UNIFAC Gibbs Excess Model (thermo.unifac)

This module contains functions and classes related to the UNIFAC and its many variants. The bulk of the code relates to calculating derivativies, or is tables of data.

For reporting bugs, adding feature requests, or submitting pull requests, please use the GitHub issue tracker or contact the author at Caleb.Andrew.Bell@gmail.com.

Main Model (Object-Oriented)

class thermo.unifac.UNIFAC(*, xs, rs, qs, Qs, vs, T=298.15, psi_coeffs=None, psi_abc=None, psi_a=None, psi_b=None, psi_c=None, version=0)

Class for representing an a liquid with excess gibbs energy represented by the UNIFAC equation. This model is capable of representing VL and LL behavior, provided the correct interaction parameters are used. [1] and [2] are good references on this model.

Parameters:

Tfloat

Temperature, [K]

xslist[float]

Mole fractions, [-]

rslist[float]

r parameters $r_i = \sum_{k=1}^{n} \nu_k R_k$, [-]

qslist[float]

q parameters $q_i = \sum_{k=1}^{n}\nu_k Q_k$, [-]

Qslist[float]

Q parameter for each subgroup; subgroups are not required to but are suggested to be sorted from lowest number to highest number, [-]

vslist[list[float]]

Indexed by [subgroup][count], this variable is the count of each subgroups in each compound, [-]

psi_abctuple(list[list[float]], 3), optional

psi interaction parameters between each subgroup; indexed [subgroup][subgroup], not symmetrical; first arg is the matrix for a, then b, and then c. Only one of psi_abc or psi_coeffs or psi_a and psi_b and psi_c is required, [-]

psi_coeffslist[list[tuple(float, 3)]], optional

psi interaction parameters between each subgroup; indexed [subgroup][subgroup][letter], not symmetrical. Only one of psi_abc or psi_coeffs or psi_a and psi_b and psi_c is required, [-]

psi_alist[list[float]], optional

psi a term interaction parameters between each subgroup; indexed [subgroup][subgroup]. Only one of psi_abc or psi_coeffs or psi_a and psi_b and psi_c is required, [-]

psi_blist[list[float]], optional

psi b term interaction parameters between each subgroup; indexed [subgroup][subgroup]. Only one of psi_abc or psi_coeffs or psi_a and psi_b and psi_c is required, [-]

psi_clist[list[float]], optional

psi c term interaction parameters between each subgroup; indexed [subgroup][subgroup]. Only one of psi_abc or psi_coeffs or psi_a and psi_b and psi_c is required, [-]

versionint, optional

Which version of the model to use [-]

• 0 - original UNIFAC, OR UNIFAC LLE

• 1 - Dortmund UNIFAC (adds T dept, 3/4 power)

• 2 - PSRK (original with T dept function)

• 3 - VTPR (drops combinatorial term, Dortmund UNIFAC otherwise)

• 4 - Lyngby/Larsen has different combinatorial, 2/3 power

• 5 - UNIFAC KT (2 params for psi, Lyngby/Larsen formulation; otherwise same as original)

Attributes:

Tfloat

Temperature, [K]

xslist[float]

Mole fractions, [-]

Methods

CpE()	Calculate and return the first temperature derivative of excess enthalpy of a liquid phase using an activity coefficient model.
Fis()	Calculate the $F_i$ terms used in calculating the combinatorial part.
Fs()	Computes the following:
Fs_pure()	Computes the following:
GE()	Calculate the excess Gibbs energy with the UNIFAC model.
Gs()	Computes the following:
Gs_pure()	Computes the following:
HE()	Calculate and return the excess entropy of a liquid phase using an activity coefficient model.
Hs()	Computes the following:
Hs_pure()	Computes the following:
SE()	Calculates the excess entropy of a liquid phase using an activity coefficient model.
Theta_Psi_sum_invs()	Computes the following term for each group k, size number of groups.
Theta_Psi_sums()	Computes the following term for each group k, size number of groups.
Theta_pure_Psi_sum_invs()	Computes the following term for each group k, size number of groups.
Thetas()	Calculate the $\Theta_m$ parameters used in calculating the residual part.
Thetas_pure()	Calculate the $\Theta_m$ parameters for each chemical in the mixture as a pure species, used in calculating the residual part.
Vis()	Calculate the $V_i$ terms used in calculating the combinatorial part.
Vis_modified()	Calculate the $V_i'$ terms used in calculating the combinatorial part.
Ws()	Computes the following for each k and each i, indexed by [k][i] k is in groups, and i is in components.
Xs()	Calculate the $X_m$ parameters used in calculating the residual part.
Xs_pure()	Calculate the $X_m$ parameters for each chemical in the mixture as a pure species, used in calculating the residual part.
as_json([cache, option])	Method to create a JSON-friendly representation of the Gibbs Excess model which can be stored, and reloaded later.
d2Fis_dxixjs()	Calculate the second mole fraction derivative of the $F_i$ terms used in calculating the combinatorial part.
d2GE_dT2()	Calculate the second temperature derivative of excess Gibbs energy with the UNIFAC model.
d2GE_dTdns()	Calculate and return the mole number derivative of the first temperature derivative of excess Gibbs energy of a liquid phase using an activity coefficient model.
d2GE_dTdxs()	Calculate the first composition derivative and temperature derivative of excess Gibbs energy with the UNIFAC model.
d2GE_dxixjs()	Calculate the second composition derivative of excess Gibbs energy with the UNIFAC model.
d2Thetas_dxixjs()	Calculate the mole fraction derivatives of the $\Theta_m$ parameters.
d2Vis_dxixjs()	Calculate the second mole fraction derivative of the $V_i$ terms used in calculating the combinatorial part.
d2Vis_modified_dxixjs()	Calculate the second mole fraction derivative of the $V_i'$ terms used in calculating the combinatorial part.
d2lnGammas_subgroups_dT2()	Calculate the second temperature derivative of the $\ln \Gamma_k$ parameters for the phase; depends on the phases's composition and temperature.
d2lnGammas_subgroups_dTdxs()	Calculate the temperature and mole fraction derivatives of the $\ln \Gamma_k$ parameters for the phase; depends on the phases's composition and temperature.
d2lnGammas_subgroups_dxixjs()	Calculate the second mole fraction derivatives of the $\ln \Gamma_k$ parameters for the phase; depends on the phases's composition and temperature.
d2lnGammas_subgroups_pure_dT2()	Calculate the second temperature derivative of $\ln \Gamma_k$ pure component parameters for the phase; depends on the phases's temperature only.
d2lngammas_c_dT2()	Second temperature derivatives of the combinatorial part of the UNIFAC model.
d2lngammas_c_dTdx()	Second temperature derivative and first mole fraction derivative of the combinatorial part of the UNIFAC model.
d2lngammas_c_dxixjs()	Second composition derivative of the combinatorial part of the UNIFAC model.
d2lngammas_dT2()	Calculates the second temperature derivative of the residual part of the UNIFAC model.
d2lngammas_r_dT2()	Calculates the second temperature derivative of the residual part of the UNIFAC model.
d2lngammas_r_dTdxs()	Calculates the first mole fraction derivative of the temperature derivative of the residual part of the UNIFAC model.
d2lngammas_r_dxixjs()	Calculates the second mole fraction derivative of the residual part of the UNIFAC model.
d2nGE_dTdns()	Calculate and return the partial mole number derivative of the first temperature derivative of excess Gibbs energy of a liquid phase using an activity coefficient model.
d2nGE_dninjs()	Calculate and return the second partial mole number derivative of excess Gibbs energy of a liquid phase using an activity coefficient model.
d2psis_dT2()	Calculate the $\Psi$ term second temperature derivative matrix for all groups interacting with all other groups.
d3Fis_dxixjxks()	Calculate the third mole fraction derivative of the $F_i$ terms used in calculating the combinatorial part.
d3GE_dT3()	Calculate the third temperature derivative of excess Gibbs energy with the UNIFAC model.
d3Vis_dxixjxks()	Calculate the third mole fraction derivative of the $V_i$ terms used in calculating the combinatorial part.
d3Vis_modified_dxixjxks()	Calculate the third mole fraction derivative of the $V_i'$ terms used in calculating the combinatorial part.
d3lnGammas_subgroups_dT3()	Calculate the third temperature derivative of the $\ln \Gamma_k$ parameters for the phase; depends on the phases's composition and temperature.
d3lnGammas_subgroups_pure_dT3()	Calculate the third temperature derivative of $\ln \Gamma_k$ pure component parameters for the phase; depends on the phases's temperature only.
d3lngammas_c_dT3()	Third temperature derivatives of the combinatorial part of the UNIFAC model.
d3lngammas_c_dxixjxks()	Third composition derivative of the combinatorial part of the UNIFAC model.
d3lngammas_dT3()	Calculates the third temperature derivative of the residual part of the UNIFAC model.
d3lngammas_r_dT3()	Calculates the third temperature derivative of the residual part of the UNIFAC model.
d3psis_dT3()	Calculate the $\Psi$ term third temperature derivative matrix for all groups interacting with all other groups.
dFis_dxs()	Calculate the mole fraction derivative of the $F_i$ terms used in calculating the combinatorial part.
dGE_dT()	Calculate the first temperature derivative of excess Gibbs energy with the UNIFAC model.
dGE_dns()	Calculate and return the mole number derivative of excess Gibbs energy of a liquid phase using an activity coefficient model.
dGE_dxs()	Calculate the first composition derivative of excess Gibbs energy with the UNIFAC model.
dHE_dT()	Calculate and return the first temperature derivative of excess enthalpy of a liquid phase using an activity coefficient model.
dHE_dns()	Calculate and return the mole number derivative of excess enthalpy of a liquid phase using an activity coefficient model.
dHE_dxs()	Calculate and return the mole fraction derivative of excess enthalpy of a liquid phase using an activity coefficient model.
dSE_dT()	Calculate and return the first temperature derivative of excess entropy of a liquid phase using an activity coefficient model.
dSE_dns()	Calculate and return the mole number derivative of excess entropy of a liquid phase using an activity coefficient model.
dSE_dxs()	Calculate and return the mole fraction derivative of excess entropy of a liquid phase using an activity coefficient model.
dThetas_dxs()	Calculate the mole fraction derivatives of the $\Theta_m$ parameters.
dVis_dxs()	Calculate the mole fraction derivative of the $V_i$ terms used in calculating the combinatorial part.
dVis_modified_dxs()	Calculate the mole fraction derivative of the $V_i'$ terms used in calculating the combinatorial part.
dgammas_dT()	Calculates the first temperature derivative of activity coefficients with the UNIFAC model.
dgammas_dns()	Calculate and return the mole number derivative of activity coefficients of a liquid phase using an activity coefficient model.
dgammas_dxs()	Calculates the first mole fraction derivative of activity coefficients with the UNIFAC model.
dlnGammas_subgroups_dT()	Calculate the first temperature derivative of the $\ln \Gamma_k$ parameters for the phase; depends on the phases's composition and temperature.
dlnGammas_subgroups_dxs()	Calculate the mole fraction derivatives of the $\ln \Gamma_k$ parameters for the phase; depends on the phases's composition and temperature.
dlnGammas_subgroups_pure_dT()	Calculate the first temperature derivative of $\ln \Gamma_k$ pure component parameters for the phase; depends on the phases's temperature only.
dlngammas_c_dT()	Temperature derivatives of the combinatorial part of the UNIFAC model.
dlngammas_c_dxs()	First composition derivative of the combinatorial part of the UNIFAC model.
dlngammas_dT()	Calculates the first temperature derivative of the residual part of the UNIFAC model.
dlngammas_r_dT()	Calculates the first temperature derivative of the residual part of the UNIFAC model.
dlngammas_r_dxs()	Calculates the first mole fraction derivative of the residual part of the UNIFAC model.
dnGE_dns()	Calculate and return the partial mole number derivative of excess Gibbs energy of a liquid phase using an activity coefficient model.
dnHE_dns()	Calculate and return the partial mole number derivative of excess enthalpy of a liquid phase using an activity coefficient model.
dnSE_dns()	Calculate and return the partial mole number derivative of excess entropy of a liquid phase using an activity coefficient model.
dpsis_dT()	Calculate the $\Psi$ term first temperature derivative matrix for all groups interacting with all other groups.
from_json(json_repr[, cache])	Method to create a Gibbs Excess model from a JSON-friendly serialization of another Gibbs Excess model.
from_subgroups(T, xs, chemgroups[, ...])	Method to construct a UNIFAC object from a dictionary of interaction parameters parameters and a list of dictionaries of UNIFAC keys.
gammas()	Calculates the activity coefficients with the UNIFAC model.
gammas_args([T])	Return a tuple of arguments at the specified tempearture that can be used to efficiently compute gammas at the specified temperature but with varying compositions.
gammas_infinite_dilution()	Calculate and return the infinite dilution activity coefficients of each component.
lnGammas_subgroups()	Calculate the $\ln \Gamma_k$ parameters for the phase; depends on the phases's composition and temperature.
lnGammas_subgroups_pure()	Calculate the $\ln \Gamma_k$ pure component parameters for the phase; depends on the phases's temperature only.
lngammas()	Calculate and return the natural logarithm of the activity coefficients of a liquid phase using an activity coefficient model.
lngammas_c()	Calculates the combinatorial part of the UNIFAC model.
lngammas_r()	Calculates the residual part of the UNIFAC model.
missing_interaction_parameters()	Return a list of tuples (main_group_a_int, main_group_b_int) for each interaction between main groups where the a interaction parameter is zero.
model_hash()	Basic method to calculate a hash of the non-state parts of the model This is useful for comparing to models to determine if they are the same, i.e. in a VLL flash it is important to know if both liquids have the same model.
psis()	Calculate the $\Psi$ term matrix for all groups interacting with all other groups.
state_hash()	Basic method to calculate a hash of the state of the model and its model parameters.
to_T_xs(T, xs)	Method to construct a new UNIFAC instance at temperature T, and mole fractions xs with the same parameters as the existing object.

Theta_pure_Psi_sums
Thetas_sum_inv
VSXS
Xs_sum_inv
d2GE_dT2_numerical
d2GE_dTdxs_numerical
d2GE_dxixjs_numerical
d3GE_dT2dxs_numerical
d3GE_dT3_numerical
d3GE_dTdxixjs_numerical
d4GE_dT2dxixjs_numerical
d4GE_dT3dxs_numerical
d4GE_dT4_numerical
d5GE_dT3dxixjs_numerical
dGE_dT_numerical
dGE_dxs_numerical
gammas_dGE_dxs
gammas_from_args
gammas_numerical

Notes

In addition to the methods presented here, the methods of its base class thermo.activity.GibbsExcess are available as well.

References

[1]

Poling, Bruce E., John M. Prausnitz, and John P. O`Connell. The Properties of Gases and Liquids. 5th edition. New York: McGraw-Hill Professional, 2000.

[2] (1,2)

Gmehling, Jürgen, Michael Kleiber, Bärbel Kolbe, and Jürgen Rarey. Chemical Thermodynamics for Process Simulation. John Wiley & Sons, 2019.

Examples

The DDBST has published numerous sample problems using UNIFAC; a simple binary system from example P05.22a in [2] with n-hexane and butanone-2 is shown below:

>>> from thermo.unifac import UFIP, UFSG
>>> GE = UNIFAC.from_subgroups(chemgroups=[{1:2, 2:4}, {1:1, 2:1, 18:1}], T=60+273.15, xs=[0.5, 0.5], version=0, interaction_data=UFIP, subgroups=UFSG)
>>> GE.gammas()
[1.4276025835, 1.3646545010]
>>> GE.GE(), GE.dGE_dT(), GE.d2GE_dT2()
(923.641197, 0.206721488, -0.00380070204)
>>> GE.HE(), GE.SE(), GE.dHE_dT(), GE.dSE_dT()
(854.77193363, -0.2067214889, 1.266203886, 0.0038007020460)

The solution given by the DDBST has the same values [1.428, 1.365], and can be found here: http://chemthermo.ddbst.com/Problems_Solutions/Mathcad_Files/05.22a%20VLE%20of%20Hexane-Butanone-2%20Via%20UNIFAC%20-%20Step%20by%20Step.xps

Fis()

Calculate the $F_i$ terms used in calculating the combinatorial part. A function of mole fractions and the parameters q only.

$$F_i = \frac{q_i}{\sum_j q_j x_j}$$

This is used in the UNIFAC, UNIFAC-LLE, UNIFAC Dortmund, UNIFAC-NIST, and PSRK models.

Returns:

Fislist[float]

F terms size number of components, [-]

Fs()

Computes the following:

$$F(k) = \sum_m^{gr} \theta_m \frac{\partial \psi_{m,k}}{\partial T}$$

Fs_pure()

Computes the following:

$$F(k) = \sum_m^{gr} \theta_m \frac{\partial \psi_{m,k}}{\partial T}$$

GE()

Calculate the excess Gibbs energy with the UNIFAC model.

$$G^E = RT\sum_i x_i \left(\ln \gamma_i^c + \ln \gamma_i^r \right)$$

For the VTPR model, the combinatorial component is set to zero.

