Hydrodynamics of transient processes in a well with an electric submersible pump

Abstract

The relevance. Associated with the problem of increase in efficiency of algorithms for monitoring and controlling the dynamic operation modes of wells equipped with an electric submersible pump with adjustable supply. The result summarizes and develops the previously published solution on the design of a dynamic well model, through the transition from linearized correlations to quadratic relationships between states at key points of a lift. These points properly reflect the observed forms of behavior in transient and equilibrium operating modes at full start-stop control ranges. The main aim. Updated description of a comprehensive quadratic barometric model of the «reservoir–lift–electric pump–well head» type well, focused on the tasks of automatic control and regulation in real time. Objects. Well with frequency-regulated submersible pump. Methods. Material balance, percolation, hydrostatics, quadratic kinetics of friction losses, numerical modeling of differential equations, finite-dimensional description of the complex hydrodynamics of the well, taking into account the potential and kinetic head losses in the lift. Results: (1) Updated mathematical description of the hydrodynamics of the well with an electric submersible pump creates the basis for: more reliable solution of inverse problems of parametric model support according to the data of field control, refined assessment of the adjustment potential, predicting the dynamics of a possible system output beyond the boundaries of functional stability, technologies of numerical and analytical design of optimal solutions when selecting the parameters of arrangement and laws of operational regulation, synthesis of dynamic observers of an extended state vector synchronously operating with the dynamics of controlling well-head and deep pressure. (2) The results of the computational analysis demonstrate a complex behavior that does not match the graph of the inflow and pump supply, when changing the frequency and wellhead pressure. This explains the observed effect of the multi-tempoity of transient processes during starts and stops and possible instability of the supply with a sharp decrease in frequency. (3) Estimates of discrepancy between the solutions for a quadratic model and a linearized prototype indicate an increase in errors of linearized analysis with strong deviations of operating modes from the equilibrium-calculated states. The refinements in dynamically disturbed operating modes delivered by the updated model are important for improving the reliability of operational control systems and parametric estimation for data control mode states.