Kunal
flywheel stores the energy and release it when ever required...... during compression we need more energy than suction but we cant change torque of motor so rapidly..... :)

Hem
Fly wheel is a reservoir of energy and therefore it releases / stores as and when required. As a result compressor ( reciprocating ) can run without pulsation.

oil field trash
A flywheel on any reciprocating machine is designed to smooth out the power flow requirements between the driver and the driven equipment. It does nothing for the pulsations generated by the compressor. That is a separate problem using other technology for a solution. The actual design of the flywheel in some cases serves another purpose. This is related to torsional vibration. Reciprocating machines that are drive by electric motors can on occasion have this problem and it results in shaft failures due to fatigue. It usually appears at a key way or other point in the shaft where there is a stress riser.