Returns:

GEfloat

Excess Gibbs energy, [J/mol]

Gs()

Computes the following:

$$G(k) = \sum_m^{gr} \theta_m \frac{\partial^2 \psi_{m,k}}{\partial T^2}$$

Gs_pure()

Computes the following:

$$G(k) = \sum_m^{gr} \theta_m \frac{\partial^2 \psi_{m,k}}{\partial T^2}$$

Hs()

Computes the following:

$$H(k) = \sum_m^{gr} \theta_m \frac{\partial^3 \psi_{m,k}}{\partial T^3}$$

Hs_pure()

Computes the following:

$$H(k) = \sum_m^{gr} \theta_m \frac{\partial^3 \psi_{m,k}}{\partial T^3}$$

Theta_Psi_sum_invs()

Computes the following term for each group k, size number of groups.

$$U(k) = \frac{1}{\sum_m \Theta_m \Psi_{m,k}}$$

Theta_Psi_sums()

Computes the following term for each group k, size number of groups.

$$\sum_m \Theta_m \Psi_{mk}$$

Theta_pure_Psi_sum_invs()

Computes the following term for each group k, size number of groups.

$$U(k) = \frac{1}{\sum_m \Theta_m \Psi_{m,k}}$$

Thetas()

Calculate the $\Theta_m$ parameters used in calculating the residual part. A function of mole fractions and group counts only.

$$\Theta_m = \frac{Q_m X_m}{\sum_{n} Q_n X_n}$$

Returns:

Thetaslist[float]

$\Theta_m$ terms, size number of subgroups, [-]

Thetas_pure()

Calculate the $\Theta_m$ parameters for each chemical in the mixture as a pure species, used in calculating the residual part. A function of group counts only.

$$\Theta_m = \frac{Q_m X_m}{\sum_{n} Q_n X_n}$$

Returns:

Thetas_purelist[list[float]]

$\Theta_m$ terms, size number of components by number of subgroups and indexed in that order, [-]

Vis()

Calculate the $V_i$ terms used in calculating the combinatorial part. A function of mole fractions and the parameters r only.

$$V_i = \frac{r_i}{\sum_j r_j x_j}$$

This is used in the UNIFAC, UNIFAC-LLE, UNIFAC Dortmund, UNIFAC-NIST, and PSRK models.

Returns:

Vislist[float]

V terms size number of components, [-]

Vis_modified()

Calculate the $V_i'$ terms used in calculating the combinatorial part. A function of mole fractions and the parameters r only.

$$V_i' = \frac{r_i^n}{\sum_j r_j^n x_j}$$

This is used in the UNIFAC Dortmund and UNIFAC-NIST model with n=0.75, and the Lyngby model with n=2/3.

Returns:

Vis_modifiedlist[float]

Modified V terms size number of components, [-]

Ws()

Computes the following for each k and each i, indexed by [k][i] k is in groups, and i is in components.

$$W(k,i) = \sum_m^{gr} \psi_{m,k} \frac{\partial \theta_m}{\partial x_i}$$

Xs()

Calculate the $X_m$ parameters used in calculating the residual part. A function of mole fractions and group counts only.

$$X_m = \frac{ \sum_j \nu^j_m x_j}{\sum_j \sum_n \nu_n^j x_j}$$

Returns:

Xslist[float]

$X_m$ terms, size number of subgroups, [-]

Xs_pure()

Calculate the $X_m$ parameters for each chemical in the mixture as a pure species, used in calculating the residual part. A function of group counts only, not even mole fractions or temperature.

$$X_m = \frac{\nu_m}{\sum^{gr}_n \nu_n}$$

Returns:

Xs_purelist[list[float]]

$X_m$ terms, size number of subgroups by number of components and indexed in that order, [-]

d2Fis_dxixjs()

Calculate the second mole fraction derivative of the $F_i$ terms used in calculating the combinatorial part. A function of mole fractions and the parameters q only.

$$\frac{\partial F_i}{\partial x_j \partial x_k} = 2 q_i q_j q_k G_{sum}^3$$

$$G_{sum} = \frac{1}{\sum_j q_j x_j}$$

This is used in the UNIFAC, UNIFAC-LLE, UNIFAC Dortmund, UNIFAC-NIST, and PSRK models.

Returns:

d2Fis_dxixjslist[list[list[float]]]

F terms size number of components by number of components by number of components, [-]

d2GE_dT2()

Calculate the second temperature derivative of excess Gibbs energy with the UNIFAC model.

$$\frac{\partial^2 G^E}{\partial T^2} = RT\sum_i x_i \frac{\partial^2 \ln \gamma_i^r}{\partial T^2} + 2R\sum_i x_i \frac{\partial \ln \gamma_i^r}{\partial T}$$

Returns:

d2GE_dT2float

Second temperature derivative of excess Gibbs energy, [J/mol/K^2]

d2GE_dTdxs()

Calculate the first composition derivative and temperature derivative of excess Gibbs energy with the UNIFAC model.

$$\frac{\partial^2 G^E}{\partial T\partial x_i} = RT\left(\frac{\partial \ln \gamma_i^r}{\partial T} + \sum_j x_j \frac{\partial \ln \gamma_j^r}{\partial x_i} \right) + R\left[ \frac{\partial \ln \gamma_i^c}{\partial x_i} + \frac{\partial \ln \gamma_i^r}{\partial x_i} + \sum_j x_j \left( \frac{\partial \ln \gamma_j^c}{\partial x_i} + \frac{\partial \ln \gamma_j^r}{\partial x_i}\right)\right]$$

Returns:

dGE_dxslist[float]

First composition derivative and first temperature derivative of excess Gibbs energy, [J/mol/K]

d2GE_dxixjs()

Calculate the second composition derivative of excess Gibbs energy with the UNIFAC model.

$$\frac{\partial^2 G^E}{\partial x_j \partial x_k} = RT \left[\sum_i \left( \frac{\partial \ln \gamma_i^c}{\partial x_j \partial x_k} + \frac{\partial \ln \gamma_i^r}{\partial x_j \partial x_k} \right) + \frac{\partial \ln \gamma_j^c}{\partial x_k} + \frac{\partial \ln \gamma_j^r}{\partial x_k} + \frac{\partial \ln \gamma_k^c}{\partial x_j} + \frac{\partial \ln \gamma_k^r}{\partial x_j}\right]$$

Returns:

d2GE_dxixjslist[list[float]]

Second composition derivative of excess Gibbs energy, [J/mol]

d2Thetas_dxixjs()

Calculate the mole fraction derivatives of the $\Theta_m$ parameters. A function of mole fractions and group counts only.

$$\frac{\partial^2 \Theta_i}{\partial x_j \partial x_k} = \frac{Q_i}{\sum_n Q_n (\nu x)_{sum,n}}\left[ -F(\nu)_{sum,j} \nu_{i,k} - F (\nu)_{sum,k}\nu_{i,j} + 2F^2(\nu)_{sum,j} (\nu)_{sum,k} (\nu x)_{sum,i} + \frac{F (\nu x)_{sum,i}\left[ \sum_n(-2 F Q_n (\nu)_{sum,j} (\nu)_{sum,k} (\nu x)_{sum,n} + Q_n (\nu)_{sum,j} \nu_{n,k} + Q_n (\nu)_{sum,k}\nu_{n,j} )\right] } {\sum_n^{gr} Q_n (\nu x)_{sum,n} } + \frac{2(\nu x)_{sum,i}(\sum_n^{gr}[-FQ_n (\nu)_{sum,j} (\nu x)_{sum,n} + Q_n \nu_{n,j}]) (\sum_n^{gr}[-FQ_n (\nu)_{sum,k} (\nu x)_{sum,n} + Q_n \nu_{n,k}]) } {\left( \sum_n^{gr} Q_n (\nu x)_{sum,n} \right)^2} - \frac{\nu_{i,j}(\sum_n^{gr} -FQ_n (\nu)_{sum,k} (\nu x)_{sum,n} + Q_n \nu_{n,k} )} {\left( \sum_n^{gr} Q_n (\nu x)_{sum,n} \right)} - \frac{\nu_{i,k}(\sum_n^{gr} -FQ_n (\nu)_{sum,j} (\nu x)_{sum,n} + Q_n \nu_{n,j} )} {\left( \sum_n^{gr} Q_n (\nu x)_{sum,n} \right)} + \frac{F(\nu)_{sum,j} (\nu x)_{sum,i} (\sum_n^{gr} -FQ_n (\nu)_{sum,k} (\nu x)_{sum,n} + Q_n \nu_{n,k})} {\left(\sum_n^{gr} Q_n (\nu x)_{sum,n} \right)} + \frac{F(\nu)_{sum,k} (\nu x)_{sum,i} (\sum_n^{gr} -FQ_n (\nu)_{sum,j} (\nu x)_{sum,n} + Q_n \nu_{n,j})} {\left(\sum_n^{gr} Q_n (\nu x)_{sum,n} \right)} \right]$$

$$G = \frac{1}{\sum_j Q_j X_j}$$

$$F = \frac{1}{\sum_j \sum_n \nu_n^j x_j}$$

$$(\nu)_{sum,i} = \sum_j \nu_{j,i}$$

$$(\nu x)_{sum,i} = \sum_j \nu_{i,j}x_j$$

Returns:

d2Thetas_dxixjslist[list[list[float]]]

$\Theta_m$ terms, size number of subgroups by mole fractions and indexed in that order, [-]

d2Vis_dxixjs()

Calculate the second mole fraction derivative of the $V_i$ terms used in calculating the combinatorial part. A function of mole fractions and the parameters r only.

$$\frac{\partial V_i}{\partial x_j \partial x_k} = 2 r_i r_j r_k V_{sum}^3$$

$$V_{sum} = \frac{1}{\sum_j r_j x_j}$$

This is used in the UNIFAC, UNIFAC-LLE, UNIFAC Dortmund, UNIFAC-NIST, and PSRK models.

Returns:

d2Vis_dxixjslist[list[list[float]]]

V terms size number of components by number of components by number of components, [-]

d2Vis_modified_dxixjs()

Calculate the second mole fraction derivative of the $V_i'$ terms used in calculating the combinatorial part. A function of mole fractions and the parameters r only.

$$\frac{\partial V_i'}{\partial x_j \partial x_k} = 2 r_i^n r_j^n r_k^n V_{sum}^3$$

$$V_{sum} = \frac{1}{\sum_j r_j^n x_j}$$

This is used in the UNIFAC Dortmund and UNIFAC-NIST model with n=0.75, and the Lyngby model with n=2/3.

Returns:

d2Vis_modified_dxixjslist[list[list[float]]]

V’ terms size number of components by number of components by number of components, [-]

d2lnGammas_subgroups_dT2()

Calculate the second temperature derivative of the $\ln \Gamma_k$ parameters for the phase; depends on the phases’s composition and temperature.

$$\frac{\partial^2 \ln \Gamma_i}{\partial T^2} = -Q_i\left[ Z(i)G(i) - F(i)^2 Z(i)^2 + \sum_j\left( \theta_j Z(j)\frac{\partial^2 \psi_{i,j}}{\partial T} - Z(j)^2 \left(G(j)\theta_j \psi_{i,j} + 2 F_j \theta_j \frac{\partial \psi_{i,j}}{\partial T}\right) + 2Z(j)^3F(j)^2 \theta_j \psi_{i,j} \right)\right]$$

$$F(k) = \sum_m^{gr} \theta_m \frac{\partial \psi_{m,k}}{\partial T}$$

$$G(k) = \sum_m^{gr} \theta_m \frac{\partial^2 \psi_{m,k}}{\partial T^2}$$

$$Z(k) = \frac{1}{\sum_m \Theta_m \Psi_{m,k}}$$

Returns:

d2lnGammas_subgroups_dT2list[float]

Second temperature derivative of ln Gamma parameters for each subgroup, size number of subgroups, [1/K^2]

d2lnGammas_subgroups_dTdxs()

Calculate the temperature and mole fraction derivatives of the $\ln \Gamma_k$ parameters for the phase; depends on the phases’s composition and temperature.

$$\frac{\partial^2 \ln \Gamma_k}{\partial x_i \partial T} = -Q_k\left( D(k,i) Z(k) - B(k)W(k,i) Z(k)^2 + \sum_m^{gr} (Z(m) \frac{\partial \theta_m}{\partial x_i}\frac{\partial \psi_{k,m}}{\partial T}) -\sum_m^{gr} (B(m) Z(m)^2 \psi_{k,m} \frac{\partial \theta_m}{\partial x_i}) -\sum_m^{gr}(D(m,i) Z(m)^2 \theta_m \psi_{k,m}) - \sum_m^{gr} (W(m,i) Z(m)^2 \theta_m \frac{\partial \psi_{k,m}}{\partial T}) + \sum_m^{gr} 2 B(m) W(m,i) Z(m)^3 \theta_m \psi_{k,m} \right)$$

The following groups are used as follows to simplfy the number of evaluations:

$$W(k,i) = \sum_m^{gr} \psi_{m,k} \frac{\partial \theta_m}{\partial x_i}$$

$$Z(k) = \frac{1}{\sum_m \Theta_m \Psi_{mk}}$$

$$F(k) = \sum_m^{gr} \theta_m \frac{\partial \psi_{m,k}}{\partial T}$$

In the below expression, k` refers to a group, and i refers to a component.

$$D(k,i) = \sum_m^{gr} \frac{\partial \theta_m}{\partial x_i} \frac{\partial \psi_{m,k}}{\partial T}$$

Returns:

d2lnGammas_subgroups_dTdxslist[list[float]]

Temperature and mole fraction derivatives of Gamma parameters for each subgroup, size number of subgroups by number of components and indexed in that order, [1/K]

d2lnGammas_subgroups_dxixjs()

Calculate the second mole fraction derivatives of the $\ln \Gamma_k$ parameters for the phase; depends on the phases’s composition and temperature.

$$\frac{\partial^2 \ln \Gamma_k}{\partial x_i \partial x_j} = -Q_k\left( -Z(k) K(k,i,j) - \sum_m^{gr} Z(m)^2 K(m,i,j)\theta_m \psi_{k,m} -W(k,i) W(k,j) Z(k)^2 + \sum_m^{gr} Z_m \psi_{k,m} \frac{\partial^2 \theta_m}{\partial x_i \partial x_j} - \sum_m \left(W(m,j) Z(m)^2 \psi_{k,m} \frac{\partial \theta_m}{\partial x_i} + W(m,i) Z(m)^2 \psi(k,m) \frac{\partial \theta_m}{\partial x_j}\right) + \sum_m^{gr} 2 W(m,i) W(m,j) Z(m)^3 \theta_m \psi_{k,m}\right)$$

The following groups are used as follows to simplfy the number of evaluations:

$$W(k,i) = \sum_m^{gr} \psi_{m,k} \frac{\partial \theta_m}{\partial x_i}$$

$$Z(k) = \frac{1}{\sum_m \Theta_m \Psi_{mk}}$$

$$K(k, i, j) = \sum_m^{gr} \psi_{m,k} \frac{\partial^2 \theta_m}{\partial x_i \partial x_j}$$

Returns:

d2lnGammas_subgroups_dxixjslist[list[list[float]]]

Second mole fraction derivatives of Gamma parameters for each subgroup, size number of components by number of components by number of subgroups and indexed in that order, [-]

d2lnGammas_subgroups_pure_dT2()

Calculate the second temperature derivative of $\ln \Gamma_k$ pure component parameters for the phase; depends on the phases’s temperature only.

$$\frac{\partial^2 \ln \Gamma_i}{\partial T^2} = -Q_i\left[ Z(i)G(i) - F(i)^2 Z(i)^2 + \sum_j\left( \theta_j Z(j)\frac{\partial^2 \psi_{i,j}}{\partial T} - Z(j)^2 \left(G(j)\theta_j \psi_{i,j} + 2 F_j \theta_j \frac{\partial \psi_{i,j}}{\partial T}\right) + 2Z(j)^3F(j)^2 \theta_j \psi_{i,j} \right)\right]$$

$$F(k) = \sum_m^{gr} \theta_m \frac{\partial \psi_{m,k}}{\partial T}$$

$$G(k) = \sum_m^{gr} \theta_m \frac{\partial^2 \psi_{m,k}}{\partial T^2}$$

$$Z(k) = \frac{1}{\sum_m \Theta_m \Psi_{m,k}}$$

In this model, the $\Theta$ values come from the UNIFAC.Thetas_pure method, where each compound is assumed to be pure.

