Substantiation of the method of modeling circulating flows during the rotation of the overhead jet pump

Abstract

The scheme of theoretical analysis of the influence of rotational motion on the working process of the near-bit jet pump is chosen, the methods of its realization and limits of use are determined. On the basis of the potential flows theory with the application of elementary hydrodynamic functions of a complex variable, basics for the development of analytical models of the near-bit ejector pump operation for conditions of its rotation in a well have been worked out. Components of a mixed flow are modeled as functions of the vortex flow and parallel jet flow. Application of certain hydrodynamic functions of a complex variable has allowed to combine partial outcomes of differential equations of elementary streams motions and to determine the structure of the mixed flow function. The equation of the mixed flow motion is given in the form of a complex potential, components of which are equal to Laplace’s equation and Cauchy-Riemann Conditions, and determine the kinematics of irrotational flow. Possibility of application of the complex variable functions’ theory for velocities profiles modeling and determination of limits for dissociation of mixed flows by rotation of the near-bit jet pump in a well has been shown. The list of hydro-dynamic parameters, which should be taken into consideration by modeling of the ejector system working process, has been determined, and the structure of initial equations, that characterize kinematic picture of velocities field in the chamber of the ejector pump mixing has been established. Limit conditions for determination of a complex potential of mixed flows and application limits of the proposed method of circulation flows modeling have been stated. The class of hydrodynamic problems has been established, to which one may relate the problem of finding the complex potential of mixed flows in a chamber for mixing of an ejector pump by its rotation in a well.