Two Film Approach to Continuum Scale Mixing and Dispersion with Equilibrium Bimolecular Reaction

• Published in: Transport in porous media 2024-06, Vol.151 (8), p.1709-1727
• Main Authors: Mathias, Simon A., Bolster, Diogo, Veremieiev, Sergii
• Format: Article
• Language: English
• Subjects: Chemical reactions; Civil Engineering; Classical and Continuum Physics; Earth and Environmental Science; Earth Sciences; Equilibrium; Experiments; Fluids; Geotechnical Engineering & Applied Earth Sciences; Hydrogeology; Hydrology/Water Resources; Industrial Chemistry/Chemical Engineering; Mass transfer; Time dependence
• ISSN: 0169-3913; 1573-1634
• DOI: 10.1007/s11242-024-02091-y

Reliable reactive transport models require careful separation of mixing and dispersion processes. Here we treat displacing and displaced fluids as two separate fluid phases and invoke Whitman’s classical two-film theory to model mass transfer between the two phases. We use experimental data from Gramling’s bimolecular reaction experiment to assess model performance. Gramling’s original model involved just three coupled PDEs. In this context, our new formulation leads to a set of seven coupled PDEs but only requires the specification of two extra parameters, associated with the mass transfer coefficient and its dependence on time. The two film mass transfer model provides a simple and theoretically based method for separating mixing from dispersion in Eulerian continuum-scale methods. The advantage of this approach over existing methods is that it enables the simulation of equilibrium chemical reactions without having to invoke unrealistically small reaction rate coefficients. The comparison with Gramling’s experimental data confirms that our proposed method is suitable for simulating realistic and complicated bimolecular reaction behaviour. However, further work is needed to explore alternative methods for avoiding the need of a time-dependent mass transfer rate coefficient.