) and (3) into Equation (1) yields

(4)\[\frac{A}{RT} \mathrm{d}\Pi = \sum_i q_i \mathrm{d} \ln{\hat{f}_i^\text{g}}\]

If we have a good description of the multicomponent isotherms,

\[q_i = F(\{\hat{f}_k\})\]

where \(F\) is an isotherm function, Equation (4) can be simplified to

\[\frac{A\Pi}{RT} = \sum_i \int_0^{\hat{f}_i^\text{g}}\frac{q_i}{f_i^\prime}\mathrm{d}f_i^\prime\]

where \(f_i^\prime\) is a dummy variable for integration.

Data Sets

CO2 and N2 on BEA

Experiment from [PXSL14]

N2 adsorption on BEA, scanned from images in paper

P [atm]	Q [mmol/g]	T [K]	adsorbate
0.5254701189156284	0.07017543859649145		N2
0.5923867910171959	0.0789473684210531		N2
0.6568240613926388	0.08333333333333348		N2
0.7225015761212199	0.09210526315789469		N2
0.788179090849801	0.10087719298245634		N2
0.8526163612252438	0.10526315789473673		N2
0.9195330333268112	0.11403508771929838		N2
0.9988401921780905	0.1184210526315792		N2
0.41270462401356545	0.06140350877192979		N2
0.47590273701602204	0.06578947368421062		N2

CO2 adsorption on BEA, scanned from images in paper

P [atm]	Q [mmol/g]	T [K]	adsorbate
0.02981369160199132	0.09649122807017552		CO2
0.055855562077436444	0.17543859649122817		CO2
0.10917737342116132	0.3289473684210531		CO2
0.24682058305615331	0.7192982456140355		CO2
0.3137807343637904	0.9035087719298249		CO2
0.3832192004174003	1.0877192982456143		CO2
0.45017500380443043	1.254385964912281		CO2
0.5171318941716123	1.4254385964912284		CO2
0.5828463662253526	1.5833333333333337		CO2
0.6497989086719275	1.7368421052631582		CO2
0.6683960520880888	1.7763157894736845		CO2
0.6894736842105261	1.8245614035087723		CO2
0.7328670188482358	1.9166666666666672		CO2
0.8196504271831995	2.0877192982456148		CO2
0.9113904650101088	2.2587719298245617		CO2
0.9994075958173001	2.4078947368421058		CO2
0.15004021826561445	0.21052631578947345		CO2
0.21573729863692678	0.29824561403508776		CO2
0.2801941346551011	0.38157894736842124		CO2
0.34464988369312377	0.4605263157894739		CO2
0.4103447901041326	0.5394736842105265		CO2
0.4785190982412659	0.6228070175438596		CO2
0.5429759342594404	0.7061403508771931		CO2
0.6086686667101457	0.7763157894736845		CO2
0.6731244157481683	0.8552631578947372		CO2
0.7375779908258874	0.9254385964912284		CO2
0.8020326528837582	1.0000000000000002		CO2
0.8677253853344638	1.0701754385964914		CO2
0.9321789604121826	1.1403508771929827		CO2
0.9656438183438771	1.1710526315789478		CO2
0.9991108502358745	1.210526315789474		CO2
0.08434205091415034	0.1184210526315792		CO2
0.13265397073849425	0.05701754385964941		CO2
0.10539142155264239	0.052631578947368585		CO2
0.0595360768712363	0.02631578947368407		CO2
0.20948933672471134	0.08771929824561386		CO2
0.26154155525120115	0.1184210526315792		CO2
0.3297017326463618	0.14473684210526327		CO2
0.39414552490271526	0.17543859649122817		CO2
0.4610676319050413	0.20614035087719307		CO2
0.5267484075740776	0.2280701754385963		CO2
0.5911911128502791	0.2543859649122808		CO2
0.6581132198526054	0.2850877192982457		CO2
0.7225548381486553	0.3070175438596494		CO2
0.7869986304050085	0.3377192982456143		CO2
0.8539196504271831	0.3640350877192984		CO2
0.9196004260962194	0.38596491228070207		CO2
0.9989141068284091	0.4166666666666665		CO2

H2S and CH4 on MFI

Molecular simulation from [STS15],

H2S adsorption on MFI, taken from tables in SI

P [bar]	Q [mmol/g]	d Q [mmol/g]	adsorbate	T [K]
0.001	0.01	0.0003	H2S	298
0.01	0.098	0.001	H2S	298
0.1	0.90	0.01	H2S	298
0.3	1.91	0.01	H2S	298
0.5	2.28	0.01	H2S	298
	2.61	0.01	H2S	298
1.5	2.742	0.004	H2S	298
2	2.810	0.005	H2S	298
3	2.90	0.01	H2S	298
4	2.95	0.01	H2S	298
5	2.983	0.004	H2S	298
6	3.010	0.003	H2S	298
7	3.030	0.004	H2S	298
8	3.050	0.004	H2S	298
9	3.064	0.004	H2S	298
10	3.079	0.003	H2S	298
0.001	0.00226	0.00002	H2S	343
0.01	0.0226	0.0002	H2S	343
0.1	0.221	0.003	H2S	343
0.3	0.62	0.01	H2S	343
0.5	0.96	0.01	H2S	343
	1.54	0.01	H2S	343
1.5	1.87	0.01	H2S	343
2	2.074	0.004	H2S	343
3	2.321	0.004	H2S	343
4	2.46	0.01	H2S	343
5	2.55	0.01	H2S	343
6	2.62	0.01	H2S	343
7	2.665	0.003	H2S	343
8	2.704	0.004	H2S	343
9	2.737	0.004	H2S	343
10	2.762	0.003	H2S	343
20	2.905	0.004	H2S	343
30	2.969	0.002	H2S	343
40	3.005	0.002	H2S	343
50	3.030	0.003	H2S	343