Returns:

d2lnGammas_subgroups_pure_dT2list[list[float]]

Second temperature derivative of ln Gamma parameters for each subgroup, size number of subgroups by number of components and indexed in that order, [1/K^2]

d2lngammas_c_dT2()

Second temperature derivatives of the combinatorial part of the UNIFAC model. Zero in all variations.

$$\frac{\partial^2 \ln \gamma_i^c}{\partial T^2} = 0$$

Returns:

d2lngammas_c_dT2list[float]

Combinatorial lngammas term second temperature derivatives, size number of components, [-]

d2lngammas_c_dTdx()

Second temperature derivative and first mole fraction derivative of the combinatorial part of the UNIFAC model. Zero in all variations.

$$\frac{\partial^3 \ln \gamma_i^c}{\partial T^2 \partial x_j} = 0$$

Returns:

d2lngammas_c_dTdxlist[list[float]]

Combinatorial lngammas term second temperature derivatives, size number of components by number of components, [-]

d2lngammas_c_dxixjs()

Second composition derivative of the combinatorial part of the UNIFAC model. For the modified UNIFAC model, the equation is as follows; for the original UNIFAC and UNIFAC LLE, replace $V_i'$ with $V_i$.

$$\frac{\partial \ln \gamma^c_i}{\partial x_j \partial x_k} = 5 q_{i} \left(\frac{- \frac{d^{2}}{d x_{k}d x_{j}} V_{i} + \frac{V_{i} \frac{d^{2}}{d x_{k}d x_{j}} F_{i}}{F_{i}} + \frac{\frac{d}{d x_{j}} F_{i} \frac{d}{d x_{k}} V_{i}}{F_{i}} + \frac{\frac{d}{d x_{k}} F_{i} \frac{d}{d x_{j}} V_{i}}{F_{i}} - \frac{2 V_{i} \frac{d}{d x_{j}} F_{i} \frac{d}{d x_{k}} F_{i}}{F_{i}^{2}}}{V_{i}} + \frac{\left( \frac{d}{d x_{j}} V_{i} - \frac{V_{i} \frac{d}{d x_{j}} F_{i}} {F_{i}}\right) \frac{d}{d x_{k}} V_{i}}{V_{i}^{2}} + \frac{\frac{d^{2}}{d x_{k}d x_{j}} V_{i}}{F_{i}} - \frac{\left( \frac{d}{d x_{j}} V_{i} - \frac{V_{i} \frac{d}{d x_{j}} F_{i}}{ F_{i}}\right) \frac{d}{d x_{k}} F_{i}}{F_{i} V_{i}} - \frac{V_{i} \frac{d^{2}}{d x_{k}d x_{j}} F_{i}}{F_{i}^{2}} - \frac{\frac{d} {d x_{j}} F_{i} \frac{d}{d x_{k}} V_{i}}{F_{i}^{2}} - \frac{\frac{d}{d x_{k}} F_{i} \frac{d}{d x_{j}} V_{i}}{F_{i}^{2}} + \frac{2 V_{i} \frac{d}{d x_{j}} F_{i} \frac{d}{d x_{k}} F_{i}} {F_{i}^{3}}\right) - \frac{d^{2}}{d x_{k}d x_{j}} Vi' + \frac{\frac{d^{2}}{d x_{k}d x_{j}} Vi'}{Vi'} - \frac{\frac{d} {d x_{j}} Vi' \frac{d}{d x_{k}} Vi'}{Vi'^{2}}$$

For the Lyngby model, the following equations are used:

$$\frac{\partial^2 \ln \gamma^c_i}{\partial x_j \partial x_k} = -\frac{\partial^2 V_i'}{\partial x_j \partial x_k} + \frac{1}{V_i'} \frac{\partial^2 V_i'}{\partial x_j \partial x_k} - \frac{1}{\left(V_i'\right)^2} \frac{\partial V_i'}{\partial x_j} \frac{\partial V_i'}{\partial x_k}$$

Returns:

d2lngammas_c_dxixjslist[list[list[float]]]

Combinatorial lngammas term second composition derivative, size number of components by number of components by number of components, [-]

d2lngammas_dT2()

Calculates the second temperature derivative of the residual part of the UNIFAC model.

$$\frac{\partial^2 \ln \gamma_i^r}{\partial T^2} = \sum_{k}^{gr} \nu_k^{(i)} \left[ \frac{\partial^2 \ln \Gamma_k}{\partial T^2} - \frac{\partial^2 \ln \Gamma_k^{(i)}}{\partial T^2} \right]$$

where the second Gamma is the pure-component Gamma of group k in component i.

Returns:

d2lngammas_r_dT2list[float]

Residual lngammas terms second temperature derivative, size number of components [1/K^2]

d2lngammas_r_dT2()

Calculates the second temperature derivative of the residual part of the UNIFAC model.

$$\frac{\partial^2 \ln \gamma_i^r}{\partial T^2} = \sum_{k}^{gr} \nu_k^{(i)} \left[ \frac{\partial^2 \ln \Gamma_k}{\partial T^2} - \frac{\partial^2 \ln \Gamma_k^{(i)}}{\partial T^2} \right]$$

where the second Gamma is the pure-component Gamma of group k in component i.

Returns:

d2lngammas_r_dT2list[float]

Residual lngammas terms second temperature derivative, size number of components [1/K^2]

d2lngammas_r_dTdxs()

Calculates the first mole fraction derivative of the temperature derivative of the residual part of the UNIFAC model.

$$\frac{\partial^2 \ln \gamma_i^r}{\partial x_j \partial T} = \sum_{m}^{gr} \nu_m^{(i)} \frac{\partial^2 \ln \Gamma_m} {\partial x_j \partial T}$$

Returns:

d2lngammas_r_dTdxslist[list[float]]

First mole fraction derivative and temperature derivative of residual lngammas terms, size number of components by number of components [-]

d2lngammas_r_dxixjs()

Calculates the second mole fraction derivative of the residual part of the UNIFAC model.

$$\frac{\partial^2 \ln \gamma_i^r}{\partial x_j^2} = \sum_{m}^{gr} \nu_m^{(i)} \frac{\partial^2 \ln \Gamma_m}{\partial x_j^2}$$

Returns:

d2lngammas_r_dxixjslist[list[list[float]]]

Second mole fraction derivative of the residual lngammas terms, size number of components by number of components by number of components [-]

d2psis_dT2()

Calculate the $\Psi$ term second temperature derivative matrix for all groups interacting with all other groups.

The main model calculates the derivative as a function of three coefficients;

$$\frac{\partial^2 \Psi_{mn}}{\partial T^2} = \frac{\left(- 2 c_{mn} + \frac{2 \left(2 T c_{mn} + b_{mn}\right)}{T} + \frac{\left(2 T c_{mn} + b_{mn} - \frac{T^{2} c_{mn} + T b_{mn} + a_{mn}}{T} \right)^{2}}{T} - \frac{2 \left(T^{2} c_{mn} + T b_{mn} + a_{mn} \right)}{T^{2}}\right) e^{- \frac{T^{2} c_{mn} + T b_{mn} + a_{mn}} {T}}}{T}$$

Only the first, a coefficient, is used in the original UNIFAC model as well as the UNIFAC-LLE model, so the expression simplifies to:

$$\frac{\partial^2 \Psi_{mn}}{\partial T^2} = \frac{a_{mn} \left(-2 + \frac{a_{mn}}{T}\right) e^{- \frac{a_{mn}}{T}}}{T^{3}}$$

For the Lyngby model, the second temperature derivative is:

$$\frac{\partial^2 \Psi_{mk}}{\partial T^2} = \frac{\left(2 a_{2} + 2 a_{3} \ln{\left(\frac{T_{0}}{T} \right)} + a_{3} + \left(a_{2} + a_{3} \ln{\left(\frac{T_{0}}{T} \right)} - \frac{a_{1} + a_{2} \left(T - T_{0}\right) + a_{3} \left(T \ln{\left(\frac{T_{0}}{T} \right)} + T - T_{0}\right)}{T}\right)^{2} - \frac{2 \left(a_{1} + a_{2} \left(T - T_{0}\right) + a_{3} \left(T \ln{\left( \frac{T_{0}}{T} \right)} + T - T_{0}\right)\right)}{T}\right) e^{- \frac{a_{1} + a_{2} \left(T - T_{0}\right) + a_{3} \left( T \ln{\left(\frac{T_{0}}{T} \right)} + T - T_{0}\right)}{T}}} {T^{2}}$$

with $T_0 = 298.15$ K and the a coefficients are specific to each pair of main groups, and they are asymmetric, so $a_{0,mk} \ne a_{0,km}$.

Returns:

d2psis_dT2list[list[float]]

Second temperature derivative of`psi` terms, size subgroups x subgroups [-]

d3Fis_dxixjxks()

Calculate the third mole fraction derivative of the $F_i$ terms used in calculating the combinatorial part. A function of mole fractions and the parameters q only.

$$\frac{\partial F_i}{\partial x_j \partial x_k \partial x_m} = -6 q_i q_j q_k q_m G_{sum}^4$$

$$G_{sum} = \frac{1}{\sum_j q_j x_j}$$

This is used in the UNIFAC, UNIFAC-LLE, UNIFAC Dortmund, UNIFAC-NIST, and PSRK models.

Returns:

d3Fis_dxixjxkslist[list[list[list[float]]]]

F terms size number of components by number of components by number of components by number of components, [-]

d3GE_dT3()

Calculate the third temperature derivative of excess Gibbs energy with the UNIFAC model.

$$\frac{\partial^3 G^E}{\partial T^3} = RT\sum_i x_i \frac{\partial^3 \ln \gamma_i^r}{\partial T^3} + 3R\sum_i x_i \frac{\partial^2 \ln \gamma_i^r}{\partial T^2}$$

Returns:

d3GE_dT3float

Third temperature derivative of excess Gibbs energy, [J/mol/K^3]

d3Vis_dxixjxks()

Calculate the third mole fraction derivative of the $V_i$ terms used in calculating the combinatorial part. A function of mole fractions and the parameters r only.

$$\frac{\partial V_i}{\partial x_j \partial x_k \partial x_m} = -6 r_i r_j r_k r_m V_{sum}^4$$

$$V_{sum} = \frac{1}{\sum_j r_j x_j}$$

This is used in the UNIFAC, UNIFAC-LLE, UNIFAC Dortmund, UNIFAC-NIST, and PSRK models.

Returns:

d3Vis_dxixjxkslist[list[list[list[float]]]]

V terms size number of components by number of components by number of components by number of components, [-]

d3Vis_modified_dxixjxks()

Calculate the third mole fraction derivative of the $V_i'$ terms used in calculating the combinatorial part. A function of mole fractions and the parameters r only.

$$\frac{\partial V_i'}{\partial x_j \partial x_k \partial x_m} = -6 r_i^n r_j^n r_k^n r_m^n V_{sum}^4$$

$$V_{sum} = \frac{1}{\sum_j r_j x_j}$$

This is used in the UNIFAC Dortmund and UNIFAC-NIST model with n=0.75, and the Lyngby model with n=2/3.

Returns:

d3Vis_modified_dxixjxkslist[list[list[list[float]]]]

V’ terms size number of components by number of components by number of components by number of components, [-]

d3lnGammas_subgroups_dT3()

Calculate the third temperature derivative of the $\ln \Gamma_k$ parameters for the phase; depends on the phases’s composition and temperature.

$$\frac{\partial^3 \ln \Gamma_i}{\partial T^3} =Q_i\left[-H(i) Z(i) - 2F(i)^3 Z(i)^3 + 3F(i) G(i) Z(i)^2+ \left( -\theta_j Z(j) \frac{\partial^3 \psi}{\partial T^3} + H(j) Z(j)^2 \theta(j)\psi_{i,j} - 6F(j)^2 Z(j)^3 \theta_j \frac{\partial \psi_{i,j}}{\partial T} + 3 F(j) Z(j)^2 \theta(j) \frac{\partial^2 \psi_{i,j}}{\partial T^2} ++ 3G(j) \theta(j) Z(j)^2 \frac{\partial \psi_{i,j}}{\partial T} + 6F(j)^3 \theta(j) Z(j)^4 \psi_{i,j} - 6F(j) G(j) \theta(j) Z(j)^3 \psi_{i,j} \right) \right]$$

$$F(k) = \sum_m^{gr} \theta_m \frac{\partial \psi_{m,k}}{\partial T}$$

$$G(k) = \sum_m^{gr} \theta_m \frac{\partial^2 \psi_{m,k}}{\partial T^2}$$

$$H(k) = \sum_m^{gr} \theta_m \frac{\partial^3 \psi_{m,k}}{\partial T^3}$$

$$Z(k) = \frac{1}{\sum_m \Theta_m \Psi_{m,k}}$$

Returns:

d3lnGammas_subgroups_dT3list[float]

Third temperature derivative of ln Gamma parameters for each subgroup, size number of subgroups, [1/K^3]

d3lnGammas_subgroups_pure_dT3()

Calculate the third temperature derivative of $\ln \Gamma_k$ pure component parameters for the phase; depends on the phases’s temperature only.

$$\frac{\partial^3 \ln \Gamma_i}{\partial T^3} =Q_i\left[-H(i) Z(i) - 2F(i)^3 Z(i)^3 + 3F(i) G(i) Z(i)^2+ \left( -\theta_j Z(j) \frac{\partial^3 \psi}{\partial T^3} + H(j) Z(j)^2 \theta(j)\psi_{i,j} - 6F(j)^2 Z(j)^3 \theta_j \frac{\partial \psi_{i,j}}{\partial T} + 3 F(j) Z(j)^2 \theta(j) \frac{\partial^2 \psi_{i,j}}{\partial T^2} ++ 3G(j) \theta(j) Z(j)^2 \frac{\partial \psi_{i,j}}{\partial T} + 6F(j)^3 \theta(j) Z(j)^4 \psi_{i,j} - 6F(j) G(j) \theta(j) Z(j)^3 \psi_{i,j} \right) \right]$$

$$F(k) = \sum_m^{gr} \theta_m \frac{\partial \psi_{m,k}}{\partial T}$$

$$G(k) = \sum_m^{gr} \theta_m \frac{\partial^2 \psi_{m,k}}{\partial T^2}$$

$$H(k) = \sum_m^{gr} \theta_m \frac{\partial^3 \psi_{m,k}}{\partial T^3}$$

$$Z(k) = \frac{1}{\sum_m \Theta_m \Psi_{m,k}}$$

In this model, the $\Theta$ values come from the UNIFAC.Thetas_pure method, where each compound is assumed to be pure.

Returns:

d3lnGammas_subgroups_pure_dT3list[list[float]]

Third temperature derivative of ln Gamma parameters for each subgroup, size number of subgroups by number of components and indexed in that order, [1/K^3]

d3lngammas_c_dT3()

Third temperature derivatives of the combinatorial part of the UNIFAC model. Zero in all variations.

$$\frac{\partial^3 \ln \gamma_i^c}{\partial T^3} = 0$$

Returns:

d3lngammas_c_dT3list[float]

Combinatorial lngammas term second temperature derivatives, size number of components, [-]

d3lngammas_c_dxixjxks()

Third composition derivative of the combinatorial part of the UNIFAC model. For the modified UNIFAC model, the equation is as follows; for the original UNIFAC and UNIFAC LLE, replace $V_i'$ with $V_i$.

$$\frac{\partial \ln \gamma^c_i}{\partial x_j \partial x_k \partial x_m} = - \frac{d^{3}}{d x_{m}d x_{k}d x_{j}} Vi' + \frac{\frac{d^{3}}{d x_{m}d x_{k}d x_{j}} Vi'}{Vi'} - \frac{\frac{d}{d x_{j}} Vi' \frac{d^{2}}{d x_{m}d x_{k}} Vi'} {Vi'^{2}} - \frac{\frac{d}{d x_{k}} Vi' \frac{d^{2}}{d x_{m}d x_{j}} Vi'}{Vi'^{2}} - \frac{\frac{d}{d x_{m}} Vi' \frac{d^{2}} {d x_{k}d x_{j}} Vi'}{Vi'^{2}} + \frac{2 \frac{d}{d x_{j}} Vi' \frac{d}{d x_{k}} Vi' \frac{d}{d x_{m}} Vi'}{Vi'^{3}} - \frac{5 q_{i} \frac{d^{3}}{d x_{m}d x_{k}d x_{j}} V_{i}}{V_{i}} + \frac{5 q_{i} \frac{d}{d x_{j}} V_{i} \frac{d^{2}}{d x_{m}d x_{k}} V_{i}}{V_{i}^{2}} + \frac{5 q_{i} \frac{d}{d x_{k}} V_{i} \frac{d^{2}}{d x_{m}d x_{j}} V_{i}}{V_{i}^{2}} + \frac{5 q_{i} \frac{d}{d x_{m}} V_{i} \frac{d^{2}}{d x_{k}d x_{j}} V_{i}}{V_{i}^{2}} - \frac{10 q_{i} \frac{d}{d x_{j}} V_{i} \frac{d}{d x_{k}} V_{i} \frac{d}{d x_{m}} V_{i}}{V_{i}^{3}} + \frac{5 q_{i} \frac{d^{3}}{d x_{m}d x_{k}d x_{j}} F_{i}}{F_{i}} + \frac{5 q_{i} \frac{d^{3}}{d x_{m}d x_{k}d x_{j}} V_{i}}{F_{i}} - \frac{5 V_{i} q_{i} \frac{d^{3}}{d x_{m}d x_{k}d x_{j}} F_{i}}{F_{i}^{2}} - \frac{5 q_{i} \frac{d}{d x_{j}} F_{i} \frac{d^{2}}{d x_{m}d x_{k}} F_{i}}{F_{i}^{2}} - \frac{5 q_{i} \frac{d}{d x_{j}} F_{i} \frac{d^{2}}{d x_{m}d x_{k}} V_{i}}{F_{i}^{2}} - \frac{5 q_{i} \frac{d}{d x_{k}} F_{i} \frac{d^{2}}{d x_{m}d x_{j}} F_{i}}{F_{i}^{2}} - \frac{5 q_{i} \frac{d}{d x_{k}} F_{i} \frac{d^{2}}{d x_{m}d x_{j}} V_{i}}{F_{i}^{2}} - \frac{5 q_{i} \frac{d}{d x_{m}} F_{i} \frac{d^{2}}{d x_{k}d x_{j}} F_{i}}{F_{i}^{2}} - \frac{5 q_{i} \frac{d}{d x_{m}} F_{i} \frac{d^{2}}{d x_{k}d x_{j}} V_{i}}{F_{i}^{2}} - \frac{5 q_{i} \frac{d}{d x_{j}} V_{i} \frac{d^{2}}{d x_{m}d x_{k}} F_{i}}{F_{i}^{2}} - \frac{5 q_{i} \frac{d}{d x_{k}} V_{i} \frac{d^{2}}{d x_{m}d x_{j}} F_{i}}{F_{i}^{2}} - \frac{5 q_{i} \frac{d}{d x_{m}} V_{i} \frac{d^{2}}{d x_{k}d x_{j}} F_{i}}{F_{i}^{2}} + \frac{10 V_{i} q_{i} \frac{d}{d x_{j}} F_{i} \frac{d^{2}}{d x_{m}d x_{k}} F_{i}}{F_{i}^{3}} + \frac{10 V_{i} q_{i} \frac{d}{d x_{k}} F_{i} \frac{d^{2}}{d x_{m}d x_{j}} F_{i}}{F_{i}^{3}} + \frac{10 V_{i} q_{i} \frac{d}{d x_{m}} F_{i} \frac{d^{2}}{d x_{k}d x_{j}} F_{i}}{F_{i}^{3}} + \frac{10 q_{i} \frac{d}{d x_{j}} F_{i} \frac{d}{d x_{k}} F_{i} \frac{d}{d x_{m}} F_{i}}{F_{i}^{3}} + \frac{10 q_{i} \frac{d}{d x_{j}} F_{i} \frac{d}{d x_{k}} F_{i} \frac{d}{d x_{m}} V_{i}}{F_{i}^{3}} + \frac{10 q_{i} \frac{d}{d x_{j}} F_{i} \frac{d}{d x_{m}} F_{i} \frac{d}{d x_{k}} V_{i}}{F_{i}^{3}} + \frac{10 q_{i} \frac{d}{d x_{k}} F_{i} \frac{d}{d x_{m}} F_{i} \frac{d}{d x_{j}} V_{i}}{F_{i}^{3}} - \frac{30 V_{i} q_{i} \frac{d}{d x_{j}} F_{i} \frac{d}{d x_{k}} F_{i} \frac{d}{d x_{m}} F_{i}}{F_{i}^{4}}$$

For the Lyngby model, the following equations are used:

$$\frac{\partial^3 \ln \gamma^c_i}{\partial x_j \partial x_k \partial x_m} = \frac{\partial^3 V_i'}{\partial x_j \partial x_k \partial x_m}\left(\frac{1}{V_i'} - 1\right) - \frac{1}{(V_i')^2}\left( \frac{\partial V_i'}{\partial x_j}\frac{\partial V_i'}{\partial x_k \partial x_m} + \frac{\partial V_i'}{\partial x_k}\frac{\partial V_i'}{\partial x_j \partial x_m} + \frac{\partial V_i'}{\partial x_m}\frac{\partial V_i'}{\partial x_j \partial x_k} \right) + \frac{2}{(V_i')^3}\frac{\partial V_i'}{\partial x_j} \frac{\partial V_i'}{\partial x_k}\frac{\partial V_i'}{\partial x_m}$$

Returns:

d3lngammas_c_dxixjxkslist[list[list[list[float]]]]

Combinatorial lngammas term third composition derivative, size number of components by number of components by number of components by number of components, [-]

d3lngammas_dT3()

Calculates the third temperature derivative of the residual part of the UNIFAC model.

$$\frac{\partial^3 \ln \gamma_i^r}{\partial T^3} = \sum_{k}^{gr} \nu_k^{(i)} \left[ \frac{\partial^23\ln \Gamma_k}{\partial T^3} - \frac{\partial^3 \ln \Gamma_k^{(i)}}{\partial T^3} \right]$$

where the second Gamma is the pure-component Gamma of group k in component i.

