tes-thermo 0.1.11

TeS is a tool for simulating reaction processes. It uses the Gibbs energy minimization approach written as a nonlinear programming problem with Pyomo and is solved using IPOPT.

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.

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Installation

First, install the required Python packages:

pip install -qU tes-thermo

Note for macOS users: The tes-thermo package requires the IPOPT solver. On macOS, you need to install IPOPT separately using Homebrew:

brew install ipopt

For other operating systems, IPOPT is typically included with the package or can be installed through your system's package manager.

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Usage Example:

Methane Steam Reforming Process

Now you have access to tes-thermo code. With this, you just need to import:

from tes_thermo.utils import Component
from tes_thermo.gibbs import Gibbs
import numpy as np

To define componentes:

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.

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:

{'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

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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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