Plunger lift state estimation and optimization using acoustic data

A method of probabilistically estimating a velocity of a plunger of a beam pump of a well, the method comprising:

• continuously monitoring well acoustics using a plurality of passive acoustic sensors attached to external structures of the beam pump;
• digitizing and filtering outputs of the plurality of passive acoustic sensors and sending the digitized and filtered outputs to a computing device for storage and processing;
• using the digitized and filtered outputs of the plurality of passive acoustic sensors, estimating, in the computing device, a probability of the velocity of the plunger using a hidden Markov model (HMM) to represent a probability of a position and the probability of the velocity of the plunger, the HMM comprising a state space model and an observational model, and
• determining, by the computing device, a volume of a liquid slug raised to a surface of the well by the plunger using the estimated probability of the velocity of the plunger;
• sending at least the estimated probability of the velocity of the plunger to a controller of the beam pump;
• controlling, by the controller, opening and closing of a motor valve through which the liquid slug raised to the surface flows, based on the at least the estimated probability of the velocity of the plunger.