CH4 adsorption on MFI, taken from tables in SI

P [bar]	Q [mmol/g]	d Q [mmol/g]	adsorbate	T [K]
0.001	0.01	0.0003	H2S	298
0.01	0.098	0.001	H2S	298
0.1	0.90	0.01	H2S	298
0.3	1.91	0.01	H2S	298
0.5	2.28	0.01	H2S	298
	2.61	0.01	H2S	298
1.5	2.742	0.004	H2S	298
2	2.810	0.005	H2S	298
3	2.90	0.01	H2S	298
4	2.95	0.01	H2S	298
5	2.983	0.004	H2S	298
6	3.010	0.003	H2S	298
7	3.030	0.004	H2S	298
8	3.050	0.004	H2S	298
9	3.064	0.004	H2S	298
10	3.079	0.003	H2S	298
0.001	0.00226	0.00002	H2S	343
0.01	0.0226	0.0002	H2S	343
0.1	0.221	0.003	H2S	343
0.3	0.62	0.01	H2S	343
0.5	0.96	0.01	H2S	343
	1.54	0.01	H2S	343
1.5	1.87	0.01	H2S	343
2	2.074	0.004	H2S	343
3	2.321	0.004	H2S	343
4	2.46	0.01	H2S	343
5	2.55	0.01	H2S	343
6	2.62	0.01	H2S	343
7	2.665	0.003	H2S	343
8	2.704	0.004	H2S	343
9	2.737	0.004	H2S	343
10	2.762	0.003	H2S	343
20	2.905	0.004	H2S	343
30	2.969	0.002	H2S	343
40	3.005	0.002	H2S	343
50	3.030	0.003	H2S	343

