How can permeation units in Darcy be converted to the SI form. For example, how would 9.0 x 10-6 darcy be converted to SI units of permeation? How would it also be converted to the permeation units: (cm^3 . mm)/m^2 . d . atm ?
To convert darcy units to SI units
... 1 darcy is equivalent to 9.869233×10−13 m² or 0.9869233 (µm)². This conversion is usually approximated as 1 (µm)². Note that this is the reciprocal of 1.013250—the conversion factor from atmospheres to bars.
Specifically in the hydrology domain, permeability of soil or rock may also be defined as the flux of water under hydrostatic pressure (~ 0.1 bar/m) at a temperature of 20°C. In this specific setup, 1 darcy is equivalent to 0.831 m/day.
For your question, 1 m2 = 10^12 Darcy.
For the next question, I think your question is units involved in Darcy's Law, i.e., the Darcy's units and SI units.
In general, we define the permeability of porous media as 1 Darcy, it means the porous media can transmit 1 cm3/s of water with viscosity of 1 cP (1 mPas) under pressure gradient of 1 atm/cm cross an area of 1 cm2. The units involved here are called Darcy's units.
For SI unit, we use flow rate of m3/s, viscosity of Pas, pressure of Pa, length of m, cross section area of m2, and we can get the permeability unit with m2.
If we use the units system for both cases, Darcy's equation is the same without any conversion factor.