# Theoretical model of thermal diffusion factors in multicomponent mixtures

## Abstract

Unlike molecular diffusion, neither measured thermal diffusion coefficients nor the theoretical framework exist for the estimation of thermal diffusion coefficients in nonideal multicomponent mixtures. This work derives a theoretical model for thermal diffusion coefficients in ideal and nonideal multicomponent mixtures, based on the thermodynamics of irreversible processes and the molecular kinetic approach incorporating explicit effects of nonequilibrium properties, such as the net heat of transport and molecular diffusion coefficients, and of equilibrium properties of the mixture, which are determined by the Peng-Robinson equation of state. An interesting feature of this model is that in nonideal multicomponent mixtures thermal diffusion coefficients depend on molecular diffusion coefficients, while in binary mixtures they do not. The model successfully describes thermal diffusion factors of binary mixtures for which experimental data are available, even those in extreme nonideal conditions and close to the critical point. Since experimental data on thermal diffusion factors in multicomponent hydrocarbon mixtures are not available, testing the model's accuracy was not possible. The model, however, successfully predicted spatial variation of composition in a ternary mixture of nC{sub 24}/nC{sub 16}/nC{sub 12}, providing an indirect verification. The six-component mixture of C{sub 1}/C{sub 3}/nC{sub 5}/nC{sub 10}/nC{sub 16}/C{sub 2} shows significant dependency of thermal diffusionmore »

- Authors:

- Publication Date:

- Research Org.:
- Reservoir Engineering Research Inst., Palo Alto, CA (US)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 20080305

- DOE Contract Number:
- FG22-96BC14850

- Resource Type:
- Journal Article

- Journal Name:
- AIChE Journal (American Institute of Chemical Engineers)

- Additional Journal Information:
- Journal Volume: 46; Journal Issue: 5; Other Information: PBD: May 2000; Journal ID: ISSN 0001-1541

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATION; DIFFUSION; BINARY MIXTURES; MIXTURES; TEMPERATURE DEPENDENCE

### Citation Formats

```
Firoozabadi, A., Ghorayeb, K., and Shukla, K.
```*Theoretical model of thermal diffusion factors in multicomponent mixtures*. United States: N. p., 2000.
Web. doi:10.1002/aic.690460504.

```
Firoozabadi, A., Ghorayeb, K., & Shukla, K.
```*Theoretical model of thermal diffusion factors in multicomponent mixtures*. United States. doi:10.1002/aic.690460504.

```
Firoozabadi, A., Ghorayeb, K., and Shukla, K. Mon .
"Theoretical model of thermal diffusion factors in multicomponent mixtures". United States. doi:10.1002/aic.690460504.
```

```
@article{osti_20080305,
```

title = {Theoretical model of thermal diffusion factors in multicomponent mixtures},

author = {Firoozabadi, A. and Ghorayeb, K. and Shukla, K.},

abstractNote = {Unlike molecular diffusion, neither measured thermal diffusion coefficients nor the theoretical framework exist for the estimation of thermal diffusion coefficients in nonideal multicomponent mixtures. This work derives a theoretical model for thermal diffusion coefficients in ideal and nonideal multicomponent mixtures, based on the thermodynamics of irreversible processes and the molecular kinetic approach incorporating explicit effects of nonequilibrium properties, such as the net heat of transport and molecular diffusion coefficients, and of equilibrium properties of the mixture, which are determined by the Peng-Robinson equation of state. An interesting feature of this model is that in nonideal multicomponent mixtures thermal diffusion coefficients depend on molecular diffusion coefficients, while in binary mixtures they do not. The model successfully describes thermal diffusion factors of binary mixtures for which experimental data are available, even those in extreme nonideal conditions and close to the critical point. Since experimental data on thermal diffusion factors in multicomponent hydrocarbon mixtures are not available, testing the model's accuracy was not possible. The model, however, successfully predicted spatial variation of composition in a ternary mixture of nC{sub 24}/nC{sub 16}/nC{sub 12}, providing an indirect verification. The six-component mixture of C{sub 1}/C{sub 3}/nC{sub 5}/nC{sub 10}/nC{sub 16}/C{sub 2} shows significant dependency of thermal diffusion factors on the distance to the critical point. It also demonstrates for the first time that there is no need to adopt a sign convention for thermal diffusion coefficients in binary and higher mixtures. The thermodynamic stability analysis shows that when the thermal diffusion coefficient is positive, the component should go to the cold region in a binary mixture.},

doi = {10.1002/aic.690460504},

journal = {AIChE Journal (American Institute of Chemical Engineers)},

issn = {0001-1541},

number = 5,

volume = 46,

place = {United States},

year = {2000},

month = {5}

}