H2S/CH4 Binary adsorption on MFI, taken from tables in SI

T [K]	P [bar]	y H2S [mol/mol]	dY H2S [mol/mol]	Q H2S [mmol/g]	dQ H2S [mmol/g]	Q CH4 [mmol/g]	dQ CH4 [mmol/g]	dH H2S [kJ/mol]	d dH H2S [kJ/mol]	dH CH4 [kJ/mol]	d dH CH4 [kJ/mol]
298	1	0.00472	0.00002	0.0406	0.0001	0.499	0.001	-28.5	0.2	-19.21	0.05
298	1	0.00944	0.00004	0.0816	0.0003	0.492	0.001	-28.5	0.2	-19.22	0.02
298	1	0.0141	0.0001	0.1231	0.0005	0.483	0.001	-28.6	0.1	-19.34	0.03
298	1	0.019	0.0001	0.164	0.001	0.476	0.001	-28.6	0.1	-19.37	0.05
298	1	0.0239	0.0001	0.204	0.001	0.47	0.001	-28.5	0.1	-19.39	0.03
298	1	0.0288	0.0002	0.246	0.001	0.462	0.001	-28.6	0.1	-19.4	0.1
298	1	0.0337	0.0002	0.287	0.001	0.455	0.001	-28.7	0.1	-19.47	0.04
298	1	0.0385	0.0001	0.33	0.001	0.4473	0.0004	-28.7	0.1	-19.53	0.04
298	1	0.1038	0.0002	0.816	0.001	0.358	0.001	-29.4	0.1	-19.88	0.04
298	1	0.1665	0.0003	1.212	0.002	0.281	0.001	-30.07	0.03	-20.43	0.05
298	1	0.2421	0.0003	1.571	0.002	0.211	0.001	-30.82	0.05	-21	0.1
298	1	0.3341	0.0003	1.873	0.002	0.149	0.001	-31.4	0.1	-21.4	0.1
298	1	0.4433	0.0002	2.112	0.001	0.1	0.0002	-32	0.1	-21.9	0.1
298	1	0.5673	0.0001	2.295	0.001	0.0623	0.0002	-32.5	0.1	-22.2	0.2
298	1	0.7038	0.0001	2.429	0.001	0.0353	0.0002	-32.8	0.1	-22.4	0.2
298	1	0.84866	0.00002	2.534	0.001	0.0151	0.0001	-33	0.1	-22.7	0.3
298	10	0.00167	0.00002	0.0633	0.0001	1.834	0.002	-29.5	0.3	-20.19	0.03
298	10	0.00339	0.00002	0.1265	0.0001	1.796	0.002	-29.8	0.1	-20.26	0.04
298	10	0.00509	0.00001	0.1898	0.0001	1.758	0.002	-29.9	0.1	-20.35	0.03
298	10	0.0069	0.0001	0.2525	0.0003	1.717	0.002	-29.8	0.1	-20.4	0.1
298	10	0.0088	0.0001	0.315	0.0004	1.682	0.001	-30	0.1	-20.48	0.05
298	10	0.0106	0.0001	0.3784	0.0005	1.643	0.001	-30.3	0.2	-20.46	0.05
298	10	0.0128	0.0001	0.439	0.001	1.605	0.001	-29.9	0.1	-20.49	0.05
298	10	0.0147	0.0001	0.502	0.001	1.567	0.001	-30.2	0.1	-20.54	0.05
298	10	0.043	0.0002	1.235	0.001	1.11	0.001	-31.3	0.1	-21.3	0.1
298	10	0.0807	0.0001	1.789	0.001	0.758	0.001	-32.1	0.1	-21.9	0.1
298	10	0.1415	0.0003	2.251	0.001	0.465	0.001	-32.8	0.1	-22.3	0.1
298	10	0.2364	0.0003	2.575	0.001	0.265	0.001	-33.2	0.1	-22.7	0.1
298	10	0.3628	0.0002	2.773	0.001	0.15	0.001	-33	0.1	-22.4	0.1
298	10	0.5091	0.0001	2.896	0.001	0.0844	0.0004	-33.1	0.1	-22.7	0.1
298	10	0.6667	0.0001	2.977	0.001	0.0443	0.0004	-32.8	0.1	-22.2	0.2
298	10	0.83109	0.00004	3.035	0.001	0.018	0.0001	-32.9	0.1	-22.5	0.4
343	1	0.0079	0.00001	0.0169	0.0001	0.2019	0.0004	-27.8	0.2	-19.15	0.05
343	1	0.01582	0.00003	0.0338	0.0002	0.1998	0.0003	-27.9	0.1	-19.14	0.03
343	1	0.02383	0.00002	0.0504	0.0001	0.1978	0.0002	-28	0.1	-19.14	0.05
343	1	0.03177	0.00003	0.0677	0.0002	0.1955	0.0002	-28	0.1	-19.22	0.03
343	1	0.03976	0.00004	0.0849	0.0003	0.1926	0.0004	-28.1	0.1	-19.2	0.1
343	1	0.0479	0.0001	0.101	0.0004	0.1902	0.0004	-28.1	0.1	-19.2	0.1
343	1	0.0561	0.0001	0.1176	0.0004	0.1872	0.0003	-27.9	0.05	-19.2	0.1
343	1	0.064	0.0001	0.136	0.001	0.1853	0.0004	-28.1	0.1	-19.34	0.05
343	1	0.1643	0.0002	0.339	0.001	0.1577	0.0001	-28.3	0.1	-19.43	0.04
343	1	0.2519	0.0001	0.509	0.001	0.1346	0.0003	-28.47	0.04	-19.57	0.04
343	1	0.344	0.0001	0.675	0.001	0.112	0.0002	-28.75	0.05	-19.78	0.04
343	1	0.4403	0.0001	0.84	0.001	0.09	0.0002	-28.9	0.1	-19.9	0.1
343	1	0.542	0	0.995	0.001	0.0695	0.0001	-29.23	0.04	-20.11	0.03
343	1	0.6487	0.0001	1.146	0.001	0.0498	0.0001	-29.46	0.03	-20.2	0.1
343	1	0.76069	0.00004	1.285	0.001	0.0316	0.00005	-29.74	0.02	-20.6	0.1
343	1	0.87781	0.00002	1.418	0.001	0.01502	0.00005	-29.96	0.02	-20.6	0.2
343	10	0.00368	0.00002	0.0502	0.0001	1.191	0.001	-29	0.1	-19.84	0.04
343	10	0.00743	0.00004	0.1002	0.0003	1.169	0.001	-28.8	0.2	-19.85	0.02
