Fuel Property Prediction Model

FuelLib utilizes the group contribution method (GCM), as developed by Constantinou and Gani[1] [2] in the mid-1990s, to provide a systematic approach for estimating the thermodynamic properties of pure organic compounds. The GCM decomposes molecules into structural groups, each contributing to a target property based on predefined group values. By summing these contributions, the GCM accurately predicts essential properties, including the acentric factor, normal boiling point, liquid molar volume at standard conditions (298 K) and more. This predictive capability is particularly useful for complex mixtures such as synthetic aviation turbine fuels (SATFs), where experimental thermodynamic data is limited. FuelLib provides SATF developers with a means to estimate these critical properties without extensive physical testing, thereby aiding in the identification of promising fuel compositions before committing to large-scale production.

FuelLib builds on Pavan B. Govindaraju’s Matlab implementation, and includes gas chromatography data (GC x GC) for various jet fuels from the National Jet Fuel Combustion Program[3] (NJFCP) Air Force Research Laboratory[4] [5] (AFRL) and Vozka et al.[6]. Additionally, FuelLib includes correlations for the thermodynamic properties of mixture such as density, viscosity, vapor pressure, surface tension, and thermal conductivity. Table of GCM properties outlines the properties for the i-th compound in a mixture, which depends on the k-th first-order and j-th second-order group contributions.

Table of GCM properties

Table 1 GCM properties of the i-th component in a mixture. The subscript stp denotes a standard pressure assumption.

Property	Units	Group Contributions	Units	Description
\(M_{w,i}\)	kg/mol	\(m_{w1k}\)	g/mol	Molecular weight.
\(T_{c,i}\)	K	\(t_{c1k}\), \(t_{c2j}\)	1	Critical temperature[1].
\(p_{c,i}\)	Pa	\(p_{c1k}\), \(p_{c2j}\)	bar-0.5	Critical pressure[1].
\(V_{c,i}\)	m3/mol	\(v_{c1k}\), \(v_{c2j}\)	m3/kmol	Critical volume[1].
\(T_{b,i}\)	K	\(t_{b1k}\), \(t_{b2j}\)	1	Normal boiling point[1].
\(T_{m,i}\)	K	\(t_{m1k}\), \(t_{m2j}\)	1	Normal melting point[1].
\(\Delta H_{f,i}\)	J/mol	\(h_{f1k}\), \(h_{f2j}\)	kJ/mol	Enthalpy of formation at 298 K[1].
\(\Delta G_{f,i}\)	J/mol	\(g_{f1k}\), \(g_{f2j}\)	kJ/mol	Standard Gibbs free energy at 298 K[1].
\(\Delta H_{v,\textit{stp},i}\)	J/mol	\(h_{v1k}\), \(h_{v2j}\)	kJ/mol	Enthalpy of vaporization at 298 K[1].
\(\omega_i\)	1	\(\omega_{1k}\), \(\omega_{2j}\)	1	Acentric factor[2].
\(V_{m,\textit{stp},i}\)	m3/mol	\(v_{m1k}\), \(v_{m2j}\)	m3/kmol	Liquid molar volume at 298 K[2].
\(C_{p,i}\)	J/mol/K	\(C_{pA1_k}\), \(C_{pA2_k}\),…	J/mol/K	Specific heat capacity[7] [8].

Equations for GCM properties

The properties of each compound in a mixture can be calculated as the sum of contributions from the first- and second-order groups that make up the compound. For a given mixture, let \(\mathbf{N}\) be an \(N_c \times N_{g_1}\) matrix that represents the number of first-order groups in each compound, where \(N_c\) is the number of compounds in the mixture and \(N_{g_1}\) is the total number of first-order groups as defined by Constantinou and Gani[1][2]. Similarly, let \(\mathbf{M}\) be an \(N_c \times N_{g_2}\) matrix that specifies the number of second-order groups in each compound, where \(N_{g_2}\) is the total number of second-order groups. The total number of groups \(N_g = N_{g_1} + N_{g_2} = 121\). The GCM properties for the i-th compound in the mixture are calculated as follows[1] [2] [8]:

\[\begin{split}\begin{align*} M_{w,i} &= \bigg[\sum_{k = 1}^{N_{g_1}}\mathbf{N}_{ik}m_{w1k} \bigg] \times 10^{-3}, \\ T_{c,i} &= 181.28 \ln \bigg[ \sum_{k=1}^{N_{g_1}} \mathbf{N}_{ik} t_{c1k} + \sum_{j=1}^{N_{g_2}} \mathbf{M}_{ij} t_{c2j} \bigg],\\ p_{c,i} &= \Bigg( \bigg[ \sum_{k=1}^{N_{g_1}} \mathbf{N}_{ik} p_{c1k} + \sum_{j=1}^{N_{g_2}} \mathbf{M}_{ij} p_{c2j} + 0.10022\bigg]^{-2} + 1.3705\Bigg)\times 10^{5}, \label{eq:gcm-pc}\\ V_{c,i} &= \Bigg( \bigg[ \sum_{k=1}^{N_{g_1}} \mathbf{N}_{ik} v_{c1k} + \sum_{j=1}^{N_{g_2}} \mathbf{M}_{ij} v_{c2j} \bigg] -0.00435 \Bigg)\times 10^{-3}, \\ T_{b,i} &= 204.359 \ln \bigg[ \sum_{k = 1}^{N_{g_1}} \mathbf{N}_{ik} t_{b1k} + \sum_{j=1}^{N_{g_2}} \mathbf{M}_{ij} t_{b2j}\bigg],\\ T_{m,i} &= 102.425 \ln \bigg[ \sum_{k = 1}^{N_{g_1}} \mathbf{N}_{ik} t_{m1k} + \sum_{j=1}^{N_{g_2}} \mathbf{M}_{ij} t_{m2j}\bigg],\\ \Delta H_{f,i} &= \Bigg( \bigg[ \sum_{k = 1}^{N_{g_1}} \mathbf{N}_{ik} h_{f1k} + \sum_{j=1}^{N_{g_2}} \mathbf{M}_{ij} h_{f2j} \bigg] + 10.835\Bigg) \times 10^3,\\ \Delta G_{f,i} &= \Bigg( \bigg[ \sum_{k = 1}^{N_{g_1}} \mathbf{N}_{ik} g_{f1k} + \sum_{j=1}^{N_{g_2}} \mathbf{M}_{ij} g_{f2j} \bigg] -14.828 \Bigg) \times 10^3,\\ \Delta H_{v,\textit{stp},i} &= \Bigg( \bigg[ \sum_{k = 1}^{N_{g_1}} \mathbf{N}_{ik} h_{v1k} + \sum_{j=1}^{N_{g_2}} \mathbf{M}_{ij} h_{v2j} \bigg] + 6.829\Bigg) \times 10^3, \\ \omega_i &= 0.4085 \ln \bigg( \Big[ \sum_{k=1}^{N_{g_1}} \mathbf{N}_{ik} \omega_{1k} + \sum_{j=1}^{N_{g_2}} \mathbf{M}_{ij} \omega_{2j} + 1.1507\Big]^{1/0.5050} \bigg), \label{eq:gcm-omega}\\ V_{m,\textit{stp},i} &= \Bigg( \bigg[ \sum_{k=1}^{N_{g_1}} \mathbf{N}_{ik} v_{m1k} + \sum_{j=1}^{N_{g_2}} \mathbf{M}_{ij} v_{m2j} \bigg] + 0.01211 \Bigg)\times 10^{-3}, \\ C_{p,i} & =\bigg[\sum_{k=1}^{N_{g_1}} \mathbf{N}_{ik} C_{pA1_k} + \sum_{j=1}^{N_{g_2}} \mathbf{M}_{ij} C_{pA2_j} -19.7779\bigg] \nonumber \\ & +\bigg[\sum_{k=1}^{N_{g_1}} \mathbf{N}_{ik} C_{pB1_k} + \sum_{j=1}^{N_{g_2}} \mathbf{M}_{ij} C_{pB2_j} + 22.5981\bigg] \theta \nonumber\\ & +\bigg[\sum_{k=1}^{N_{g_1}} \mathbf{N}_{ik} C_{pC1_k} + \sum_{j=1}^{N_{g_2}} \mathbf{M}_{ij} C_{pC2_j} - 10.7983\bigg] \theta^2 \\ \theta &= \frac{T - 298.15}{700} \end{align*}\end{split}\]

Equations for individual compound correlations

This section presents correlations for physical properties that leverage the individual compound properties defined in Equations for GCM properties. These correlations make it possible to evaluate physical properties at non-standard temperatures and pressures, given that group contribution properties are only defined at standard conditions. Unless noted otherwise in the individual correlation, all units are assumed to be SI: length (m), mass (kg), time (s), temperature (K), mole (mol). The Reduced temperature quantities are used throughout this section for each compound i, provided \(T\) in K unless noted otherwise.