Returns:

d3lngammas_r_dT3list[float]

Residual lngammas terms third temperature derivative, size number of components [1/K^3]

d3lngammas_r_dT3()

Calculates the third temperature derivative of the residual part of the UNIFAC model.

$$\frac{\partial^3 \ln \gamma_i^r}{\partial T^3} = \sum_{k}^{gr} \nu_k^{(i)} \left[ \frac{\partial^23\ln \Gamma_k}{\partial T^3} - \frac{\partial^3 \ln \Gamma_k^{(i)}}{\partial T^3} \right]$$

where the second Gamma is the pure-component Gamma of group k in component i.

Returns:

d3lngammas_r_dT3list[float]

Residual lngammas terms third temperature derivative, size number of components [1/K^3]

d3psis_dT3()

Calculate the $\Psi$ term third temperature derivative matrix for all groups interacting with all other groups.

The main model calculates the derivative as a function of three coefficients;

$$\frac{\partial^3 \Psi_{mn}}{\partial T^3} = \frac{\left(6 c_{mn} + 6 \left(c_{mn} - \frac{2 T c_{mn} + b_{mn}}{T} + \frac{T^{2} c_{mn} + T b_{mn} + a_{mn}}{T^{2}}\right) \left(2 T c_{mn} + b_{mn} - \frac{T^{2} c_{mn} + T b_{mn} + a_{mn}}{T}\right) - \frac{6 \left(2 T c_{mn} + b_{mn}\right)}{T} - \frac{\left(2 T c_{mn} + b_{mn} - \frac{T^{2} c_{mn} + T b_{mn} + a_{mn}}{T}\right)^{3}} {T} + \frac{6 \left(T^{2} c_{mn} + T b_{mn} + a_{mn}\right)}{T^{2}} \right) e^{- \frac{T^{2} c_{mn} + T b_{mn} + a_{mn}}{T}}}{T^{2}}$$

Only the first, a coefficient, is used in the original UNIFAC model as well as the UNIFAC-LLE model, so the expression simplifies to:

$$\frac{\partial^3 \Psi_{mn}}{\partial T^3} = \frac{a_{mn} \left(6 - \frac{6 a_{mn}}{T} + \frac{a_{mn}^{2}}{T^{2}}\right) e^{- \frac{a_{mn}}{T}}}{T^{4}}$$

For the Lyngby model, the third temperature derivative is:

$$\frac{\partial^3 \Psi_{mk}}{\partial T^3} = - \frac{\left(6 a_{2} + 6 a_{3} \ln{\left(\frac{T_{0}}{T} \right)} + 4 a_{3} + \left(a_{2} + a_{3} \ln{\left(\frac{T_{0}}{T} \right)} - \frac{a_{1} + a_{2} \left(T - T_{0}\right) + a_{3} \left(T \ln{ \left(\frac{T_{0}}{T} \right)} + T - T_{0}\right)}{T}\right)^{3} + 3 \left(a_{2} + a_{3} \ln{\left(\frac{T_{0}}{T} \right)} - \frac{a_{1} + a_{2} \left(T - T_{0}\right) + a_{3} \left(T \ln{ \left(\frac{T_{0}}{T} \right)} + T - T_{0}\right)}{T}\right) \left( 2 a_{2} + 2 a_{3} \ln{\left(\frac{T_{0}}{T} \right)} + a_{3} - \frac{2 \left(a_{1} + a_{2} \left(T - T_{0}\right) + a_{3} \left( T \ln{\left(\frac{T_{0}}{T} \right)} + T - T_{0}\right)\right)}{T} \right) - \frac{6 \left(a_{1} + a_{2} \left(T - T_{0}\right) + a_{3} \left(T \ln{\left(\frac{T_{0}}{T} \right)} + T - T_{0} \right)\right)}{T}\right) e^{- \frac{a_{1} + a_{2} \left(T - T_{0} \right) + a_{3} \left(T \ln{\left(\frac{T_{0}}{T} \right)} + T - T_{0}\right)}{T}}}{T^{3}}$$

with $T_0 = 298.15$ K and the a coefficients are specific to each pair of main groups, and they are asymmetric, so $a_{0,mk} \ne a_{0,km}$.

Returns:

d3psis_dT3list[list[float]]

Third temperature derivative of`psi` terms, size subgroups x subgroups [-]

dFis_dxs()

Calculate the mole fraction derivative of the $F_i$ terms used in calculating the combinatorial part. A function of mole fractions and the parameters q only.

$$\frac{\partial F_i}{\partial x_j} = -q_i q_j G_{sum}^2$$

$$G_{sum} = \frac{1}{\sum_j q_j x_j}$$

This is used in the UNIFAC, UNIFAC-LLE, UNIFAC Dortmund, UNIFAC-NIST, and PSRK models.

Returns:

dFis_dxslist[list[float]]

F terms size number of components by number of components, [-]

dGE_dT()

Calculate the first temperature derivative of excess Gibbs energy with the UNIFAC model.

$$\frac{\partial G^E}{\partial T} = RT\sum_i x_i \frac{\partial \ln \gamma_i^r}{\partial T} + \frac{G^E}{T}$$

Returns:

dGE_dTfloat

First temperature derivative of excess Gibbs energy, [J/mol/K]

dGE_dxs()

Calculate the first composition derivative of excess Gibbs energy with the UNIFAC model.

$$\frac{\partial G^E}{\partial x_i} = RT\left(\ln \gamma_i^c + \ln \gamma_i^r \right) + RT\sum_j x_j \left(\frac{\partial \ln \gamma_j^c}{\partial x_i} + \frac{\partial \ln \gamma_j^r}{\partial x_i} \right)$$

Returns:

dGE_dxslist[float]

First composition derivative of excess Gibbs energy, [J/mol]

dThetas_dxs()

Calculate the mole fraction derivatives of the $\Theta_m$ parameters. A function of mole fractions and group counts only.

$$\frac{\partial \Theta_i}{\partial x_j} = FGQ_i\left[FG (\nu x)_{sum,i} \left(\sum_k^{gr} FQ_k (\nu)_{sum,j} (\nu x)_{sum,k} -\sum_k^{gr} Q_k \nu_{k,j} \right) - F (\nu)_{sum,j}(\nu x)_{sum,i} + \nu_{ij} \right]$$

$$G = \frac{1}{\sum_j Q_j X_j}$$

$$F = \frac{1}{\sum_j \sum_n \nu_n^j x_j}$$

$$(\nu)_{sum,i} = \sum_j \nu_{j,i}$$

$$(\nu x)_{sum,i} = \sum_j \nu_{i,j}x_j$$

Returns:

dThetas_dxslist[list[float]]

Mole fraction derivatives of $\Theta_m$ terms, size number of subgroups by mole fractions and indexed in that order, [-]

dVis_dxs()

Calculate the mole fraction derivative of the $V_i$ terms used in calculating the combinatorial part. A function of mole fractions and the parameters r only.

$$\frac{\partial V_i}{\partial x_j} = -r_i r_j V_{sum}^2$$

$$V_{sum} = \frac{1}{\sum_j r_j x_j}$$

This is used in the UNIFAC, UNIFAC-LLE, UNIFAC Dortmund, UNIFAC-NIST, and PSRK models.

Returns:

dVis_dxslist[list[float]]

V terms size number of components by number of components, [-]

dVis_modified_dxs()

Calculate the mole fraction derivative of the $V_i'$ terms used in calculating the combinatorial part. A function of mole fractions and the parameters r only.

$$\frac{\partial V_i'}{\partial x_j} = -r_i^n r_j^n V_{sum}^2$$

$$V_{sum} = \frac{1}{\sum_j r_j^n x_j}$$

This is used in the UNIFAC Dortmund and UNIFAC-NIST model with n=0.75, and the Lyngby model with n=2/3.

Returns:

dVis_modified_dxslist[list[float]]

V’ terms size number of components by number of components, [-]

dgammas_dT()

Calculates the first temperature derivative of activity coefficients with the UNIFAC model.

$$\frac{\partial \gamma_i}{\partial T} = \gamma_i\frac{\partial \ln \gamma_i^r}{\partial T}$$

Returns:

dgammas_dTlist[float]

First temperature derivative of activity coefficients, size number of components [1/K]

dgammas_dns()

Calculate and return the mole number derivative of activity coefficients of a liquid phase using an activity coefficient model.

$$\frac{\partial \gamma_i}{\partial n_i} = \gamma_i \left(\frac{\frac{\partial^2 G^E}{\partial x_i \partial x_j}}{RT}\right)$$

Returns:

dgammas_dnslist[list[float]]

Mole number derivatives of activity coefficients, [1/mol]

dgammas_dxs()

Calculates the first mole fraction derivative of activity coefficients with the UNIFAC model.

$$\frac{\partial \gamma_i}{\partial x_j} = \gamma_i \left(\frac{\partial \ln \gamma_i^r}{\partial x_j} + \frac{\partial \ln \gamma_i^c}{\partial x_j} \right)$$

For the VTPR variant, the combinatorial part is skipped:

$$\frac{\partial \gamma_i}{\partial x_j} = \gamma_i \left(\frac{\partial \ln \gamma_i^r}{\partial x_j} \right)$$

Returns:

dgammas_dxslist[list[float]]

First mole fraction derivative of activity coefficients, size number of components by number of components [-]

dlnGammas_subgroups_dT()

Calculate the first temperature derivative of the $\ln \Gamma_k$ parameters for the phase; depends on the phases’s composition and temperature.

$$\frac{\partial \ln \Gamma_i}{\partial T} = Q_i\left( \sum_j^{gr} Z(j) \left[{\theta_j \frac{\partial \psi_{i,j}}{\partial T}} + {\theta_j \psi_{i,j} F(j)}Z(j) \right]- F(i) Z(i) \right)$$

$$F(k) = \sum_m^{gr} \theta_m \frac{\partial \psi_{m,k}}{\partial T}$$

$$Z(k) = \frac{1}{\sum_m \Theta_m \Psi_{m,k}}$$

Returns:

dlnGammas_subgroups_dTlist[float]

First temperature derivative of ln Gamma parameters for each subgroup, size number of subgroups, [1/K]

dlnGammas_subgroups_dxs()

Calculate the mole fraction derivatives of the $\ln \Gamma_k$ parameters for the phase; depends on the phases’s composition and temperature.

$$\frac{\partial \ln \Gamma_k}{\partial x_i} = Q_k\left( -\frac{\sum_m^{gr} \psi_{m,k} \frac{\partial \theta_m}{\partial x_i}}{\sum_m^{gr} \theta_m \psi_{m,k}} - \sum_m^{gr} \frac{\psi_{k,m} \frac{\partial \theta_m}{\partial x_i}}{\sum_n^{gr} \theta_n \psi_{n,m}} + \sum_m^{gr} \frac{(\sum_n^{gr} \psi_{n,m}\frac{\partial \theta_n}{\partial x_i})\theta_m \psi_{k,m}}{(\sum_n^{gr} \theta_n \psi_{n,m})^2} \right)$$

The group W is used internally as follows to simplfy the number of evaluations.

$$W(k,i) = \sum_m^{gr} \psi_{m,k} \frac{\partial \theta_m}{\partial x_i}$$

Returns:

dlnGammas_subgroups_dxslist[list[float]]

Mole fraction derivatives of Gamma parameters for each subgroup, size number of subgroups by number of components and indexed in that order, [-]

dlnGammas_subgroups_pure_dT()

Calculate the first temperature derivative of $\ln \Gamma_k$ pure component parameters for the phase; depends on the phases’s temperature only.

$$\frac{\partial \ln \Gamma_i}{\partial T} = Q_i\left( \sum_j^{gr} Z(j) \left[{\theta_j \frac{\partial \psi_{i,j}}{\partial T}} + {\theta_j \psi_{i,j} F(j)}Z(j) \right]- F(i) Z(i) \right)$$

$$F(k) = \sum_m^{gr} \theta_m \frac{\partial \psi_{m,k}}{\partial T}$$

$$Z(k) = \frac{1}{\sum_m \Theta_m \Psi_{m,k}}$$

In this model, the $\Theta$ values come from the UNIFAC.Thetas_pure method, where each compound is assumed to be pure.

Returns:

dlnGammas_subgroups_pure_dTlist[list[float]]

First temperature derivative of ln Gamma parameters for each subgroup, size number of subgroups by number of components and indexed in that order, [1/K]

dlngammas_c_dT()

Temperature derivatives of the combinatorial part of the UNIFAC model. Zero in all variations.

$$\frac{\partial \ln \gamma_i^c}{\partial T} = 0$$

Returns:

dlngammas_c_dTlist[float]

Combinatorial lngammas term temperature derivatives, size number of components, [-]

dlngammas_c_dxs()

First composition derivative of the combinatorial part of the UNIFAC model. For the modified UNIFAC model, the equation is as follows; for the original UNIFAC and UNIFAC LLE, replace $V_i'$ with $V_i$.

$$\frac{\partial \ln \gamma^c_i}{\partial x_j} = -5q_i\left[ \left( \frac{\frac{\partial V_i}{\partial x_j}}{F_i} - \frac{V_i \frac{\partial F_i}{\partial x_j}}{F_i^2} \right)\frac{F_i}{V_i} - \frac{\frac{\partial V_i}{\partial x_j}}{F_i} + \frac{V_i\frac{\partial F_i}{\partial x_j}}{F_i^2} \right] - \frac{\partial V_i'}{\partial x_j} + \frac{\frac{\partial V_i'}{\partial x_j}}{V_i'}$$

For the Lyngby model, the following equations are used:

$$\frac{\partial \ln \gamma^c_i}{\partial x_j} = \frac{-\partial V_i'}{\partial x_j} + \frac{1}{V_i'} \frac{\partial V_i'}{\partial x_j}$$

Returns:

dlngammas_c_dxslist[list[float]]

Combinatorial lngammas term first composition derivative, size number of components by number of components, [-]

dlngammas_dT()

Calculates the first temperature derivative of the residual part of the UNIFAC model.

$$\frac{\partial \ln \gamma_i^r}{\partial T} = \sum_{k}^{gr} \nu_k^{(i)} \left[ \frac{\partial \ln \Gamma_k}{\partial T} - \frac{\partial \ln \Gamma_k^{(i)}}{\partial T} \right]$$

where the second Gamma is the pure-component Gamma of group k in component i.

Returns:

dlngammas_r_dTlist[float]

Residual lngammas terms first temperature derivative, size number of components [1/K]

dlngammas_r_dT()

Calculates the first temperature derivative of the residual part of the UNIFAC model.

$$\frac{\partial \ln \gamma_i^r}{\partial T} = \sum_{k}^{gr} \nu_k^{(i)} \left[ \frac{\partial \ln \Gamma_k}{\partial T} - \frac{\partial \ln \Gamma_k^{(i)}}{\partial T} \right]$$

where the second Gamma is the pure-component Gamma of group k in component i.

Returns:

dlngammas_r_dTlist[float]

Residual lngammas terms first temperature derivative, size number of components [1/K]

dlngammas_r_dxs()

Calculates the first mole fraction derivative of the residual part of the UNIFAC model.

$$\frac{\partial \ln \gamma_i^r}{\partial x_j} = \sum_{m}^{gr} \nu_m^{(i)} \frac{\partial \ln \Gamma_m}{\partial x_j}$$

Returns:

dlngammas_r_dxslist[list[float]]

First mole fraction derivative of residual lngammas terms, size number of components by number of components [-]

dpsis_dT()

Calculate the $\Psi$ term first temperature derivative matrix for all groups interacting with all other groups.