343	10	0.01121	0.00004	0.1502	0.0003	1.146	0.001	-28.8	0.2	-19.91	0.05
343	10	0.0151	0.0001	0.2	0.001	1.124	0.002	-29	0.2	-19.92	0.04
343	10	0.0192	0.0001	0.248	0.001	1.102	0.001	-28.9	0.1	-20.01	0.03
343	10	0.0231	0.0001	0.298	0.001	1.079	0.001	-29	0.1	-20.06	0.04
343	10	0.027	0	0.3483	0.0002	1.056	0.002	-29	0.1	-20	0.1
343	10	0.0313	0.0001	0.396	0.001	1.036	0.002	-29.2	0.1	-20.05	0.02
343	10	0.0867	0.0005	0.97	0.003	0.78	0.001	-30	0.1	-20.8	0.1
343	10	0.1463	0.0004	1.4	0.003	0.586	0.001	-30.8	0.1	-21.2	0.1
343	10	0.2215	0.0003	1.774	0.001	0.419	0.001	-31.4	0.1	-21.8	0.1
343	10	0.3161	0.0002	2.074	0.001	0.288	0.001	-31.9	0.1	-22.09	0.05
343	10	0.4289	0.0002	2.304	0.001	0.187	0.001	-32.3	0.04	-22.5	0.1
343	10	0.5576	0.0002	2.472	0.001	0.1171	0.0004	-32.5	0.1	-22.7	0.1
343	10	0.6977	0.0001	2.595	0.001	0.0658	0.0004	-32.8	0.1	-22.7	0.2
343	10	0.84586	0.00004	2.69	0.001	0.028	0.0001	-33	0.1	-22.9	0.2
343	50	0.00243	0.00002	0.0599	0.0001	2.097	0.001	-28.5	0.1	-20.06	0.04
343	50	0.00488	0.00003	0.1198	0.0002	2.055	0.001	-28.7	0.2	-20.2	0.02
343	50	0.0075	0.0001	0.1789	0.0004	2.012	0.001	-29	0.2	-20.17	0.05
343	50	0.0101	0.0001	0.2385	0.0003	1.968	0.001	-29.1	0.2	-20.16	0.04
343	50	0.0126	0.0001	0.2979	0.0003	1.925	0.001	-28.9	0.1	-20.21	0.03
343	50	0.0154	0.0001	0.357	0.001	1.882	0.001	-29.2	0.1	-20.25	0.04
343	50	0.0183	0.0001	0.414	0.001	1.84	0.001	-29.2	0.1	-20.3	0.1
343	50	0.021	0.0002	0.474	0.001	1.798	0.001	-29.4	0.1	-20.37	0.02
343	50	0.0614	0.0004	1.152	0.002	1.306	0.002	-29.8	0.1	-20.8	0.1
343	50	0.1101	0.0002	1.657	0.001	0.941	0.001	-30.3	0.1	-21.4	0.1
343	50	0.1794	0.0002	2.081	0.001	0.637	0.001	-31	0.1	-21.8	0.1
343	50	0.2746	0.0002	2.4	0.001	0.412	0.001	-31.2	0.1	-21.96	0.05
343	50	0.3939	0.0002	2.624	0.001	0.259	0.001	-30.83	0.04	-22	0.1
343	50	0.5315	0.0003	2.776	0.002	0.157	0.001	-30.9	0.1	-22.3	0.1
343	50	0.6808	0.0001	2.885	0.001	0.0887	0.0004	-30.5	0.1	-22.1	0.2
343	50	0.8379	0.0001	2.966	0.001	0.0387	0.0002	-30.3	0.1	-23.1	0.2
298	0.001	0	0			0.0006	0.00001
298	0.01	0	0			0.006	0.0001
298	0.1	0	0			0.058	0.001
298	0.3	0	0			0.168	0.003
298	0.5	0	0			0.274	0.005
298	1	0	0			0.5	0.01
298	1.5	0	0			0.7	0.01
298	2	0	0			0.85	0.01
298	5	0	0			1.46	0.01
298	10	0	0			1.88	0.01
298	12	0	0			1.98	0.01
298	15	0	0			2.09	0.01
298	18	0	0			2.18	0.01
298	20	0	0			2.22	0.01
298	25	0	0			2.33	0.01
298	30	0	0			2.39	0.01
343	0.001	0	0			0.000217	0.000001
343	0.01	0	0			0.00218	0.000001
343	0.1	0	0			0.0217	0.0001
343	0.3	0	0			0.0639	0.0003
343	0.5	0	0			0.106	0.001
343	1	0	0			0.204	0.001
343	1.5	0	0			0.297	0.001
343	2	0	0			0.379	0.001
343	5	0	0			0.788	0.004
343	10	0	0			1.213	0.003
343	12	0	0			1.327	0.003
343	15	0	0			1.472	0.003
343	18	0	0			1.585	0.002
343	20	0	0			1.643	0.003
343	25	0	0			1.779	0.002
343	30	0	0			1.877	0.003
343	40	0	0			2.032	0.002
343	50	0	0			2.141	0.002
298	0.001	1	0	0.01	0.0003
298	0.01	1	0	0.098	0.001
298	0.1	1	0	0.9	0.01
298	0.3	1	0	1.91	0.01
298	0.5	1	0	2.28	0.01
298	1	1	0	2.61	0.01
298	1.5	1	0	2.742	0.004
298	2	1	0	2.81	0.005
298	3	1	0	2.9	0.01
298	4	1	0	2.95	0.01
298	5	1	0	2.983	0.004
298	6	1	0	3.01	0.003
298	7	1	0	3.03	0.004
298	8	1	0	3.05	0.004
298	9	1	0	3.064	0.004
298	10	1	0	3.079	0.003
343	0.001	1	0	0.00226	0.00002
343	0.01	1	0	0.0226	0.0002
343	0.1	1	0	0.221	0.003
343	0.3	1	0	0.62	0.01
343	0.5	1	0	0.96	0.01
343	1	1	0	1.54	0.01
343	1.5	1	0	1.87	0.01
343	2	1	0	2.074	0.004
343	3	1	0	2.321	0.004
343	4	1	0	2.46	0.01
343	5	1	0	2.55	0.01
343	6	1	0	2.62	0.01
343	7	1	0	2.665	0.003
343	8	1	0	2.704	0.004
343	9	1	0	2.737	0.004
343	10	1	0	2.762	0.003
343	20	1	0	2.905	0.004
343	30	1	0	2.969	0.002
343	40	1	0	3.005	0.002
343	50	1	0	3.03	0.003

