We need a minimum pressure to circulate the oil. Circulation of oil is critical for cooling of the rotary screws and for the lubrication of the bearings.
A rotary screw compressor has no oil pumps. The oil is pumped through the system by the differences in pressure that exists inside the compressor.
When the compressor just starts up, a minimum pressure is required to circulate the oil. Circulation of oil is critical for cooling of the rotary screws and for the lubrication of the bearings.
If the compressor is connected to an empty air receiver or piping system, it will take a long time for the pressure to build up. Therefore, the minimum pressure valve stays closed until a minimum pressure has been reached inside the air compressor to help minimise the time taken to reach the minimum pressure required to circulate the oil.