The main model calculates the derivative as a function of three coefficients;

$$\frac{\partial \Psi_{mn}}{\partial T} = \left(\frac{- 2 T c_{mn} - b_{mn}}{T} - \frac{- T^{2} c_{mn} - T b_{mn} - a_{mn}}{T^{2}} \right) e^{\frac{- T^{2} c_{mn} - T b_{mn} - a_{mn}}{T}}$$

Only the first, a coefficient, is used in the original UNIFAC model as well as the UNIFAC-LLE model, so the expression simplifies to:

$$\frac{\partial \Psi_{mn}}{\partial T} = \frac{a_{mn} e^{- \frac{a_{mn}}{T}}}{T^{2}}$$

For the Lyngby model, the first temperature derivative is:

$$\frac{\partial \Psi_{mk}}{\partial T} = \left(\frac{- a_{2} - a_{3} \ln{\left(\frac{T_{0}}{T} \right)}}{T} - \frac{- a_{1} - a_{2} \left(T - T_{0}\right) - a_{3} \left(T \ln{\left(\frac{T_{0}}{T} \right)} + T - T_{0}\right)}{T^{2}}\right) e^{\frac{- a_{1} - a_{2} \left(T - T_{0}\right) - a_{3} \left(T \ln{\left(\frac{T_{0}}{T} \right)} + T - T_{0}\right)}{T}}$$

with $T_0 = 298.15$ K and the a coefficients are specific to each pair of main groups, and they are asymmetric, so $a_{0,mk} \ne a_{0,km}$.

Returns:

dpsis_dTlist[list[float]]

First temperature derivative of`psi` terms, size subgroups x subgroups [-]

static from_subgroups(T, xs, chemgroups, subgroups=None, interaction_data=None, version=0)

Method to construct a UNIFAC object from a dictionary of interaction parameters parameters and a list of dictionaries of UNIFAC keys. As the actual implementation is matrix based not dictionary based, this method can be quite convenient.

Parameters:

Tfloat

Temperature, [K]

xslist[float]

Mole fractions, [-]

chemgroupslist[dict]

List of dictionaries of subgroup IDs and their counts for all species in the mixture, [-]

subgroupsdict[int: UNIFAC_subgroup], optional

UNIFAC subgroup data; available dictionaries in this module include UFSG (original), DOUFSG (Dortmund), or NISTUFSG. The default depends on the given version, [-]

interaction_datadict[int: dict[int: tuple(a_mn, b_mn, c_mn)]], optional

UNIFAC interaction parameter data; available dictionaries in this module include UFIP (original), DOUFIP2006 (Dortmund parameters published in 2006), DOUFIP2016 (Dortmund parameters published in 2016), NISTUFIP, UF2IP (matrix completion - all interactions are present), and DOUF2IP (modified UNIFAC 2.0 with matrix completion - all interactions are present). The default depends on the given version, [-]

versionint, optional

Which version of the model to use. Defaults to 0, [-]

• 0 - original UNIFAC, OR UNIFAC LLE

• 1 - Dortmund UNIFAC (adds T dept, 3/4 power)

• 2 - PSRK (original with T dept function)

• 3 - VTPR (drops combinatorial term, Dortmund UNIFAC otherwise)

• 4 - Lyngby/Larsen has different combinatorial, 2/3 power

• 5 - UNIFAC KT (2 params for psi, Lyngby/Larsen formulation; otherwise same as original)

Returns:

UNIFACUNIFAC

Object for performing calculations with the UNIFAC activity coefficient model, [-]

Notes

Warning

For version 0, the interaction data and subgroups default to the original UNIFAC model (not LLE).

For version 1, the interaction data defaults to the Dortmund parameters publshed in 2016 (not 2006).

Examples

Mixture of [‘benzene’, ‘cyclohexane’, ‘acetone’, ‘ethanol’] according to the Dortmund UNIFAC model:

>>> from thermo.unifac import DOUFIP2006, DOUFSG
>>> T = 373.15
>>> xs = [0.2, 0.3, 0.1, 0.4]
>>> chemgroups = [{9: 6}, {78: 6}, {1: 1, 18: 1}, {1: 1, 2: 1, 14: 1}]
>>> GE = UNIFAC.from_subgroups(T=T, xs=xs, chemgroups=chemgroups, version=1, interaction_data=DOUFIP2006, subgroups=DOUFSG)
>>> GE
UNIFAC(T=373.15, xs=[0.2, 0.3, 0.1, 0.4], rs=[2.2578, 4.2816, 2.3373, 2.4951999999999996], qs=[2.5926, 5.181, 2.7308, 2.6616], Qs=[1.0608, 0.7081, 0.4321, 0.8927, 1.67, 0.8635], vs=[[0.0, 0.0, 1.0, 1.0], [0.0, 0.0, 0.0, 1.0], [6.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 1.0], [0.0, 0.0, 1.0, 0.0], [0.0, 6.0, 0.0, 0.0]], psi_a=[[0.0, 0.0, 114.2, 2777.0, 433.6, -117.1], [0.0, 0.0, 114.2, 2777.0, 433.6, -117.1], [16.07, 16.07, 0.0, 3972.0, 146.2, 134.6], [1606.0, 1606.0, 3049.0, 0.0, -250.0, 3121.0], [199.0, 199.0, -57.53, 653.3, 0.0, 168.2], [170.9, 170.9, -2.619, 2601.0, 464.5, 0.0]], psi_b=[[0.0, 0.0, 0.0933, -4.674, 0.1473, 0.5481], [0.0, 0.0, 0.0933, -4.674, 0.1473, 0.5481], [-0.2998, -0.2998, 0.0, -13.16, -1.237, -1.231], [-4.746, -4.746, -12.77, 0.0, 2.857, -13.69], [-0.8709, -0.8709, 1.212, -1.412, 0.0, -0.8197], [-0.8062, -0.8062, 1.094, -1.25, 0.1542, 0.0]], psi_c=[[0.0, 0.0, 0.0, 0.001551, 0.0, -0.00098], [0.0, 0.0, 0.0, 0.001551, 0.0, -0.00098], [0.0, 0.0, 0.0, 0.01208, 0.004237, 0.001488], [0.0009181, 0.0009181, 0.01435, 0.0, -0.006022, 0.01446], [0.0, 0.0, -0.003715, 0.000954, 0.0, 0.0], [0.001291, 0.001291, -0.001557, -0.006309, 0.0, 0.0]], version=1)

gammas()

Calculates the activity coefficients with the UNIFAC model.

$$\gamma_i = \exp\left(\ln \gamma_i^c + \ln \gamma_i^r \right)$$

For the VTPR variant, the combinatorial part is skipped:

$$\gamma_i = \exp(\ln \gamma_i^r)$$

Returns:

gammaslist[float]

Activity coefficients, size number of components [-]

gammas_args(T=None)

Return a tuple of arguments at the specified tempearture that can be used to efficiently compute gammas at the specified temperature but with varying compositions. This is useful in the context of a TP flash.

lnGammas_subgroups()

Calculate the $\ln \Gamma_k$ parameters for the phase; depends on the phases’s composition and temperature.

$$\ln \Gamma_k = Q_k \left[1 - \ln \sum_m \Theta_m \Psi_{mk} - \sum_m \frac{\Theta_m \Psi_{km}}{\sum_n \Theta_n \Psi_{nm}}\right]$$

Returns:

lnGammas_subgroupslist[float]

Gamma parameters for each subgroup, size number of subgroups, [-]

lnGammas_subgroups_pure()

Calculate the $\ln \Gamma_k$ pure component parameters for the phase; depends on the phases’s temperature only.

$$\ln \Gamma_k = Q_k \left[1 - \ln \sum_m \Theta_m \Psi_{mk} - \sum_m \frac{\Theta_m \Psi_{km}}{\sum_n \Theta_n \Psi_{nm}}\right]$$

In this model, the $\Theta$ values come from the UNIFAC.Thetas_pure method, where each compound is assumed to be pure.

Returns:

lnGammas_subgroups_purelist[list[float]]

Gamma parameters for each subgroup, size number of subgroups by number of components and indexed in that order, [-]

lngammas_c()

Calculates the combinatorial part of the UNIFAC model. For the modified UNIFAC model, the equation is as follows; for the original UNIFAC and UNIFAC LLE, replace $V_i'$ with $V_i$.

$$\ln \gamma_i^c = 1 - {V'}_i + \ln({V'}_i) - 5q_i \left(1 - \frac{V_i}{F_i}+ \ln\left(\frac{V_i}{F_i}\right)\right)$$

For the Lyngby model:

$$\ln \gamma_i^c = \ln \left(V_i'\right) + 1 - V_i'$$

Returns:

lngammas_clist[float]

Combinatorial lngammas terms, size number of components [-]

lngammas_r()

Calculates the residual part of the UNIFAC model.

$$\ln \gamma_i^r = \sum_{k}^{gr} \nu_k^{(i)} \left[ \ln \Gamma_k - \ln \Gamma_k^{(i)} \right]$$

where the second Gamma is the pure-component Gamma of group k in component i.

Returns:

lngammas_rlist[float]

Residual lngammas terms, size number of components [-]

missing_interaction_parameters()

Return a list of tuples (main_group_a_int, main_group_b_int) for each interaction between main groups where the a interaction parameter is zero. As UNIFAC parameters are asymmetric, (i,j) will also be returned as (j, i). Zero parameters are considered missing.

Returns:

missing_paramslist[tuple[int, int]]

List of tuples of the main group indices with missing interaction parameters, [-].

property model_id

A unique numerical identifier refering to the thermodynamic model being implemented. For internal use.

psis()

Calculate the $\Psi$ term matrix for all groups interacting with all other groups.

The main model calculates it as a function of three coefficients;

$$\Psi_{mn} = \exp\left(\frac{-a_{mn} - b_{mn}T - c_{mn}T^2}{T}\right)$$

Only the first, a coefficient, is used in the original UNIFAC model as well as the UNIFAC-LLE model, so the expression simplifies to:

$$\Psi_{mn} = \exp\left(\frac{-a_{mn}}{T}\right)$$

For the Lyngby model, the temperature dependence is modified slightly, as follows:

$$\Psi_{mk} = e^{\frac{- a_{1} - a_{2} \left(T - T_{0}\right) - a_{3} \left(T \ln{\left(\frac{T_{0}}{T} \right)} + T - T_{0}\right)}{T}}$$

with $T_0 = 298.15$ K and the a coefficients are specific to each pair of main groups, and they are asymmetric, so $a_{0,mk} \ne a_{0,km}$.

Returns:

psislist[list[float]]

psi terms, size subgroups x subgroups [-]

to_T_xs(T, xs)

Method to construct a new UNIFAC instance at temperature T, and mole fractions xs with the same parameters as the existing object.

Parameters:

Tfloat

Temperature, [K]

xslist[float]

Mole fractions of each component, [-]

Returns:

objUNIFAC

New UNIFAC object at the specified conditions [-]

Notes

If the new temperature is the same temperature as the existing temperature, if the psi terms or their derivatives have been calculated, they will be set to the new object as well. If the mole fractions are the same, various subgroup terms are also kept.

Main Model (Functional)

thermo.unifac.UNIFAC_gammas(T, xs, chemgroups, cached=None, subgroup_data=None, interaction_data=None, modified=False)

Calculates activity coefficients using the UNIFAC model (optionally modified), given a mixture’s temperature, liquid mole fractions, and optionally the subgroup data and interaction parameter data of your choice. The default is to use the original UNIFAC model, with the latest parameters published by DDBST. The model supports modified forms (Dortmund, NIST) when the modified parameter is True.

Parameters:

Tfloat

Temperature of the system, [K]

xslist[float]

Mole fractions of all species in the system in the liquid phase, [-]

chemgroupslist[dict]

List of dictionaries of subgroup IDs and their counts for all species in the mixture, [-]

subgroup_datadict[UNIFAC_subgroup]

UNIFAC subgroup data; available dictionaries in this module are UFSG (original), DOUFSG (Dortmund), or NISTUFSG ([4]).

interaction_datadict[dict[tuple(a_mn, b_mn, c_mn)]]

UNIFAC interaction parameter data; available dictionaries in this module are UFIP (original), DOUFIP2006 (Dortmund parameters as published by 2006), DOUFIP2016 (Dortmund parameters as published by 2016), NISTUFIP ([4]), UF2IP (UNIFAC 2.0 with matrix completion), and DOUF2IP (modified UNIFAC 2.0 with matrix completion).

modifiedbool

True if using the modified form and temperature dependence, otherwise False.

Returns:

gammaslist[float]

Activity coefficients of all species in the mixture, [-]

Notes

The actual implementation of UNIFAC is formulated slightly different than the formulas above for computational efficiency. DDBST switched to using the more efficient forms in their publication, but the numerical results are identical.

The model is as follows:

$$\ln \gamma_i = \ln \gamma_i^c + \ln \gamma_i^r$$

Combinatorial component

$$\ln \gamma_i^c = \ln \frac{\phi_i}{x_i} + \frac{z}{2} q_i \ln\frac{\theta_i}{\phi_i} + L_i - \frac{\phi_i}{x_i} \sum_{j=1}^{n} x_j L_j$$

$$\theta_i = \frac{x_i q_i}{\sum_{j=1}^{n} x_j q_j}$$

$$\phi_i = \frac{x_i r_i}{\sum_{j=1}^{n} x_j r_j}$$

$$L_i = 5(r_i - q_i)-(r_i-1)$$

Residual component

$$\ln \gamma_i^r = \sum_{k}^n \nu_k^{(i)} \left[ \ln \Gamma_k - \ln \Gamma_k^{(i)} \right]$$

$$\ln \Gamma_k = Q_k \left[1 - \ln \sum_m \Theta_m \Psi_{mk} - \sum_m \frac{\Theta_m \Psi_{km}}{\sum_n \Theta_n \Psi_{nm}}\right]$$

$$\Theta_m = \frac{Q_m X_m}{\sum_{n} Q_n X_n}$$

$$X_m = \frac{ \sum_j \nu^j_m x_j}{\sum_j \sum_n \nu_n^j x_j}$$

R and Q

$$r_i = \sum_{k=1}^{n} \nu_k R_k$$

$$q_i = \sum_{k=1}^{n}\nu_k Q_k$$

The newer forms of UNIFAC (Dortmund, NIST) calculate the combinatorial part slightly differently:

$$\ln \gamma_i^c = 1 - {V'}_i + \ln({V'}_i) - 5q_i \left(1 - \frac{V_i}{F_i}+ \ln\left(\frac{V_i}{F_i}\right)\right)$$

$$V'_i = \frac{r_i^{3/4}}{\sum_j r_j^{3/4}x_j}$$

$$V_i = \frac{r_i}{\sum_j r_j x_j}$$

$$F_i = \frac{q_i}{\sum_j q_j x_j}$$

Although this form looks substantially different than the original, it infact reverts to the original form if only $V'_i$ is replaced by $V_i$. This is more clear when looking at the full rearranged form as in [3].

In some publications such as [5], the nomenclature is such that $\theta_i$ and $\phi$ do not contain the top $x_i$, making $\theta_i = F_i$ and $\phi_i = V_i$. [5] is also notable for having supporting information containing very nice sets of analytical derivatives.

UNIFAC LLE uses the original formulation of UNIFAC, and otherwise only different interaction parameters.

References

[1]

Gmehling, Jurgen. Chemical Thermodynamics: For Process Simulation. Weinheim, Germany: Wiley-VCH, 2012.

[2]

Fredenslund, Aage, Russell L. Jones, and John M. Prausnitz. “Group Contribution Estimation of Activity Coefficients in Nonideal Liquid Mixtures.” AIChE Journal 21, no. 6 (November 1, 1975): 1086-99. doi:10.1002/aic.690210607.

[3]

Jakob, Antje, Hans Grensemann, Jürgen Lohmann, and Jürgen Gmehling. “Further Development of Modified UNIFAC (Dortmund): Revision and Extension 5.” Industrial & Engineering Chemistry Research 45, no. 23 (November 1, 2006): 7924-33. doi:10.1021/ie060355c.

[4] (1,2)

Kang, Jeong Won, Vladimir Diky, and Michael Frenkel. “New Modified UNIFAC Parameters Using Critically Evaluated Phase Equilibrium Data.” Fluid Phase Equilibria 388 (February 25, 2015): 128-41. doi:10.1016/j.fluid.2014.12.042.

[5] (1,2)

Jäger, Andreas, Ian H. Bell, and Cornelia Breitkopf. “A Theoretically Based Departure Function for Multi-Fluid Mixture Models.” Fluid Phase Equilibria 469 (August 15, 2018): 56-69. https://doi.org/10.1016/j.fluid.2018.04.015.

Examples

>>> UNIFAC_gammas(T=333.15, xs=[0.5, 0.5], chemgroups=[{1:2, 2:4}, {1:1, 2:1, 18:1}])
[1.427602583562, 1.364654501010]

>>> from thermo.unifac import DOUFIP2006
>>> UNIFAC_gammas(373.15, [0.2, 0.3, 0.2, 0.2],
... [{9:6}, {78:6}, {1:1, 18:1}, {1:1, 2:1, 14:1}],
... subgroup_data=DOUFSG, interaction_data=DOUFIP2006, modified=True)
[1.1864311137, 1.44028013391, 1.20447983349, 1.972070609029]

thermo.unifac.UNIFAC_psi(T, subgroup1, subgroup2, subgroup_data, interaction_data, modified=False)

Calculates the interaction parameter psi(m, n) for two UNIFAC subgroups, given the system temperature, the UNIFAC subgroups considered for the variant of UNIFAC used, the interaction parameters for the variant of UNIFAC used, and whether or not the temperature dependence is modified from the original form, as shown below.

