Augmenters

Augmenters are generic simu.ThermoContribution objects that add derived physical properties to a thermodynamic model, but without impacting its definition. These can be purely informative properties, such as average molecular weight, but also add new information, such as transport properties.

General Properties

class simu.app.thermo.contributions.augmenters.general.GenericProperties

Bases: ThermoContribution

Provide basic derived thermodynamic properties:

Property	Description	Symbol
G	Total Gibbs free energy [J]/[W]	\(G\)
H	Total enthalpy [J]/[W]	\(H\)
A	Total Helmholtz energy [J]/[W]	\(A\)
U	Total inner energy [J]/[W]	\(U\)
N	Total moles [mol]/[mol/s]	\(N\)
M	Total mass [kg]/[kg/s]	\(M\)
m	Partial mass (flows) [kg]/[kg/s]	\(m_i\)
x	Mole fractions [-]	\(x_i\)
w	Mass fractions [-]	\(w_i\)
Mw	Average molecular weight [kg/mol]	\(\bar M\)
rho	Density [kg/m3]	\(\varrho\)
rho_n	Molar density [mol/m3]	\(\varrho_n\)
c	Mass concentrations [kg/m3]	\(c_i\)
c_n	Molar concentrations [mol/m3]	\(c_{n,i}\)

With entropy \(S\), chemical potential \(\mu_i\) and molecular weights \(M_i\), it is

\begin{alignat*}{4} G &= \sum_i \mu_i\,n_i &\qquad H &= G + T\,S &\qquad A &= G - p\,V &\qquad U &= A + T\,S \\ N &= \sum_i n_i & m_i &= n_i\,M_i & M &= \sum_i m_i & \bar M &= \frac{M}{N} \\ x_i &= \frac{n_i}{N} & w_i &= \frac{m_i}{M} \varrho_n &= \frac{N}{V} & \varrho &= \frac{M}{V}\\ c_i &= \frac{m_i}{V} & c_{n,i} &= \frac{n_i}{V} \end{alignat*}

Activities

class simu.app.thermo.contributions.augmenters.general.Activities

Bases: ThermoContribution

This contribution defines the activity coefficients gamma (\(\gamma_i\)), mole-fraction-based activities a_x (\(a_x\)), and concentration-based activities a_c (\(a_c\)).

These properties are mainly used to describe the nonideality in the liquid phase represented by Gibbs excess models.

Based on chemical potential \(\mu_i\) and standard state chemical potential \(\mu_i^0\), it is

\[a_{x,i} = \frac{\mu_i - \mu_i^0}{R\,T}\qquad \gamma_i = \frac{a_{x,i}}{x_i}\qquad a_{c,i} = \gamma_i\,c_{n,i}\]

Elemental flows and fractions

class simu.app.thermo.contributions.augmenters.general.Elemental

Bases: ThermoContribution

Provide flows or quantities per chemical element as follows:

Property	Description	Symbol
n_e	Elemental moles	\(n_{e,j}\)
x_e	Elemental mole fractions	\(x_{e,j}\)
N_e	Total elemental moles	\(N_{e}\)
m_e	Elemental masses	\(m_{e,j}\)
w_e	Elemental mass fractions	\(w_{e,j}\)

Based on the parsed chemical formulae of each species, the contribution first determines the super-set of occurring elements \(\mathbb E_\cup = \bigcup_{i\in\mathbb S} \mathbb E_i\). The set is handled as a sorted list for reproducibility. Stoichiometric coefficients \(\nu_{ij}\) describe the occurrence of element \(j\) in species \(i\). Then, and with atomic weights \(M_j\):

\begin{alignat}{3} n_{e,j} &= \sum_{i\in\mathbb S} \nu_{ij}\cdot n_i &\qquad \dot N_e & = \sum_{j\in\mathbb E_\cup} \dot n_{e,j} &\qquad x_e & = n_{e,j} / N_e\\ m_{e,j} &= M_j \, n_{e,j} &&& w_{e,j} & = m_{e,j} / \sum_{k\in\mathbb E_\cup} m_{e, k} \end{alignat}