Fugacity coefficients and fugacities

Calculated from :code`RealGas` python package using virial equation of state. The critical temperatures and densities were obtained from the TraPPE website. The accentric factors and critical compressibilities were obtained from DIPPR [RWO+07]. The critical pressure was calculated from all the other critical properties above. The \(k_ij\) parameter was set to 0.

H2S/CH4 Binary adsorption on MFI, taken from tables in SI and added fugacities

T [K]	P [bar]	y H2S [mol/mol]	dY H2S [mol/mol]	Q H2S [mmol/g]	dQ H2S [mmol/g]	Q CH4 [mmol/g]	dQ CH4 [mmol/g]	dH H2S [kJ/mol]	d dH H2S [kJ/mol]	dH CH4 [kJ/mol]	d dH CH4 [kJ/mol]	fugacity CH4 [Pa]	fugacity H2S [Pa]	activity coefficient CH4	activity coefficient H2S
298	1.0	0.00472	2e-05	0.0406	0.0001	0.499	0.001	-28.5	0.2	-19.21	0.05	99354.64683398815	467.70268175311554	0.9982582472669816	0.9908955121888041
298	1.0	0.00944	4e-05	0.0816	0.0003	0.49200000000000005	0.001	-28.5	0.2	-19.22	0.02	98883.45755026388	935.4204755461337	0.9982581322712797	0.99091152070565
298	1.0	0.0141	0.0001	0.1231	0.0005	0.483	0.001	-28.6	0.1	-19.34	0.03	98418.25065254685	1397.2074243643547	0.9982579435292306	0.9909272513222372
298	1.0	0.019	0.0001	0.16399999999999998	0.001	0.47600000000000003	0.001	-28.6	0.1	-19.37	0.05	97929.07688426304	1882.7930534842294	0.9982576644675131	0.9909437123601208
298	1.0	0.0239	0.0001	0.204	0.001	0.47	0.001	-28.5	0.1	-19.39	0.03	97439.89532468858	2368.3946190505576	0.9982573027834093	0.9909600916529528
298	1.0	0.0288	0.0002	0.24600000000000002	0.001	0.462	0.001	-28.6	0.1	-19.4	0.1	96950.70609528711	2854.012000886412	0.998256858477009	0.9909763891966709
298	1.0	0.0337	0.0002	0.287	0.001	0.455	0.001	-28.7	0.1	-19.47	0.04	96461.50931752406	3339.6450788069737	0.9982563315484224	0.9909926049872324
298	1.0	0.0385	0.0001	0.33	0.001	0.4473	0.0004	-28.7	0.1	-19.53	0.04	95982.28894558216	3815.38238070176	0.9982557352634649	0.9910084105718858
298	1.0	0.1038	0.0002	0.816	0.001	0.358	0.001	-29.4	0.1	-19.88	0.04	89462.24616376412	10288.81831126354	0.9982397474198184	0.9912156369232696
298	1.0	0.1665	0.0003	1.212	0.002	0.281	0.001	-30.07	0.03	-20.43	0.05	83200.85252827851	16506.825636128993	0.9982105882216977	0.9914009391068465
298	1.0	0.2421	0.0003	1.571	0.002	0.21100000000000002	0.001	-30.82	0.05	-21.0	0.1	75650.35260477995	24006.794379045048	0.9981574429974925	0.9916065418853799
298	1.0	0.3341	0.0003	1.8730000000000002	0.002	0.149	0.001	-31.4	0.1	-21.4	0.1	66461.23141587035	33137.05514274732	0.9980662474225915	0.9918304442606202
298	1.0	0.4433	0.0002	2.112	0.001	0.1	0.0002	-32.0	0.1	-21.9	0.1	55554.21876296531	43977.96231550829	0.9979202220758993	0.9920587032598306
298	1.0	0.5673	0.0001	2.295	0.001	0.0623	0.0002	-32.5	0.1	-22.2	0.2	43170.682549052566	56291.392323458014	0.9977047041611409	0.9922685056135733
298	1.0	0.7038	0.0001	2.4290000000000003	0.001	0.0353	0.0002	-32.8	0.1	-22.4	0.2	29543.17708750116	69847.83447293856	0.9974063837778919	0.9924386824799454
298	1.0	0.8486600000000001	2e-05	2.5340000000000003	0.001	0.0151	0.0001	-33.0	0.1	-22.7	0.3	15088.898370840641	84233.71308811927	0.9970198474190993	0.9925495850884839
298	10.0	0.0016699999999999998	2e-05	0.0633	0.0001	1.834	0.002	-29.5	0.3	-20.19	0.03	981077.5470453583	1523.8757940066832	0.9827186872530709	0.9125004754531038
298	10.0	0.00339	2e-05	0.1265	0.0001	1.796	0.002	-29.8	0.1	-20.26	0.04	979387.1239880387	3093.5595638865707	0.9827185398380899	0.9125544436243572
298	10.0	0.00509	1e-05	0.1898	0.0001	1.758	0.002	-29.9	0.1	-20.35	0.03	977716.2595347259	4645.1731723511175	0.9827182956596335	0.9126076959432451
298	10.0	0.0069	0.0001	0.2525	0.0003	1.7169999999999999	0.002	-29.8	0.1	-20.4	0.1	975937.1743688908	6297.383652599459	0.9827179280725917	0.9126642974781825
298	10.0	0.0088	0.0001	0.315	0.0004	1.682	0.001	-30.0	0.1	-20.48	0.05	974069.5094911745	8031.967735781164	0.9827174228119193	0.9127236063387687
298	10.0	0.0106	0.0001	0.3784	0.0005	1.643	0.001	-30.3	0.2	-20.46	0.05	972300.0329249608	9675.464740041176	0.9827168313371345	0.9127796924567146
298	10.0	0.0128	0.0001	0.439	0.001	1.605	0.001	-29.9	0.1	-20.49	0.05	970137.1950898683	11684.45578726241	0.9827159593698018	0.9128481083798757
298	10.0	0.0147	0.0001	0.502	0.001	1.567	0.001	-30.2	0.1	-20.54	0.05	968269.162767907	13419.734023255814	0.9827150743610139	0.9129070764119602
298	10.0	0.043	0.0002	1.235	0.001	1.11	0.001	-31.3	0.1	-21.3	0.1	940431.8576733811	39292.21234277575	0.9826874165866052	0.9137723800645523
298	10.0	0.0807	0.0001	1.7890000000000001	0.001	0.758	0.001	-32.1	0.1	-21.9	0.1	903311.9315181902	73831.39189822483	0.9826084319788864	0.9148871362853139
298	10.0	0.1415	0.0003	2.251	0.001	0.465	0.001	-32.8	0.1	-22.3	0.1	843372.9343998154	129697.93604663569	0.982379655678294	0.9165931876087329
