# TeS - Themodynamic Equilibrium Simulation
TeS - Thermodynamic Equilibrium Simulation is an open-source software designed to optimize studies in thermodynamic equilibrium and related subjects. TeS is recommended for initial analyses of reactional systems. The current version contains the following simulation module:
### 1. Gibbs Energy Minimization (minG):
This module allows the user to simulate an isothermal reactor using the Gibbs energy minimization approach. References on the mathematical development can be found in previous work reported by Mitoura and Mariano (2024).
As stated, the objective is to minimize the Gibbs energy, which is formulated as a non-linear programming problem, as shown in the equation below:
$$min G = \sum_{i=1}^{NC} \sum_{j=1}^{NF} n_i^j \mu_i^j$$
The next step is the calculation of the Gibbs energy. The equation below shows the relationship between enthalpy and heat capacity.
$$\frac{\partial \bar{H}_i^g}{\partial T} = Cp_i^g \text{ para } i=1,\ldots,NC$$
Knowing the relationship between enthalpy and temperature, the next step is to calculate the chemical potential. The equation below presents the correlation for calculating chemical potentials.
$$\frac{\partial}{\partial T} \left( \frac{\mu_i^g}{RT} \right) = -\frac{\bar{H}_i^g}{RT^2} \quad \text{para } i=1,\ldots,NC$$
We then have the calculation of the chemical potential for component i:
$$
\mu_i^0 = \frac {T}{T^0} \Delta G_f^{298.15 K} - T \int_{T_0}^{T} \frac {\Delta H_f^{298.15 K} + \int_{T_0}^{T} (CPA + CPB \cdot T + CPC \cdot T^2 + \frac{CPD}{T^2}) \, dT}{T^2} \, dT
$$
With the chemical potentials known, we can define the objective function:
$$\min G = \sum_{i=1}^{NC} n_i^g \mu_i^g $$
Where:
$$\mu _i^g = \mu _i^0 + R.T.(ln(\phi_i)+ln(P)+ln(y_i)) $$
For the calculation of fugacity coefficients, we will have two possibilities:
1. Ideal Gas:
$$\phi = 1 $$
2. Non-ideal Gas:
For non-ideal gases, the calculation of fugacity coefficients is based on the Virial equation of state, as detailed in section 1.1.
The space of possible solutions must be restricted by two conditions:
1. Non-negativity of moles:
$$ n_i^j \geq 0 $$
2. Conservation of atoms:
$$
\sum_{i=1}^{NC} a_{mi} \left(\sum_{j=1}^{NF} n_{i}^{j}\right) = \sum_{i=1}^{NC} a_{mi} n_{i}^{0}
$$
References:
Mitoura, Julles.; Mariano, A.P. Gasification of Lignocellulosic Waste in Supercritical Water: Study of Thermodynamic Equilibrium as a Nonlinear Programming Problem. Eng 2024, 5, 1096-1111. https://doi.org/10.3390/eng5020060
### 1.1 Fugacity Coefficient Calculation Methods
#### Available Equations of State
The following methods are available for calculating fugacity coefficients:
#### 1. Virial Equation of State
- Uses the virial equation truncated at the second term
- Employs mixing rules for the second virial coefficient
- Suitable for moderate pressures and gas-phase calculations
#### 2. Peng-Robinson (PR) Equation of State
- Cubic equation of state with temperature-dependent attraction parameter
- Uses binary interaction parameters for mixture calculations
- Good accuracy for hydrocarbon systems and wide range of conditions
#### 3. Soave-Redlich-Kwong (SRK) Equation of State
- Modified Redlich-Kwong equation with temperature correction
- Incorporates acentric factor correlation
- Reliable for gas-phase and vapor-liquid equilibrium calculations
Each method calculates the fugacity coefficient for individual components in mixtures, accounting for non-ideal behavior and intermolecular interactions.
---
### Usage Example:
#### Methane Steam Reforming Process
First, you need to install tes-thermo:
```python
pip intsall -qU tes-thermo
```
Now you have access to tes-thermo code. With this, you just need to import:
```python
from tes_thermo.utils import Component
from tes_thermo.gibbs import Gibbs
import numpy as np
```
To define componentes:
```python
new_components = {
"methane": {
"name": "methane",
"Tc": 190.6, "Tc_unit": "K",
"Pc": 45.99, "Pc_unit": "bar",
"omega": 0.012,
"Vc": 98.6, "Vc_unit": "cm³/mol",
"Zc": 0.286,
"Hfgm": -74520, "Hfgm_unit": "J/mol",
"Gfgm": -50460, "Gfgm_unit": "J/mol",
"structure": {"C": 1, "H": 4},
"phase": "g",
# "kijs": [0, 0, 0, 0, 0, 0]
"cp_polynomial": lambda T: 8.314 * (1.702 + 0.009081* T -0.000002164*T**2),
}
}
components = ['water','carbon monoxide', 'carbon dioxide', 'hydrogen', 'methanol']
```
In the example above, `new_components` refers to the components to be added. For these, the user must specify all thermodynamic properties as well as the polynomial to be used to calculate `Cp`. For this example, the following polynomial was used:
$$C_p(T) = R \times \left( 1.702 + 0.009081T - 0.000002164T^2 \right)$$
where $T$ is the temperature in Kelvin and `Cp` is the heat capacity in J/(mol·K).
