No abstract

Purpose. Determination of deformation and force parameters that describe the strain-stress state of the casing string in non-vertical well-bore areas. Methodology. In a curvilinear well, the casing functions as a long permanent continuous rod. Its weight might cause some deformations that can be determined by a heterogeneous system of four differential equations. Taking into consideration the technological requirements for pipe installation on centralizers allows us to make the first integral of the system linear. findings. It is proved that the elastic rod deformation under the impact of the longitudinal and transverse forces of the distributed weight can be calculated by a heterogeneous second order differential equation with variable coefficients. Its solution is the clue to the formulas of deflections, angular slopes, internal bending moments and transverse forces in the rod with the arbitrary arrangement of supports and boundary conditions in their intersections. Originality. The solution of the governing differential equation of angular deformations of a long bar is found in the form of a linear combination of Airy and Scorer's functions and in the form of three linearly independent polynomial series in the sum with a partial answer. Practical value. The obtained formulas of flexure and power parameters allow us to calculate stress and strain in the tubing during the process of casing the borehole of an arbitrary profile which increases the reliability and durability of the well.

Розвідка та розробка нафтових і газових родовищ 2019. № 2(71) УДК 622.691 1 ІФНТУНГ; 76019, м. Івано-Франківськ, вул. Карпатська, 15, e-mail: s r g g 4 2 9 @ g m a i l . c o m 2 Виробниче ремонтно-технічне підприємство «Укргазенергосервіс» ; 08150, м. Боярка, вул. Маяковського, 49, e-mail: t e r e s c e n k o -r v @ u t g . u a

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.

The nature of the flow distribution in the hydraulic system of the near-bit jet pump has been analyzed. The peculiarities of searching the pumping station operating point have been shown and the equation for determining hydraulic losses in the elements of the ejection system has been given. Based on experimental studies, an error in the theoretical determination of the relative pressure of a jet pump has been established when using a known and advanced model of its working process. In contrast to the known method, the proposed model provides for the determination of the hydraulic resistance of the chisel flushing system,which is located in the area of mixed flow at the cost of working, not mixed flow. Improving the mathematical model of the ejection system allows to reduce the error of theoretical determination of the relative pressure of the jet pump.