Table 2 Derived quantities and temperature corrections

Property	Units	Description
\(\nu_i\)	m2/s	Kinematic viscosity[9].
\(L_{v,\textit{stp},i}\)	J/kg	Latent heat of vaporization at 298 K[10].
\(L_{v,i}\)	J/kg	Temperature-adjusted latent heat of vaporization at 298 K[10].
\(V_{m,i}\)	m3/mol	Temperature-adjusted liquid molar volume[11] [12] [10].
\(\rho_i\)	kg/m3	Density
\(C_{\ell,i}\)	J/kg/K	Liquid specific heat capacity[10].
\(p_{sat,i}\)	Pa	Saturated vapor pressure[13] [14].
\(\sigma_i\)	N/m	Surface tension[15].
\(\lambda_i\)	W/m/K	Thermal conductivity[8].

Table 3 Reduced temperature quantities

Symbol	Definition	Description
\(T_{r,i}\)	\(\frac{T}{T_{c,i}}\)	Reduced temperature.
\(T_{r,b,i}\)	\(\frac{T_{b,i}}{T_{c,i}}\)	Reduced boiling point temperature.
\(T_{r,\textit{stp},i}\)	\(\frac{298 \text{ (K)}}{T_{c,i}}\)	Reduced standard temperature.

Kinematic viscosity

fuel.viscosity_kinematic(T)

Calculate the viscosity using Dutt’s equation.

Parameters:

T (float) – Temperature in Kelvin.

Returns:

Viscosity of each component in m^2/s.

Return type:

np.ndarray

The kinematic viscosity of the i-th compound of the fuel,

\[\nu_i = \frac{\mu_i}{\rho_i},\]

is calculated from Dutt’s equation (Eq. 4.23 in Viscosity of Liquids[9]) provided \(T\) in \(^{\circ}\) C:

\[\begin{align*} \nu_i = 10^{-6} \times \exp \bigg\{-3.0171 + \frac{442.78 + 1.6452 \,T_{b,i}}{T + 239 - 0.19 \,T_{b,i}} \bigg\}. \end{align*}\]

Latent heat of vaporization

fuel.latent_heat_vaporization(T)

Calculate latent heat of vaporization adjusted for temperature.

Parameters:

T (float) – Temperature in Kelvin.

Returns:

Latent heat of vaporization in J/kg.

Return type:

np.ndarray

The latent heat of vaporization for each compound at standard pressure and temperature is calculated from the enthalpy of vaporization as:

\[L_{v,\textit{stp},i} = \frac{\Delta H_{v,\textit{stp},i}}{M_{w,i}}.\]

The heat of vaporization for each compound is then adjusted for variations in temperature[10]:

\[L_{v,i} = L_{v,\textit{stp},i} \bigg(\frac{1 - T_{r,i}}{1-T_{r,b,i}} \bigg)^{0.38}.\]

Liquid molar volume

fuel.molar_liquid_vol(T)

Compute molar liquid volume with temperature correction.

Parameters:

T (float) – Temperature in Kelvin.

Returns:

Molar liquid volume in m^3/mol.

Return type:

np.ndarray

The liquid molar volume is calculated at a specific temperature \(T\) using the generalized Rackett equation[11] [12] with an updated \(\phi_i\) parameter[10]:

\[V_{m,i} = V_{m,\textit{stp},i} Z^{\phi_i}_{c,i},\]

where

\[\begin{split}\begin{align*} Z_{c,i} &= 0.29056 - 0.08775 \omega_i, \\ \phi_i &= \begin{cases} (1 - T_{r,i})^{2/7} - (1 - T_{r,\textit{stp},i})^{2/7}, & \text{ if } T \leq T_{c,i} \\ - (1 - T_{r,\textit{stp},i})^{2/7}, & \text{ if } T > T_{c,i} \end{cases}. \label{eq:phi} \end{align*}\end{split}\]

Density

fuel.density(T)

Calculate the density of each component at temperature T.

Parameters:

T (float) – Temperature of the mixture in Kelvin.

Returns:

Density of each compound in kg/m^3.

Return type:

np.ndarray

The density of the i-th compound is given by

\[\rho_i = \frac{M_{w,i}}{V_{m,i}}.\]

Liquid specific heat capacity

fuel.Cl(T)

Compute liquid specific heat capacity in J/kg/K at a given temperature.

Parameters:

T (float) – Temperature in Kelvin.

Returns:

Specific heat capacity in J/kg/K.

