The main challenges during the operation of electric submersible pumps (ESP) lifted wells include running the well at its optimal point, while honoring operational constraints posed by the production system, and extending the service life of the equipment. Overcoming these challenges will typically require building and continuously updating a model of the system. Now, due to issues such as high cost of sensors (including installation, calibration and maintenance), difficulty to reach the sensing point or lack of adequate technology, measuring some variables may be very hard or even impossible. An alternative is to develop a virtual sensor (model) to estimate unmeasured variables from measured values of other variables at different locations along the well. This work presents a model developed based on physical principles to accurately estimate key operational parameters of ESP lifted wells. The model comprises three differential equations that express the derivatives of pump flowrate, submergence level and well head pressure. Assuming as known the pump frequency, casing head pressure and production line pressure, these equations are solved numerically to estimate time profiles of submergence level, well head pressure, pump flowrate, pump intake pressure, pump discharge pressure and flowing bottomhole pressure. The model was instantiated and simulated for a particular ESP lifted well, and showed outstanding performance when estimating pump intake pressure and pump flowrate, as compared to a commercial simulator. The proposed virtual sensor exhibits high accuracy using a model with simplified equations, which can be executed quickly and reliably using few computational resources (processing time and memory); therefore, this sensor is completely suitable for direct installation in the ESP well (on a PLC or a RTU) for real-time monitoring, control and optimization. Other advantages of the proposed model include that it (i) reduces the required surface and bottomhole instrumentation, (ii) estimates the values of the variables during the transient between operating points, (iii) can be used to analyze the influence of operating parameters in the well behavior, without affecting production rate, (iv) incorporates a service factor to account for the equipment wear due to normal operation and (v) can be used in the implementation of optimization and control strategies.

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