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arXiv · 1606.06438

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

Alain Rapaport·Alejandro Rojas-Palma·Jean-Raynald De Dreuzy·Hector Ramirez
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Abstract

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.

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Alain Rapaport, Alejandro Rojas-Palma, Jean-Raynald De Dreuzy, Hector Ramirez. 2016-06-21. Equivalence of finite dimensional input-output models of solute transport and diffusion in geosciences. https://arxiv.org/abs/1606.06438

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