I want to know how permeability (k, measured in darcies)(units of
metres squared?) is related to specific impedance (impedance per metre
of flow distance)(i, with units of Pa/(m3/sec)/m).

Dimensional analysis suggests that k is related to square root of
(u/i), where u is viscosity (in poise) (units Pa secs?).

Specifically, I'm interested in the relationship between permeability
and impedance (per metre flow distance) for water at high temperature
(+200C) under sufficient pressure to keep the water in liquid phase.

The background to this question is a geothermal power project.