  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.
