jessicathompson37 is right on the process side, keep the check valves. I drew a compressor room for a client last year.
Palette: Compressor, Compressed-air receiver and Compressed-air dryer are in the Process library, not the core set, so if you only see some of them, check which libraries your organisation bought. Check valve is in the core set under the Water network family; search the palette for “check valve”.
The animation: a connection has no value of its own. It follows its “from” symbol, so a pipe shows flow while the symbol at its start runs. If your pipe from compressor 2 keeps flowing, it was probably drawn from the receiver towards the compressor, or both pipes start at the same running symbol. Draw them in the flow direction:
Compressor 1 -> Check valve 1 -> Receiver -> Dryer -> header
Compressor 2 -> Check valve 2 ----^and bind each compressor’s Running to its own running value on its Views. Tick Flow arrow on the pipes so the direction is visible. A check valve placed on the line takes the medium of the first connection that touches it. Pipes, cables and connections