Return type:

np.ndarray

The liquid specific heat capacity for each compound at standard pressure temperature is calculated from the specific heat capacity as:

\[C_{\ell,i} = \dfrac{C_{p,i}}{M_{w,i}}\]

Saturated vapor pressure

fuel.psat(T, correlation='Lee-Kesler')

Compute saturated vapor pressure.

Parameters:

• T (float) – Temperature in Kelvin.

• correlation (str, optional) – Correlation method (“Ambrose-Walton” or “Lee-Kesler”).

Returns:

Saturated vapor pressure in Pa.

Return type:

np.ndarray

The saturated vapor pressure for each compound is calculated as a function of temperature using either the Lee–Kesler method[13] or the Ambrose-Walton method[14]. Both methods solve

\[\ln p_{r,\text{sat},i} = f_i^{(0)} + \omega_i f_i^{(1)} + \omega_i^2 f_i^{(2)}\]

for the reduced saturated vapor pressure for each compound, \(p_{r,\text{sat},i} = p_{\text{sat},i}/p_{c,i}\). The default method in FuelLib is the Lee-Kesler method, as it is more stable at higher temperatures. The Lee-Kesler[13] method defines

\[\begin{split}\begin{align*} f_i^{(0)} &= 5.92714 - \frac{6.09648}{T_{r,i}} - 1.28862 \ln T_{r,i} + 0.169347 \, T_{r,i}^6, \\ f_i^{(1)} &= 15.2518 - \frac{15.6875}{T_{r,i}} - 13.4721 \ln T_{r,i} + 0.43577 \, T_{r,i}^6, \\ f_i^{(2)} &= 0, \end{align*}\end{split}\]

The Ambrose-Walton[14] correlation sets:

\[\begin{split}\begin{align*} f_i^{(0)} &= \frac{- 5.97616\tau_i + 1.29874\tau_i^{1.5} - 0.60394\tau_i^{2.5} - 1.06841\tau_i^{5}}{T_{r,i}}, \\ f_i^{(1)} &= \frac{- 5.03365\tau_i + 1.11505\tau_i^{1.5} - 5.41217\tau_i^{2.5} - 7.46628\tau_i^{5},}{T_{r,i}}, \\ f_i^{(2)} &= \frac{- 0.64771\tau_i + 2.41539\tau_i^{1.5} - 4.26979\tau_i^{2.5} - 3.25259\tau_i^{5}}{T_{r,i}}, \end{align*}\end{split}\]

with \(\tau_i = 1 - T_{r,i}\).

fuel.psat_antoine_coeffs(Tvals=None, units='mks', correlation='Lee-Kesler')

Estimate Antoine coefficients for vapor pressure of an individual compound.

Parameters:

• Tvals (np.ndarray, optional) – Temperature range or nodes for Antoine fit in Kelvin (default [273.15, Tb_i]).

• units (str, optional) – Units for pressure in fit (“mks”, “cgs”, “bar”, “atm”)

• correlation (str, optional) – Correlation method (“Ambrose-Walton” or “Lee-Kesler”).

Returns:

Coefficients A, B, C, D

Return type:

4 np.ndarrays

Users also have the option to return the coefficients from an Antoine fit based on the mixture vapor pressure calculated from Raoult’s law above. Antoine’s equation is:

\[\begin{align*} \log_{10}\Big(\frac{p_{v,i}}{D_i}\Big) = A_i - \frac{B_i}{C_i + T}, \end{align*}\]

where \(D_i\) is a conversion factor for converting \(p_{v,i}\) to units of bar (\(D_i = 10^5\)) or dyne/cm ² (\(D_i = 10^{-1}\)) from Pa. This feature was added to provide Pele users an option for estimating these coefficients for use in CFD simulations with spray. See the PelePhysics documentation for additional information.

Surface tension

fuel.surface_tension(T, correlation='Brock-Bird')

Calculate surface tension of each compound at a given temperature.

Parameters:

• T (float) – Temperature in Kelvin.

• correlation (str, optional) – Correlation method (“Brock-Bird” or “Pitzer”).

Returns:

Surface tension in N/m.

Return type:

np.ndarray

Surface tension for each compound is approximated using the relation:

\[\sigma_i = p_{c,i}^{2/3} T_{c,i}^{1/3} Q_i (1 - T_{r,i})^{11/9},\]

provided \(p_{c,i}\) in bar. The \(Q_i\) term is defined by Brock and Bird[15] (default in FuelLib) as

\[Q_i = 0.1196 \bigg[1 + \frac{T_{r,b,i} \log(p_{c,i}/1.01325)}{1 - T_{r,b,i}}\bigg] - 0.279,\]

or by Curl and Pitzer[8] [16] [17] as

\[Q_i = \frac{1.86 + 1.18 \omega_i}{19.05} \bigg[ \frac{3.75 + 0.91 \omega_i}{0.291 - 0.08\omega_i} \bigg]^{2/3}.\]

Thermal conductivity

fuel.thermal_conductivity(T)

Calculate thermal conductivity at a given temperature.

