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20 refineries on advanced oil processing make 11 petroleum gas per second each (55 in 5 seconds) for a total of 220 petroleum gas per second.
Plastic is made in a chemical plant, not an assembling machine so there is no mk2, it makes 2 per second at the cost of 40 petroleum gas per second.
Your 220 per second are enough to feed 5.5 chemical plant making plastic, assuming that coal is not the issue you would produce 11 plastic per second.
Your issue is just that refineries are slow, taking 5 seconds per cycle so you will need a lot more of them (and potentially more crude oil), it's definitely not the pipes reching a trhoughput cap or anything like that.
I'm using the 20-5-17 ratio for Advanced Oil Processing-Heavy Oil Cracking-Light Oil Cracking from Factorio Cheat Sheet. No modules or beacons. And I store 10k each of Light Oil and Lubricant before cracking the excess to petroleum. I'm just now reaching the point of using oil products, so nothing is consuming the light oil or lubricant yet.
Thanks for inadvertently steering me in the right direction! I appreciate you.