298	10.0	0.2364	0.0003	2.575	0.001	0.265	0.001	-33.2	0.1	-22.7	0.1	749681.564622155	217258.3049635014	0.9817726095104178	0.9190283627897691
298	10.0	0.3628	0.0002	2.773	0.001	0.15	0.001	-33.0	0.1	-22.4	0.1	624769.3838252344	334442.58751575556	0.9804918139127972	0.9218373415539017
298	10.0	0.5091	0.0001	2.8960000000000004	0.001	0.0844	0.0004	-33.1	0.1	-22.7	0.1	480266.3604646813	470644.29587924975	0.9783384812888191	0.9244633586314079
298	10.0	0.6667	0.0001	2.977	0.001	0.0443	0.0004	-32.8	0.1	-22.2	0.2	325040.40524152294	617721.150628149	0.9752187375983286	0.9265353991722649
298	10.0	0.83109	4e-05	3.035	0.001	0.018000000000000002	0.0001	-32.9	0.1	-22.5	0.4	164026.61381715562	771130.8167478166	0.971088827287642	0.9278547651250967
343	1.0	0.0079	1e-05	0.0169	0.0001	0.2019	0.0004	-27.8	0.2	-19.15	0.05	99110.89024172857	785.3482956137495	0.9990010103994412	0.9941117665996828
343	1.0	0.015819999999999997	2.9999999999999997e-05	0.0338	0.0002	0.1998	0.0003	-27.9	0.1	-19.14	0.03	98319.66096250119	1572.7121075165753	0.9990008023176776	0.9941290186577595
343	1.0	0.02383	2e-05	0.0504	0.0001	0.1978	0.0002	-28.0	0.1	-19.14	0.05	97519.42698024753	2369.0506958603496	0.9990004505388154	0.9941463264206251
343	1.0	0.03177	2.9999999999999997e-05	0.0677	0.0002	0.1955	0.0002	-28.0	0.1	-19.22	0.03	96726.17327822208	3158.4569427216143	0.9989999615610141	0.9941633436328657
343	1.0	0.039760000000000004	4e-05	0.0849	0.0003	0.1926	0.0004	-28.1	0.1	-19.2	0.1	95927.91152225775	3952.860984131869	0.9989993285247205	0.994180328000973
343	1.0	0.0479	0.0001	0.10099999999999999	0.0004	0.1902	0.0004	-28.1	0.1	-19.2	0.1	95114.65081966543	4762.20596173629	0.9989985381752489	0.9941974867925448
343	1.0	0.0561	0.0001	0.1176	0.0004	0.1872	0.0003	-27.9	0.05	-19.2	0.1	94295.38285917533	5577.544044360629	0.9989975935922802	0.9942146246632139
343	1.0	0.064	0.0001	0.136	0.001	0.1853	0.0004	-28.1	0.1	-19.34	0.05	93506.07639572746	6363.078371912866	0.998996542689396	0.9942309956113853
343	1.0	0.1643	0.0002	0.33899999999999997	0.001	0.1577	0.0001	-28.3	0.1	-19.43	0.04	83484.02152096899	16338.434006332393	0.9989711801001434	0.9944269023939374
343	1.0	0.2519	0.0001	0.509	0.001	0.1346	0.0003	-28.47	0.04	-19.57	0.04	74730.01306979323	25053.46727590841	0.9989307989545947	0.9945798839185553
343	1.0	0.344	0.0001	0.675	0.001	0.11199999999999999	0.0002	-28.75	0.05	-19.78	0.04	65525.87303426274	34218.45386724007	0.9988700157662003	0.9947224961406997
343	1.0	0.4403	0.0001	0.84	0.001	0.09	0.0002	-28.9	0.1	-19.9	0.1	55902.0733056576	43803.316888868176	0.9987863731580775	0.9948516213687979
343	1.0	0.542	0.0	0.995	0.001	0.0695	0.0001	-29.23	0.04	-20.11	0.03	45739.34939814717	53927.14589545035	0.9986757510512483	0.994965791428973
343	1.0	0.6487	0.0001	1.146	0.001	0.0498	0.0001	-29.46	0.03	-20.2	0.1	35078.53753985252	64549.610699230274	0.9985350851082416	0.9950610559462043
343	1.0	0.76069	4e-05	1.285	0.001	0.0316	5e-05	-29.74	0.02	-20.6	0.1	23891.761691274674	75698.85059828975	0.9983603564947002	0.995134030923106
343	1.0	0.8778100000000001	2e-05	1.4180000000000001	0.001	0.015019999999999999	5e-05	-29.96	0.02	-20.6	0.2	12196.369925855415	87357.9610867268	0.9981479602140457	0.995180746251772
343	10.0	0.0036799999999999997	2e-05	0.0502	0.0001	1.1909999999999998	0.001	-29.0	0.1	-19.84	0.04	986412.0261184953	3468.642623528989	0.9900554301012678	0.9425659303067906
343	10.0	0.00743	4e-05	0.1002	0.0003	1.169	0.001	-28.8	0.2	-19.85	0.02	982698.8643201104	7003.844009180555	0.9900549727677751	0.9426438774132645
343	10.0	0.01121	4e-05	0.1502	0.0003	1.146	0.001	-28.8	0.2	-19.91	0.05	978955.6917559687	10567.915381225455	0.9900541993304633	0.9427221571119943
343	10.0	0.0151	0.0001	0.2	0.001	1.124	0.002	-29.0	0.2	-19.92	0.04	975103.2744252512	14236.316386376398	0.9900530758709017	0.9428024096938011
343	10.0	0.0192	0.0001	0.248	0.001	1.102	0.001	-28.9	0.1	-20.01	0.03	971042.5427480503	18103.423864423006	0.9900515321656304	0.942886659605365
343	10.0	0.0231	0.0001	0.298	0.001	1.079	0.001	-29.0	0.1	-20.06	0.04	967179.5727199535	21782.52570083111	0.9900497212815574	0.9429664805554593
343	10.0	0.027000000000000003	0.0	0.3483	0.0002	1.056	0.002	-29.0	0.1	-20.0	0.1	963316.2919149265	25462.241735252624	0.9900475764798834	0.9430459901945416
343	10.0	0.0313	0.0001	0.396	0.001	1.036	0.002	-29.2	0.1	-20.05	0.02	959056.4216436056	29520.072093756335	0.9900448246553171	0.9431332937302342
343	10.0	0.0867	0.0005	0.97	0.003	0.78	0.001	-30.0	0.1	-20.8	0.1	904142.4034608224	81864.23690740153	0.9899730684997509	0.944224185783178
343	10.0	0.1463	0.0004	1.4	0.003	0.586	0.001	-30.8	0.1	-21.2	0.1	845009.8940832004	138301.39116035856	0.9898206560655972	0.9453273490113365
343	10.0	0.2215	0.0003	1.774	0.001	0.419	0.001	-31.4	0.1	-21.8	0.1	770339.1119457926	209675.15623515385	0.9895171637068626	0.9466147008359089