Parameters:

T (float) – Temperature in Kelvin.

Returns:

Thermal conductivity in W/m/K.

Return type:

np.ndarray

Thermal conductivity for each compound is computed according to the method of Latini et al. as summarized in Poling’s[8] book:

\[\lambda_i = \frac{A_i(1 - T_{r,i})^{0.38}}{T_{r,i}^{1/6}}.\]

The constant \(A_i\) is defined by:

\[A_i = \frac{A^\ast T_{b,i}^\alpha}{M_{w,i}^\beta T_{c,i}^{\gamma}},\]

provided \(M_{w,i}\) in g/mol. The exponents vary depending on the family of the compound as defined in Thermal conductivity relation parameters. It is assumed that:

• aromatics have contain aromatic group contributions (e.g. ACCH)

• cycloparaffins contain a ring (e.g. 5-membered ring) and do not contain aromatic groups

• olefins contain one or more pairs of carbon atoms linked by a double bond and do not contain aromatic groups or rings

• all other compounds are assumed to be saturated hydrocarbons.

Table 4 Thermal conductivity relation parameters

Identifier	Family	\(A^\ast\)	\(\alpha\)	\(\beta\)	\(\gamma\)
0	Saturated hydrocarbons	0.00350	1.2	0.5	0.167
1	Aromatics	0.0346	1.2	1.0	0.167
2	Cycloparaffins	0.0310	1.2	1.0	0.167
3	Olefins	0.0361	1.2	1.0	0.167

Equations for mixture properties from GCM

This section contains correlations for estimating physical properties of the mixture from the individual compound and physical properties defined in Equations for GCM properties and Equations for individual compound correlations. These correlations make it possible to evaluate physical properties at non-standard temperatures and pressures, as the group contribution properties are only defined at standard conditions. The Mixture properties available in FuelLib are listed in table below. Mass and mole fractions defined in Table Mass and mole fractions are used throughout this section.

Table 5 Mixture properties

Symbol	Units	Description
\(\rho\)	kg/m3	Density
\(\nu\)	m2/s	Kinematic viscosity
\(p_v\)	Pa	Vapor pressure
\(\sigma\)	N/m	Surface tension
\(\lambda\)	W/m/K	Thermal conductivity

Table 6 Mass and mole fractions

Symbol	Definition	Description
\(Y_i\)	\(\frac{m_i}{\sum_{k=1}^{N_c} m_k}\)	Mass fraction of compound i. \(m_i\) is the mass of compound i.
\(X_i\)	\(\frac{n_i}{\sum_{k=1}^{N_c} n_k}\)	Mole fraction of compound i. \(n_i\) is the number of moles compound i.

Conventional mixing rules

FuelLib.mixing_rule(var_n, X, pseudo_prop='arithmetic')

Mixing rules for computing mixture properties.

Parameters:

• var_n (np.ndarray) – Individual compound properties.

• X (np.ndarray) – Mole fractions of the compounds.

• pseudo_prop (str, optional) – Type of mean (“arithmetic” or “geometric”).

Returns:

Mixture property value.

Return type:

float

While many of the mixture properties in FuelLib have a unique mixing rule, FuelLib’s mixing_rule function provides a general mixing rule based on the suggestions of Harstad et al[18]. For a given property \(Q\)

\[Q = \sum_{i=1}^{N_c} \sum_{j=1}^{N_c} X_i X_j Q_{ij},\]

where the pseudo-property for the couple of components, \(Q_{ij}\) is computed using an arithmetic,

\[Q_{ij} = \frac{Q_i + Q_j}{2},\]

or a geometric mean,

\[Q_{ij} = \sqrt{Q_i \cdot Q_j},\]

where \(Q_i\) is the property of the i-th compound of the multicomponent mixture.

Mixture density

fuel.mixture_density(Yi, T)

Calculate mixture density at a given temperature.

Parameters:

• Yi (np.ndarray) – Mass fractions of each compound.

• T (float) – Temperature in Kelvin.

Returns:

Mixture density in kg/m^3.

