Equivalence of finite dimensional input-output models of solute transport and diffusion in geosciences

Alain Rapaport (1) , Alejandro Rojas-Palma (1, 2, 3) , Jean-Raynald de Dreuzy (4) , Hector Ramirez (2, 3)

1 MISTEA - Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie
2 DIM - Departamento de Ingeniería Matemática [Santiago]
3 CMM - Center for Mathematical Modeling
4 GR - Géosciences Rennes

We show that for a large class of finite dimensional input-output positive systems that represent networks of transport and diffusion of solute in geological media, there exist equivalent multi-rate mass transfer and multiple interacting continua representations, which are quite popular in geo-sciences. Moreover, we provide explicit methods to construct these equivalent representations. The proofs show that controllability property is playing a crucial role for obtaining equivalence. These results contribute to our fundamental understanding on the effect of fine-scale geological structures on the transfer and dispersion of solute, and, eventually, on their interaction with soil microbes and minerals.

Mots clés: Equivalent mass transfer models; positive linear systems; controllability

Domaines: Optimisation et contrôle [math.OC]; Milieux fluides et réactifs

Alain Rapaport, Alejandro Rojas-Palma, Jean-Raynald de Dreuzy, Hector Ramirez. Equivalence of finite dimensional input-output models of solute transport and diffusion in geosciences. 2016. ⟨hal-01334540v2⟩