Original temperature dependence:

$$\Psi_{mn} = \exp\left(\frac{-a_{mn}}{T}\right)$$

Modified temperature dependence:

$$\Psi_{mn} = \exp\left(\frac{-a_{mn} - b_{mn}T - c_{mn}T^2}{T}\right)$$

Parameters:

Tfloat

Temperature of the system, [K]

subgroup1int

First UNIFAC subgroup for identifier, [-]

subgroup2int

Second UNIFAC subgroup for identifier, [-]

subgroup_datadict[UNIFAC_subgroup]

Normally provided as inputs to UNIFAC.

interaction_datadict[dict[tuple(a_mn, b_mn, c_mn)]]

Normally provided as inputs to UNIFAC.

modifiedbool

True if the modified temperature dependence is used by the interaction parameters, otherwise False

Returns:

psifloat

UNIFAC interaction parameter term, [-]

Notes

UNIFAC interaction parameters are asymmetric. No warning is raised if an interaction parameter is missing.

References

[1]

Gmehling, Jurgen. Chemical Thermodynamics: For Process Simulation. Weinheim, Germany: Wiley-VCH, 2012.

[2]

Fredenslund, Aage, Russell L. Jones, and John M. Prausnitz. “Group Contribution Estimation of Activity Coefficients in Nonideal Liquid Mixtures.” AIChE Journal 21, no. 6 (November 1, 1975): 1086-99. doi:10.1002/aic.690210607.

Examples

>>> from thermo.unifac import UFSG, UFIP, DOUFSG, DOUFIP2006

>>> UNIFAC_psi(307, 18, 1, UFSG, UFIP)
0.9165248264184787

>>> UNIFAC_psi(373.15, 9, 78, DOUFSG, DOUFIP2006, modified=True)
1.3703140538273264

Misc Functions

thermo.unifac.UNIFAC_RQ(groups, subgroup_data=None)

Calculates UNIFAC parameters R and Q for a chemical, given a dictionary of its groups, as shown in [1]. Most UNIFAC methods use the same subgroup values; however, a dictionary of UNIFAC_subgroup instances may be specified as an optional second parameter.

$$r_i = \sum_{k=1}^{n} \nu_k R_k$$

$$q_i = \sum_{k=1}^{n}\nu_k Q_k$$

Parameters:

groupsdict[count]

Dictionary of numeric subgroup IDs : their counts

subgroup_dataNone or dict[UNIFAC_subgroup]

Optional replacement for standard subgroups; leave as None to use the original UNIFAC subgroup r and q values.

Returns:

Rfloat

R UNIFAC parameter (normalized Van der Waals Volume) [-]

Qfloat

Q UNIFAC parameter (normalized Van der Waals Area) [-]

Notes

These parameters have some predictive value for other chemical properties.

References

[1]

Gmehling, Jurgen. Chemical Thermodynamics: For Process Simulation. Weinheim, Germany: Wiley-VCH, 2012.

Examples

Hexane

>>> UNIFAC_RQ({1:2, 2:4})
(4.4998000000000005, 3.856)

thermo.unifac.Van_der_Waals_volume(R)

Calculates a species Van der Waals molar volume with the UNIFAC method, given a species’s R parameter.

$$V_{wk} = 15.17R_k$$

Parameters:

Rfloat

R UNIFAC parameter (normalized Van der Waals Volume) [-]

Returns:

V_vdwfloat

Unnormalized Van der Waals volume, [m^3/mol]

Notes

The volume was originally given in cm^3/mol, but is converted to SI here.

References

[1]

Wei, James, Morton M. Denn, John H. Seinfeld, Arup Chakraborty, Jackie Ying, Nicholas Peppas, and George Stephanopoulos. Molecular Modeling and Theory in Chemical Engineering. Academic Press, 2001.

Examples

>>> Van_der_Waals_volume(4.4998)
6.826196599999999e-05

thermo.unifac.Van_der_Waals_area(Q)

Calculates a species Van der Waals molar surface area with the UNIFAC method, given a species’s Q parameter.

$$A_{wk} = 2.5\times 10^9 Q_k$$

Parameters:

Qfloat

Q UNIFAC parameter (normalized Van der Waals Area) [-]

Returns:

A_vdwfloat

Unnormalized Van der Waals surface area, [m^2/mol]

Notes

The volume was originally given in cm^2/mol, but is converted to SI here.

References

[1]

Wei, James, Morton M. Denn, John H. Seinfeld, Arup Chakraborty, Jackie Ying, Nicholas Peppas, and George Stephanopoulos. Molecular Modeling and Theory in Chemical Engineering. Academic Press, 2001.

Examples

>>> Van_der_Waals_area(3.856)
964000.0

thermo.unifac.chemgroups_to_matrix(chemgroups)

Index by [group index][compound index]

>>> chemgroups_to_matrix([{9: 6}, {2: 6}, {1: 1, 18: 1}, {1: 1, 2: 1, 14: 1}])
[[0, 0, 1, 1], [0, 6, 0, 1], [6, 0, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]]

thermo.unifac.UNIFAC_group_assignment_DDBST(CAS, model)

Lookup the group assignment of a compound in either the ‘UNIFAC’ the ‘MODIFIED_UNIFAC’, or the ‘PSRK’ model. These values are read from a sqlite database on demand.

Parameters:

CASstr

CAS number, [-]

modelstr

One of ‘UNIFAC’, ‘MODIFIED_UNIFAC’, or ‘PSRK’, [-]

Returns:

assignmentsdict

The group assignments and their counts; note that an empty dictionary indicates the fragmentation is not available, [-]

Examples

>>> UNIFAC_group_assignment_DDBST('50-14-6', 'UNIFAC')
{1: 5, 2: 8, 3: 6, 4: 1, 6: 1, 7: 1, 8: 2, 14: 1}

Data for Original UNIFAC

thermo.unifac.UFSG = {1: <CH3>, 2: <CH2>, 3: <CH>, 4: <C>, 5: <CH2=CH>, 6: <CH=CH>, 7: <CH2=C>, 8: <CH=C>, 9: <ACH>, 10: <AC>, 11: <ACCH3>, 12: <ACCH2>, 13: <ACCH>, 14: <OH>, 15: <CH3OH>, 16: <H2O>, 17: <ACOH>, 18: <CH3CO>, 19: <CH2CO>, 20: <CHO>, 21: <CH3COO>, 22: <CH2COO>, 23: <HCOO>, 24: <CH3O>, 25: <CH2O>, 26: <CHO>, 27: <THF>, 28: <CH3NH2>, 29: <CH2NH2>, 30: <CHNH2>, 31: <CH3NH>, 32: <CH2NH>, 33: <CHNH>, 34: <CH3N>, 35: <CH2N>, 36: <ACNH2>, 37: <C5H5N>, 38: <C5H4N>, 39: <C5H3N>, 40: <CH3CN>, 41: <CH2CN>, 42: <COOH>, 43: <HCOOH>, 44: <CH2CL>, 45: <CHCL>, 46: <CCL>, 47: <CH2CL2>, 48: <CHCL2>, 49: <CCL2>, 50: <CHCL3>, 51: <CCL3>, 52: <CCL4>, 53: <ACCL>, 54: <CH3NO2>, 55: <CH2NO2>, 56: <CHNO2>, 57: <ACNO2>, 58: <CS2>, 59: <CH3SH>, 60: <CH2SH>, 61: <FURFURAL>, 62: <DOH>, 63: <I>, 64: <BR>, 65: <CH=-C>, 66: <C=-C>, 67: <DMSO>, 68: <ACRY>, 69: <CL-(C=C)>, 70: <C=C>, 71: <ACF>, 72: <DMF>, 73: <HCON(CH2)2>, 74: <CF3>, 75: <CF2>, 76: <CF>, 77: <COO>, 78: <SIH3>, 79: <SIH2>, 80: <SIH>, 81: <SI>, 82: <SIH2O>, 83: <SIHO>, 84: <SIO>, 85: <NMP>, 86: <CCL3F>, 87: <CCL2F>, 88: <HCCL2F>, 89: <HCCLF>, 90: <CCLF2>, 91: <HCCLF2>, 92: <CCLF3>, 93: <CCL2F2>, 94: <AMH2>, 95: <AMHCH3>, 96: <AMHCH2>, 97: <AM(CH3)2>, 98: <AMCH3CH2>, 99: <AM(CH2)2>, 100: <C2H5O2>, 101: <C2H4O2>, 102: <CH3S>, 103: <CH2S>, 104: <CHS>, 105: <MORPH>, 106: <C4H4S>, 107: <C4H3S>, 108: <C4H2S>, 109: <NCO>, 118: <(CH2)2SU>, 119: <CH2CHSU>, 178: <IMIDAZOL>, 179: <BTI>}

thermo.unifac.UFMG = {1: ('CH2', [1, 2, 3, 4]), 2: ('C=C', [5, 6, 7, 8, 70]), 3: ('ACH', [9, 10]), 4: ('ACCH2', [11, 12, 13]), 5: ('OH', [14]), 6: ('CH3OH', [15]), 7: ('H2O', [16]), 8: ('ACOH', [17]), 9: ('CH2CO', [18, 19]), 10: ('CHO', [20]), 11: ('CCOO', [21, 22]), 12: ('HCOO', [23]), 13: ('CH2O', [24, 25, 26, 27]), 14: ('CNH2', [28, 29, 30]), 15: ('CNH', [31, 32, 33]), 16: ('(C)3N', [34, 35]), 17: ('ACNH2', [36]), 18: ('PYRIDINE', [37, 38, 39]), 19: ('CCN', [40, 41]), 20: ('COOH', [42, 43]), 21: ('CCL', [44, 45, 46]), 22: ('CCL2', [47, 48, 49]), 23: ('CCL3', [50, 51]), 24: ('CCL4', [52]), 25: ('ACCL', [53]), 26: ('CNO2', [54, 55, 56]), 27: ('ACNO2', [57]), 28: ('CS2', [58]), 29: ('CH3SH', [59, 60]), 30: ('FURFURAL', [61]), 31: ('DOH', [62]), 32: ('I', [63]), 33: ('BR', [64]), 34: ('C=-C', [65, 66]), 35: ('DMSO', [67]), 36: ('ACRY', [68]), 37: ('CLCC', [69]), 38: ('ACF', [71]), 39: ('DMF', [72, 73]), 40: ('CF2', [74, 75, 76]), 41: ('COO', [77]), 42: ('SIH2', [78, 79, 80, 81]), 43: ('SIO', [82, 83, 84]), 44: ('NMP', [85]), 45: ('CCLF', [86, 87, 88, 89, 90, 91, 92, 93]), 46: ('CON(AM)', [94, 95, 96, 97, 98, 99]), 47: ('OCCOH', [100, 101]), 48: ('CH2S', [102, 103, 104]), 49: ('MORPH', [105]), 50: ('THIOPHEN', [106, 107, 108]), 51: ('NCO', [109]), 55: ('SULFONES', [118, 119]), 84: ('IMIDAZOL', [178]), 85: ('BTI', [179])}

thermo.unifac.UFIP

Interaction parameters for the original unifac model.

Type:

dict[int: dict[int: float]]

Data for Dortmund UNIFAC

thermo.unifac.DOUFSG = {1: <CH3>, 2: <CH2>, 3: <CH>, 4: <C>, 5: <CH2=CH>, 6: <CH=CH>, 7: <CH2=C>, 8: <CH=C>, 9: <ACH>, 10: <AC>, 11: <ACCH3>, 12: <ACCH2>, 13: <ACCH>, 14: <OH(P)>, 15: <CH3OH>, 16: <H2O>, 17: <ACOH>, 18: <CH3CO>, 19: <CH2CO>, 20: <CHO>, 21: <CH3COO>, 22: <CH2COO>, 23: <HCOO>, 24: <CH3O>, 25: <CH2O>, 26: <CHO>, 27: <THF>, 28: <CH3NH2>, 29: <CH2NH2>, 30: <CHNH2>, 31: <CH3NH>, 32: <CH2NH>, 33: <CHNH>, 34: <CH3N>, 35: <CH2N>, 36: <ACNH2>, 37: <AC2H2N>, 38: <AC2HN>, 39: <AC2N>, 40: <CH3CN>, 41: <CH2CN>, 42: <COOH>, 43: <HCOOH>, 44: <CH2CL>, 45: <CHCL>, 46: <CCL>, 47: <CH2CL2>, 48: <CHCL2>, 49: <CCL2>, 50: <CHCL3>, 51: <CCL3>, 52: <CCL4>, 53: <ACCL>, 54: <CH3NO2>, 55: <CH2NO2>, 56: <CHNO2>, 57: <ACNO2>, 58: <CS2>, 59: <CH3SH>, 60: <CH2SH>, 61: <FURFURAL>, 62: <DOH>, 63: <I>, 64: <BR>, 65: <CH=-C>, 66: <C=-C>, 67: <DMSO>, 68: <ACRY>, 69: <CL-(C=C)>, 70: <C=C>, 71: <ACF>, 72: <DMF>, 73: <HCON(CH2)2>, 74: <CF3>, 75: <CF2>, 76: <CF>, 77: <COO>, 78: <CY-CH2>, 79: <CY-CH>, 80: <CY-C>, 81: <OH(S)>, 82: <OH(T)>, 83: <CY-CH2O>, 84: <TRIOXAN>, 85: <CNH2>, 86: <NMP>, 87: <NEP>, 88: <NIPP>, 89: <NTBP>, 91: <CONH2>, 92: <CONHCH3>, 93: <HCONHCH3>, 94: <HCONHCH2>, 100: <CONHCH2>, 101: <AM(CH3)2>, 102: <AMCH3CH2>, 103: <AM(CH2)2>, 104: <AC2H2S>, 105: <AC2HS>, 106: <AC2S>, 107: <H2COCH>, 108: <COCH>, 109: <HCOCH>, 110: <(CH2)2SU>, 111: <CH2SUCH>, 112: <(CH3)2CB>, 113: <(CH2)2CB>, 114: <CH2CH3CB>, 119: <H2COCH2>, 122: <CH3S>, 123: <CH2S>, 124: <CHS>, 153: <H2COC>, 178: <C3H2N2+>, 184: <C3H3N2+>, 189: <C4H8N+>, 195: <BF4->, 196: <C5H5N+>, 197: <OTF->, 201: <-S-S->, 209: <SO4>, 210: <HSO4>, 211: <PF6>, 220: <C5H4N+>}

thermo.unifac.DOUFMG = {1: ('CH2', [1, 2, 3, 4]), 2: ('C=C', [5, 6, 7, 8, 70]), 3: ('ACH', [9, 10]), 4: ('ACCH2', [11, 12, 13]), 5: ('OH', [14, 81, 82]), 6: ('CH3OH', [15]), 7: ('H2O', [16]), 8: ('ACOH', [17]), 9: ('CH2CO', [18, 19]), 10: ('CHO', [20]), 11: ('CCOO', [21, 22]), 12: ('HCOO', [23]), 13: ('CH2O', [24, 25, 26]), 14: ('CH2NH2', [28, 29, 30, 85]), 15: ('CH2NH', [31, 32, 33]), 16: ('(C)3N', [34, 35]), 17: ('ACNH2', [36]), 18: ('PYRIDINE', [37, 38, 39]), 19: ('CH2CN', [40, 41]), 20: ('COOH', [42]), 21: ('CCL', [44, 45, 46]), 22: ('CCL2', [47, 48, 49]), 23: ('CCL3', [51]), 24: ('CCL4', [52]), 25: ('ACCL', [53]), 26: ('CNO2', [54, 55, 56]), 27: ('ACNO2', [57]), 28: ('CS2', [58]), 29: ('CH3SH', [59, 60]), 30: ('FURFURAL', [61]), 31: ('DOH', [62]), 32: ('I', [63]), 33: ('BR', [64]), 34: ('C=-C', [65, 66]), 35: ('DMSO', [67]), 36: ('ACRY', [68]), 37: ('CLCC', [69]), 38: ('ACF', [71]), 39: ('DMF', [72, 73]), 40: ('CF2', [74, 75, 76]), 41: ('COO', [77]), 42: ('CY-CH2', [78, 79, 80]), 43: ('CY-CH2O', [27, 83, 84]), 44: ('HCOOH', [43]), 45: ('CHCL3', [50]), 46: ('CY-CONC', [86, 87, 88, 89]), 47: ('CONR', [91, 92, 100]), 48: ('CONR2', [101, 102, 103]), 49: ('HCONR', [93, 94]), 52: ('ACS', [104, 105, 106]), 53: ('EPOXIDES', [107, 108, 109, 119, 153]), 55: ('CARBONAT', [112, 113, 114]), 56: ('SULFONE', [110, 111]), 61: ('SULFIDES', [122, 123, 124]), 84: ('IMIDAZOL', [178, 184]), 85: ('BTI', [179]), 87: ('PYRROL', [189]), 89: ('BF4', [195]), 90: ('PYRIDIN', [196, 220]), 91: ('OTF', [197]), 93: ('DISULFIDES', [201]), 98: ('SO4', [209, 210]), 99: ('PF6', [211])}

thermo.unifac.DOUFIP2016

Interaction parameters for the Dornmund unifac model.