Return type:

float

The mixture’s density is calculated as:

\[\rho = \sum_{i=1}^{N_c}Y_i\frac{M_{w,i}}{V_{m,i}}.\]

Mixture kinematic viscosity

fuel.mixture_kinematic_viscosity(Yi, T, correlation='Kendall-Monroe')

Calculate kinematic viscosity of the mixture.

Parameters:

• Yi (np.ndarray) – Mass fractions of each compound.

• T (float) – Temperature in Kelvin.

• correlation (str, optional) – Mixing model (“Kendall-Monroe” or “Arrhenius”).

Returns:

Mixture kinematic viscosity in m^2/s.

Return type:

float

The kinematic viscosity of the mixture is computed using the Kendall-Monroe[19] mixing rule, with an option to use the Arrhenius[20] mixing rule. The viscosity of each component. After evaluating thirty mixing rules, Hernandez et al.[21] found that both Kendall-Monroe and Arrhenius were among the most effective without relying on additional data or parameter fitting. The Kendall-Monroe rule is:

\[\nu_{KM}^{1/3} = \sum_{i=1}^{N_c} X_i \, \nu_i^{1/3}.\]

The Arrhenius rule is:

\[\ln \nu_{Arr} = \sum_{i=1}^{N_c} X_i\ln\nu_i .\]

Mixture vapor pressure

fuel.mixture_vapor_pressure(Yi, T, correlation='Lee-Kesler')

Calculate vapor pressure of the mixture.

Parameters:

• Yi (np.ndarray) – Mass fractions of each compound in the mixture.

• T (float) – Temperature in Kelvin.

• correlation (str, optional) – Correlation method (“Ambrose-Walton” or “Lee-Kesler”).

Returns:

Mixture vapor pressure in Pa.

Return type:

float

The vapor pressure of the mixture is calculated according to Raoult’s law:

\[\begin{align*} p_{v} = \sum_{i = 1}^{N_c} X_i \, p_{\textit{sat},i}. \end{align*}\]

fuel.mixture_vapor_pressure_antoine_coeffs(Yi, Tvals=None, units='mks', correlation='Lee-Kesler')

Estimate Antoine coefficients for vapor pressure of the mixture.

Parameters:

• Yi (np.ndarray) – Mass fractions of each compound in the mixture.

• Tvals (np.ndarray, optional) – Temperature range or nodes for Antoine fit in Kelvin (default [273.15, min(Tb)]).

• units (str, optional) – Units for pressure in fit (“mks”, “cgs”, “bar”, “atm”)

• correlation (str, optional) – Correlation method (“Ambrose-Walton” or “Lee-Kesler”).

Returns:

Coefficients A, B, C, D

Return type:

float

Users also have the option to return the coefficients from an Antoine fit based on the mixture vapor pressure calculated from Raoult’s law above. Antoine’s equation is:

\[\begin{align*} \log_{10}\Big(\frac{p_{v}}{D}\Big) = A - \frac{B}{C + T}, \end{align*}\]

where \(D\) is a conversion factor for converting \(p_v\) to units of bar (\(D = 10^5\)) or dyne/cm ² (\(D = 10^{-1}\)) from Pa. This feature was added to provide Pele users an option for estimating these coefficients for use in CFD simulations with spray. See the PelePhysics documentation for additional information.

Mixture surface tension

fuel.mixture_surface_tension(Yi, T, correlation='Brock-Bird')

Calculate surface tension of the mixture.

Parameters:

• Yi (np.ndarray) – Mass fractions of each compound in the mixture.

• T (float) – Temperature in Kelvin.

• correlation (str, optional) – Correlation method (“Pitzer” or “Brock-Bird”).

Returns:

Mixture surface tension in N/m.

Return type:

float

The surface tension of the mixture is calculated using the Conventional mixing rules with an arithmetic mean for the pseudo-property \(\sigma_{i,j}\) as recommended by Hugill and van Welsenes[22]:

\[\sigma = \sum_{i=1}^{N_c} \sum_{j=1}^{N_c} X_i X_j \frac{\sigma_i + \sigma_j}{2}.\]

Mixture thermal conductivity

fuel.mixture_thermal_conductivity(Yi, T)

Calculate thermal conductivity of the mixture.

Parameters:

• Yi (np.ndarray) – Mass fractions of each compound in the mixture.

• T (float) – Temperature in Kelvin.

Returns:

Thermal conductivity in W/m/K.