343	10.0	0.3161	0.0002	2.074	0.001	0.28800000000000003	0.001	-31.9	0.1	-22.09	0.05	676349.3079143139	299684.2280836276	0.9889593623546045	0.9480677889390308
343	10.0	0.4289	0.0002	2.3040000000000003	0.001	0.187	0.001	-32.3	0.04	-22.5	0.1	564268.6964458781	407265.0048124523	0.988038340826262	0.9495570175156267
343	10.0	0.5576	0.0002	2.472	0.001	0.1171	0.0004	-32.5	0.1	-22.7	0.1	436493.2864851499	530239.2746809563	0.9866484775884943	0.9509312673618298
343	10.0	0.6977	0.0001	2.595	0.001	0.0658	0.0004	-32.8	0.1	-22.7	0.2	297682.8146374437	664232.6667354767	0.9847264791182391	0.9520319144839855
343	10.0	0.8458600000000001	4e-05	2.69	0.001	0.027999999999999997	0.0001	-33.0	0.1	-22.9	0.2	151401.35731376952	805889.7413609043	0.9822327579717761	0.9527460115869106
343	50.0	0.00243	2e-05	0.0599	0.0001	2.097	0.001	-28.5	0.1	-20.06	0.04	4744725.791674324	9038.054612506701	0.9512567121453781	0.7438728076137203
343	50.0	0.00488	2.9999999999999997e-05	0.1198	0.0002	2.055	0.001	-28.7	0.2	-20.2	0.02	4733068.197742039	18155.409558026655	0.9512557676947584	0.7440741622142072
343	50.0	0.0075	0.0001	0.1789	0.0004	2.012	0.001	-29.0	0.2	-20.17	0.05	4720598.25894536	27910.837521734065	0.9512540572182085	0.7442890005795751
343	50.0	0.0101	0.0001	0.2385	0.0003	1.9680000000000002	0.001	-29.1	0.2	-20.16	0.04	4708220.012427124	37597.33585631338	0.9512516440907414	0.7445017001250175
343	50.0	0.0126	0.0001	0.2979	0.0003	1.925	0.001	-28.9	0.1	-20.21	0.03	4696314.592062534	46916.46224170486	0.9512486514204038	0.744705749868331
343	50.0	0.0154	0.0001	0.35700000000000004	0.001	1.882	0.001	-29.2	0.1	-20.25	0.04	4682976.757527794	57359.89791314146	0.9512445170684123	0.7449337391317072
343	50.0	0.0183	0.0001	0.414	0.001	1.84	0.001	-29.2	0.1	-20.3	0.1	4669158.415208578	68182.98743634831	0.9512393633917853	0.745169261599435
343	50.0	0.021	0.0002	0.474	0.001	1.798	0.001	-29.4	0.1	-20.37	0.02	4656289.293563722	78265.73824523445	0.9512337678373283	0.745387983287947
343	50.0	0.0614	0.0004	1.1520000000000001	0.002	1.306	0.002	-29.8	0.1	-20.8	0.1	4463316.305076584	229819.00908587684	0.9510582367518824	0.7485961208009018
343	50.0	0.1101	0.0002	1.6569999999999998	0.001	0.941	0.001	-30.3	0.1	-21.4	0.1	4229774.738500736	414141.5507812322	0.9506179882010868	0.7523007280313028
343	50.0	0.1794	0.0002	2.081	0.001	0.637	0.001	-31.0	0.1	-21.8	0.1	3896050.0362489764	679262.7923860186	0.9495613054469842	0.7572606381115033
343	50.0	0.2746	0.0002	2.4	0.001	0.41200000000000003	0.001	-31.2	0.1	-21.96	0.05	3435816.686986997	1048236.7764820578	0.947288857730079	0.7634645130969102
343	50.0	0.3939	0.0002	2.6239999999999997	0.001	0.259	0.001	-30.83	0.04	-22.0	0.1	2858094.701124538	1516942.951154272	0.943109949224398	0.7702172892380158
343	50.0	0.5315	0.0003	2.7760000000000002	0.002	0.157	0.001	-30.9	0.1	-22.3	0.1	2193694.8712352514	2063699.7841704178	0.9364759322242269	0.7765568331779559
343	50.0	0.6808	0.0001	2.885	0.001	0.0887	0.0004	-30.5	0.1	-22.1	0.2	1479693.8057825833	2660689.587876201	0.9271264447259293	0.7816361891528205
343	50.0	0.8379	0.0001	2.966	0.001	0.0387	0.0002	-30.3	0.1	-23.1	0.2	741562.5205293724	3288420.039826111	0.9149445040461102	0.7849194509669677
298	0.001	0.0	0.0			0.0006	1e-05					99.99982567685703	0.0	0.9999982567685702
298	0.01	0.0	0.0			0.006	0.0001					999.9825678224506	0.0	0.9999825678224507
298	0.1	0.0	0.0			0.057999999999999996	0.001					9998.256918985078	0.0	0.9998256918985078
298	0.3	0.0	0.0			0.168	0.003					29984.315005205095	0.0	0.9994771668401699
298	0.5	0.0	0.0			0.27399999999999997	0.005					49956.43816363626	0.0	0.9991287632727252
298	1.0	0.0	0.0			0.5	0.01					99825.82855988853	0.0	0.9982582855988853
298	1.5	0.0	0.0			0.7	0.01					149608.28494757478	0.0	0.9973885663171651
298	2.0	0.0	0.0			0.85	0.01					199303.9209533651	0.0	0.9965196047668256
298	5.0	0.0	0.0			1.46	0.01					495660.8554474322	0.0	0.9913217108948644
298	10.0	0.0	0.0			1.88	0.01					982718.7344915213	0.0	0.9827187344915213
298	12.0	0.0	0.0			1.98	0.01					1175158.181870935	0.0	0.9792984848924458
298	15.0	0.0	0.0			2.09	0.01					1461285.6258068562	0.0	0.9741904172045708
298	18.0	0.0	0.0			2.18	0.01					1744396.188195273	0.0	0.9691089934418183
298	20.0	0.0	0.0			2.22	0.01					1931472.222241234	0.0	0.965736111120617
298	25.0	0.0	0.0			2.33	0.01					2393387.9348726072	0.0	0.9573551739490429
298	30.0	0.0	0.0			2.39	0.01					2847140.906919647	0.0	0.9490469689732157
343	0.001	0.0	0.0			0.000217	1e-06					99.99990005807724	0.0	0.9999990005807724
343	0.01	0.0	0.0			0.00218	1e-06					999.9900058526717	0.0	0.9999900058526717
343	0.1	0.0	0.0			0.0217	0.0001					9999.000630213317	0.0	0.9999000630213316
343	0.3	0.0	0.0			0.0639	0.0003					29991.00657075588	0.0	0.9997002190251959
343	0.5	0.0	0.0			0.106	0.001					49975.02074853373	0.0	0.9995004149706745
343	1.0	0.0	0.0			0.204	0.001					99900.10795265506	0.0	0.9990010795265506
