Model matematyczny procesu pracy układu wyrzutowego podczas obrotu pompy strumieniowej w otworze

Abstract

A mathematical model of an above-bit jet pump has been developed for the conditions of its rotation in a well, based on the use of hydrodynamic functions of a complex variable. These functions take the form of a sum of partial solutions of differential equations describing the potential motion of radial, circulation and homogeneous flows. The working flow is considered as a leak for a stationary jet pump or as a vortex in the case of rotation. The injected flow corresponds to a homogeneous one. The mixed flow is assessed in accordance with the principle of superposition by summing the complex potentials of elementary flows. The complex potential of the total flow determines the velocity field in the mixing chamber of the jet pump and allows us to set the configuration of the zero flow line, which separates the working and injected flows. In the process of integrating the velocity profile, the coefficient of uneven distribution of kinematic parameters is assessed, the value of which is included in the structure of the equation for the pressure characteristic of the jet pump and determines the effect of circulation flows on the working process of the ejection system. It has been established that the maximum velocity of the symmetrical rotation of the jet pump in the well increases the generated pressure and efficiency by 7.79% and 9.57%, respectively. Using the experimental head characteristic of the jet pump, obtained for the case of simultaneous swirling of the working and injected flows by the guide elements, the value of the relative head corresponding to the same rotation velocity of the mixed media has been assessed. The investigated values of the relative head pressure are used to verify the adequacy of the developed mathematical model of the ejection system for the rotation of the jet pump in the well. The maximum discrepancy between the theoretical and experimental values of the relative head pressure of the jet pump is 3.64%.