``components`` refers to the components that will be queried using the thermo library, so it is not necessary to indicate thermodynamic properties.
Note that when adding a new component, adding ``kij`` values is optional. If not specified, they will be estimated using the critical volume values.
The next step is to instantiate the components using the ``Component`` class.
```python
comps = Component(components, new_components)
comps = comps.get_components()
gibbs = Gibbs(components=comps,equation='Peng-Robinson')
res = gibbs.solve_gibbs(T=800, T_unit= 'K',
P=60, P_unit='bar',
initial=np.array([0, 1, 0, 0, 1, 0]))
```
After defining the components, the ``Gibbs`` class is used, and the parameters must be the components and the equation of state to be used. The Gibbs class has the ``solve_gibbs`` method, where the user must specify the parameters to be considered in the simulation.
The results are as follows:
```python
{'Temperature (K)': 800.0,
'Pressure (bar)': 60.00000000000001,
'Water': 0.04337941510960611,
'Carbon monoxide': 0.11003626275025695,
'Carbon dioxide': 0.923292149916935,
'Hydrogen': 0.023277493427407873,
'Methanol': 5.225802852767064e-08,
'Methane': 0.9666715055286526}
````
The current version of `tes-thermo` also includes `thermo-agent`. To verify its use, use the example shown in:
```
tes-thermo
├─ notebooks
│ ├─ smr.ipynb
│ └─ thermo_agent.ipynb <- This example!
```
Repository link: https://github.com/JullesMitoura/tes-thermo
---
### Third-Party Dependencies and Licenses
This project uses the Ipopt solver, which is made available under the Eclipse Public License v1.0 (EPL-1.0). A full copy of the Ipopt license can be verified here: https://github.com/coin-or/Ipopt/blob/stable/3.14/LICENSE
---
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"description": "# TeS - Themodynamic Equilibrium Simulation\n\nTeS - Thermodynamic Equilibrium Simulation is an open-source software designed to optimize studies in thermodynamic equilibrium and related subjects. TeS is recommended for initial analyses of reactional systems. The current version contains the following simulation module:\n\n### 1. Gibbs Energy Minimization (minG):\n\nThis module allows the user to simulate an isothermal reactor using the Gibbs energy minimization approach. References on the mathematical development can be found in previous work reported by Mitoura and Mariano (2024).\n\nAs stated, the objective is to minimize the Gibbs energy, which is formulated as a non-linear programming problem, as shown in the equation below:\n\n$$min G = \\sum_{i=1}^{NC} \\sum_{j=1}^{NF} n_i^j \\mu_i^j$$\n\nThe next step is the calculation of the Gibbs energy. The equation below shows the relationship between enthalpy and heat capacity.\n\n$$\\frac{\\partial \\bar{H}_i^g}{\\partial T} = Cp_i^g \\text{ para } i=1,\\ldots,NC$$\n\nKnowing the relationship between enthalpy and temperature, the next step is to calculate the chemical potential. The equation below presents the correlation for calculating chemical potentials.\n\n$$\\frac{\\partial}{\\partial T} \\left( \\frac{\\mu_i^g}{RT} \\right) = -\\frac{\\bar{H}_i^g}{RT^2} \\quad \\text{para } i=1,\\ldots,NC$$\n\nWe then have the calculation of the chemical potential for component i:\n\n$$\n\\mu_i^0 = \\frac {T}{T^0} \\Delta G_f^{298.15 K} - T \\int_{T_0}^{T} \\frac {\\Delta H_f^{298.15 K} + \\int_{T_0}^{T} (CPA + CPB \\cdot T + CPC \\cdot T^2 + \\frac{CPD}{T^2}) \\, dT}{T^2} \\, dT\n$$\n\nWith the chemical potentials known, we can define the objective function:\n\n$$\\min G = \\sum_{i=1}^{NC} n_i^g \\mu_i^g $$\n\nWhere:\n\n$$\\mu _i^g = \\mu _i^0 + R.T.(ln(\\phi_i)+ln(P)+ln(y_i)) $$\n\nFor the calculation of fugacity coefficients, we will have two possibilities:\n\n1. Ideal Gas:\n\n$$\\phi = 1 $$\n\n2. Non-ideal Gas:\nFor non-ideal gases, the calculation of fugacity coefficients is based on the Virial equation of state, as detailed in section 1.1.