343	1.5	0.0	0.0			0.297	0.001					149775.2990314409	0.0	0.9985019935429392
343	2.0	0.0	0.0			0.379	0.001					199600.63137904272	0.0	0.9980031568952136
343	5.0	0.0	0.0			0.7879999999999999	0.004					497507.6830456021	0.0	0.9950153660912042
343	10.0	0.0	0.0			1.213	0.003					990055.5787576132	0.0	0.9900555787576132
343	12.0	0.0	0.0			1.327	0.003					1185694.311722179	0.0	0.9880785931018158
343	15.0	0.0	0.0			1.472	0.003					1477680.7712222184	0.0	0.9851205141481456
343	18.0	0.0	0.0			1.585	0.002					1767908.3237986022	0.0	0.9821712909992235
343	20.0	0.0	0.0			1.643	0.003					1960420.098058145	0.0	0.9802100490290725
343	25.0	0.0	0.0			1.7790000000000001	0.002					2438310.1519523496	0.0	0.9753240607809398
343	30.0	0.0	0.0			1.8769999999999998	0.003					2911387.2821865203	0.0	0.9704624273955068
343	40.0	0.0	0.0			2.032	0.002					3843246.9608703065	0.0	0.9608117402175766
343	50.0	0.0	0.0			2.141	0.002					4756285.117691112	0.0	0.9512570235382224
298	0.001	1.0	0.0	0.01	0.0003							0.0	99.99925611964946		0.9999925611964946
298	0.01	1.0	0.0	0.098	0.001							0.0	999.9256144550077		0.9999256144550077
298	0.1	1.0	0.0	0.9	0.01							0.0	9992.563934951111		0.9992563934951112
298	0.3	1.0	0.0	1.91	0.01							0.0	29933.125167781745		0.9977708389260582
298	0.5	1.0	0.0	2.28	0.01							0.0	49814.37464358243		0.9962874928716486
298	1.0	1.0	0.0	2.61	0.01							0.0	99258.87684524755		0.9925887684524755
298	1.5	1.0	0.0	2.742	0.004							0.0	148335.56633611114		0.9889037755740742
298	2.0	1.0	0.0	2.81	0.005							0.0	197046.4926516004		0.985232463258002
298	3.0	1.0	0.0	2.9	0.01							0.0	293379.2032033977		0.9779306773446589
298	4.0	1.0	0.0	2.95	0.01							0.0	388273.20266297203		0.9706830066574301
298	5.0	1.0	0.0	2.983	0.004							0.0	481744.52506792225		0.9634890501358445
298	6.0	1.0	0.0	3.01	0.003							0.0	573809.04581507		0.9563484096917834
298	7.0	1.0	0.0	3.03	0.004							0.0	664482.4831312154		0.9492606901874506
298	8.0	1.0	0.0	3.05	0.004							0.0	753780.3995308068		0.9422254994135085
298	9.0	1.0	0.0	3.0639999999999996	0.004							0.0	841718.2032606357		0.935242448067373
298	10.0	1.0	0.0	3.0789999999999997	0.003							0.0	928311.1497316719		0.928311149731672
343	0.001	1.0	0.0	0.0022600000000000003	2e-05							0.0	99.99951856616649		0.9999951856616649
343	0.01	1.0	0.0	0.0226	0.0002							0.0	999.9518576596396		0.9999518576596396
343	0.1	1.0	0.0	0.221	0.003							0.0	9995.18680878829		0.9995186808788291
343	0.3	1.0	0.0	0.62	0.01							0.0	29956.702125878106		0.9985567375292702
343	0.5	1.0	0.0	0.96	0.01							0.0	49879.785998015745		0.9975957199603149
343	1.0	1.0	0.0	1.54	0.01							0.0	99519.72204831392		0.9951972204831392
343	1.5	1.0	0.0	1.87	0.01							0.0	148920.67315055724		0.9928044876703815
343	2.0	1.0	0.0	2.074	0.004							0.0	198083.5015314732		0.9904175076573659
343	3.0	1.0	0.0	2.3209999999999997	0.004							0.0	295698.22522153467		0.9856607507384488
343	4.0	1.0	0.0	2.46	0.01							0.0	392370.7357896914		0.9809268394742285
343	5.0	1.0	0.0	2.55	0.01							0.0	488107.8320710314		0.9762156641420627
343	6.0	1.0	0.0	2.62	0.01							0.0	582916.2693277695		0.9715271155462826
343	7.0	1.0	0.0	2.665	0.003							0.0	676802.7595109635		0.966861085015662
343	8.0	1.0	0.0	2.7039999999999997	0.004							0.0	769773.9715207191		0.962217464400899
343	9.0	1.0	0.0	2.737	0.004							0.0	861836.5314648978		0.9575961460721086
343	10.0	1.0	0.0	2.762	0.003							0.0	952997.0229163286		0.9529970229163286
343	20.0	1.0	0.0	2.905	0.004							0.0	1816406.6513747708		0.9082033256873854
343	30.0	1.0	0.0	2.969	0.002							0.0	2596545.196748361		0.865515065582787
343	40.0	1.0	0.0	3.005	0.002							0.0	3299333.1231585075		0.8248332807896269
343	50.0	1.0	0.0	3.03	0.003							0.0	3930318.304974113		0.7860636609948226

References

PXSL14

T D Pham, R Xiong, S I Sandler, and R F Lobo. Experimental and Computational Studies on the Adsorption o CO$_2$ and N$_2$ on Pure Silica Zeolites. Microporous and Mesoporous Materials, 185:157–166, 2014. doi:10.1016/j.micromeso.2013.10.030.

RWO+07

R L Rowley, W V Wilding, J L Oscarson, Y Yang, N A Zundel, T E Daubert, and R P Danner. DIPPR$^\mathrm ®$ Data Compilation of Pure Chemical Properties, Design Institute for Physical Properties. In Design Institute for Physical Properties of the American Institute of Chemical Engineers. AIChE, New York, 2007.

STS15

M S Shah, M Tsapatsis, and J Ilja Siepmann. Monte Carlo Simulations Probing the Adsorptive Separation of Hydrogen Sulfide/Methane Mixtures Using All-Silica Zeolites. Langmuir, 31:12268–12278, 2015. doi:10.1021/acs.langmuir.5b03015.

TM88

O Talu and A L Myers. Rigorous Thermodynamic Treatment of Gas Adsorption. AIChE J., 34:1887–1893, 1988. doi:10.1002/aic.690341114.

Indices and tables

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