Return type:

float

The thermal conductivity of the mixture is calculated using the power law method of Vredeveld as described in Poling[8]:

\[\lambda = \bigg(\sum_{i=1}^{N_c} Y_i \lambda_i^{-2} \bigg)^{-1/2}.\]

Reference Compounds for Jet Fuels

It is difficult to identify individual components of complex multicomponent jet fuels using GCxGC analysis, which generally provides weight percentages of a given hydrocarbon family and carbon number within a sample (e.g., 5% C10 iso-alkane, 2% C13 cycloalkane, etc.). To address this challenge, FuelLib uses a set of reference compounds that represent the major hydrocarbon families and carbon numbers found in jet fuels. A comprehensive list of the reference compounds used in FuelLib can be found in the fuelData/refCompounds.csv file, with associated functional group decompositions in fuelData/groupDecompositionData/refCompounds.csv.

For ease of reference, the reference compounds and keys corresponding to a PelePhysics mechanism fuellib_posf_nonreacting are provided in the table below. When provided, the PelePhysics keys can be used to link the compounds in FuelLib to species in PelePhysics simulations via Export4Pele.py as described in Exporting to PelePhysics.

Table 7 Reference compounds, chemical formulas, and corresponding PelePhysics keys by GCxGC bin.

GCxGC Bin	Formula	Reference Compound	PelePhysics Key
Toluene	C7H8	toluene	C6H5CH3
C2-Benzene	C8H10	ethyl benzene	C6H5C2H5
C3-Benzene	C9H12	propyl benzene	C6H5C3H7
C4-Benzene	C10H14	butyl benzene	C6H5C4H9
C5-Benzene	C11H16	pentyl benzene	C6H5C5H11
C6-Benzene	C12H18	hexyl benzene	C6H5C6H13
C7-Benzene	C13H20	heptyl benzene	C6H5C7H15
C8-Benzene	C14H22	octyl benzene	C6H5C8H17
C9-Benzene	C15H24	nonyl benzene	C6H5C9H19
C10-Benzene	C16H26	decyl benzene	C6H5C10H21
Diaromatic-C10	C10H8	naphthalene	NAPH
Diaromatic-C11	C11H10	1-methyl naphthalene	METHYLNAPH-1
Diaromatic-C12	C12H12	1-ethyl naphthalene	ETHYLNAPH-1
Diaromatic-C13	C13H14	1-propyl naphthalene	PROPYLNAPH-1
Diaromatic-C14	C14H16	1-butyl naphthalene	BUTYLNAPH-1
Cycloaromatic-C09	C9H10	indane	INDANE
Cycloaromatic-C10	C10H12	tetralin	TETRA
Cycloaromatic-C11	C11H14	2-methyl tetralin	METHYLTETRA-2
Cycloaromatic-C12	C12H16	2-ethly tetralin	ETHYLTETRA-2
Cycloaromatic-C13	C13H18	2-propyl tetralin	PROPYLTETRA-2
Cycloaromatic-C14	C14H20	2-butyl tetralin	BUTYLTETRA-2
Cycloaromatic-C15	C15H22	2-pentyl tetralin	PENTYLTETRA-2
C07-Isoparaffin	C7H16	2-methyl hexane	C7H16-2
C08-Isoparaffin	C8H18	2-methyl heptane	C8H18-2
C09-Isoparaffin	C9H20	2-methyl octane	C9H20-2
C10-Isoparaffin	C10H22	2-methyl nonane	C10H22-2
C11-Isoparaffin	C11H24	2-methyl decane	C11H24-2
C12-Isoparaffin	C12H26	2-methyl undecane	C12H26-2
C13-Isoparaffin	C13H28	2-methyl dodecane	C13H28-2
C14-Isoparaffin	C14H30	2-methyl tridecane	C14H30-2
C15-Isoparaffin	C15H32	2-methyl tetradecane	C15H32-2
C16-Isoparaffin	C16H34	2-methyl pentadecane	C16H34-2
C17-Isoparaffin	C17H36	2-methyl hexadecane	C17H36-2
C18-Isoparaffin	C18H38	2-methyl heptadecane	C18H38-2
C19-Isoparaffin	C19H40	2-methyl octadecane	C19H40-2
C20-Isoparaffin	C20H42	2-methyl nonadecane	C20H42-2
C21-Isoparaffin	C21H44	2-methyl icosane	C21H44-2
