Velocity analyzer for objects traveling in pipes

A plunger lift system for use with a gas well, the gas well comprising a well head and a tube string disposed within a well bore, the tube string comprising a plurality of tube sections having a substantially similar length and being connectable longitudinally with adjacent tube sections at a tube joint, wherein each tube joint comprises a gap, the system comprising:

• a plunger positioned in the tube string to travel between the well head and a lower portion of the well bore;
• a sensor that detects vibration, connected to the tube string, to transmit a sensor signal each time the plunger encounters a gap that detects vibrations as the plunger moves along the tube string;
• a flow valve assembly in operable fluid communication with the tube string, wherein the flow valve assembly is operable between an open position and a closed position to control movement of the plunger between the well head and the lower portion of the well bore;
• and
• a controller comprising a sensor signal potentiometer, programmed to store a maximum plunger velocity, to receive the sensor signal from sensor each time the plunger engages the gap, to determine a velocity of the plunger based on a time interval between each transmission of the sensor signal, and to command the flow valve assembly to selectively open and close to maintain the velocity of the plunger below the maximum velocity.