When the garage was equipped with a new belt driven V twin compressor on a 200 gallon (not litre ) reservoir, the installers just used ordinary 1/2" iron pipe. The main ran down one side and across the end of a building some 200 feet long 50 feet wide.
15 mm copper pipe should be quite adequate. Air is very low viscosity, you are unlikely to suffer much restriction to flow, unless you are consuming it at enormous rate. Look how quickly air exits an inner tube inflated to less than 20 psi through a hole less than 1 mm diameter.
The average 3 hp direct drive compressor cannot keep up, for long, with a tyre inflator or a small blow gun, so a pipe with a bore of 12 – 13 mm will be way beyond its capacity, and so cause negligible pressure drop.
A 2 hp direct drive compressor can barely cope with 1.5 mm hole when delivering at 5 psi; it runs on a 50% duty cycle.
Howard