C22-Isoparaffin	C22H46	2-methyl henicosane	C22H46-2
C23-Isoparaffin	C23H48	2-methyl docosane	C23H48-2
C24-Isoparaffin	C24H50	2-methyl tricosane	C24H50-2
n-C07	C7H16	n-heptane	NC7H16
n-C08	C8H18	n-octane	NC8H18
n-C09	C9H20	n-nonane	NC9H20
n-C10	C10H22	n-decane	NC10H22
n-C11	C11H24	n-undecane	NC11H24
n-C12	C12H26	n-dodecane	NC12H26
n-C13	C13H28	n-tridecane	NC13H28
n-C14	C14H30	n-tetradecane	NC14H30
n-C15	C15H32	n-pentadecane	NC15H32
n-C16	C16H34	n-hexadecane	NC16H34
n-C17	C17H36	n-heptadecane	NC17H36
n-C18	C18H38	n-octadecane	NC18H38
n-C19	C19H40	n-nonadecane	NC19H40
n-C20	C20H42	n-icosane	NC20H42
n-C21	C21H44	n-henicosane	NC21H44
n-C22	C22H46	n-docosane	NC22H46
n-C23	C23H48	n-tricosane	NC23H48
C07-Monocycloparaffin	C7C14	methyl cyclohexane	C6H11CH3
C08-Monocycloparaffin	C8H16	ethyl cyclohexane	C6H11C2H5
C09-Monocycloparaffin	C9H18	propyl cyclohexane	C6H11C3H7
C10-Monocycloparaffin	C10H20	butyl cyclohexane	C6H11C4H9
C11-Monocycloparaffin	C11H22	pentyl cyclohexane	C6H11C5H11
C12-Monocycloparaffin	C12H24	hexyl cyclohexane	C6H11C6H13
C13-Monocycloparaffin	C13H26	heptyl cyclohexane	C6H11C7H15
C14-Monocycloparaffin	C14H28	octyl cyclohexane	C6H11C8H17
C15-Monocycloparaffin	C15H30	nonyl cyclohexane	C6H11C9H19
C16-Monocycloparaffin	C16H32	decyl cyclohexane	C6H11C10H21
C17-Monocycloparaffin	C17H34	undecyl cyclohexane	C6H11C11H23
C18-Monocycloparaffin	C18H36	dodecyl cyclohexane	C6H11C12H25
C19-Monocycloparaffin	C19H38	tridecyl cyclohexane	C6H11C13H27
C08-Dicycloparaffin	C8H14	Octahydropentalene	OHPEN
C09-Dicycloparaffin	C9H16	Hydrindane	HYDRIND
C10-Dicycloparaffin	C10H18	Decalin	DECALIN
C11-Dicycloparaffin	C11H20	2-methyldecalin	METHYLDECALIN-2
C12-Dicycloparaffin	C12H22	2-ethyldecalin	ETHYLDECALIN-2
C13-Dicycloparaffin	C13H24	2-propyldecalin	PROPYLDECALIN-2
C14-Dicycloparaffin	C14H26	2-butyldecalin	BUTYLDECALIN-2
C15-Dicycloparaffin	C15H28	2-pentyldecalin	PENTYLDECALIN-2
C16-Dicycloparaffin	C16H30	2-hexyldecalin	HEXYLDECALIN-2
C17-Dicycloparaffin	C17H32	2-heptyldecalin	HEPTYLDECALIN-2
C10-Tricycloparaffin	C10H16	C1CC2C(C1)C1CCCC21	TRICYCLO-C10
C11-Tricycloparaffin	C11H18	C1CC2CC3CCCC3C2C1	TRICYCLO-C11
C12-Tricycloparaffin	C12H20	C1CC2CC3CCCC3CC2C1	TRICYCLO-C12
C13-Tricycloparaffin	C13H22	C1CCC2C(C1)CC1CCCCC12	TRICYCLO-C13
C14-Tricycloparaffin	C13H22	C1CCC2CC3CCCCC3CC2C1	TRICYCLO-C14
C10-Alkene	C10H20	1-decene	DECENE-1
C12-Alkene	C12H24	1-dodecene	DODECENE-1
C14-Alkene	C14H28	1-tetradecene	TETRADECENE-1
C16-Alkene	C16H32	1-hexadecene	HEXADECENE-1

Validation

Single Component Fuels

Fig. 1 Properties of heptane, decane, and dodecane against predictive data from NIST Chemistry WebBook.

Multicomponent Fuels

Fig. 2 Properties of conventional jet fuels JP-8 (POSF10264), Jet A (POSF10325), and JP-5 (POSF10289) against data from the Air Force Research Laboratory[5]. Note that the data sets for thermal conductivity are very inconsistent, but they typically show linear decreases in thermal conductivity with temperature.

Fuel Blends

Fig. 3 Properties of three HEFA fuels produced from different feedstocks (camelina, tallow, and mixed fat) blended with Jet-A. Measurement and GCxGC data from Vozka et al.[6].

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