How to figure out the duration of use before refill on a compressed air tank

What minimum and maximum pressures for the tank are you dealing with?

the following calculations have not been checked, and some rogue decimal points have been spotted on my desk hiding amongst the cookie crumbs.

65 minimum psi.
1.1 cfm
4 hours or 240 minutes
240 X 1.1 ≈ 250 cubic feet ≈ 1500 gallons

If you pressurize it to 130 psi initially maybe a 1500 gallon tank.

If you can pressurize it initially to 1000s of psi maybe one of these -

How about running the machine on argon or CO2 ?
or acetylene ?

Acetylene is dissolved in acetone and those cylinders are fairly low pressure, I believe.
Nitrogen might be a possibility.
Is the volume the compressed volume at 0.45 MPa, or volume at standard conditions?

Acetylene self-detonates at far below the target pressure unless stabilized in acetone liquid.

There are some very quiet, claimed 40 dBA, air compressors in that range. They are somewhat expensive, but compared to swapping out a high pressure rather large air tank, they are very reasonable for anything but a one-time event.

40 dBa is far quieter than typical conversation.

Attached is a nice short note on sizing air receivers

Sorry TMoose but you missed the pressure factor.
A tank at 130psi with 65psi min is roughly 4atm of usable pressure.
So the required tank volume is about 1/4 of the 250cu ft, or 375gal.

I actually started with assuming 150psi to start with and 75psi min for some margin.
That is 5atm so 240*1.1=265cu ft and 265/5=53cu ft which rounds up to 400gal.

Would it be easier to order HP cylinders of Nitrogen from your local welding gas supplier?
These tanks typically will 2000-2700psi depending on the tank and supplier.
There are high pressure tanks available but they are not common.
You can get tanks in a rack, usually either 6 or 12 and perhaps get enough gas to run a week.
This gas is very clean and dry even if it isn't the high purity grade.
Pneumatic equipment that I have run on nitrogen lasted forever.

Another option are the tanks that we use for precharged pneumatic airguns.
Such as This tank will hold 98 std cu ft of air at 4500psi.
But then you would need a way to fill it.
But the tanks are small and light and easy to handle.
the same source would also sell a compressor to fill these.

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P.E. Metallurgy, consulting work welcomed