## Abstract

Thermodynamic ideality is often assumed in diffusion calculation, implying concentrations are assumed equal to the activities with activity coefficients of one. A general set of diffusion flux and molar flux equations are developed, incorporating equilibrium thermodynamic models for non-ideal conditions in well-known non-equilibrium diffusion theory. Derivations are based on the Maxwell-Stefan friction theory with the chemical potential as the driving force. Isothermal and isobaric conditions are assumed, and the theory does not include the Soret coefficient or the Onsager formalism.

In this work, Fick's law is derived from the general diffusion theory, also as a function of activity gradients. The results illustrate that concentration cannot just be substituted by activity. Using a similar approach demonstrates that the Nernst-Planck (NP) equation may be derived from the general theory incorporating terms for migration and convection. An extended NP equation is derived including the thermodynamic correction factors (TCF) to account for the non-ideality of the liquid. The derived equation shows the improvement of the self-diffusion terms and friction coefficients in the NP equation and that the TCF enhances the observed effective diffusivities.

Examples of TCF are presented using the extended UNIQUAC thermodynamic model. This is done for the CO2-NaOH-monoethyleneglycol-water system, which is typically found in wet natural gas pipeline CO2 corrosion systems. pH-stabilization is classically used in the prevention of corrosion, but the results show that glycol has a noticeable effect of the diffusion on key components in the corrosion mechanism. A TCF of 0.4 to 1.3 may be expected. This indicates that the flux calculation deviates up to 60% from the real-life scenario if ideality is assumed. The thermodynamic model may therefore improve the diffusion calculations considerably.

In this work, Fick's law is derived from the general diffusion theory, also as a function of activity gradients. The results illustrate that concentration cannot just be substituted by activity. Using a similar approach demonstrates that the Nernst-Planck (NP) equation may be derived from the general theory incorporating terms for migration and convection. An extended NP equation is derived including the thermodynamic correction factors (TCF) to account for the non-ideality of the liquid. The derived equation shows the improvement of the self-diffusion terms and friction coefficients in the NP equation and that the TCF enhances the observed effective diffusivities.

Examples of TCF are presented using the extended UNIQUAC thermodynamic model. This is done for the CO2-NaOH-monoethyleneglycol-water system, which is typically found in wet natural gas pipeline CO2 corrosion systems. pH-stabilization is classically used in the prevention of corrosion, but the results show that glycol has a noticeable effect of the diffusion on key components in the corrosion mechanism. A TCF of 0.4 to 1.3 may be expected. This indicates that the flux calculation deviates up to 60% from the real-life scenario if ideality is assumed. The thermodynamic model may therefore improve the diffusion calculations considerably.

Original language | English |
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Article number | 114126 |

Journal | Fluid Phase Equilibria |

Volume | 584 |

Number of pages | 14 |

ISSN | 0378-3812 |

DOIs | |

Publication status | Published - 2024 |

## Keywords

- Fick's law
- Maxwell-Stefan
- Nernst-Planck
- Non-ideal mixed solvent electrolyte diffusion
- Carbon dioxide capture corrosion reservoir simulation
- Extended UNIQUAC activity coefficients thermodynamic correction factors