The Improvement of the Mathematical Model of the Work Process of Borehole Ejection Systems

Abstract

The article presents the sequence of deriving the equations which characterize the hydraulic system of jet pumps that carry out suction and injection-suction bottom flushing while drilling the production wells. The nature of flow distribution in the borehole ejection systems of the suction and injection-suction types is analyzed. The analysis is carried out taking into consideration the peculiarities of the calculation of branched hydraulic systems. While studying the movement of the flows in the bottom circulation circuits, the authors take into account the equation of the balance of the flow-rate at nodal points and hydraulic losses in parallel parts of the system. The developed mathematical models are based on the study of the changes in hydrodynamic pressures which occur in characteristic sections of a jet pump. The pressure ratio of mixed, injected and operating flows is presented as non-dimensional relative pressure of the ejection system. The dependence of non-dimensional relative pressure on the relative flow rate determines the characteristic of the hydraulic system of a jet pump. The relative flow rate or injection ratio of a jet pump is defined as the ratio of flow rate to injected and work flow. While analyzing the developed mathematical models, the authors specify the relation between the design and operating parameters of a jet pump. These parameters ensure its operation with maximum efficiency. Based on the study of the influence of the correlation between the diameters of the jet pump nozzles and the flushing system of the bit, the authors specify parameters which are optimal in terms of energy performance. The article provides the example of graphical determination of the operating point of a pumping unit. This determination is based on a simultaneous solution of the equations of the characteristics of the jet pump and the hydraulic system in which it operates. The improved techniques allow to predict the mode parameters of ejection systems and to determine the size of flowing part of the jet pump. They provide maximum energy performance of its workflow.