Type:

dict[int: dict[int: tuple(float, 3)]]

Data for NIST UNIFAC (2015)

thermo.unifac.NISTUFSG = {1: <CH3>, 2: <CH2>, 3: <CH>, 4: <C>, 5: <CH2=CH>, 6: <CH=CH>, 7: <CH2=C>, 8: <CH=C>, 9: <ACH>, 10: <AC>, 11: <ACCH3>, 12: <ACCH2>, 13: <ACCH>, 14: <OH prim>, 15: <CH3OH>, 16: <H2O>, 17: <ACOH>, 18: <CH3CO>, 19: <CH2CO>, 20: <CHO>, 21: <CH3COO>, 22: <CH2COO>, 23: <HCOO>, 24: <CH3O>, 25: <CH2O>, 26: <CHO>, 27: <CH2-O-CH2>, 28: <CH3NH2>, 29: <CH2NH2>, 30: <CHNH2>, 31: <CH3NH>, 32: <CH2NH>, 33: <CHNH>, 34: <CH3N>, 35: <CH2N>, 36: <ACNH2>, 37: <AC2H2N>, 38: <AC2HN>, 39: <AC2N>, 40: <CH3CN>, 41: <CH2CN>, 42: <COOH>, 43: <HCOOH>, 44: <CH2Cl>, 45: <CHCl>, 46: <CCl>, 47: <CH2Cl2>, 48: <CHCl2>, 49: <CCl2>, 50: <CHCl3>, 51: <CCl3>, 52: <CCl4>, 53: <ACCl>, 54: <CH3NO2>, 55: <CH2NO2>, 56: <CHNO2>, 57: <ACNO2>, 58: <CS2>, 59: <CH3SH>, 60: <CH2SH>, 61: <Furfural>, 62: <CH2(OH)-CH2(OH)>, 63: <I>, 64: <Br>, 65: <CH#C>, 66: <C#C>, 67: <DMSO>, 68: <Acrylonitrile>, 69: <Cl-(C=C)>, 70: <C=C>, 71: <ACF>, 72: <DMF>, 73: <HCON(CH2)2>, 74: <CF3>, 75: <CF2>, 76: <CF>, 77: <COO>, 78: <c-CH2>, 79: <c-CH>, 80: <c-C>, 81: <OH sec>, 82: <OH tert>, 83: <CH2-O-[CH2-O]1/2>, 84: <[O-CH2]1/2-O-[CH2-O]1/2>, 85: <CNH2>, 86: <c-CON-CH3>, 87: <c-CON-CH2>, 88: <c-CON-CH>, 89: <c-CON-C>, 92: <CONHCH3>, 93: <HCONHCH3>, 94: <HCONHCH2>, 100: <CONHCH2>, 101: <CON(CH3)2>, 102: <CON(CH3)CH2>, 103: <CON(CH2)2>, 104: <AC2H2S>, 105: <AC2HS>, 106: <AC2S>, 107: <H2COCH>, 109: <HCOCH>, 110: <CH2SuCH2>, 111: <CH2SuCH>, 112: <(CH3O)2CO>, 113: <(CH2O)2CO>, 114: <(CH3O)COOCH2>, 116: <ACCN>, 117: <CH3NCO>, 118: <CH2NCO>, 119: <CHNCO>, 120: <ACNCO>, 121: <COOCO>, 122: <ACSO2>, 123: <ACCHO>, 124: <ACCOOH>, 125: <c-CO-NH>, 126: <c-CO-O>, 127: <AC-O-CO-CH3>, 128: <AC-O-CO-CH2>, 129: <AC-O-CO-CH>, 130: <AC-O-CO-C>, 131: <-O-CH2-CH2-OH>, 132: <-O-CH-CH2-OH>, 133: <-O-CH2-CH-OH>, 134: <CH3-S->, 135: <-CH2-S->, 136: <>CH-S->, 137: <->C-S->, 138: <CH3O-(O)>, 139: <CH2O-(O)>, 140: <CHO-(O)>, 141: <CO-(O)>, 142: <ACO-(O)>, 143: <CFH>, 144: <CFCl>, 145: <CFCl2>, 146: <CF2H>, 147: <CF2ClH>, 148: <CF2Cl2>, 149: <CF3H>, 150: <CF3Cl>, 151: <CF4>, 152: <C(O)2>, 153: <ACN(CH3)2>, 154: <ACN(CH3)CH2>, 155: <ACN(CH2)2>, 156: <ACNHCH3>, 157: <ACNHCH2>, 158: <ACNHCH>, 159: <AC2H2O>, 160: <AC2HO>, 161: <AC2O>, 162: <c-CH-NH>, 163: <c-C-NH>, 164: <c-CH-NCH3>, 165: <c-CH-NCH2>, 166: <c-CH-NCH>, 170: <SiH3->, 171: <-SiH2->, 172: <>SiH->, 173: <>Si<>, 174: <-SiH2-O->, 175: <>SiH-O->, 176: <->Si-O->, 177: <C=NOH>, 178: <ACCO>, 179: <C2Cl4>, 180: <c-CHH2>, 187: <ACS>, 188: <c-CH2-NH>, 189: <c-CH2-NCH3>, 190: <c-CH2-NCH2>, 191: <c-CH2-NCH>, 192: <CHSH>, 193: <CSH>, 194: <ACSH>, 195: <ACC>, 196: <AC2H2NH>, 197: <AC2HNH>, 198: <AC2NH>, 199: <(ACO)COOCH2>, 200: <(ACO)CO(OAC)>, 201: <c-CH=CH>, 202: <c-CH=C>, 203: <c-C=C>, 204: <Glycerol>, 205: <-CH(OH)-CH2(OH)>, 206: <-CH(OH)-CH(OH)->, 207: <>C(OH)-CH2(OH)>, 208: <>C(OH)-CH(OH)->, 209: <>C(OH)-C(OH)<>, 301: <CHCO>, 302: <CCO>, 303: <CHCN>, 304: <CCN>, 305: <CNO2>, 306: <ACNH>, 307: <ACN>, 308: <HCHO>, 309: <CH2(O)2>, 1309: <CH=NOH>}

thermo.unifac.NISTUFMG = {1: ('CH2', [1, 2, 3, 4], 'Alkyl chains'), 2: ('C=C', [5, 6, 7, 8, 9], 'Double bonded alkyl chains'), 3: ('ACH', [15, 16, 17], 'Aromatic carbon'), 4: ('ACCH2', [18, 19, 20, 21], 'Aromatic carbon plus alkyl chain'), 5: ('OH', [34, 204, 205], 'Alcohols'), 6: ('CH3OH', [35], 'Methanol'), 7: ('H2O', [36], 'Water'), 8: ('ACOH', [37], 'Phenolic –OH groups '), 9: ('CH2CO', [42, 43, 44, 45], 'Ketones'), 10: ('CHO', [48], 'Aldehydes'), 11: ('CCOO', [51, 52, 53, 54], 'Esters'), 12: ('HCOO', [55], 'Formates'), 13: ('CH2O', [59, 60, 61, 62, 63], 'Ethers'), 14: ('CNH2', [66, 67, 68, 69], 'Amines with 1-alkyl group'), 15: ('(C)2NH', [71, 72, 73], 'Amines with 2-alkyl groups'), 16: ('(C)3N', [74, 75], 'Amines with 3-alkyl groups'), 17: ('ACNH2', [79, 80, 81], 'Anilines'), 18: ('PYRIDINE', [76, 77, 78], 'Pyridines'), 19: ('CCN', [85, 86, 87, 88], 'Nitriles'), 20: ('COOH', [94, 95], 'Acids'), 21: ('CCl', [99, 100, 101], 'Chlorocarbons'), 22: ('CCl2', [102, 103, 104], 'Dichlorocarbons'), 23: ('CCl3', [105, 106], 'Trichlorocarbons'), 24: ('CCl4', [107], 'Tetrachlorocarbons'), 25: ('ACCl', [109], 'Chloroaromatics'), 26: ('CNO2', [132, 133, 134, 135], 'Nitro alkanes'), 27: ('ACNO2', [136], 'Nitroaromatics'), 28: ('CS2', [146], 'Carbon disulfide'), 29: ('CH3SH', [138, 139, 140, 141], 'Mercaptans'), 30: ('FURFURAL', [50], 'Furfural'), 31: ('DOH', [38], 'Ethylene Glycol'), 32: ('I', [128], 'Iodides'), 33: ('BR', [130], 'Bromides'), 34: ('C≡C', [13, 14], 'Triplebonded alkyl chains'), 35: ('DMSO', [153], 'Dimethylsulfoxide'), 36: ('ACRY', [90], 'Acrylic'), 37: ('ClC=C', [108], 'Chlorine attached to double bonded alkyl chain'), 38: ('ACF', [118], 'Fluoroaromatics'), 39: ('DMF', [161, 162, 163, 164, 165], 'Amides'), 40: ('CF2', [111, 112, 113, 114, 115, 116, 117], 'Fluorines'), 41: ('COO', [58], 'Esters'), 42: ('SiH2', [197, 198, 199, 200], 'Silanes'), 43: ('SiO', [201, 202, 203], 'Siloxanes'), 44: ('NMP', [195], 'N-Methyl-2-pyrrolidone'), 45: ('CClF', [120, 121, 122, 123, 124, 125, 126, 127], 'Chloro-Fluorides'), 46: ('CONCH2', [166, 167, 168, 169], 'Amides'), 47: ('OCCOH', [39, 40, 41], 'Oxygenated Alcohols'), 48: ('CH2S', [142, 143, 144, 145], 'Sulfides'), 49: ('MORPHOLIN', [196], 'Morpholine'), 50: ('THIOPHENE', [147, 148, 149], 'Thiophene'), 51: ('CH2(cy)', [27, 28, 29], 'Cyclic hydrocarbon chains'), 52: ('C=C(cy)', [30, 31, 32], 'Cyclic unsaturated hydrocarbon chains')}

thermo.unifac.NISTUFIP

Interaction parameters for the NIST (2015) unifac model.

Type:

dict[int: dict[int: tuple(float, 3)]]

Data for NIST KT UNIFAC (2011)

thermo.unifac.NISTKTUFSG = {1: <CH3->, 2: <-CH2->, 3: <-CH<>, 4: <>C<>, 5: <CH2=CH->, 6: <-CH=CH->, 7: <CH2=C<>, 8: <-CH=C<>, 9: <>C=C<>, 13: <CH≡C->, 14: <-C≡C->, 15: <-ACH->, 16: <>AC- (link)>, 17: <>AC- (cond)>, 18: <>AC-CH3>, 19: <>AC-CH2->, 20: <>AC-CH<>, 21: <>AC-C<->, 27: <-CH2- (cy)>, 28: <>CH- (cy)>, 29: <>C< (cy)>, 30: <-CH=CH- (cy)>, 31: <CH2=C< (cy)>, 32: <-CH=C< (cy)>, 34: <-OH(primary)>, 35: <CH3OH>, 36: <H2O>, 37: <>AC-OH>, 38: <(CH2OH)2>, 39: <-O-CH2-CH2-OH>, 40: <-O-CH-CH2-OH>, 41: <-O-CH2-CH-OH>, 42: <CH3-CO->, 43: <-CH2-CO->, 44: <>CH-CO->, 45: <->C-CO->, 48: <-CHO>, 50: <C5H4O2>, 51: <CH3-COO->, 52: <-CH2-COO->, 53: <>CH-COO->, 54: <->C-COO->, 55: <HCOO->, 58: <-COO->, 59: <CH3-O->, 60: <-CH2-O->, 61: <>CH-O->, 62: <->CO->, 63: <-CH2-O- (cy)>, 66: <CH3-NH2>, 67: <-CH2-NH2>, 68: <>CH-NH2>, 69: <->C-NH2>, 71: <CH3-NH->, 72: <-CH2-NH->, 73: <>CH-NH->, 74: <CH3-N<>, 75: <-CH2-N<>, 76: <C5H5N>, 77: <C5H4N->, 78: <C5H3N<>, 79: <>AC-NH2>, 80: <>AC-NH->, 81: <>AC-N<>, 85: <CH3-CN>, 86: <-CH2-CN>, 87: <>CH-CN>, 88: <->C-CN>, 90: <CH2=CH-CN>, 94: <-COOH>, 95: <HCOOH>, 99: <-CH2-Cl>, 100: <>CH-Cl>, 101: <->CCl>, 102: <CH2Cl2>, 103: <-CHCl2>, 104: <>CCl2>, 105: <CHCl3>, 106: <-CCl3>, 107: <CCl4>, 108: <Cl(C=C)>, 109: <>AC-Cl>, 111: <CHF3>, 112: <-CF3>, 113: <-CHF2>, 114: <>CF2>, 115: <-CH2F>, 116: <>CH-F>, 117: <->CF>, 118: <>AC-F>, 120: <CCl3F>, 121: <-CCl2F>, 122: <HCCl2F>, 123: <-HCClF>, 124: <-CClF2>, 125: <HCClF2>, 126: <CClF3>, 127: <CCl2F2>, 128: <-I>, 130: <-Br>, 132: <CH3-NO2>, 133: <-CH2-NO2>, 134: <>CH-NO2>, 135: <->C-NO2>, 136: <>AC-NO2>, 138: <CH3-SH>, 139: <-CH2-SH>, 140: <>CH-SH>, 141: <->C-SH>, 142: <CH3-S->, 143: <-CH2-S->, 144: <>CH-S->, 145: <->C-S->, 146: <CS2>, 147: <THIOPHENE>, 148: <C4H3S->, 149: <C4H2S<>, 153: <DMSO>, 161: <DMF>, 162: <-CON(CH3)2>, 163: <-CON(CH2)(CH3)->, 164: <HCON(CH2)2<>, 165: <-CON(CH2)2<>, 166: <-CONH(CH3)>, 167: <HCONH(CH2)->, 168: <-CONH(CH2)->, 169: <-CONH2>, 195: <NMP>, 196: <MORPHOLIN>, 197: <SiH3->, 198: <-SiH2->, 199: <>SiH->, 200: <>Si<>, 201: <-SiH2-O->, 202: <>SiH-O->, 203: <->Si-O->, 204: <-OH(secondary)>, 205: <-OH(tertiary)>}

thermo.unifac.NISTKTUFMG = {1: ('C', [1, 2, 3, 4]), 2: ('C=C', [5, 6, 7, 8, 9]), 3: ('ACH', [15, 16, 17]), 4: ('ACCH2', [18, 19, 20, 21]), 5: ('OH', [34, 204, 205]), 6: ('CH2OH', [35]), 7: ('H2O', [36]), 8: ('ACOH', [37]), 9: ('CH2CO', [42, 43, 44, 45]), 10: ('CHO', [48]), 11: ('CCOO', [51, 52, 53, 54]), 12: ('HCOO', [55]), 13: ('CH2O', [59, 60, 61, 62]), 14: ('CNH2', [66, 67, 68, 69]), 15: ('(C)2NH', [71, 72, 73]), 16: ('(C)3N', [74, 75]), 17: ('ACNH2', [79, 80, 81]), 18: ('Pyridine', [76, 77, 78]), 19: ('CCN', [85, 86, 87, 88]), 20: ('COOH', [94, 95]), 21: ('CCl', [99, 100, 101]), 22: ('CCl2', [102, 103, 104]), 23: ('CCl3', [105, 106]), 24: ('CCl4', [107]), 25: ('ACCl', [109]), 26: ('CNO2', [132, 133, 134, 135]), 27: ('ACNO2', [136]), 28: ('CS2', [146]), 29: ('CH3SH', [138, 139, 140, 141]), 30: ('Furfural', [50]), 31: ('DOH', [38]), 32: ('I', [128]), 33: ('Br', [130]), 34: ('C=-C', [13, 14]), 35: ('DMSO', [153]), 36: ('ACRY', [90]), 37: ('Cl(C=C)', [108]), 38: ('ACF', [118]), 39: ('DMF', [161, 162, 163, 164, 165]), 40: ('CF2', [111, 112, 113, 114, 115, 116, 117]), 41: ('COO', [58]), 42: ('SiH2', [197, 198, 199, 200]), 43: ('SiO', [201, 202, 203]), 44: ('NMP', [195]), 45: ('CClF', [120, 121, 122, 123, 124, 125, 126, 127]), 46: ('CONCH2', [166, 167, 168, 169]), 47: ('OCCOH', [39, 40, 41]), 48: ('CH2S', [142, 143, 144, 145]), 49: ('Morpholin', [196]), 50: ('THIOPHENE', [147, 148, 149]), 51: ('CH2(cyc)', [27, 28, 29]), 52: ('C=C(cyc)', [30, 31, 32])}

Compared to storing the values in dict[(int1, int2)] = (values), the dict-in-dict structure is found emperically to take 111608 bytes vs. 79096 bytes, or 30% less memory.

thermo.unifac.NISTKTUFIP

Interaction parameters for the NIST KT UNIFAC (2011) model.

