Considering a short segment of pipe immediately following the PD pump discharge into the system, the resulting pressure in that segment is a function of three things, the initial pressure in that segment, the mass of gas leaving and the mass of gas entering during the PD cycle time.
During the time of one PD cycle, if certain conditions are met, a specific mass of gas is ejected into the system segment. Yes, pressure in the PD must be slightly higher than system inlet pressure in order for the discharge valve to open. The critical question becomes, how much higher.
Well, the pressure must be higher by 1.) enough to open the valve; we'll say a pretty small amount there, and 2.) The cylinder pressure must be high enough such that, if the gas is ejected into the system segment, the resulting pressure of the segment equals the initial downstream pressure plus the increase in pressure due to the entering mass of gas from the compressor, minus the decrease in pressure due to the mass of gas exiting the segment to downstream points. So, yes, the mass of gas coming from the PD's cylinder affects the system pressure. And we also note that the downstream pressure affects the compressor's discharge pressure. Just as you say. However, we must also look at the mass of gas entering the system segment from the compressor, as we have shown that it affects the system pressure too. So, is not the mass of gas entering the system a function of the PD's cycle volume, and the mass of gas entering the system will increase with decreased cycle time? And, therefore isn't the mass of gas entering the system hence also a function of RPM? There is no way for the compressor to create an internal pressure greater than what is needed for the valve to open and eject its gas into the system downstream. It can't create any pressure higher than that, because the compressor's outlet valve is open by then. If it tries to increase pressure more than that, mass simply escapes the cylinder into the downstream segment. It is possible that the downstream segment pressure tends to increase, if and only if the downstream segment's net mass at the end of the timestep is greater than the original mass at t0, or decrease if net mass is less. If incoming mass equals outgoing mass, the system remains at the same operating point, so flowrates and pressures remain as they began at t0.
Don't try to separate the compressor from the system, or the system from the compressor. They function together as a unit. Each depends on the other equally, except for the small differential pressure needed to open the valve and pack the first segment of pipe. The length of pipe making up that segment that we need to consider is the same distance that the pressure wave will travel, at the velocity of sound inside the pipeline, during the time of one compressor cycle.
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"Pumping accounts for 20% of the world’s energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that
99% for pipeline companies)