engineer here, so I fully understand. One of the biggest factors is going to be the Z-factor for non-linear compressibility. This is not often talked about outside of this forum and some other unique groups in technical diving, but it is very real.
@DiveGearExpress thankfully did a good reference article about it which saves me from having to explain a lot about it.
Cylinder volume is defined by the internal dimensions of the tank, and normally measured in cubic inches or liters of water. Free capacity is ...
www.divegearexpress.com
There is other factors going on with the increased amount of work required as the resistance to flow increases at higher pressure, increased heat that reduces gas density, etc etc. When you're working on large systems with big cascades like
@Wookie is used to, or the one that
@The Chairman and I are working on installing you will rarely notice it. Primary reason being that the pump will get heat soaked fairly quickly and is running under relatively constant load for long periods of time so as the psi/min goes down you aren't really going to notice it since the net system change is incredibly slow. Some of the banks that I'm used to take multiple hours to refill and you're also usually doing it while filling scuba tanks so you really aren't paying attention to the flow rates. This is in stark contrast to a personal use compressor that is directly filling a scuba tank in <30mins where you do actually start to notice the psi/min differences during a fill session.
Oh, and one other factor that is going to be very different on a personal pump vs. a cascade system. When you are filling from a cascade system your fill rate to the tank is usually higher than the fill rate from the compressor, this causes the tank to get quite warm fairly quickly. The compressor however is filling into a massive heat sink that has relatively low psi/min changes so the banks act as a massive heat sink. When you are direct filling from a small pump you actually have adiabatic cooling after the PMV when you are filling at lower pressure than the PMV setpoint and because the flow rate is relatively low you then have less heating in the tank. Once you get above the PMV pressure you are filling with hot gas into a hot tank. All this to say there are a LOT of thermodynamics going on in these systems that will ultimately affect your net flow rate and your pressure drop after temperature has equalized and you are going to notice that more from a direct fill system than you would in a cascade which doesn't usually settle nearly as much from filling.