Type:

dict[int: dict[int: tuple(float, 3)]]

Data for UNIFAC LLE

thermo.unifac.LLEUFSG = {1: <CH3>, 2: <CH2>, 3: <CH>, 4: <C>, 5: <CH2=CH>, 6: <CH=CH>, 7: <CH=C>, 8: <CH2=C>, 9: <ACH>, 10: <AC>, 11: <ACCH3>, 12: <ACCH2>, 13: <ACCH>, 14: <OH>, 15: <P1>, 16: <P2>, 17: <H2O>, 18: <ACOH>, 19: <CH3CO>, 20: <CH2CO>, 21: <CHO>, 22: <Furfural>, 23: <COOH>, 24: <HCOOH>, 25: <CH3COO>, 26: <CH2COO>, 27: <CH3O>, 28: <CH2O>, 29: <CHO>, 30: <FCH2O>, 31: <CH2CL>, 32: <CHCL>, 33: <CCL>, 34: <CH2CL2>, 35: <CHCL2>, 36: <CCL2>, 37: <CHCL3>, 38: <CCL3>, 39: <CCL4>, 40: <ACCL>, 41: <CH3CN>, 42: <CH2CN>, 43: <ACNH2>, 44: <CH3NO2>, 45: <CH2NO2>, 46: <CHNO2>, 47: <ACNO2>, 48: <DOH>, 49: <(HOCH2CH2)2O>, 50: <C5H5N>, 51: <C5H4N>, 52: <C5H3N>, 53: <CCl2=CHCl>, 54: <HCONHCH3>, 55: <DMF>, 56: <(CH2)4SO2>, 57: <DMSO>}

thermo.unifac.LLEMG = {1: ('CH2', [1, 2, 3, 4]), 2: ('C=C', [5, 6, 7, 8]), 3: ('ACH', [9, 10]), 4: ('ACCH2', [11, 12, 13]), 5: ('OH', [14]), 6: ('P1', [15]), 7: ('P2', [16]), 8: ('H2O', [17]), 9: ('ACOH', [18]), 10: ('CH2CO', [19, 20]), 11: ('CHO', [21]), 12: ('Furfural', [22]), 13: ('COOH', [23, 24]), 14: ('CCOO', [25, 26]), 15: ('CH2O', [27, 28, 29, 30]), 16: ('CCL', [31, 32, 33]), 17: ('CCL2', [34, 35, 36]), 18: ('CCL3', [37, 38]), 19: ('CCL4', [39]), 20: ('ACCL', [40]), 21: ('CCN', [41, 42]), 22: ('ACNH2', [43]), 23: ('CNO2', [44, 45, 46]), 24: ('ACNO2', [47]), 25: ('DOH', [48]), 26: ('DEOH', [49]), 27: ('PYRIDINE', [50, 51, 52]), 28: ('TCE', [53]), 29: ('MFA', [54]), 30: ('DMFA', [55]), 31: ('TMS', [56]), 32: ('DMSO', [57])}

Larsen, Bent L., Peter Rasmussen, and Aage Fredenslund. “A Modified UNIFAC Group-Contribution Model for Prediction of Phase Equilibria and Heats of Mixing.” Industrial & Engineering Chemistry Research 26, no. 11 (November 1, 1987): 2274-86. https://doi.org/10.1021/ie00071a018.

thermo.unifac.LLEUFIP

Interaction parameters for the LLE unifac model.

Type:

dict[int: dict[int: float]]

Data for Lyngby UNIFAC

thermo.unifac.LUFSG = {1: <CH3>, 2: <CH2>, 3: <CH>, 4: <C>, 5: <CH2=CH>, 6: <CH=CH>, 7: <CH2=C>, 8: <CH=C>, 9: <C=C>, 10: <ACH>, 11: <AC>, 12: <OH>, 13: <CH3OH>, 14: <H2O>, 15: <CH3CO>, 16: <CH2CO>, 17: <CHO>, 18: <CH3COO>, 19: <CH2COO>, 20: <CH3O>, 21: <CH2O>, 22: <CHO>, 23: <THF>, 24: <NH2>, 25: <CH3NH>, 26: <CH2NH>, 27: <CHNH>, 28: <CH3N>, 29: <CH2N>, 30: <ANH2>, 31: <C5H5N>, 32: <C5H4N>, 33: <C5H3N>, 34: <CH3CN>, 35: <CH2CN>, 36: <COOH>, 37: <CH2CL>, 38: <CHCL>, 39: <CCL>, 40: <CH2CL2>, 41: <CHCL2>, 42: <CCL2>, 43: <CHCL3>, 44: <CCL3>, 45: <CCL4>}

thermo.unifac.LUFMG = {1: ('CH2', [1, 2, 3, 4]), 2: ('C=C', [5, 6, 7, 8, 9]), 3: ('ACH', [10, 11]), 4: ('OH', [12]), 5: ('CH3OH', [13]), 6: ('H2O', [14]), 7: ('CH2CO', [15, 16]), 8: ('CHO', [17]), 9: ('CCOO', [18, 19]), 10: ('CH2O', [20, 21, 22, 23]), 11: ('NH2', [24]), 12: ('CNH2NG', [25, 26, 27]), 13: ('CH2N', [28, 29]), 14: ('ANH2', [30]), 15: ('PYRIDINE', [31, 32, 33]), 16: ('CCN', [34, 35]), 17: ('COOH', [36]), 18: ('CCL', [37, 38, 39]), 19: ('CCL2', [40, 41, 42]), 20: ('CCL3', [43, 44]), 21: ('CCL4', [45])}

thermo.unifac.LUFIP

Interaction parameters for the Lyngby UNIFAC model.

Type:

dict[int: dict[int: tuple(float, 3)]]

Data for PSRK UNIFAC

thermo.unifac.PSRKSG = {1: <CH3>, 2: <CH2>, 3: <CH>, 4: <C>, 5: <CH2=CH>, 6: <CH=CH>, 7: <CH2=C>, 8: <CH=C>, 9: <ACH>, 10: <AC>, 11: <ACCH3>, 12: <ACCH2>, 13: <ACCH>, 14: <OH>, 15: <CH3OH>, 16: <H2O>, 17: <ACOH>, 18: <CH3CO>, 19: <CH2CO>, 20: <CHO>, 21: <CH3COO>, 22: <CH2COO>, 23: <HCOO>, 24: <CH3O>, 25: <CH2O>, 26: <CHO>, 27: <THF>, 28: <CH3NH2>, 29: <CH2NH2>, 30: <CHNH2>, 31: <CH3NH>, 32: <CH2NH>, 33: <CHNH>, 34: <CH3N>, 35: <CH2N>, 36: <ACNH2>, 37: <C5H5N>, 38: <C5H4N>, 39: <C5H3N>, 40: <CH3CN>, 41: <CH2CN>, 42: <COOH>, 43: <HCOOH>, 44: <CH2CL>, 45: <CHCL>, 46: <CCL>, 47: <CH2CL2>, 48: <CHCL2>, 49: <CCL2>, 50: <CHCL3>, 51: <CCL3>, 52: <CCL4>, 53: <ACCL>, 54: <CH3NO2>, 55: <CH2NO2>, 56: <CHNO2>, 57: <ACNO2>, 58: <CS2>, 59: <CH3SH>, 60: <CH2SH>, 61: <FURFURAL>, 62: <DOH>, 63: <I>, 64: <BR>, 65: <CH=-C>, 66: <C=-C>, 67: <DMSO>, 68: <ACRY>, 69: <CL-(C=C)>, 70: <C=C>, 71: <ACF>, 72: <DMF>, 73: <HCON(CH2)2>, 74: <CF3>, 75: <CF2>, 76: <CF>, 77: <COO>, 78: <SIH3>, 79: <SIH2>, 80: <SIH>, 81: <SI>, 82: <SIH2O>, 83: <SIHO>, 84: <SIO>, 85: <NMP>, 86: <CCL3F>, 87: <CCL2F>, 88: <HCCL2F>, 89: <HCCLF>, 90: <CCLF2>, 91: <HCCLF2>, 92: <CCLF3>, 93: <CCL2F2>, 94: <AMH2>, 95: <AMHCH3>, 96: <AMHCH2>, 97: <AM(CH3)2>, 98: <AMCH3CH2>, 99: <AM(CH2)2>, 100: <C2H5O2>, 101: <C2H4O2>, 102: <CH3S>, 103: <CH2S>, 104: <CHS>, 105: <MORPH>, 106: <C4H4S>, 107: <C4H3S>, 108: <C4H2S>, 109: <H2C=CH2>, 110: <CH=-CH>, 111: <NH3>, 112: <CO>, 113: <H2>, 114: <H2S>, 115: <N2>, 116: <AR>, 117: <CO2>, 118: <CH4>, 119: <O2>, 120: <D2>, 121: <SO2>, 122: <NO>, 123: <N2O>, 124: <SF6>, 125: <HE>, 126: <NE>, 127: <KR>, 128: <XE>, 129: <HF>, 130: <HCL>, 131: <HBR>, 132: <HI>, 133: <COS>, 134: <CHSH>, 135: <CSH>, 136: <H2COCH>, 137: <HCOCH>, 138: <HCOC>, 139: <H2COCH2>, 140: <H2COC>, 141: <COC>, 142: <F2>, 143: <CL2>, 144: <BR2>, 145: <HCN>, 146: <NO2>, 147: <CF4>, 148: <O3>, 149: <CLNO>, 152: <CNH2>}

thermo.unifac.PSRKMG = {1: ('CH2', [1, 2, 3, 4]), 2: ('C=C', [5, 6, 7, 8, 70, 109]), 3: ('ACH', [9, 10]), 4: ('ACCH2', [11, 12, 13]), 5: ('OH', [14]), 6: ('CH3OH', [15]), 7: ('H2O', [16]), 8: ('ACOH', [17]), 9: ('CH2CO', [18, 19]), 10: ('CHO', [20]), 11: ('CCOO', [21, 22]), 12: ('HCOO', [23]), 13: ('CH2O', [24, 25, 26, 27]), 14: ('CNH2', [28, 29, 30, 152]), 15: ('CNH', [31, 32, 33]), 16: ('(C)3N', [34, 35]), 17: ('ACNH2', [36]), 18: ('PYRIDINE', [37, 38, 39]), 19: ('CCN', [40, 41]), 20: ('COOH', [42, 43]), 21: ('CCL', [44, 45, 46]), 22: ('CCL2', [47, 48, 49]), 23: ('CCL3', [50, 51]), 24: ('CCL4', [52]), 25: ('ACCL', [53]), 26: ('CNO2', [54, 55, 56]), 27: ('ACNO2', [57]), 28: ('CS2', [58]), 29: ('CH3SH', [59, 60, 134, 135]), 30: ('FURFURAL', [61]), 31: ('DOH', [62]), 32: ('I', [63]), 33: ('BR', [64]), 34: ('C=-C', [65, 66, 110]), 35: ('DMSO', [67]), 36: ('ACRY', [68]), 37: ('CLCC', [69]), 38: ('ACF', [71]), 39: ('DMF', [72, 73]), 40: ('CF2', [74, 75, 76]), 41: ('COO', [77]), 42: ('SIH2', [78, 79, 80, 81]), 43: ('SIO', [82, 83, 84]), 44: ('NMP', [85]), 45: ('CCLF', [86, 87, 88, 89, 90, 91, 92, 93]), 46: ('CON (AM)', [94, 95, 96, 97, 98, 99]), 47: ('OCCOH', [100, 101]), 48: ('CH2S', [102, 103, 104]), 49: ('MORPH', [105]), 50: ('THIOPHEN', [106, 107, 108]), 51: ('EPOXY', [136, 137, 138, 139, 140, 141]), 55: ('NH3', [111]), 56: ('CO2', [117]), 57: ('CH4', [118]), 58: ('O2', [119]), 59: ('AR', [116]), 60: ('N2', [115]), 61: ('H2S', [114]), 62: ('H2', [113, 120]), 63: ('CO', [112]), 65: ('SO2', [121]), 66: ('NO', [122]), 67: ('N2O', [123]), 68: ('SF6', [124]), 69: ('HE', [125]), 70: ('NE', [126]), 71: ('KR', [127]), 72: ('XE', [128]), 73: ('HF', [129]), 74: ('HCL', [130]), 75: ('HBR', [131]), 76: ('HI', [132]), 77: ('COS', [133]), 78: ('F2', [142]), 79: ('CL2', [143]), 80: ('BR2', [144]), 81: ('HCN', [145]), 82: ('NO2', [146]), 83: ('CF4', [147]), 84: ('O3', [148]), 85: ('CLNO', [149])}

Magnussen, Thomas, Peter Rasmussen, and Aage Fredenslund. “UNIFAC Parameter Table for Prediction of Liquid-Liquid Equilibriums.”

Industrial & Engineering Chemistry Process Design and Development 20, no. 2 (April 1, 1981): 331-39. https://doi.org/10.1021/i200013a024.

thermo.unifac.PSRKIP

Interaction parameters for the PSRKIP UNIFAC model.

Type:

dict[int: dict[int: tuple(float, 3)]]

Data for VTPR UNIFAC

thermo.unifac.VTPRSG = {1: <CH3>, 2: <CH2>, 3: <CH>, 4: <C>, 5: <CH2=CH>, 6: <CH=CH>, 7: <CH2=C>, 8: <CH=C>, 9: <ACH>, 10: <AC>, 11: <ACCH3>, 12: <ACCH2>, 13: <ACCH>, 14: <OH(P)>, 15: <CH3OH>, 16: <H2O>, 17: <ACOH>, 18: <CH3CO>, 19: <CH2CO>, 20: <CHO>, 21: <CH3COO>, 22: <CH2COO>, 23: <HCOO>, 24: <CH3O>, 25: <CH2O>, 26: <CHO>, 27: <THF>, 28: <CH3NH2>, 29: <CH2NH2>, 30: <CHNH2>, 31: <CH3NH>, 32: <CH2NH>, 33: <CHNH>, 34: <CH3N>, 35: <CH2N>, 36: <ACNH2>, 40: <CH3CN>, 41: <CH2CN>, 44: <CH2CL>, 45: <CHCL>, 46: <CCL>, 47: <CH2CL2>, 48: <CHCL2>, 49: <CCL2>, 50: <CHCL3>, 51: <CCL3>, 52: <CCL4>, 53: <ACCL>, 54: <CH3NO2>, 55: <CH2NO2>, 56: <CHNO2>, 58: <CS2>, 59: <CH3SH>, 60: <CH2SH>, 61: <FURFURAL>, 62: <DOH>, 63: <I>, 64: <BR>, 67: <DMSO>, 70: <C=C>, 72: <DMF>, 73: <HCON(..>, 78: <CY-CH2>, 79: <CY-CH>, 80: <CY-C>, 81: <OH(S)>, 82: <OH(T)>, 83: <CY-CH2O>, 84: <TRIOXAN>, 85: <CNH2>, 86: <NMP>, 87: <NEP>, 88: <NIPP>, 89: <NTBP>, 97: <Allene>, 98: <=CHCH=>, 99: <=CCH=>, 107: <H2COCH>, 108: <COCH>, 109: <HCOCH>, 116: <AC-CHO>, 119: <H2COCH2>, 129: <CHCOO>, 139: <CF2H>, 140: <CF2H2>, 142: <CF2Cl>, 143: <CF2Cl2>, 146: <CF4>, 148: <CF3Br>, 153: <H2COC>, 180: <CCOO>, 250: <H2C=CH2>, 300: <NH3>, 301: <CO>, 302: <H2>, 303: <H2S>, 304: <N2>, 305: <Ar>, 306: <CO2>, 307: <CH4>, 308: <O2>, 309: <D2>, 310: <SO2>, 312: <N2O>, 314: <He>, 315: <Ne>, 319: <HCl>, 345: <Hg>}

thermo.unifac.VTPRMG = {1: ('CH2', [1, 2, 3, 4]), 2: ('H2C=CH2', [5, 6, 7, 8, 70, 97, 98, 99, 250]), 3: ('ACH', [9, 10]), 4: ('ACCH2', [11, 12, 13]), 5: ('OH', [14, 81, 82]), 6: ('CH3OH', [15]), 7: ('H2O', [16]), 8: ('ACOH', [17]), 9: ('CH2CO', [18, 19]), 10: ('CHO', [20]), 11: ('CCOO', [21, 22, 129, 180]), 12: ('HCOO', [23]), 13: ('CH2O', [24, 25, 26]), 14: ('CH2NH2', [28, 29, 30, 85]), 15: ('CH2NH', [31, 32, 33]), 16: ('(C)3N', [34, 35]), 17: ('ACNH2', [36]), 19: ('CH2CN', [40, 41]), 21: ('CCL', [44, 45, 46]), 22: ('CCL2', [47, 48, 49]), 23: ('CCL3', [51]), 24: ('CCL4', [52]), 25: ('ACCL', [53]), 26: ('CNO2', [54, 55, 56]), 28: ('CS2', [58]), 29: ('CH3SH', [59, 60]), 30: ('FURFURAL', [61]), 31: ('DOH', [62]), 32: ('I', [63]), 33: ('BR', [64]), 35: ('DMSO', [67]), 39: ('DMF', [72, 73]), 42: ('CY-CH2', [78, 79, 80]), 43: ('CY-CH2O', [27, 83, 84]), 45: ('CHCL3', [50]), 46: ('CY-CONC', [86, 87, 88, 89]), 53: ('EPOXIDES', [107, 108, 109, 119, 153]), 57: ('AC-CHO', [116]), 68: ('CF2H', [139, 140]), 70: ('CF2Cl2', [142, 143, 148]), 73: ('CF4', [146]), 150: ('NH3', [300]), 151: ('CO2', [306]), 152: ('CH4', [307]), 153: ('O2', [308]), 154: ('Ar', [305]), 155: ('N2', [304]), 156: ('H2S', [303]), 157: ('D2', [302, 309]), 158: ('CO', [301]), 160: ('SO2', [310]), 162: ('N2O', [312]), 164: ('He', [314]), 165: ('Ne', [315]), 169: ('HCl', [319]), 185: ('Hg', [345])}

thermo.unifac.VTPRIP

Interaction parameters for the VTPRIP UNIFAC model.

Type:

dict[int: dict[int: tuple(float, 3)]]

Data for UNIFAC 2.0

thermo.unifac.UF2IP

Interaction parameters for the unifac 2.0 model - note there is a variant for the Dortmund modified UNIFAC as well. All groups and subgroups are the same as the original model. These are not used by default in this module. The citation is

Hayer, Nicolas, Thorsten Wendel, Stephan Mandt, Hans Hasse, and Fabian Jirasek. “Advancing Thermodynamic Group-Contribution Methods by Machine Learning: UNIFAC 2.0.” Chemical Engineering Journal 504 (January 15, 2025): 158667. https://doi.org/10.1016/j.cej.2024.158667.

Type:

dict[int: dict[int: float]]

thermo.unifac.DOUF2IP

Interaction parameters for the modified UNIFAC 2.0 model. All groups and subgroups are the same as the modified UNIFAC model. These are not used by default in this module. The citation is

Hayer, Nicolas, Hans Hasse, and Fabian Jirasek. “Modified UNIFAC 2.0-A Group-Contribution Method Completed with Machine Learning.” Industrial & Engineering Chemistry Research 64, no. 20 (2025): 10304-13. https://doi.org/10.1021/acs.iecr.5c00077.

Type:

dict[int: dict[int: float]]