A novel approach is presented to model the interplay between the gas volume fraction (GVF) and the driving force of the pumping unit. A physics-based model is proposed to predict the down-hole pressure for a constant, but unknown GVF and given oil flow-rate out of the well. The identified down-hole pressure is used to model the saddle-bearings axial displacements, which are indicative of polished-rod loading. The imbalance between the data obtained from the detailed model of the pumping unit, and predicted bearing’s displacements can be employed then to estimate the value of the GVF. The resulted GVF is incorporated into the sucker-rod string dynamics to determine the natural frequency of the system. A control strategy is then used to adjust the pump speed to compensate for the GVF variations while avoiding the resonance frequency of the sucker-rod string. A low dimensional simulation is performed and the results are demonstrated for upstroke movement of the sucker-rod.

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