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

TL;DR

This paper demonstrates that a broad class of finite-dimensional models for solute transport and diffusion in geosciences can be equivalently represented using multi-rate mass transfer and interacting continua models, with explicit construction methods.

Contribution

It establishes the equivalence of different modeling frameworks for solute transport in geological media and provides explicit methods for constructing these equivalent models.

Findings

Controllability is key to establishing model equivalence.

Explicit methods for constructing equivalent models are provided.

Results enhance understanding of geological structures' impact on solute transfer.

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.