\n\nThe space of possible solutions must be restricted by two conditions:\n1. Non-negativity of moles:\n\n$$ n_i^j \\geq 0 $$\n\n2. Conservation of atoms:\n\n$$\n\\sum_{i=1}^{NC} a_{mi} \\left(\\sum_{j=1}^{NF} n_{i}^{j}\\right) = \\sum_{i=1}^{NC} a_{mi} n_{i}^{0}\n$$\n\nReferences:\n\nMitoura, Julles.; Mariano, A.P. Gasification of Lignocellulosic Waste in Supercritical Water: Study of Thermodynamic Equilibrium as a Nonlinear Programming Problem. Eng 2024, 5, 1096-1111. https://doi.org/10.3390/eng5020060\n\n### 1.1 Fugacity Coefficient Calculation Methods\n\n#### Available Equations of State\n\nThe following methods are available for calculating fugacity coefficients:\n\n#### 1. Virial Equation of State\n- Uses the virial equation truncated at the second term\n- Employs mixing rules for the second virial coefficient\n- Suitable for moderate pressures and gas-phase calculations\n\n#### 2. Peng-Robinson (PR) Equation of State\n- Cubic equation of state with temperature-dependent attraction parameter\n- Uses binary interaction parameters for mixture calculations\n- Good accuracy for hydrocarbon systems and wide range of conditions\n\n#### 3. Soave-Redlich-Kwong (SRK) Equation of State\n- Modified Redlich-Kwong equation with temperature correction\n- Incorporates acentric factor correlation\n- Reliable for gas-phase and vapor-liquid equilibrium calculations\n\nEach method calculates the fugacity coefficient for individual components in mixtures, accounting for non-ideal behavior and intermolecular interactions.\n\n---\n### Usage Example:\n#### Methane Steam Reforming Process\n\nFirst, you need to install tes-thermo:\n\n```python\npip intsall -qU tes-thermo\n```\nNow you have access to tes-thermo code. With this, you just need to import:\n\n```python\nfrom tes_thermo.utils import Component\nfrom tes_thermo.gibbs import Gibbs\nimport numpy as np\n```\nTo define componentes:\n```python\nnew_components = {\n \"methane\": {\n \"name\": \"methane\",\n \"Tc\": 190.6, \"Tc_unit\": \"K\",\n \"Pc\": 45.99, \"Pc_unit\": \"bar\",\n \"omega\": 0.012,\n \"Vc\": 98.6, \"Vc_unit\": \"cm\u00b3/mol\",\n \"Zc\": 0.286,\n \"Hfgm\": -74520, \"Hfgm_unit\": \"J/mol\",\n \"Gfgm\": -50460, \"Gfgm_unit\": \"J/mol\",\n \"structure\": {\"C\": 1, \"H\": 4},\n \"phase\": \"g\",\n# \"kijs\": [0, 0, 0, 0, 0, 0]\n \"cp_polynomial\": lambda T: 8.314 * (1.702 + 0.009081* T -0.000002164*T**2),\n }\n }\n\ncomponents = ['water','carbon monoxide', 'carbon dioxide', 'hydrogen', 'methanol']\n```\nIn the example above, `new_components` refers to the components to be added. For these, the user must specify all thermodynamic properties as well as the polynomial to be used to calculate `Cp`. For this example, the following polynomial was used:\n\n$$C_p(T) = R \\times \\left( 1.702 + 0.009081T - 0.000002164T^2 \\right)$$\n\nwhere $T$ is the temperature in Kelvin and `Cp` is the heat capacity in J/(mol\u00b7K).\n\n``components`` refers to the components that will be queried using the thermo library, so it is not necessary to indicate thermodynamic properties.\n\nNote that when adding a new component, adding ``kij`` values is optional. If not specified, they will be estimated using the critical volume values.\n\nThe next step is to instantiate the components using the ``Component`` class.\n\n```python\ncomps = Component(components, new_components)\ncomps = comps.get_components()\ngibbs = Gibbs(components=comps,equation='Peng-Robinson')\nres = gibbs.solve_gibbs(T=800, T_unit= 'K',\n P=60, P_unit='bar',\n initial=np.array([0, 1, 0, 0, 1, 0]))\n```\n\nAfter defining the components, the ``Gibbs`` class is used, and the parameters must be the components and the equation of state to be used. The Gibbs class has the ``solve_gibbs`` method, where the user must specify the parameters to be considered in the simulation.\n\nThe results are as follows:\n```python\n{'Temperature (K)': 800.0,\n 'Pressure (bar)': 60.00000000000001,\n 'Water': 0.04337941510960611,\n 'Carbon monoxide': 0.11003626275025695,\n 'Carbon dioxide': 0.923292149916935,\n 'Hydrogen': 0.023277493427407873,\n 'Methanol': 5.225802852767064e-08,\n 'Methane': 0.9666715055286526}\n````\nThe current version of `tes-thermo` also includes `thermo-agent`. To verify its use, use the example shown in:\n\n```\ntes-thermo\n\u251c\u2500 notebooks\n\u2502 \u251c\u2500 smr.ipynb\n\u2502 \u2514\u2500 thermo_agent.ipynb <- This example!\n```\nRepository link: https://github.com/JullesMitoura/tes-thermo\n\n---\n\n### Third-Party Dependencies and Licenses\n\nThis project uses the Ipopt solver, which is made available under the Eclipse Public License v1.0 (EPL-1.0). A full copy of the Ipopt license can be verified here: https://github.com/coin-or/Ipopt/blob/stable/3.14/LICENSE\n\n---\n",
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